diff --git a/changelog b/changelog
index e684837..f766cd4 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,99 @@
+20130804 tpd src/axiom-website/patches.html 20130804.01.tpd.patch
+20130804 tpd src/axiom-website/CATS/index.html
+20130804 tpd src/axiom-website/CATS/rich1a.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich1a.input.pdf
+20130804 tpd src/axiom-website/CATS/rich1b.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich1b.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3a.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3a.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3c.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3c.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3d.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3d.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3e.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3e.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3f.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3f.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3g.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3g.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3h.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3h.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3i.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3i.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3j.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3j.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3k.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3k.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3l.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3l.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3m.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3m.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3n.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3n.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3o.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3o.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3p.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3p.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3q.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3q.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3r.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3r.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3s.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3s.input.pdf
+20130804 tpd src/axiom-website/CATS/rich3t.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich3t.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4a.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4a.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4b.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4b.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4c.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4c.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4d.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4d.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4e.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4e.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4f.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4f.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4g.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4g.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4h.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4h.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4i.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4i.input.pdf
+20130804 tpd src/axiom-website/CATS/rich4j.input.pamphlet
+20130804 tpd src/axiom-website/CATS/rich4j.input.pdf
+20130804 tpd src/input/Makefile.pamphlet
+20130804 tpd src/input/rich1a.input.pamphlet
+20130804 tpd src/input/rich1b.input.pamphlet
+20130804 tpd src/input/rich3a.input.pamphlet
+20130804 tpd src/input/rich3c.input.pamphlet
+20130804 tpd src/input/rich3d.input.pamphlet
+20130804 tpd src/input/rich3e.input.pamphlet
+20130804 tpd src/input/rich3f.input.pamphlet
+20130804 tpd src/input/rich3g.input.pamphlet
+20130804 tpd src/input/rich3h.input.pamphlet
+20130804 tpd src/input/rich3i.input.pamphlet
+20130804 tpd src/input/rich3j.input.pamphlet
+20130804 tpd src/input/rich3k.input.pamphlet
+20130804 tpd src/input/rich3l.input.pamphlet
+20130804 tpd src/input/rich3m.input.pamphlet
+20130804 tpd src/input/rich3n.input.pamphlet
+20130804 tpd src/input/rich3o.input.pamphlet
+20130804 tpd src/input/rich3p.input.pamphlet
+20130804 tpd src/input/rich3q.input.pamphlet
+20130804 tpd src/input/rich3r.input.pamphlet
+20130804 tpd src/input/rich3s.input.pamphlet
+20130804 tpd src/input/rich3t.input.pamphlet
+20130804 tpd src/input/rich4a.input.pamphlet
+20130804 tpd src/input/rich4b.input.pamphlet
+20130804 tpd src/input/rich4c.input.pamphlet
+20130804 tpd src/input/rich4d.input.pamphlet
+20130804 tpd src/input/rich4e.input.pamphlet
+20130804 tpd src/input/rich4f.input.pamphlet
+20130804 tpd src/input/rich4g.input.pamphlet
+20130804 tpd src/input/rich4h.input.pamphlet
+20130804 tpd src/input/rich4i.input.pamphlet
+20130804 tpd src/input/rich4j.input.pamphlet
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 7303013..cc3cf50 100644
--- a/src/axiom-website/CATS/index.html
+++ b/src/axiom-website/CATS/index.html
@@ -293,10 +293,12 @@ They have been rewritten using Axiom syntax.
(a+b x)^m (c+d x)^n (part 2)
source
pdf
+
(a+b x)^m (A+B x) (d+e x)^p
source
pdf
(a+b x)^m (c+d)^n (e+f x)^p (part 1)
+
source
pdf
(a+b x)^m (c+d)^n (e+f x)^p (part 2)
@@ -305,6 +307,88 @@ They have been rewritten using Axiom syntax.
(a+b x)^m (c+d)^n (e+f x)^p (part 3)
source
pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 4)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 5)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 6)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 7)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 8)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 9)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 10)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 11)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 12)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 13)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 14)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 15)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 16)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 17)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 18)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 19)
+ source
+ pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 20)
+ source
+ pdf
+
+ x^m (a+b x^n)^p (part 1)
+ source
+ pdf
+ x^m (a+b x^n)^p (part 2)
+ source
+ pdf
+ x^m (a+b x^n)^p (part 3)
+ source
+ pdf
+ x^m (a+b x^n)^p (part 4)
+ source
+ pdf
+ x^m (a+b x^n)^p (part 5)
+ source
+ pdf
+ x^m (a+b x^n)^p (part 6)
+ source
+ pdf
+ x^m (a+b x^n)^p (part 7)
+ source
+ pdf
+ x^m (a+b x^n)^p (part 8)
+ source
+ pdf
+ x^m (a+b x^n)^p (part 9)
+ source
+ pdf
+ x^m (a+b x^n)^p (part 10)
+ source
+ pdf
Rich
diff --git a/src/axiom-website/CATS/rich1a.input.pamphlet b/src/axiom-website/CATS/rich1a.input.pamphlet
index 06f6586..b6a7a8b 100644
--- a/src/axiom-website/CATS/rich1a.input.pamphlet
+++ b/src/axiom-website/CATS/rich1a.input.pamphlet
@@ -33369,7 +33369,7 @@ r0000:=-2/3*(a+b*x)^(3/2)/(a*x^(3/2))
--R Type: Expression(Integer)
--E 2555
---S 2556 of 3333
+--S 2556 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -33381,7 +33381,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2556
---S 2557 of 3333
+--S 2557 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -33426,7 +33426,7 @@ r0000:=-2/5*(a+b*x)^(3/2)/(a*x^(5/2))+4/15*b*(a+b*x)^(3/2)/(a^2*x^(3/2))
--R Type: Expression(Integer)
--E 2560
---S 2561 of 3333
+--S 2561 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -33442,7 +33442,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2561
---S 2562 of 3333
+--S 2562 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -33489,7 +33489,7 @@ r0000:=-2/7*(a+b*x)^(3/2)/(a*x^(7/2))+8/35*b*(a+b*x)^(3/2)/(a^2*x^(5/2))-_
--R Type: Expression(Integer)
--E 2565
---S 2566 of 3333
+--S 2566 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -33505,7 +33505,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2566
---S 2567 of 3333
+--S 2567 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -33756,7 +33756,7 @@ r0000:=-2/3*(a-b*x)^(3/2)/(a*x^(3/2))
--R Type: Expression(Integer)
--E 2595
---S 2596 of 3333
+--S 2596 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -33768,7 +33768,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2596
---S 2597 of 3333
+--S 2597 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -33813,7 +33813,7 @@ r0000:=-2/5*(a-b*x)^(3/2)/(a*x^(5/2))-4/15*b*(a-b*x)^(3/2)/(a^2*x^(3/2))
--R Type: Expression(Integer)
--E 2600
---S 2601 of 3333
+--S 2601 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -33829,7 +33829,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2601
---S 2602 of 3333
+--S 2602 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -33876,7 +33876,7 @@ r0000:=-2/7*(a-b*x)^(3/2)/(a*x^(7/2))-8/35*b*(a-b*x)^(3/2)/(a^2*x^(5/2))-_
--R Type: Expression(Integer)
--E 2605
---S 2606 of 3333
+--S 2606 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -33892,7 +33892,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2606
---S 2607 of 3333
+--S 2607 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -34138,7 +34138,7 @@ r0000:=-1/3*(2+b*x)^(3/2)/x^(3/2)
--R Type: Expression(Integer)
--E 2635
---S 2636 of 3333
+--S 2636 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -34150,7 +34150,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2636
---S 2637 of 3333
+--S 2637 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -34195,7 +34195,7 @@ r0000:=-1/5*(2+b*x)^(3/2)/x^(5/2)+1/15*b*(2+b*x)^(3/2)/x^(3/2)
--R Type: Expression(Integer)
--E 2640
---S 2641 of 3333
+--S 2641 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -34207,7 +34207,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2641
---S 2642 of 3333
+--S 2642 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -34253,7 +34253,7 @@ r0000:=-1/7*(2+b*x)^(3/2)/x^(7/2)+2/35*b*(2+b*x)^(3/2)/x^(5/2)-_
--R Type: Expression(Integer)
--E 2645
---S 2646 of 3333
+--S 2646 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -34269,7 +34269,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2646
---S 2647 of 3333
+--S 2647 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -34515,7 +34515,7 @@ r0000:=-1/3*(2-b*x)^(3/2)/x^(3/2)
--R Type: Expression(Integer)
--E 2675
---S 2676 of 3333
+--S 2676 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -34527,7 +34527,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2676
---S 2677 of 3333
+--S 2677 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -34572,7 +34572,7 @@ r0000:=-1/5*(2-b*x)^(3/2)/x^(5/2)-1/15*b*(2-b*x)^(3/2)/x^(3/2)
--R Type: Expression(Integer)
--E 2680
---S 2681 of 3333
+--S 2681 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -34584,7 +34584,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2681
---S 2682 of 3333
+--S 2682 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -36903,7 +36903,7 @@ r0000:=-2*sqrt(a+b*x)/(a*sqrt(x))
--R Type: Expression(Integer)
--E 2950
---S 2951 of 3333
+--S 2951 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -36914,7 +36914,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2951
---S 2952 of 3333
+--S 2952 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -36957,7 +36957,7 @@ r0000:=-2/3*sqrt(a+b*x)/(a*x^(3/2))+4/3*b*sqrt(a+b*x)/(a^2*sqrt(x))
--R Type: Expression(Integer)
--E 2955
---S 2956 of 3333
+--S 2956 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -36969,7 +36969,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2956
---S 2957 of 3333
+--S 2957 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -36984,7 +36984,7 @@ m0000:=a0000 - r0000
--S 2958 of 3333
d0000:=D(m0000,x)
--R
---R
+--R
--R (5) 0
--R Type: Expression(Integer)
--E 2958
@@ -37077,7 +37077,7 @@ r0000:=-2/7*sqrt(a+b*x)/(a*x^(7/2))+12/35*b*sqrt(a+b*x)/(a^2*x^(5/2))-_
--R Type: Expression(Integer)
--E 2965
---S 2966 of 3333
+--S 2966 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -37093,7 +37093,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2966
---S 2967 of 3333
+--S 2967 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -37264,7 +37264,7 @@ r0000:=2*sqrt(x)/(a*sqrt(a+b*x))
--R Type: Expression(Integer)
--E 2985
---S 2986 of 3333
+--S 2986 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -37276,7 +37276,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2986
---S 2987 of 3333
+--S 2987 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -37381,7 +37381,7 @@ r0000:=2/(a*x^(3/2)*sqrt(a+b*x))-8/3*sqrt(a+b*x)/(a^2*x^(3/2))+_
--R Type: Expression(Integer)
--E 2995
---S 2996 of 3333
+--S 2996 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -37400,7 +37400,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 2996
---S 2997 of 3333
+--S 2997 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -37446,7 +37446,7 @@ r0000:=2/(a*x^(5/2)*sqrt(a+b*x))-12/5*sqrt(a+b*x)/(a^2*x^(5/2))+_
--R Type: Expression(Integer)
--E 3000
---S 3001 of 3333
+--S 3001 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -37477,7 +37477,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 3001
---S 3002 of 3333
+--S 3002 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -37613,7 +37613,7 @@ r0000:=2/3*x^(3/2)/(a*(a+b*x)^(3/2))
--R Type: Expression(Integer)
--E 3015
---S 3016 of 3333
+--S 3016 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -37632,7 +37632,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 3016
---S 3017 of 3333
+--S 3017 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -37676,7 +37676,7 @@ r0000:=2/3*sqrt(x)/(a*(a+b*x)^(3/2))+4/3*sqrt(x)/(a^2*sqrt(a+b*x))
--R Type: Expression(Integer)
--E 3020
---S 3021 of 3333
+--S 3021 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -37695,7 +37695,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 3021
---S 3022 of 3333
+--S 3022 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -37741,7 +37741,7 @@ r0000:=2/3/(a*(a+b*x)^(3/2)*sqrt(x))+8/3/(a^2*sqrt(x)*sqrt(a+b*x))-_
--R Type: Expression(Integer)
--E 3025
---S 3026 of 3333
+--S 3026 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -37772,7 +37772,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 3026
---S 3027 of 3333
+--S 3027 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -37818,7 +37818,7 @@ r0000:=2/3/(a*x^(3/2)*(a+b*x)^(3/2))+4/(a^2*x^(3/2)*sqrt(a+b*x))-_
--R Type: Expression(Integer)
--E 3030
---S 3031 of 3333 ok to fail, random algorithm
+--S 3031 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -37867,7 +37867,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 3031
---S 3032 of 3333 ok to fail, random algorithm
+--S 3032 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -40512,7 +40512,7 @@ r0000:=1/(x^(3/2)*sqrt(2-b*x))-2/3*sqrt(2-b*x)/x^(3/2)-_
--R Type: Expression(Integer)
--E 3285
---S 3286 of 3333
+--S 3286 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -40528,7 +40528,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 3286
---S 3287 of 3333
+--S 3287 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
@@ -40658,7 +40658,7 @@ r0000:=1/3*x^(3/2)/(2-b*x)^(3/2)
--R Type: Expression(Integer)
--E 3300
---S 3301 of 3333 ok to fail, random algorithm
+--S 3301 of 3333 ok to fail, differs by a constant
a0000:=integrate(t0000,x)
--R
--R
@@ -40673,7 +40673,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 3301
---S 3302 of 3333 ok to fail, random algorithm
+--S 3302 of 3333 ok to fail, differs by a constant
m0000:=a0000 - r0000
--R
--R
diff --git a/src/axiom-website/CATS/rich1a.input.pdf b/src/axiom-website/CATS/rich1a.input.pdf
index 4366ac0..1cfad11 100644
Binary files a/src/axiom-website/CATS/rich1a.input.pdf and b/src/axiom-website/CATS/rich1a.input.pdf differ
diff --git a/src/axiom-website/CATS/rich1b.input.pamphlet b/src/axiom-website/CATS/rich1b.input.pamphlet
index 7234288..1f09a0d 100644
--- a/src/axiom-website/CATS/rich1b.input.pamphlet
+++ b/src/axiom-website/CATS/rich1b.input.pamphlet
@@ -49865,7 +49865,7 @@ r0000:=2*asinh(sqrt(b*x)/sqrt(2))/b
--R Type: Expression(Integer)
--E 1964
---S 1965 of 2952
+--S 1965 of 2952 ok to fail, (non-algebraic residues)
a0000:=integrate(t0000,x)
--R
--R
@@ -49876,7 +49876,7 @@ a0000:=integrate(t0000,x)
--R Type: Union(Expression(Integer),...)
--E 1965
---S 1966 of 2952
+--S 1966 of 2952
m0000:=a0000 - r0000
--R
--R
diff --git a/src/axiom-website/CATS/rich1b.input.pdf b/src/axiom-website/CATS/rich1b.input.pdf
index 079dacf..ff54c9e 100644
Binary files a/src/axiom-website/CATS/rich1b.input.pdf and b/src/axiom-website/CATS/rich1b.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3a.input.pamphlet b/src/axiom-website/CATS/rich3a.input.pamphlet
index fc946de..29348ed 100644
--- a/src/axiom-website/CATS/rich3a.input.pamphlet
+++ b/src/axiom-website/CATS/rich3a.input.pamphlet
@@ -28,16 +28,16 @@ There are:
)set message auto off
)clear all
---S 1 of 1092
+--S 1 of 1092
t0:=x^2*(a+b*x)^n*(c+d*x)
--R
--R
--R 3 2 n
--R (1) (d x + c x )(b x + a)
--R Type: Expression(Integer)
---E 1
+--E 1
---S 2 of 1092
+--S 2 of 1092
r0:=a^2*(b*c-a*d)*(a+b*x)^(1+n)/(b^4*(1+n))-_
a*(2*b*c-3*a*d)*(a+b*x)^(2+n)/(b^4*(2+n))+_
(b*c-3*a*d)*(a+b*x)^(3+n)/(b^4*(3+n))+d*(a+b*x)^(4+n)/(b^4*(4+n))
@@ -75,9 +75,9 @@ r0:=a^2*(b*c-a*d)*(a+b*x)^(1+n)/(b^4*(1+n))-_
--R 4 4 4 3 4 2 4 4
--R b n + 10b n + 35b n + 50b n + 24b
--R Type: Expression(Integer)
---E 2
+--E 2
---S 3 of 1092
+--S 3 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -100,9 +100,9 @@ a0:=integrate(t0,x)
--R 4 4 4 3 4 2 4 4
--R b n + 10b n + 35b n + 50b n + 24b
--R Type: Union(Expression(Integer),...)
---E 3
+--E 3
---S 4 of 1092
+--S 4 of 1092
m0:=a0-r0
--R
--R
@@ -152,28 +152,28 @@ m0:=a0-r0
--R 4 4 4 3 4 2 4 4
--R b n + 10b n + 35b n + 50b n + 24b
--R Type: Expression(Integer)
---E 4
+--E 4
---S 5 of 1092
+--S 5 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 5
+--E 5
)clear all
---S 6 of 1092
+--S 6 of 1092
t0:=x*(a+b*x)^n*(c+d*x)
--R
--R
--R 2 n
--R (1) (d x + c x)(b x + a)
--R Type: Expression(Integer)
---E 6
+--E 6
---S 7 of 1092
+--S 7 of 1092
r0:=-a*(b*c-a*d)*(a+b*x)^(1+n)/(b^3*(1+n))+_
(b*c-2*a*d)*(a+b*x)^(2+n)/(b^3*(2+n))+d*(a+b*x)^(3+n)/(b^3*(3+n))
--R
@@ -191,9 +191,9 @@ r0:=-a*(b*c-a*d)*(a+b*x)^(1+n)/(b^3*(1+n))+_
--R 3 3 3 2 3 3
--R b n + 6b n + 11b n + 6b
--R Type: Expression(Integer)
---E 7
+--E 7
---S 8 of 1092
+--S 8 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -213,9 +213,9 @@ a0:=integrate(t0,x)
--R 3 3 3 2 3 3
--R b n + 6b n + 11b n + 6b
--R Type: Union(Expression(Integer),...)
---E 8
+--E 8
---S 9 of 1092
+--S 9 of 1092
m0:=a0-r0
--R
--R
@@ -244,28 +244,28 @@ m0:=a0-r0
--R 3 3 3 2 3 3
--R b n + 6b n + 11b n + 6b
--R Type: Expression(Integer)
---E 9
+--E 9
---S 10 of 1092
+--S 10 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 10
+--E 10
)clear all
---S 11 of 1092
+--S 11 of 1092
t0:=(a+b*x)^n*(c+d*x)
--R
--R
--R n
--R (1) (d x + c)(b x + a)
--R Type: Expression(Integer)
---E 11
+--E 11
---S 12 of 1092
+--S 12 of 1092
r0:=(b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d*(a+b*x)^(2+n)/(b^2*(2+n))
--R
--R
@@ -275,9 +275,9 @@ r0:=(b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d*(a+b*x)^(2+n)/(b^2*(2+n))
--R 2 2 2 2
--R b n + 3b n + 2b
--R Type: Expression(Integer)
---E 12
+--E 12
---S 13 of 1092
+--S 13 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -291,9 +291,9 @@ a0:=integrate(t0,x)
--R 2 2 2 2
--R b n + 3b n + 2b
--R Type: Union(Expression(Integer),...)
---E 13
+--E 13
---S 14 of 1092
+--S 14 of 1092
m0:=a0-r0
--R
--R
@@ -310,19 +310,19 @@ m0:=a0-r0
--R 2 2 2 2
--R b n + 3b n + 2b
--R Type: Expression(Integer)
---E 14
+--E 14
---S 15 of 1092
+--S 15 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 15
+--E 15
)clear all
---S 16 of 1092
+--S 16 of 1092
t0:=(a+b*x)^n*(c+d*x)/x
--R
--R
@@ -331,28 +331,28 @@ t0:=(a+b*x)^n*(c+d*x)/x
--R (1) -------------------
--R x
--R Type: Expression(Integer)
---E 16
+--E 16
---S 17 of 1092
+--S 17 of 1092
--r0:=d*(a+b*x)^(1+n)/(b*(1+n))-c*(a+b*x)^(1+n)*_
-- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n))
---E 17
+--E 17
---S 18 of 1092
+--S 18 of 1092
--a0:=integrate(t0,x)
---E 18
+--E 18
---S 19 of 1092
+--S 19 of 1092
--m0:=a0-r0
---E 19
+--E 19
---S 20 of 1092
+--S 20 of 1092
--d0:=D(m0,x)
---E 20
+--E 20
)clear all
---S 21 of 1092
+--S 21 of 1092
t0:=x^m*(a+b*x)*(c+d*x)^5
--R
--R
@@ -366,9 +366,9 @@ t0:=x^m*(a+b*x)*(c+d*x)^5
--R m
--R x
--R Type: Expression(Integer)
---E 21
+--E 21
---S 22 of 1092
+--S 22 of 1092
r0:=a*c^5*x^(1+m)/(1+m)+c^4*(b*c+5*a*d)*x^(2+m)/(2+m)+_
5*c^3*d*(b*c+2*a*d)*x^(3+m)/(3+m)+10*c^2*d^2*(b*c+a*d)*_
x^(4+m)/(4+m)+5*c*d^3*(2*b*c+a*d)*x^(5+m)/(5+m)+_
@@ -466,9 +466,9 @@ r0:=a*c^5*x^(1+m)/(1+m)+c^4*(b*c+5*a*d)*x^(2+m)/(2+m)+_
--R 7 6 5 4 3 2
--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040
--R Type: Expression(Integer)
---E 22
+--E 22
---S 23 of 1092
+--S 23 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -568,9 +568,9 @@ a0:=integrate(t0,x)
--R 7 6 5 4 3 2
--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040
--R Type: Union(Expression(Integer),...)
---E 23
+--E 23
---S 24 of 1092
+--S 24 of 1092
m0:=a0-r0
--R
--R
@@ -766,19 +766,19 @@ m0:=a0-r0
--R 7 6 5 4 3 2
--R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040
--R Type: Expression(Integer)
---E 24
+--E 24
---S 25 of 1092
+--S 25 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 25
+--E 25
)clear all
---S 26 of 1092
+--S 26 of 1092
t0:=x^3*(a+b*x)*(c+d*x)^5
--R
--R
@@ -789,9 +789,9 @@ t0:=x^3*(a+b*x)*(c+d*x)^5
--R 2 3 3 2 6 3 2 4 5 4 5 4 5 3
--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x
--R Type: Polynomial(Integer)
---E 26
+--E 26
---S 27 of 1092
+--S 27 of 1092
r0:=1/4*a*c^5*x^4+1/5*c^4*(b*c+5*a*d)*x^5+5/6*c^3*d*(b*c+2*a*d)*x^6+_
10/7*c^2*d^2*(b*c+a*d)*x^7+5/8*c*d^3*(2*b*c+a*d)*x^8+_
1/9*d^4*(5*b*c+a*d)*x^9+1/10*b*d^5*x^10
@@ -810,9 +810,9 @@ r0:=1/4*a*c^5*x^4+1/5*c^4*(b*c+5*a*d)*x^5+5/6*c^3*d*(b*c+2*a*d)*x^6+_
--R - a c x
--R 4
--R Type: Polynomial(Fraction(Integer))
---E 27
+--E 27
---S 28 of 1092
+--S 28 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -829,27 +829,27 @@ a0:=integrate(t0,x)
--R - a c x
--R 4
--R Type: Polynomial(Fraction(Integer))
---E 28
+--E 28
---S 29 of 1092
+--S 29 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Polynomial(Fraction(Integer))
---E 29
+--E 29
---S 30 of 1092
+--S 30 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Polynomial(Fraction(Integer))
---E 30
+--E 30
)clear all
---S 31 of 1092
+--S 31 of 1092
t0:=x^2*(a+b*x)*(c+d*x)^5
--R
--R
@@ -860,9 +860,9 @@ t0:=x^2*(a+b*x)*(c+d*x)^5
--R 2 3 3 2 5 3 2 4 4 4 5 3 5 2
--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x
--R Type: Polynomial(Integer)
---E 31
+--E 31
---S 32 of 1092
+--S 32 of 1092
r0:=-1/6*c^2*(b*c-a*d)*(c+d*x)^6/d^4+1/7*c*(3*b*c-2*a*d)*(c+d*x)^7/d^4-_
1/8*(3*b*c-a*d)*(c+d*x)^8/d^4+1/9*b*(c+d*x)^9/d^4
--R
@@ -883,9 +883,9 @@ r0:=-1/6*c^2*(b*c-a*d)*(c+d*x)^6/d^4+1/7*c*(3*b*c-2*a*d)*(c+d*x)^7/d^4-_
--R 4
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 32
+--E 32
---S 33 of 1092
+--S 33 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -902,9 +902,9 @@ a0:=integrate(t0,x)
--R - a c x
--R 3
--R Type: Polynomial(Fraction(Integer))
---E 33
+--E 33
---S 34 of 1092
+--S 34 of 1092
m0:=a0-r0
--R
--R
@@ -915,19 +915,19 @@ m0:=a0-r0
--R 4
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 34
+--E 34
---S 35 of 1092
+--S 35 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 35
+--E 35
)clear all
---S 36 of 1092
+--S 36 of 1092
t0:=x*(a+b*x)*(c+d*x)^5
--R
--R
@@ -938,9 +938,9 @@ t0:=x*(a+b*x)*(c+d*x)^5
--R 2 3 3 2 4 3 2 4 3 4 5 2 5
--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x
--R Type: Polynomial(Integer)
---E 36
+--E 36
---S 37 of 1092
+--S 37 of 1092
r0:=1/6*c*(b*c-a*d)*(c+d*x)^6/d^3-1/7*(2*b*c-a*d)*(c+d*x)^7/d^3+_
1/8*b*(c+d*x)^8/d^3
--R
@@ -961,9 +961,9 @@ r0:=1/6*c*(b*c-a*d)*(c+d*x)^6/d^3-1/7*(2*b*c-a*d)*(c+d*x)^7/d^3+_
--R 3
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 37
+--E 37
---S 38 of 1092
+--S 38 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -980,9 +980,9 @@ a0:=integrate(t0,x)
--R - a c x
--R 2
--R Type: Polynomial(Fraction(Integer))
---E 38
+--E 38
---S 39 of 1092
+--S 39 of 1092
m0:=a0-r0
--R
--R
@@ -993,19 +993,19 @@ m0:=a0-r0
--R 3
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 39
+--E 39
---S 40 of 1092
+--S 40 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 40
+--E 40
)clear all
---S 41 of 1092
+--S 41 of 1092
t0:=(a+b*x)*(c+d*x)^5
--R
--R
@@ -1016,9 +1016,9 @@ t0:=(a+b*x)*(c+d*x)^5
--R 2 3 3 2 3 3 2 4 2 4 5 5
--R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c
--R Type: Polynomial(Integer)
---E 41
+--E 41
---S 42 of 1092
+--S 42 of 1092
r0:=-1/6*(b*c-a*d)*(c+d*x)^6/d^2+1/7*b*(c+d*x)^7/d^2
--R
--R
@@ -1038,9 +1038,9 @@ r0:=-1/6*(b*c-a*d)*(c+d*x)^6/d^2+1/7*b*(c+d*x)^7/d^2
--R 2
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 42
+--E 42
---S 43 of 1092
+--S 43 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -1056,9 +1056,9 @@ a0:=integrate(t0,x)
--R 5
--R a c x
--R Type: Polynomial(Fraction(Integer))
---E 43
+--E 43
---S 44 of 1092
+--S 44 of 1092
m0:=a0-r0
--R
--R
@@ -1069,19 +1069,19 @@ m0:=a0-r0
--R 2
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 44
+--E 44
---S 45 of 1092
+--S 45 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 45
+--E 45
)clear all
---S 46 of 1092
+--S 46 of 1092
t0:=(a+b*x)*(c+d*x)^5/x
--R
--R
@@ -1094,9 +1094,9 @@ t0:=(a+b*x)*(c+d*x)^5/x
--R /
--R x
--R Type: Fraction(Polynomial(Integer))
---E 46
+--E 46
---S 47 of 1092
+--S 47 of 1092
r0:=5*a*c^4*d*x+5*a*c^3*d^2*x^2+10/3*a*c^2*d^3*x^3+_
5/4*a*c*d^4*x^4+1/5*a*d^5*x^5+1/6*b*(c+d*x)^6/d+a*c^5*log(x)
--R
@@ -1113,9 +1113,9 @@ r0:=5*a*c^4*d*x+5*a*c^3*d^2*x^2+10/3*a*c^2*d^3*x^3+_
--R /
--R 60d
--R Type: Expression(Integer)
---E 47
+--E 47
---S 48 of 1092
+--S 48 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -1131,9 +1131,9 @@ a0:=integrate(t0,x)
--R /
--R 60
--R Type: Union(Expression(Integer),...)
---E 48
+--E 48
---S 49 of 1092
+--S 49 of 1092
m0:=a0-r0
--R
--R
@@ -1142,19 +1142,19 @@ m0:=a0-r0
--R (4) - ----
--R 6d
--R Type: Expression(Integer)
---E 49
+--E 49
---S 50 of 1092
+--S 50 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 50
+--E 50
)clear all
---S 51 of 1092
+--S 51 of 1092
t0:=(a+b*x)*(c+d*x)^5/x^2
--R
--R
@@ -1168,9 +1168,9 @@ t0:=(a+b*x)*(c+d*x)^5/x^2
--R 2
--R x
--R Type: Fraction(Polynomial(Integer))
---E 51
+--E 51
---S 52 of 1092
+--S 52 of 1092
r0:=-a*c^5/x+5*c^3*d*(b*c+2*a*d)*x+5*c^2*d^2*(b*c+a*d)*x^2+_
5/3*c*d^3*(2*b*c+a*d)*x^3+1/4*d^4*(5*b*c+a*d)*x^4+_
1/5*b*d^5*x^5+c^4*(b*c+5*a*d)*log(x)
@@ -1188,9 +1188,9 @@ r0:=-a*c^5/x+5*c^3*d*(b*c+2*a*d)*x+5*c^2*d^2*(b*c+a*d)*x^2+_
--R /
--R 60x
--R Type: Expression(Integer)
---E 52
+--E 52
---S 53 of 1092
+--S 53 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -1206,27 +1206,27 @@ a0:=integrate(t0,x)
--R /
--R 60x
--R Type: Union(Expression(Integer),...)
---E 53
+--E 53
---S 54 of 1092
+--S 54 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 54
+--E 54
---S 55 of 1092
+--S 55 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 55
+--E 55
)clear all
---S 56 of 1092
+--S 56 of 1092
t0:=(a+b*x)*(c+d*x)^5/x^3
--R
--R
@@ -1240,9 +1240,9 @@ t0:=(a+b*x)*(c+d*x)^5/x^3
--R 3
--R x
--R Type: Fraction(Polynomial(Integer))
---E 56
+--E 56
---S 57 of 1092
+--S 57 of 1092
r0:=-1/2*a*c^5/x^2-c^4*(b*c+5*a*d)/x+10*c^2*d^2*(b*c+a*d)*x+_
5/2*c*d^3*(2*b*c+a*d)*x^2+1/3*d^4*(5*b*c+a*d)*x^3+_
1/4*b*d^5*x^4+5*c^3*d*(b*c+2*a*d)*log(x)
@@ -1261,9 +1261,9 @@ r0:=-1/2*a*c^5/x^2-c^4*(b*c+5*a*d)/x+10*c^2*d^2*(b*c+a*d)*x+_
--R 2
--R 12x
--R Type: Expression(Integer)
---E 57
+--E 57
---S 58 of 1092
+--S 58 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -1280,27 +1280,27 @@ a0:=integrate(t0,x)
--R 2
--R 12x
--R Type: Union(Expression(Integer),...)
---E 58
+--E 58
---S 59 of 1092
+--S 59 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 59
+--E 59
---S 60 of 1092
+--S 60 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 60
+--E 60
)clear all
---S 61 of 1092
+--S 61 of 1092
t0:=x*(a+b*x)*(c+d*x)^16
--R
--R
@@ -1329,9 +1329,9 @@ t0:=x*(a+b*x)*(c+d*x)^16
--R 14 2 15 3 15 16 2 16
--R (120a c d + 16b c d)x + (16a c d + b c )x + a c x
--R Type: Polynomial(Integer)
---E 61
+--E 61
---S 62 of 1092
+--S 62 of 1092
r0:=1/17*c*(b*c-a*d)*(c+d*x)^17/d^3-1/18*(2*b*c-a*d)*(c+d*x)^18/d^3+_
1/19*b*(c+d*x)^19/d^3
--R
@@ -1374,9 +1374,9 @@ r0:=1/17*c*(b*c-a*d)*(c+d*x)^17/d^3-1/18*(2*b*c-a*d)*(c+d*x)^18/d^3+_
--R 3
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 62
+--E 62
---S 63 of 1092
+--S 63 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -1411,9 +1411,9 @@ a0:=integrate(t0,x)
--R (30a c d + 4b c d)x + (-- a c d + - b c )x + - a c x
--R 3 3 2
--R Type: Polynomial(Fraction(Integer))
---E 63
+--E 63
---S 64 of 1092
+--S 64 of 1092
m0:=a0-r0
--R
--R
@@ -1424,19 +1424,19 @@ m0:=a0-r0
--R 3
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 64
+--E 64
---S 65 of 1092
+--S 65 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 65
+--E 65
)clear all
---S 66 of 1092
+--S 66 of 1092
t0:=x^2*(a+b*x)*(c+d*x)^16
--R
--R
@@ -1465,9 +1465,9 @@ t0:=x^2*(a+b*x)*(c+d*x)^16
--R 14 2 15 4 15 16 3 16 2
--R (120a c d + 16b c d)x + (16a c d + b c )x + a c x
--R Type: Polynomial(Integer)
---E 66
+--E 66
---S 67 of 1092
+--S 67 of 1092
r0:=-1/17*c^2*(b*c-a*d)*(c+d*x)^17/d^4+1/18*c*(3*b*c-2*a*d)*(c+d*x)^18/d^4-_
1/19*(3*b*c-a*d)*(c+d*x)^19/d^4+1/20*b*(c+d*x)^20/d^4
--R
@@ -1512,9 +1512,9 @@ r0:=-1/17*c^2*(b*c-a*d)*(c+d*x)^17/d^4+1/18*c*(3*b*c-2*a*d)*(c+d*x)^18/d^4-_
--R 4
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 67
+--E 67
---S 68 of 1092
+--S 68 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -1551,9 +1551,9 @@ a0:=integrate(t0,x)
--R (24a c d + -- b c d)x + (4a c d + - b c )x + - a c x
--R 5 4 3
--R Type: Polynomial(Fraction(Integer))
---E 68
+--E 68
---S 69 of 1092
+--S 69 of 1092
m0:=a0-r0
--R
--R
@@ -1564,19 +1564,19 @@ m0:=a0-r0
--R 4
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 69
+--E 69
---S 70 of 1092
+--S 70 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 70
+--E 70
)clear all
---S 71 of 1092
+--S 71 of 1092
t0:=x^3*(a+b*x)*(c+d*x)^16
--R
--R
@@ -1605,9 +1605,9 @@ t0:=x^3*(a+b*x)*(c+d*x)^16
--R 14 2 15 5 15 16 4 16 3
--R (120a c d + 16b c d)x + (16a c d + b c )x + a c x
--R Type: Polynomial(Integer)
---E 71
+--E 71
---S 72 of 1092
+--S 72 of 1092
r0:=1/17*c^3*(b*c-a*d)*(c+d*x)^17/d^5-1/18*c^2*(4*b*c-3*a*d)*(c+d*x)^18/d^5+_
3/19*c*(2*b*c-a*d)*(c+d*x)^19/d^5-1/20*(4*b*c-a*d)*(c+d*x)^20/d^5+_
1/21*b*(c+d*x)^21/d^5
@@ -1653,9 +1653,9 @@ r0:=1/17*c^3*(b*c-a*d)*(c+d*x)^17/d^5-1/18*c^2*(4*b*c-3*a*d)*(c+d*x)^18/d^5+_
--R 5
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 72
+--E 72
---S 73 of 1092
+--S 73 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -1692,9 +1692,9 @@ a0:=integrate(t0,x)
--R (20a c d + - b c d)x + (-- a c d + - b c )x + - a c x
--R 3 5 5 4
--R Type: Polynomial(Fraction(Integer))
---E 73
+--E 73
---S 74 of 1092
+--S 74 of 1092
m0:=a0-r0
--R
--R
@@ -1705,28 +1705,28 @@ m0:=a0-r0
--R 5
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 74
+--E 74
---S 75 of 1092
+--S 75 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 75
+--E 75
)clear all
---S 76 of 1092
+--S 76 of 1092
t0:=x^2*(2+x)^5*(2+3*x)
--R
--R
--R 8 7 6 5 4 3 2
--R (1) 3x + 32x + 140x + 320x + 400x + 256x + 64x
--R Type: Polynomial(Integer)
---E 76
+--E 76
---S 77 of 1092
+--S 77 of 1092
r0:=1/3*x^3*(2+x)^6
--R
--R
@@ -1734,9 +1734,9 @@ r0:=1/3*x^3*(2+x)^6
--R (2) - x + 4x + 20x + --- x + 80x + 64x + -- x
--R 3 3 3
--R Type: Polynomial(Fraction(Integer))
---E 77
+--E 77
---S 78 of 1092
+--S 78 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -1744,36 +1744,36 @@ a0:=integrate(t0,x)
--R (3) - x + 4x + 20x + --- x + 80x + 64x + -- x
--R 3 3 3
--R Type: Polynomial(Fraction(Integer))
---E 78
+--E 78
---S 79 of 1092
+--S 79 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Polynomial(Fraction(Integer))
---E 79
+--E 79
---S 80 of 1092
+--S 80 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Polynomial(Fraction(Integer))
---E 80
+--E 80
)clear all
---S 81 of 1092
+--S 81 of 1092
t0:=x^2*(a+b*x)^n*(c+d*x)^2
--R
--R
--R 2 4 3 2 2 n
--R (1) (d x + 2c d x + c x )(b x + a)
--R Type: Expression(Integer)
---E 81
+--E 81
---S 82 of 1092
+--S 82 of 1092
r0:=a^2*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^5*(1+n))-2*a*(b*c-2*a*d)*(b*c-a*d)*_
(a+b*x)^(2+n)/(b^5*(2+n))+(b^2*c^2-6*a*b*c*d+6*a^2*d^2)*_
(a+b*x)^(3+n)/(b^5*(3+n))+2*d*(b*c-2*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_
@@ -1838,9 +1838,9 @@ r0:=a^2*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^5*(1+n))-2*a*(b*c-2*a*d)*(b*c-a*d)*_
--R 5 5 5 4 5 3 5 2 5 5
--R b n + 15b n + 85b n + 225b n + 274b n + 120b
--R Type: Expression(Integer)
---E 82
+--E 82
---S 83 of 1092
+--S 83 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -1898,9 +1898,9 @@ a0:=integrate(t0,x)
--R 5 5 5 4 5 3 5 2 5 5
--R b n + 15b n + 85b n + 225b n + 274b n + 120b
--R Type: Union(Expression(Integer),...)
---E 83
+--E 83
---S 84 of 1092
+--S 84 of 1092
m0:=a0-r0
--R
--R
@@ -2009,28 +2009,28 @@ m0:=a0-r0
--R 5 5 5 4 5 3 5 2 5 5
--R b n + 15b n + 85b n + 225b n + 274b n + 120b
--R Type: Expression(Integer)
---E 84
+--E 84
---S 85 of 1092
+--S 85 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 85
+--E 85
)clear all
---S 86 of 1092
+--S 86 of 1092
t0:=x*(a+b*x)^n*(c+d*x)^2
--R
--R
--R 2 3 2 2 n
--R (1) (d x + 2c d x + c x)(b x + a)
--R Type: Expression(Integer)
---E 86
+--E 86
---S 87 of 1092
+--S 87 of 1092
r0:=-a*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^4*(1+n))+(b*c-3*a*d)*(b*c-a*d)*_
(a+b*x)^(2+n)/(b^4*(2+n))+d*(2*b*c-3*a*d)*(a+b*x)^(3+n)/_
(b^4*(3+n))+d^2*(a+b*x)^(4+n)/(b^4*(4+n))
@@ -2070,9 +2070,9 @@ r0:=-a*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^4*(1+n))+(b*c-3*a*d)*(b*c-a*d)*_
--R 4 4 4 3 4 2 4 4
--R b n + 10b n + 35b n + 50b n + 24b
--R Type: Expression(Integer)
---E 87
+--E 87
---S 88 of 1092
+--S 88 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -2115,9 +2115,9 @@ a0:=integrate(t0,x)
--R 4 4 4 3 4 2 4 4
--R b n + 10b n + 35b n + 50b n + 24b
--R Type: Union(Expression(Integer),...)
---E 88
+--E 88
---S 89 of 1092
+--S 89 of 1092
m0:=a0-r0
--R
--R
@@ -2190,28 +2190,28 @@ m0:=a0-r0
--R 4 4 4 3 4 2 4 4
--R b n + 10b n + 35b n + 50b n + 24b
--R Type: Expression(Integer)
---E 89
+--E 89
---S 90 of 1092
+--S 90 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 90
+--E 90
)clear all
---S 91 of 1092
+--S 91 of 1092
t0:=(a+b*x)^n*(c+d*x)^2
--R
--R
--R 2 2 2 n
--R (1) (d x + 2c d x + c )(b x + a)
--R Type: Expression(Integer)
---E 91
+--E 91
---S 92 of 1092
+--S 92 of 1092
r0:=(b*c-a*d)^2*(a+b*x)^(1+n)/(b^3*(1+n))+2*d*(b*c-a*d)*(a+b*x)^(2+n)/_
(b^3*(2+n))+d^2*(a+b*x)^(3+n)/(b^3*(3+n))
--R
@@ -2238,9 +2238,9 @@ r0:=(b*c-a*d)^2*(a+b*x)^(1+n)/(b^3*(1+n))+2*d*(b*c-a*d)*(a+b*x)^(2+n)/_
--R 3 3 3 2 3 3
--R b n + 6b n + 11b n + 6b
--R Type: Expression(Integer)
---E 92
+--E 92
---S 93 of 1092
+--S 93 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -2263,9 +2263,9 @@ a0:=integrate(t0,x)
--R 3 3 3 2 3 3
--R b n + 6b n + 11b n + 6b
--R Type: Union(Expression(Integer),...)
---E 93
+--E 93
---S 94 of 1092
+--S 94 of 1092
m0:=a0-r0
--R
--R
@@ -2303,19 +2303,19 @@ m0:=a0-r0
--R 3 3 3 2 3 3
--R b n + 6b n + 11b n + 6b
--R Type: Expression(Integer)
---E 94
+--E 94
---S 95 of 1092
+--S 95 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 95
+--E 95
)clear all
---S 96 of 1092
+--S 96 of 1092
t0:=(a+b*x)^n*(c+d*x)^2/x
--R
--R
@@ -2324,29 +2324,29 @@ t0:=(a+b*x)^n*(c+d*x)^2/x
--R (1) ------------------------------
--R x
--R Type: Expression(Integer)
---E 96
+--E 96
---S 97 of 1092
+--S 97 of 1092
--r0:=-d*(a*d-b*c*(3+n))*(a+b*x)^(1+n)/(b^2*(1+n)*(2+n))+_
-- d*(a+b*x)^(1+n)*(c+d*x)/(b*(2+n))-c^2*(a+b*x)^(1+n)*_
-- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n))
---E 97
+--E 97
---S 98 of 1092
+--S 98 of 1092
--a0:=integrate(t0,x)
---E 98
+--E 98
---S 99 of 1092
+--S 99 of 1092
--m0:=a0-r0
---E 99
+--E 99
---S 100 of 1092
+--S 100 of 1092
--d0:=D(m0,x)
---E 100
+--E 100
)clear all
---S 101 of 1092
+--S 101 of 1092
t0:=x^m*(a+b*x)^2*(c+d*x)^5
--R
--R
@@ -2363,9 +2363,9 @@ t0:=x^m*(a+b*x)^2*(c+d*x)^5
--R m
--R x
--R Type: Expression(Integer)
---E 101
+--E 101
---S 102 of 1092
+--S 102 of 1092
r0:=a^2*c^5*x^(1+m)/(1+m)+a*c^4*(2*b*c+5*a*d)*x^(2+m)/(2+m)+_
c^3*(b^2*c^2+10*a*b*c*d+10*a^2*d^2)*x^(3+m)/(3+m)+_
5*c^2*d*(b^2*c^2+4*a*b*c*d+2*a^2*d^2)*x^(4+m)/(4+m)+_
@@ -2531,9 +2531,9 @@ r0:=a^2*c^5*x^(1+m)/(1+m)+a*c^4*(2*b*c+5*a*d)*x^(2+m)/(2+m)+_
--R 8 7 6 5 4 3 2
--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320
--R Type: Expression(Integer)
---E 102
+--E 102
---S 103 of 1092
+--S 103 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -2699,9 +2699,9 @@ a0:=integrate(t0,x)
--R 8 7 6 5 4 3 2
--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320
--R Type: Union(Expression(Integer),...)
---E 103
+--E 103
---S 104 of 1092
+--S 104 of 1092
m0:=a0-r0
--R
--R
@@ -3023,19 +3023,19 @@ m0:=a0-r0
--R 8 7 6 5 4 3 2
--R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320
--R Type: Expression(Integer)
---E 104
+--E 104
---S 105 of 1092
+--S 105 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 105
+--E 105
)clear all
---S 106 of 1092
+--S 106 of 1092
t0:=x^3*(a+b*x)^2*(c+d*x)^16
--R
--R
@@ -3088,9 +3088,9 @@ t0:=x^3*(a+b*x)^2*(c+d*x)^16
--R 2 14 2 15 2 16 5 2 15 16 4 2 16 3
--R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x
--R Type: Polynomial(Integer)
---E 106
+--E 106
---S 107 of 1092
+--S 107 of 1092
r0:=-1/17*c^3*(b*c-a*d)^2*(c+d*x)^17/d^6+1/18*c^2*(5*b*c-3*a*d)*_
(b*c-a*d)*(c+d*x)^18/d^6-1/19*c*(10*b^2*c^2-12*a*b*c*d+_
3*a^2*d^2)*(c+d*x)^19/d^6+1/20*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_
@@ -3169,9 +3169,9 @@ r0:=-1/17*c^3*(b*c-a*d)^2*(c+d*x)^17/d^6+1/18*c^2*(5*b*c-3*a*d)*_
--R 6
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 107
+--E 107
---S 108 of 1092
+--S 108 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -3239,9 +3239,9 @@ a0:=integrate(t0,x)
--R (20a c d + -- a b c d + - b c )x + (-- a c d + - a b c )x + - a c x
--R 3 6 5 5 4
--R Type: Polynomial(Fraction(Integer))
---E 108
+--E 108
---S 109 of 1092
+--S 109 of 1092
m0:=a0-r0
--R
--R
@@ -3252,19 +3252,19 @@ m0:=a0-r0
--R 6
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 109
+--E 109
---S 110 of 1092
+--S 110 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 110
+--E 110
)clear all
---S 111 of 1092
+--S 111 of 1092
t0:=x^2*(a+b*x)^2*(c+d*x)^16
--R
--R
@@ -3317,9 +3317,9 @@ t0:=x^2*(a+b*x)^2*(c+d*x)^16
--R 2 14 2 15 2 16 4 2 15 16 3 2 16 2
--R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x
--R Type: Polynomial(Integer)
---E 111
+--E 111
---S 112 of 1092
+--S 112 of 1092
r0:=1/17*c^2*(b*c-a*d)^2*(c+d*x)^17/d^5-1/9*c*(b*c-a*d)*(2*b*c-a*d)*_
(c+d*x)^18/d^5+1/19*(6*b^2*c^2-6*a*b*c*d+a^2*d^2)*(c+d*x)^19/d^5-_
1/10*b*(2*b*c-a*d)*(c+d*x)^20/d^5+1/21*b^2*(c+d*x)^21/d^5
@@ -3394,9 +3394,9 @@ r0:=1/17*c^2*(b*c-a*d)^2*(c+d*x)^17/d^5-1/9*c*(b*c-a*d)*(2*b*c-a*d)*_
--R 5
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 112
+--E 112
---S 113 of 1092
+--S 113 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -3462,9 +3462,9 @@ a0:=integrate(t0,x)
--R (24a c d + -- a b c d + - b c )x + (4a c d + - a b c )x + - a c x
--R 5 5 2 3
--R Type: Polynomial(Fraction(Integer))
---E 113
+--E 113
---S 114 of 1092
+--S 114 of 1092
m0:=a0-r0
--R
--R
@@ -3475,19 +3475,19 @@ m0:=a0-r0
--R 5
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 114
+--E 114
---S 115 of 1092
+--S 115 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 115
+--E 115
)clear all
---S 116 of 1092
+--S 116 of 1092
t0:=x*(a+b*x)^2*(c+d*x)^16
--R
--R
@@ -3540,9 +3540,9 @@ t0:=x*(a+b*x)^2*(c+d*x)^16
--R 2 14 2 15 2 16 3 2 15 16 2 2 16
--R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x
--R Type: Polynomial(Integer)
---E 116
+--E 116
---S 117 of 1092
+--S 117 of 1092
r0:=-1/17*c*(b*c-a*d)^2*(c+d*x)^17/d^4+1/18*(b*c-a*d)*(3*b*c-a*d)*_
(c+d*x)^18/d^4-1/19*b*(3*b*c-2*a*d)*(c+d*x)^19/d^4+_
1/20*b^2*(c+d*x)^20/d^4
@@ -3616,9 +3616,9 @@ r0:=-1/17*c*(b*c-a*d)^2*(c+d*x)^17/d^4+1/18*(b*c-a*d)*(3*b*c-a*d)*_
--R 4
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 117
+--E 117
---S 118 of 1092
+--S 118 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -3683,9 +3683,9 @@ a0:=integrate(t0,x)
--R (30a c d + 8a b c d + - b c )x + (-- a c d + - a b c )x + - a c x
--R 4 3 3 2
--R Type: Polynomial(Fraction(Integer))
---E 118
+--E 118
---S 119 of 1092
+--S 119 of 1092
m0:=a0-r0
--R
--R
@@ -3696,28 +3696,28 @@ m0:=a0-r0
--R 4
--R d
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 119
+--E 119
---S 120 of 1092
+--S 120 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Fraction(Polynomial(Fraction(Integer)))
---E 120
+--E 120
)clear all
---S 121 of 1092
+--S 121 of 1092
t0:=x^2*(a+b*x)^n*(c+d*x)^3
--R
--R
--R 3 5 2 4 2 3 3 2 n
--R (1) (d x + 3c d x + 3c d x + c x )(b x + a)
--R Type: Expression(Integer)
---E 121
+--E 121
---S 122 of 1092
+--S 122 of 1092
r0:=a^2*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^6*(1+n))-a*(2*b*c-5*a*d)*_
(b*c-a*d)^2*(a+b*x)^(2+n)/(b^6*(2+n))+(b*c-a*d)*_
(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*(a+b*x)^(3+n)/(b^6*(3+n))+_
@@ -3828,9 +3828,9 @@ r0:=a^2*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^6*(1+n))-a*(2*b*c-5*a*d)*_
--R 6 6 6 5 6 4 6 3 6 2 6 6
--R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b
--R Type: Expression(Integer)
---E 122
+--E 122
---S 123 of 1092
+--S 123 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -3921,9 +3921,9 @@ a0:=integrate(t0,x)
--R 6 6 6 5 6 4 6 3 6 2 6 6
--R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b
--R Type: Union(Expression(Integer),...)
---E 123
+--E 123
---S 124 of 1092
+--S 124 of 1092
m0:=a0-r0
--R
--R
@@ -4113,28 +4113,28 @@ m0:=a0-r0
--R 6 6 6 5 6 4 6 3 6 2 6 6
--R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b
--R Type: Expression(Integer)
---E 124
+--E 124
---S 125 of 1092
+--S 125 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 125
+--E 125
)clear all
---S 126 of 1092
+--S 126 of 1092
t0:=x*(a+b*x)^n*(c+d*x)^3
--R
--R
--R 3 4 2 3 2 2 3 n
--R (1) (d x + 3c d x + 3c d x + c x)(b x + a)
--R Type: Expression(Integer)
---E 126
+--E 126
---S 127 of 1092
+--S 127 of 1092
r0:=-a*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^5*(1+n))+(b*c-4*a*d)*(b*c-a*d)^2*_
(a+b*x)^(2+n)/(b^5*(2+n))+3*d*(b*c-2*a*d)*(b*c-a*d)*(a+b*x)^(3+n)/_
(b^5*(3+n))+d^2*(3*b*c-4*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_
@@ -4208,9 +4208,9 @@ r0:=-a*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^5*(1+n))+(b*c-4*a*d)*(b*c-a*d)^2*_
--R 5 5 5 4 5 3 5 2 5 5
--R b n + 15b n + 85b n + 225b n + 274b n + 120b
--R Type: Expression(Integer)
---E 127
+--E 127
---S 128 of 1092
+--S 128 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -4277,9 +4277,9 @@ a0:=integrate(t0,x)
--R 5 5 5 4 5 3 5 2 5 5
--R b n + 15b n + 85b n + 225b n + 274b n + 120b
--R Type: Union(Expression(Integer),...)
---E 128
+--E 128
---S 129 of 1092
+--S 129 of 1092
m0:=a0-r0
--R
--R
@@ -4412,28 +4412,28 @@ m0:=a0-r0
--R 5 5 5 4 5 3 5 2 5 5
--R b n + 15b n + 85b n + 225b n + 274b n + 120b
--R Type: Expression(Integer)
---E 129
+--E 129
---S 130 of 1092
+--S 130 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 130
+--E 130
)clear all
---S 131 of 1092
+--S 131 of 1092
t0:=(a+b*x)^n*(c+d*x)^3
--R
--R
--R 3 3 2 2 2 3 n
--R (1) (d x + 3c d x + 3c d x + c )(b x + a)
--R Type: Expression(Integer)
---E 131
+--E 131
---S 132 of 1092
+--S 132 of 1092
r0:=(b*c-a*d)^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*d*(b*c-a*d)^2*_
(a+b*x)^(2+n)/(b^4*(2+n))+3*d^2*(b*c-a*d)*(a+b*x)^(3+n)/_
(b^4*(3+n))+d^3*(a+b*x)^(4+n)/(b^4*(4+n))
@@ -4479,9 +4479,9 @@ r0:=(b*c-a*d)^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*d*(b*c-a*d)^2*_
--R 4 4 4 3 4 2 4 4
--R b n + 10b n + 35b n + 50b n + 24b
--R Type: Expression(Integer)
---E 132
+--E 132
---S 133 of 1092
+--S 133 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -4530,9 +4530,9 @@ a0:=integrate(t0,x)
--R 4 4 4 3 4 2 4 4
--R b n + 10b n + 35b n + 50b n + 24b
--R Type: Union(Expression(Integer),...)
---E 133
+--E 133
---S 134 of 1092
+--S 134 of 1092
m0:=a0-r0
--R
--R
@@ -4620,19 +4620,19 @@ m0:=a0-r0
--R 4 4 4 3 4 2 4 4
--R b n + 10b n + 35b n + 50b n + 24b
--R Type: Expression(Integer)
---E 134
+--E 134
---S 135 of 1092
+--S 135 of 1092
d0:=normalize m0
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 135
+--E 135
)clear all
---S 136 of 1092
+--S 136 of 1092
t0:=(a+b*x)^n*(c+d*x)^3/x
--R
--R
@@ -4641,30 +4641,30 @@ t0:=(a+b*x)^n*(c+d*x)^3/x
--R (1) ----------------------------------------
--R x
--R Type: Expression(Integer)
---E 136
+--E 136
---S 137 of 1092
+--S 137 of 1092
--r0:=3*c^2*d*(a+b*x)^(1+n)/(b*(1+n))-3*a*c*d^2*(a+b*x)^(1+n)/(b^2*(1+n))+_
-- a^2*d^3*(a+b*x)^(1+n)/(b^3*(1+n))+3*c*d^2*(a+b*x)^(2+n)/(b^2*(2+n))-_
-- 2*a*d^3*(a+b*x)^(2+n)/(b^3*(2+n))+d^3*(a+b*x)^(3+n)/(b^3*(3+n))-_
-- c^3*(a+b*x)^(1+n)*hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n))
---E 137
+--E 137
---S 138 of 1092
+--S 138 of 1092
--a0:=integrate(t0,x)
---E 138
+--E 138
---S 139 of 1092
+--S 139 of 1092
--m0:=a0-r0
---E 139
+--E 139
---S 140 of 1092
+--S 140 of 1092
--d0:=D(m0,x)
---E 140
+--E 140
)clear all
---S 141 of 1092
+--S 141 of 1092
t0:=x^m*(c+d*x)/(a+b*x)
--R
--R
@@ -4673,28 +4673,28 @@ t0:=x^m*(c+d*x)/(a+b*x)
--R (1) -----------
--R b x + a
--R Type: Expression(Integer)
---E 141
+--E 141
---S 142 of 1092
+--S 142 of 1092
--r0:=d*x^(1+m)/(b*(1+m))+(b*c-a*d)*x^(1+m)*_
-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b*(1+m))
---E 142
+--E 142
---S 143 of 1092
+--S 143 of 1092
--a0:=integrate(t0,x)
---E 143
+--E 143
---S 144 of 1092
+--S 144 of 1092
--m0:=a0-r0
---E 144
+--E 144
---S 145 of 1092
+--S 145 of 1092
--d0:=D(m0,x)
---E 145
+--E 145
)clear all
---S 146 of 1092
+--S 146 of 1092
t0:=x^4*(c+d*x)/(a+b*x)
--R
--R
@@ -4703,9 +4703,9 @@ t0:=x^4*(c+d*x)/(a+b*x)
--R (1) -----------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 146
+--E 146
---S 147 of 1092
+--S 147 of 1092
r0:=-a^3*(b*c-a*d)*x/b^5+1/2*a^2*(b*c-a*d)*x^2/b^4-1/3*a*(b*c-a*d)*x^3/b^3+_
1/4*(b*c-a*d)*x^4/b^2+1/5*d*x^5/b+a^4*(b*c-a*d)*log(a+b*x)/b^6
--R
@@ -4720,9 +4720,9 @@ r0:=-a^3*(b*c-a*d)*x/b^5+1/2*a^2*(b*c-a*d)*x^2/b^4-1/3*a*(b*c-a*d)*x^3/b^3+_
--R 6
--R 60b
--R Type: Expression(Integer)
---E 147
+--E 147
---S 148 of 1092
+--S 148 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -4736,27 +4736,27 @@ a0:=integrate(t0,x)
--R 6
--R 60b
--R Type: Union(Expression(Integer),...)
---E 148
+--E 148
---S 149 of 1092
+--S 149 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 149
+--E 149
---S 150 of 1092
+--S 150 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 150
+--E 150
)clear all
---S 151 of 1092
+--S 151 of 1092
t0:=x^3*(c+d*x)/(a+b*x)
--R
--R
@@ -4765,9 +4765,9 @@ t0:=x^3*(c+d*x)/(a+b*x)
--R (1) -----------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 151
+--E 151
---S 152 of 1092
+--S 152 of 1092
r0:=a^2*(b*c-a*d)*x/b^4-1/2*a*(b*c-a*d)*x^2/b^3+1/3*(b*c-a*d)*x^3/b^2+_
1/4*d*x^4/b-a^3*(b*c-a*d)*log(a+b*x)/b^5
--R
@@ -4782,9 +4782,9 @@ r0:=a^2*(b*c-a*d)*x/b^4-1/2*a*(b*c-a*d)*x^2/b^3+1/3*(b*c-a*d)*x^3/b^2+_
--R 5
--R 12b
--R Type: Expression(Integer)
---E 152
+--E 152
---S 153 of 1092
+--S 153 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -4798,27 +4798,27 @@ a0:=integrate(t0,x)
--R 5
--R 12b
--R Type: Union(Expression(Integer),...)
---E 153
+--E 153
---S 154 of 1092
+--S 154 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 154
+--E 154
---S 155 of 1092
+--S 155 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 155
+--E 155
)clear all
---S 156 of 1092
+--S 156 of 1092
t0:=x^2*(c+d*x)/(a+b*x)
--R
--R
@@ -4827,9 +4827,9 @@ t0:=x^2*(c+d*x)/(a+b*x)
--R (1) -----------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 156
+--E 156
---S 157 of 1092
+--S 157 of 1092
r0:=-a*(b*c-a*d)*x/b^3+1/2*(b*c-a*d)*x^2/b^2+1/3*d*x^3/b+_
a^2*(b*c-a*d)*log(a+b*x)/b^4
--R
@@ -4844,9 +4844,9 @@ r0:=-a*(b*c-a*d)*x/b^3+1/2*(b*c-a*d)*x^2/b^2+1/3*d*x^3/b+_
--R 4
--R 6b
--R Type: Expression(Integer)
---E 157
+--E 157
---S 158 of 1092
+--S 158 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -4860,27 +4860,27 @@ a0:=integrate(t0,x)
--R 4
--R 6b
--R Type: Union(Expression(Integer),...)
---E 158
+--E 158
---S 159 of 1092
+--S 159 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 159
+--E 159
---S 160 of 1092
+--S 160 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 160
+--E 160
)clear all
---S 161 of 1092
+--S 161 of 1092
t0:=x*(c+d*x)/(a+b*x)
--R
--R
@@ -4889,9 +4889,9 @@ t0:=x*(c+d*x)/(a+b*x)
--R (1) ----------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 161
+--E 161
---S 162 of 1092
+--S 162 of 1092
r0:=(b*c-a*d)*x/b^2+1/2*d*x^2/b-a*(b*c-a*d)*log(a+b*x)/b^3
--R
--R
@@ -4901,9 +4901,9 @@ r0:=(b*c-a*d)*x/b^2+1/2*d*x^2/b-a*(b*c-a*d)*log(a+b*x)/b^3
--R 3
--R 2b
--R Type: Expression(Integer)
---E 162
+--E 162
---S 163 of 1092
+--S 163 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -4913,27 +4913,27 @@ a0:=integrate(t0,x)
--R 3
--R 2b
--R Type: Union(Expression(Integer),...)
---E 163
+--E 163
---S 164 of 1092
+--S 164 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 164
+--E 164
---S 165 of 1092
+--S 165 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 165
+--E 165
)clear all
---S 166 of 1092
+--S 166 of 1092
t0:=(c+d*x)/(a+b*x)
--R
--R
@@ -4941,9 +4941,9 @@ t0:=(c+d*x)/(a+b*x)
--R (1) -------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 166
+--E 166
---S 167 of 1092
+--S 167 of 1092
r0:=d*x/b+(b*c-a*d)*log(a+b*x)/b^2
--R
--R
@@ -4952,9 +4952,9 @@ r0:=d*x/b+(b*c-a*d)*log(a+b*x)/b^2
--R 2
--R b
--R Type: Expression(Integer)
---E 167
+--E 167
---S 168 of 1092
+--S 168 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -4963,27 +4963,27 @@ a0:=integrate(t0,x)
--R 2
--R b
--R Type: Union(Expression(Integer),...)
---E 168
+--E 168
---S 169 of 1092
+--S 169 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 169
+--E 169
---S 170 of 1092
+--S 170 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 170
+--E 170
)clear all
---S 171 of 1092
+--S 171 of 1092
t0:=(c+d*x)/(x*(a+b*x))
--R
--R
@@ -4992,9 +4992,9 @@ t0:=(c+d*x)/(x*(a+b*x))
--R 2
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 171
+--E 171
---S 172 of 1092
+--S 172 of 1092
r0:=c*log(x)/a-(b*c-a*d)*log(a+b*x)/(a*b)
--R
--R
@@ -5002,9 +5002,9 @@ r0:=c*log(x)/a-(b*c-a*d)*log(a+b*x)/(a*b)
--R (2) ------------------------------------
--R a b
--R Type: Expression(Integer)
---E 172
+--E 172
---S 173 of 1092
+--S 173 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5012,27 +5012,27 @@ a0:=integrate(t0,x)
--R (3) ------------------------------------
--R a b
--R Type: Union(Expression(Integer),...)
---E 173
+--E 173
---S 174 of 1092
+--S 174 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 174
+--E 174
---S 175 of 1092
+--S 175 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 175
+--E 175
)clear all
---S 176 of 1092
+--S 176 of 1092
t0:=(c+d*x)/(x^2*(a+b*x))
--R
--R
@@ -5041,9 +5041,9 @@ t0:=(c+d*x)/(x^2*(a+b*x))
--R 3 2
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 176
+--E 176
---S 177 of 1092
+--S 177 of 1092
r0:=-c/(a*x)-(b*c-a*d)*log(x)/a^2+(b*c-a*d)*log(a+b*x)/a^2
--R
--R
@@ -5052,9 +5052,9 @@ r0:=-c/(a*x)-(b*c-a*d)*log(x)/a^2+(b*c-a*d)*log(a+b*x)/a^2
--R 2
--R a x
--R Type: Expression(Integer)
---E 177
+--E 177
---S 178 of 1092
+--S 178 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5063,27 +5063,27 @@ a0:=integrate(t0,x)
--R 2
--R a x
--R Type: Union(Expression(Integer),...)
---E 178
+--E 178
---S 179 of 1092
+--S 179 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 179
+--E 179
---S 180 of 1092
+--S 180 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 180
+--E 180
)clear all
---S 181 of 1092
+--S 181 of 1092
t0:=(c+d*x)/(x^3*(a+b*x))
--R
--R
@@ -5092,9 +5092,9 @@ t0:=(c+d*x)/(x^3*(a+b*x))
--R 4 3
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 181
+--E 181
---S 182 of 1092
+--S 182 of 1092
r0:=-1/2*c/(a*x^2)+(b*c-a*d)/(a^2*x)+b*(b*c-a*d)*log(x)/a^3-_
b*(b*c-a*d)*log(a+b*x)/a^3
--R
@@ -5109,9 +5109,9 @@ r0:=-1/2*c/(a*x^2)+(b*c-a*d)/(a^2*x)+b*(b*c-a*d)*log(x)/a^3-_
--R 3 2
--R 2a x
--R Type: Expression(Integer)
---E 182
+--E 182
---S 183 of 1092
+--S 183 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5125,27 +5125,27 @@ a0:=integrate(t0,x)
--R 3 2
--R 2a x
--R Type: Union(Expression(Integer),...)
---E 183
+--E 183
---S 184 of 1092
+--S 184 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 184
+--E 184
---S 185 of 1092
+--S 185 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 185
+--E 185
)clear all
---S 186 of 1092
+--S 186 of 1092
t0:=(c+d*x)/(x^4*(a+b*x))
--R
--R
@@ -5154,9 +5154,9 @@ t0:=(c+d*x)/(x^4*(a+b*x))
--R 5 4
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 186
+--E 186
---S 187 of 1092
+--S 187 of 1092
r0:=-1/3*c/(a*x^3)+1/2*(b*c-a*d)/(a^2*x^2)-b*(b*c-a*d)/(a^3*x)-_
b^2*(b*c-a*d)*log(x)/a^4+b^2*(b*c-a*d)*log(a+b*x)/a^4
--R
@@ -5171,9 +5171,9 @@ r0:=-1/3*c/(a*x^3)+1/2*(b*c-a*d)/(a^2*x^2)-b*(b*c-a*d)/(a^3*x)-_
--R 4 3
--R 6a x
--R Type: Expression(Integer)
---E 187
+--E 187
---S 188 of 1092
+--S 188 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5187,27 +5187,27 @@ a0:=integrate(t0,x)
--R 4 3
--R 6a x
--R Type: Union(Expression(Integer),...)
---E 188
+--E 188
---S 189 of 1092
+--S 189 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 189
+--E 189
---S 190 of 1092
+--S 190 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 190
+--E 190
)clear all
---S 191 of 1092
+--S 191 of 1092
t0:=(c+d*x)/(x^5*(a+b*x))
--R
--R
@@ -5216,9 +5216,9 @@ t0:=(c+d*x)/(x^5*(a+b*x))
--R 6 5
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 191
+--E 191
---S 192 of 1092
+--S 192 of 1092
r0:=-1/4*c/(a*x^4)+1/3*(b*c-a*d)/(a^2*x^3)-1/2*b*(b*c-a*d)/(a^3*x^2)+_
b^2*(b*c-a*d)/(a^4*x)+b^3*(b*c-a*d)*log(x)/a^5-_
b^3*(b*c-a*d)*log(a+b*x)/a^5
@@ -5234,9 +5234,9 @@ r0:=-1/4*c/(a*x^4)+1/3*(b*c-a*d)/(a^2*x^3)-1/2*b*(b*c-a*d)/(a^3*x^2)+_
--R 5 4
--R 12a x
--R Type: Expression(Integer)
---E 192
+--E 192
---S 193 of 1092
+--S 193 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5250,27 +5250,27 @@ a0:=integrate(t0,x)
--R 5 4
--R 12a x
--R Type: Union(Expression(Integer),...)
---E 193
+--E 193
---S 194 of 1092
+--S 194 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 194
+--E 194
---S 195 of 1092
+--S 195 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 195
+--E 195
)clear all
---S 196 of 1092
+--S 196 of 1092
t0:=x^m*(c+d*x)^2/(a+b*x)
--R
--R
@@ -5279,29 +5279,29 @@ t0:=x^m*(c+d*x)^2/(a+b*x)
--R (1) ----------------------
--R b x + a
--R Type: Expression(Integer)
---E 196
+--E 196
---S 197 of 1092
+--S 197 of 1092
--r0:=-d*(a*d*(2+m)-b*c*(3+m))*x^(1+m)/(b^2*(1+m)*(2+m))+_
-- d*x^(1+m)*(c+d*x)/(b*(2+m))+(b*c-a*d)^2*x^(1+m)*_
-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^2*(1+m))
---E 197
+--E 197
---S 198 of 1092
+--S 198 of 1092
--a0:=integrate(t0,x)
---E 198
+--E 198
---S 199 of 1092
+--S 199 of 1092
--m0:=a0-r0
---E 199
+--E 199
---S 200 of 1092
+--S 200 of 1092
--d0:=D(m0,x)
---E 200
+--E 200
)clear all
---S 201 of 1092
+--S 201 of 1092
t0:=x^4*(c+d*x)^2/(a+b*x)
--R
--R
@@ -5310,9 +5310,9 @@ t0:=x^4*(c+d*x)^2/(a+b*x)
--R (1) ---------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 201
+--E 201
---S 202 of 1092
+--S 202 of 1092
r0:=-a^3*(b*c-a*d)^2*x/b^6+1/2*a^2*(b*c-a*d)^2*x^2/b^5-_
1/3*a*(b*c-a*d)^2*x^3/b^4+1/4*(b*c-a*d)^2*x^4/b^3+_
1/5*d*(2*b*c-a*d)*x^5/b^2+1/6*d^2*x^6/b+a^4*(b*c-a*d)^2*log(a+b*x)/b^7
@@ -5334,9 +5334,9 @@ r0:=-a^3*(b*c-a*d)^2*x/b^6+1/2*a^2*(b*c-a*d)^2*x^2/b^5-_
--R 7
--R 60b
--R Type: Expression(Integer)
---E 202
+--E 202
---S 203 of 1092
+--S 203 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5356,27 +5356,27 @@ a0:=integrate(t0,x)
--R 7
--R 60b
--R Type: Union(Expression(Integer),...)
---E 203
+--E 203
---S 204 of 1092
+--S 204 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 204
+--E 204
---S 205 of 1092
+--S 205 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 205
+--E 205
)clear all
---S 206 of 1092
+--S 206 of 1092
t0:=x^3*(c+d*x)^2/(a+b*x)
--R
--R
@@ -5385,9 +5385,9 @@ t0:=x^3*(c+d*x)^2/(a+b*x)
--R (1) ---------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 206
+--E 206
---S 207 of 1092
+--S 207 of 1092
r0:=a^2*(b*c-a*d)^2*x/b^5-1/2*a*(b*c-a*d)^2*x^2/b^4+_
1/3*(b*c-a*d)^2*x^3/b^3+1/4*d*(2*b*c-a*d)*x^4/b^2+1/5*d^2*x^5/b-_
a^3*(b*c-a*d)^2*log(a+b*x)/b^6
@@ -5406,9 +5406,9 @@ r0:=a^2*(b*c-a*d)^2*x/b^5-1/2*a*(b*c-a*d)^2*x^2/b^4+_
--R 6
--R 60b
--R Type: Expression(Integer)
---E 207
+--E 207
---S 208 of 1092
+--S 208 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5425,27 +5425,27 @@ a0:=integrate(t0,x)
--R 6
--R 60b
--R Type: Union(Expression(Integer),...)
---E 208
+--E 208
---S 209 of 1092
+--S 209 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 209
+--E 209
---S 210 of 1092
+--S 210 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 210
+--E 210
)clear all
---S 211 of 1092
+--S 211 of 1092
t0:=x^2*(c+d*x)^2/(a+b*x)
--R
--R
@@ -5454,9 +5454,9 @@ t0:=x^2*(c+d*x)^2/(a+b*x)
--R (1) ---------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 211
+--E 211
---S 212 of 1092
+--S 212 of 1092
r0:=-a*(b*c-a*d)^2*x/b^4+1/2*(b*c-a*d)^2*x^2/b^3+1/3*d*(2*b*c-a*d)*x^3/b^2+_
1/4*d^2*x^4/b+a^2*(b*c-a*d)^2*log(a+b*x)/b^5
--R
@@ -5474,9 +5474,9 @@ r0:=-a*(b*c-a*d)^2*x/b^4+1/2*(b*c-a*d)^2*x^2/b^3+1/3*d*(2*b*c-a*d)*x^3/b^2+_
--R 5
--R 12b
--R Type: Expression(Integer)
---E 212
+--E 212
---S 213 of 1092
+--S 213 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5493,27 +5493,27 @@ a0:=integrate(t0,x)
--R 5
--R 12b
--R Type: Union(Expression(Integer),...)
---E 213
+--E 213
---S 214 of 1092
+--S 214 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 214
+--E 214
---S 215 of 1092
+--S 215 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 215
+--E 215
)clear all
---S 216 of 1092
+--S 216 of 1092
t0:=x*(c+d*x)^2/(a+b*x)
--R
--R
@@ -5522,9 +5522,9 @@ t0:=x*(c+d*x)^2/(a+b*x)
--R (1) --------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 216
+--E 216
---S 217 of 1092
+--S 217 of 1092
r0:=(b*c-a*d)^2*x/b^3+1/2*d*(2*b*c-a*d)*x^2/b^2+1/3*d^2*x^3/b-_
a*(b*c-a*d)^2*log(a+b*x)/b^4
--R
@@ -5539,9 +5539,9 @@ r0:=(b*c-a*d)^2*x/b^3+1/2*d*(2*b*c-a*d)*x^2/b^2+1/3*d^2*x^3/b-_
--R 4
--R 6b
--R Type: Expression(Integer)
---E 217
+--E 217
---S 218 of 1092
+--S 218 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5555,27 +5555,27 @@ a0:=integrate(t0,x)
--R 4
--R 6b
--R Type: Union(Expression(Integer),...)
---E 218
+--E 218
---S 219 of 1092
+--S 219 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 219
+--E 219
---S 220 of 1092
+--S 220 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 220
+--E 220
)clear all
---S 221 of 1092
+--S 221 of 1092
t0:=(c+d*x)^2/(a+b*x)
--R
--R
@@ -5584,9 +5584,9 @@ t0:=(c+d*x)^2/(a+b*x)
--R (1) ------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 221
+--E 221
---S 222 of 1092
+--S 222 of 1092
r0:=d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3
--R
--R
@@ -5600,9 +5600,9 @@ r0:=d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3
--R 3
--R 2b
--R Type: Expression(Integer)
---E 222
+--E 222
---S 223 of 1092
+--S 223 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5613,9 +5613,9 @@ a0:=integrate(t0,x)
--R 3
--R 2b
--R Type: Union(Expression(Integer),...)
---E 223
+--E 223
---S 224 of 1092
+--S 224 of 1092
m0:=a0-r0
--R
--R
@@ -5624,19 +5624,19 @@ m0:=a0-r0
--R (4) - --
--R 2b
--R Type: Expression(Integer)
---E 224
+--E 224
---S 225 of 1092
+--S 225 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 225
+--E 225
)clear all
---S 226 of 1092
+--S 226 of 1092
t0:=(c+d*x)^2/(x*(a+b*x))
--R
--R
@@ -5646,9 +5646,9 @@ t0:=(c+d*x)^2/(x*(a+b*x))
--R 2
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 226
+--E 226
---S 227 of 1092
+--S 227 of 1092
r0:=d^2*x/b+c^2*log(x)/a-(b*c-a*d)^2*log(a+b*x)/(a*b^2)
--R
--R
@@ -5658,9 +5658,9 @@ r0:=d^2*x/b+c^2*log(x)/a-(b*c-a*d)^2*log(a+b*x)/(a*b^2)
--R 2
--R a b
--R Type: Expression(Integer)
---E 227
+--E 227
---S 228 of 1092
+--S 228 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5670,27 +5670,27 @@ a0:=integrate(t0,x)
--R 2
--R a b
--R Type: Union(Expression(Integer),...)
---E 228
+--E 228
---S 229 of 1092
+--S 229 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 229
+--E 229
---S 230 of 1092
+--S 230 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 230
+--E 230
)clear all
---S 231 of 1092
+--S 231 of 1092
t0:=(c+d*x)^2/(x^2*(a+b*x))
--R
--R
@@ -5700,9 +5700,9 @@ t0:=(c+d*x)^2/(x^2*(a+b*x))
--R 3 2
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 231
+--E 231
---S 232 of 1092
+--S 232 of 1092
r0:=-c^2/(a*x)-c*(b*c-2*a*d)*log(x)/a^2+(b*c-a*d)^2*log(a+b*x)/(a^2*b)
--R
--R
@@ -5713,9 +5713,9 @@ r0:=-c^2/(a*x)-c*(b*c-2*a*d)*log(x)/a^2+(b*c-a*d)^2*log(a+b*x)/(a^2*b)
--R 2
--R a b x
--R Type: Expression(Integer)
---E 232
+--E 232
---S 233 of 1092
+--S 233 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5726,27 +5726,27 @@ a0:=integrate(t0,x)
--R 2
--R a b x
--R Type: Union(Expression(Integer),...)
---E 233
+--E 233
---S 234 of 1092
+--S 234 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 234
+--E 234
---S 235 of 1092
+--S 235 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 235
+--E 235
)clear all
---S 236 of 1092
+--S 236 of 1092
t0:=(c+d*x)^2/(x^3*(a+b*x))
--R
--R
@@ -5756,9 +5756,9 @@ t0:=(c+d*x)^2/(x^3*(a+b*x))
--R 4 3
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 236
+--E 236
---S 237 of 1092
+--S 237 of 1092
r0:=-1/2*c^2/(a*x^2)+c*(b*c-2*a*d)/(a^2*x)+(b*c-a*d)^2*log(x)/a^3-_
(b*c-a*d)^2*log(a+b*x)/a^3
--R
@@ -5773,9 +5773,9 @@ r0:=-1/2*c^2/(a*x^2)+c*(b*c-2*a*d)/(a^2*x)+(b*c-a*d)^2*log(x)/a^3-_
--R 3 2
--R 2a x
--R Type: Expression(Integer)
---E 237
+--E 237
---S 238 of 1092
+--S 238 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5789,27 +5789,27 @@ a0:=integrate(t0,x)
--R 3 2
--R 2a x
--R Type: Union(Expression(Integer),...)
---E 238
+--E 238
---S 239 of 1092
+--S 239 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 239
+--E 239
---S 240 of 1092
+--S 240 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 240
+--E 240
)clear all
---S 241 of 1092
+--S 241 of 1092
t0:=(c+d*x)^2/(x^4*(a+b*x))
--R
--R
@@ -5819,9 +5819,9 @@ t0:=(c+d*x)^2/(x^4*(a+b*x))
--R 5 4
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 241
+--E 241
---S 242 of 1092
+--S 242 of 1092
r0:=-1/3*c^2/(a*x^3)+1/2*c*(b*c-2*a*d)/(a^2*x^2)-(b*c-a*d)^2/(a^3*x)-_
b*(b*c-a*d)^2*log(x)/a^4+b*(b*c-a*d)^2*log(a+b*x)/a^4
--R
@@ -5839,9 +5839,9 @@ r0:=-1/3*c^2/(a*x^3)+1/2*c*(b*c-2*a*d)/(a^2*x^2)-(b*c-a*d)^2/(a^3*x)-_
--R 4 3
--R 6a x
--R Type: Expression(Integer)
---E 242
+--E 242
---S 243 of 1092
+--S 243 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5858,27 +5858,27 @@ a0:=integrate(t0,x)
--R 4 3
--R 6a x
--R Type: Union(Expression(Integer),...)
---E 243
+--E 243
---S 244 of 1092
+--S 244 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 244
+--E 244
---S 245 of 1092
+--S 245 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 245
+--E 245
)clear all
---S 246 of 1092
+--S 246 of 1092
t0:=(c+d*x)^2/(x^5*(a+b*x))
--R
--R
@@ -5888,9 +5888,9 @@ t0:=(c+d*x)^2/(x^5*(a+b*x))
--R 6 5
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 246
+--E 246
---S 247 of 1092
+--S 247 of 1092
r0:=-1/4*c^2/(a*x^4)+1/3*c*(b*c-2*a*d)/(a^2*x^3)-_
1/2*(b*c-a*d)^2/(a^3*x^2)+b*(b*c-a*d)^2/(a^4*x)+_
b^2*(b*c-a*d)^2*log(x)/a^5-b^2*(b*c-a*d)^2*log(a+b*x)/a^5
@@ -5912,9 +5912,9 @@ r0:=-1/4*c^2/(a*x^4)+1/3*c*(b*c-2*a*d)/(a^2*x^3)-_
--R 5 4
--R 12a x
--R Type: Expression(Integer)
---E 247
+--E 247
---S 248 of 1092
+--S 248 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -5934,27 +5934,27 @@ a0:=integrate(t0,x)
--R 5 4
--R 12a x
--R Type: Union(Expression(Integer),...)
---E 248
+--E 248
---S 249 of 1092
+--S 249 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 249
+--E 249
---S 250 of 1092
+--S 250 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 250
+--E 250
)clear all
---S 251 of 1092
+--S 251 of 1092
t0:=(c+d*x)^2/(x^6*(a+b*x))
--R
--R
@@ -5964,9 +5964,9 @@ t0:=(c+d*x)^2/(x^6*(a+b*x))
--R 7 6
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 251
+--E 251
---S 252 of 1092
+--S 252 of 1092
r0:=-1/5*c^2/(a*x^5)+1/4*c*(b*c-2*a*d)/(a^2*x^4)-_
1/3*(b*c-a*d)^2/(a^3*x^3)+1/2*b*(b*c-a*d)^2/(a^4*x^2)-_
b^2*(b*c-a*d)^2/(a^5*x)-b^3*(b*c-a*d)^2*log(x)/a^6+_
@@ -5992,9 +5992,9 @@ r0:=-1/5*c^2/(a*x^5)+1/4*c*(b*c-2*a*d)/(a^2*x^4)-_
--R 6 5
--R 60a x
--R Type: Expression(Integer)
---E 252
+--E 252
---S 253 of 1092
+--S 253 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6017,27 +6017,27 @@ a0:=integrate(t0,x)
--R 6 5
--R 60a x
--R Type: Union(Expression(Integer),...)
---E 253
+--E 253
---S 254 of 1092
+--S 254 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 254
+--E 254
---S 255 of 1092
+--S 255 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 255
+--E 255
)clear all
---S 256 of 1092
+--S 256 of 1092
t0:=x^m*(c+d*x)^3/(a+b*x)
--R
--R
@@ -6046,29 +6046,29 @@ t0:=x^m*(c+d*x)^3/(a+b*x)
--R (1) --------------------------------
--R b x + a
--R Type: Expression(Integer)
---E 256
+--E 256
---S 257 of 1092
+--S 257 of 1092
--r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^(1+m)/(b^3*(1+m))+_
-- d^2*(3*b*c-a*d)*x^(2+m)/(b^2*(2+m))+d^3*x^(3+m)/(b*(3+m))+_
-- (b*c-a*d)^3*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^3*(1+m))
---E 257
+--E 257
---S 258 of 1092
+--S 258 of 1092
--a0:=integrate(t0,x)
---E 258
+--E 258
---S 259 of 1092
+--S 259 of 1092
--m0:=a0-r0
---E 259
+--E 259
---S 260 of 1092
+--S 260 of 1092
--d0:=D(m0,x)
---E 260
+--E 260
)clear all
---S 261 of 1092
+--S 261 of 1092
t0:=x^4*(c+d*x)^3/(a+b*x)
--R
--R
@@ -6077,9 +6077,9 @@ t0:=x^4*(c+d*x)^3/(a+b*x)
--R (1) -------------------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 261
+--E 261
---S 262 of 1092
+--S 262 of 1092
r0:=-a^3*(b*c-a*d)^3*x/b^7+1/2*a^2*(b*c-a*d)^3*x^2/b^6-1/3*a*(b*c-a*d)^3*_
x^3/b^5+1/4*(b*c-a*d)^3*x^4/b^4+1/5*d*(3*b^2*c^2-_
3*a*b*c*d+a^2*d^2)*x^5/b^3+1/6*d^2*(3*b*c-a*d)*x^6/b^2+_
@@ -6111,9 +6111,9 @@ r0:=-a^3*(b*c-a*d)^3*x/b^7+1/2*a^2*(b*c-a*d)^3*x^2/b^6-1/3*a*(b*c-a*d)^3*_
--R 8
--R 420b
--R Type: Expression(Integer)
---E 262
+--E 262
---S 263 of 1092
+--S 263 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6142,27 +6142,27 @@ a0:=integrate(t0,x)
--R 8
--R 420b
--R Type: Union(Expression(Integer),...)
---E 263
+--E 263
---S 264 of 1092
+--S 264 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 264
+--E 264
---S 265 of 1092
+--S 265 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 265
+--E 265
)clear all
---S 266 of 1092
+--S 266 of 1092
t0:=x^3*(c+d*x)^3/(a+b*x)
--R
--R
@@ -6171,9 +6171,9 @@ t0:=x^3*(c+d*x)^3/(a+b*x)
--R (1) -------------------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 266
+--E 266
---S 267 of 1092
+--S 267 of 1092
r0:=a^2*(b*c-a*d)^3*x/b^6-1/2*a*(b*c-a*d)^3*x^2/b^5+1/3*(b*c-a*d)^3*x^3/b^4+_
1/4*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^4/b^3+_
1/5*d^2*(3*b*c-a*d)*x^5/b^2+1/6*d^3*x^6/b-a^3*(b*c-a*d)^3*log(a+b*x)/b^7
@@ -6198,9 +6198,9 @@ r0:=a^2*(b*c-a*d)^3*x/b^6-1/2*a*(b*c-a*d)^3*x^2/b^5+1/3*(b*c-a*d)^3*x^3/b^4+_
--R 7
--R 60b
--R Type: Expression(Integer)
---E 267
+--E 267
---S 268 of 1092
+--S 268 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6223,27 +6223,27 @@ a0:=integrate(t0,x)
--R 7
--R 60b
--R Type: Union(Expression(Integer),...)
---E 268
+--E 268
---S 269 of 1092
+--S 269 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 269
+--E 269
---S 270 of 1092
+--S 270 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 270
+--E 270
)clear all
---S 271 of 1092
+--S 271 of 1092
t0:=x^2*(c+d*x)^3/(a+b*x)
--R
--R
@@ -6252,9 +6252,9 @@ t0:=x^2*(c+d*x)^3/(a+b*x)
--R (1) -------------------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 271
+--E 271
---S 272 of 1092
+--S 272 of 1092
r0:=-a*(b*c-a*d)^3*x/b^5+1/2*(b*c-a*d)^3*x^2/b^4+_
1/3*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^3/b^3+_
1/4*d^2*(3*b*c-a*d)*x^4/b^2+1/5*d^3*x^5/b+a^2*(b*c-a*d)^3*log(a+b*x)/b^6
@@ -6276,9 +6276,9 @@ r0:=-a*(b*c-a*d)^3*x/b^5+1/2*(b*c-a*d)^3*x^2/b^4+_
--R 6
--R 60b
--R Type: Expression(Integer)
---E 272
+--E 272
---S 273 of 1092
+--S 273 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6298,27 +6298,27 @@ a0:=integrate(t0,x)
--R 6
--R 60b
--R Type: Union(Expression(Integer),...)
---E 273
+--E 273
---S 274 of 1092
+--S 274 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 274
+--E 274
---S 275 of 1092
+--S 275 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 275
+--E 275
)clear all
---S 276 of 1092
+--S 276 of 1092
t0:=x*(c+d*x)^3/(a+b*x)
--R
--R
@@ -6327,9 +6327,9 @@ t0:=x*(c+d*x)^3/(a+b*x)
--R (1) ------------------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 276
+--E 276
---S 277 of 1092
+--S 277 of 1092
r0:=(b*c-a*d)^3*x/b^4+1/2*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^2/b^3+_
1/3*d^2*(3*b*c-a*d)*x^3/b^2+1/4*d^3*x^4/b-a*(b*c-a*d)^3*log(a+b*x)/b^5
--R
@@ -6347,9 +6347,9 @@ r0:=(b*c-a*d)^3*x/b^4+1/2*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^2/b^3+_
--R 5
--R 12b
--R Type: Expression(Integer)
---E 277
+--E 277
---S 278 of 1092
+--S 278 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6366,27 +6366,27 @@ a0:=integrate(t0,x)
--R 5
--R 12b
--R Type: Union(Expression(Integer),...)
---E 278
+--E 278
---S 279 of 1092
+--S 279 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 279
+--E 279
---S 280 of 1092
+--S 280 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 280
+--E 280
)clear all
---S 281 of 1092
+--S 281 of 1092
t0:=(c+d*x)^3/(a+b*x)
--R
--R
@@ -6395,9 +6395,9 @@ t0:=(c+d*x)^3/(a+b*x)
--R (1) ----------------------------
--R b x + a
--R Type: Fraction(Polynomial(Integer))
---E 281
+--E 281
---S 282 of 1092
+--S 282 of 1092
r0:=d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+_
1/3*(c+d*x)^3/b+(b*c-a*d)^3*log(a+b*x)/b^4
--R
@@ -6415,9 +6415,9 @@ r0:=d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+_
--R 4
--R 6b
--R Type: Expression(Integer)
---E 282
+--E 282
---S 283 of 1092
+--S 283 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6431,9 +6431,9 @@ a0:=integrate(t0,x)
--R 4
--R 6b
--R Type: Union(Expression(Integer),...)
---E 283
+--E 283
---S 284 of 1092
+--S 284 of 1092
m0:=a0-r0
--R
--R
@@ -6443,19 +6443,19 @@ m0:=a0-r0
--R 2
--R 6b
--R Type: Expression(Integer)
---E 284
+--E 284
---S 285 of 1092
+--S 285 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 285
+--E 285
)clear all
---S 286 of 1092
+--S 286 of 1092
t0:=(c+d*x)^3/(x*(a+b*x))
--R
--R
@@ -6465,9 +6465,9 @@ t0:=(c+d*x)^3/(x*(a+b*x))
--R 2
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 286
+--E 286
---S 287 of 1092
+--S 287 of 1092
r0:=d^2*(3*b*c-a*d)*x/b^2+1/2*d^3*x^2/b+_
c^3*log(x)/a-(b*c-a*d)^3*log(a+b*x)/(a*b^3)
--R
@@ -6482,9 +6482,9 @@ r0:=d^2*(3*b*c-a*d)*x/b^2+1/2*d^3*x^2/b+_
--R 3
--R 2a b
--R Type: Expression(Integer)
---E 287
+--E 287
---S 288 of 1092
+--S 288 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6498,27 +6498,27 @@ a0:=integrate(t0,x)
--R 3
--R 2a b
--R Type: Union(Expression(Integer),...)
---E 288
+--E 288
---S 289 of 1092
+--S 289 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 289
+--E 289
---S 290 of 1092
+--S 290 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 290
+--E 290
)clear all
---S 291 of 1092
+--S 291 of 1092
t0:=(c+d*x)^3/(x^2*(a+b*x))
--R
--R
@@ -6528,9 +6528,9 @@ t0:=(c+d*x)^3/(x^2*(a+b*x))
--R 3 2
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 291
+--E 291
---S 292 of 1092
+--S 292 of 1092
r0:=-c^3/(a*x)+d^3*x/b-c^2*(b*c-3*a*d)*log(x)/a^2+_
(b*c-a*d)^3*log(a+b*x)/(a^2*b^2)
--R
@@ -6545,9 +6545,9 @@ r0:=-c^3/(a*x)+d^3*x/b-c^2*(b*c-3*a*d)*log(x)/a^2+_
--R 2 2
--R a b x
--R Type: Expression(Integer)
---E 292
+--E 292
---S 293 of 1092
+--S 293 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6561,27 +6561,27 @@ a0:=integrate(t0,x)
--R 2 2
--R a b x
--R Type: Union(Expression(Integer),...)
---E 293
+--E 293
---S 294 of 1092
+--S 294 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 294
+--E 294
---S 295 of 1092
+--S 295 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 295
+--E 295
)clear all
---S 296 of 1092
+--S 296 of 1092
t0:=(c+d*x)^3/(x^3*(a+b*x))
--R
--R
@@ -6591,9 +6591,9 @@ t0:=(c+d*x)^3/(x^3*(a+b*x))
--R 4 3
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 296
+--E 296
---S 297 of 1092
+--S 297 of 1092
r0:=-1/2*c^3/(a*x^2)+c^2*(b*c-3*a*d)/(a^2*x)+_
c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(x)/a^3-(b*c-a*d)^3*log(a+b*x)/(a^3*b)
--R
@@ -6608,9 +6608,9 @@ r0:=-1/2*c^3/(a*x^2)+c^2*(b*c-3*a*d)/(a^2*x)+_
--R 3 2
--R 2a b x
--R Type: Expression(Integer)
---E 297
+--E 297
---S 298 of 1092
+--S 298 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6624,27 +6624,27 @@ a0:=integrate(t0,x)
--R 3 2
--R 2a b x
--R Type: Union(Expression(Integer),...)
---E 298
+--E 298
---S 299 of 1092
+--S 299 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 299
+--E 299
---S 300 of 1092
+--S 300 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 300
+--E 300
)clear all
---S 301 of 1092
+--S 301 of 1092
t0:=(c+d*x)^3/(x^4*(a+b*x))
--R
--R
@@ -6654,9 +6654,9 @@ t0:=(c+d*x)^3/(x^4*(a+b*x))
--R 5 4
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 301
+--E 301
---S 302 of 1092
+--S 302 of 1092
r0:=-1/3*c^3/(a*x^3)+1/2*c^2*(b*c-3*a*d)/(a^2*x^2)-_
c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x)-_
(b*c-a*d)^3*log(x)/a^4+(b*c-a*d)^3*log(a+b*x)/a^4
@@ -6675,9 +6675,9 @@ r0:=-1/3*c^3/(a*x^3)+1/2*c^2*(b*c-3*a*d)/(a^2*x^2)-_
--R 4 3
--R 6a x
--R Type: Expression(Integer)
---E 302
+--E 302
---S 303 of 1092
+--S 303 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6694,27 +6694,27 @@ a0:=integrate(t0,x)
--R 4 3
--R 6a x
--R Type: Union(Expression(Integer),...)
---E 303
+--E 303
---S 304 of 1092
+--S 304 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 304
+--E 304
---S 305 of 1092
+--S 305 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 305
+--E 305
)clear all
---S 306 of 1092
+--S 306 of 1092
t0:=(c+d*x)^3/(x^5*(a+b*x))
--R
--R
@@ -6724,9 +6724,9 @@ t0:=(c+d*x)^3/(x^5*(a+b*x))
--R 6 5
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 306
+--E 306
---S 307 of 1092
+--S 307 of 1092
r0:=-1/4*c^3/(a*x^4)+1/3*c^2*(b*c-3*a*d)/(a^2*x^3)-_
1/2*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^2)+_
(b*c-a*d)^3/(a^4*x)+b*(b*c-a*d)^3*log(x)/a^5-b*(b*c-a*d)^3*log(a+b*x)/a^5
@@ -6748,9 +6748,9 @@ r0:=-1/4*c^3/(a*x^4)+1/3*c^2*(b*c-3*a*d)/(a^2*x^3)-_
--R 5 4
--R 12a x
--R Type: Expression(Integer)
---E 307
+--E 307
---S 308 of 1092
+--S 308 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6770,27 +6770,27 @@ a0:=integrate(t0,x)
--R 5 4
--R 12a x
--R Type: Union(Expression(Integer),...)
---E 308
+--E 308
---S 309 of 1092
+--S 309 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 309
+--E 309
---S 310 of 1092
+--S 310 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 310
+--E 310
)clear all
---S 311 of 1092
+--S 311 of 1092
t0:=(c+d*x)^3/(x^6*(a+b*x))
--R
--R
@@ -6800,9 +6800,9 @@ t0:=(c+d*x)^3/(x^6*(a+b*x))
--R 7 6
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 311
+--E 311
---S 312 of 1092
+--S 312 of 1092
r0:=-1/5*c^3/(a*x^5)+1/4*c^2*(b*c-3*a*d)/(a^2*x^4)-_
1/3*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^3)+_
1/2*(b*c-a*d)^3/(a^4*x^2)-b*(b*c-a*d)^3/(a^5*x)-_
@@ -6828,9 +6828,9 @@ r0:=-1/5*c^3/(a*x^5)+1/4*c^2*(b*c-3*a*d)/(a^2*x^4)-_
--R 6 5
--R 60a x
--R Type: Expression(Integer)
---E 312
+--E 312
---S 313 of 1092
+--S 313 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6853,27 +6853,27 @@ a0:=integrate(t0,x)
--R 6 5
--R 60a x
--R Type: Union(Expression(Integer),...)
---E 313
+--E 313
---S 314 of 1092
+--S 314 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 314
+--E 314
---S 315 of 1092
+--S 315 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 315
+--E 315
)clear all
---S 316 of 1092
+--S 316 of 1092
t0:=(c+d*x)^3/(x^7*(a+b*x))
--R
--R
@@ -6883,9 +6883,9 @@ t0:=(c+d*x)^3/(x^7*(a+b*x))
--R 8 7
--R b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 316
+--E 316
---S 317 of 1092
+--S 317 of 1092
r0:=-1/6*c^3/(a*x^6)+1/5*c^2*(b*c-3*a*d)/(a^2*x^5)-_
1/4*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^4)+_
1/3*(b*c-a*d)^3/(a^4*x^3)-1/2*b*(b*c-a*d)^3/(a^5*x^2)+_
@@ -6915,9 +6915,9 @@ r0:=-1/6*c^3/(a*x^6)+1/5*c^2*(b*c-3*a*d)/(a^2*x^5)-_
--R 7 6
--R 60a x
--R Type: Expression(Integer)
---E 317
+--E 317
---S 318 of 1092
+--S 318 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -6943,27 +6943,27 @@ a0:=integrate(t0,x)
--R 7 6
--R 60a x
--R Type: Union(Expression(Integer),...)
---E 318
+--E 318
---S 319 of 1092
+--S 319 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 319
+--E 319
---S 320 of 1092
+--S 320 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 320
+--E 320
)clear all
---S 321 of 1092
+--S 321 of 1092
t0:=x^m/((a+b*x)*(c+d*x))
--R
--R
@@ -6973,28 +6973,28 @@ t0:=x^m/((a+b*x)*(c+d*x))
--R 2
--R b d x + (a d + b c)x + a c
--R Type: Expression(Integer)
---E 321
+--E 321
---S 322 of 1092
+--S 322 of 1092
--r0:=b*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)*(1+m))-_
-- d*x^(1+m)*hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)*(1+m))
---E 322
+--E 322
---S 323 of 1092
+--S 323 of 1092
--a0:=integrate(t0,x)
---E 323
+--E 323
---S 324 of 1092
+--S 324 of 1092
--m0:=a0-r0
---E 324
+--E 324
---S 325 of 1092
+--S 325 of 1092
--d0:=D(m0,x)
---E 325
+--E 325
)clear all
---S 326 of 1092
+--S 326 of 1092
t0:=x^5/((a+b*x)*(c+d*x))
--R
--R
@@ -7004,9 +7004,9 @@ t0:=x^5/((a+b*x)*(c+d*x))
--R 2
--R b d x + (a d + b c)x + a c
--R Type: Fraction(Polynomial(Integer))
---E 326
+--E 326
---S 327 of 1092
+--S 327 of 1092
r0:=-(b*c+a*d)*(b^2*c^2+a^2*d^2)*x/(b^4*d^4)+_
1/2*(b^2*c^2+a*b*c*d+a^2*d^2)*x^2/(b^3*d^3)-_
1/3*(b*c+a*d)*x^3/(b^2*d^2)+1/4*x^4/(b*d)-_
@@ -7023,9 +7023,9 @@ r0:=-(b*c+a*d)*(b^2*c^2+a^2*d^2)*x/(b^4*d^4)+_
--R 5 6 6 5
--R 12a b d - 12b c d
--R Type: Expression(Integer)
---E 327
+--E 327
---S 328 of 1092
+--S 328 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7039,27 +7039,27 @@ a0:=integrate(t0,x)
--R 5 6 6 5
--R 12a b d - 12b c d
--R Type: Union(Expression(Integer),...)
---E 328
+--E 328
---S 329 of 1092
+--S 329 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 329
+--E 329
---S 330 of 1092
+--S 330 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 330
+--E 330
)clear all
---S 331 of 1092
+--S 331 of 1092
t0:=x^4/((a+b*x)*(c+d*x))
--R
--R
@@ -7069,9 +7069,9 @@ t0:=x^4/((a+b*x)*(c+d*x))
--R 2
--R b d x + (a d + b c)x + a c
--R Type: Fraction(Polynomial(Integer))
---E 331
+--E 331
---S 332 of 1092
+--S 332 of 1092
r0:=(b^2*c^2+a*b*c*d+a^2*d^2)*x/(b^3*d^3)-_
1/2*(b*c+a*d)*x^2/(b^2*d^2)+1/3*x^3/(b*d)+_
a^4*log(a+b*x)/(b^4*(b*c-a*d))-c^4*log(c+d*x)/(d^4*(b*c-a*d))
@@ -7087,9 +7087,9 @@ r0:=(b^2*c^2+a*b*c*d+a^2*d^2)*x/(b^3*d^3)-_
--R 4 5 5 4
--R 6a b d - 6b c d
--R Type: Expression(Integer)
---E 332
+--E 332
---S 333 of 1092
+--S 333 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7103,27 +7103,27 @@ a0:=integrate(t0,x)
--R 4 5 5 4
--R 6a b d - 6b c d
--R Type: Union(Expression(Integer),...)
---E 333
+--E 333
---S 334 of 1092
+--S 334 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 334
+--E 334
---S 335 of 1092
+--S 335 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 335
+--E 335
)clear all
---S 336 of 1092
+--S 336 of 1092
t0:=x^3/((a+b*x)*(c+d*x))
--R
--R
@@ -7133,9 +7133,9 @@ t0:=x^3/((a+b*x)*(c+d*x))
--R 2
--R b d x + (a d + b c)x + a c
--R Type: Fraction(Polynomial(Integer))
---E 336
+--E 336
---S 337 of 1092
+--S 337 of 1092
r0:=-(b*c+a*d)*x/(b^2*d^2)+1/2*x^2/(b*d)-a^3*log(a+b*x)/(b^3*(b*c-a*d))+_
c^3*log(c+d*x)/(d^3*(b*c-a*d))
--R
@@ -7150,9 +7150,9 @@ r0:=-(b*c+a*d)*x/(b^2*d^2)+1/2*x^2/(b*d)-a^3*log(a+b*x)/(b^3*(b*c-a*d))+_
--R 3 4 4 3
--R 2a b d - 2b c d
--R Type: Expression(Integer)
---E 337
+--E 337
---S 338 of 1092
+--S 338 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7166,27 +7166,27 @@ a0:=integrate(t0,x)
--R 3 4 4 3
--R 2a b d - 2b c d
--R Type: Union(Expression(Integer),...)
---E 338
+--E 338
---S 339 of 1092
+--S 339 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 339
+--E 339
---S 340 of 1092
+--S 340 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 340
+--E 340
)clear all
---S 341 of 1092
+--S 341 of 1092
t0:=x^2/((a+b*x)*(c+d*x))
--R
--R
@@ -7196,9 +7196,9 @@ t0:=x^2/((a+b*x)*(c+d*x))
--R 2
--R b d x + (a d + b c)x + a c
--R Type: Fraction(Polynomial(Integer))
---E 341
+--E 341
---S 342 of 1092
+--S 342 of 1092
r0:=x/(b*d)+a^2*log(a+b*x)/(b^2*(b*c-a*d))-c^2*log(c+d*x)/(d^2*(b*c-a*d))
--R
--R
@@ -7208,9 +7208,9 @@ r0:=x/(b*d)+a^2*log(a+b*x)/(b^2*(b*c-a*d))-c^2*log(c+d*x)/(d^2*(b*c-a*d))
--R 2 3 3 2
--R a b d - b c d
--R Type: Expression(Integer)
---E 342
+--E 342
---S 343 of 1092
+--S 343 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7220,27 +7220,27 @@ a0:=integrate(t0,x)
--R 2 3 3 2
--R a b d - b c d
--R Type: Union(Expression(Integer),...)
---E 343
+--E 343
---S 344 of 1092
+--S 344 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 344
+--E 344
---S 345 of 1092
+--S 345 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 345
+--E 345
)clear all
---S 346 of 1092
+--S 346 of 1092
t0:=x/((a+b*x)*(c+d*x))
--R
--R
@@ -7249,9 +7249,9 @@ t0:=x/((a+b*x)*(c+d*x))
--R 2
--R b d x + (a d + b c)x + a c
--R Type: Fraction(Polynomial(Integer))
---E 346
+--E 346
---S 347 of 1092
+--S 347 of 1092
r0:=-a*log(a+b*x)/(b*(b*c-a*d))+c*log(c+d*x)/(d*(b*c-a*d))
--R
--R
@@ -7260,9 +7260,9 @@ r0:=-a*log(a+b*x)/(b*(b*c-a*d))+c*log(c+d*x)/(d*(b*c-a*d))
--R 2 2
--R a b d - b c d
--R Type: Expression(Integer)
---E 347
+--E 347
---S 348 of 1092
+--S 348 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7271,27 +7271,27 @@ a0:=integrate(t0,x)
--R 2 2
--R a b d - b c d
--R Type: Union(Expression(Integer),...)
---E 348
+--E 348
---S 349 of 1092
+--S 349 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 349
+--E 349
---S 350 of 1092
+--S 350 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 350
+--E 350
)clear all
---S 351 of 1092
+--S 351 of 1092
t0:=1/((a+b*x)*(c+d*x))
--R
--R
@@ -7300,9 +7300,9 @@ t0:=1/((a+b*x)*(c+d*x))
--R 2
--R b d x + (a d + b c)x + a c
--R Type: Fraction(Polynomial(Integer))
---E 351
+--E 351
---S 352 of 1092
+--S 352 of 1092
r0:=log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d)
--R
--R
@@ -7310,9 +7310,9 @@ r0:=log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d)
--R (2) ---------------------------
--R a d - b c
--R Type: Expression(Integer)
---E 352
+--E 352
---S 353 of 1092
+--S 353 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7320,27 +7320,27 @@ a0:=integrate(t0,x)
--R (3) ---------------------------
--R a d - b c
--R Type: Union(Expression(Integer),...)
---E 353
+--E 353
---S 354 of 1092
+--S 354 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 354
+--E 354
---S 355 of 1092
+--S 355 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 355
+--E 355
)clear all
---S 356 of 1092
+--S 356 of 1092
t0:=1/(x*(a+b*x)*(c+d*x))
--R
--R
@@ -7349,9 +7349,9 @@ t0:=1/(x*(a+b*x)*(c+d*x))
--R 3 2
--R b d x + (a d + b c)x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 356
+--E 356
---S 357 of 1092
+--S 357 of 1092
r0:=log(x)/(a*c)-b*log(a+b*x)/(a*(b*c-a*d))+d*log(c+d*x)/(c*(b*c-a*d))
--R
--R
@@ -7360,9 +7360,9 @@ r0:=log(x)/(a*c)-b*log(a+b*x)/(a*(b*c-a*d))+d*log(c+d*x)/(c*(b*c-a*d))
--R 2 2
--R a c d - a b c
--R Type: Expression(Integer)
---E 357
+--E 357
---S 358 of 1092
+--S 358 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7371,27 +7371,27 @@ a0:=integrate(t0,x)
--R 2 2
--R a c d - a b c
--R Type: Union(Expression(Integer),...)
---E 358
+--E 358
---S 359 of 1092
+--S 359 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 359
+--E 359
---S 360 of 1092
+--S 360 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 360
+--E 360
)clear all
---S 361 of 1092
+--S 361 of 1092
t0:=1/(x^2*(a+b*x)*(c+d*x))
--R
--R
@@ -7400,9 +7400,9 @@ t0:=1/(x^2*(a+b*x)*(c+d*x))
--R 4 3 2
--R b d x + (a d + b c)x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 361
+--E 361
---S 362 of 1092
+--S 362 of 1092
r0:=(-1)/(a*c*x)-(b*c+a*d)*log(x)/(a^2*c^2)+_
b^2*log(a+b*x)/(a^2*(b*c-a*d))-d^2*log(c+d*x)/(c^2*(b*c-a*d))
--R
@@ -7417,9 +7417,9 @@ r0:=(-1)/(a*c*x)-(b*c+a*d)*log(x)/(a^2*c^2)+_
--R 3 2 2 3
--R (a c d - a b c )x
--R Type: Expression(Integer)
---E 362
+--E 362
---S 363 of 1092
+--S 363 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7433,27 +7433,27 @@ a0:=integrate(t0,x)
--R 3 2 2 3
--R (a c d - a b c )x
--R Type: Union(Expression(Integer),...)
---E 363
+--E 363
---S 364 of 1092
+--S 364 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 364
+--E 364
---S 365 of 1092
+--S 365 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 365
+--E 365
)clear all
---S 366 of 1092
+--S 366 of 1092
t0:=1/(x^3*(a+b*x)*(c+d*x))
--R
--R
@@ -7462,9 +7462,9 @@ t0:=1/(x^3*(a+b*x)*(c+d*x))
--R 5 4 3
--R b d x + (a d + b c)x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 366
+--E 366
---S 367 of 1092
+--S 367 of 1092
r0:=(-1/2)/(a*c*x^2)+(b*c+a*d)/(a^2*c^2*x)+(b^2*c^2+a*b*c*d+a^2*d^2)*_
log(x)/(a^3*c^3)-b^3*log(a+b*x)/(a^3*(b*c-a*d))+_
d^3*log(c+d*x)/(c^3*(b*c-a*d))
@@ -7480,9 +7480,9 @@ r0:=(-1/2)/(a*c*x^2)+(b*c+a*d)/(a^2*c^2*x)+(b^2*c^2+a*b*c*d+a^2*d^2)*_
--R 4 3 3 4 2
--R (2a c d - 2a b c )x
--R Type: Expression(Integer)
---E 367
+--E 367
---S 368 of 1092
+--S 368 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7496,27 +7496,27 @@ a0:=integrate(t0,x)
--R 4 3 3 4 2
--R (2a c d - 2a b c )x
--R Type: Union(Expression(Integer),...)
---E 368
+--E 368
---S 369 of 1092
+--S 369 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 369
+--E 369
---S 370 of 1092
+--S 370 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 370
+--E 370
)clear all
---S 371 of 1092
+--S 371 of 1092
t0:=1/(x^4*(a+b*x)*(c+d*x))
--R
--R
@@ -7525,9 +7525,9 @@ t0:=1/(x^4*(a+b*x)*(c+d*x))
--R 6 5 4
--R b d x + (a d + b c)x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 371
+--E 371
---S 372 of 1092
+--S 372 of 1092
r0:=(-1/3)/(a*c*x^3)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+_
(-b^2*c^2-a*b*c*d-a^2*d^2)/(a^3*c^3*x)-(b*c+a*d)*(b^2*c^2+a^2*d^2)*_
log(x)/(a^4*c^4)+b^4*log(a+b*x)/(a^4*(b*c-a*d))-_
@@ -7544,9 +7544,9 @@ r0:=(-1/3)/(a*c*x^3)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+_
--R 5 4 4 5 3
--R (6a c d - 6a b c )x
--R Type: Expression(Integer)
---E 372
+--E 372
---S 373 of 1092
+--S 373 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7560,27 +7560,27 @@ a0:=integrate(t0,x)
--R 5 4 4 5 3
--R (6a c d - 6a b c )x
--R Type: Union(Expression(Integer),...)
---E 373
+--E 373
---S 374 of 1092
+--S 374 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 374
+--E 374
---S 375 of 1092
+--S 375 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 375
+--E 375
)clear all
---S 376 of 1092
+--S 376 of 1092
t0:=x^m/((a+b*x)*(c+d*x)^2)
--R
--R
@@ -7590,30 +7590,30 @@ t0:=x^m/((a+b*x)*(c+d*x)^2)
--R 2 3 2 2 2 2
--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
--R Type: Expression(Integer)
---E 376
+--E 376
---S 377 of 1092
+--S 377 of 1092
--r0:=-d*x^(1+m)/(c*(b*c-a*d)*(c+d*x))+b^2*x^(1+m)*_
-- hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)^2*(1+m))-b*d*x^(1+m)*_
-- hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)^2*(1+m))+d*m*x^(1+m)*_
-- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)*(1+m))
---E 377
+--E 377
---S 378 of 1092
+--S 378 of 1092
--a0:=integrate(t0,x)
---E 378
+--E 378
---S 379 of 1092
+--S 379 of 1092
--m0:=a0-r0
---E 379
+--E 379
---S 380 of 1092
+--S 380 of 1092
--d0:=D(m0,x)
---E 380
+--E 380
)clear all
---S 381 of 1092
+--S 381 of 1092
t0:=x^m/((1-a*x)^2*(1+a*x))
--R
--R
@@ -7623,30 +7623,30 @@ t0:=x^m/((1-a*x)^2*(1+a*x))
--R 3 3 2 2
--R a x - a x - a x + 1
--R Type: Expression(Integer)
---E 381
+--E 381
---S 382 of 1092
+--S 382 of 1092
--r0:=1/2*x^(1+m)/(1-a*x)+1/4*x^(1+m)*_
-- hypergeometric(1,1+m,2+m,-a*x)/(1+m)+1/4*x^(1+m)*_
-- hypergeometric(1,1+m,2+m,a*x)/(1+m)-1/2*m*x^(1+m)*_
-- hypergeometric(1,1+m,2+m,a*x)/(1+m)
---E 382
+--E 382
---S 383 of 1092
+--S 383 of 1092
--a0:=integrate(t0,x)
---E 383
+--E 383
---S 384 of 1092
+--S 384 of 1092
--m0:=a0-r0
---E 384
+--E 384
---S 385 of 1092
+--S 385 of 1092
--d0:=D(m0,x)
---E 385
+--E 385
)clear all
---S 386 of 1092
+--S 386 of 1092
t0:=x^5/((a+b*x)*(c+d*x)^2)
--R
--R
@@ -7656,9 +7656,9 @@ t0:=x^5/((a+b*x)*(c+d*x)^2)
--R 2 3 2 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 386
+--E 386
---S 387 of 1092
+--S 387 of 1092
r0:=(3*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^3*d^4)-_
1/2*(2*b*c+a*d)*x^2/(b^2*d^3)+1/3*x^3/(b*d^2)-_
c^5/(d^5*(b*c-a*d)*(c+d*x))-a^5*log(a+b*x)/(b^4*(b*c-a*d)^2)-_
@@ -7684,9 +7684,9 @@ r0:=(3*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^3*d^4)-_
--R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5
--R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d
--R Type: Expression(Integer)
---E 387
+--E 387
---S 388 of 1092
+--S 388 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7709,27 +7709,27 @@ a0:=integrate(t0,x)
--R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5
--R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d
--R Type: Union(Expression(Integer),...)
---E 388
+--E 388
---S 389 of 1092
+--S 389 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 389
+--E 389
---S 390 of 1092
+--S 390 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 390
+--E 390
)clear all
---S 391 of 1092
+--S 391 of 1092
t0:=x^4/((a+b*x)*(c+d*x)^2)
--R
--R
@@ -7739,9 +7739,9 @@ t0:=x^4/((a+b*x)*(c+d*x)^2)
--R 2 3 2 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 391
+--E 391
---S 392 of 1092
+--S 392 of 1092
r0:=-(2*b*c+a*d)*x/(b^2*d^3)+1/2*x^2/(b*d^2)+_
c^4/(d^4*(b*c-a*d)*(c+d*x))+a^4*log(a+b*x)/(b^3*(b*c-a*d)^2)+_
c^3*(3*b*c-4*a*d)*log(c+d*x)/(d^4*(b*c-a*d)^2)
@@ -7763,9 +7763,9 @@ r0:=-(2*b*c+a*d)*x/(b^2*d^3)+1/2*x^2/(b*d^2)+_
--R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4
--R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d
--R Type: Expression(Integer)
---E 392
+--E 392
---S 393 of 1092
+--S 393 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7785,27 +7785,27 @@ a0:=integrate(t0,x)
--R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4
--R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d
--R Type: Union(Expression(Integer),...)
---E 393
+--E 393
---S 394 of 1092
+--S 394 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 394
+--E 394
---S 395 of 1092
+--S 395 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 395
+--E 395
)clear all
---S 396 of 1092
+--S 396 of 1092
t0:=x^3/((a+b*x)*(c+d*x)^2)
--R
--R
@@ -7815,9 +7815,9 @@ t0:=x^3/((a+b*x)*(c+d*x)^2)
--R 2 3 2 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 396
+--E 396
---S 397 of 1092
+--S 397 of 1092
r0:=x/(b*d^2)-c^3/(d^3*(b*c-a*d)*(c+d*x))-_
a^3*log(a+b*x)/(b^2*(b*c-a*d)^2)-c^2*(2*b*c-3*a*d)*log(c+d*x)/_
(d^3*(b*c-a*d)^2)
@@ -7836,9 +7836,9 @@ r0:=x/(b*d^2)-c^3/(d^3*(b*c-a*d)*(c+d*x))-_
--R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3
--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d
--R Type: Expression(Integer)
---E 397
+--E 397
---S 398 of 1092
+--S 398 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7855,27 +7855,27 @@ a0:=integrate(t0,x)
--R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3
--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d
--R Type: Union(Expression(Integer),...)
---E 398
+--E 398
---S 399 of 1092
+--S 399 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 399
+--E 399
---S 400 of 1092
+--S 400 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 400
+--E 400
)clear all
---S 401 of 1092
+--S 401 of 1092
t0:=x^2/((a+b*x)*(c+d*x)^2)
--R
--R
@@ -7885,9 +7885,9 @@ t0:=x^2/((a+b*x)*(c+d*x)^2)
--R 2 3 2 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 401
+--E 401
---S 402 of 1092
+--S 402 of 1092
r0:=c^2/(d^2*(b*c-a*d)*(c+d*x))+a^2*log(a+b*x)/(b*(b*c-a*d)^2)+_
c*(b*c-2*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^2)
--R
@@ -7902,9 +7902,9 @@ r0:=c^2/(d^2*(b*c-a*d)*(c+d*x))+a^2*log(a+b*x)/(b*(b*c-a*d)^2)+_
--R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2
--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d
--R Type: Expression(Integer)
---E 402
+--E 402
---S 403 of 1092
+--S 403 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7918,27 +7918,27 @@ a0:=integrate(t0,x)
--R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2
--R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d
--R Type: Union(Expression(Integer),...)
---E 403
+--E 403
---S 404 of 1092
+--S 404 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 404
+--E 404
---S 405 of 1092
+--S 405 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 405
+--E 405
)clear all
---S 406 of 1092
+--S 406 of 1092
t0:=x/((a+b*x)*(c+d*x)^2)
--R
--R
@@ -7947,9 +7947,9 @@ t0:=x/((a+b*x)*(c+d*x)^2)
--R 2 3 2 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 406
+--E 406
---S 407 of 1092
+--S 407 of 1092
r0:=-c/(d*(b*c-a*d)*(c+d*x))-a*log(a+b*x)/(b*c-a*d)^2+a*log(c+d*x)/(b*c-a*d)^2
--R
--R
@@ -7960,9 +7960,9 @@ r0:=-c/(d*(b*c-a*d)*(c+d*x))-a*log(a+b*x)/(b*c-a*d)^2+a*log(c+d*x)/(b*c-a*d)^2
--R 2 4 3 2 2 2 2 3 2 2 2 3
--R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d
--R Type: Expression(Integer)
---E 407
+--E 407
---S 408 of 1092
+--S 408 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -7973,27 +7973,27 @@ a0:=integrate(t0,x)
--R 2 4 3 2 2 2 2 3 2 2 2 3
--R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d
--R Type: Union(Expression(Integer),...)
---E 408
+--E 408
---S 409 of 1092
+--S 409 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 409
+--E 409
---S 410 of 1092
+--S 410 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 410
+--E 410
)clear all
---S 411 of 1092
+--S 411 of 1092
t0:=1/((a+b*x)*(c+d*x)^2)
--R
--R
@@ -8002,9 +8002,9 @@ t0:=1/((a+b*x)*(c+d*x)^2)
--R 2 3 2 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 411
+--E 411
---S 412 of 1092
+--S 412 of 1092
r0:=1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2
--R
--R
@@ -8013,9 +8013,9 @@ r0:=1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2
--R 2 3 2 2 2 2 2 2 2 3
--R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c
--R Type: Expression(Integer)
---E 412
+--E 412
---S 413 of 1092
+--S 413 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8024,27 +8024,27 @@ a0:=integrate(t0,x)
--R 2 3 2 2 2 2 2 2 2 3
--R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c
--R Type: Union(Expression(Integer),...)
---E 413
+--E 413
---S 414 of 1092
+--S 414 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 414
+--E 414
---S 415 of 1092
+--S 415 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 415
+--E 415
)clear all
---S 416 of 1092
+--S 416 of 1092
t0:=1/(x*(a+b*x)*(c+d*x)^2)
--R
--R
@@ -8053,9 +8053,9 @@ t0:=1/(x*(a+b*x)*(c+d*x)^2)
--R 2 4 2 3 2 2 2
--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 416
+--E 416
---S 417 of 1092
+--S 417 of 1092
r0:=-d/(c*(b*c-a*d)*(c+d*x))+log(x)/(a*c^2)-_
b^2*log(a+b*x)/(a*(b*c-a*d)^2)+d*(2*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^2)
--R
@@ -8076,9 +8076,9 @@ r0:=-d/(c*(b*c-a*d)*(c+d*x))+log(x)/(a*c^2)-_
--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5
--R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c
--R Type: Expression(Integer)
---E 417
+--E 417
---S 418 of 1092
+--S 418 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8098,27 +8098,27 @@ a0:=integrate(t0,x)
--R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5
--R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c
--R Type: Union(Expression(Integer),...)
---E 418
+--E 418
---S 419 of 1092
+--S 419 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 419
+--E 419
---S 420 of 1092
+--S 420 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 420
+--E 420
)clear all
---S 421 of 1092
+--S 421 of 1092
t0:=1/(x^2*(a+b*x)*(c+d*x)^2)
--R
--R
@@ -8127,9 +8127,9 @@ t0:=1/(x^2*(a+b*x)*(c+d*x)^2)
--R 2 5 2 4 2 3 2 2
--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 421
+--E 421
---S 422 of 1092
+--S 422 of 1092
r0:=(-1)/(a*c^2*x)+d^2/(c^2*(b*c-a*d)*(c+d*x))-_
(b*c+2*a*d)*log(x)/(a^2*c^3)+b^3*log(a+b*x)/(a^2*(b*c-a*d)^2)-_
d^2*(3*b*c-2*a*d)*log(c+d*x)/(c^3*(b*c-a*d)^2)
@@ -8151,9 +8151,9 @@ r0:=(-1)/(a*c^2*x)+d^2/(c^2*(b*c-a*d)*(c+d*x))-_
--R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6
--R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x
--R Type: Expression(Integer)
---E 422
+--E 422
---S 423 of 1092
+--S 423 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8173,27 +8173,27 @@ a0:=integrate(t0,x)
--R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6
--R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x
--R Type: Union(Expression(Integer),...)
---E 423
+--E 423
---S 424 of 1092
+--S 424 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 424
+--E 424
---S 425 of 1092
+--S 425 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 425
+--E 425
)clear all
---S 426 of 1092
+--S 426 of 1092
t0:=1/(x^3*(a+b*x)*(c+d*x)^2)
--R
--R
@@ -8202,9 +8202,9 @@ t0:=1/(x^3*(a+b*x)*(c+d*x)^2)
--R 2 6 2 5 2 4 2 3
--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 426
+--E 426
---S 427 of 1092
+--S 427 of 1092
r0:=(-1/2)/(a*c^2*x^2)+(b*c+2*a*d)/(a^2*c^3*x)-_
d^3/(c^3*(b*c-a*d)*(c+d*x))+(b^2*c^2+2*a*b*c*d+3*a^2*d^2)*log(x)/_
(a^3*c^4)-b^4*log(a+b*x)/(a^3*(b*c-a*d)^2)+d^3*(4*b*c-3*a*d)*_
@@ -8230,9 +8230,9 @@ r0:=(-1/2)/(a*c^2*x^2)+(b*c+2*a*d)/(a^2*c^3*x)-_
--R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2
--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x
--R Type: Expression(Integer)
---E 427
+--E 427
---S 428 of 1092
+--S 428 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8255,27 +8255,27 @@ a0:=integrate(t0,x)
--R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2
--R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x
--R Type: Union(Expression(Integer),...)
---E 428
+--E 428
---S 429 of 1092
+--S 429 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 429
+--E 429
---S 430 of 1092
+--S 430 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 430
+--E 430
)clear all
---S 431 of 1092
+--S 431 of 1092
t0:=x^m/((a+b*x)*(c+d*x)^3)
--R
--R
@@ -8286,9 +8286,9 @@ t0:=x^m/((a+b*x)*(c+d*x)^3)
--R 3 4 3 2 3 2 2 2 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 + a c
--R Type: Expression(Integer)
---E 431
+--E 431
---S 432 of 1092
+--S 432 of 1092
--r0:=-1/2*d*x^(1+m)/(c*(b*c-a*d)*(c+d*x)^2)-_
-- b*d*x^(1+m)/(c*(b*c-a*d)^2*(c+d*x))-_
-- 1/2*d*(1-m)*x^(1+m)/(c^2*(b*c-a*d)*(c+d*x))+_
@@ -8298,23 +8298,23 @@ t0:=x^m/((a+b*x)*(c+d*x)^3)
-- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)^2*(1+m))+_
-- 1/2*d*(1-m)*m*x^(1+m)*_
-- hypergeometric(1,1+m,2+m,-d*x/c)/(c^3*(b*c-a*d)*(1+m))
---E 432
+--E 432
---S 433 of 1092
+--S 433 of 1092
--a0:=integrate(t0,x)
---E 433
+--E 433
---S 434 of 1092
+--S 434 of 1092
--m0:=a0-r0
---E 434
+--E 434
---S 435 of 1092
+--S 435 of 1092
--d0:=D(m0,x)
---E 435
+--E 435
)clear all
---S 436 of 1092
+--S 436 of 1092
t0:=x^6/((a+b*x)*(c+d*x)^3)
--R
--R
@@ -8325,9 +8325,9 @@ t0:=x^6/((a+b*x)*(c+d*x)^3)
--R 3 4 3 2 3 2 2 2 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 + a c
--R Type: Fraction(Polynomial(Integer))
---E 436
+--E 436
---S 437 of 1092
+--S 437 of 1092
r0:=(6*b^2*c^2+3*a*b*c*d+a^2*d^2)*x/(b^3*d^5)-_
1/2*(3*b*c+a*d)*x^2/(b^2*d^4)+1/3*x^3/(b*d^3)+_
1/2*c^6/(d^6*(b*c-a*d)*(c+d*x)^2)-_
@@ -8378,9 +8378,9 @@ r0:=(6*b^2*c^2+3*a*b*c*d+a^2*d^2)*x/(b^3*d^5)-_
--R 2 5 3 8 6 4 7 7 5 6
--R - 18a b c d + 18a b c d - 6b c d
--R Type: Expression(Integer)
---E 437
+--E 437
---S 438 of 1092
+--S 438 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8426,27 +8426,27 @@ a0:=integrate(t0,x)
--R 2 5 3 8 6 4 7 7 5 6
--R - 18a b c d + 18a b c d - 6b c d
--R Type: Union(Expression(Integer),...)
---E 438
+--E 438
---S 439 of 1092
+--S 439 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 439
+--E 439
---S 440 of 1092
+--S 440 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 440
+--E 440
)clear all
---S 441 of 1092
+--S 441 of 1092
t0:=x^5/((a+b*x)*(c+d*x)^3)
--R
--R
@@ -8457,9 +8457,9 @@ t0:=x^5/((a+b*x)*(c+d*x)^3)
--R 3 4 3 2 3 2 2 2 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 + a c
--R Type: Fraction(Polynomial(Integer))
---E 441
+--E 441
---S 442 of 1092
+--S 442 of 1092
r0:=-(3*b*c+a*d)*x/(b^2*d^4)+1/2*x^2/(b*d^3)-_
1/2*c^5/(d^5*(b*c-a*d)*(c+d*x)^2)+c^4*(4*b*c-5*a*d)/_
(d^5*(b*c-a*d)^2*(c+d*x))-a^5*log(a+b*x)/(b^3*(b*c-a*d)^3)+_
@@ -8505,9 +8505,9 @@ r0:=-(3*b*c+a*d)*x/(b^2*d^4)+1/2*x^2/(b*d^3)-_
--R 5 4 6 6 5 5
--R 6a b c d - 2b c d
--R Type: Expression(Integer)
---E 442
+--E 442
---S 443 of 1092
+--S 443 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8550,27 +8550,27 @@ a0:=integrate(t0,x)
--R 5 4 6 6 5 5
--R 6a b c d - 2b c d
--R Type: Union(Expression(Integer),...)
---E 443
+--E 443
---S 444 of 1092
+--S 444 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 444
+--E 444
---S 445 of 1092
+--S 445 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 445
+--E 445
)clear all
---S 446 of 1092
+--S 446 of 1092
t0:=x^4/((a+b*x)*(c+d*x)^3)
--R
--R
@@ -8581,9 +8581,9 @@ t0:=x^4/((a+b*x)*(c+d*x)^3)
--R 3 4 3 2 3 2 2 2 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 + a c
--R Type: Fraction(Polynomial(Integer))
---E 446
+--E 446
---S 447 of 1092
+--S 447 of 1092
r0:=x/(b*d^3)+1/2*c^4/(d^4*(b*c-a*d)*(c+d*x)^2)-_
c^3*(3*b*c-4*a*d)/(d^4*(b*c-a*d)^2*(c+d*x))+_
a^4*log(a+b*x)/(b^2*(b*c-a*d)^3)-_
@@ -8623,9 +8623,9 @@ r0:=x/(b*d^3)+1/2*c^4/(d^4*(b*c-a*d)*(c+d*x)^2)-_
--R 4 4 5 5 5 4
--R 6a b c d - 2b c d
--R Type: Expression(Integer)
---E 447
+--E 447
---S 448 of 1092
+--S 448 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8662,27 +8662,27 @@ a0:=integrate(t0,x)
--R 4 4 5 5 5 4
--R 6a b c d - 2b c d
--R Type: Union(Expression(Integer),...)
---E 448
+--E 448
---S 449 of 1092
+--S 449 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 449
+--E 449
---S 450 of 1092
+--S 450 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 450
+--E 450
)clear all
---S 451 of 1092
+--S 451 of 1092
t0:=x^3/((a+b*x)*(c+d*x)^3)
--R
--R
@@ -8693,9 +8693,9 @@ t0:=x^3/((a+b*x)*(c+d*x)^3)
--R 3 4 3 2 3 2 2 2 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 + a c
--R Type: Fraction(Polynomial(Integer))
---E 451
+--E 451
---S 452 of 1092
+--S 452 of 1092
r0:=-1/2*c^3/(d^3*(b*c-a*d)*(c+d*x)^2)+c^2*(2*b*c-3*a*d)/_
(d^3*(b*c-a*d)^2*(c+d*x))-a^3*log(a+b*x)/(b*(b*c-a*d)^3)+_
c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(d^3*(b*c-a*d)^3)
@@ -8725,9 +8725,9 @@ r0:=-1/2*c^3/(d^3*(b*c-a*d)*(c+d*x)^2)+c^2*(2*b*c-3*a*d)/_
--R 3 4 4 4 5 3
--R 6a b c d - 2b c d
--R Type: Expression(Integer)
---E 452
+--E 452
---S 453 of 1092
+--S 453 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8755,27 +8755,27 @@ a0:=integrate(t0,x)
--R 3 4 4 4 5 3
--R 6a b c d - 2b c d
--R Type: Union(Expression(Integer),...)
---E 453
+--E 453
---S 454 of 1092
+--S 454 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 454
+--E 454
---S 455 of 1092
+--S 455 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 455
+--E 455
)clear all
---S 456 of 1092
+--S 456 of 1092
t0:=x^2/((a+b*x)*(c+d*x)^3)
--R
--R
@@ -8786,9 +8786,9 @@ t0:=x^2/((a+b*x)*(c+d*x)^3)
--R 3 4 3 2 3 2 2 2 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 + a c
--R Type: Fraction(Polynomial(Integer))
---E 456
+--E 456
---S 457 of 1092
+--S 457 of 1092
r0:=1/2*c^2/(d^2*(b*c-a*d)*(c+d*x)^2)-c*(b*c-2*a*d)/_
(d^2*(b*c-a*d)^2*(c+d*x))+a^2*log(a+b*x)/(b*c-a*d)^3-_
a^2*log(c+d*x)/(b*c-a*d)^3
@@ -8813,9 +8813,9 @@ r0:=1/2*c^2/(d^2*(b*c-a*d)*(c+d*x)^2)-c*(b*c-2*a*d)/_
--R 2 4 3 3 5 2
--R 6a b c d - 2b c d
--R Type: Expression(Integer)
---E 457
+--E 457
---S 458 of 1092
+--S 458 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8838,27 +8838,27 @@ a0:=integrate(t0,x)
--R 2 4 3 3 5 2
--R 6a b c d - 2b c d
--R Type: Union(Expression(Integer),...)
---E 458
+--E 458
---S 459 of 1092
+--S 459 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 459
+--E 459
---S 460 of 1092
+--S 460 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 460
+--E 460
)clear all
---S 461 of 1092
+--S 461 of 1092
t0:=x/((a+b*x)*(c+d*x)^3)
--R
--R
@@ -8868,9 +8868,9 @@ t0:=x/((a+b*x)*(c+d*x)^3)
--R 3 4 3 2 3 2 2 2 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 + a c
--R Type: Fraction(Polynomial(Integer))
---E 461
+--E 461
---S 462 of 1092
+--S 462 of 1092
r0:=-1/2*c/(d*(b*c-a*d)*(c+d*x)^2)-a/((b*c-a*d)^2*(c+d*x))-_
a*b*log(a+b*x)/(b*c-a*d)^3+a*b*log(c+d*x)/(b*c-a*d)^3
--R
@@ -8894,9 +8894,9 @@ r0:=-1/2*c/(d*(b*c-a*d)*(c+d*x)^2)-a/((b*c-a*d)^2*(c+d*x))-_
--R 2 4 2 3 5
--R 6a b c d - 2b c d
--R Type: Expression(Integer)
---E 462
+--E 462
---S 463 of 1092
+--S 463 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -8919,27 +8919,27 @@ a0:=integrate(t0,x)
--R 2 4 2 3 5
--R 6a b c d - 2b c d
--R Type: Union(Expression(Integer),...)
---E 463
+--E 463
---S 464 of 1092
+--S 464 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 464
+--E 464
---S 465 of 1092
+--S 465 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 465
+--E 465
)clear all
---S 466 of 1092
+--S 466 of 1092
t0:=1/((a+b*x)*(c+d*x)^3)
--R
--R
@@ -8949,9 +8949,9 @@ t0:=1/((a+b*x)*(c+d*x)^3)
--R 3 4 3 2 3 2 2 2 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 + a c
--R Type: Fraction(Polynomial(Integer))
---E 466
+--E 466
---S 467 of 1092
+--S 467 of 1092
r0:=1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+_
b^2*log(a+b*x)/(b*c-a*d)^3-b^2*log(c+d*x)/(b*c-a*d)^3
--R
@@ -8975,9 +8975,9 @@ r0:=1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+_
--R 2 4 3 5
--R 6a b c d - 2b c
--R Type: Expression(Integer)
---E 467
+--E 467
---S 468 of 1092
+--S 468 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9000,27 +9000,27 @@ a0:=integrate(t0,x)
--R 2 4 3 5
--R 6a b c d - 2b c
--R Type: Union(Expression(Integer),...)
---E 468
+--E 468
---S 469 of 1092
+--S 469 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 469
+--E 469
---S 470 of 1092
+--S 470 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 470
+--E 470
)clear all
---S 471 of 1092
+--S 471 of 1092
t0:=1/(x*(a+b*x)*(c+d*x)^3)
--R
--R
@@ -9033,9 +9033,9 @@ t0:=1/(x*(a+b*x)*(c+d*x)^3)
--R 3
--R a c x
--R Type: Fraction(Polynomial(Integer))
---E 471
+--E 471
---S 472 of 1092
+--S 472 of 1092
r0:=-1/2*d/(c*(b*c-a*d)*(c+d*x)^2)-d*(2*b*c-a*d)/_
(c^2*(b*c-a*d)^2*(c+d*x))+log(x)/(a*c^3)-_
b^3*log(a+b*x)/(a*(b*c-a*d)^3)+d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*_
@@ -9077,9 +9077,9 @@ r0:=-1/2*d/(c*(b*c-a*d)*(c+d*x)^2)-d*(2*b*c-a*d)/_
--R 2 2 7 3 8
--R 6a b c d - 2a b c
--R Type: Expression(Integer)
---E 472
+--E 472
---S 473 of 1092
+--S 473 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9118,27 +9118,27 @@ a0:=integrate(t0,x)
--R 2 2 7 3 8
--R 6a b c d - 2a b c
--R Type: Union(Expression(Integer),...)
---E 473
+--E 473
---S 474 of 1092
+--S 474 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 474
+--E 474
---S 475 of 1092
+--S 475 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 475
+--E 475
)clear all
---S 476 of 1092
+--S 476 of 1092
t0:=1/(x^2*(a+b*x)*(c+d*x)^3)
--R
--R
@@ -9151,9 +9151,9 @@ t0:=1/(x^2*(a+b*x)*(c+d*x)^3)
--R 3 2
--R a c x
--R Type: Fraction(Polynomial(Integer))
---E 476
+--E 476
---S 477 of 1092
+--S 477 of 1092
r0:=(-1)/(a*c^3*x)+1/2*d^2/(c^2*(b*c-a*d)*(c+d*x)^2)+_
d^2*(3*b*c-2*a*d)/(c^3*(b*c-a*d)^2*(c+d*x))-(b*c+3*a*d)*_
log(x)/(a^2*c^4)+b^4*log(a+b*x)/(a^2*(b*c-a*d)^3)-_
@@ -9204,9 +9204,9 @@ r0:=(-1)/(a*c^3*x)+1/2*d^2/(c^2*(b*c-a*d)*(c+d*x)^2)+_
--R 5 6 3 4 7 2 3 2 8 2 3 9
--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
--R Type: Expression(Integer)
---E 477
+--E 477
---S 478 of 1092
+--S 478 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9254,27 +9254,27 @@ a0:=integrate(t0,x)
--R 5 6 3 4 7 2 3 2 8 2 3 9
--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
--R Type: Union(Expression(Integer),...)
---E 478
+--E 478
---S 479 of 1092
+--S 479 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 479
+--E 479
---S 480 of 1092
+--S 480 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 480
+--E 480
)clear all
---S 481 of 1092
+--S 481 of 1092
t0:=1/(x^3*(a+b*x)*(c+d*x)^3)
--R
--R
@@ -9287,9 +9287,9 @@ t0:=1/(x^3*(a+b*x)*(c+d*x)^3)
--R 3 3
--R a c x
--R Type: Fraction(Polynomial(Integer))
---E 481
+--E 481
---S 482 of 1092
+--S 482 of 1092
r0:=(-1/2)/(a*c^3*x^2)+(b*c+3*a*d)/(a^2*c^4*x)-1/2*d^3/(c^3*(b*c-a*d)*_
(c+d*x)^2)-d^3*(4*b*c-3*a*d)/(c^4*(b*c-a*d)^2*(c+d*x))+_
(b^2*c^2+3*a*b*c*d+6*a^2*d^2)*log(x)/(a^3*c^5)-b^5*_
@@ -9344,9 +9344,9 @@ r0:=(-1/2)/(a*c^3*x^2)+(b*c+3*a*d)/(a^2*c^4*x)-1/2*d^3/(c^3*(b*c-a*d)*_
--R 6 7 3 5 8 2 4 2 9 3 3 10 2
--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
--R Type: Expression(Integer)
---E 482
+--E 482
---S 483 of 1092
+--S 483 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9397,27 +9397,27 @@ a0:=integrate(t0,x)
--R 6 7 3 5 8 2 4 2 9 3 3 10 2
--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
--R Type: Union(Expression(Integer),...)
---E 483
+--E 483
---S 484 of 1092
+--S 484 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 484
+--E 484
---S 485 of 1092
+--S 485 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 485
+--E 485
)clear all
---S 486 of 1092
+--S 486 of 1092
t0:=x^4*(c+d*x)^2/(a+b*x)^2
--R
--R
@@ -9427,9 +9427,9 @@ t0:=x^4*(c+d*x)^2/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 486
+--E 486
---S 487 of 1092
+--S 487 of 1092
r0:=a^2*(3*b*c-5*a*d)*(b*c-a*d)*x/b^6-a*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+_
1/3*(b*c-3*a*d)*(b*c-a*d)*x^3/b^4+1/2*d*(b*c-a*d)*x^4/b^3+_
1/5*d^2*x^5/b^2-a^4*(b*c-a*d)^2/(b^7*(a+b*x))-_
@@ -9460,9 +9460,9 @@ r0:=a^2*(3*b*c-5*a*d)*(b*c-a*d)*x/b^6-a*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+_
--R 8 7
--R 30b x + 30a b
--R Type: Expression(Integer)
---E 487
+--E 487
---S 488 of 1092
+--S 488 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9490,27 +9490,27 @@ a0:=integrate(t0,x)
--R 8 7
--R 30b x + 30a b
--R Type: Union(Expression(Integer),...)
---E 488
+--E 488
---S 489 of 1092
+--S 489 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 489
+--E 489
---S 490 of 1092
+--S 490 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 490
+--E 490
)clear all
---S 491 of 1092
+--S 491 of 1092
t0:=x^3*(c+d*x)^2/(a+b*x)^2
--R
--R
@@ -9520,9 +9520,9 @@ t0:=x^3*(c+d*x)^2/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 491
+--E 491
---S 492 of 1092
+--S 492 of 1092
r0:=-2*a*(b*c-2*a*d)*(b*c-a*d)*x/b^5+1/2*(b*c-3*a*d)*(b*c-a*d)*x^2/b^4+_
2/3*d*(b*c-a*d)*x^3/b^3+1/4*d^2*x^4/b^2+_
a^3*(b*c-a*d)^2/(b^6*(a+b*x))+a^2*(3*b*c-5*a*d)*(b*c-a*d)*log(a+b*x)/b^6
@@ -9546,9 +9546,9 @@ r0:=-2*a*(b*c-2*a*d)*(b*c-a*d)*x/b^5+1/2*(b*c-3*a*d)*(b*c-a*d)*x^2/b^4+_
--R 7 6
--R 12b x + 12a b
--R Type: Expression(Integer)
---E 492
+--E 492
---S 493 of 1092
+--S 493 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9570,27 +9570,27 @@ a0:=integrate(t0,x)
--R 7 6
--R 12b x + 12a b
--R Type: Union(Expression(Integer),...)
---E 493
+--E 493
---S 494 of 1092
+--S 494 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 494
+--E 494
---S 495 of 1092
+--S 495 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 495
+--E 495
)clear all
---S 496 of 1092
+--S 496 of 1092
t0:=x^2*(c+d*x)^2/(a+b*x)^2
--R
--R
@@ -9600,9 +9600,9 @@ t0:=x^2*(c+d*x)^2/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 496
+--E 496
---S 497 of 1092
+--S 497 of 1092
r0:=(b*c-3*a*d)*(b*c-a*d)*x/b^4+d*(b*c-a*d)*x^2/b^3+1/3*d^2*x^3/b^2-_
a^2*(b*c-a*d)^2/(b^5*(a+b*x))-2*a*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5
--R
@@ -9622,9 +9622,9 @@ r0:=(b*c-3*a*d)*(b*c-a*d)*x/b^4+d*(b*c-a*d)*x^2/b^3+1/3*d^2*x^3/b^2-_
--R 6 5
--R 3b x + 3a b
--R Type: Expression(Integer)
---E 497
+--E 497
---S 498 of 1092
+--S 498 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9643,27 +9643,27 @@ a0:=integrate(t0,x)
--R 6 5
--R 3b x + 3a b
--R Type: Union(Expression(Integer),...)
---E 498
+--E 498
---S 499 of 1092
+--S 499 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 499
+--E 499
---S 500 of 1092
+--S 500 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 500
+--E 500
)clear all
---S 501 of 1092
+--S 501 of 1092
t0:=x*(c+d*x)^2/(a+b*x)^2
--R
--R
@@ -9673,9 +9673,9 @@ t0:=x*(c+d*x)^2/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 501
+--E 501
---S 502 of 1092
+--S 502 of 1092
r0:=2*d*(b*c-a*d)*x/b^3+1/2*d^2*x^2/b^2+a*(b*c-a*d)^2/(b^4*(a+b*x))+_
(b*c-3*a*d)*(b*c-a*d)*log(a+b*x)/b^4
--R
@@ -9693,9 +9693,9 @@ r0:=2*d*(b*c-a*d)*x/b^3+1/2*d^2*x^2/b^2+a*(b*c-a*d)^2/(b^4*(a+b*x))+_
--R 5 4
--R 2b x + 2a b
--R Type: Expression(Integer)
---E 502
+--E 502
---S 503 of 1092
+--S 503 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9712,27 +9712,27 @@ a0:=integrate(t0,x)
--R 5 4
--R 2b x + 2a b
--R Type: Union(Expression(Integer),...)
---E 503
+--E 503
---S 504 of 1092
+--S 504 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 504
+--E 504
---S 505 of 1092
+--S 505 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 505
+--E 505
)clear all
---S 506 of 1092
+--S 506 of 1092
t0:=(c+d*x)^2/(a+b*x)^2
--R
--R
@@ -9742,9 +9742,9 @@ t0:=(c+d*x)^2/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 506
+--E 506
---S 507 of 1092
+--S 507 of 1092
r0:=d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3
--R
--R
@@ -9758,9 +9758,9 @@ r0:=d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3
--R 4 3
--R b x + a b
--R Type: Expression(Integer)
---E 507
+--E 507
---S 508 of 1092
+--S 508 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9774,27 +9774,27 @@ a0:=integrate(t0,x)
--R 4 3
--R b x + a b
--R Type: Union(Expression(Integer),...)
---E 508
+--E 508
---S 509 of 1092
+--S 509 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 509
+--E 509
---S 510 of 1092
+--S 510 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 510
+--E 510
)clear all
---S 511 of 1092
+--S 511 of 1092
t0:=(c+d*x)^2/(x*(a+b*x)^2)
--R
--R
@@ -9804,9 +9804,9 @@ t0:=(c+d*x)^2/(x*(a+b*x)^2)
--R 2 3 2 2
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 511
+--E 511
---S 512 of 1092
+--S 512 of 1092
r0:=(b*c-a*d)^2/(a*b^2*(a+b*x))+c^2*log(x)/a^2-(c^2/a^2-d^2/b^2)*log(a+b*x)
--R
--R
@@ -9820,9 +9820,9 @@ r0:=(b*c-a*d)^2/(a*b^2*(a+b*x))+c^2*log(x)/a^2-(c^2/a^2-d^2/b^2)*log(a+b*x)
--R 2 3 3 2
--R a b x + a b
--R Type: Expression(Integer)
---E 512
+--E 512
---S 513 of 1092
+--S 513 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9836,27 +9836,27 @@ a0:=integrate(t0,x)
--R 2 3 3 2
--R a b x + a b
--R Type: Union(Expression(Integer),...)
---E 513
+--E 513
---S 514 of 1092
+--S 514 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 514
+--E 514
---S 515 of 1092
+--S 515 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 515
+--E 515
)clear all
---S 516 of 1092
+--S 516 of 1092
t0:=(c+d*x)^2/(x^2*(a+b*x)^2)
--R
--R
@@ -9866,9 +9866,9 @@ t0:=(c+d*x)^2/(x^2*(a+b*x)^2)
--R 2 4 3 2 2
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 516
+--E 516
---S 517 of 1092
+--S 517 of 1092
r0:=-c^2/(a^2*x)-(b*c-a*d)^2/(a^2*b*(a+b*x))-2*c*(b*c-a*d)*_
log(x)/a^3+2*c*(b*c-a*d)*log(a+b*x)/a^3
--R
@@ -9886,9 +9886,9 @@ r0:=-c^2/(a^2*x)-(b*c-a*d)^2/(a^2*b*(a+b*x))-2*c*(b*c-a*d)*_
--R 3 2 2 4
--R a b x + a b x
--R Type: Expression(Integer)
---E 517
+--E 517
---S 518 of 1092
+--S 518 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9905,27 +9905,27 @@ a0:=integrate(t0,x)
--R 3 2 2 4
--R a b x + a b x
--R Type: Union(Expression(Integer),...)
---E 518
+--E 518
---S 519 of 1092
+--S 519 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 519
+--E 519
---S 520 of 1092
+--S 520 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 520
+--E 520
)clear all
---S 521 of 1092
+--S 521 of 1092
t0:=(c+d*x)^2/(x^3*(a+b*x)^2)
--R
--R
@@ -9935,9 +9935,9 @@ t0:=(c+d*x)^2/(x^3*(a+b*x)^2)
--R 2 5 4 2 3
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 521
+--E 521
---S 522 of 1092
+--S 522 of 1092
r0:=-1/2*c^2/(a^2*x^2)+2*c*(b*c-a*d)/(a^3*x)+(b*c-a*d)^2/(a^3*(a+b*x))+_
(b*c-a*d)*(3*b*c-a*d)*log(x)/a^4-(b*c-a*d)*(3*b*c-a*d)*log(a+b*x)/a^4
--R
@@ -9957,9 +9957,9 @@ r0:=-1/2*c^2/(a^2*x^2)+2*c*(b*c-a*d)/(a^3*x)+(b*c-a*d)^2/(a^3*(a+b*x))+_
--R 4 3 5 2
--R 2a b x + 2a x
--R Type: Expression(Integer)
---E 522
+--E 522
---S 523 of 1092
+--S 523 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -9978,27 +9978,27 @@ a0:=integrate(t0,x)
--R 4 3 5 2
--R 2a b x + 2a x
--R Type: Union(Expression(Integer),...)
---E 523
+--E 523
---S 524 of 1092
+--S 524 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 524
+--E 524
---S 525 of 1092
+--S 525 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 525
+--E 525
)clear all
---S 526 of 1092
+--S 526 of 1092
t0:=(c+d*x)^2/(x^4*(a+b*x)^2)
--R
--R
@@ -10008,9 +10008,9 @@ t0:=(c+d*x)^2/(x^4*(a+b*x)^2)
--R 2 6 5 2 4
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 526
+--E 526
---S 527 of 1092
+--S 527 of 1092
r0:=-1/3*c^2/(a^2*x^3)+c*(b*c-a*d)/(a^3*x^2)-(b*c-a*d)*(3*b*c-a*d)/_
(a^4*x)-b*(b*c-a*d)^2/(a^4*(a+b*x))-2*b*(b*c-a*d)*(2*b*c-a*d)*_
log(x)/a^5+2*b*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5
@@ -10039,9 +10039,9 @@ r0:=-1/3*c^2/(a^2*x^3)+c*(b*c-a*d)/(a^3*x^2)-(b*c-a*d)*(3*b*c-a*d)/_
--R 5 4 6 3
--R 3a b x + 3a x
--R Type: Expression(Integer)
---E 527
+--E 527
---S 528 of 1092
+--S 528 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10068,27 +10068,27 @@ a0:=integrate(t0,x)
--R 5 4 6 3
--R 3a b x + 3a x
--R Type: Union(Expression(Integer),...)
---E 528
+--E 528
---S 529 of 1092
+--S 529 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 529
+--E 529
---S 530 of 1092
+--S 530 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 530
+--E 530
)clear all
---S 531 of 1092
+--S 531 of 1092
t0:=(c+d*x)^2/(x^5*(a+b*x)^2)
--R
--R
@@ -10098,9 +10098,9 @@ t0:=(c+d*x)^2/(x^5*(a+b*x)^2)
--R 2 7 6 2 5
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 531
+--E 531
---S 532 of 1092
+--S 532 of 1092
r0:=-1/4*c^2/(a^2*x^4)+2/3*c*(b*c-a*d)/(a^3*x^3)-1/2*(b*c-a*d)*_
(3*b*c-a*d)/(a^4*x^2)+2*b*(b*c-a*d)*(2*b*c-a*d)/(a^5*x)+_
b^2*(b*c-a*d)^2/(a^5*(a+b*x))+b^2*(5*b*c-3*a*d)*(b*c-a*d)*_
@@ -10133,9 +10133,9 @@ r0:=-1/4*c^2/(a^2*x^4)+2/3*c*(b*c-a*d)/(a^3*x^3)-1/2*(b*c-a*d)*_
--R 6 5 7 4
--R 12a b x + 12a x
--R Type: Expression(Integer)
---E 532
+--E 532
---S 533 of 1092
+--S 533 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10165,27 +10165,27 @@ a0:=integrate(t0,x)
--R 6 5 7 4
--R 12a b x + 12a x
--R Type: Union(Expression(Integer),...)
---E 533
+--E 533
---S 534 of 1092
+--S 534 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 534
+--E 534
---S 535 of 1092
+--S 535 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 535
+--E 535
)clear all
---S 536 of 1092
+--S 536 of 1092
t0:=x^4*(c+d*x)^3/(a+b*x)^2
--R
--R
@@ -10195,9 +10195,9 @@ t0:=x^4*(c+d*x)^3/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 536
+--E 536
---S 537 of 1092
+--S 537 of 1092
r0:=3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*x/b^7-1/2*a*(2*b*c-5*a*d)*_
(b*c-a*d)^2*x^2/b^6+1/3*(b*c-4*a*d)*(b*c-a*d)^2*x^3/b^5+_
3/4*d*(b*c-a*d)^2*x^4/b^4+1/5*d^2*(3*b*c-2*a*d)*x^5/b^3+_
@@ -10238,9 +10238,9 @@ r0:=3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*x/b^7-1/2*a*(2*b*c-5*a*d)*_
--R 9 8
--R 60b x + 60a b
--R Type: Expression(Integer)
---E 537
+--E 537
---S 538 of 1092
+--S 538 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10277,27 +10277,27 @@ a0:=integrate(t0,x)
--R 9 8
--R 60b x + 60a b
--R Type: Union(Expression(Integer),...)
---E 538
+--E 538
---S 539 of 1092
+--S 539 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 539
+--E 539
---S 540 of 1092
+--S 540 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 540
+--E 540
)clear all
---S 541 of 1092
+--S 541 of 1092
t0:=x^3*(c+d*x)^3/(a+b*x)^2
--R
--R
@@ -10307,9 +10307,9 @@ t0:=x^3*(c+d*x)^3/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 541
+--E 541
---S 542 of 1092
+--S 542 of 1092
r0:=-a*(2*b*c-5*a*d)*(b*c-a*d)^2*x/b^6+1/2*(b*c-4*a*d)*(b*c-a*d)^2*_
x^2/b^5+d*(b*c-a*d)^2*x^3/b^4+1/4*d^2*(3*b*c-2*a*d)*x^4/b^3+_
1/5*d^3*x^5/b^2+a^3*(b*c-a*d)^3/(b^7*(a+b*x))+_
@@ -10343,9 +10343,9 @@ r0:=-a*(2*b*c-5*a*d)*(b*c-a*d)^2*x/b^6+1/2*(b*c-4*a*d)*(b*c-a*d)^2*_
--R 8 7
--R 20b x + 20a b
--R Type: Expression(Integer)
---E 542
+--E 542
---S 543 of 1092
+--S 543 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10376,27 +10376,27 @@ a0:=integrate(t0,x)
--R 8 7
--R 20b x + 20a b
--R Type: Union(Expression(Integer),...)
---E 543
+--E 543
---S 544 of 1092
+--S 544 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 544
+--E 544
---S 545 of 1092
+--S 545 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 545
+--E 545
)clear all
---S 546 of 1092
+--S 546 of 1092
t0:=x^2*(c+d*x)^3/(a+b*x)^2
--R
--R
@@ -10406,9 +10406,9 @@ t0:=x^2*(c+d*x)^3/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 546
+--E 546
---S 547 of 1092
+--S 547 of 1092
r0:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+3/2*d*(b*c-a*d)^2*x^2/b^4+_
1/3*d^2*(3*b*c-2*a*d)*x^3/b^3+1/4*d^3*x^4/b^2-a^2*_
(b*c-a*d)^3/(b^6*(a+b*x))-a*(2*b*c-5*a*d)*(b*c-a*d)^2*log(a+b*x)/b^6
@@ -10438,9 +10438,9 @@ r0:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+3/2*d*(b*c-a*d)^2*x^2/b^4+_
--R 7 6
--R 12b x + 12a b
--R Type: Expression(Integer)
---E 547
+--E 547
---S 548 of 1092
+--S 548 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10468,27 +10468,27 @@ a0:=integrate(t0,x)
--R 7 6
--R 12b x + 12a b
--R Type: Union(Expression(Integer),...)
---E 548
+--E 548
---S 549 of 1092
+--S 549 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 549
+--E 549
---S 550 of 1092
+--S 550 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 550
+--E 550
)clear all
---S 551 of 1092
+--S 551 of 1092
t0:=x*(c+d*x)^3/(a+b*x)^2
--R
--R
@@ -10498,7 +10498,7 @@ t0:=x*(c+d*x)^3/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 551
+--E 551
--S 552 of 1092
r0:=3*d*(b*c-a*d)^2*x/b^4+1/2*d^2*(3*b*c-2*a*d)*x^2/b^3+1/3*d^3*x^3/b^2+_
@@ -10528,7 +10528,7 @@ r0:=3*d*(b*c-a*d)^2*x/b^4+1/2*d^2*(3*b*c-2*a*d)*x^2/b^3+1/3*d^3*x^3/b^2+_
--R Type: Expression(Integer)
--E 552
---S 553 of 1092
+--S 553 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10553,27 +10553,27 @@ a0:=integrate(t0,x)
--R 6 5
--R 6b x + 6a b
--R Type: Union(Expression(Integer),...)
---E 553
+--E 553
---S 554 of 1092
+--S 554 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 554
+--E 554
---S 555 of 1092
+--S 555 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 555
+--E 555
)clear all
---S 556 of 1092
+--S 556 of 1092
t0:=(c+d*x)^3/(a+b*x)^2
--R
--R
@@ -10583,9 +10583,9 @@ t0:=(c+d*x)^3/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 556
+--E 556
---S 557 of 1092
+--S 557 of 1092
r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+_
3*d*(b*c-a*d)^2*log(a+b*x)/b^4
--R
@@ -10605,9 +10605,9 @@ r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+_
--R 5 4
--R 2b x + 2a b
--R Type: Expression(Integer)
---E 557
+--E 557
---S 558 of 1092
+--S 558 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10626,27 +10626,27 @@ a0:=integrate(t0,x)
--R 5 4
--R 2b x + 2a b
--R Type: Union(Expression(Integer),...)
---E 558
+--E 558
---S 559 of 1092
+--S 559 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 559
+--E 559
---S 560 of 1092
+--S 560 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 560
+--E 560
)clear all
---S 561 of 1092
+--S 561 of 1092
t0:=(c+d*x)^3/(x*(a+b*x)^2)
--R
--R
@@ -10656,9 +10656,9 @@ t0:=(c+d*x)^3/(x*(a+b*x)^2)
--R 2 3 2 2
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 561
+--E 561
---S 562 of 1092
+--S 562 of 1092
r0:=d^3*x/b^2+(b*c-a*d)^3/(a*b^3*(a+b*x))+c^3*log(x)/a^2-_
(b*c-a*d)^2*(b*c+2*a*d)*log(a+b*x)/(a^2*b^3)
--R
@@ -10678,9 +10678,9 @@ r0:=d^3*x/b^2+(b*c-a*d)^3/(a*b^3*(a+b*x))+c^3*log(x)/a^2-_
--R 2 4 3 3
--R a b x + a b
--R Type: Expression(Integer)
---E 562
+--E 562
---S 563 of 1092
+--S 563 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10699,27 +10699,27 @@ a0:=integrate(t0,x)
--R 2 4 3 3
--R a b x + a b
--R Type: Union(Expression(Integer),...)
---E 563
+--E 563
---S 564 of 1092
+--S 564 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 564
+--E 564
---S 565 of 1092
+--S 565 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 565
+--E 565
)clear all
---S 566 of 1092
+--S 566 of 1092
t0:=(c+d*x)^3/(x^2*(a+b*x)^2)
--R
--R
@@ -10729,9 +10729,9 @@ t0:=(c+d*x)^3/(x^2*(a+b*x)^2)
--R 2 4 3 2 2
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 566
+--E 566
---S 567 of 1092
+--S 567 of 1092
r0:=-c^3/(a^2*x)-(b*c-a*d)^3/(a^2*b^2*(a+b*x))-c^2*(2*b*c-3*a*d)*_
log(x)/a^3+(b*c-a*d)^2*(2*b*c+a*d)*log(a+b*x)/(a^3*b^2)
--R
@@ -10751,9 +10751,9 @@ r0:=-c^3/(a^2*x)-(b*c-a*d)^3/(a^2*b^2*(a+b*x))-c^2*(2*b*c-3*a*d)*_
--R 3 3 2 4 2
--R a b x + a b x
--R Type: Expression(Integer)
---E 567
+--E 567
---S 568 of 1092
+--S 568 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10772,27 +10772,27 @@ a0:=integrate(t0,x)
--R 3 3 2 4 2
--R a b x + a b x
--R Type: Union(Expression(Integer),...)
---E 568
+--E 568
---S 569 of 1092
+--S 569 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 569
+--E 569
---S 570 of 1092
+--S 570 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 570
+--E 570
)clear all
---S 571 of 1092
+--S 571 of 1092
t0:=(c+d*x)^3/(x^3*(a+b*x)^2)
--R
--R
@@ -10802,9 +10802,9 @@ t0:=(c+d*x)^3/(x^3*(a+b*x)^2)
--R 2 5 4 2 3
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 571
+--E 571
---S 572 of 1092
+--S 572 of 1092
r0:=-1/2*c^3/(a^2*x^2)+c^2*(2*b*c-3*a*d)/(a^3*x)+(b*c-a*d)^3/_
(a^3*b*(a+b*x))+3*c*(b*c-a*d)^2*log(x)/a^4-3*c*(b*c-a*d)^2*log(a+b*x)/a^4
--R
@@ -10835,9 +10835,9 @@ r0:=-1/2*c^3/(a^2*x^2)+c^2*(2*b*c-3*a*d)/(a^3*x)+(b*c-a*d)^3/_
--R 4 2 3 5 2
--R 2a b x + 2a b x
--R Type: Expression(Integer)
---E 572
+--E 572
---S 573 of 1092
+--S 573 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10867,27 +10867,27 @@ a0:=integrate(t0,x)
--R 4 2 3 5 2
--R 2a b x + 2a b x
--R Type: Union(Expression(Integer),...)
---E 573
+--E 573
---S 574 of 1092
+--S 574 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 574
+--E 574
---S 575 of 1092
+--S 575 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 575
+--E 575
)clear all
---S 576 of 1092
+--S 576 of 1092
t0:=(c+d*x)^3/(x^4*(a+b*x)^2)
--R
--R
@@ -10897,9 +10897,9 @@ t0:=(c+d*x)^3/(x^4*(a+b*x)^2)
--R 2 6 5 2 4
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 576
+--E 576
---S 577 of 1092
+--S 577 of 1092
r0:=-1/3*c^3/(a^2*x^3)+1/2*c^2*(2*b*c-3*a*d)/(a^3*x^2)-3*c*(b*c-a*d)^2/_
(a^4*x)-(b*c-a*d)^3/(a^4*(a+b*x))-(b*c-a*d)^2*(4*b*c-a*d)*log(x)/_
a^5+(b*c-a*d)^2*(4*b*c-a*d)*log(a+b*x)/a^5
@@ -10931,9 +10931,9 @@ r0:=-1/3*c^3/(a^2*x^3)+1/2*c^2*(2*b*c-3*a*d)/(a^3*x^2)-3*c*(b*c-a*d)^2/_
--R 5 4 6 3
--R 6a b x + 6a x
--R Type: Expression(Integer)
---E 577
+--E 577
---S 578 of 1092
+--S 578 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -10963,27 +10963,27 @@ a0:=integrate(t0,x)
--R 5 4 6 3
--R 6a b x + 6a x
--R Type: Union(Expression(Integer),...)
---E 578
+--E 578
---S 579 of 1092
+--S 579 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 579
+--E 579
---S 580 of 1092
+--S 580 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 580
+--E 580
)clear all
---S 581 of 1092
+--S 581 of 1092
t0:=(c+d*x)^3/(x^5*(a+b*x)^2)
--R
--R
@@ -10993,9 +10993,9 @@ t0:=(c+d*x)^3/(x^5*(a+b*x)^2)
--R 2 7 6 2 5
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 581
+--E 581
---S 582 of 1092
+--S 582 of 1092
r0:=-1/4*c^3/(a^2*x^4)+1/3*c^2*(2*b*c-3*a*d)/(a^3*x^3)-_
3/2*c*(b*c-a*d)^2/(a^4*x^2)+(b*c-a*d)^2*(4*b*c-a*d)/_
(a^5*x)+b*(b*c-a*d)^3/(a^5*(a+b*x))+b*(5*b*c-2*a*d)*_
@@ -11031,9 +11031,9 @@ r0:=-1/4*c^3/(a^2*x^4)+1/3*c^2*(2*b*c-3*a*d)/(a^3*x^3)-_
--R 6 5 7 4
--R 12a b x + 12a x
--R Type: Expression(Integer)
---E 582
+--E 582
---S 583 of 1092
+--S 583 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -11066,27 +11066,27 @@ a0:=integrate(t0,x)
--R 6 5 7 4
--R 12a b x + 12a x
--R Type: Union(Expression(Integer),...)
---E 583
+--E 583
---S 584 of 1092
+--S 584 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 584
+--E 584
---S 585 of 1092
+--S 585 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 585
+--E 585
)clear all
---S 586 of 1092
+--S 586 of 1092
t0:=(c+d*x)^3/(x^6*(a+b*x)^2)
--R
--R
@@ -11096,9 +11096,9 @@ t0:=(c+d*x)^3/(x^6*(a+b*x)^2)
--R 2 8 7 2 6
--R b x + 2a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 586
+--E 586
---S 587 of 1092
+--S 587 of 1092
r0:=-1/5*c^3/(a^2*x^5)+1/4*c^2*(2*b*c-3*a*d)/(a^3*x^4)-c*(b*c-a*d)^2/_
(a^4*x^3)+1/2*(b*c-a*d)^2*(4*b*c-a*d)/(a^5*x^2)-_
b*(5*b*c-2*a*d)*(b*c-a*d)^2/(a^6*x)-b^2*(b*c-a*d)^3/_
@@ -11138,9 +11138,9 @@ r0:=-1/5*c^3/(a^2*x^5)+1/4*c^2*(2*b*c-3*a*d)/(a^3*x^4)-c*(b*c-a*d)^2/_
--R 7 6 8 5
--R 20a b x + 20a x
--R Type: Expression(Integer)
---E 587
+--E 587
---S 588 of 1092
+--S 588 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -11176,27 +11176,27 @@ a0:=integrate(t0,x)
--R 7 6 8 5
--R 20a b x + 20a x
--R Type: Union(Expression(Integer),...)
---E 588
+--E 588
---S 589 of 1092
+--S 589 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 589
+--E 589
---S 590 of 1092
+--S 590 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 590
+--E 590
)clear all
---S 591 of 1092
+--S 591 of 1092
t0:=(2-3*x)^3*sqrt(x)/(1+x)^2
--R
--R
@@ -11206,9 +11206,9 @@ t0:=(2-3*x)^3*sqrt(x)/(1+x)^2
--R 2
--R x + 2x + 1
--R Type: Expression(Integer)
---E 591
+--E 591
---S 592 of 1092
+--S 592 of 1092
r0a:=72*x^(3/2)-54/5*x^(5/2)+575*atan(sqrt(x))-450*sqrt(x)-_
125*sqrt(x)/(1+x)
--R
@@ -11218,9 +11218,9 @@ r0a:=72*x^(3/2)-54/5*x^(5/2)+575*atan(sqrt(x))-450*sqrt(x)-_
--R (2) --------------------------------------------------------------
--R 5x + 5
--R Type: Expression(Integer)
---E 592
+--E 592
---S 593 of 1092
+--S 593 of 1092
r0b:=575*atan(sqrt(x))-2689/5*sqrt(x)-_
1/5*(62-513*x)*sqrt(x)-21/5*(2-3*x)^2*sqrt(x)-(2-3*x)^3*sqrt(x)/(1+x)
--R
@@ -11230,9 +11230,9 @@ r0b:=575*atan(sqrt(x))-2689/5*sqrt(x)-_
--R (3) --------------------------------------------------------------
--R 5x + 5
--R Type: Expression(Integer)
---E 593
+--E 593
---S 594 of 1092
+--S 594 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -11241,43 +11241,43 @@ a0:=integrate(t0,x)
--R (4) --------------------------------------------------------------
--R 5x + 5
--R Type: Union(Expression(Integer),...)
---E 594
+--E 594
---S 595 of 1092
+--S 595 of 1092
m0a:=a0-r0a
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 595
+--E 595
---S 596 of 1092
+--S 596 of 1092
d0:=D(m0a,x)
--R
--R
--R (6) 0
--R Type: Expression(Integer)
---E 596
+--E 596
---S 597 of 1092
+--S 597 of 1092
m0b:=a0-r0b
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 597
+--E 597
---S 598 of 1092
+--S 598 of 1092
d0:=D(m0b,x)
--R
--R
--R (8) 0
--R Type: Expression(Integer)
---E 598
+--E 598
)clear all
---S 599 of 1092
+--S 599 of 1092
t0:=x^6/((a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -11291,9 +11291,9 @@ t0:=x^6/((a+b*x)^2*(c+d*x)^2)
--R 2 2 2 2
--R (2a c d + 2a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 599
+--E 599
---S 600 of 1092
+--S 600 of 1092
r0:=(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*x/(b^4*d^4)-(b*c+a*d)*x^2/(b^3*d^3)+_
1/3*x^3/(b^2*d^2)-a^6/(b^5*(b*c-a*d)^2*(a+b*x))-_
c^6/(d^5*(b*c-a*d)^2*(c+d*x))-2*a^5*(3*b*c-2*a*d)*log(a+b*x)/_
@@ -11344,9 +11344,9 @@ r0:=(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*x/(b^4*d^4)-(b*c+a*d)*x^2/(b^3*d^3)+_
--R 2 7 3 6 8 4 5
--R 9a b c d - 3a b c d
--R Type: Expression(Integer)
---E 600
+--E 600
---S 601 of 1092
+--S 601 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -11394,27 +11394,27 @@ a0:=integrate(t0,x)
--R 2 7 3 6 8 4 5
--R 9a b c d - 3a b c d
--R Type: Union(Expression(Integer),...)
---E 601
+--E 601
---S 602 of 1092
+--S 602 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 602
+--E 602
---S 603 of 1092
+--S 603 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 603
+--E 603
)clear all
---S 604 of 1092
+--S 604 of 1092
t0:=x^5/((a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -11428,9 +11428,9 @@ t0:=x^5/((a+b*x)^2*(c+d*x)^2)
--R 2 2 2 2
--R (2a c d + 2a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 604
+--E 604
---S 605 of 1092
+--S 605 of 1092
r0:=-2*(b*c+a*d)*x/(b^3*d^3)+1/2*x^2/(b^2*d^2)+a^5/(b^4*(b*c-a*d)^2*_
(a+b*x))+c^5/(d^4*(b*c-a*d)^2*(c+d*x))+a^4*(5*b*c-3*a*d)*_
log(a+b*x)/(b^4*(b*c-a*d)^3)+c^4*(3*b*c-5*a*d)*log(c+d*x)/_
@@ -11478,9 +11478,9 @@ r0:=-2*(b*c+a*d)*x/(b^3*d^3)+1/2*x^2/(b^2*d^2)+a^5/(b^4*(b*c-a*d)^2*_
--R 2 6 3 5 7 4 4
--R 6a b c d - 2a b c d
--R Type: Expression(Integer)
---E 605
+--E 605
---S 606 of 1092
+--S 606 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -11525,27 +11525,27 @@ a0:=integrate(t0,x)
--R 2 6 3 5 7 4 4
--R 6a b c d - 2a b c d
--R Type: Union(Expression(Integer),...)
---E 606
+--E 606
---S 607 of 1092
+--S 607 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 607
+--E 607
---S 608 of 1092
+--S 608 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 608
+--E 608
)clear all
---S 609 of 1092
+--S 609 of 1092
t0:=x^4/((a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -11559,9 +11559,9 @@ t0:=x^4/((a+b*x)^2*(c+d*x)^2)
--R 2 2 2 2
--R (2a c d + 2a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 609
+--E 609
---S 610 of 1092
+--S 610 of 1092
r0:=x/(b^2*d^2)-a^4/(b^3*(b*c-a*d)^2*(a+b*x))-c^4/(d^3*(b*c-a*d)^2*(c+d*x))-_
2*a^3*(2*b*c-a*d)*log(a+b*x)/(b^3*(b*c-a*d)^3)-_
2*c^3*(b*c-2*a*d)*log(c+d*x)/(d^3*(b*c-a*d)^3)
@@ -11605,9 +11605,9 @@ r0:=x/(b^2*d^2)-a^4/(b^3*(b*c-a*d)^2*(a+b*x))-c^4/(d^3*(b*c-a*d)^2*(c+d*x))-_
--R 2 5 3 4 6 4 3
--R 3a b c d - a b c d
--R Type: Expression(Integer)
---E 610
+--E 610
---S 611 of 1092
+--S 611 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -11649,27 +11649,27 @@ a0:=integrate(t0,x)
--R 2 5 3 4 6 4 3
--R 3a b c d - a b c d
--R Type: Union(Expression(Integer),...)
---E 611
+--E 611
---S 612 of 1092
+--S 612 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 612
+--E 612
---S 613 of 1092
+--S 613 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 613
+--E 613
)clear all
---S 614 of 1092
+--S 614 of 1092
t0:=x^3/((a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -11683,9 +11683,9 @@ t0:=x^3/((a+b*x)^2*(c+d*x)^2)
--R 2 2 2 2
--R (2a c d + 2a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 614
+--E 614
---S 615 of 1092
+--S 615 of 1092
r0:=a^3/(b^2*(b*c-a*d)^2*(a+b*x))+c^3/(d^2*(b*c-a*d)^2*(c+d*x))+_
a^2*(3*b*c-a*d)*log(a+b*x)/(b^2*(b*c-a*d)^3)+_
c^2*(b*c-3*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^3)
@@ -11720,9 +11720,9 @@ r0:=a^3/(b^2*(b*c-a*d)^2*(a+b*x))+c^3/(d^2*(b*c-a*d)^2*(c+d*x))+_
--R 2 4 3 3 5 4 2
--R 3a b c d - a b c d
--R Type: Expression(Integer)
---E 615
+--E 615
---S 616 of 1092
+--S 616 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -11755,27 +11755,27 @@ a0:=integrate(t0,x)
--R 2 4 3 3 5 4 2
--R 3a b c d - a b c d
--R Type: Union(Expression(Integer),...)
---E 616
+--E 616
---S 617 of 1092
+--S 617 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 617
+--E 617
---S 618 of 1092
+--S 618 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 618
+--E 618
)clear all
---S 619 of 1092
+--S 619 of 1092
t0:=x^2/((a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -11789,9 +11789,9 @@ t0:=x^2/((a+b*x)^2*(c+d*x)^2)
--R 2 2 2 2
--R (2a c d + 2a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 619
+--E 619
---S 620 of 1092
+--S 620 of 1092
r0:=-a^2/(b*(b*c-a*d)^2*(a+b*x))-c^2/(d*(b*c-a*d)^2*(c+d*x))-_
2*a*c*log(a+b*x)/(b*c-a*d)^3+2*a*c*log(c+d*x)/(b*c-a*d)^3
--R
@@ -11815,9 +11815,9 @@ r0:=-a^2/(b*(b*c-a*d)^2*(a+b*x))-c^2/(d*(b*c-a*d)^2*(c+d*x))-_
--R 2 3 3 2 4 4
--R 3a b c d - a b c d
--R Type: Expression(Integer)
---E 620
+--E 620
---S 621 of 1092
+--S 621 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -11840,27 +11840,27 @@ a0:=integrate(t0,x)
--R 2 3 3 2 4 4
--R 3a b c d - a b c d
--R Type: Union(Expression(Integer),...)
---E 621
+--E 621
---S 622 of 1092
+--S 622 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 622
+--E 622
---S 623 of 1092
+--S 623 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 623
+--E 623
)clear all
---S 624 of 1092
+--S 624 of 1092
t0:=x/((a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -11873,9 +11873,9 @@ t0:=x/((a+b*x)^2*(c+d*x)^2)
--R 2 2 2 2
--R (2a c d + 2a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 624
+--E 624
---S 625 of 1092
+--S 625 of 1092
r0:=a/((b*c-a*d)^2*(a+b*x))+c/((b*c-a*d)^2*(c+d*x))+_
(b*c+a*d)*log(a+b*x)/(b*c-a*d)^3-(b*c+a*d)*log(c+d*x)/(b*c-a*d)^3
--R
@@ -11903,9 +11903,9 @@ r0:=a/((b*c-a*d)^2*(a+b*x))+c/((b*c-a*d)^2*(c+d*x))+_
--R 3 4
--R - a b c
--R Type: Expression(Integer)
---E 625
+--E 625
---S 626 of 1092
+--S 626 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -11932,27 +11932,27 @@ a0:=integrate(t0,x)
--R 3 4
--R - a b c
--R Type: Union(Expression(Integer),...)
---E 626
+--E 626
---S 627 of 1092
+--S 627 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 627
+--E 627
---S 628 of 1092
+--S 628 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 628
+--E 628
)clear all
---S 629 of 1092
+--S 629 of 1092
t0:=1/((a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -11965,9 +11965,9 @@ t0:=1/((a+b*x)^2*(c+d*x)^2)
--R 2 2 2 2
--R (2a c d + 2a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 629
+--E 629
---S 630 of 1092
+--S 630 of 1092
r0:=-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-_
2*b*d*log(a+b*x)/(b*c-a*d)^3+2*b*d*log(c+d*x)/(b*c-a*d)^3
--R
@@ -11991,9 +11991,9 @@ r0:=-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-_
--R 3 4
--R - a b c
--R Type: Expression(Integer)
---E 630
+--E 630
---S 631 of 1092
+--S 631 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -12016,27 +12016,27 @@ a0:=integrate(t0,x)
--R 3 4
--R - a b c
--R Type: Union(Expression(Integer),...)
---E 631
+--E 631
---S 632 of 1092
+--S 632 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 632
+--E 632
---S 633 of 1092
+--S 633 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 633
+--E 633
)clear all
---S 634 of 1092
+--S 634 of 1092
t0:=1/(x*(a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -12049,9 +12049,9 @@ t0:=1/(x*(a+b*x)^2*(c+d*x)^2)
--R 2 2 2 2 2
--R (2a c d + 2a b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 634
+--E 634
---S 635 of 1092
+--S 635 of 1092
r0:=b^2/(a*(b*c-a*d)^2*(a+b*x))+d^2/(c*(b*c-a*d)^2*(c+d*x))+_
log(x)/(a^2*c^2)-b^2*(b*c-3*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^3)-_
d^2*(3*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^3)
@@ -12097,9 +12097,9 @@ r0:=b^2/(a*(b*c-a*d)^2*(a+b*x))+d^2/(c*(b*c-a*d)^2*(c+d*x))+_
--R 3 3 6
--R - a b c
--R Type: Expression(Integer)
---E 635
+--E 635
---S 636 of 1092
+--S 636 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -12143,27 +12143,27 @@ a0:=integrate(t0,x)
--R 3 3 6
--R - a b c
--R Type: Union(Expression(Integer),...)
---E 636
+--E 636
---S 637 of 1092
+--S 637 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 637
+--E 637
---S 638 of 1092
+--S 638 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 638
+--E 638
)clear all
---S 639 of 1092
+--S 639 of 1092
t0:=1/(x^2*(a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -12176,9 +12176,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^2)
--R 2 2 3 2 2 2
--R (2a c d + 2a b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 639
+--E 639
---S 640 of 1092
+--S 640 of 1092
r0:=(-1)/(a^2*c^2*x)-b^3/(a^2*(b*c-a*d)^2*(a+b*x))-_
d^3/(c^2*(b*c-a*d)^2*(c+d*x))-2*(b*c+a*d)*log(x)/(a^3*c^3)+_
2*b^3*(b*c-2*a*d)*log(a+b*x)/(a^3*(b*c-a*d)^3)+_
@@ -12231,9 +12231,9 @@ r0:=(-1)/(a^2*c^2*x)-b^3/(a^2*(b*c-a*d)^2*(a+b*x))-_
--R 7 4 3 6 5 2 5 2 6 4 3 7
--R (a c d - 3a b c d + 3a b c d - a b c )x
--R Type: Expression(Integer)
---E 640
+--E 640
---S 641 of 1092
+--S 641 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -12283,27 +12283,27 @@ a0:=integrate(t0,x)
--R 7 4 3 6 5 2 5 2 6 4 3 7
--R (a c d - 3a b c d + 3a b c d - a b c )x
--R Type: Union(Expression(Integer),...)
---E 641
+--E 641
---S 642 of 1092
+--S 642 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 642
+--E 642
---S 643 of 1092
+--S 643 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 643
+--E 643
)clear all
---S 644 of 1092
+--S 644 of 1092
t0:=1/(x^3*(a+b*x)^2*(c+d*x)^2)
--R
--R
@@ -12316,9 +12316,9 @@ t0:=1/(x^3*(a+b*x)^2*(c+d*x)^2)
--R 2 2 4 2 2 3
--R (2a c d + 2a b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 644
+--E 644
---S 645 of 1092
+--S 645 of 1092
r0:=(-1/2)/(a^2*c^2*x^2)+2*(b*c+a*d)/(a^3*c^3*x)+_
b^4/(a^3*(b*c-a*d)^2*(a+b*x))+d^4/(c^3*(b*c-a*d)^2*(c+d*x))+_
(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*log(x)/(a^4*c^4)-b^4*(3*b*c-5*a*d)*_
@@ -12375,9 +12375,9 @@ r0:=(-1/2)/(a^2*c^2*x^2)+2*(b*c+a*d)/(a^3*c^3*x)+_
--R 8 5 3 7 6 2 6 2 7 5 3 8 2
--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
--R Type: Expression(Integer)
---E 645
+--E 645
---S 646 of 1092
+--S 646 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -12430,27 +12430,27 @@ a0:=integrate(t0,x)
--R 8 5 3 7 6 2 6 2 7 5 3 8 2
--R (2a c d - 6a b c d + 6a b c d - 2a b c )x
--R Type: Union(Expression(Integer),...)
---E 646
+--E 646
---S 647 of 1092
+--S 647 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 647
+--E 647
---S 648 of 1092
+--S 648 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 648
+--E 648
)clear all
---S 649 of 1092
+--S 649 of 1092
t0:=x^7/((a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -12464,9 +12464,9 @@ t0:=x^7/((a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 2 2 2 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: Fraction(Polynomial(Integer))
---E 649
+--E 649
---S 650 of 1092
+--S 650 of 1092
r0:=3*(2*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^4*d^5)-1/2*(3*b*c+2*a*d)*x^2/_
(b^3*d^4)+1/3*x^3/(b^2*d^3)+a^7/(b^5*(b*c-a*d)^3*(a+b*x))+1/2*c^7/_
(d^6*(b*c-a*d)^2*(c+d*x)^2)-c^6*(5*b*c-7*a*d)/(d^6*(b*c-a*d)^3*_
@@ -12570,9 +12570,9 @@ r0:=3*(2*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^4*d^5)-1/2*(3*b*c+2*a*d)*x^2/_
--R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6
--R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d
--R Type: Expression(Integer)
---E 650
+--E 650
---S 651 of 1092
+--S 651 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -12672,27 +12672,27 @@ a0:=integrate(t0,x)
--R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6
--R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d
--R Type: Union(Expression(Integer),...)
---E 651
+--E 651
---S 652 of 1092
+--S 652 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 652
+--E 652
---S 653 of 1092
+--S 653 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 653
+--E 653
)clear all
---S 654 of 1092
+--S 654 of 1092
t0:=x^6/((a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -12706,9 +12706,9 @@ t0:=x^6/((a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 2 2 2 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: Fraction(Polynomial(Integer))
---E 654
+--E 654
---S 655 of 1092
+--S 655 of 1092
r0:=-(3*b*c+2*a*d)*x/(b^3*d^4)+1/2*x^2/(b^2*d^3)-a^6/(b^4*(b*c-a*d)^3*_
(a+b*x))-1/2*c^6/(d^5*(b*c-a*d)^2*(c+d*x)^2)+2*c^5*(2*b*c-3*a*d)/_
(d^5*(b*c-a*d)^3*(c+d*x))-3*a^5*(2*b*c-a*d)*log(a+b*x)/_
@@ -12786,9 +12786,9 @@ r0:=-(3*b*c+2*a*d)*x/(b^3*d^4)+1/2*x^2/(b^2*d^3)-a^6/(b^4*(b*c-a*d)^3*_
--R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5
--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Expression(Integer)
---E 655
+--E 655
---S 656 of 1092
+--S 656 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -12862,27 +12862,27 @@ a0:=integrate(t0,x)
--R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5
--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Union(Expression(Integer),...)
---E 656
+--E 656
---S 657 of 1092
+--S 657 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 657
+--E 657
---S 658 of 1092
+--S 658 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 658
+--E 658
)clear all
---S 659 of 1092
+--S 659 of 1092
t0:=x^5/((a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -12896,9 +12896,9 @@ t0:=x^5/((a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 2 2 2 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: Fraction(Polynomial(Integer))
---E 659
+--E 659
---S 660 of 1092
+--S 660 of 1092
r0:=x/(b^2*d^3)+a^5/(b^3*(b*c-a*d)^3*(a+b*x))+1/2*c^5/(d^4*(b*c-a*d)^2*_
(c+d*x)^2)-c^4*(3*b*c-5*a*d)/(d^4*(b*c-a*d)^3*(c+d*x))+_
a^4*(5*b*c-2*a*d)*log(a+b*x)/(b^3*(b*c-a*d)^4)-c^3*_
@@ -12966,9 +12966,9 @@ r0:=x/(b^2*d^3)+a^5/(b^3*(b*c-a*d)^3*(a+b*x))+1/2*c^5/(d^4*(b*c-a*d)^2*_
--R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4
--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Expression(Integer)
---E 660
+--E 660
---S 661 of 1092
+--S 661 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -13033,27 +13033,27 @@ a0:=integrate(t0,x)
--R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4
--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Union(Expression(Integer),...)
---E 661
+--E 661
---S 662 of 1092
+--S 662 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 662
+--E 662
---S 663 of 1092
+--S 663 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 663
+--E 663
)clear all
---S 664 of 1092
+--S 664 of 1092
t0:=x^4/((a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -13067,9 +13067,9 @@ t0:=x^4/((a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 2 2 2 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: Fraction(Polynomial(Integer))
---E 664
+--E 664
---S 665 of 1092
+--S 665 of 1092
r0:=-a^4/(b^2*(b*c-a*d)^3*(a+b*x))-1/2*c^4/(d^3*(b*c-a*d)^2*(c+d*x)^2)+_
2*c^3*(b*c-2*a*d)/(d^3*(b*c-a*d)^3*(c+d*x))-a^3*(4*b*c-a*d)*_
log(a+b*x)/(b^2*(b*c-a*d)^4)+c^2*(b^2*c^2-4*a*b*c*d+6*a^2*d^2)*_
@@ -13120,9 +13120,9 @@ r0:=-a^4/(b^2*(b*c-a*d)^3*(a+b*x))-1/2*c^4/(d^3*(b*c-a*d)^2*(c+d*x)^2)+_
--R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3
--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Expression(Integer)
---E 665
+--E 665
---S 666 of 1092
+--S 666 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -13170,27 +13170,27 @@ a0:=integrate(t0,x)
--R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3
--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Union(Expression(Integer),...)
---E 666
+--E 666
---S 667 of 1092
+--S 667 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 667
+--E 667
---S 668 of 1092
+--S 668 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 668
+--E 668
)clear all
---S 669 of 1092
+--S 669 of 1092
t0:=x^3/((a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -13204,9 +13204,9 @@ t0:=x^3/((a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 2 2 2 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: Fraction(Polynomial(Integer))
---E 669
+--E 669
---S 670 of 1092
+--S 670 of 1092
r0:=a^3/(b*(b*c-a*d)^3*(a+b*x))+1/2*c^3/(d^2*(b*c-a*d)^2*(c+d*x)^2)-_
c^2*(b*c-3*a*d)/(d^2*(b*c-a*d)^3*(c+d*x))+3*a^2*c*log(a+b*x)/_
(b*c-a*d)^4-3*a^2*c*log(c+d*x)/(b*c-a*d)^4
@@ -13250,9 +13250,9 @@ r0:=a^3/(b*(b*c-a*d)^3*(a+b*x))+1/2*c^3/(d^2*(b*c-a*d)^2*(c+d*x)^2)-_
--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2
--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Expression(Integer)
---E 670
+--E 670
---S 671 of 1092
+--S 671 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -13294,27 +13294,27 @@ a0:=integrate(t0,x)
--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2
--R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Union(Expression(Integer),...)
---E 671
+--E 671
---S 672 of 1092
+--S 672 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 672
+--E 672
---S 673 of 1092
+--S 673 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 673
+--E 673
)clear all
---S 674 of 1092
+--S 674 of 1092
t0:=x^2/((a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -13328,9 +13328,9 @@ t0:=x^2/((a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 2 2 2 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: Fraction(Polynomial(Integer))
---E 674
+--E 674
---S 675 of 1092
+--S 675 of 1092
r0:=-a^2/((b*c-a*d)^3*(a+b*x))-1/2*c^2/(d*(b*c-a*d)^2*(c+d*x)^2)-_
2*a*c/((b*c-a*d)^3*(c+d*x))-a*(2*b*c+a*d)*log(a+b*x)/(b*c-a*d)^4+_
a*(2*b*c+a*d)*log(c+d*x)/(b*c-a*d)^4
@@ -13371,9 +13371,9 @@ r0:=-a^2/((b*c-a*d)^3*(a+b*x))-1/2*c^2/(d*(b*c-a*d)^2*(c+d*x)^2)-_
--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6
--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Expression(Integer)
---E 675
+--E 675
---S 676 of 1092
+--S 676 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -13412,27 +13412,27 @@ a0:=integrate(t0,x)
--R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6
--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d
--R Type: Union(Expression(Integer),...)
---E 676
+--E 676
---S 677 of 1092
+--S 677 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 677
+--E 677
---S 678 of 1092
+--S 678 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 678
+--E 678
)clear all
---S 679 of 1092
+--S 679 of 1092
t0:=x/((a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -13445,9 +13445,9 @@ t0:=x/((a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 2 2 2 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: Fraction(Polynomial(Integer))
---E 679
+--E 679
---S 680 of 1092
+--S 680 of 1092
r0:=a*b/((b*c-a*d)^3*(a+b*x))+1/2*c/((b*c-a*d)^2*(c+d*x)^2)+(b*c+a*d)/_
((b*c-a*d)^3*(c+d*x))+b*(b*c+2*a*d)*log(a+b*x)/(b*c-a*d)^4-_
b*(b*c+2*a*d)*log(c+d*x)/(b*c-a*d)^4
@@ -13488,9 +13488,9 @@ r0:=a*b/((b*c-a*d)^3*(a+b*x))+1/2*c/((b*c-a*d)^2*(c+d*x)^2)+(b*c+a*d)/_
--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c
--R Type: Expression(Integer)
---E 680
+--E 680
---S 681 of 1092
+--S 681 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -13529,27 +13529,27 @@ a0:=integrate(t0,x)
--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c
--R Type: Union(Expression(Integer),...)
---E 681
+--E 681
---S 682 of 1092
+--S 682 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 682
+--E 682
---S 683 of 1092
+--S 683 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 683
+--E 683
)clear all
---S 684 of 1092
+--S 684 of 1092
t0:=1/((a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -13562,9 +13562,9 @@ t0:=1/((a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 2 2 2 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: Fraction(Polynomial(Integer))
---E 684
+--E 684
---S 685 of 1092
+--S 685 of 1092
r0:=-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-_
2*b*d/((b*c-a*d)^3*(c+d*x))-3*b^2*d*log(a+b*x)/(b*c-a*d)^4+_
3*b^2*d*log(c+d*x)/(b*c-a*d)^4
@@ -13602,9 +13602,9 @@ r0:=-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-_
--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c
--R Type: Expression(Integer)
---E 685
+--E 685
---S 686 of 1092
+--S 686 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -13640,27 +13640,27 @@ a0:=integrate(t0,x)
--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6
--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c
--R Type: Union(Expression(Integer),...)
---E 686
+--E 686
---S 687 of 1092
+--S 687 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 687
+--E 687
---S 688 of 1092
+--S 688 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 688
+--E 688
)clear all
---S 689 of 1092
+--S 689 of 1092
t0:=1/(x*(a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -13673,9 +13673,9 @@ t0:=1/(x*(a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 3 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 x
--R Type: Fraction(Polynomial(Integer))
---E 689
+--E 689
---S 690 of 1092
+--S 690 of 1092
r0:=b^3/(a*(b*c-a*d)^3*(a+b*x))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x)^2)+_
d^2*(3*b*c-a*d)/(c^2*(b*c-a*d)^3*(c+d*x))+log(x)/(a^2*c^3)-_
b^3*(b*c-4*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^4)-d^2*(6*b^2*c^2-_
@@ -13740,9 +13740,9 @@ r0:=b^3/(a*(b*c-a*d)^3*(a+b*x))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x)^2)+_
--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c
--R Type: Expression(Integer)
---E 690
+--E 690
---S 691 of 1092
+--S 691 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -13804,27 +13804,27 @@ a0:=integrate(t0,x)
--R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9
--R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c
--R Type: Union(Expression(Integer),...)
---E 691
+--E 691
---S 692 of 1092
+--S 692 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 692
+--E 692
---S 693 of 1092
+--S 693 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 693
+--E 693
)clear all
---S 694 of 1092
+--S 694 of 1092
t0:=1/(x^2*(a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -13837,9 +13837,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 4 2 2 3 3 2 3 2
--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 694
+--E 694
---S 695 of 1092
+--S 695 of 1092
r0:=(-1)/(a^2*c^3*x)-b^4/(a^2*(b*c-a*d)^3*(a+b*x))-_
1/2*d^3/(c^2*(b*c-a*d)^2*(c+d*x)^2)-2*d^3*(2*b*c-a*d)/_
(c^3*(b*c-a*d)^3*(c+d*x))-(2*b*c+3*a*d)*log(x)/(a^3*c^4)+_
@@ -13926,112 +13926,23 @@ r0:=(-1)/(a^2*c^3*x)-b^4/(a^2*(b*c-a*d)^3*(a+b*x))-_
--R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10
--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x
--R Type: Expression(Integer)
---E 695
+--E 695
---S 696 of 1092
-a0:=integrate(t0,x)
---R
---R
---R (3)
---R 5 7 4 2 6 3 3 2 5 4
---R (6a b d - 20a b c d + 20a b c d )x
---R +
---R 6 7 5 6 4 2 2 5 3 3 3 4 3
---R (6a d - 8a b c d - 20a b c d + 40a b c d )x
---R +
---R 6 6 5 2 5 4 2 3 4 3 3 4 3 2
---R (12a c d - 34a b c d + 20a b c d + 20a b c d )x
---R +
---R 6 2 5 5 3 4 4 2 4 3
---R (6a c d - 20a b c d + 20a b c d )x
---R *
---R log(d x + c)
---R +
---R 5 4 3 6 5 2 4 2 4 4 3 5 5 2 6 6 3
---R (- 10a b c d + 4b c d )x + (- 10a b c d - 16a b c d + 8b c d)x
---R +
---R 2 4 5 2 5 6 6 7 2 2 4 6 5 7
---R (- 20a b c d - 2a b c d + 4b c )x + (- 10a b c d + 4a b c )x
---R *
---R log(b x + a)
---R +
---R 5 7 4 2 6 3 3 2 5 5 4 3 6 5 2 4
---R (- 6a b d + 20a b c d - 20a b c d + 10a b c d - 4b c d )x
---R +
---R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3
---R - 6a d + 8a b c d + 20a b c d - 40a b c d + 10a b c d
---R +
---R 5 5 2 6 6
---R 16a b c d - 8b c d
---R *
---R 3
---R x
---R +
---R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
---R - 12a c d + 34a b c d - 20a b c d - 20a b c d + 20a b c d
---R +
---R 5 6 6 7
---R 2a b c d - 4b c
---R *
---R 2
---R x
---R +
---R 6 2 5 5 3 4 4 2 4 3 2 4 6 5 7
---R (- 6a c d + 20a b c d - 20a b c d + 10a b c d - 4a b c )x
---R *
---R log(x)
---R +
---R 5 6 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 3
---R (- 6a b c d + 20a b c d - 20a b c d + 10a b c d - 4a b c d )x
---R +
---R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
---R - 6a c d + 11a b c d + 10a b c d - 25a b c d + 18a b c d
---R +
---R 5 6
---R - 8a b c d
---R *
---R 2
---R x
---R +
---R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7
---R (- 9a c d + 28a b c d - 25a b c d + 4a b c d + 6a b c d - 4a b c )x
---R +
---R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7
---R - 2a c d + 8a b c d - 12a b c d + 8a b c d - 2a b c
---R /
---R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4
---R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x
---R +
---R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3
---R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x
---R +
---R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2
---R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x
---R +
---R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10
---R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x
---R Type: Union(Expression(Integer),...)
---E 696
+--S 696 of 1092
+--a0:=integrate(t0,x)
+--E 696
---S 697 of 1092
-m0:=a0-r0
---R
---R
---R (4) 0
---R Type: Expression(Integer)
---E 697
+--S 697 of 1092
+--m0:=a0-r0
+--E 697
---S 698 of 1092
-d0:=D(m0,x)
---R
---R
---R (5) 0
---R Type: Expression(Integer)
---E 698
+--S 698 of 1092
+--d0:=D(m0,x)
+--E 698
)clear all
---S 699 of 1092
+--S 699 of 1092
t0:=1/(x^3*(a+b*x)^2*(c+d*x)^3)
--R
--R
@@ -14044,9 +13955,9 @@ t0:=1/(x^3*(a+b*x)^2*(c+d*x)^3)
--R 2 2 2 2 3 5 2 2 3 4 2 3 3
--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 699
+--E 699
---S 700 of 1092
+--S 700 of 1092
r0:=(-1/2)/(a^2*c^3*x^2)+(2*b*c+3*a*d)/(a^3*c^4*x)+b^5/(a^3*(b*c-a*d)^3*_
(a+b*x))+1/2*d^4/(c^3*(b*c-a*d)^2*(c+d*x)^2)+d^4*(5*b*c-3*a*d)/_
(c^4*(b*c-a*d)^3*(c+d*x))+3*(b^2*c^2+2*a*b*c*d+2*a^2*d^2)*log(x)/_
@@ -14142,9 +14053,9 @@ r0:=(-1/2)/(a^2*c^3*x^2)+(2*b*c+3*a*d)/(a^3*c^4*x)+b^5/(a^3*(b*c-a*d)^3*_
--R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2
--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x
--R Type: Expression(Integer)
---E 700
+--E 700
---S 701 of 1092
+--S 701 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -14236,27 +14147,27 @@ a0:=integrate(t0,x)
--R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2
--R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x
--R Type: Union(Expression(Integer),...)
---E 701
+--E 701
---S 702 of 1092
+--S 702 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 702
+--E 702
---S 703 of 1092
+--S 703 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 703
+--E 703
)clear all
---S 704 of 1092
+--S 704 of 1092
t0:=x^2/((-1+x)^2*(1+x)^2)
--R
--R
@@ -14266,9 +14177,9 @@ t0:=x^2/((-1+x)^2*(1+x)^2)
--R 4 2
--R x - 2x + 1
--R Type: Fraction(Polynomial(Integer))
---E 704
+--E 704
---S 705 of 1092
+--S 705 of 1092
r0:=1/2*x/(1-x^2)-1/2*atanh(x)
--R
--R
@@ -14278,9 +14189,9 @@ r0:=1/2*x/(1-x^2)-1/2*atanh(x)
--R 2
--R 2x - 2
--R Type: Expression(Integer)
---E 705
+--E 705
---S 706 of 1092
+--S 706 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -14290,9 +14201,9 @@ a0:=integrate(t0,x)
--R 2
--R 4x - 4
--R Type: Union(Expression(Integer),...)
---E 706
+--E 706
---S 707 of 1092
+--S 707 of 1092
m0:=a0-r0
--R
--R
@@ -14300,19 +14211,19 @@ m0:=a0-r0
--R (4) -------------------------------------
--R 4
--R Type: Expression(Integer)
---E 707
+--E 707
---S 708 of 1092
+--S 708 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 708
+--E 708
)clear all
---S 709 of 1092
+--S 709 of 1092
t0:=b^2*x^m/(b+a*x^2)^2
--R
--R
@@ -14322,28 +14233,28 @@ t0:=b^2*x^m/(b+a*x^2)^2
--R 2 4 2 2
--R a x + 2a b x + b
--R Type: Expression(Integer)
---E 709
+--E 709
---S 710 of 1092
+--S 710 of 1092
--r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_
-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m)
---E 710
+--E 710
---S 711 of 1092
+--S 711 of 1092
--a0:=integrate(t0,x)
---E 711
+--E 711
---S 712 of 1092
+--S 712 of 1092
--m0:=a0-r0
---E 712
+--E 712
---S 713 of 1092
+--S 713 of 1092
--d0:=D(m0,x)
---E 713
+--E 713
)clear all
---S 714 of 1092
+--S 714 of 1092
t0:=x^m/((1-x*sqrt(a)/sqrt(-b))^2*(1+x*sqrt(a)/sqrt(-b))^2)
--R
--R
@@ -14353,28 +14264,28 @@ t0:=x^m/((1-x*sqrt(a)/sqrt(-b))^2*(1+x*sqrt(a)/sqrt(-b))^2)
--R 2 4 2 2
--R a x + 2a b x + b
--R Type: Expression(Integer)
---E 714
+--E 714
---S 715 of 1092
+--S 715 of 1092
--r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_
-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m)
---E 715
+--E 715
---S 716 of 1092
+--S 716 of 1092
--a0:=integrate(t0,x)
---E 716
+--E 716
---S 717 of 1092
+--S 717 of 1092
--m0:=a0-r0
---E 717
+--E 717
---S 718 of 1092
+--S 718 of 1092
--d0:=D(m0,x)
---E 718
+--E 718
)clear all
---S 719 of 1092
+--S 719 of 1092
t0:=x^3*(c+d*x)^3/(a+b*x)^3
--R
--R
@@ -14384,9 +14295,9 @@ t0:=x^3*(c+d*x)^3/(a+b*x)^3
--R 3 3 2 2 2 3
--R b x + 3a b x + 3a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 719
+--E 719
---S 720 of 1092
+--S 720 of 1092
r0:=(b*c-a*d)*(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*x/b^6+_
3/2*d*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+d^2*(b*c-a*d)*x^3/b^4+_
1/4*d^3*x^4/b^3+1/2*a^3*(b*c-a*d)^3/(b^7*(a+b*x)^2)-_
@@ -14424,9 +14335,9 @@ r0:=(b*c-a*d)*(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*x/b^6+_
--R 9 2 8 2 7
--R 4b x + 8a b x + 4a b
--R Type: Expression(Integer)
---E 720
+--E 720
---S 721 of 1092
+--S 721 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -14460,27 +14371,27 @@ a0:=integrate(t0,x)
--R 9 2 8 2 7
--R 4b x + 8a b x + 4a b
--R Type: Union(Expression(Integer),...)
---E 721
+--E 721
---S 722 of 1092
+--S 722 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 722
+--E 722
---S 723 of 1092
+--S 723 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 723
+--E 723
)clear all
---S 724 of 1092
+--S 724 of 1092
t0:=x^2*(c+d*x)^3/(a+b*x)^3
--R
--R
@@ -14490,9 +14401,9 @@ t0:=x^2*(c+d*x)^3/(a+b*x)^3
--R 3 3 2 2 2 3
--R b x + 3a b x + 3a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 724
+--E 724
---S 725 of 1092
+--S 725 of 1092
r0:=3*d*(b*c-2*a*d)*(b*c-a*d)*x/b^5+3/2*d^2*(b*c-a*d)*x^2/b^4+_
1/3*d^3*x^3/b^3-1/2*a^2*(b*c-a*d)^3/(b^6*(a+b*x)^2)+_
a*(2*b*c-5*a*d)*(b*c-a*d)^2/(b^6*(a+b*x))+(b*c-a*d)*_
@@ -14526,9 +14437,9 @@ r0:=3*d*(b*c-2*a*d)*(b*c-a*d)*x/b^5+3/2*d^2*(b*c-a*d)*x^2/b^4+_
--R 8 2 7 2 6
--R 6b x + 12a b x + 6a b
--R Type: Expression(Integer)
---E 725
+--E 725
---S 726 of 1092
+--S 726 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -14559,27 +14470,27 @@ a0:=integrate(t0,x)
--R 8 2 7 2 6
--R 6b x + 12a b x + 6a b
--R Type: Union(Expression(Integer),...)
---E 726
+--E 726
---S 727 of 1092
+--S 727 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 727
+--E 727
---S 728 of 1092
+--S 728 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 728
+--E 728
)clear all
---S 729 of 1092
+--S 729 of 1092
t0:=x*(c+d*x)^3/(a+b*x)^3
--R
--R
@@ -14589,9 +14500,9 @@ t0:=x*(c+d*x)^3/(a+b*x)^3
--R 3 3 2 2 2 3
--R b x + 3a b x + 3a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 729
+--E 729
---S 730 of 1092
+--S 730 of 1092
r0:=3*d^2*(b*c-a*d)*x/b^4+1/2*d^3*x^2/b^3+1/2*a*(b*c-a*d)^3/_
(b^5*(a+b*x)^2)-(b*c-4*a*d)*(b*c-a*d)^2/(b^5*(a+b*x))+_
3*d*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5
@@ -14618,9 +14529,9 @@ r0:=3*d^2*(b*c-a*d)*x/b^4+1/2*d^3*x^2/b^3+1/2*a*(b*c-a*d)^3/_
--R 7 2 6 2 5
--R 2b x + 4a b x + 2a b
--R Type: Expression(Integer)
---E 730
+--E 730
---S 731 of 1092
+--S 731 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -14645,27 +14556,27 @@ a0:=integrate(t0,x)
--R 7 2 6 2 5
--R 2b x + 4a b x + 2a b
--R Type: Union(Expression(Integer),...)
---E 731
+--E 731
---S 732 of 1092
+--S 732 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 732
+--E 732
---S 733 of 1092
+--S 733 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 733
+--E 733
)clear all
---S 734 of 1092
+--S 734 of 1092
t0:=(c+d*x)^3/(a+b*x)^3
--R
--R
@@ -14675,9 +14586,9 @@ t0:=(c+d*x)^3/(a+b*x)^3
--R 3 3 2 2 2 3
--R b x + 3a b x + 3a b x + a
--R Type: Fraction(Polynomial(Integer))
---E 734
+--E 734
---S 735 of 1092
+--S 735 of 1092
r0:=d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-3*d*(b*c-a*d)^2/_
(b^4*(a+b*x))+3*d^2*(b*c-a*d)*log(a+b*x)/b^4
--R
@@ -14700,9 +14611,9 @@ r0:=d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-3*d*(b*c-a*d)^2/_
--R 6 2 5 2 4
--R 2b x + 4a b x + 2a b
--R Type: Expression(Integer)
---E 735
+--E 735
---S 736 of 1092
+--S 736 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -14724,27 +14635,27 @@ a0:=integrate(t0,x)
--R 6 2 5 2 4
--R 2b x + 4a b x + 2a b
--R Type: Union(Expression(Integer),...)
---E 736
+--E 736
---S 737 of 1092
+--S 737 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 737
+--E 737
---S 738 of 1092
+--S 738 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 738
+--E 738
)clear all
---S 739 of 1092
+--S 739 of 1092
t0:=(c+d*x)^3/(x*(a+b*x)^3)
--R
--R
@@ -14754,9 +14665,9 @@ t0:=(c+d*x)^3/(x*(a+b*x)^3)
--R 3 4 2 3 2 2 3
--R b x + 3a b x + 3a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 739
+--E 739
---S 740 of 1092
+--S 740 of 1092
r0:=1/2*(b*c-a*d)^3/(a*b^3*(a+b*x)^2)+(b*c-a*d)^2*(b*c+2*a*d)/_
(a^2*b^3*(a+b*x))+c^3*log(x)/a^3-(c^3/a^3-d^3/b^3)*log(a+b*x)
--R
@@ -14776,9 +14687,9 @@ r0:=1/2*(b*c-a*d)^3/(a*b^3*(a+b*x)^2)+(b*c-a*d)^2*(b*c+2*a*d)/_
--R 3 5 2 4 4 5 3
--R 2a b x + 4a b x + 2a b
--R Type: Expression(Integer)
---E 740
+--E 740
---S 741 of 1092
+--S 741 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -14797,27 +14708,27 @@ a0:=integrate(t0,x)
--R 3 5 2 4 4 5 3
--R 2a b x + 4a b x + 2a b
--R Type: Union(Expression(Integer),...)
---E 741
+--E 741
---S 742 of 1092
+--S 742 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 742
+--E 742
---S 743 of 1092
+--S 743 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 743
+--E 743
)clear all
---S 744 of 1092
+--S 744 of 1092
t0:=(c+d*x)^3/(x^2*(a+b*x)^3)
--R
--R
@@ -14827,9 +14738,9 @@ t0:=(c+d*x)^3/(x^2*(a+b*x)^3)
--R 3 5 2 4 2 3 3 2
--R b x + 3a b x + 3a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 744
+--E 744
---S 745 of 1092
+--S 745 of 1092
r0:=-c^3/(a^3*x)-1/2*(b*c-a*d)^3/(a^2*b^2*(a+b*x)^2)-(b*c-a*d)^2*_
(2*b*c+a*d)/(a^3*b^2*(a+b*x))-3*c^2*(b*c-a*d)*log(x)/a^4+_
3*c^2*(b*c-a*d)*log(a+b*x)/a^4
@@ -14861,9 +14772,9 @@ r0:=-c^3/(a^3*x)-1/2*(b*c-a*d)^3/(a^2*b^2*(a+b*x)^2)-(b*c-a*d)^2*_
--R 4 4 3 5 3 2 6 2
--R 2a b x + 4a b x + 2a b x
--R Type: Expression(Integer)
---E 745
+--E 745
---S 746 of 1092
+--S 746 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -14893,27 +14804,27 @@ a0:=integrate(t0,x)
--R 4 4 3 5 3 2 6 2
--R 2a b x + 4a b x + 2a b x
--R Type: Union(Expression(Integer),...)
---E 746
+--E 746
---S 747 of 1092
+--S 747 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 747
+--E 747
---S 748 of 1092
+--S 748 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 748
+--E 748
)clear all
---S 749 of 1092
+--S 749 of 1092
t0:=(c+d*x)^3/(x^3*(a+b*x)^3)
--R
--R
@@ -14923,9 +14834,9 @@ t0:=(c+d*x)^3/(x^3*(a+b*x)^3)
--R 3 6 2 5 2 4 3 3
--R b x + 3a b x + 3a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 749
+--E 749
---S 750 of 1092
+--S 750 of 1092
r0:=-1/2*c^3/(a^3*x^2)+3*c^2*(b*c-a*d)/(a^4*x)+1/2*(b*c-a*d)^3/_
(a^3*b*(a+b*x)^2)+3*c*(b*c-a*d)^2/(a^4*(a+b*x))+3*c*(b*c-a*d)*_
(2*b*c-a*d)*log(x)/a^5-3*c*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5
@@ -14966,9 +14877,9 @@ r0:=-1/2*c^3/(a^3*x^2)+3*c^2*(b*c-a*d)/(a^4*x)+1/2*(b*c-a*d)^3/_
--R 5 3 4 6 2 3 7 2
--R 2a b x + 4a b x + 2a b x
--R Type: Expression(Integer)
---E 750
+--E 750
---S 751 of 1092
+--S 751 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -15007,27 +14918,27 @@ a0:=integrate(t0,x)
--R 5 3 4 6 2 3 7 2
--R 2a b x + 4a b x + 2a b x
--R Type: Union(Expression(Integer),...)
---E 751
+--E 751
---S 752 of 1092
+--S 752 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 752
+--E 752
---S 753 of 1092
+--S 753 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 753
+--E 753
)clear all
---S 754 of 1092
+--S 754 of 1092
t0:=(c+d*x)^3/(x^4*(a+b*x)^3)
--R
--R
@@ -15037,9 +14948,9 @@ t0:=(c+d*x)^3/(x^4*(a+b*x)^3)
--R 3 7 2 6 2 5 3 4
--R b x + 3a b x + 3a b x + a x
--R Type: Fraction(Polynomial(Integer))
---E 754
+--E 754
---S 755 of 1092
+--S 755 of 1092
r0:=-1/3*c^3/(a^3*x^3)+3/2*c^2*(b*c-a*d)/(a^4*x^2)-3*c*(b*c-a*d)*_
(2*b*c-a*d)/(a^5*x)-1/2*(b*c-a*d)^3/(a^4*(a+b*x)^2)-(b*c-a*d)^2*_
(4*b*c-a*d)/(a^5*(a+b*x))-(b*c-a*d)*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_
@@ -15081,9 +14992,9 @@ r0:=-1/3*c^3/(a^3*x^3)+3/2*c^2*(b*c-a*d)/(a^4*x^2)-3*c*(b*c-a*d)*_
--R 6 2 5 7 4 8 3
--R 6a b x + 12a b x + 6a x
--R Type: Expression(Integer)
---E 755
+--E 755
---S 756 of 1092
+--S 756 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -15122,27 +15033,27 @@ a0:=integrate(t0,x)
--R 6 2 5 7 4 8 3
--R 6a b x + 12a b x + 6a x
--R Type: Union(Expression(Integer),...)
---E 756
+--E 756
---S 757 of 1092
+--S 757 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 757
+--E 757
---S 758 of 1092
+--S 758 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 758
+--E 758
)clear all
---S 759 of 1092
+--S 759 of 1092
t0:=x^7/((a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -15159,9 +15070,9 @@ t0:=x^7/((a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 3 3
--R (3a c d + 3a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 759
+--E 759
---S 760 of 1092
+--S 760 of 1092
r0:=-3*(b*c+a*d)*x/(b^4*d^4)+1/2*x^2/(b^3*d^3)+1/2*a^7/(b^5*(b*c-a*d)^3*_
(a+b*x)^2)-a^6*(7*b*c-4*a*d)/(b^5*(b*c-a*d)^4*(a+b*x))-1/2*c^7/_
(d^5*(b*c-a*d)^3*(c+d*x)^2)+c^6*(4*b*c-7*a*d)/(d^5*(b*c-a*d)^4*(c+d*x))-_
@@ -15292,9 +15203,9 @@ r0:=-3*(b*c+a*d)*x/(b^4*d^4)+1/2*x^2/(b^3*d^3)+1/2*a^7/(b^5*(b*c-a*d)^3*_
--R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Expression(Integer)
---E 760
+--E 760
---S 761 of 1092
+--S 761 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -15421,27 +15332,27 @@ a0:=integrate(t0,x)
--R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Union(Expression(Integer),...)
---E 761
+--E 761
---S 762 of 1092
+--S 762 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 762
+--E 762
---S 763 of 1092
+--S 763 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 763
+--E 763
)clear all
---S 764 of 1092
+--S 764 of 1092
t0:=x^6/((a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -15458,9 +15369,9 @@ t0:=x^6/((a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 3 3
--R (3a c d + 3a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 764
+--E 764
---S 765 of 1092
+--S 765 of 1092
r0:=x/(b^3*d^3)-1/2*a^6/(b^4*(b*c-a*d)^3*(a+b*x)^2)+3*a^5*(2*b*c-a*d)/_
(b^4*(b*c-a*d)^4*(a+b*x))+1/2*c^6/(d^4*(b*c-a*d)^3*(c+d*x)^2)-_
3*c^5*(b*c-2*a*d)/(d^4*(b*c-a*d)^4*(c+d*x))+3*a^4*(5*b^2*c^2-_
@@ -15576,9 +15487,9 @@ r0:=x/(b^3*d^3)-1/2*a^6/(b^4*(b*c-a*d)^3*(a+b*x)^2)+3*a^5*(2*b*c-a*d)/_
--R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Expression(Integer)
---E 765
+--E 765
---S 766 of 1092
+--S 766 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -15690,27 +15601,27 @@ a0:=integrate(t0,x)
--R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Union(Expression(Integer),...)
---E 766
+--E 766
---S 767 of 1092
+--S 767 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 767
+--E 767
---S 768 of 1092
+--S 768 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 768
+--E 768
)clear all
---S 769 of 1092
+--S 769 of 1092
t0:=x^5/((a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -15727,9 +15638,9 @@ t0:=x^5/((a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 3 3
--R (3a c d + 3a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 769
+--E 769
---S 770 of 1092
+--S 770 of 1092
r0:=1/2*a^5/(b^3*(b*c-a*d)^3*(a+b*x)^2)-a^4*(5*b*c-2*a*d)/_
(b^3*(b*c-a*d)^4*(a+b*x))-1/2*c^5/(d^3*(b*c-a*d)^3*(c+d*x)^2)+_
c^4*(2*b*c-5*a*d)/(d^3*(b*c-a*d)^4*(c+d*x))-a^3*(10*b^2*c^2-_
@@ -15828,9 +15739,9 @@ r0:=1/2*a^5/(b^3*(b*c-a*d)^3*(a+b*x)^2)-a^4*(5*b*c-2*a*d)/_
--R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Expression(Integer)
---E 770
+--E 770
---S 771 of 1092
+--S 771 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -15925,27 +15836,27 @@ a0:=integrate(t0,x)
--R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Union(Expression(Integer),...)
---E 771
+--E 771
---S 772 of 1092
+--S 772 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 772
+--E 772
---S 773 of 1092
+--S 773 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 773
+--E 773
)clear all
---S 774 of 1092
+--S 774 of 1092
t0:=x^4/((a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -15962,9 +15873,9 @@ t0:=x^4/((a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 3 3
--R (3a c d + 3a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 774
+--E 774
---S 775 of 1092
+--S 775 of 1092
r0:=-1/2*a^4/(b^2*(b*c-a*d)^3*(a+b*x)^2)+a^3*(4*b*c-a*d)/(b^2*(b*c-a*d)^4*_
(a+b*x))+1/2*c^4/(d^2*(b*c-a*d)^3*(c+d*x)^2)-c^3*(b*c-4*a*d)/_
(d^2*(b*c-a*d)^4*(c+d*x))+6*a^2*c^2*log(a+b*x)/(b*c-a*d)^5-_
@@ -16032,9 +15943,9 @@ r0:=-1/2*a^4/(b^2*(b*c-a*d)^3*(a+b*x)^2)+a^3*(4*b*c-a*d)/(b^2*(b*c-a*d)^4*_
--R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Expression(Integer)
---E 775
+--E 775
---S 776 of 1092
+--S 776 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -16099,27 +16010,27 @@ a0:=integrate(t0,x)
--R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Union(Expression(Integer),...)
---E 776
+--E 776
---S 777 of 1092
+--S 777 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 777
+--E 777
---S 778 of 1092
+--S 778 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 778
+--E 778
)clear all
---S 779 of 1092
+--S 779 of 1092
t0:=x^3/((a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -16136,9 +16047,9 @@ t0:=x^3/((a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 3 3
--R (3a c d + 3a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 779
+--E 779
---S 780 of 1092
+--S 780 of 1092
r0:=1/2*a^3/(b*(b*c-a*d)^3*(a+b*x)^2)-3*a^2*c/((b*c-a*d)^4*(a+b*x))-_
1/2*c^3/(d*(b*c-a*d)^3*(c+d*x)^2)-3*a*c^2/((b*c-a*d)^4*(c+d*x))-_
3*a*c*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*a*c*(b*c+a*d)*log(c+d*x)/_
@@ -16209,9 +16120,9 @@ r0:=1/2*a^3/(b*(b*c-a*d)^3*(a+b*x)^2)-3*a^2*c/((b*c-a*d)^4*(a+b*x))-_
--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Expression(Integer)
---E 780
+--E 780
---S 781 of 1092
+--S 781 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -16279,27 +16190,27 @@ a0:=integrate(t0,x)
--R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7
--R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d
--R Type: Union(Expression(Integer),...)
---E 781
+--E 781
---S 782 of 1092
+--S 782 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 782
+--E 782
---S 783 of 1092
+--S 783 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 783
+--E 783
)clear all
---S 784 of 1092
+--S 784 of 1092
t0:=x^2/((a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -16316,9 +16227,9 @@ t0:=x^2/((a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 3 3
--R (3a c d + 3a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 784
+--E 784
---S 785 of 1092
+--S 785 of 1092
r0:=-1/2*a^2/((b*c-a*d)^3*(a+b*x)^2)+a*(2*b*c+a*d)/((b*c-a*d)^4*(a+b*x))+_
1/2*c^2/((b*c-a*d)^3*(c+d*x)^2)+c*(b*c+2*a*d)/((b*c-a*d)^4*(c+d*x))+_
(b^2*c^2+4*a*b*c*d+a^2*d^2)*log(a+b*x)/(b*c-a*d)^5-(b^2*c^2+4*a*b*c*d+_
@@ -16390,9 +16301,9 @@ r0:=-1/2*a^2/((b*c-a*d)^3*(a+b*x)^2)+a*(2*b*c+a*d)/((b*c-a*d)^4*(a+b*x))+_
--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7
--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c
--R Type: Expression(Integer)
---E 785
+--E 785
---S 786 of 1092
+--S 786 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -16461,27 +16372,27 @@ a0:=integrate(t0,x)
--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7
--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c
--R Type: Union(Expression(Integer),...)
---E 786
+--E 786
---S 787 of 1092
+--S 787 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 787
+--E 787
---S 788 of 1092
+--S 788 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 788
+--E 788
)clear all
---S 789 of 1092
+--S 789 of 1092
t0:=x/((a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -16497,9 +16408,9 @@ t0:=x/((a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 3 3
--R (3a c d + 3a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 789
+--E 789
---S 790 of 1092
+--S 790 of 1092
r0:=1/2*a*b/((b*c-a*d)^3*(a+b*x)^2)-b*(b*c+2*a*d)/((b*c-a*d)^4*(a+b*x))-_
1/2*c*d/((b*c-a*d)^3*(c+d*x)^2)-d*(2*b*c+a*d)/((b*c-a*d)^4*(c+d*x))-_
3*b*d*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*b*d*(b*c+a*d)*_
@@ -16559,9 +16470,9 @@ r0:=1/2*a*b/((b*c-a*d)^3*(a+b*x)^2)-b*(b*c+2*a*d)/((b*c-a*d)^4*(a+b*x))-_
--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7
--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c
--R Type: Expression(Integer)
---E 790
+--E 790
---S 791 of 1092
+--S 791 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -16618,27 +16529,27 @@ a0:=integrate(t0,x)
--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7
--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c
--R Type: Union(Expression(Integer),...)
---E 791
+--E 791
---S 792 of 1092
+--S 792 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 792
+--E 792
---S 793 of 1092
+--S 793 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 793
+--E 793
)clear all
---S 794 of 1092
+--S 794 of 1092
t0:=1/((a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -16654,9 +16565,9 @@ t0:=1/((a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 3 3
--R (3a c d + 3a b c )x + a c
--R Type: Fraction(Polynomial(Integer))
---E 794
+--E 794
---S 795 of 1092
+--S 795 of 1092
r0:=-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+_
1/2*d^2/((b*c-a*d)^3*(c+d*x)^2)+3*b*d^2/((b*c-a*d)^4*(c+d*x))+_
6*b^2*d^2*log(a+b*x)/(b*c-a*d)^5-6*b^2*d^2*log(c+d*x)/(b*c-a*d)^5
@@ -16715,9 +16626,9 @@ r0:=-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+_
--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7
--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c
--R Type: Expression(Integer)
---E 795
+--E 795
---S 796 of 1092
+--S 796 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -16774,27 +16685,27 @@ a0:=integrate(t0,x)
--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7
--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c
--R Type: Union(Expression(Integer),...)
---E 796
+--E 796
---S 797 of 1092
+--S 797 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 797
+--E 797
---S 798 of 1092
+--S 798 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 798
+--E 798
)clear all
---S 799 of 1092
+--S 799 of 1092
t0:=1/(x*(a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -16810,9 +16721,9 @@ t0:=1/(x*(a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 2 3 3
--R (3a c d + 3a b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 799
+--E 799
---S 800 of 1092
+--S 800 of 1092
r0:=1/2*b^3/(a*(b*c-a*d)^3*(a+b*x)^2)+b^3*(b*c-4*a*d)/(a^2*(b*c-a*d)^4*_
(a+b*x))-1/2*d^3/(c*(b*c-a*d)^3*(c+d*x)^2)-d^3*(4*b*c-a*d)/_
(c^2*(b*c-a*d)^4*(c+d*x))+log(x)/(a^3*c^3)-b^3*(b^2*c^2-_
@@ -16946,9 +16857,9 @@ r0:=1/2*b^3/(a*(b*c-a*d)^3*(a+b*x)^2)+b^3*(b*c-4*a*d)/(a^2*(b*c-a*d)^4*_
--R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10
--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c
--R Type: Expression(Integer)
---E 800
+--E 800
---S 801 of 1092
+--S 801 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -17078,27 +16989,27 @@ a0:=integrate(t0,x)
--R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10
--R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c
--R Type: Union(Expression(Integer),...)
---E 801
+--E 801
---S 802 of 1092
+--S 802 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 802
+--E 802
---S 803 of 1092
+--S 803 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 803
+--E 803
)clear all
---S 804 of 1092
+--S 804 of 1092
t0:=1/(x^2*(a+b*x)^3*(c+d*x)^3)
--R
--R
@@ -17114,9 +17025,9 @@ t0:=1/(x^2*(a+b*x)^3*(c+d*x)^3)
--R 3 2 2 3 3 3 3 2
--R (3a c d + 3a b c )x + a c x
--R Type: Fraction(Polynomial(Integer))
---E 804
+--E 804
---S 805 of 1092
+--S 805 of 1092
r0:=(-1)/(a^3*c^3*x)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x)^2)-b^4*(2*b*c-5*a*d)/_
(a^3*(b*c-a*d)^4*(a+b*x))+1/2*d^4/(c^2*(b*c-a*d)^3*_
(c+d*x)^2)+d^4*(5*b*c-2*a*d)/(c^3*(b*c-a*d)^4*(c+d*x))-_
@@ -17278,9 +17189,9 @@ r0:=(-1)/(a^3*c^3*x)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x)^2)-b^4*(2*b*c-5*a*d)/_
--R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11
--R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x
--R Type: Expression(Integer)
---E 805
+--E 805
---S 806 of 1092
+--S 806 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -17437,27 +17348,27 @@ a0:=integrate(t0,x)
--R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11
--R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x
--R Type: Union(Expression(Integer),...)
---E 806
+--E 806
---S 807 of 1092
+--S 807 of 1092
m0:=a0-r0
--R
--R
--R (4) 0
--R Type: Expression(Integer)
---E 807
+--E 807
---S 808 of 1092
+--S 808 of 1092
d0:=D(m0,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 808
+--E 808
)clear all
---S 809 of 1092
+--S 809 of 1092
t0:=(a+b*x)^2/(x^2*sqrt(c+d*x))
--R
--R
@@ -17467,9 +17378,9 @@ t0:=(a+b*x)^2/(x^2*sqrt(c+d*x))
--R 2 +-------+
--R x \|d x + c
--R Type: Expression(Integer)
---E 809
+--E 809
---S 810 of 1092
+--S 810 of 1092
r0:=-a*(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/c^(3/2)+2*b^2*sqrt(c+d*x)/d-_
a^2*sqrt(c+d*x)/(c*x)
--R
@@ -17483,9 +17394,9 @@ r0:=-a*(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/c^(3/2)+2*b^2*sqrt(c+d*x)/d-_
--R +-+
--R c d x\|c
--R Type: Expression(Integer)
---E 810
+--E 810
---S 811 of 1092
+--S 811 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -17510,9 +17421,9 @@ a0:=integrate(t0,x)
--R +---+
--R c d x\|- c
--R Type: Union(List(Expression(Integer)),...)
---E 811
+--E 811
---S 812 of 1092
+--S 812 of 1092
m0a:=a0.1-r0
--R
--R
@@ -17531,17 +17442,17 @@ m0a:=a0.1-r0
--R +-+
--R 2c\|c
--R Type: Expression(Integer)
---E 812
+--E 812
---S 813 of 1092
+--S 813 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 813
+--E 813
---S 814 of 1092
+--S 814 of 1092
m0b:=a0.2-r0
--R
--R
@@ -17560,19 +17471,19 @@ m0b:=a0.2-r0
--R +---+ +-+
--R c\|- c \|c
--R Type: Expression(Integer)
---E 814
+--E 814
---S 815 of 1092
+--S 815 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 815
+--E 815
)clear all
---S 816 of 1092
+--S 816 of 1092
t0:=(c+d*x)^(3/2)/(x^2*(a+b*x)^2)
--R
--R
@@ -17582,9 +17493,9 @@ t0:=(c+d*x)^(3/2)/(x^2*(a+b*x)^2)
--R 2 4 3 2 2
--R b x + 2a b x + a x
--R Type: Expression(Integer)
---E 816
+--E 816
---S 817 of 1092
+--S 817 of 1092
r0:=-(c+d*x)^(3/2)/(a*x*(a+b*x))+(4*b*c-3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))*_
sqrt(c)/a^3-(4*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_
sqrt(b*c-a*d)/(a^3*sqrt(b))-2*(b*c-a*d)*sqrt(c+d*x)/(a^2*(a+b*x))
@@ -17609,9 +17520,9 @@ r0:=-(c+d*x)^(3/2)/(a*x*(a+b*x))+(4*b*c-3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))*_
--R 3 2 4 +-+
--R (a b x + a x)\|b
--R Type: Expression(Integer)
---E 817
+--E 817
---S 818 of 1092
+--S 818 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -17713,9 +17624,9 @@ a0:=integrate(t0,x)
--R a b x + a x
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 818
+--E 818
---S 819 of 1092
+--S 819 of 1092
m0a:=a0.1-r0
--R
--R
@@ -17752,17 +17663,17 @@ m0a:=a0.1-r0
--R 3 +-+
--R 2a \|b
--R Type: Expression(Integer)
---E 819
+--E 819
---S 820 of 1092
+--S 820 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 820
+--E 820
---S 821 of 1092
+--S 821 of 1092
m0b:=a0.2-r0
--R
--R
@@ -17795,19 +17706,19 @@ m0b:=a0.2-r0
--R 3 +-+
--R 2a \|b
--R Type: Expression(Integer)
---E 821
+--E 821
---S 822 of 1092
+--S 822 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 822
+--E 822
)clear all
---S 823 of 1092
+--S 823 of 1092
t0:=(c+d*x)^(1/2)/(x^2*(a+b*x)^2)
--R
--R
@@ -17817,9 +17728,9 @@ t0:=(c+d*x)^(1/2)/(x^2*(a+b*x)^2)
--R 2 4 3 2 2
--R b x + 2a b x + a x
--R Type: Expression(Integer)
---E 823
+--E 823
---S 824 of 1092
+--S 824 of 1092
r0:=(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*sqrt(c))-(4*b*c-3*a*d)*_
atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(a^3*sqrt(b*c-a*d))-_
2*b*sqrt(c+d*x)/(a^2*(a+b*x))-sqrt(c+d*x)/(a*x*(a+b*x))
@@ -17844,9 +17755,9 @@ r0:=(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*sqrt(c))-(4*b*c-3*a*d)*_
--R 3 2 4 +-----------+ +-+
--R (a b x + a x)\|- a d + b c \|c
--R Type: Expression(Integer)
---E 824
+--E 824
---S 825 of 1092
+--S 825 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -17956,9 +17867,9 @@ a0:=integrate(t0,x)
--R (a b x + a x)\|- c
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 825
+--E 825
---S 826 of 1092
+--S 826 of 1092
m0a:=a0.1-r0
--R
--R
@@ -17995,17 +17906,17 @@ m0a:=a0.1-r0
--R 3 +-----------+ +-+
--R 2a \|- a d + b c \|c
--R Type: Expression(Integer)
---E 826
+--E 826
---S 827 of 1092
+--S 827 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 827
+--E 827
---S 828 of 1092
+--S 828 of 1092
m0b:=a0.2-r0
--R
--R
@@ -18038,19 +17949,19 @@ m0b:=a0.2-r0
--R 3 +-----------+ +-+
--R 2a \|- a d + b c \|c
--R Type: Expression(Integer)
---E 828
+--E 828
---S 829 of 1092
+--S 829 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 829
+--E 829
)clear all
---S 830 of 1092
+--S 830 of 1092
t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(1/2))
--R
--R
@@ -18059,9 +17970,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(1/2))
--R 2 4 3 2 2 +-------+
--R (b x + 2a b x + a x )\|d x + c
--R Type: Expression(Integer)
---E 830
+--E 830
---S 831 of 1092
+--S 831 of 1092
r0:=(4*b*c+a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(3/2))-b^(3/2)*_
(4*b*c-5*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*_
(b*c-a*d)^(3/2))-b*(2*b*c-a*d)*sqrt(c+d*x)/(a^2*c*(b*c-a*d)*(a+b*x))-_
@@ -18093,9 +18004,9 @@ r0:=(4*b*c+a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(3/2))-b^(3/2)*_
--R 4 3 2 2 2 5 4 2 +-----------+ +-+
--R ((a b c d - a b c )x + (a c d - a b c )x)\|- a d + b c \|c
--R Type: Expression(Integer)
---E 831
+--E 831
---S 832 of 1092
+--S 832 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -18211,9 +18122,9 @@ a0:=integrate(t0,x)
--R ((a b c d - a b c )x + (a c d - a b c )x)\|- c
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 832
+--E 832
---S 833 of 1092
+--S 833 of 1092
m0a:=a0.1-r0
--R
--R
@@ -18250,17 +18161,17 @@ m0a:=a0.1-r0
--R 4 3 2 +-----------+ +-+
--R (2a c d - 2a b c )\|- a d + b c \|c
--R Type: Expression(Integer)
---E 833
+--E 833
---S 834 of 1092
+--S 834 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 834
+--E 834
---S 835 of 1092
+--S 835 of 1092
m0b:=a0.2-r0
--R
--R
@@ -18298,19 +18209,19 @@ m0b:=a0.2-r0
--R 4 3 2 +-----------+ +-+
--R (2a c d - 2a b c )\|- a d + b c \|c
--R Type: Expression(Integer)
---E 835
+--E 835
---S 836 of 1092
+--S 836 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 836
+--E 836
)clear all
---S 837 of 1092
+--S 837 of 1092
t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(3/2))
--R
--R
@@ -18319,9 +18230,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(3/2))
--R 2 5 2 4 2 3 2 2 +-------+
--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c
--R Type: Expression(Integer)
---E 837
+--E 837
---S 838 of 1092
+--S 838 of 1092
r0:=(4*b*c+3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(5/2))-b^(5/2)*_
(4*b*c-7*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_
(a^3*(b*c-a*d)^(5/2))-d*(2*b^2*c^2-2*a*b*c*d+3*a^2*d^2)/_
@@ -18366,9 +18277,9 @@ r0:=(4*b*c+3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(5/2))-b^(5/2)*_
--R +-----------+ +-+ +-------+
--R \|- a d + b c \|c \|d x + c
--R Type: Expression(Integer)
---E 838
+--E 838
---S 839 of 1092
+--S 839 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -18550,9 +18461,9 @@ a0:=integrate(t0,x)
--R \|- c \|d x + c
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 839
+--E 839
---S 840 of 1092
+--S 840 of 1092
m0a:=a0.1-r0
--R
--R
@@ -18592,17 +18503,17 @@ m0a:=a0.1-r0
--R 5 2 2 4 3 3 2 4 +-----------+ +-+
--R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c
--R Type: Expression(Integer)
---E 840
+--E 840
---S 841 of 1092
+--S 841 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 841
+--E 841
---S 842 of 1092
+--S 842 of 1092
m0b:=a0.2-r0
--R
--R
@@ -18643,19 +18554,19 @@ m0b:=a0.2-r0
--R 5 2 2 4 3 3 2 4 +-----------+ +-+
--R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c
--R Type: Expression(Integer)
---E 842
+--E 842
---S 843 of 1092
+--S 843 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 843
+--E 843
)clear all
---S 844 of 1092
+--S 844 of 1092
t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(5/2))
--R
--R
@@ -18671,9 +18582,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(5/2))
--R +-------+
--R \|d x + c
--R Type: Expression(Integer)
---E 844
+--E 844
---S 845 of 1092
+--S 845 of 1092
r0:=-1/3*d*(6*b^2*c^2-6*a*b*c*d+5*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*_
(c+d*x)^(3/2))-b*(2*b*c-a*d)/(a^2*c*(b*c-a*d)*(a+b*x)*(c+d*x)^(3/2))+_
(-1)/(a*c*x*(a+b*x)*(c+d*x)^(3/2))+(4*b*c+5*a*d)*atanh(sqrt(c+d*x)/_
@@ -18737,9 +18648,9 @@ r0:=-1/3*d*(6*b^2*c^2-6*a*b*c*d+5*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*_
--R +-----------+ +-+ +-------+
--R \|- a d + b c \|c \|d x + c
--R Type: Expression(Integer)
---E 845
+--E 845
---S 846 of 1092
+--S 846 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -19001,9 +18912,9 @@ a0:=integrate(t0,x)
--R \|- c \|d x + c
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 846
+--E 846
---S 847 of 1092
+--S 847 of 1092
m0a:=a0.1-r0
--R
--R
@@ -19046,17 +18957,17 @@ m0a:=a0.1-r0
--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+
--R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c
--R Type: Expression(Integer)
---E 847
+--E 847
---S 848 of 1092
+--S 848 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 848
+--E 848
---S 849 of 1092
+--S 849 of 1092
m0b:=a0.2-r0
--R
--R
@@ -19100,19 +19011,19 @@ m0b:=a0.2-r0
--R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+
--R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c
--R Type: Expression(Integer)
---E 849
+--E 849
---S 850 of 1092
+--S 850 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 850
+--E 850
)clear all
---S 851 of 1092
+--S 851 of 1092
t0:=x^3*(c+d*x)^(5/2)/(a+b*x)
--R
--R
@@ -19121,9 +19032,9 @@ t0:=x^3*(c+d*x)^(5/2)/(a+b*x)
--R (1) ---------------------------------
--R b x + a
--R Type: Expression(Integer)
---E 851
+--E 851
---S 852 of 1092
+--S 852 of 1092
r0:=-2/3*a^3*(b*c-a*d)*(c+d*x)^(3/2)/b^5+2/3465*(40*b^3*c^3+110*a*b^2*c^2*d+_
495*a^2*b*c*d^2-693*a^3*d^3)*(c+d*x)^(5/2)/(b^4*d^3)-2/693*_
(20*b^2*c^2+55*a*b*c*d-99*a^2*d^2)*x*(c+d*x)^(5/2)/(b^3*d^2)+_
@@ -19166,9 +19077,9 @@ r0:=-2/3*a^3*(b*c-a*d)*(c+d*x)^(3/2)/b^5+2/3465*(40*b^3*c^3+110*a*b^2*c^2*d+_
--R 6 3 +-+
--R 3465b d \|b
--R Type: Expression(Integer)
---E 852
+--E 852
---S 853 of 1092
+--S 853 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -19244,9 +19155,9 @@ a0:=integrate(t0,x)
--R 3465b d
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 853
+--E 853
---S 854 of 1092
+--S 854 of 1092
m0a:=a0.1-r0
--R
--R
@@ -19272,17 +19183,17 @@ m0a:=a0.1-r0
--R 6 +-+
--R b \|b
--R Type: Expression(Integer)
---E 854
+--E 854
---S 855 of 1092
+--S 855 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 855
+--E 855
---S 856 of 1092
+--S 856 of 1092
m0b:=a0.2-r0
--R
--R
@@ -19304,19 +19215,19 @@ m0b:=a0.2-r0
--R 6 +-+
--R b \|b
--R Type: Expression(Integer)
---E 856
+--E 856
---S 857 of 1092
+--S 857 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 857
+--E 857
)clear all
---S 858 of 1092
+--S 858 of 1092
t0:=x^2*(c+d*x)^(5/2)/(a+b*x)
--R
--R
@@ -19325,9 +19236,9 @@ t0:=x^2*(c+d*x)^(5/2)/(a+b*x)
--R (1) ---------------------------------
--R b x + a
--R Type: Expression(Integer)
---E 858
+--E 858
---S 859 of 1092
+--S 859 of 1092
r0:=2/3*a^2*(b*c-a*d)*(c+d*x)^(3/2)/b^4+2/5*a^2*(c+d*x)^(5/2)/b^3-_
2/63*(2*b*c+9*a*d)*(c+d*x)^(7/2)/(b^2*d^2)+2/9*x*(c+d*x)^(7/2)/(b*d)-_
2*a^2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/_
@@ -19362,9 +19273,9 @@ r0:=2/3*a^2*(b*c-a*d)*(c+d*x)^(3/2)/b^4+2/5*a^2*(c+d*x)^(5/2)/b^3-_
--R 5 2 +-+
--R 315b d \|b
--R Type: Expression(Integer)
---E 859
+--E 859
---S 860 of 1092
+--S 860 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -19428,9 +19339,9 @@ a0:=integrate(t0,x)
--R 315b d
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 860
+--E 860
---S 861 of 1092
+--S 861 of 1092
m0a:=a0.1-r0
--R
--R
@@ -19456,17 +19367,17 @@ m0a:=a0.1-r0
--R 5 +-+
--R b \|b
--R Type: Expression(Integer)
---E 861
+--E 861
---S 862 of 1092
+--S 862 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 862
+--E 862
---S 863 of 1092
+--S 863 of 1092
m0b:=a0.2-r0
--R
--R
@@ -19488,19 +19399,19 @@ m0b:=a0.2-r0
--R 5 +-+
--R b \|b
--R Type: Expression(Integer)
---E 863
+--E 863
---S 864 of 1092
+--S 864 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 864
+--E 864
)clear all
---S 865 of 1092
+--S 865 of 1092
t0:=x*(c+d*x)^(5/2)/(a+b*x)
--R
--R
@@ -19509,9 +19420,9 @@ t0:=x*(c+d*x)^(5/2)/(a+b*x)
--R (1) --------------------------------
--R b x + a
--R Type: Expression(Integer)
---E 865
+--E 865
---S 866 of 1092
+--S 866 of 1092
r0:=-2/3*a*(b*c-a*d)*(c+d*x)^(3/2)/b^3-2/5*a*(c+d*x)^(5/2)/b^2+_
2/7*(c+d*x)^(7/2)/(b*d)+2*a*(b*c-a*d)^(5/2)*atanh(sqrt(b)*_
sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)-2*a*(b*c-a*d)^2*sqrt(c+d*x)/b^4
@@ -19539,9 +19450,9 @@ r0:=-2/3*a*(b*c-a*d)*(c+d*x)^(3/2)/b^3-2/5*a*(c+d*x)^(5/2)/b^2+_
--R 4 +-+
--R 105b d\|b
--R Type: Expression(Integer)
---E 866
+--E 866
---S 867 of 1092
+--S 867 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -19599,9 +19510,9 @@ a0:=integrate(t0,x)
--R 105b d
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 867
+--E 867
---S 868 of 1092
+--S 868 of 1092
m0a:=a0.1-r0
--R
--R
@@ -19627,17 +19538,17 @@ m0a:=a0.1-r0
--R 4 +-+
--R b \|b
--R Type: Expression(Integer)
---E 868
+--E 868
---S 869 of 1092
+--S 869 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 869
+--E 869
---S 870 of 1092
+--S 870 of 1092
m0b:=a0.2-r0
--R
--R
@@ -19659,19 +19570,19 @@ m0b:=a0.2-r0
--R 4 +-+
--R b \|b
--R Type: Expression(Integer)
---E 870
+--E 870
---S 871 of 1092
+--S 871 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 871
+--E 871
)clear all
---S 872 of 1092
+--S 872 of 1092
t0:=(c+d*x)^(5/2)/(a+b*x)
--R
--R
@@ -19680,9 +19591,9 @@ t0:=(c+d*x)^(5/2)/(a+b*x)
--R (1) ------------------------------
--R b x + a
--R Type: Expression(Integer)
---E 872
+--E 872
---S 873 of 1092
+--S 873 of 1092
r0:=2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-2*(b*c-a*d)^(5/2)*_
atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+2*(b*c-a*d)^2*_
sqrt(c+d*x)/b^3
@@ -19704,9 +19615,9 @@ r0:=2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-2*(b*c-a*d)^(5/2)*_
--R 3 +-+
--R 15b \|b
--R Type: Expression(Integer)
---E 873
+--E 873
---S 874 of 1092
+--S 874 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -19752,9 +19663,9 @@ a0:=integrate(t0,x)
--R 15b
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 874
+--E 874
---S 875 of 1092
+--S 875 of 1092
m0a:=a0.1-r0
--R
--R
@@ -19780,17 +19691,17 @@ m0a:=a0.1-r0
--R 3 +-+
--R b \|b
--R Type: Expression(Integer)
---E 875
+--E 875
---S 876 of 1092
+--S 876 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 876
+--E 876
---S 877 of 1092
+--S 877 of 1092
m0b:=a0.2-r0
--R
--R
@@ -19812,19 +19723,19 @@ m0b:=a0.2-r0
--R 3 +-+
--R b \|b
--R Type: Expression(Integer)
---E 877
+--E 877
---S 878 of 1092
+--S 878 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 878
+--E 878
)clear all
---S 879 of 1092
+--S 879 of 1092
t0:=(c+d*x)^(5/2)/(x*(a+b*x))
--R
--R
@@ -19834,9 +19745,9 @@ t0:=(c+d*x)^(5/2)/(x*(a+b*x))
--R 2
--R b x + a x
--R Type: Expression(Integer)
---E 879
+--E 879
---S 880 of 1092
+--S 880 of 1092
r0:=2/3*d*(c+d*x)^(3/2)/b-2*c^(5/2)*atanh(sqrt(c+d*x)/sqrt(c))/a+_
2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_
(a*b^(5/2))+2*d*(2*b*c-a*d)*sqrt(c+d*x)/b^2
@@ -19861,9 +19772,9 @@ r0:=2/3*d*(c+d*x)^(3/2)/b-2*c^(5/2)*atanh(sqrt(c+d*x)/sqrt(c))/a+_
--R 2 +-+
--R 3a b \|b
--R Type: Expression(Integer)
---E 880
+--E 880
---S 881 of 1092
+--S 881 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -19956,9 +19867,9 @@ a0:=integrate(t0,x)
--R 3a b
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 881
+--E 881
---S 882 of 1092
+--S 882 of 1092
m0a:=a0.1-r0
--R
--R
@@ -19995,17 +19906,17 @@ m0a:=a0.1-r0
--R 2 +-+
--R a b \|b
--R Type: Expression(Integer)
---E 882
+--E 882
---S 883 of 1092
+--S 883 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 883
+--E 883
---S 884 of 1092
+--S 884 of 1092
m0b:=a0.2-r0
--R
--R
@@ -20038,19 +19949,19 @@ m0b:=a0.2-r0
--R 2 +-+
--R a b \|b
--R Type: Expression(Integer)
---E 884
+--E 884
---S 885 of 1092
+--S 885 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 885
+--E 885
)clear all
---S 886 of 1092
+--S 886 of 1092
t0:=(c+d*x)^(5/2)/(x^2*(a+b*x))
--R
--R
@@ -20060,9 +19971,9 @@ t0:=(c+d*x)^(5/2)/(x^2*(a+b*x))
--R 3 2
--R b x + a x
--R Type: Expression(Integer)
---E 886
+--E 886
---S 887 of 1092
+--S 887 of 1092
r0:=d*(c+d*x)^(3/2)/a-(c+d*x)^(5/2)/(a*x)+c^(3/2)*(2*b*c-5*a*d)*_
atanh(sqrt(c+d*x)/sqrt(c))/a^2-2*(b*c-a*d)^(5/2)*_
atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(3/2))+_
@@ -20088,9 +19999,9 @@ r0:=d*(c+d*x)^(3/2)/a-(c+d*x)^(5/2)/(a*x)+c^(3/2)*(2*b*c-5*a*d)*_
--R 2 +-+
--R a b x\|b
--R Type: Expression(Integer)
---E 887
+--E 887
---S 888 of 1092
+--S 888 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -20183,9 +20094,9 @@ a0:=integrate(t0,x)
--R a b x
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 888
+--E 888
---S 889 of 1092
+--S 889 of 1092
m0a:=a0.1-r0
--R
--R
@@ -20222,17 +20133,17 @@ m0a:=a0.1-r0
--R 2 +-+
--R 2a b\|b
--R Type: Expression(Integer)
---E 889
+--E 889
---S 890 of 1092
+--S 890 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 890
+--E 890
---S 891 of 1092
+--S 891 of 1092
m0b:=a0.2-r0
--R
--R
@@ -20265,19 +20176,19 @@ m0b:=a0.2-r0
--R 2 +-+
--R 2a b\|b
--R Type: Expression(Integer)
---E 891
+--E 891
---S 892 of 1092
+--S 892 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 892
+--E 892
)clear all
---S 893 of 1092
+--S 893 of 1092
t0:=(c+d*x)^(5/2)/(x^3*(a+b*x))
--R
--R
@@ -20287,9 +20198,9 @@ t0:=(c+d*x)^(5/2)/(x^3*(a+b*x))
--R 4 3
--R b x + a x
--R Type: Expression(Integer)
---E 893
+--E 893
---S 894 of 1092
+--S 894 of 1092
r0:=1/4*(4*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x)-1/2*(c+d*x)^(5/2)/(a*x^2)+_
2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_
(a^3*sqrt(b))-1/4*(8*b^2*c^2-20*a*b*c*d+15*a^2*d^2)*_
@@ -20316,9 +20227,9 @@ r0:=1/4*(4*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x)-1/2*(c+d*x)^(5/2)/(a*x^2)+_
--R 3 2 +-+
--R 4a x \|b
--R Type: Expression(Integer)
---E 894
+--E 894
---S 895 of 1092
+--S 895 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -20414,9 +20325,9 @@ a0:=integrate(t0,x)
--R 4a x
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 895
+--E 895
---S 896 of 1092
+--S 896 of 1092
m0a:=a0.1-r0
--R
--R
@@ -20453,17 +20364,17 @@ m0a:=a0.1-r0
--R 3 +-+
--R 8a \|b
--R Type: Expression(Integer)
---E 896
+--E 896
---S 897 of 1092
+--S 897 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 897
+--E 897
---S 898 of 1092
+--S 898 of 1092
m0b:=a0.2-r0
--R
--R
@@ -20496,19 +20407,19 @@ m0b:=a0.2-r0
--R 3 +-+
--R 8a \|b
--R Type: Expression(Integer)
---E 898
+--E 898
---S 899 of 1092
+--S 899 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 899
+--E 899
)clear all
---S 900 of 1092
+--S 900 of 1092
t0:=(c+d*x)^(5/2)/(x^4*(a+b*x))
--R
--R
@@ -20518,9 +20429,9 @@ t0:=(c+d*x)^(5/2)/(x^4*(a+b*x))
--R 5 4
--R b x + a x
--R Type: Expression(Integer)
---E 900
+--E 900
---S 901 of 1092
+--S 901 of 1092
r0:=1/12*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2)-1/3*(c+d*x)^(5/2)/(a*x^3)-_
2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_
sqrt(b)/a^4+1/8*(16*b^3*c^3-40*a*b^2*c^2*d+30*a^2*b*c*d^2-5*a^3*d^3)*_
@@ -20553,9 +20464,9 @@ r0:=1/12*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2)-1/3*(c+d*x)^(5/2)/(a*x^3)-_
--R 4 3 +-+
--R 24a x \|c
--R Type: Expression(Integer)
---E 901
+--E 901
---S 902 of 1092
+--S 902 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -20681,9 +20592,9 @@ a0:=integrate(t0,x)
--R 24a x \|- c
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 902
+--E 902
---S 903 of 1092
+--S 903 of 1092
m0a:=a0.1-r0
--R
--R
@@ -20721,17 +20632,17 @@ m0a:=a0.1-r0
--R 4 +-+
--R 16a \|c
--R Type: Expression(Integer)
---E 903
+--E 903
---S 904 of 1092
+--S 904 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 904
+--E 904
---S 905 of 1092
+--S 905 of 1092
m0b:=a0.2-r0
--R
--R
@@ -20766,19 +20677,19 @@ m0b:=a0.2-r0
--R 4 +-+
--R 16a \|c
--R Type: Expression(Integer)
---E 905
+--E 905
---S 906 of 1092
+--S 906 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 906
+--E 906
)clear all
---S 907 of 1092
+--S 907 of 1092
t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^2
--R
--R
@@ -20788,9 +20699,9 @@ t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Expression(Integer)
---E 907
+--E 907
---S 908 of 1092
+--S 908 of 1092
r0:=1/3*a^2*(6*b*c-11*a*d)*(c+d*x)^(3/2)/b^5-1/315*(20*b^2*c^2+_
180*a*b*c*d-693*a^2*d^2)*(c+d*x)^(5/2)/(b^4*d^2)+_
1/63*(10*b*c-99*a*d)*x*(c+d*x)^(5/2)/(b^3*d)+11/9*x^2*(c+d*x)^(5/2)/_
@@ -20833,9 +20744,9 @@ r0:=1/3*a^2*(6*b*c-11*a*d)*(c+d*x)^(3/2)/b^5-1/315*(20*b^2*c^2+_
--R 7 2 6 2 +-+
--R (315b d x + 315a b d )\|b
--R Type: Expression(Integer)
---E 908
+--E 908
---S 909 of 1092
+--S 909 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -20912,9 +20823,9 @@ a0:=integrate(t0,x)
--R 315b d x + 315a b d
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 909
+--E 909
---S 910 of 1092
+--S 910 of 1092
m0a:=a0.1-r0
--R
--R
@@ -20940,17 +20851,17 @@ m0a:=a0.1-r0
--R 6 +-+
--R 2b \|b
--R Type: Expression(Integer)
---E 910
+--E 910
---S 911 of 1092
+--S 911 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 911
+--E 911
---S 912 of 1092
+--S 912 of 1092
m0b:=a0.2-r0
--R
--R
@@ -20972,19 +20883,19 @@ m0b:=a0.2-r0
--R 6 +-+
--R b \|b
--R Type: Expression(Integer)
---E 912
+--E 912
---S 913 of 1092
+--S 913 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 913
+--E 913
)clear all
---S 914 of 1092
+--S 914 of 1092
t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^2
--R
--R
@@ -20994,9 +20905,9 @@ t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Expression(Integer)
---E 914
+--E 914
---S 915 of 1092
+--S 915 of 1092
r0:=-1/3*a*(4*b*c-9*a*d)*(c+d*x)^(3/2)/b^4-1/5*a*(4*b*c-9*a*d)*_
(c+d*x)^(5/2)/(b^3*(b*c-a*d))+2/7*(c+d*x)^(7/2)/(b^2*d)-_
a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x))+a*(4*b*c-9*a*d)*_
@@ -21035,9 +20946,9 @@ r0:=-1/3*a*(4*b*c-9*a*d)*(c+d*x)^(3/2)/b^4-1/5*a*(4*b*c-9*a*d)*_
--R 6 5 +-+
--R (105b d x + 105a b d)\|b
--R Type: Expression(Integer)
---E 915
+--E 915
---S 916 of 1092
+--S 916 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -21108,9 +21019,9 @@ a0:=integrate(t0,x)
--R 105b d x + 105a b d
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 916
+--E 916
---S 917 of 1092
+--S 917 of 1092
m0a:=a0.1-r0
--R
--R
@@ -21136,17 +21047,17 @@ m0a:=a0.1-r0
--R 5 +-+
--R 2b \|b
--R Type: Expression(Integer)
---E 917
+--E 917
---S 918 of 1092
+--S 918 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 918
+--E 918
---S 919 of 1092
+--S 919 of 1092
m0b:=a0.2-r0
--R
--R
@@ -21168,19 +21079,19 @@ m0b:=a0.2-r0
--R 5 +-+
--R b \|b
--R Type: Expression(Integer)
---E 919
+--E 919
---S 920 of 1092
+--S 920 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 920
+--E 920
)clear all
---S 921 of 1092
+--S 921 of 1092
t0:=x*(c+d*x)^(5/2)/(a+b*x)^2
--R
--R
@@ -21190,9 +21101,9 @@ t0:=x*(c+d*x)^(5/2)/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Expression(Integer)
---E 921
+--E 921
---S 922 of 1092
+--S 922 of 1092
r0:=1/3*(2*b*c-7*a*d)*(c+d*x)^(3/2)/b^3+1/5*(2*b*c-7*a*d)*(c+d*x)^(5/2)/_
(b^2*(b*c-a*d))+a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x))-(2*b*c-7*a*d)*_
(b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)+_
@@ -21224,9 +21135,9 @@ r0:=1/3*(2*b*c-7*a*d)*(c+d*x)^(3/2)/b^3+1/5*(2*b*c-7*a*d)*(c+d*x)^(5/2)/_
--R 5 4 +-+
--R (15b x + 15a b )\|b
--R Type: Expression(Integer)
---E 922
+--E 922
---S 923 of 1092
+--S 923 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -21285,9 +21196,9 @@ a0:=integrate(t0,x)
--R 15b x + 15a b
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 923
+--E 923
---S 924 of 1092
+--S 924 of 1092
m0a:=a0.1-r0
--R
--R
@@ -21313,17 +21224,17 @@ m0a:=a0.1-r0
--R 4 +-+
--R 2b \|b
--R Type: Expression(Integer)
---E 924
+--E 924
---S 925 of 1092
+--S 925 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 925
+--E 925
---S 926 of 1092
+--S 926 of 1092
m0b:=a0.2-r0
--R
--R
@@ -21345,19 +21256,19 @@ m0b:=a0.2-r0
--R 4 +-+
--R b \|b
--R Type: Expression(Integer)
---E 926
+--E 926
---S 927 of 1092
+--S 927 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 927
+--E 927
)clear all
---S 928 of 1092
+--S 928 of 1092
t0:=(c+d*x)^(5/2)/(a+b*x)^2
--R
--R
@@ -21367,9 +21278,9 @@ t0:=(c+d*x)^(5/2)/(a+b*x)^2
--R 2 2 2
--R b x + 2a b x + a
--R Type: Expression(Integer)
---E 928
+--E 928
---S 929 of 1092
+--S 929 of 1092
r0:=5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-5*d*(b*c-a*d)^(3/2)*_
atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+5*d*(b*c-a*d)*_
sqrt(c+d*x)/b^3
@@ -21394,9 +21305,9 @@ r0:=5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-5*d*(b*c-a*d)^(3/2)*_
--R 4 3 +-+
--R (3b x + 3a b )\|b
--R Type: Expression(Integer)
---E 929
+--E 929
---S 930 of 1092
+--S 930 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -21447,9 +21358,9 @@ a0:=integrate(t0,x)
--R 3b x + 3a b
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 930
+--E 930
---S 931 of 1092
+--S 931 of 1092
m0a:=a0.1-r0
--R
--R
@@ -21475,17 +21386,17 @@ m0a:=a0.1-r0
--R 3 +-+
--R 2b \|b
--R Type: Expression(Integer)
---E 931
+--E 931
---S 932 of 1092
+--S 932 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 932
+--E 932
---S 933 of 1092
+--S 933 of 1092
m0b:=a0.2-r0
--R
--R
@@ -21507,19 +21418,19 @@ m0b:=a0.2-r0
--R 3 +-+
--R b \|b
--R Type: Expression(Integer)
---E 933
+--E 933
---S 934 of 1092
+--S 934 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 934
+--E 934
)clear all
---S 935 of 1092
+--S 935 of 1092
t0:=(c+d*x)^(5/2)/(x*(a+b*x)^2)
--R
--R
@@ -21529,9 +21440,9 @@ t0:=(c+d*x)^(5/2)/(x*(a+b*x)^2)
--R 2 3 2 2
--R b x + 2a b x + a x
--R Type: Expression(Integer)
---E 935
+--E 935
---S 936 of 1092
+--S 936 of 1092
r0:=-d*(c+d*x)^(3/2)/(a*b)+(c+d*x)^(5/2)/(a*(a+b*x))-2*c^(5/2)*_
atanh(sqrt(c+d*x)/sqrt(c))/a^2+(b*c-a*d)^(3/2)*(2*b*c+3*a*d)*_
atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(5/2))-_
@@ -21560,9 +21471,9 @@ r0:=-d*(c+d*x)^(3/2)/(a*b)+(c+d*x)^(5/2)/(a*(a+b*x))-2*c^(5/2)*_
--R 2 3 3 2 +-+
--R (a b x + a b )\|b
--R Type: Expression(Integer)
---E 936
+--E 936
---S 937 of 1092
+--S 937 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -21660,9 +21571,9 @@ a0:=integrate(t0,x)
--R a b x + a b
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 937
+--E 937
---S 938 of 1092
+--S 938 of 1092
m0a:=a0.1-r0
--R
--R
@@ -21699,17 +21610,17 @@ m0a:=a0.1-r0
--R 2 2 +-+
--R 2a b \|b
--R Type: Expression(Integer)
---E 938
+--E 938
---S 939 of 1092
+--S 939 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 939
+--E 939
---S 940 of 1092
+--S 940 of 1092
m0b:=a0.2-r0
--R
--R
@@ -21742,19 +21653,19 @@ m0b:=a0.2-r0
--R 2 2 +-+
--R a b \|b
--R Type: Expression(Integer)
---E 940
+--E 940
---S 941 of 1092
+--S 941 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 941
+--E 941
)clear all
---S 942 of 1092
+--S 942 of 1092
t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^2)
--R
--R
@@ -21764,9 +21675,9 @@ t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^2)
--R 2 4 3 2 2
--R b x + 2a b x + a x
--R Type: Expression(Integer)
---E 942
+--E 942
---S 943 of 1092
+--S 943 of 1092
r0a:=c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_
(4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))-_
c^2*sqrt(c+d*x)/(a^2*x)-(b*c-a*d)^2*sqrt(c+d*x)/(a^2*b*(a+b*x))
@@ -21797,9 +21708,9 @@ r0a:=c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_
--R 3 2 2 4 +-+
--R (a b x + a b x)\|b
--R Type: Expression(Integer)
---E 943
+--E 943
---S 944 of 1092
+--S 944 of 1092
r0b:=-2*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x))-(c+d*x)^(5/2)/(a*x*(a+b*x))+_
c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_
(4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))+_
@@ -21831,9 +21742,9 @@ r0b:=-2*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x))-(c+d*x)^(5/2)/(a*x*(a+b*x))+_
--R 3 2 2 4 +-+
--R (a b x + a b x)\|b
--R Type: Expression(Integer)
---E 944
+--E 944
---S 945 of 1092
+--S 945 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -21943,9 +21854,9 @@ a0:=integrate(t0,x)
--R a b x + a b x
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 945
+--E 945
---S 946 of 1092
+--S 946 of 1092
m0a:=a0.1-r0a
--R
--R
@@ -21982,17 +21893,17 @@ m0a:=a0.1-r0a
--R 3 +-+
--R 2a b\|b
--R Type: Expression(Integer)
---E 946
+--E 946
---S 947 of 1092
+--S 947 of 1092
d0a:=D(m0a,x)
--R
--R
--R (6) 0
--R Type: Expression(Integer)
---E 947
+--E 947
---S 948 of 1092
+--S 948 of 1092
m0b:=a0.1-r0b
--R
--R
@@ -22029,17 +21940,17 @@ m0b:=a0.1-r0b
--R 3 +-+
--R 2a b\|b
--R Type: Expression(Integer)
---E 948
+--E 948
---S 949 of 1092
+--S 949 of 1092
d0b:=D(m0b,x)
--R
--R
--R (8) 0
--R Type: Expression(Integer)
---E 949
+--E 949
---S 950 of 1092
+--S 950 of 1092
m0c:=a0.2-r0a
--R
--R
@@ -22072,17 +21983,17 @@ m0c:=a0.2-r0a
--R 3 +-+
--R 2a b\|b
--R Type: Expression(Integer)
---E 950
+--E 950
---S 951 of 1092
+--S 951 of 1092
d0c:=D(m0c,x)
--R
--R
--R (10) 0
--R Type: Expression(Integer)
---E 951
+--E 951
---S 952 of 1092
+--S 952 of 1092
m0d:=a0.2-r0b
--R
--R
@@ -22115,19 +22026,19 @@ m0d:=a0.2-r0b
--R 3 +-+
--R 2a b\|b
--R Type: Expression(Integer)
---E 952
+--E 952
---S 953 of 1092
+--S 953 of 1092
d0d:=D(m0d,x)
--R
--R
--R (12) 0
--R Type: Expression(Integer)
---E 953
+--E 953
)clear all
---S 954 of 1092
+--S 954 of 1092
t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^2)
--R
--R
@@ -22137,9 +22048,9 @@ t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^2)
--R 2 5 4 2 3
--R b x + 2a b x + a x
--R Type: Expression(Integer)
---E 954
+--E 954
---S 955 of 1092
+--S 955 of 1092
r0:=1/4*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x))-1/2*(c+d*x)^(5/2)/_
(a*x^2*(a+b*x))+(b*c-a*d)^(3/2)*(6*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/_
sqrt(b*c-a*d))/(a^4*sqrt(b))-1/4*(24*b^2*c^2-40*a*b*c*d+15*a^2*d^2)*_
@@ -22178,9 +22089,9 @@ r0:=1/4*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x))-1/2*(c+d*x)^(5/2)/_
--R 4 3 5 2 +-+
--R (4a b x + 4a x )\|b
--R Type: Expression(Integer)
---E 955
+--E 955
---S 956 of 1092
+--S 956 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -22314,9 +22225,9 @@ a0:=integrate(t0,x)
--R 4a b x + 4a x
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 956
+--E 956
---S 957 of 1092
+--S 957 of 1092
m0a:=a0.1-r0
--R
--R
@@ -22353,17 +22264,17 @@ m0a:=a0.1-r0
--R 4 +-+
--R 8a \|b
--R Type: Expression(Integer)
---E 957
+--E 957
---S 958 of 1092
+--S 958 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 958
+--E 958
---S 959 of 1092
+--S 959 of 1092
m0b:=a0.2-r0
--R
--R
@@ -22396,19 +22307,19 @@ m0b:=a0.2-r0
--R 4 +-+
--R 8a \|b
--R Type: Expression(Integer)
---E 959
+--E 959
---S 960 of 1092
+--S 960 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 960
+--E 960
)clear all
---S 961 of 1092
+--S 961 of 1092
t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^2)
--R
--R
@@ -22418,9 +22329,9 @@ t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^2)
--R 2 6 5 2 4
--R b x + 2a b x + a x
--R Type: Expression(Integer)
---E 961
+--E 961
---S 962 of 1092
+--S 962 of 1092
r0:=1/12*(8*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x))-1/3*(c+d*x)^(5/2)/_
(a*x^3*(a+b*x))-(8*b*c-3*a*d)*(b*c-a*d)^(3/2)*atanh(sqrt(b)*_
sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/a^5+1/8*(64*b^3*c^3-_
@@ -22467,9 +22378,9 @@ r0:=1/12*(8*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x))-1/3*(c+d*x)^(5/2)/_
--R 5 4 6 3 +-+
--R (24a b x + 24a x )\|c
--R Type: Expression(Integer)
---E 962
+--E 962
---S 963 of 1092
+--S 963 of 1092
a0:=integrate(t0,x)
--R
--R
@@ -22635,9 +22546,9 @@ a0:=integrate(t0,x)
--R (24a b x + 24a x )\|- c
--R ]
--R Type: Union(List(Expression(Integer)),...)
---E 963
+--E 963
---S 964 of 1092
+--S 964 of 1092
m0a:=a0.1-r0
--R
--R
@@ -22678,17 +22589,17 @@ m0a:=a0.1-r0
--R 5 +-+
--R 16a \|c
--R Type: Expression(Integer)
---E 964
+--E 964
---S 965 of 1092
+--S 965 of 1092
d0a:=D(m0a,x)
--R
--R
--R (5) 0
--R Type: Expression(Integer)
---E 965
+--E 965
---S 966 of 1092
+--S 966 of 1092
m0b:=a0.2-r0
--R
--R
@@ -22726,28 +22637,28 @@ m0b:=a0.2-r0
--R 5 +-+
--R 16a \|c
--R Type: Expression(Integer)
---E 966
+--E 966
---S 967 of 1092
+--S 967 of 1092
d0b:=D(m0b,x)
--R
--R
--R (7) 0
--R Type: Expression(Integer)
---E 967
+--E 967
)clear all
---S 968 of 1092
+--S 968 of 1092
t0:=x^3*sqrt(a+b*x)*sqrt(c+d*x)
--R
--R
--R 3 +-------+ +-------+
--R (1) x \|b x + a \|d x + c
--R Type: Expression(Integer)
---E 968
+--E 968
---S 969 of 1092
+--S 969 of 1092
r0:=1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_
atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))-_
1/960*(105*b^3*c^3-5*a*b^2*c^2*d-17*a^2*b*c*d^2-35*a^3*d^3)*_
@@ -22786,32 +22697,32 @@ r0:=1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_
--R 4 4 +-+ +-+
--R 1920b d \|b \|d
--R Type: Expression(Integer)
---E 969
+--E 969
---S 970 of 1092
+--S 970 of 1092
--a0:=integrate(t0,x)
---E 970
+--E 970
---S 971 of 1092
+--S 971 of 1092
--m0:=a0-r0
---E 971
+--E 971
---S 972 of 1092
+--S 972 of 1092
--d0:=D(m0,x)
---E 972
+--E 972
)clear all
---S 973 of 1092
+--S 973 of 1092
t0:=x^2*sqrt(a+b*x)*sqrt(c+d*x)
--R
--R
--R 2 +-------+ +-------+
--R (1) x \|b x + a \|d x + c
--R Type: Expression(Integer)
---E 973
+--E 973
---S 974 of 1092
+--S 974 of 1092
r0:=-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/4*x*_
(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/64*(b*c-a*d)^2*_
(4*a*b*c*d-5*(b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_
@@ -22845,32 +22756,32 @@ r0:=-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/4*x*_
--R 3 3 +-+ +-+
--R 192b d \|b \|d
--R Type: Expression(Integer)
---E 974
+--E 974
---S 975 of 1092
+--S 975 of 1092
--a0:=integrate(t0,x)
---E 975
+--E 975
---S 976 of 1092
+--S 976 of 1092
--m0:=a0-r0
---E 976
+--E 976
---S 977 of 1092
+--S 977 of 1092
--d0:=D(m0,x)
---E 977
+--E 977
)clear all
---S 978 of 1092
+--S 978 of 1092
t0:=x*sqrt(a+b*x)*sqrt(c+d*x)
--R
--R
--R +-------+ +-------+
--R (1) x\|b x + a \|d x + c
--R Type: Expression(Integer)
---E 978
+--E 978
---S 979 of 1092
+--S 979 of 1092
r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/8*(b*c-a*d)^2*(b*c+a*d)*_
atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-_
1/4*(b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d)+1/8*_
@@ -22893,32 +22804,32 @@ r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/8*(b*c-a*d)^2*(b*c+a*d)*_
--R 2 2 +-+ +-+
--R 24b d \|b \|d
--R Type: Expression(Integer)
---E 979
+--E 979
---S 980 of 1092
+--S 980 of 1092
--a0:=integrate(t0,x)
---E 980
+--E 980
---S 981 of 1092
+--S 981 of 1092
--m0:=a0-r0
---E 981
+--E 981
---S 982 of 1092
+--S 982 of 1092
--d0:=D(m0,x)
---E 982
+--E 982
)clear all
---S 983 of 1092
+--S 983 of 1092
t0:=sqrt(a+b*x)*sqrt(c+d*x)
--R
--R
--R +-------+ +-------+
--R (1) \|b x + a \|d x + c
--R Type: Expression(Integer)
---E 983
+--E 983
---S 984 of 1092
+--S 984 of 1092
r0:=-1/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
(b^(3/2)*d^(3/2))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/b+1/4*(b*c-a*d)*_
sqrt(a+b*x)*sqrt(c+d*x)/(b*d)
@@ -22937,23 +22848,23 @@ r0:=-1/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
--R +-+ +-+
--R 4b d\|b \|d
--R Type: Expression(Integer)
---E 984
+--E 984
---S 985 of 1092
+--S 985 of 1092
--a0:=integrate(t0,x)
---E 985
+--E 985
---S 986 of 1092
+--S 986 of 1092
--m0:=a0-r0
---E 986
+--E 986
---S 987 of 1092
+--S 987 of 1092
--d0:=D(m0,x)
---E 987
+--E 987
)clear all
---S 988 of 1092
+--S 988 of 1092
t0:=sqrt(a+b*x)*sqrt(c+d*x)/x
--R
--R
@@ -22962,9 +22873,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x
--R (1) --------------------
--R x
--R Type: Expression(Integer)
---E 988
+--E 988
---S 989 of 1092
+--S 989 of 1092
r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+_
(b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
(sqrt(b)*sqrt(d))+sqrt(a+b*x)*sqrt(c+d*x)
@@ -22983,23 +22894,23 @@ r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+_
--R +-+ +-+
--R \|b \|d
--R Type: Expression(Integer)
---E 989
+--E 989
---S 990 of 1092 (non-algebraic residues)
+--S 990 of 1092 (non-algebraic residues)
--a0:=integrate(t0,x)
---E 990
+--E 990
---S 991 of 1092
+--S 991 of 1092
--m0:=a0-r0
---E 991
+--E 991
---S 992 of 1092
+--S 992 of 1092
--d0:=D(m0,x)
---E 992
+--E 992
)clear all
---S 993 of 1092
+--S 993 of 1092
t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^2
--R
--R
@@ -23009,9 +22920,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^2
--R 2
--R x
--R Type: Expression(Integer)
---E 993
+--E 993
---S 994 of 1092
+--S 994 of 1092
r0:=-(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
(sqrt(a)*sqrt(c))+2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_
sqrt(b)*sqrt(d)-sqrt(a+b*x)*sqrt(c+d*x)/x
@@ -23033,23 +22944,23 @@ r0:=-(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
--R +-+ +-+
--R x\|a \|c
--R Type: Expression(Integer)
---E 994
+--E 994
---S 995 of 1092
+--S 995 of 1092
--a0:=integrate(t0,x)
---E 995
+--E 995
---S 996 of 1092
+--S 996 of 1092
--m0:=a0-r0
---E 996
+--E 996
---S 997 of 1092
+--S 997 of 1092
--d0:=D(m0,x)
---E 997
+--E 997
)clear all
---S 998 of 1092
+--S 998 of 1092
t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^3
--R
--R
@@ -23059,9 +22970,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^3
--R 3
--R x
--R Type: Expression(Integer)
---E 998
+--E 998
---S 999 of 1092
+--S 999 of 1092
r0:=1/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
(a^(3/2)*c^(3/2))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x^2)-_
1/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x)
@@ -23080,23 +22991,23 @@ r0:=1/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
--R 2 +-+ +-+
--R 4a c x \|a \|c
--R Type: Expression(Integer)
---E 999
+--E 999
---S 1000 of 1092
+--S 1000 of 1092
--a0:=integrate(t0,x)
---E 1000
+--E 1000
---S 1001 of 1092
+--S 1001 of 1092
--m0:=a0-r0
---E 1001
+--E 1001
---S 1002 of 1092
+--S 1002 of 1092
--d0:=D(m0,x)
---E 1002
+--E 1002
)clear all
---S 1003 of 1092
+--S 1003 of 1092
t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^4
--R
--R
@@ -23106,9 +23017,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^4
--R 4
--R x
--R Type: Expression(Integer)
---E 1003
+--E 1003
---S 1004 of 1092
+--S 1004 of 1092
r0:=-1/8*(b*c-a*d)^2*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-1/3*sqrt(a+b*x)*sqrt(c+d*x)/x^3-_
1/12*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^2)+_
@@ -23131,23 +23042,23 @@ r0:=-1/8*(b*c-a*d)^2*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
--R 2 2 3 +-+ +-+
--R 24a c x \|a \|c
--R Type: Expression(Integer)
---E 1004
+--E 1004
---S 1005 of 1092
+--S 1005 of 1092
--a0:=integrate(t0,x)
---E 1005
+--E 1005
---S 1006 of 1092
+--S 1006 of 1092
--m0:=a0-r0
---E 1006
+--E 1006
---S 1007 of 1092
+--S 1007 of 1092
--d0:=D(m0,x)
---E 1007
+--E 1007
)clear all
---S 1008 of 1092
+--S 1008 of 1092
t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^5
--R
--R
@@ -23157,9 +23068,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^5
--R 5
--R x
--R Type: Expression(Integer)
---E 1008
+--E 1008
---S 1009 of 1092
+--S 1009 of 1092
r0:=1/64*(b*c-a*d)^2*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_
sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_
1/4*sqrt(a+b*x)*sqrt(c+d*x)/x^4-1/24*(b*c+a*d)*sqrt(a+b*x)*_
@@ -23190,23 +23101,23 @@ r0:=1/64*(b*c-a*d)^2*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_
--R 3 3 4 +-+ +-+
--R 192a c x \|a \|c
--R Type: Expression(Integer)
---E 1009
+--E 1009
---S 1010 of 1092
+--S 1010 of 1092
--a0:=integrate(t0,x)
---E 1010
+--E 1010
---S 1011 of 1092
+--S 1011 of 1092
--m0:=a0-r0
---E 1011
+--E 1011
---S 1012 of 1092
+--S 1012 of 1092
--d0:=D(m0,x)
---E 1012
+--E 1012
)clear all
---S 1013 of 1092
+--S 1013 of 1092
t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^6
--R
--R
@@ -23216,9 +23127,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^6
--R 6
--R x
--R Type: Expression(Integer)
---E 1013
+--E 1013
---S 1014 of 1092
+--S 1014 of 1092
r0:=-1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_
atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))-_
1/5*sqrt(a+b*x)*sqrt(c+d*x)/x^5-1/40*(b*c+a*d)*sqrt(a+b*x)*_
@@ -23258,32 +23169,32 @@ r0:=-1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_
--R 4 4 5 +-+ +-+
--R 1920a c x \|a \|c
--R Type: Expression(Integer)
---E 1014
+--E 1014
---S 1015 of 1092
+--S 1015 of 1092
--a0:=integrate(t0,x)
---E 1015
+--E 1015
---S 1016 of 1092
+--S 1016 of 1092
--m0:=a0-r0
---E 1016
+--E 1016
---S 1017 of 1092
+--S 1017 of 1092
--d0:=D(m0,x)
---E 1017
+--E 1017
)clear all
---S 1018 of 1092
+--S 1018 of 1092
t0:=x^2*(c+d*x)^(3/2)*sqrt(a+b*x)
--R
--R
--R 3 2 +-------+ +-------+
--R (1) (d x + c x )\|b x + a \|d x + c
--R Type: Expression(Integer)
---E 1018
+--E 1018
---S 1019 of 1092
+--S 1019 of 1092
r0:=1/48*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/_
(b^3*d^2)-1/40*(5*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d^2)+_
1/5*x*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)-1/128*(b*c-a*d)^3*_
@@ -23322,32 +23233,32 @@ r0:=1/48*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/_
--R 4 3 +-+ +-+
--R 1920b d \|b \|d
--R Type: Expression(Integer)
---E 1019
+--E 1019
---S 1020 of 1092
+--S 1020 of 1092
--a0:=integrate(t0,x)
---E 1020
+--E 1020
---S 1021 of 1092
+--S 1021 of 1092
--m0:=a0-r0
---E 1021
+--E 1021
---S 1022 of 1092
+--S 1022 of 1092
--d0:=D(m0,x)
---E 1022
+--E 1022
)clear all
---S 1023 of 1092
+--S 1023 of 1092
t0:=x*(c+d*x)^(3/2)*sqrt(a+b*x)
--R
--R
--R 2 +-------+ +-------+
--R (1) (d x + c x)\|b x + a \|d x + c
--R Type: Expression(Integer)
---E 1023
+--E 1023
---S 1024 of 1092
+--S 1024 of 1092
r0:=-1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d)+1/4*_
(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)+1/64*(b*c-a*d)^3*(3*b*c+5*a*d)*_
atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))-_
@@ -23380,32 +23291,32 @@ r0:=-1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d)+1/4*_
--R 3 2 +-+ +-+
--R 192b d \|b \|d
--R Type: Expression(Integer)
---E 1024
+--E 1024
---S 1025 of 1092
+--S 1025 of 1092
--a0:=integrate(t0,x)
---E 1025
+--E 1025
---S 1026 of 1092
+--S 1026 of 1092
--m0:=a0-r0
---E 1026
+--E 1026
---S 1027 of 1092
+--S 1027 of 1092
--d0:=D(m0,x)
---E 1027
+--E 1027
)clear all
---S 1028 of 1092
+--S 1028 of 1092
t0:=(c+d*x)^(3/2)*sqrt(a+b*x)
--R
--R
--R +-------+ +-------+
--R (1) (d x + c)\|b x + a \|d x + c
--R Type: Expression(Integer)
---E 1028
+--E 1028
---S 1029 of 1092
+--S 1029 of 1092
r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*atanh(sqrt(d)*_
sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/4*(b*c-a*d)*_
(a+b*x)^(3/2)*sqrt(c+d*x)/b^2+1/8*(b*c-a*d)^2*sqrt(a+b*x)*_
@@ -23428,23 +23339,23 @@ r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*atanh(sqrt(d)*_
--R 2 +-+ +-+
--R 24b d\|b \|d
--R Type: Expression(Integer)
---E 1029
+--E 1029
---S 1030 of 1092
+--S 1030 of 1092
--a0:=integrate(t0,x)
---E 1030
+--E 1030
---S 1031 of 1092
+--S 1031 of 1092
--m0:=a0-r0
---E 1031
+--E 1031
---S 1032 of 1092
+--S 1032 of 1092
--d0:=D(m0,x)
---E 1032
+--E 1032
)clear all
---S 1033 of 1092
+--S 1033 of 1092
t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x
--R
--R
@@ -23453,9 +23364,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x
--R (1) -----------------------------
--R x
--R Type: Expression(Integer)
---E 1033
+--E 1033
---S 1034 of 1092
+--S 1034 of 1092
r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
sqrt(a)+1/4*(3*b^2*c^2+6*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_
sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*sqrt(d))+_
@@ -23481,23 +23392,23 @@ r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
--R +-+ +-+
--R 4b\|b \|d
--R Type: Expression(Integer)
---E 1034
+--E 1034
---S 1035 of 1092 (non-algebraic residues)
+--S 1035 of 1092 (non-algebraic residues)
--a0:=integrate(t0,x)
---E 1035
+--E 1035
---S 1036 of 1092
+--S 1036 of 1092
--m0:=a0-r0
---E 1036
+--E 1036
---S 1037 of 1092
+--S 1037 of 1092
--d0:=D(m0,x)
---E 1037
+--E 1037
)clear all
---S 1038 of 1092
+--S 1038 of 1092
t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^2
--R
--R
@@ -23507,9 +23418,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^2
--R 2
--R x
--R Type: Expression(Integer)
---E 1038
+--E 1038
---S 1039 of 1092
+--S 1039 of 1092
r0:=-(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
sqrt(c)/sqrt(a)+(3*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/_
(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)-(c+d*x)^(3/2)*_
@@ -23535,23 +23446,23 @@ r0:=-(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_
--R +-+ +-+
--R x\|a \|b
--R Type: Expression(Integer)
---E 1039
+--E 1039
---S 1040 of 1092 (non-algebraic residues)
+--S 1040 of 1092 (non-algebraic residues)
--a0:=integrate(t0,x)
---E 1040
+--E 1040
---S 1041 of 1092
+--S 1041 of 1092
--m0:=a0-r0
---E 1041
+--E 1041
---S 1042 of 1092
+--S 1042 of 1092
--d0:=D(m0,x)
---E 1042
+--E 1042
)clear all
---S 1043 of 1092
+--S 1043 of 1092
t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^3
--R
--R
@@ -23561,9 +23472,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^3
--R 3
--R x
--R Type: Expression(Integer)
---E 1043
+--E 1043
---S 1044 of 1092
+--S 1044 of 1092
r0:=2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+_
1/4*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*atanh(sqrt(c)*_
sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*sqrt(c))-_
@@ -23590,23 +23501,23 @@ r0:=2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+_
--R 2 +-+ +-+
--R 4a x \|a \|c
--R Type: Expression(Integer)
---E 1044
+--E 1044
---S 1045 of 1092 (non-algebraic residues)
+--S 1045 of 1092 (non-algebraic residues)
--a0:=integrate(t0,x)
---E 1045
+--E 1045
---S 1046 of 1092
+--S 1046 of 1092
--m0:=a0-r0
---E 1046
+--E 1046
---S 1047 of 1092
+--S 1047 of 1092
--d0:=D(m0,x)
---E 1047
+--E 1047
)clear all
---S 1048 of 1092
+--S 1048 of 1092
t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^4
--R
--R
@@ -23616,9 +23527,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^4
--R 4
--R x
--R Type: Expression(Integer)
---E 1048
+--E 1048
---S 1049 of 1092
+--S 1049 of 1092
r0:=-1/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
(a^(5/2)*c^(3/2))-1/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c*x^2)-_
1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^3)+1/8*(b*c-a*d)^2*_
@@ -23641,23 +23552,23 @@ r0:=-1/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
--R 2 3 +-+ +-+
--R 24a c x \|a \|c
--R Type: Expression(Integer)
---E 1049
+--E 1049
---S 1050 of 1092
+--S 1050 of 1092
--a0:=integrate(t0,x)
---E 1050
+--E 1050
---S 1051 of 1092
+--S 1051 of 1092
--m0:=a0-r0
---E 1051
+--E 1051
---S 1052 of 1092
+--S 1052 of 1092
--d0:=D(m0,x)
---E 1052
+--E 1052
)clear all
---S 1053 of 1092
+--S 1053 of 1092
t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^5
--R
--R
@@ -23667,9 +23578,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^5
--R 5
--R x
--R Type: Expression(Integer)
---E 1053
+--E 1053
---S 1054 of 1092
+--S 1054 of 1092
r0:=1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
sqrt(c+d*x)))/(a^(7/2)*c^(5/2))-1/4*(c+d*x)^(3/2)*_
sqrt(a+b*x)/x^4-1/24*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^3)+_
@@ -23700,23 +23611,23 @@ r0:=1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_
--R 3 2 4 +-+ +-+
--R 192a c x \|a \|c
--R Type: Expression(Integer)
---E 1054
+--E 1054
---S 1055 of 1092
+--S 1055 of 1092
--a0:=integrate(t0,x)
---E 1055
+--E 1055
---S 1056 of 1092
+--S 1056 of 1092
--m0:=a0-r0
---E 1056
+--E 1056
---S 1057 of 1092
+--S 1057 of 1092
--d0:=D(m0,x)
---E 1057
+--E 1057
)clear all
---S 1058 of 1092
+--S 1058 of 1092
t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^6
--R
--R
@@ -23726,9 +23637,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^6
--R 6
--R x
--R Type: Expression(Integer)
---E 1058
+--E 1058
---S 1059 of 1092
+--S 1059 of 1092
r0:=-1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_
sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(7/2))-_
1/5*(c+d*x)^(3/2)*sqrt(a+b*x)/x^5-1/40*(b*c+3*a*d)*_
@@ -23768,32 +23679,32 @@ r0:=-1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_
--R 4 3 5 +-+ +-+
--R 1920a c x \|a \|c
--R Type: Expression(Integer)
---E 1059
+--E 1059
---S 1060 of 1092
+--S 1060 of 1092
--a0:=integrate(t0,x)
---E 1060
+--E 1060
---S 1061 of 1092
+--S 1061 of 1092
--m0:=a0-r0
---E 1061
+--E 1061
---S 1062 of 1092
+--S 1062 of 1092
--d0:=D(m0,x)
---E 1062
+--E 1062
)clear all
---S 1063 of 1092
+--S 1063 of 1092
t0:=x^2*(c+d*x)^(5/2)*sqrt(a+b*x)
--R
--R
--R 2 4 3 2 2 +-------+ +-------+
--R (1) (d x + 2c d x + c x )\|b x + a \|d x + c
--R Type: Expression(Integer)
---E 1063
+--E 1063
---S 1064 of 1092
+--S 1064 of 1092
r0:=1/192*(b*c-a*d)*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*_
(c+d*x)^(3/2)/(b^4*d^2)+1/160*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*_
(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^3*d^2)-1/60*(5*b*c+9*a*d)*_
@@ -23840,32 +23751,32 @@ r0:=1/192*(b*c-a*d)*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*_
--R 5 3 +-+ +-+
--R 7680b d \|b \|d
--R Type: Expression(Integer)
---E 1064
+--E 1064
---S 1065 of 1092
+--S 1065 of 1092
--a0:=integrate(t0,x)
---E 1065
+--E 1065
---S 1066 of 1092
+--S 1066 of 1092
--m0:=a0-r0
---E 1066
+--E 1066
---S 1067 of 1092
+--S 1067 of 1092
--d0:=D(m0,x)
---E 1067
+--E 1067
)clear all
---S 1068 of 1092
+--S 1068 of 1092
t0:=x*(c+d*x)^(5/2)*sqrt(a+b*x)
--R
--R
--R 2 3 2 2 +-------+ +-------+
--R (1) (d x + 2c d x + c x)\|b x + a \|d x + c
--R Type: Expression(Integer)
---E 1068
+--E 1068
---S 1069 of 1092
+--S 1069 of 1092
r0:=-1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d)-_
1/40*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d)+_
1/5*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(b*d)+1/128*(b*c-a*d)^4*_
@@ -23906,32 +23817,32 @@ r0:=-1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d)-_
--R 4 2 +-+ +-+
--R 1920b d \|b \|d
--R Type: Expression(Integer)
---E 1069
+--E 1069
---S 1070 of 1092
+--S 1070 of 1092
--a0:=integrate(t0,x)
---E 1070
+--E 1070
---S 1071 of 1092
+--S 1071 of 1092
--m0:=a0-r0
---E 1071
+--E 1071
---S 1072 of 1092
+--S 1072 of 1092
--d0:=D(m0,x)
---E 1072
+--E 1072
)clear all
---S 1073 of 1092
+--S 1073 of 1092
t0:=(c+d*x)^(5/2)*sqrt(a+b*x)
--R
--R
--R 2 2 2 +-------+ +-------+
--R (1) (d x + 2c d x + c )\|b x + a \|d x + c
--R Type: Expression(Integer)
---E 1073
+--E 1073
---S 1074 of 1092
+--S 1074 of 1092
r0:=5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+1/4*(a+b*x)^(3/2)*_
(c+d*x)^(5/2)/b-5/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/_
(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(3/2))+5/32*(b*c-a*d)^2*_
@@ -23964,23 +23875,23 @@ r0:=5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+1/4*(a+b*x)^(3/2)*_
--R 3 +-+ +-+
--R 192b d\|b \|d
--R Type: Expression(Integer)
---E 1074
+--E 1074
---S 1075 of 1092
+--S 1075 of 1092
--a0:=integrate(t0,x)
---E 1075
+--E 1075
---S 1076 of 1092
+--S 1076 of 1092
--m0:=a0-r0
---E 1076
+--E 1076
---S 1077 of 1092
+--S 1077 of 1092
--d0:=D(m0,x)
---E 1077
+--E 1077
)clear all
---S 1078 of 1092
+--S 1078 of 1092
t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x
--R
--R
@@ -23989,9 +23900,9 @@ t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x
--R (1) ----------------------------------------
--R x
--R Type: Expression(Integer)
---E 1078
+--E 1078
---S 1079 of 1092
+--S 1079 of 1092
r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+_
1/8*(5*b^3*c^3+15*a*b^2*c^2*d-5*a^2*b*c*d^2+a^3*d^3)*_
atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))+_
@@ -24021,23 +23932,23 @@ r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+_
--R 2 +-+ +-+
--R 24b \|b \|d
--R Type: Expression(Integer)
---E 1079
+--E 1079
---S 1080 of 1092 (non-algebraic residues)
+--S 1080 of 1092 (non-algebraic residues)
--a0:=integrate(t0,x)
---E 1080
+--E 1080
---S 1081 of 1092
+--S 1081 of 1092
--m0:=a0-r0
---E 1081
+--E 1081
---S 1082 of 1092
+--S 1082 of 1092
--d0:=D(m0,x)
---E 1082
+--E 1082
)clear all
---S 1083 of 1092
+--S 1083 of 1092
t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^2
--R
--R
@@ -24047,9 +23958,9 @@ t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^2
--R 2
--R x
--R Type: Expression(Integer)
---E 1083
+--E 1083
---S 1084 of 1092
+--S 1084 of 1092
r0:=-c^(3/2)*(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
sqrt(a)+1/4*(15*b^2*c^2+10*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_
sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(3/2)+3/2*d*_
@@ -24076,23 +23987,23 @@ r0:=-c^(3/2)*(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_
--R +-+ +-+
--R 4b x\|a \|b
--R Type: Expression(Integer)
---E 1084
+--E 1084
---S 1085 of 1092 (non-algebraic residues)
+--S 1085 of 1092 (non-algebraic residues)
--a0:=integrate(t0,x)
---E 1085
+--E 1085
---S 1086 of 1092
+--S 1086 of 1092
--m0:=a0-r0
---E 1086
+--E 1086
---S 1087 of 1092
+--S 1087 of 1092
--d0:=D(m0,x)
---E 1087
+--E 1087
)clear all
---S 1088 of 1092
+--S 1088 of 1092
t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^3
--R
--R
@@ -24102,9 +24013,9 @@ t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^3
--R 3
--R x
--R Type: Expression(Integer)
---E 1088
+--E 1088
---S 1089 of 1092
+--S 1089 of 1092
r0:=d^(3/2)*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
sqrt(b)+1/4*(b^2*c^2-10*a*b*c*d-15*a^2*d^2)*atanh(sqrt(c)*_
sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(3/2)-_
@@ -24132,17 +24043,17 @@ r0:=d^(3/2)*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_
--R 2 +-+ +-+
--R 4a x \|a \|b
--R Type: Expression(Integer)
---E 1089
+--E 1089
---S 1090 of 1092 (non-algebraic residues)
+--S 1090 of 1092 (non-algebraic residues)
--a0:=integrate(t0,x)
---E 1090
+--E 1090
---S 1091 of 1092
+--S 1091 of 1092
--m0:=a0-r0
---E 1091
+--E 1091
---S 1092 of 1092
+--S 1092 of 1092
--d0:=D(m0,x)
--E 1092
diff --git a/src/axiom-website/CATS/rich3a.input.pdf b/src/axiom-website/CATS/rich3a.input.pdf
index 4bb733e..9e0e1fb 100644
Binary files a/src/axiom-website/CATS/rich3a.input.pdf and b/src/axiom-website/CATS/rich3a.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3c.input.pamphlet b/src/axiom-website/CATS/rich3c.input.pamphlet
index 88bdf31..e55f406 100644
--- a/src/axiom-website/CATS/rich3c.input.pamphlet
+++ b/src/axiom-website/CATS/rich3c.input.pamphlet
@@ -4200,7 +4200,7 @@ r0:=sqrt(-1+x)*sqrt(1+x)
--R Type: Expression(Integer)
--E 267
---S 268 of 500
+--S 268 of 500 ok to fail, differs by a constant
a0:=integrate(t0,x)
--R
--R
@@ -4209,7 +4209,7 @@ a0:=integrate(t0,x)
--R Type: Union(Expression(Integer),...)
--E 268
---S 269 of 500
+--S 269 of 500 ok to fail, differs by a constant
m0:=a0-r0
--R
--R
diff --git a/src/axiom-website/CATS/rich3c.input.pdf b/src/axiom-website/CATS/rich3c.input.pdf
index 5182c84..8f08e4b 100644
Binary files a/src/axiom-website/CATS/rich3c.input.pdf and b/src/axiom-website/CATS/rich3c.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3d.input.pamphlet b/src/axiom-website/CATS/rich3d.input.pamphlet
new file mode 100644
index 0000000..12ebaa2
--- /dev/null
+++ b/src/axiom-website/CATS/rich3d.input.pamphlet
@@ -0,0 +1,5940 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3d.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 95 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 5 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3d.output
+)spool rich3d.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(1-%i*x)^(1/6*%i)/((1+%i*x)^(1/6*%i)*x^2)
+--R
+--R
+--R %i
+--R --
+--R 6
+--R (- %i x + 1)
+--R (1) --------------
+--R %i
+--R --
+--R 2 6
+--R x (%i x + 1)
+--R Type: Expression(Complex(Integer))
+--E 1
+
+--S 2 of 500
+--r0:=(-3/37-18/37*%i)*2^(1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*(%i*x)^(-1-1/6*%i)*_
+-- hypergeometric(1/6*%i,1+1/6*%i,2+1/6*%i,1/2*%i*(2-2*%i*x+%i*(%i+x))/x)
+--E 2
+
+--S 3 of 500
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 500
+--m0:=a0-r0
+--E 4
+
+--S 5 of 500
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(1-%i*x)^(1/6*%i)/((1+%i*x)^(1/6*%i)*x^3)
+--R
+--R
+--R %i
+--R --
+--R 6
+--R (- %i x + 1)
+--R (1) --------------
+--R %i
+--R --
+--R 3 6
+--R x (%i x + 1)
+--R Type: Expression(Complex(Integer))
+--E 6
+
+--S 7 of 500
+--r0:=(2/37-1/111*%i)*2^(-1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*(3-18*%i+_
+-- 37*x+(3+19*%i)*x^2-2*%i*x^2*_
+-- hypergeometric(1,1+1/6*%i,2+1/6*%i,(%i+x)/(%i-x)))/_
+-- ((%i-x)*x^2*(1+1/2*%i*(%i+x))^(1/6*%i))
+--E 7
+
+--S 8 of 500
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 500
+--m0:=a0-r0
+--E 9
+
+--S 10 of 500
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(1-2*x)*(2+3*x)^m*(3+5*x)
+--R
+--R
+--R 2 m
+--R (1) (- 10x - x + 3)(3x + 2)
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+r0:=-7/27*(2+3*x)^(1+m)/(1+m)+37/27*(2+3*x)^(2+m)/(2+m)-_
+ 10/27*(2+3*x)^(3+m)/(3+m)
+--R
+--R
+--R (2)
+--R 2 m + 3 2 m + 2
+--R (- 10m - 30m - 20)(3x + 2) + (37m + 148m + 111)(3x + 2)
+--R +
+--R 2 m + 1
+--R (- 7m - 35m - 42)(3x + 2)
+--R /
+--R 3 2
+--R 27m + 162m + 297m + 162
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2
+--R (- 270m - 810m - 540)x + (- 207m - 288m - 81)x
+--R +
+--R 2 2
+--R (63m + 591m + 486)x + 54m + 282m + 200
+--R *
+--R m log(3x + 2)
+--R %e
+--R /
+--R 3 2
+--R 27m + 162m + 297m + 162
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2
+--R (- 270m - 810m - 540)x + (- 207m - 288m - 81)x
+--R +
+--R 2 2
+--R (63m + 591m + 486)x + 54m + 282m + 200
+--R *
+--R m log(3x + 2)
+--R %e
+--R +
+--R 2 m + 3 2 m + 2
+--R (10m + 30m + 20)(3x + 2) + (- 37m - 148m - 111)(3x + 2)
+--R +
+--R 2 m + 1
+--R (7m + 35m + 42)(3x + 2)
+--R /
+--R 3 2
+--R 27m + 162m + 297m + 162
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 500
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(1-2*x)*(2+3*x)^8*(3+5*x)
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5
+--R - 65610x - 356481x - 831789x - 1065312x - 771120x - 247968x
+--R +
+--R 4 3 2
+--R 62496x + 98304x + 42752x + 8960x + 768
+--R Type: Polynomial(Integer)
+--E 16
+
+--S 17 of 500
+r0:=-7/243*(2+3*x)^9+37/270*(2+3*x)^10-10/297*(2+3*x)^11
+--R
+--R
+--R (2)
+--R 65610 11 356481 10 9 8 7 6
+--R - ----- x - ------ x - 92421x - 133164x - 110160x - 41328x
+--R 11 10
+--R +
+--R 62496 5 4 42752 3 2 756736
+--R ----- x + 24576x + ----- x + 4480x + 768x + ------
+--R 5 3 13365
+--R Type: Polynomial(Fraction(Integer))
+--E 17
+
+--S 18 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 65610 11 356481 10 9 8 7 6
+--R - ----- x - ------ x - 92421x - 133164x - 110160x - 41328x
+--R 11 10
+--R +
+--R 62496 5 4 42752 3 2
+--R ----- x + 24576x + ----- x + 4480x + 768x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 18
+
+--S 19 of 500
+m0:=a0-r0
+--R
+--R
+--R 756736
+--R (4) - ------
+--R 13365
+--R Type: Polynomial(Fraction(Integer))
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(1-2*x)*(2+3*x)^7*(3+5*x)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3
+--R - 21870x - 104247x - 207765x - 216594x - 112644x - 7560x + 25872x
+--R +
+--R 2
+--R 15520x + 3904x + 384
+--R Type: Polynomial(Integer)
+--E 21
+
+--S 22 of 500
+r0:=-7/216*(2+3*x)^8+37/243*(2+3*x)^9-1/27*(2+3*x)^10
+--R
+--R
+--R (2)
+--R 10 9 207765 8 7 6 5 4
+--R - 2187x - 11583x - ------ x - 30942x - 18774x - 1512x + 6468x
+--R 8
+--R +
+--R 15520 3 2 7712
+--R ----- x + 1952x + 384x + ----
+--R 3 243
+--R Type: Polynomial(Fraction(Integer))
+--E 22
+
+--S 23 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 207765 8 7 6 5 4
+--R - 2187x - 11583x - ------ x - 30942x - 18774x - 1512x + 6468x
+--R 8
+--R +
+--R 15520 3 2
+--R ----- x + 1952x + 384x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 23
+
+--S 24 of 500
+m0:=a0-r0
+--R
+--R
+--R 7712
+--R (4) - ----
+--R 243
+--R Type: Polynomial(Fraction(Integer))
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(1-2*x)*(2+3*x)^6*(3+5*x)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 7290x - 29889x - 49329x - 39312x - 11340x + 5040x + 5264x + 1664x
+--R +
+--R 192
+--R Type: Polynomial(Integer)
+--E 26
+
+--S 27 of 500
+r0:=-1/27*(2+3*x)^7+37/216*(2+3*x)^8-10/243*(2+3*x)^9
+--R
+--R
+--R (2)
+--R 9 29889 8 7 6 5 4 5264 3 2
+--R - 810x - ----- x - 7047x - 6552x - 2268x + 1260x + ---- x + 832x
+--R 8 3
+--R +
+--R 4384
+--R 192x + ----
+--R 243
+--R Type: Polynomial(Fraction(Integer))
+--E 27
+
+--S 28 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 29889 8 7 6 5 4 5264 3 2
+--R - 810x - ----- x - 7047x - 6552x - 2268x + 1260x + ---- x + 832x
+--R 8 3
+--R +
+--R 192x
+--R Type: Polynomial(Fraction(Integer))
+--E 28
+
+--S 29 of 500
+m0:=a0-r0
+--R
+--R
+--R 4384
+--R (4) - ----
+--R 243
+--R Type: Polynomial(Fraction(Integer))
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(1-2*x)*(2+3*x)^5*(3+5*x)
+--R
+--R
+--R 7 6 5 4 3 2
+--R (1) - 2430x - 8343x - 10881x - 5850x + 120x + 1600x + 688x + 96
+--R Type: Polynomial(Integer)
+--E 31
+
+--S 32 of 500
+r0:=96*x+344*x^2+1600/3*x^3+30*x^4-1170*x^5-3627/2*x^6-8343/7*x^7-1215/4*x^8
+--R
+--R
+--R 1215 8 8343 7 3627 6 5 4 1600 3 2
+--R (2) - ---- x - ---- x - ---- x - 1170x + 30x + ---- x + 344x + 96x
+--R 4 7 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 32
+
+--S 33 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 1215 8 8343 7 3627 6 5 4 1600 3 2
+--R (3) - ---- x - ---- x - ---- x - 1170x + 30x + ---- x + 344x + 96x
+--R 4 7 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 33
+
+--S 34 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(1-2*x)*(2+3*x)^4*(3+5*x)
+--R
+--R
+--R 6 5 4 3 2
+--R (1) - 810x - 2241x - 2133x - 528x + 392x + 272x + 48
+--R Type: Polynomial(Integer)
+--E 36
+
+--S 37 of 500
+r0:=48*x+136*x^2+392/3*x^3-132*x^4-2133/5*x^5-747/2*x^6-810/7*x^7
+--R
+--R
+--R 810 7 747 6 2133 5 4 392 3 2
+--R (2) - --- x - --- x - ---- x - 132x + --- x + 136x + 48x
+--R 7 2 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 37
+
+--S 38 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 810 7 747 6 2133 5 4 392 3 2
+--R (3) - --- x - --- x - ---- x - 132x + --- x + 136x + 48x
+--R 7 2 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 38
+
+--S 39 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(1-2*x)*(2+3*x)^3*(3+5*x)
+--R
+--R
+--R 5 4 3 2
+--R (1) - 270x - 567x - 333x + 46x + 100x + 24
+--R Type: Polynomial(Integer)
+--E 41
+
+--S 42 of 500
+r0:=24*x+50*x^2+46/3*x^3-333/4*x^4-567/5*x^5-45*x^6
+--R
+--R
+--R 6 567 5 333 4 46 3 2
+--R (2) - 45x - --- x - --- x + -- x + 50x + 24x
+--R 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 42
+
+--S 43 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 567 5 333 4 46 3 2
+--R (3) - 45x - --- x - --- x + -- x + 50x + 24x
+--R 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 43
+
+--S 44 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(1-2*x)*(2+3*x)^2*(3+5*x)
+--R
+--R
+--R 4 3 2
+--R (1) - 90x - 129x - 25x + 32x + 12
+--R Type: Polynomial(Integer)
+--E 46
+
+--S 47 of 500
+r0:=12*x+16*x^2-25/3*x^3-129/4*x^4-18*x^5
+--R
+--R
+--R 5 129 4 25 3 2
+--R (2) - 18x - --- x - -- x + 16x + 12x
+--R 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 47
+
+--S 48 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 129 4 25 3 2
+--R (3) - 18x - --- x - -- x + 16x + 12x
+--R 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 48
+
+--S 49 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(1-2*x)*(2+3*x)*(3+5*x)
+--R
+--R
+--R 3 2
+--R (1) - 30x - 23x + 7x + 6
+--R Type: Polynomial(Integer)
+--E 51
+
+--S 52 of 500
+r0:=6*x+7/2*x^2-23/3*x^3-15/2*x^4
+--R
+--R
+--R 15 4 23 3 7 2
+--R (2) - -- x - -- x + - x + 6x
+--R 2 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 52
+
+--S 53 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 15 4 23 3 7 2
+--R (3) - -- x - -- x + - x + 6x
+--R 2 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 53
+
+--S 54 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(1-2*x)*(3+5*x)
+--R
+--R
+--R 2
+--R (1) - 10x - x + 3
+--R Type: Polynomial(Integer)
+--E 56
+
+--S 57 of 500
+r0:=3*x-1/2*x^2-10/3*x^3
+--R
+--R
+--R 10 3 1 2
+--R (2) - -- x - - x + 3x
+--R 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 57
+
+--S 58 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 10 3 1 2
+--R (3) - -- x - - x + 3x
+--R 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 58
+
+--S 59 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(1-2*x)*(3+5*x)/(2+3*x)
+--R
+--R
+--R 2
+--R - 10x - x + 3
+--R (1) --------------
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 61
+
+--S 62 of 500
+r0:=17/9*x-5/3*x^2-7/27*log(2+3*x)
+--R
+--R
+--R 2
+--R - 7log(3x + 2) - 45x + 51x
+--R (2) ---------------------------
+--R 27
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 7log(3x + 2) - 45x + 51x
+--R (3) ---------------------------
+--R 27
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(1-2*x)*(3+5*x)/(2+3*x)^2
+--R
+--R
+--R 2
+--R - 10x - x + 3
+--R (1) --------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 66
+
+--S 67 of 500
+r0:=-10/9*x+7/27/(2+3*x)+37/27*log(2+3*x)
+--R
+--R
+--R 2
+--R (111x + 74)log(3x + 2) - 90x - 60x + 7
+--R (2) ---------------------------------------
+--R 81x + 54
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (111x + 74)log(3x + 2) - 90x - 60x + 7
+--R (3) ---------------------------------------
+--R 81x + 54
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(1-2*x)*(3+5*x)/(2+3*x)^3
+--R
+--R
+--R 2
+--R - 10x - x + 3
+--R (1) ---------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 71
+
+--S 72 of 500
+r0:=7/54/(2+3*x)^2+(-37/27)/(2+3*x)-10/27*log(2+3*x)
+--R
+--R
+--R 2
+--R (- 180x - 240x - 80)log(3x + 2) - 222x - 141
+--R (2) ---------------------------------------------
+--R 2
+--R 486x + 648x + 216
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (- 180x - 240x - 80)log(3x + 2) - 222x - 141
+--R (3) ---------------------------------------------
+--R 2
+--R 486x + 648x + 216
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(1-2*x)*(3+5*x)/(2+3*x)^4
+--R
+--R
+--R 2
+--R - 10x - x + 3
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 76
+
+--S 77 of 500
+r0:=7/81/(2+3*x)^3+(-37/54)/(2+3*x)^2+10/27/(2+3*x)
+--R
+--R
+--R 10 2 43 16
+--R -- x + --- x + ----
+--R 81 486 2187
+--R (2) --------------------
+--R 3 2 4 8
+--R x + 2x + - x + --
+--R 3 27
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 77
+
+--S 78 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 540x + 387x + 32
+--R (3) ------------------------------
+--R 3 2
+--R 4374x + 8748x + 5832x + 1296
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(1-2*x)*(3+5*x)/(2+3*x)^5
+--R
+--R
+--R 2
+--R - 10x - x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 81
+
+--S 82 of 500
+r0:=7/108/(2+3*x)^4+(-37/81)/(2+3*x)^3+5/27/(2+3*x)^2
+--R
+--R
+--R 5 2 23 35
+--R --- x + ---- x - -----
+--R 243 2187 26244
+--R (2) ----------------------------
+--R 4 8 3 8 2 32 16
+--R x + - x + - x + -- x + --
+--R 3 3 27 81
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 82
+
+--S 83 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 540x + 276x - 35
+--R (3) -------------------------------------------
+--R 4 3 2
+--R 26244x + 69984x + 69984x + 31104x + 5184
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(1-2*x)*(3+5*x)/(2+3*x)^6
+--R
+--R
+--R 2
+--R - 10x - x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 86
+
+--S 87 of 500
+r0:=7/135/(2+3*x)^5+(-37/108)/(2+3*x)^4+10/81/(2+3*x)^3
+--R
+--R
+--R 10 2 49 113
+--R ---- x + ----- x - ------
+--R 2187 26244 196830
+--R (2) ---------------------------------------
+--R 5 10 4 40 3 80 2 80 32
+--R x + -- x + -- x + -- x + -- x + ---
+--R 3 9 27 81 243
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 87
+
+--S 88 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 1800x + 735x - 226
+--R (3) --------------------------------------------------------------
+--R 5 4 3 2
+--R 393660x + 1312200x + 1749600x + 1166400x + 388800x + 51840
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(1-2*x)*(2+3*x)^m*(3+5*x)^2
+--R
+--R
+--R 3 2 m
+--R (1) (- 50x - 35x + 12x + 9)(3x + 2)
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+r0:=7/81*(2+3*x)^(1+m)/(1+m)-8/9*(2+3*x)^(2+m)/(2+m)+_
+ 65/27*(2+3*x)^(3+m)/(3+m)-50/81*(2+3*x)^(4+m)/(4+m)
+--R
+--R
+--R (2)
+--R 3 2 m + 4
+--R (- 50m - 300m - 550m - 300)(3x + 2)
+--R +
+--R 3 2 m + 3
+--R (195m + 1365m + 2730m + 1560)(3x + 2)
+--R +
+--R 3 2 m + 2
+--R (- 72m - 576m - 1368m - 864)(3x + 2)
+--R +
+--R 3 2 m + 1
+--R (7m + 63m + 182m + 168)(3x + 2)
+--R /
+--R 4 3 2
+--R 81m + 810m + 2835m + 4050m + 1944
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4
+--R (- 1350m - 8100m - 14850m - 8100)x
+--R +
+--R 3 2 3
+--R (- 1845m - 9315m - 15030m - 7560)x
+--R +
+--R 3 2 2 3 2
+--R (- 306m + 1242m + 5436m + 3888)x + (459m + 4539m + 9870m + 5832)x
+--R +
+--R 3 2
+--R 162m + 1314m + 2644m + 1520
+--R *
+--R m log(3x + 2)
+--R %e
+--R /
+--R 4 3 2
+--R 27m + 270m + 945m + 1350m + 648
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 2 4
+--R (- 4050m - 24300m - 44550m - 24300)x
+--R +
+--R 3 2 3
+--R (- 5535m - 27945m - 45090m - 22680)x
+--R +
+--R 3 2 2
+--R (- 918m + 3726m + 16308m + 11664)x
+--R +
+--R 3 2 3 2
+--R (1377m + 13617m + 29610m + 17496)x + 486m + 3942m + 7932m + 4560
+--R *
+--R m log(3x + 2)
+--R %e
+--R +
+--R 3 2 m + 4
+--R (50m + 300m + 550m + 300)(3x + 2)
+--R +
+--R 3 2 m + 3
+--R (- 195m - 1365m - 2730m - 1560)(3x + 2)
+--R +
+--R 3 2 m + 2
+--R (72m + 576m + 1368m + 864)(3x + 2)
+--R +
+--R 3 2 m + 1
+--R (- 7m - 63m - 182m - 168)(3x + 2)
+--R /
+--R 4 3 2
+--R 81m + 810m + 2835m + 4050m + 1944
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(1-2*x)*(2+3*x)^8*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 11 10 9 8 7 6
+--R - 328050x - 1979235x - 5228388x - 7821927x - 7051536x - 3553200x
+--R +
+--R 5 4 3 2
+--R - 431424x + 679008x + 508672x + 173056x + 30720x + 2304
+--R Type: Polynomial(Integer)
+--E 96
+
+--S 97 of 500
+r0:=7/729*(2+3*x)^9-4/45*(2+3*x)^10+65/297*(2+3*x)^11-25/486*(2+3*x)^12
+--R
+--R
+--R (2)
+--R 54675 12 1979235 11 2614194 10 9 8 7
+--R - ----- x - ------- x - ------- x - 869103x - 881442x - 507600x
+--R 2 11 5
+--R +
+--R 6 679008 5 4 173056 3 2 6070784
+--R - 71904x + ------ x + 127168x + ------ x + 15360x + 2304x + -------
+--R 5 3 40095
+--R Type: Polynomial(Fraction(Integer))
+--E 97
+
+--S 98 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 54675 12 1979235 11 2614194 10 9 8 7
+--R - ----- x - ------- x - ------- x - 869103x - 881442x - 507600x
+--R 2 11 5
+--R +
+--R 6 679008 5 4 173056 3 2
+--R - 71904x + ------ x + 127168x + ------ x + 15360x + 2304x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 98
+
+--S 99 of 500
+m0:=a0-r0
+--R
+--R
+--R 6070784
+--R (4) - -------
+--R 40095
+--R Type: Polynomial(Fraction(Integer))
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(1-2*x)*(2+3*x)^7*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5
+--R - 109350x - 586845x - 1351566x - 1706265x - 1213002x - 375732x
+--R +
+--R 4 3 2
+--R 106680x + 155216x + 66080x + 13632x + 1152
+--R Type: Polynomial(Integer)
+--E 101
+
+--S 102 of 500
+r0:=7/648*(2+3*x)^8-8/81*(2+3*x)^9+13/54*(2+3*x)^10-50/891*(2+3*x)^11
+--R
+--R
+--R (2)
+--R 109350 11 117369 10 9 1706265 8 7 6
+--R - ------ x - ------ x - 150174x - ------- x - 173286x - 62622x
+--R 11 2 8
+--R +
+--R 5 4 66080 3 2 74656
+--R 21336x + 38804x + ----- x + 6816x + 1152x + -----
+--R 3 891
+--R Type: Polynomial(Fraction(Integer))
+--E 102
+
+--S 103 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 109350 11 117369 10 9 1706265 8 7 6
+--R - ------ x - ------ x - 150174x - ------- x - 173286x - 62622x
+--R 11 2 8
+--R +
+--R 5 4 66080 3 2
+--R 21336x + 38804x + ----- x + 6816x + 1152x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 103
+
+--S 104 of 500
+m0:=a0-r0
+--R
+--R
+--R 74656
+--R (4) - -----
+--R 891
+--R Type: Polynomial(Fraction(Integer))
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(1-2*x)*(2+3*x)^6*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3
+--R - 36450x - 171315x - 336312x - 344547x - 174636x - 8820x + 41440x
+--R +
+--R 2
+--R 24112x + 5952x + 576
+--R Type: Polynomial(Integer)
+--E 106
+
+--S 107 of 500
+r0:=576*x+2976*x^2+24112/3*x^3+10360*x^4-1764*x^5-29106*x^6-_
+ 49221*x^7-42039*x^8-19035*x^9-3645*x^10
+--R
+--R
+--R (2)
+--R 10 9 8 7 6 5 4
+--R - 3645x - 19035x - 42039x - 49221x - 29106x - 1764x + 10360x
+--R +
+--R 24112 3 2
+--R ----- x + 2976x + 576x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 107
+
+--S 108 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 8 7 6 5 4
+--R - 3645x - 19035x - 42039x - 49221x - 29106x - 1764x + 10360x
+--R +
+--R 24112 3 2
+--R ----- x + 2976x + 576x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 108
+
+--S 109 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(1-2*x)*(2+3*x)^5*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 12150x - 49005x - 79434x - 61893x - 16950x + 8360x + 8240x + 2544x
+--R +
+--R 288
+--R Type: Polynomial(Integer)
+--E 111
+
+--S 112 of 500
+r0:=288*x+1272*x^2+8240/3*x^3+2090*x^4-3390*x^5-20631/2*x^6-79434/7*x^7-_
+ 49005/8*x^8-1350*x^9
+--R
+--R
+--R (2)
+--R 9 49005 8 79434 7 20631 6 5 4 8240 3
+--R - 1350x - ----- x - ----- x - ----- x - 3390x + 2090x + ---- x
+--R 8 7 2 3
+--R +
+--R 2
+--R 1272x + 288x
+--R Type: Polynomial(Fraction(Integer))
+--E 112
+
+--S 113 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 49005 8 79434 7 20631 6 5 4 8240 3
+--R - 1350x - ----- x - ----- x - ----- x - 3390x + 2090x + ---- x
+--R 8 7 2 3
+--R +
+--R 2
+--R 1272x + 288x
+--R Type: Polynomial(Fraction(Integer))
+--E 113
+
+--S 114 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(1-2*x)*(2+3*x)^4*(3+5*x)^2
+--R
+--R
+--R 7 6 5 4 3 2
+--R (1) - 4050x - 13635x - 17388x - 9039x + 376x + 2536x + 1056x + 144
+--R Type: Polynomial(Integer)
+--E 116
+
+--S 117 of 500
+r0:=144*x+528*x^2+2536/3*x^3+94*x^4-9039/5*x^5-2898*x^6-13635/7*x^7-2025/4*x^8
+--R
+--R
+--R (2)
+--R 2025 8 13635 7 6 9039 5 4 2536 3 2
+--R - ---- x - ----- x - 2898x - ---- x + 94x + ---- x + 528x + 144x
+--R 4 7 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 117
+
+--S 118 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2025 8 13635 7 6 9039 5 4 2536 3 2
+--R - ---- x - ----- x - 2898x - ---- x + 94x + ---- x + 528x + 144x
+--R 4 7 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 118
+
+--S 119 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(1-2*x)*(2+3*x)^3*(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R (1) - 1350x - 3645x - 3366x - 769x + 638x + 420x + 72
+--R Type: Polynomial(Integer)
+--E 121
+
+--S 122 of 500
+r0:=72*x+210*x^2+638/3*x^3-769/4*x^4-3366/5*x^5-1215/2*x^6-1350/7*x^7
+--R
+--R
+--R 1350 7 1215 6 3366 5 769 4 638 3 2
+--R (2) - ---- x - ---- x - ---- x - --- x + --- x + 210x + 72x
+--R 7 2 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 122
+
+--S 123 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 1350 7 1215 6 3366 5 769 4 638 3 2
+--R (3) - ---- x - ---- x - ---- x - --- x + --- x + 210x + 72x
+--R 7 2 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 123
+
+--S 124 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(1-2*x)*(2+3*x)^2*(3+5*x)^2
+--R
+--R
+--R 5 4 3 2
+--R (1) - 450x - 915x - 512x + 85x + 156x + 36
+--R Type: Polynomial(Integer)
+--E 126
+
+--S 127 of 500
+r0:=36*x+78*x^2+85/3*x^3-128*x^4-183*x^5-75*x^6
+--R
+--R
+--R 6 5 4 85 3 2
+--R (2) - 75x - 183x - 128x + -- x + 78x + 36x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 127
+
+--S 128 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 5 4 85 3 2
+--R (3) - 75x - 183x - 128x + -- x + 78x + 36x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 128
+
+--S 129 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(1-2*x)*(2+3*x)*(3+5*x)^2
+--R
+--R
+--R 4 3 2
+--R (1) - 150x - 205x - 34x + 51x + 18
+--R Type: Polynomial(Integer)
+--E 131
+
+--S 132 of 500
+r0:=18*x+51/2*x^2-34/3*x^3-205/4*x^4-30*x^5
+--R
+--R
+--R 5 205 4 34 3 51 2
+--R (2) - 30x - --- x - -- x + -- x + 18x
+--R 4 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 132
+
+--S 133 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 205 4 34 3 51 2
+--R (3) - 30x - --- x - -- x + -- x + 18x
+--R 4 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 133
+
+--S 134 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(1-2*x)*(3+5*x)^2
+--R
+--R
+--R 3 2
+--R (1) - 50x - 35x + 12x + 9
+--R Type: Polynomial(Integer)
+--E 136
+
+--S 137 of 500
+r0:=9*x+6*x^2-35/3*x^3-25/2*x^4
+--R
+--R
+--R 25 4 35 3 2
+--R (2) - -- x - -- x + 6x + 9x
+--R 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 137
+
+--S 138 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 25 4 35 3 2
+--R (3) - -- x - -- x + 6x + 9x
+--R 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 138
+
+--S 139 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(1-2*x)*(3+5*x)^2/(2+3*x)
+--R
+--R
+--R 3 2
+--R - 50x - 35x + 12x + 9
+--R (1) -----------------------
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 141
+
+--S 142 of 500
+r0:=118/27*x-5/18*x^2-50/9*x^3+7/81*log(2+3*x)
+--R
+--R
+--R 3 2
+--R 14log(3x + 2) - 900x - 45x + 708x
+--R (2) -----------------------------------
+--R 162
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 14log(3x + 2) - 900x - 45x + 708x
+--R (3) -----------------------------------
+--R 162
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^2
+--R
+--R
+--R 3 2
+--R - 50x - 35x + 12x + 9
+--R (1) -----------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 500
+r0:=95/27*x-25/9*x^2+(-7/81)/(2+3*x)-8/9*log(2+3*x)
+--R
+--R
+--R 3 2
+--R (- 216x - 144)log(3x + 2) - 675x + 405x + 570x - 7
+--R (2) ----------------------------------------------------
+--R 243x + 162
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R (- 216x - 144)log(3x + 2) - 675x + 405x + 570x - 7
+--R (3) ----------------------------------------------------
+--R 243x + 162
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^3
+--R
+--R
+--R 3 2
+--R - 50x - 35x + 12x + 9
+--R (1) -----------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 151
+
+--S 152 of 500
+r0:=-50/27*x+(-7/162)/(2+3*x)^2+8/9/(2+3*x)+65/27*log(2+3*x)
+--R
+--R
+--R 2 3 2
+--R (3510x + 4680x + 1560)log(3x + 2) - 2700x - 3600x - 768x + 281
+--R (2) -----------------------------------------------------------------
+--R 2
+--R 1458x + 1944x + 648
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2
+--R (3510x + 4680x + 1560)log(3x + 2) - 2700x - 3600x - 768x + 281
+--R (3) -----------------------------------------------------------------
+--R 2
+--R 1458x + 1944x + 648
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^4
+--R
+--R
+--R 3 2
+--R - 50x - 35x + 12x + 9
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 500
+r0:=(-7/243)/(2+3*x)^3+4/9/(2+3*x)^2+(-65/27)/(2+3*x)-50/81*log(2+3*x)
+--R
+--R
+--R 3 2 2
+--R (- 4050x - 8100x - 5400x - 1200)log(3x + 2) - 5265x - 6696x - 2131
+--R (2) ---------------------------------------------------------------------
+--R 3 2
+--R 6561x + 13122x + 8748x + 1944
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 2
+--R (- 4050x - 8100x - 5400x - 1200)log(3x + 2) - 5265x - 6696x - 2131
+--R (3) ---------------------------------------------------------------------
+--R 3 2
+--R 6561x + 13122x + 8748x + 1944
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^5
+--R
+--R
+--R 3 2
+--R - 50x - 35x + 12x + 9
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 500
+r0:=7/12*(3+5*x)^3/(2+3*x)^4+3/4*(3+5*x)^3/(2+3*x)^3
+--R
+--R
+--R 125 4 2300 3 515 2 38 25
+--R --- x + ---- x + --- x + -- x + --
+--R 36 243 54 9 36
+--R (2) -------------------------------------
+--R 4 8 3 8 2 32 16
+--R x + - x + - x + -- x + --
+--R 3 3 27 81
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 600x + 810x + 312x + 25
+--R (3) --------------------------------------
+--R 4 3 2
+--R 2916x + 7776x + 7776x + 3456x + 576
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R 125
+--R (4) - ---
+--R 36
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^6
+--R
+--R
+--R 3 2
+--R - 50x - 35x + 12x + 9
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 166
+
+--S 167 of 500
+r0:=(-7/405)/(2+3*x)^5+2/9/(2+3*x)^4+(-65/81)/(2+3*x)^3+25/81/(2+3*x)^2
+--R
+--R
+--R 25 3 85 2 58 127
+--R --- x + ---- x + ---- x - -----
+--R 729 2187 6561 98415
+--R (2) ---------------------------------------
+--R 5 10 4 40 3 80 2 80 32
+--R x + -- x + -- x + -- x + -- x + ---
+--R 3 9 27 81 243
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 167
+
+--S 168 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 3375x + 3825x + 870x - 127
+--R (3) ---------------------------------------------------------
+--R 5 4 3 2
+--R 98415x + 328050x + 437400x + 291600x + 97200x + 12960
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^7
+--R
+--R
+--R 3 2
+--R - 50x - 35x + 12x + 9
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 171
+
+--S 172 of 500
+r0:=(-7/486)/(2+3*x)^6+8/45/(2+3*x)^5+(-65/108)/(2+3*x)^4+50/243/(2+3*x)^3
+--R
+--R
+--R 50 3 205 2 97 1021
+--R ---- x + ----- x + ----- x - -------
+--R 6561 26244 98415 1771470
+--R (2) ----------------------------------------------
+--R 6 5 20 4 160 3 80 2 64 64
+--R x + 4x + -- x + --- x + -- x + -- x + ---
+--R 3 27 27 81 729
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 172
+
+--S 173 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R 27000x + 27675x + 3492x - 2042
+--R /
+--R 6 5 4 3 2
+--R 3542940x + 14171760x + 23619600x + 20995200x + 10497600x + 2799360x
+--R +
+--R 311040
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 3 2
+--R - 50x - 35x + 12x + 9
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 176
+
+--S 177 of 500
+r0:=(-1/81)/(2+3*x)^7+4/27/(2+3*x)^6+(-13/27)/(2+3*x)^5+25/162/(2+3*x)^4
+--R
+--R
+--R 25 3 4 2 2 11
+--R ----- x + ---- x + ----- x - -----
+--R 13122 2187 19683 59049
+--R (2) ------------------------------------------------------------
+--R 7 14 6 28 5 280 4 560 3 224 2 448 128
+--R x + -- x + -- x + --- x + --- x + --- x + --- x + ----
+--R 3 3 27 81 81 729 2187
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 177
+
+--S 178 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R 225x + 216x + 12x - 22
+--R /
+--R 7 6 5 4 3 2
+--R 118098x + 551124x + 1102248x + 1224720x + 816480x + 326592x
+--R +
+--R 72576x + 6912
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(1-2*x)*(2+3*x)^m*(3+5*x)^3
+--R
+--R
+--R 4 3 2 m
+--R (1) (- 250x - 325x - 45x + 81x + 27)(3x + 2)
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+r0:=-7/243*(2+3*x)^(1+m)/(1+m)+107/243*(2+3*x)^(2+m)/(2+m)-_
+ 185/81*(2+3*x)^(3+m)/(3+m)+1025/243*(2+3*x)^(4+m)/(4+m)-_
+ 250/243*(2+3*x)^(5+m)/(5+m)
+--R
+--R
+--R (2)
+--R 4 3 2 m + 5
+--R (- 250m - 2500m - 8750m - 12500m - 6000)(3x + 2)
+--R +
+--R 4 3 2 m + 4
+--R (1025m + 11275m + 42025m + 62525m + 30750)(3x + 2)
+--R +
+--R 4 3 2 m + 3
+--R (- 555m - 6660m - 27195m - 43290m - 22200)(3x + 2)
+--R +
+--R 4 3 2 m + 2
+--R (107m + 1391m + 6313m + 11449m + 6420)(3x + 2)
+--R +
+--R 4 3 2 m + 1
+--R (- 7m - 98m - 497m - 1078m - 840)(3x + 2)
+--R /
+--R 5 4 3 2
+--R 243m + 3645m + 20655m + 54675m + 66582m + 29160
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 5
+--R (- 20250m - 202500m - 708750m - 1012500m - 486000)x
+--R +
+--R 4 3 2 4
+--R (- 39825m - 370575m - 1227825m - 1686825m - 789750)x
+--R +
+--R 4 3 2 3
+--R (- 21195m - 148140m - 368955m - 387810m - 145800)x
+--R +
+--R 4 3 2 2
+--R (4131m + 96093m + 455229m + 756927m + 393660)x
+--R +
+--R 4 3 2 4 3
+--R (6561m + 86346m + 343215m + 526038m + 262440)x + 1458m + 17496m
+--R +
+--R 2
+--R 66366m + 99240m + 48800
+--R *
+--R m log(3x + 2)
+--R %e
+--R /
+--R 5 4 3 2
+--R 81m + 1215m + 6885m + 18225m + 22194m + 9720
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 3 2 5
+--R (- 60750m - 607500m - 2126250m - 3037500m - 1458000)x
+--R +
+--R 4 3 2 4
+--R (- 119475m - 1111725m - 3683475m - 5060475m - 2369250)x
+--R +
+--R 4 3 2 3
+--R (- 63585m - 444420m - 1106865m - 1163430m - 437400)x
+--R +
+--R 4 3 2 2
+--R (12393m + 288279m + 1365687m + 2270781m + 1180980)x
+--R +
+--R 4 3 2 4
+--R (19683m + 259038m + 1029645m + 1578114m + 787320)x + 4374m
+--R +
+--R 3 2
+--R 52488m + 199098m + 297720m + 146400
+--R *
+--R m log(3x + 2)
+--R %e
+--R +
+--R 4 3 2 m + 5
+--R (250m + 2500m + 8750m + 12500m + 6000)(3x + 2)
+--R +
+--R 4 3 2 m + 4
+--R (- 1025m - 11275m - 42025m - 62525m - 30750)(3x + 2)
+--R +
+--R 4 3 2 m + 3
+--R (555m + 6660m + 27195m + 43290m + 22200)(3x + 2)
+--R +
+--R 4 3 2 m + 2
+--R (- 107m - 1391m - 6313m - 11449m - 6420)(3x + 2)
+--R +
+--R 4 3 2 m + 1
+--R (7m + 98m + 497m + 1078m + 840)(3x + 2)
+--R /
+--R 5 4 3 2
+--R 243m + 3645m + 20655m + 54675m + 66582m + 29160
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(1-2*x)*(2+3*x)^8*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 12 11 10 9 8
+--R - 1640250x - 10880325x - 32079645x - 54794799x - 58723461x
+--R +
+--R 7 6 5 4 3 2
+--R - 38920608x - 12816720x + 2100768x + 4580384x + 2391296x + 672768x
+--R +
+--R 103680x + 6912
+--R Type: Polynomial(Integer)
+--E 186
+
+--S 187 of 500
+r0:=-7/2187*(2+3*x)^9+107/2430*(2+3*x)^10-185/891*(2+3*x)^11+_
+ 1025/2916*(2+3*x)^12-250/3159*(2+3*x)^13
+--R
+--R
+--R (2)
+--R 1640250 13 3626775 12 32079645 11 54794799 10 9
+--R - ------- x - ------- x - -------- x - -------- x - 6524829x
+--R 13 4 11 10
+--R +
+--R 8 7 6 4580384 5 4 3
+--R - 4865076x - 1830960x + 350128x + ------- x + 597824x + 224256x
+--R 5
+--R +
+--R 2 640642048
+--R 51840x + 6912x + ---------
+--R 1563705
+--R Type: Polynomial(Fraction(Integer))
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1640250 13 3626775 12 32079645 11 54794799 10 9
+--R - ------- x - ------- x - -------- x - -------- x - 6524829x
+--R 13 4 11 10
+--R +
+--R 8 7 6 4580384 5 4 3
+--R - 4865076x - 1830960x + 350128x + ------- x + 597824x + 224256x
+--R 5
+--R +
+--R 2
+--R 51840x + 6912x
+--R Type: Polynomial(Fraction(Integer))
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R 640642048
+--R (4) - ---------
+--R 1563705
+--R Type: Polynomial(Fraction(Integer))
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(1-2*x)*(2+3*x)^7*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 11 10 9 8 7 6
+--R - 546750x - 3262275x - 8518365x - 12586023x - 11183805x - 5517666x
+--R +
+--R 5 4 3 2
+--R - 593796x + 1096120x + 796048x + 266400x + 46656x + 3456
+--R Type: Polynomial(Integer)
+--E 191
+
+--S 192 of 500
+r0:=3456*x+23328*x^2+88800*x^3+199012*x^4+219224*x^5-98966*x^6-_
+ 788238*x^7-11183805/8*x^8-1398447*x^9-1703673/2*x^10-_
+ 3262275/11*x^11-91125/2*x^12
+--R
+--R
+--R (2)
+--R 91125 12 3262275 11 1703673 10 9 11183805 8
+--R - ----- x - ------- x - ------- x - 1398447x - -------- x
+--R 2 11 2 8
+--R +
+--R 7 6 5 4 3 2
+--R - 788238x - 98966x + 219224x + 199012x + 88800x + 23328x + 3456x
+--R Type: Polynomial(Fraction(Integer))
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 91125 12 3262275 11 1703673 10 9 11183805 8
+--R - ----- x - ------- x - ------- x - 1398447x - -------- x
+--R 2 11 2 8
+--R +
+--R 7 6 5 4 3 2
+--R - 788238x - 98966x + 219224x + 199012x + 88800x + 23328x + 3456x
+--R Type: Polynomial(Fraction(Integer))
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(1-2*x)*(2+3*x)^6*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5
+--R - 182250x - 965925x - 2195505x - 2731671x - 1906821x - 568008x
+--R +
+--R 4 3 2
+--R 180740x + 244880x + 102096x + 20736x + 1728
+--R Type: Polynomial(Integer)
+--E 196
+
+--S 197 of 500
+r0:=1728*x+10368*x^2+34032*x^3+61220*x^4+36148*x^5-94668*x^6-_
+ 272403*x^7-2731671/8*x^8-243945*x^9-193185/2*x^10-182250/11*x^11
+--R
+--R
+--R (2)
+--R 182250 11 193185 10 9 2731671 8 7 6
+--R - ------ x - ------ x - 243945x - ------- x - 272403x - 94668x
+--R 11 2 8
+--R +
+--R 5 4 3 2
+--R 36148x + 61220x + 34032x + 10368x + 1728x
+--R Type: Polynomial(Fraction(Integer))
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 182250 11 193185 10 9 2731671 8 7 6
+--R - ------ x - ------ x - 243945x - ------- x - 272403x - 94668x
+--R 11 2 8
+--R +
+--R 5 4 3 2
+--R 36148x + 61220x + 34032x + 10368x + 1728x
+--R Type: Polynomial(Fraction(Integer))
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(1-2*x)*(2+3*x)^5*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3
+--R - 60750x - 281475x - 544185x - 547767x - 270429x - 9050x + 66280x
+--R +
+--R 2
+--R 37440x + 9072x + 864
+--R Type: Polynomial(Integer)
+--E 201
+
+--S 202 of 500
+r0:=864*x+4536*x^2+12480*x^3+16570*x^4-1810*x^5-90143/2*x^6-_
+ 547767/7*x^7-544185/8*x^8-31275*x^9-6075*x^10
+--R
+--R
+--R (2)
+--R 10 9 544185 8 547767 7 90143 6 5 4
+--R - 6075x - 31275x - ------ x - ------ x - ----- x - 1810x + 16570x
+--R 8 7 2
+--R +
+--R 3 2
+--R 12480x + 4536x + 864x
+--R Type: Polynomial(Fraction(Integer))
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 544185 8 547767 7 90143 6 5 4
+--R - 6075x - 31275x - ------ x - ------ x - ----- x - 1810x + 16570x
+--R 8 7 2
+--R +
+--R 3 2
+--R 12480x + 4536x + 864x
+--R Type: Polynomial(Fraction(Integer))
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(1-2*x)*(2+3*x)^4*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 20250x - 80325x - 127845x - 97359x - 25237x + 13808x + 12888x
+--R +
+--R 3888x + 432
+--R Type: Polynomial(Integer)
+--E 206
+
+--S 207 of 500
+r0:=432*x+1944*x^2+4296*x^3+3452*x^4-25237/5*x^5-32453/2*x^6-_
+ 127845/7*x^7-80325/8*x^8-2250*x^9
+--R
+--R
+--R (2)
+--R 9 80325 8 127845 7 32453 6 25237 5 4 3
+--R - 2250x - ----- x - ------ x - ----- x - ----- x + 3452x + 4296x
+--R 8 7 2 5
+--R +
+--R 2
+--R 1944x + 432x
+--R Type: Polynomial(Fraction(Integer))
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 80325 8 127845 7 32453 6 25237 5 4 3
+--R - 2250x - ----- x - ------ x - ----- x - ----- x + 3452x + 4296x
+--R 8 7 2 5
+--R +
+--R 2
+--R 1944x + 432x
+--R Type: Polynomial(Fraction(Integer))
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(1-2*x)*(2+3*x)^3*(3+5*x)^3
+--R
+--R
+--R 7 6 5 4 3 2
+--R (1) - 6750x - 22275x - 27765x - 13943x + 883x + 4014x + 1620x + 216
+--R Type: Polynomial(Integer)
+--E 211
+
+--S 212 of 500
+r0:=216*x+810*x^2+1338*x^3+883/4*x^4-13943/5*x^5-9255/2*x^6-_
+ 22275/7*x^7-3375/4*x^8
+--R
+--R
+--R (2)
+--R 3375 8 22275 7 9255 6 13943 5 883 4 3 2
+--R - ---- x - ----- x - ---- x - ----- x + --- x + 1338x + 810x + 216x
+--R 4 7 2 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3375 8 22275 7 9255 6 13943 5 883 4 3 2
+--R - ---- x - ----- x - ---- x - ----- x + --- x + 1338x + 810x + 216x
+--R 4 7 2 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(1-2*x)*(2+3*x)^2*(3+5*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R (1) - 2250x - 5925x - 5305x - 1111x + 1035x + 648x + 108
+--R Type: Polynomial(Integer)
+--E 216
+
+--S 217 of 500
+r0:=108*x+324*x^2+345*x^3-1111/4*x^4-1061*x^5-1975/2*x^6-2250/7*x^7
+--R
+--R
+--R 2250 7 1975 6 5 1111 4 3 2
+--R (2) - ---- x - ---- x - 1061x - ---- x + 345x + 324x + 108x
+--R 7 2 4
+--R Type: Polynomial(Fraction(Integer))
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2250 7 1975 6 5 1111 4 3 2
+--R (3) - ---- x - ---- x - 1061x - ---- x + 345x + 324x + 108x
+--R 7 2 4
+--R Type: Polynomial(Fraction(Integer))
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(1-2*x)*(2+3*x)*(3+5*x)^3
+--R
+--R
+--R 5 4 3 2
+--R (1) - 750x - 1475x - 785x + 153x + 243x + 54
+--R Type: Polynomial(Integer)
+--E 221
+
+--S 222 of 500
+r0:=54*x+243/2*x^2+51*x^3-785/4*x^4-295*x^5-125*x^6
+--R
+--R
+--R 6 5 785 4 3 243 2
+--R (2) - 125x - 295x - --- x + 51x + --- x + 54x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 222
+
+--S 223 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 5 785 4 3 243 2
+--R (3) - 125x - 295x - --- x + 51x + --- x + 54x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 223
+
+--S 224 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(1-2*x)*(3+5*x)^3
+--R
+--R
+--R 4 3 2
+--R (1) - 250x - 325x - 45x + 81x + 27
+--R Type: Polynomial(Integer)
+--E 226
+
+--S 227 of 500
+r0:=27*x+81/2*x^2-15*x^3-325/4*x^4-50*x^5
+--R
+--R
+--R 5 325 4 3 81 2
+--R (2) - 50x - --- x - 15x + -- x + 27x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 227
+
+--S 228 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 325 4 3 81 2
+--R (3) - 50x - --- x - 15x + -- x + 27x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 228
+
+--S 229 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(1-2*x)*(3+5*x)^3/(2+3*x)
+--R
+--R
+--R 4 3 2
+--R - 250x - 325x - 45x + 81x + 27
+--R (1) ---------------------------------
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 500
+r0:=1097/81*x+545/54*x^2-475/27*x^3-125/6*x^4-7/243*log(2+3*x)
+--R
+--R
+--R 4 3 2
+--R - 14log(3x + 2) - 10125x - 8550x + 4905x + 6582x
+--R (2) ---------------------------------------------------
+--R 486
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R - 14log(3x + 2) - 10125x - 8550x + 4905x + 6582x
+--R (3) ---------------------------------------------------
+--R 486
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^2
+--R
+--R
+--R 4 3 2
+--R - 250x - 325x - 45x + 81x + 27
+--R (1) ---------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 500
+r0:=55/9*x+25/54*x^2-250/27*x^3+7/243/(2+3*x)+107/243*log(2+3*x)
+--R
+--R
+--R 4 3 2
+--R (642x + 428)log(3x + 2) - 13500x - 8325x + 9360x + 5940x + 14
+--R (2) ----------------------------------------------------------------
+--R 1458x + 972
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R (642x + 428)log(3x + 2) - 13500x - 8325x + 9360x + 5940x + 14
+--R (3) ----------------------------------------------------------------
+--R 1458x + 972
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^3
+--R
+--R
+--R 4 3 2
+--R - 250x - 325x - 45x + 81x + 27
+--R (1) ---------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 500
+r0:=175/27*x-125/27*x^2+7/486/(2+3*x)^2+(-107/243)/(2+3*x)-185/81*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2
+--R (- 9990x - 13320x - 4440)log(3x + 2) - 20250x + 1350x + 28800x
+--R +
+--R 11958x - 421
+--R /
+--R 2
+--R 4374x + 5832x + 1944
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2
+--R (- 9990x - 13320x - 4440)log(3x + 2) - 20250x + 1350x + 28800x
+--R +
+--R 11958x - 421
+--R /
+--R 2
+--R 4374x + 5832x + 1944
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^4
+--R
+--R
+--R 4 3 2
+--R - 250x - 325x - 45x + 81x + 27
+--R (1) ---------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 500
+r0:=-250/81*x+7/729/(2+3*x)^3+(-107/486)/(2+3*x)^2+185/81/(2+3*x)+_
+ 1025/243*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 4 3
+--R (166050x + 332100x + 221400x + 49200)log(3x + 2) - 121500x - 243000x
+--R +
+--R 2
+--R - 132030x + 2997x + 12692
+--R /
+--R 3 2
+--R 39366x + 78732x + 52488x + 11664
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 3
+--R (166050x + 332100x + 221400x + 49200)log(3x + 2) - 121500x - 243000x
+--R +
+--R 2
+--R - 132030x + 2997x + 12692
+--R /
+--R 3 2
+--R 39366x + 78732x + 52488x + 11664
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^5
+--R
+--R
+--R 4 3 2
+--R - 250x - 325x - 45x + 81x + 27
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 500
+r0:=7/972/(2+3*x)^4+(-107/729)/(2+3*x)^3+185/162/(2+3*x)^2+_
+ (-1025/243)/(2+3*x)-250/243*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 243000x - 648000x - 648000x - 288000x - 48000)log(3x + 2)
+--R +
+--R 3 2
+--R - 332100x - 634230x - 404124x - 85915
+--R /
+--R 4 3 2
+--R 236196x + 629856x + 629856x + 279936x + 46656
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 243000x - 648000x - 648000x - 288000x - 48000)log(3x + 2)
+--R +
+--R 3 2
+--R - 332100x - 634230x - 404124x - 85915
+--R /
+--R 4 3 2
+--R 236196x + 629856x + 629856x + 279936x + 46656
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^6
+--R
+--R
+--R 4 3 2
+--R - 250x - 325x - 45x + 81x + 27
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 500
+r0:=7/15*(3+5*x)^4/(2+3*x)^5+5/12*(3+5*x)^4/(2+3*x)^4
+--R
+--R
+--R 3125 5 5375 4 2425 3 2 119 13
+--R ---- x + ---- x + ---- x + 10x + --- x + --
+--R 972 486 162 36 30
+--R (2) -----------------------------------------------
+--R 5 10 4 40 3 80 2 80 32
+--R x + -- x + -- x + -- x + -- x + ---
+--R 3 9 27 81 243
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 257
+
+--S 258 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R 405000x + 803250x + 559800x + 153795x + 11758
+--R (3) -----------------------------------------------------------------
+--R 5 4 3 2
+--R 1180980x + 3936600x + 5248800x + 3499200x + 1166400x + 155520
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 500
+m0:=a0-r0
+--R
+--R
+--R 3125
+--R (4) - ----
+--R 972
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^7
+--R
+--R
+--R 4 3 2
+--R - 250x - 325x - 45x + 81x + 27
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 500
+r0:=7/18*(3+5*x)^4/(2+3*x)^6+29/45*(3+5*x)^4/(2+3*x)^5+_
+ 29/36*(3+5*x)^4/(2+3*x)^4
+--R
+--R
+--R 18125 6 18125 5 30250 4 8975 3 665 2 664 49
+--R ----- x + ----- x + ----- x + ---- x + --- x + --- x + --
+--R 2916 729 729 243 36 135 90
+--R (2) --------------------------------------------------------------
+--R 6 5 20 4 160 3 80 2 64 64
+--R x + 4x + -- x + --- x + -- x + -- x + ---
+--R 3 27 27 81 729
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 262
+
+--S 263 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 607500x + 1066500x + 587925x + 78048x - 13198
+--R /
+--R 6 5 4 3 2
+--R 10628820x + 42515280x + 70858800x + 62985600x + 31492800x + 8398080x
+--R +
+--R 933120
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500
+m0:=a0-r0
+--R
+--R
+--R 18125
+--R (4) - -----
+--R 2916
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 4 3 2
+--R - 250x - 325x - 45x + 81x + 27
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 266
+
+--S 267 of 500
+r0:=1/243/(2+3*x)^7+(-107/1458)/(2+3*x)^6+37/81/(2+3*x)^5+_
+ (-1025/972)/(2+3*x)^4+250/729/(2+3*x)^3
+--R
+--R
+--R 250 4 4925 3 1147 2 107 922
+--R ----- x + ------ x + ------ x + ------- x - -------
+--R 19683 236196 118098 1062882 1594323
+--R (2) ------------------------------------------------------------
+--R 7 14 6 28 5 280 4 560 3 224 2 448 128
+--R x + -- x + -- x + --- x + --- x + --- x + --- x + ----
+--R 3 3 27 81 81 729 2187
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 267
+
+--S 268 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 81000x + 132975x + 61938x + 642x - 3688
+--R /
+--R 7 6 5 4 3
+--R 6377292x + 29760696x + 59521392x + 66134880x + 44089920x
+--R +
+--R 2
+--R 17635968x + 3919104x + 373248
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(5-2*x)^6*(2+3*x)^3*(-16+33*x)
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5
+--R 57024x - 768960x + 4070736x - 10051008x + 8647828x + 8983380x
+--R +
+--R 4 3 2
+--R - 19081125x - 196250x + 11962500x - 75000x - 2000000
+--R Type: Polynomial(Integer)
+--E 271
+
+--S 272 of 500
+r0:=-1/2*(5-2*x)^7*(2+3*x)^4
+--R
+--R
+--R (2)
+--R 11 10 9 8 7 6
+--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x
+--R +
+--R 5 98125 4 3 2
+--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x - 625000
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 272
+
+--S 273 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 11 10 9 8 7 6
+--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x
+--R +
+--R 5 98125 4 3 2
+--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 273
+
+--S 274 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 625000
+--R Type: Polynomial(Fraction(Integer))
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(1-2*x)*(2+3*x)^m/(3+5*x)
+--R
+--R
+--R m
+--R (- 2x + 1)(3x + 2)
+--R (1) -------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+--r0:=-2/15*(2+3*x)^(1+m)/(1+m)-11/5*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)
+--E 277
+
+--S 278 of 500
+--a0:=integrate(t0,x)
+--E 278
+
+--S 279 of 500
+--m0:=a0-r0
+--E 279
+
+--S 280 of 500
+--d0:=D(m0,x)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(1-2*x)*(2+3*x)^6/(3+5*x)
+--R
+--R
+--R 7 6 5 4 2
+--R - 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64
+--R (1) --------------------------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 500
+r0:=1666663/78125*x+1777779/31250*x^2+152469/3125*x^3-_
+ 152469/2500*x^4-106677/625*x^5-7047/50*x^6-1458/35*x^7+_
+ 11/390625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 308log(5x + 3) - 455625000x - 1541531250x - 1866847500x - 667051875x
+--R +
+--R 3 2
+--R 533641500x + 622222650x + 233332820x
+--R /
+--R 10937500
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 308log(5x + 3) - 455625000x - 1541531250x - 1866847500x - 667051875x
+--R +
+--R 3 2
+--R 533641500x + 622222650x + 233332820x
+--R /
+--R 10937500
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(1-2*x)*(2+3*x)^5/(3+5*x)
+--R
+--R
+--R 6 5 4 3 2
+--R - 486x - 1377x - 1350x - 360x + 240x + 176x + 32
+--R (1) -----------------------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 500
+r0:=166663/15625*x+127779/6250*x^2+2469/625*x^3-17469/500*x^4-_
+ 5427/125*x^5-81/5*x^6+11/78125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 44log(5x + 3) - 5062500x - 13567500x - 10918125x + 1234500x
+--R +
+--R 2
+--R 6388950x + 3333260x
+--R /
+--R 312500
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 44log(5x + 3) - 5062500x - 13567500x - 10918125x + 1234500x
+--R +
+--R 2
+--R 6388950x + 3333260x
+--R /
+--R 312500
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(1-2*x)*(2+3*x)^4/(3+5*x)
+--R
+--R
+--R 5 4 3 2
+--R - 162x - 351x - 216x + 24x + 64x + 16
+--R (1) -----------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 500
+r0:=16663/3125*x+7779/1250*x^2-531/125*x^3-1269/100*x^4-_
+ 162/25*x^5+11/15625*log(3+5*x)
+--R
+--R
+--R 5 4 3 2
+--R 44log(5x + 3) - 405000x - 793125x - 265500x + 388950x + 333260x
+--R (2) -------------------------------------------------------------------
+--R 62500
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R 44log(5x + 3) - 405000x - 793125x - 265500x + 388950x + 333260x
+--R (3) -------------------------------------------------------------------
+--R 62500
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(1-2*x)*(2+3*x)^3/(3+5*x)
+--R
+--R
+--R 4 3 2
+--R - 54x - 81x - 18x + 20x + 8
+--R (1) ------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 296
+
+--S 297 of 500
+r0:=1663/625*x+279/250*x^2-81/25*x^3-27/10*x^4+11/3125*log(3+5*x)
+--R
+--R
+--R 4 3 2
+--R 22log(5x + 3) - 16875x - 20250x + 6975x + 16630x
+--R (2) ---------------------------------------------------
+--R 6250
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R 22log(5x + 3) - 16875x - 20250x + 6975x + 16630x
+--R (3) ---------------------------------------------------
+--R 6250
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(1-2*x)*(2+3*x)^2/(3+5*x)
+--R
+--R
+--R 3 2
+--R - 18x - 15x + 4x + 4
+--R (1) ----------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 301
+
+--S 302 of 500
+r0:=163/125*x-21/50*x^2-6/5*x^3+11/625*log(3+5*x)
+--R
+--R
+--R 3 2
+--R 22log(5x + 3) - 1500x - 525x + 1630x
+--R (2) --------------------------------------
+--R 1250
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 22log(5x + 3) - 1500x - 525x + 1630x
+--R (3) --------------------------------------
+--R 1250
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(1-2*x)*(2+3*x)/(3+5*x)
+--R
+--R
+--R 2
+--R - 6x - x + 2
+--R (1) -------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 306
+
+--S 307 of 500
+r0:=13/25*x-3/5*x^2+11/125*log(3+5*x)
+--R
+--R
+--R 2
+--R 11log(5x + 3) - 75x + 65x
+--R (2) --------------------------
+--R 125
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 11log(5x + 3) - 75x + 65x
+--R (3) --------------------------
+--R 125
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(1-2*x)/(3+5*x)
+--R
+--R
+--R - 2x + 1
+--R (1) --------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 311
+
+--S 312 of 500
+r0:=-2/5*x+11/25*log(3+5*x)
+--R
+--R
+--R 11log(5x + 3) - 10x
+--R (2) -------------------
+--R 25
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 11log(5x + 3) - 10x
+--R (3) -------------------
+--R 25
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R - 2x + 1
+--R (1) --------------
+--R 2
+--R 15x + 19x + 6
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 500
+r0:=-7/3*log(2+3*x)+11/5*log(3+5*x)
+--R
+--R
+--R 33log(5x + 3) - 35log(3x + 2)
+--R (2) -----------------------------
+--R 15
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 33log(5x + 3) - 35log(3x + 2)
+--R (3) -----------------------------
+--R 15
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(1-2*x)/((2+3*x)^2*(3+5*x))
+--R
+--R
+--R - 2x + 1
+--R (1) ----------------------
+--R 3 2
+--R 45x + 87x + 56x + 12
+--R Type: Fraction(Polynomial(Integer))
+--E 321
+
+--S 322 of 500
+r0:=7/3/(2+3*x)-11*log(2+3*x)+11*log(3+5*x)
+--R
+--R
+--R (99x + 66)log(5x + 3) + (- 99x - 66)log(3x + 2) + 7
+--R (2) ---------------------------------------------------
+--R 9x + 6
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (99x + 66)log(5x + 3) + (- 99x - 66)log(3x + 2) + 7
+--R (3) ---------------------------------------------------
+--R 9x + 6
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(1-2*x)/((2+3*x)^3*(3+5*x))
+--R
+--R
+--R - 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 135x + 351x + 342x + 148x + 24
+--R Type: Fraction(Polynomial(Integer))
+--E 326
+
+--S 327 of 500
+r0:=7/6/(2+3*x)^2+11/(2+3*x)-55*log(2+3*x)+55*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (2970x + 3960x + 1320)log(5x + 3) + (- 2970x - 3960x - 1320)log(3x + 2)
+--R +
+--R 198x + 139
+--R /
+--R 2
+--R 54x + 72x + 24
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (2970x + 3960x + 1320)log(5x + 3) + (- 2970x - 3960x - 1320)log(3x + 2)
+--R +
+--R 198x + 139
+--R /
+--R 2
+--R 54x + 72x + 24
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(1-2*x)/((2+3*x)^4*(3+5*x))
+--R
+--R
+--R - 2x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 405x + 1323x + 1728x + 1128x + 368x + 48
+--R Type: Fraction(Polynomial(Integer))
+--E 331
+
+--S 332 of 500
+r0:=7/9/(2+3*x)^3+11/2/(2+3*x)^2+55/(2+3*x)-275*log(2+3*x)+275*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (133650x + 267300x + 178200x + 39600)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 133650x - 267300x - 178200x - 39600)log(3x + 2) + 8910x + 12177x
+--R +
+--R 4172
+--R /
+--R 3 2
+--R 486x + 972x + 648x + 144
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (133650x + 267300x + 178200x + 39600)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 133650x - 267300x - 178200x - 39600)log(3x + 2) + 8910x + 12177x
+--R +
+--R 4172
+--R /
+--R 3 2
+--R 486x + 972x + 648x + 144
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(1-2*x)/((2+3*x)^5*(3+5*x))
+--R
+--R
+--R - 2x + 1
+--R (1) ------------------------------------------------------
+--R 6 5 4 3 2
+--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96
+--R Type: Fraction(Polynomial(Integer))
+--E 336
+
+--S 337 of 500
+r0:=7/12/(2+3*x)^4+11/3/(2+3*x)^3+55/2/(2+3*x)^2+275/(2+3*x)-_
+ 1375*log(2+3*x)+1375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (1336500x + 3564000x + 3564000x + 1584000x + 264000)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 1336500x - 3564000x - 3564000x - 1584000x - 264000)log(3x + 2)
+--R +
+--R 3 2
+--R 89100x + 181170x + 122892x + 27815
+--R /
+--R 4 3 2
+--R 972x + 2592x + 2592x + 1152x + 192
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (1336500x + 3564000x + 3564000x + 1584000x + 264000)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 1336500x - 3564000x - 3564000x - 1584000x - 264000)log(3x + 2)
+--R +
+--R 3 2
+--R 89100x + 181170x + 122892x + 27815
+--R /
+--R 4 3 2
+--R 972x + 2592x + 2592x + 1152x + 192
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(1-2*x)/((2+3*x)^6*(3+5*x))
+--R
+--R
+--R - 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 500
+r0:=7/15/(2+3*x)^5+11/4/(2+3*x)^4+55/3/(2+3*x)^3+275/2/(2+3*x)^2+_
+ 1375/(2+3*x)-6875*log(2+3*x)+6875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 33412500x + 111375000x + 148500000x + 99000000x + 33000000x
+--R +
+--R 4400000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 33412500x - 111375000x - 148500000x - 99000000x - 33000000x
+--R +
+--R - 4400000
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 2227500x + 6014250x + 6091800x + 2743565x + 463586
+--R /
+--R 5 4 3 2
+--R 4860x + 16200x + 21600x + 14400x + 4800x + 640
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 33412500x + 111375000x + 148500000x + 99000000x + 33000000x
+--R +
+--R 4400000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 33412500x - 111375000x - 148500000x - 99000000x - 33000000x
+--R +
+--R - 4400000
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 2227500x + 6014250x + 6091800x + 2743565x + 463586
+--R /
+--R 5 4 3 2
+--R 4860x + 16200x + 21600x + 14400x + 4800x + 640
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(1-2*x)/((2+3*x)^7*(3+5*x))
+--R
+--R
+--R (1)
+--R - 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x
+--R +
+--R 4672x + 384
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 500
+r0:=7/18/(2+3*x)^6+11/5/(2+3*x)^5+55/4/(2+3*x)^4+275/3/(2+3*x)^3+_
+ 1375/2/(2+3*x)^2+6875/(2+3*x)-34375*log(2+3*x)+34375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 4510687500x + 18042750000x + 30071250000x + 26730000000x
+--R +
+--R 2
+--R 13365000000x + 3564000000x + 396000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 4510687500x - 18042750000x - 30071250000x - 26730000000x
+--R +
+--R 2
+--R - 13365000000x - 3564000000x - 396000000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 300712500x + 1012398750x + 1363675500x + 918643275x + 309504888x
+--R +
+--R 41722762
+--R /
+--R 6 5 4 3 2
+--R 131220x + 524880x + 874800x + 777600x + 388800x + 103680x + 11520
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 4510687500x + 18042750000x + 30071250000x + 26730000000x
+--R +
+--R 2
+--R 13365000000x + 3564000000x + 396000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 4510687500x - 18042750000x - 30071250000x - 26730000000x
+--R +
+--R 2
+--R - 13365000000x - 3564000000x - 396000000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 300712500x + 1012398750x + 1363675500x + 918643275x + 309504888x
+--R +
+--R 41722762
+--R /
+--R 6 5 4 3 2
+--R 131220x + 524880x + 874800x + 777600x + 388800x + 103680x + 11520
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(1-2*x)*(2+3*x)^m/(3+5*x)^2
+--R
+--R
+--R m
+--R (- 2x + 1)(3x + 2)
+--R (1) -------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+--r0:=-11/5*(2+3*x)^(1+m)/(3+5*x)+1/5*(2-33*m)*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)
+--E 352
+
+--S 353 of 500
+--a0:=integrate(t0,x)
+--E 353
+
+--S 354 of 500
+--m0:=a0-r0
+--E 354
+
+--S 355 of 500
+--d0:=D(m0,x)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(1-2*x)*(2+3*x)^7/(3+5*x)^2
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 4374x - 18225x - 30618x - 24948x - 7560x + 3024x + 3360x + 1088x
+--R +
+--R 128
+--R /
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 356
+
+--S 357 of 500
+r0:=5555478/390625*x+5740767/156250*x^2+92592/3125*x^3-_
+ 513783/12500*x^4-336798/3125*x^5-21627/250*x^6-_
+ 4374/175*x^7+(-11/1953125)/(3+5*x)+229/1953125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 8 7
+--R (32060x + 19236)log(5x + 3) - 6834375000x - 27755156250x
+--R +
+--R 6 5 4 3
+--R - 43662543750x - 28920898125x + 1358398125x + 14907422250x
+--R +
+--R 2
+--R 9916639950x + 2333300760x - 308
+--R /
+--R 273437500x + 164062500
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7
+--R (32060x + 19236)log(5x + 3) - 6834375000x - 27755156250x
+--R +
+--R 6 5 4 3
+--R - 43662543750x - 28920898125x + 1358398125x + 14907422250x
+--R +
+--R 2
+--R 9916639950x + 2333300760x - 308
+--R /
+--R 273437500x + 164062500
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(1-2*x)*(2+3*x)^6/(3+5*x)^2
+--R
+--R
+--R 7 6 5 4 2
+--R - 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64
+--R (1) --------------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 361
+
+--S 362 of 500
+r0:=555489/78125*x+40743/3125*x^2+5553/3125*x^3-14094/625*x^4-_
+ 16767/625*x^5-243/25*x^6+(-11/390625)/(3+5*x)+196/390625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R (980x + 588)log(5x + 3) - 18984375x - 63787500x - 75481875x
+--R +
+--R 4 3 2
+--R - 22955625x + 27546750x + 29165850x + 8332335x - 11
+--R /
+--R 1953125x + 1171875
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R (980x + 588)log(5x + 3) - 18984375x - 63787500x - 75481875x
+--R +
+--R 4 3 2
+--R - 22955625x + 27546750x + 29165850x + 8332335x - 11
+--R /
+--R 1953125x + 1171875
+--R Type: Union(Expression(Integer),...)
+--E 363
+
+--S 364 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(1-2*x)*(2+3*x)^5/(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R - 486x - 1377x - 1350x - 360x + 240x + 176x + 32
+--R (1) -----------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 366
+
+--S 367 of 500
+r0:=444/125*x+24093/6250*x^2-1854/625*x^3-3969/500*x^4-_
+ 486/125*x^5+(-11/78125)/(3+5*x)+163/78125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R (3260x + 1956)log(5x + 3) - 6075000x - 16048125x - 12076875x
+--R +
+--R 3 2
+--R 3242250x + 9163950x + 3330000x - 44
+--R /
+--R 1562500x + 937500
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R (3260x + 1956)log(5x + 3) - 6075000x - 16048125x - 12076875x
+--R +
+--R 3 2
+--R 3242250x + 9163950x + 3330000x - 44
+--R /
+--R 1562500x + 937500
+--R Type: Union(Expression(Integer),...)
+--E 368
+
+--S 369 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(1-2*x)*(2+3*x)^4/(3+5*x)^2
+--R
+--R
+--R 5 4 3 2
+--R - 162x - 351x - 216x + 24x + 64x + 16
+--R (1) -----------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 371
+
+--S 372 of 500
+r0:=5511/3125*x+378/625*x^2-261/125*x^3-81/50*x^4+(-11/15625)/(3+5*x)+_
+ 26/3125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (1300x + 780)log(5x + 3) - 253125x - 478125x - 101250x + 332250x
+--R +
+--R 165330x - 22
+--R /
+--R 156250x + 93750
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (1300x + 780)log(5x + 3) - 253125x - 478125x - 101250x + 332250x
+--R +
+--R 165330x - 22
+--R /
+--R 156250x + 93750
+--R Type: Union(Expression(Integer),...)
+--E 373
+
+--S 374 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(1-2*x)*(2+3*x)^3/(3+5*x)^2
+--R
+--R
+--R 4 3 2
+--R - 54x - 81x - 18x + 20x + 8
+--R (1) ------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 376
+
+--S 377 of 500
+r0:=522/625*x-81/250*x^2-18/25*x^3+(-11/3125)/(3+5*x)+97/3125*log(3+5*x)
+--R
+--R
+--R 4 3 2
+--R (970x + 582)log(5x + 3) - 22500x - 23625x + 20025x + 15660x - 22
+--R (2) -------------------------------------------------------------------
+--R 31250x + 18750
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R (970x + 582)log(5x + 3) - 22500x - 23625x + 20025x + 15660x - 22
+--R (3) -------------------------------------------------------------------
+--R 31250x + 18750
+--R Type: Union(Expression(Integer),...)
+--E 378
+
+--S 379 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(1-2*x)*(2+3*x)^2/(3+5*x)^2
+--R
+--R
+--R 3 2
+--R - 18x - 15x + 4x + 4
+--R (1) ----------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 381
+
+--S 382 of 500
+r0:=33/125*x-9/25*x^2+(-11/625)/(3+5*x)+64/625*log(3+5*x)
+--R
+--R
+--R 3 2
+--R (320x + 192)log(5x + 3) - 1125x + 150x + 495x - 11
+--R (2) ----------------------------------------------------
+--R 3125x + 1875
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R (320x + 192)log(5x + 3) - 1125x + 150x + 495x - 11
+--R (3) ----------------------------------------------------
+--R 3125x + 1875
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(1-2*x)*(2+3*x)/(3+5*x)^2
+--R
+--R
+--R 2
+--R - 6x - x + 2
+--R (1) --------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 386
+
+--S 387 of 500
+r0:=-6/25*x+(-11/125)/(3+5*x)+31/125*log(3+5*x)
+--R
+--R
+--R 2
+--R (155x + 93)log(5x + 3) - 150x - 90x - 11
+--R (2) -----------------------------------------
+--R 625x + 375
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (155x + 93)log(5x + 3) - 150x - 90x - 11
+--R (3) -----------------------------------------
+--R 625x + 375
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(1-2*x)/(3+5*x)^2
+--R
+--R
+--R - 2x + 1
+--R (1) --------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 391
+
+--S 392 of 500
+r0:=(-11/25)/(3+5*x)-2/25*log(3+5*x)
+--R
+--R
+--R (- 10x - 6)log(5x + 3) - 11
+--R (2) ---------------------------
+--R 125x + 75
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (- 10x - 6)log(5x + 3) - 11
+--R (3) ---------------------------
+--R 125x + 75
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(1-2*x)/((2+3*x)*(3+5*x)^2)
+--R
+--R
+--R - 2x + 1
+--R (1) -----------------------
+--R 3 2
+--R 75x + 140x + 87x + 18
+--R Type: Fraction(Polynomial(Integer))
+--E 396
+
+--S 397 of 500
+r0:=(-11/5)/(3+5*x)+7*log(2+3*x)-7*log(3+5*x)
+--R
+--R
+--R (- 175x - 105)log(5x + 3) + (175x + 105)log(3x + 2) - 11
+--R (2) --------------------------------------------------------
+--R 25x + 15
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (- 175x - 105)log(5x + 3) + (175x + 105)log(3x + 2) - 11
+--R (3) --------------------------------------------------------
+--R 25x + 15
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(1-2*x)/((2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R - 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 225x + 570x + 541x + 228x + 36
+--R Type: Fraction(Polynomial(Integer))
+--E 401
+
+--S 402 of 500
+r0:=(-7)/(2+3*x)+(-11)/(3+5*x)+68*log(2+3*x)-68*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (- 1020x - 1292x - 408)log(5x + 3) + (1020x + 1292x + 408)log(3x + 2)
+--R +
+--R - 68x - 43
+--R /
+--R 2
+--R 15x + 19x + 6
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (- 1020x - 1292x - 408)log(5x + 3) + (1020x + 1292x + 408)log(3x + 2)
+--R +
+--R - 68x - 43
+--R /
+--R 2
+--R 15x + 19x + 6
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(1-2*x)/((2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R - 2x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 675x + 2160x + 2763x + 1766x + 564x + 72
+--R Type: Fraction(Polynomial(Integer))
+--E 406
+
+--S 407 of 500
+r0:=(-7/2)/(2+3*x)^2+(-68)/(2+3*x)+(-55)/(3+5*x)+505*log(2+3*x)-505*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (- 45450x - 87870x - 56560x - 12120)log(5x + 3)
+--R +
+--R 3 2 2
+--R (45450x + 87870x + 56560x + 12120)log(3x + 2) - 3030x - 3939x - 1277
+--R /
+--R 3 2
+--R 90x + 174x + 112x + 24
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (- 45450x - 87870x - 56560x - 12120)log(5x + 3)
+--R +
+--R 3 2 2
+--R (45450x + 87870x + 56560x + 12120)log(3x + 2) - 3030x - 3939x - 1277
+--R /
+--R 3 2
+--R 90x + 174x + 112x + 24
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(1-2*x)/((2+3*x)^4*(3+5*x)^2)
+--R
+--R
+--R - 2x + 1
+--R (1) ----------------------------------------------------------
+--R 6 5 4 3 2
+--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144
+--R Type: Fraction(Polynomial(Integer))
+--E 411
+
+--S 412 of 500
+r0:=(-7/3)/(2+3*x)^3+(-34)/(2+3*x)^2+(-505)/(2+3*x)+(-275)/(3+5*x)+_
+ 3350*log(2+3*x)-3350*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 1356750x - 3527550x - 3437100x - 1487400x - 241200)log(5x + 3)
+--R +
+--R 4 3 2
+--R (1356750x + 3527550x + 3437100x + 1487400x + 241200)log(3x + 2)
+--R +
+--R 3 2
+--R - 90450x - 177885x - 116513x - 25413
+--R /
+--R 4 3 2
+--R 405x + 1053x + 1026x + 444x + 72
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 1356750x - 3527550x - 3437100x - 1487400x - 241200)log(5x + 3)
+--R +
+--R 4 3 2
+--R (1356750x + 3527550x + 3437100x + 1487400x + 241200)log(3x + 2)
+--R +
+--R 3 2
+--R - 90450x - 177885x - 116513x - 25413
+--R /
+--R 4 3 2
+--R 405x + 1053x + 1026x + 444x + 72
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(1-2*x)/((2+3*x)^5*(3+5*x)^2)
+--R
+--R
+--R - 2x + 1
+--R (1) ----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288
+--R Type: Fraction(Polynomial(Integer))
+--E 416
+
+--S 417 of 500
+r0:=(-7/4)/(2+3*x)^4+(-68/3)/(2+3*x)^3+(-505/2)/(2+3*x)^2+_
+ (-3350)/(2+3*x)+(-1375)/(3+5*x)+20875*log(2+3*x)-20875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 101452500x - 331411500x - 432864000x - 282564000x - 92184000x
+--R +
+--R - 12024000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 101452500x + 331411500x + 432864000x + 282564000x + 92184000x
+--R +
+--R 12024000
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R - 6763500x - 17810550x - 17580090x - 7708553x - 1266855
+--R /
+--R 5 4 3 2
+--R 4860x + 15876x + 20736x + 13536x + 4416x + 576
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 101452500x - 331411500x - 432864000x - 282564000x - 92184000x
+--R +
+--R - 12024000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 101452500x + 331411500x + 432864000x + 282564000x + 92184000x
+--R +
+--R 12024000
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R - 6763500x - 17810550x - 17580090x - 7708553x - 1266855
+--R /
+--R 5 4 3 2
+--R 4860x + 15876x + 20736x + 13536x + 4416x + 576
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(1-2*x)/((2+3*x)^6*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R - 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x
+--R +
+--R 7104x + 576
+--R Type: Fraction(Polynomial(Integer))
+--E 421
+
+--S 422 of 500
+r0:=(-7/5)/(2+3*x)^5+(-17)/(2+3*x)^4+(-505/3)/(2+3*x)^3+_
+ (-1675)/(2+3*x)^2+(-20875)/(2+3*x)+(-6875)/(3+5*x)+_
+ 125000*log(2+3*x)-125000*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R - 2278125000x - 8960625000x - 14681250000x - 12825000000x
+--R +
+--R 2
+--R - 6300000000x - 1650000000x - 180000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R 2278125000x + 8960625000x + 14681250000x + 12825000000x
+--R +
+--R 2
+--R 6300000000x + 1650000000x + 180000000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 151875000x - 501187500x - 661387500x - 436271250x - 143844850x
+--R +
+--R - 18964893
+--R /
+--R 6 5 4 3 2
+--R 18225x + 71685x + 117450x + 102600x + 50400x + 13200x + 1440
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R - 2278125000x - 8960625000x - 14681250000x - 12825000000x
+--R +
+--R 2
+--R - 6300000000x - 1650000000x - 180000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R 2278125000x + 8960625000x + 14681250000x + 12825000000x
+--R +
+--R 2
+--R 6300000000x + 1650000000x + 180000000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 151875000x - 501187500x - 661387500x - 436271250x - 143844850x
+--R +
+--R - 18964893
+--R /
+--R 6 5 4 3 2
+--R 18225x + 71685x + 117450x + 102600x + 50400x + 13200x + 1440
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(1-2*x)/((2+3*x)^7*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R - 2x + 1
+--R /
+--R 9 8 7 6 5 4
+--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x
+--R +
+--R 3 2
+--R 351120x + 97952x + 15936x + 1152
+--R Type: Fraction(Polynomial(Integer))
+--E 426
+
+--S 427 of 500
+r0:=(-7/6)/(2+3*x)^6+(-68/5)/(2+3*x)^5+(-505/4)/(2+3*x)^4+_
+ (-3350/3)/(2+3*x)^3+(-20875/2)/(2+3*x)^2+(-125000)/(2+3*x)+_
+ (-34375)/(3+5*x)+728125*log(2+3*x)-728125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R - 53080312500x - 244169437500x - 481261500000x - 526871250000x
+--R +
+--R 3 2
+--R - 346005000000x - 136305000000x - 29824000000x - 2796000000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5 4
+--R 53080312500x + 244169437500x + 481261500000x + 526871250000x
+--R +
+--R 3 2
+--R 346005000000x + 136305000000x + 29824000000x + 2796000000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 3538687500x - 14036793750x - 23195441250x - 20438672625x
+--R +
+--R 2
+--R - 10128331755x - 2676272018x - 294588002
+--R /
+--R 7 6 5 4 3 2
+--R 72900x + 335340x + 660960x + 723600x + 475200x + 187200x + 40960x
+--R +
+--R 3840
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R - 53080312500x - 244169437500x - 481261500000x - 526871250000x
+--R +
+--R 3 2
+--R - 346005000000x - 136305000000x - 29824000000x - 2796000000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5 4
+--R 53080312500x + 244169437500x + 481261500000x + 526871250000x
+--R +
+--R 3 2
+--R 346005000000x + 136305000000x + 29824000000x + 2796000000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 3538687500x - 14036793750x - 23195441250x - 20438672625x
+--R +
+--R 2
+--R - 10128331755x - 2676272018x - 294588002
+--R /
+--R 7 6 5 4 3 2
+--R 72900x + 335340x + 660960x + 723600x + 475200x + 187200x + 40960x
+--R +
+--R 3840
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(1-2*x)*(2+3*x)^m/(3+5*x)^3
+--R
+--R
+--R m
+--R (- 2x + 1)(3x + 2)
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+--r0:=-11/10*(2+3*x)^(1+m)/(3+5*x)^2+1/10*(37-33*m)*(2+3*x)^(1+m)/(3+5*x)+_
+-- 3/10*(37-33*m)*m*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)
+--E 432
+
+--S 433 of 500
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 500
+--m0:=a0-r0
+--E 434
+
+--S 435 of 500
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(1-2*x)*(2+3*x)^7/(3+5*x)^3
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 4374x - 18225x - 30618x - 24948x - 7560x + 3024x + 3360x + 1088x
+--R +
+--R 128
+--R /
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 436
+
+--S 437 of 500
+r0:=1851147/390625*x+129654/15625*x^2+2052/3125*x^3-181521/12500*x^4-_
+ 51759/3125*x^5-729/125*x^6+(-11/3906250)/(3+5*x)^2+_
+ (-229/1953125)/(3+5*x)+2037/1953125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 8 7
+--R (203700x + 244440x + 73332)log(5x + 3) - 1139062500x - 4601812500x
+--R +
+--R 6 5 4 3 2
+--R - 7128253125x - 4439846250x + 753519375x + 2916553500x + 1694131200x
+--R +
+--R 333201880x - 2770
+--R /
+--R 2
+--R 195312500x + 234375000x + 70312500
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 7
+--R (203700x + 244440x + 73332)log(5x + 3) - 1139062500x - 4601812500x
+--R +
+--R 6 5 4 3 2
+--R - 7128253125x - 4439846250x + 753519375x + 2916553500x + 1694131200x
+--R +
+--R 333201880x - 2770
+--R /
+--R 2
+--R 195312500x + 234375000x + 70312500
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(1-2*x)*(2+3*x)^6/(3+5*x)^3
+--R
+--R
+--R 7 6 5 4 2
+--R - 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64
+--R (1) --------------------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 441
+
+--S 442 of 500
+r0:=36936/15625*x+297/125*x^2-6399/3125*x^3-12393/2500*x^4-_
+ 1458/625*x^5+(-11/781250)/(3+5*x)^2+(-196/390625)/(3+5*x)+_
+ 1449/390625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 7 6
+--R (144900x + 173880x + 52164)log(5x + 3) - 91125000x - 302990625x
+--R +
+--R 5 4 3 2
+--R - 345161250x - 72883125x + 174919500x + 144220500x + 33238480x - 2374
+--R /
+--R 2
+--R 39062500x + 46875000x + 14062500
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 6
+--R (144900x + 173880x + 52164)log(5x + 3) - 91125000x - 302990625x
+--R +
+--R 5 4 3 2
+--R - 345161250x - 72883125x + 174919500x + 144220500x + 33238480x - 2374
+--R /
+--R 2
+--R 39062500x + 46875000x + 14062500
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(1-2*x)*(2+3*x)^5/(3+5*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R - 486x - 1377x - 1350x - 360x + 240x + 176x + 32
+--R (1) -----------------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 446
+
+--S 447 of 500
+r0:=3636/3125*x+1971/6250*x^2-837/625*x^3-243/250*x^4+_
+ (-11/156250)/(3+5*x)^2+(-163/78125)/(3+5*x)+192/15625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 6 5 4
+--R (48000x + 57600x + 17280)log(5x + 3) - 3796875x - 9787500x - 6412500x
+--R +
+--R 3 2
+--R 4140000x + 5897475x + 1634570x - 989
+--R /
+--R 2
+--R 3906250x + 4687500x + 1406250
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 5 4
+--R (48000x + 57600x + 17280)log(5x + 3) - 3796875x - 9787500x - 6412500x
+--R +
+--R 3 2
+--R 4140000x + 5897475x + 1634570x - 989
+--R /
+--R 2
+--R 3906250x + 4687500x + 1406250
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(1-2*x)*(2+3*x)^4/(3+5*x)^3
+--R
+--R
+--R 5 4 3 2
+--R - 162x - 351x - 216x + 24x + 64x + 16
+--R (1) -----------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 451
+
+--S 452 of 500
+r0:=1647/3125*x-297/1250*x^2-54/125*x^3+(-11/31250)/(3+5*x)^2+_
+ (-26/3125)/(3+5*x)+114/3125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 5 4 3
+--R (28500x + 34200x + 10260)log(5x + 3) - 337500x - 590625x + 67500x
+--R +
+--R 2
+--R 427275x + 146930x - 791
+--R /
+--R 2
+--R 781250x + 937500x + 281250
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4 3
+--R (28500x + 34200x + 10260)log(5x + 3) - 337500x - 590625x + 67500x
+--R +
+--R 2
+--R 427275x + 146930x - 791
+--R /
+--R 2
+--R 781250x + 937500x + 281250
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(1-2*x)*(2+3*x)^3/(3+5*x)^3
+--R
+--R
+--R 4 3 2
+--R - 54x - 81x - 18x + 20x + 8
+--R (1) ------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 456
+
+--S 457 of 500
+r0:=81/625*x-27/125*x^2+(-11/6250)/(3+5*x)^2+(-97/3125)/(3+5*x)+_
+ 279/3125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2
+--R (13950x + 16740x + 5022)log(5x + 3) - 33750x - 20250x + 12150x
+--R +
+--R 6320x - 593
+--R /
+--R 2
+--R 156250x + 187500x + 56250
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2
+--R (13950x + 16740x + 5022)log(5x + 3) - 33750x - 20250x + 12150x
+--R +
+--R 6320x - 593
+--R /
+--R 2
+--R 156250x + 187500x + 56250
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(1-2*x)*(2+3*x)^2/(3+5*x)^3
+--R
+--R
+--R 3 2
+--R - 18x - 15x + 4x + 4
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 461
+
+--S 462 of 500
+r0:=-18/125*x+(-11/1250)/(3+5*x)^2+(-64/625)/(3+5*x)+87/625*log(3+5*x)
+--R
+--R
+--R 2 3 2
+--R (4350x + 5220x + 1566)log(5x + 3) - 4500x - 5400x - 2260x - 395
+--R (2) ------------------------------------------------------------------
+--R 2
+--R 31250x + 37500x + 11250
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2
+--R (4350x + 5220x + 1566)log(5x + 3) - 4500x - 5400x - 2260x - 395
+--R (3) ------------------------------------------------------------------
+--R 2
+--R 31250x + 37500x + 11250
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(1-2*x)*(2+3*x)/(3+5*x)^3
+--R
+--R
+--R 2
+--R - 6x - x + 2
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 466
+
+--S 467 of 500
+r0:=(-11/250)/(3+5*x)^2+(-31/125)/(3+5*x)-6/125*log(3+5*x)
+--R
+--R
+--R 2
+--R (- 300x - 360x - 108)log(5x + 3) - 310x - 197
+--R (2) ----------------------------------------------
+--R 2
+--R 6250x + 7500x + 2250
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (- 300x - 360x - 108)log(5x + 3) - 310x - 197
+--R (3) ----------------------------------------------
+--R 2
+--R 6250x + 7500x + 2250
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(1-2*x)/(3+5*x)^3
+--R
+--R
+--R - 2x + 1
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 471
+
+--S 472 of 500
+r0:=-1/22*(1-2*x)^2/(3+5*x)^2
+--R
+--R
+--R 2 2 2 1
+--R - --- x + --- x - ---
+--R 275 275 550
+--R (2) ----------------------
+--R 2 6 9
+--R x + - x + --
+--R 5 25
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 472
+
+--S 473 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 20x + 1
+--R (3) --------------------
+--R 2
+--R 1250x + 1500x + 450
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 500
+m0:=a0-r0
+--R
+--R
+--R 2
+--R (4) ---
+--R 275
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(1-2*x)/((2+3*x)*(3+5*x)^3)
+--R
+--R
+--R - 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 375x + 925x + 855x + 351x + 54
+--R Type: Fraction(Polynomial(Integer))
+--E 476
+
+--S 477 of 500
+r0:=(-11/10)/(3+5*x)^2+7/(3+5*x)-21*log(2+3*x)+21*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (5250x + 6300x + 1890)log(5x + 3) + (- 5250x - 6300x - 1890)log(3x + 2)
+--R +
+--R 350x + 199
+--R /
+--R 2
+--R 250x + 300x + 90
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (5250x + 6300x + 1890)log(5x + 3) + (- 5250x - 6300x - 1890)log(3x + 2)
+--R +
+--R 350x + 199
+--R /
+--R 2
+--R 250x + 300x + 90
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(1-2*x)/((2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R - 2x + 1
+--R (1) ----------------------------------------------
+--R 5 4 3 2
+--R 1125x + 3525x + 4415x + 2763x + 864x + 108
+--R Type: Fraction(Polynomial(Integer))
+--E 481
+
+--S 482 of 500
+r0:=21/(2+3*x)+(-11/2)/(3+5*x)^2+68/(3+5*x)-309*log(2+3*x)+309*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (46350x + 86520x + 53766x + 11124)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 46350x - 86520x - 53766x - 11124)log(3x + 2) + 3090x + 3811x + 1172
+--R /
+--R 3 2
+--R 150x + 280x + 174x + 36
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (46350x + 86520x + 53766x + 11124)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 46350x - 86520x - 53766x - 11124)log(3x + 2) + 3090x + 3811x + 1172
+--R /
+--R 3 2
+--R 150x + 280x + 174x + 36
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(1-2*x)/((2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R - 2x + 1
+--R (1) -----------------------------------------------------------
+--R 6 5 4 3 2
+--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216
+--R Type: Fraction(Polynomial(Integer))
+--E 486
+
+--S 487 of 500
+r0:=21/2/(2+3*x)^2+309/(2+3*x)+(-55/2)/(3+5*x)^2+505/(3+5*x)-_
+ 3060*log(2+3*x)+3060*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (1377000x + 3488400x + 3310920x + 1395360x + 220320)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 1377000x - 3488400x - 3310920x - 1395360x - 220320)log(3x + 2)
+--R +
+--R 3 2
+--R 91800x + 174420x + 110296x + 23213
+--R /
+--R 4 3 2
+--R 450x + 1140x + 1082x + 456x + 72
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (1377000x + 3488400x + 3310920x + 1395360x + 220320)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 1377000x - 3488400x - 3310920x - 1395360x - 220320)log(3x + 2)
+--R +
+--R 3 2
+--R 91800x + 174420x + 110296x + 23213
+--R /
+--R 4 3 2
+--R 450x + 1140x + 1082x + 456x + 72
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(1-2*x)/((2+3*x)^4*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R - 2x + 1
+--R -----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432
+--R Type: Fraction(Polynomial(Integer))
+--E 491
+
+--S 492 of 500
+r0:=7/(2+3*x)^3+309/2/(2+3*x)^2+3060/(2+3*x)+(-275/2)/(3+5*x)^2+3350/(3+5*x)-_
+ 25350*log(2+3*x)+25350*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 34222500x + 109512000x + 140084100x + 89536200x + 28594800x
+--R +
+--R 3650400
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 34222500x - 109512000x - 140084100x - 89536200x - 28594800x
+--R +
+--R - 3650400
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 2281500x + 5855850x + 5631080x + 2404363x + 384608
+--R /
+--R 5 4 3 2
+--R 1350x + 4320x + 5526x + 3532x + 1128x + 144
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 34222500x + 109512000x + 140084100x + 89536200x + 28594800x
+--R +
+--R 3650400
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 34222500x - 109512000x - 140084100x - 89536200x - 28594800x
+--R +
+--R - 3650400
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 2281500x + 5855850x + 5631080x + 2404363x + 384608
+--R /
+--R 5 4 3 2
+--R 1350x + 4320x + 5526x + 3532x + 1128x + 144
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(1-2*x)/((2+3*x)^5*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R - 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x
+--R +
+--R 10800x + 864
+--R Type: Fraction(Polynomial(Integer))
+--E 496
+
+--S 497 of 500
+r0:=21/4/(2+3*x)^4+103/(2+3*x)^3+1530/(2+3*x)^2+25350/(2+3*x)+_
+ (-1375/2)/(3+5*x)^2+20875/(3+5*x)-189375*log(2+3*x)+189375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 1533937500x + 5931225000x + 9551317500x + 8199180000x
+--R +
+--R 2
+--R 3957180000x + 1018080000x + 109080000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 1533937500x - 5931225000x - 9551317500x - 8199180000x
+--R +
+--R 2
+--R - 3957180000x - 1018080000x - 109080000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 102262500x + 330648750x + 427381500x + 276035525x + 89085434x
+--R +
+--R 11492725
+--R /
+--R 6 5 4 3 2
+--R 8100x + 31320x + 50436x + 43296x + 20896x + 5376x + 576
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 1533937500x + 5931225000x + 9551317500x + 8199180000x
+--R +
+--R 2
+--R 3957180000x + 1018080000x + 109080000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 1533937500x - 5931225000x - 9551317500x - 8199180000x
+--R +
+--R 2
+--R - 3957180000x - 1018080000x - 109080000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 102262500x + 330648750x + 427381500x + 276035525x + 89085434x
+--R +
+--R 11492725
+--R /
+--R 6 5 4 3 2
+--R 8100x + 31320x + 50436x + 43296x + 20896x + 5376x + 576
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3d.input.pdf b/src/axiom-website/CATS/rich3d.input.pdf
new file mode 100644
index 0000000..727fc1b
Binary files /dev/null and b/src/axiom-website/CATS/rich3d.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3e.input.pamphlet b/src/axiom-website/CATS/rich3e.input.pamphlet
new file mode 100644
index 0000000..9146b9c
--- /dev/null
+++ b/src/axiom-website/CATS/rich3e.input.pamphlet
@@ -0,0 +1,6307 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3e.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 249 integrals in this file.
+\item 249 supplied "optimal results".
+\item 230 matching answers.
+\item 24 cases where Axiom supplied 2 results.
+\item 34 cases that Axiom failed to integrate.
+\item 6 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3e.output
+)spool rich3e.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(1-2*x)/((2+3*x)^6*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R - 2x + 1
+--R /
+--R 9 8 7 6 5 4
+--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x
+--R +
+--R 3 2
+--R 545840x + 150480x + 24192x + 1728
+--R Type: Fraction(Polynomial(Integer))
+--E 1
+
+--S 2 of 500
+r0:=21/5/(2+3*x)^5+309/4/(2+3*x)^4+1020/(2+3*x)^3+12675/(2+3*x)^2+_
+ 189375/(2+3*x)+(-6875/2)/(3+5*x)^2+125000/(3+5*x)-_
+ 1321875*log(2+3*x)+1321875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 160607812500x + 728088750000x + 1414062562500x + 1525179375000x
+--R +
+--R 3 2
+--R 986647500000x + 382815000000x + 82485000000x + 7614000000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5 4
+--R - 160607812500x - 728088750000x - 1414062562500x - 1525179375000x
+--R +
+--R 3 2
+--R - 986647500000x - 382815000000x - 82485000000x - 7614000000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 10707187500x + 41758031250x + 67828050000x + 58733814375x
+--R +
+--R 2
+--R 28595335800x + 7421662135x + 802214966
+--R /
+--R 7 6 5 4 3 2
+--R 121500x + 550800x + 1069740x + 1153800x + 746400x + 289600x
+--R +
+--R 62400x + 5760
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 160607812500x + 728088750000x + 1414062562500x + 1525179375000x
+--R +
+--R 3 2
+--R 986647500000x + 382815000000x + 82485000000x + 7614000000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5 4
+--R - 160607812500x - 728088750000x - 1414062562500x - 1525179375000x
+--R +
+--R 3 2
+--R - 986647500000x - 382815000000x - 82485000000x - 7614000000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 10707187500x + 41758031250x + 67828050000x + 58733814375x
+--R +
+--R 2
+--R 28595335800x + 7421662135x + 802214966
+--R /
+--R 7 6 5 4 3 2
+--R 121500x + 550800x + 1069740x + 1153800x + 746400x + 289600x
+--R +
+--R 62400x + 5760
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(1-2*x)^2*(2+3*x)^8*(3+5*x)
+--R
+--R
+--R (1)
+--R 11 10 9 8 7 6
+--R 131220x + 647352x + 1307097x + 1298835x + 476928x - 275184x
+--R +
+--R 5 4 3 2
+--R - 372960x - 134112x + 12800x + 24832x + 7424x + 768
+--R Type: Polynomial(Integer)
+--E 6
+
+--S 7 of 500
+r0:=-49/729*(2+3*x)^9+91/270*(2+3*x)^10-16/99*(2+3*x)^11+5/243*(2+3*x)^12
+--R
+--R
+--R (2)
+--R 12 647352 11 1307097 10 9 8 7
+--R 10935x + ------ x + ------- x + 144315x + 59616x - 39312x
+--R 11 10
+--R +
+--R 6 134112 5 4 24832 3 2 2566144
+--R - 62160x - ------ x + 3200x + ----- x + 3712x + 768x + -------
+--R 5 3 40095
+--R Type: Polynomial(Fraction(Integer))
+--E 7
+
+--S 8 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 647352 11 1307097 10 9 8 7
+--R 10935x + ------ x + ------- x + 144315x + 59616x - 39312x
+--R 11 10
+--R +
+--R 6 134112 5 4 24832 3 2
+--R - 62160x - ------ x + 3200x + ----- x + 3712x + 768x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 8
+
+--S 9 of 500
+m0:=a0-r0
+--R
+--R
+--R 2566144
+--R (4) - -------
+--R 40095
+--R Type: Polynomial(Fraction(Integer))
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(1-2*x)^2*(2+3*x)^7*(3+5*x)
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5 4
+--R 43740x + 186624x + 311283x + 225423x + 8694x - 97524x - 59304x
+--R +
+--R 3 2
+--R - 5168x + 7712x + 3136x + 384
+--R Type: Polynomial(Integer)
+--E 11
+
+--S 12 of 500
+r0:=-49/648*(2+3*x)^8+91/243*(2+3*x)^9-8/45*(2+3*x)^10+20/891*(2+3*x)^11
+--R
+--R
+--R (2)
+--R 43740 11 93312 10 9 225423 8 7 6 59304 5
+--R ----- x + ----- x + 34587x + ------ x + 1242x - 16254x - ----- x
+--R 11 5 8 5
+--R +
+--R 4 7712 3 2 485216
+--R - 1292x + ---- x + 1568x + 384x + ------
+--R 3 13365
+--R Type: Polynomial(Fraction(Integer))
+--E 12
+
+--S 13 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 43740 11 93312 10 9 225423 8 7 6 59304 5
+--R ----- x + ----- x + 34587x + ------ x + 1242x - 16254x - ----- x
+--R 11 5 8 5
+--R +
+--R 4 7712 3 2
+--R - 1292x + ---- x + 1568x + 384x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 13
+
+--S 14 of 500
+m0:=a0-r0
+--R
+--R
+--R 485216
+--R (4) - ------
+--R 13365
+--R Type: Polynomial(Fraction(Integer))
+--E 14
+
+--S 15 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(1-2*x)^2*(2+3*x)^6*(3+5*x)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3 2
+--R 14580x + 52488x + 68769x + 29295x - 16632x - 21420x - 5488x + 1936x
+--R +
+--R 1280x + 192
+--R Type: Polynomial(Integer)
+--E 16
+
+--S 17 of 500
+r0:=192*x+640*x^2+1936/3*x^3-1372*x^4-4284*x^5-2772*x^6+4185*x^7+_
+ 68769/8*x^8+5832*x^9+1458*x^10
+--R
+--R
+--R (2)
+--R 10 9 68769 8 7 6 5 4 1936 3
+--R 1458x + 5832x + ----- x + 4185x - 2772x - 4284x - 1372x + ---- x
+--R 8 3
+--R +
+--R 2
+--R 640x + 192x
+--R Type: Polynomial(Fraction(Integer))
+--E 17
+
+--S 18 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 68769 8 7 6 5 4 1936 3
+--R 1458x + 5832x + ----- x + 4185x - 2772x - 4284x - 1372x + ---- x
+--R 8 3
+--R +
+--R 2
+--R 640x + 192x
+--R Type: Polynomial(Fraction(Integer))
+--E 18
+
+--S 19 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(1-2*x)^2*(2+3*x)^5*(3+5*x)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 4860x + 14256x + 13419x + 819x - 6090x - 3080x + 224x + 496x + 96
+--R Type: Polynomial(Integer)
+--E 21
+
+--S 22 of 500
+r0:=96*x+248*x^2+224/3*x^3-770*x^4-1218*x^5+273/2*x^6+1917*x^7+1782*x^8+540*x^9
+--R
+--R
+--R (2)
+--R 9 8 7 273 6 5 4 224 3 2
+--R 540x + 1782x + 1917x + --- x - 1218x - 770x + --- x + 248x + 96x
+--R 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 22
+
+--S 23 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7 273 6 5 4 224 3 2
+--R 540x + 1782x + 1917x + --- x - 1218x - 770x + --- x + 248x + 96x
+--R 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 23
+
+--S 24 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(1-2*x)^2*(2+3*x)^4*(3+5*x)
+--R
+--R
+--R 7 6 5 4 3 2
+--R (1) 1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48
+--R Type: Polynomial(Integer)
+--E 26
+
+--S 27 of 500
+r0:=48*x+88*x^2-152/3*x^3-328*x^4-1077/5*x^5+675/2*x^6+3672/7*x^7+405/2*x^8
+--R
+--R
+--R 405 8 3672 7 675 6 1077 5 4 152 3 2
+--R (2) --- x + ---- x + --- x - ---- x - 328x - --- x + 88x + 48x
+--R 2 7 2 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 27
+
+--S 28 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 405 8 3672 7 675 6 1077 5 4 152 3 2
+--R (3) --- x + ---- x + --- x - ---- x - 328x - --- x + 88x + 48x
+--R 2 7 2 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 28
+
+--S 29 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(1-2*x)^2*(2+3*x)^3*(3+5*x)
+--R
+--R
+--R 6 5 4 3 2
+--R (1) 540x + 864x + 99x - 425x - 154x + 52x + 24
+--R Type: Polynomial(Integer)
+--E 31
+
+--S 32 of 500
+r0:=24*x+26*x^2-154/3*x^3-425/4*x^4+99/5*x^5+144*x^6+540/7*x^7
+--R
+--R
+--R 540 7 6 99 5 425 4 154 3 2
+--R (2) --- x + 144x + -- x - --- x - --- x + 26x + 24x
+--R 7 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 32
+
+--S 33 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 540 7 6 99 5 425 4 154 3 2
+--R (3) --- x + 144x + -- x - --- x - --- x + 26x + 24x
+--R 7 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 33
+
+--S 34 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(1-2*x)^2*(2+3*x)^2*(3+5*x)
+--R
+--R
+--R 5 4 3 2
+--R (1) 180x + 168x - 79x - 89x + 8x + 12
+--R Type: Polynomial(Integer)
+--E 36
+
+--S 37 of 500
+r0:=12*x+4*x^2-89/3*x^3-79/4*x^4+168/5*x^5+30*x^6
+--R
+--R
+--R 6 168 5 79 4 89 3 2
+--R (2) 30x + --- x - -- x - -- x + 4x + 12x
+--R 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 37
+
+--S 38 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 168 5 79 4 89 3 2
+--R (3) 30x + --- x - -- x - -- x + 4x + 12x
+--R 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 38
+
+--S 39 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(1-2*x)^2*(2+3*x)*(3+5*x)
+--R
+--R
+--R 4 3 2
+--R (1) 60x + 16x - 37x - 5x + 6
+--R Type: Polynomial(Integer)
+--E 41
+
+--S 42 of 500
+r0:=6*x-5/2*x^2-37/3*x^3+4*x^4+12*x^5
+--R
+--R
+--R 5 4 37 3 5 2
+--R (2) 12x + 4x - -- x - - x + 6x
+--R 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 42
+
+--S 43 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 37 3 5 2
+--R (3) 12x + 4x - -- x - - x + 6x
+--R 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 43
+
+--S 44 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(1-2*x)^2*(3+5*x)
+--R
+--R
+--R 3 2
+--R (1) 20x - 8x - 7x + 3
+--R Type: Polynomial(Integer)
+--E 46
+
+--S 47 of 500
+r0:=3*x-7/2*x^2-8/3*x^3+5*x^4
+--R
+--R
+--R 4 8 3 7 2
+--R (2) 5x - - x - - x + 3x
+--R 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 47
+
+--S 48 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 8 3 7 2
+--R (3) 5x - - x - - x + 3x
+--R 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 48
+
+--S 49 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(1-2*x)^2*(3+5*x)/(2+3*x)
+--R
+--R
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R (1) -------------------
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 500
+r0:=65/27*x-32/9*x^2+20/9*x^3-49/81*log(2+3*x)
+--R
+--R
+--R 3 2
+--R - 49log(3x + 2) + 180x - 288x + 195x
+--R (2) --------------------------------------
+--R 81
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R - 49log(3x + 2) + 180x - 288x + 195x
+--R (3) --------------------------------------
+--R 81
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^2
+--R
+--R
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R (1) -------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 56
+
+--S 57 of 500
+r0:=-104/27*x+10/9*x^2+49/81/(2+3*x)+91/27*log(2+3*x)
+--R
+--R
+--R 3 2
+--R (819x + 546)log(3x + 2) + 270x - 756x - 624x + 49
+--R (2) ---------------------------------------------------
+--R 243x + 162
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R (819x + 546)log(3x + 2) + 270x - 756x - 624x + 49
+--R (3) ---------------------------------------------------
+--R 243x + 162
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^3
+--R
+--R
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R (1) ---------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 61
+
+--S 62 of 500
+r0:=20/27*x+49/162/(2+3*x)^2+(-91/27)/(2+3*x)-16/9*log(2+3*x)
+--R
+--R
+--R 2 3 2
+--R (- 2592x - 3456x - 1152)log(3x + 2) + 1080x + 1440x - 1158x - 1043
+--R (2) ---------------------------------------------------------------------
+--R 2
+--R 1458x + 1944x + 648
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2
+--R (- 2592x - 3456x - 1152)log(3x + 2) + 1080x + 1440x - 1158x - 1043
+--R (3) ---------------------------------------------------------------------
+--R 2
+--R 1458x + 1944x + 648
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^4
+--R
+--R
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 66
+
+--S 67 of 500
+r0:=49/243/(2+3*x)^3+(-91/54)/(2+3*x)^2+16/9/(2+3*x)+20/81*log(2+3*x)
+--R
+--R
+--R 3 2 2
+--R (3240x + 6480x + 4320x + 960)log(3x + 2) + 7776x + 7911x + 1916
+--R (2) ------------------------------------------------------------------
+--R 3 2
+--R 13122x + 26244x + 17496x + 3888
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 2
+--R (3240x + 6480x + 4320x + 960)log(3x + 2) + 7776x + 7911x + 1916
+--R (3) ------------------------------------------------------------------
+--R 3 2
+--R 13122x + 26244x + 17496x + 3888
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^5
+--R
+--R
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 71
+
+--S 72 of 500
+r0:=1/84*(1-2*x)^3/(2+3*x)^4-23/294*(1-2*x)^3/(2+3*x)^3
+--R
+--R
+--R 92 4 244 3 16 2 31 85
+--R ---- x - ----- x - ---- x + ---- x - -----
+--R 3969 11907 3969 3969 47628
+--R (2) ---------------------------------------------
+--R 4 8 3 8 2 32 16
+--R x + - x + - x + -- x + --
+--R 3 3 27 81
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 72
+
+--S 73 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R - 2160x - 1728x - 516x - 167
+--R (3) -------------------------------------------
+--R 4 3 2
+--R 26244x + 69984x + 69984x + 31104x + 5184
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 500
+m0:=a0-r0
+--R
+--R
+--R 92
+--R (4) - ----
+--R 3969
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^6
+--R
+--R
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 76
+
+--S 77 of 500
+r0:=49/405/(2+3*x)^5+(-91/108)/(2+3*x)^4+16/27/(2+3*x)^3+(-10/81)/(2+3*x)^2
+--R
+--R
+--R 10 3 4 2 5 49
+--R - --- x - --- x + ---- x - -----
+--R 729 729 8748 65610
+--R (2) ---------------------------------------
+--R 5 10 4 40 3 80 2 80 32
+--R x + -- x + -- x + -- x + -- x + ---
+--R 3 9 27 81 243
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 77
+
+--S 78 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R - 1800x - 720x + 75x - 98
+--R (3) -----------------------------------------------------------
+--R 5 4 3 2
+--R 131220x + 437400x + 583200x + 388800x + 129600x + 17280
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^7
+--R
+--R
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 81
+
+--S 82 of 500
+r0:=49/486/(2+3*x)^6+(-91/135)/(2+3*x)^5+4/9/(2+3*x)^4+(-20/243)/(2+3*x)^3
+--R
+--R
+--R 20 3 4 2 47 311
+--R - ---- x - ---- x + ----- x - -------
+--R 6561 6561 98415 1771470
+--R (2) ----------------------------------------------
+--R 6 5 20 4 160 3 80 2 64 64
+--R x + 4x + -- x + --- x + -- x + -- x + ---
+--R 3 27 27 81 729
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 82
+
+--S 83 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R - 5400x - 1080x + 846x - 311
+--R /
+--R 6 5 4 3 2
+--R 1771470x + 7085880x + 11809800x + 10497600x + 5248800x + 1399680x
+--R +
+--R 155520
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 86
+
+--S 87 of 500
+r0:=7/81/(2+3*x)^7+(-91/162)/(2+3*x)^6+16/45/(2+3*x)^5+(-5/81)/(2+3*x)^4
+--R
+--R
+--R 5 3 2 2 97 44
+--R - ---- x - ----- x + ------ x - ------
+--R 6561 32805 590490 885735
+--R (2) ------------------------------------------------------------
+--R 7 14 6 28 5 280 4 560 3 224 2 448 128
+--R x + -- x + -- x + --- x + --- x + --- x + --- x + ----
+--R 3 3 27 81 81 729 2187
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 87
+
+--S 88 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R - 1350x - 108x + 291x - 88
+--R /
+--R 7 6 5 4 3 2
+--R 1771470x + 8266860x + 16533720x + 18370800x + 12247200x + 4898880x
+--R +
+--R 1088640x + 103680
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(1-2*x)^2*(2+3*x)^8*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 12 11 10 9 8 7
+--R 656100x + 3630420x + 8477541x + 10415466x + 6281145x + 54864x
+--R +
+--R 6 5 4 3 2
+--R - 2690352x - 1789440x - 338336x + 162560x + 111616x + 26112x + 2304
+--R Type: Polynomial(Integer)
+--E 91
+
+--S 92 of 500
+r0:=49/2187*(2+3*x)^9-259/1215*(2+3*x)^10+503/891*(2+3*x)^11-_
+ 185/729*(2+3*x)^12+100/3159*(2+3*x)^13
+--R
+--R
+--R (2)
+--R 656100 13 12 8477541 11 5207733 10 9 8
+--R ------ x + 302535x + ------- x + ------- x + 697905x + 6858x
+--R 13 11 5
+--R +
+--R 7 6 338336 5 4 111616 3 2
+--R - 384336x - 298240x - ------ x + 40640x + ------ x + 13056x + 2304x
+--R 5 3
+--R +
+--R 264616448
+--R ---------
+--R 1563705
+--R Type: Polynomial(Fraction(Integer))
+--E 92
+
+--S 93 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 656100 13 12 8477541 11 5207733 10 9 8
+--R ------ x + 302535x + ------- x + ------- x + 697905x + 6858x
+--R 13 11 5
+--R +
+--R 7 6 338336 5 4 111616 3 2
+--R - 384336x - 298240x - ------ x + 40640x + ------ x + 13056x + 2304x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 93
+
+--S 94 of 500
+m0:=a0-r0
+--R
+--R
+--R 264616448
+--R (4) - ---------
+--R 1563705
+--R Type: Polynomial(Fraction(Integer))
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(1-2*x)^2*(2+3*x)^7*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 11 10 9 8 7 6
+--R 218700x + 1064340x + 2116287x + 2060964x + 719739x - 461538x
+--R +
+--R 5 4 3 2
+--R - 589092x - 203752x + 23056x + 38816x + 11328x + 1152
+--R Type: Polynomial(Integer)
+--E 96
+
+--S 97 of 500
+r0:=1152*x+5664*x^2+38816/3*x^3+5764*x^4-203752/5*x^5-98182*x^6-65934*x^7+_
+ 719739/8*x^8+228996*x^9+2116287/10*x^10+1064340/11*x^11+18225*x^12
+--R
+--R
+--R (2)
+--R 12 1064340 11 2116287 10 9 719739 8 7
+--R 18225x + ------- x + ------- x + 228996x + ------ x - 65934x
+--R 11 10 8
+--R +
+--R 6 203752 5 4 38816 3 2
+--R - 98182x - ------ x + 5764x + ----- x + 5664x + 1152x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 97
+
+--S 98 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 1064340 11 2116287 10 9 719739 8 7
+--R 18225x + ------- x + ------- x + 228996x + ------ x - 65934x
+--R 11 10 8
+--R +
+--R 6 203752 5 4 38816 3 2
+--R - 98182x - ------ x + 5764x + ----- x + 5664x + 1152x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 98
+
+--S 99 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(1-2*x)^2*(2+3*x)^6*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5 4
+--R 72900x + 306180x + 501309x + 352782x + 4725x - 156996x - 91700x
+--R +
+--R 3 2
+--R - 6784x + 12208x + 4800x + 576
+--R Type: Polynomial(Integer)
+--E 101
+
+--S 102 of 500
+r0:=576*x+2400*x^2+12208/3*x^3-1696*x^4-18340*x^5-26166*x^6+675*x^7+_
+ 176391/4*x^8+55701*x^9+30618*x^10+72900/11*x^11
+--R
+--R
+--R (2)
+--R 72900 11 10 9 176391 8 7 6 5
+--R ----- x + 30618x + 55701x + ------ x + 675x - 26166x - 18340x
+--R 11 4
+--R +
+--R 4 12208 3 2
+--R - 1696x + ----- x + 2400x + 576x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 102
+
+--S 103 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 72900 11 10 9 176391 8 7 6 5
+--R ----- x + 30618x + 55701x + ------ x + 675x - 26166x - 18340x
+--R 11 4
+--R +
+--R 4 12208 3 2
+--R - 1696x + ----- x + 2400x + 576x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 103
+
+--S 104 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(1-2*x)^2*(2+3*x)^5*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3
+--R 24300x + 85860x + 109863x + 44352x - 27993x - 33670x - 8120x
+--R +
+--R 2
+--R 3152x + 1968x + 288
+--R Type: Polynomial(Integer)
+--E 106
+
+--S 107 of 500
+r0:=288*x+984*x^2+3152/3*x^3-2030*x^4-6734*x^5-9331/2*x^6+6336*x^7+_
+ 109863/8*x^8+9540*x^9+2430*x^10
+--R
+--R
+--R (2)
+--R 10 9 109863 8 7 9331 6 5 4 3152 3
+--R 2430x + 9540x + ------ x + 6336x - ---- x - 6734x - 2030x + ---- x
+--R 8 2 3
+--R +
+--R 2
+--R 984x + 288x
+--R Type: Polynomial(Fraction(Integer))
+--E 107
+
+--S 108 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 109863 8 7 9331 6 5 4 3152 3
+--R 2430x + 9540x + ------ x + 6336x - ---- x - 6734x - 2030x + ---- x
+--R 8 2 3
+--R +
+--R 2
+--R 984x + 288x
+--R Type: Polynomial(Fraction(Integer))
+--E 108
+
+--S 109 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(1-2*x)^2*(2+3*x)^4*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 8100x + 23220x + 21141x + 690x - 9791x - 4696x + 424x + 768x + 144
+--R Type: Polynomial(Integer)
+--E 111
+
+--S 112 of 500
+r0:=144*x+384*x^2+424/3*x^3-1174*x^4-9791/5*x^5+115*x^6+21141/7*x^7+_
+ 5805/2*x^8+900*x^9
+--R
+--R
+--R (2)
+--R 9 5805 8 21141 7 6 9791 5 4 424 3 2
+--R 900x + ---- x + ----- x + 115x - ---- x - 1174x + --- x + 384x + 144x
+--R 2 7 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 112
+
+--S 113 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 5805 8 21141 7 6 9791 5 4 424 3 2
+--R 900x + ---- x + ----- x + 115x - ---- x - 1174x + --- x + 384x + 144x
+--R 2 7 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 113
+
+--S 114 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(1-2*x)^2*(2+3*x)^3*(3+5*x)^2
+--R
+--R
+--R 7 6 5 4 3 2
+--R (1) 2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72
+--R Type: Polynomial(Integer)
+--E 116
+
+--S 117 of 500
+r0:=72*x+138*x^2-202/3*x^3-2045/4*x^4-1828/5*x^5+1029/2*x^6+5940/7*x^7+_
+ 675/2*x^8
+--R
+--R
+--R 675 8 5940 7 1029 6 1828 5 2045 4 202 3 2
+--R (2) --- x + ---- x + ---- x - ---- x - ---- x - --- x + 138x + 72x
+--R 2 7 2 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 117
+
+--S 118 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 675 8 5940 7 1029 6 1828 5 2045 4 202 3 2
+--R (3) --- x + ---- x + ---- x - ---- x - ---- x - --- x + 138x + 72x
+--R 2 7 2 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 118
+
+--S 119 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(1-2*x)^2*(2+3*x)^2*(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R (1) 900x + 1380x + 109x - 682x - 227x + 84x + 36
+--R Type: Polynomial(Integer)
+--E 121
+
+--S 122 of 500
+r0:=36*x+42*x^2-227/3*x^3-341/2*x^4+109/5*x^5+230*x^6+900/7*x^7
+--R
+--R
+--R 900 7 6 109 5 341 4 227 3 2
+--R (2) --- x + 230x + --- x - --- x - --- x + 42x + 36x
+--R 7 5 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 122
+
+--S 123 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 900 7 6 109 5 341 4 227 3 2
+--R (3) --- x + 230x + --- x - --- x - --- x + 42x + 36x
+--R 7 5 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 123
+
+--S 124 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(1-2*x)^2*(2+3*x)*(3+5*x)^2
+--R
+--R
+--R 5 4 3 2
+--R (1) 300x + 260x - 137x - 136x + 15x + 18
+--R Type: Polynomial(Integer)
+--E 126
+
+--S 127 of 500
+r0:=18*x+15/2*x^2-136/3*x^3-137/4*x^4+52*x^5+50*x^6
+--R
+--R
+--R 6 5 137 4 136 3 15 2
+--R (2) 50x + 52x - --- x - --- x + -- x + 18x
+--R 4 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 127
+
+--S 128 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 5 137 4 136 3 15 2
+--R (3) 50x + 52x - --- x - --- x + -- x + 18x
+--R 4 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 128
+
+--S 129 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(1-2*x)^2*(3+5*x)^2
+--R
+--R
+--R 4 3 2
+--R (1) 100x + 20x - 59x - 6x + 9
+--R Type: Polynomial(Integer)
+--E 131
+
+--S 132 of 500
+r0:=9*x-3*x^2-59/3*x^3+5*x^4+20*x^5
+--R
+--R
+--R 5 4 59 3 2
+--R (2) 20x + 5x - -- x - 3x + 9x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 132
+
+--S 133 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 59 3 2
+--R (3) 20x + 5x - -- x - 3x + 9x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 133
+
+--S 134 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)
+--R
+--R
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R (1) ----------------------------
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 136
+
+--S 137 of 500
+r0:=340/81*x-251/54*x^2-140/27*x^3+25/3*x^4+49/243*log(2+3*x)
+--R
+--R
+--R 4 3 2
+--R 98log(3x + 2) + 4050x - 2520x - 2259x + 2040x
+--R (2) ------------------------------------------------
+--R 486
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R 98log(3x + 2) + 4050x - 2520x - 2259x + 2040x
+--R (3) ------------------------------------------------
+--R 486
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^2
+--R
+--R
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R (1) ----------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 141
+
+--S 142 of 500
+r0:=143/27*x-170/27*x^2+100/27*x^3+(-49/243)/(2+3*x)-518/243*log(2+3*x)
+--R
+--R
+--R 4 3 2
+--R (- 1554x - 1036)log(3x + 2) + 2700x - 2790x + 801x + 2574x - 49
+--R (2) ------------------------------------------------------------------
+--R 729x + 486
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R (- 1554x - 1036)log(3x + 2) + 2700x - 2790x + 801x + 2574x - 49
+--R (3) ------------------------------------------------------------------
+--R 729x + 486
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^3
+--R
+--R
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R (1) ----------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 500
+r0:=-20/3*x+50/27*x^2+(-49/486)/(2+3*x)^2+518/243/(2+3*x)+503/81*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2
+--R (27162x + 36216x + 12072)log(3x + 2) + 8100x - 18360x - 35280x
+--R +
+--R - 9852x + 2023
+--R /
+--R 2
+--R 4374x + 5832x + 1944
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2
+--R (27162x + 36216x + 12072)log(3x + 2) + 8100x - 18360x - 35280x
+--R +
+--R - 9852x + 2023
+--R /
+--R 2
+--R 4374x + 5832x + 1944
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^4
+--R
+--R
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 151
+
+--S 152 of 500
+r0:=100/81*x+(-49/729)/(2+3*x)^3+259/243/(2+3*x)^2+(-503/81)/(2+3*x)-_
+ 740/243*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 4 3
+--R (- 59940x - 119880x - 79920x - 17760)log(3x + 2) + 24300x + 48600x
+--R +
+--R 2
+--R - 8343x - 44793x - 16603
+--R /
+--R 3 2
+--R 19683x + 39366x + 26244x + 5832
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 3
+--R (- 59940x - 119880x - 79920x - 17760)log(3x + 2) + 24300x + 48600x
+--R +
+--R 2
+--R - 8343x - 44793x - 16603
+--R /
+--R 3 2
+--R 19683x + 39366x + 26244x + 5832
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^5
+--R
+--R
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 500
+r0:=(-49/972)/(2+3*x)^4+518/729/(2+3*x)^3+(-503/162)/(2+3*x)^2+_
+ 740/243/(2+3*x)+100/243*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 3
+--R (97200x + 259200x + 259200x + 115200x + 19200)log(3x + 2) + 239760x
+--R +
+--R 2
+--R 398034x + 217248x + 38821
+--R /
+--R 4 3 2
+--R 236196x + 629856x + 629856x + 279936x + 46656
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 3
+--R (97200x + 259200x + 259200x + 115200x + 19200)log(3x + 2) + 239760x
+--R +
+--R 2
+--R 398034x + 217248x + 38821
+--R /
+--R 4 3 2
+--R 236196x + 629856x + 629856x + 279936x + 46656
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^6
+--R
+--R
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 500
+r0:=(-49/1215)/(2+3*x)^5+259/486/(2+3*x)^4+(-503/243)/(2+3*x)^3+_
+ 370/243/(2+3*x)^2+(-100/243)/(2+3*x)
+--R
+--R
+--R 100 4 430 3 683 2 1285 2014
+--R - --- x - ---- x - ---- x - ----- x - ------
+--R 729 2187 6561 39366 295245
+--R (2) -----------------------------------------------
+--R 5 10 4 40 3 80 2 80 32
+--R x + -- x + -- x + -- x + -- x + ---
+--R 3 9 27 81 243
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R - 81000x - 116100x - 61470x - 19275x - 4028
+--R (3) --------------------------------------------------------------
+--R 5 4 3 2
+--R 590490x + 1968300x + 2624400x + 1749600x + 583200x + 77760
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^7
+--R
+--R
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 166
+
+--S 167 of 500
+r0:=(-49/1458)/(2+3*x)^6+518/1215/(2+3*x)^5+(-503/324)/(2+3*x)^4+_
+ 740/729/(2+3*x)^3+(-50/243)/(2+3*x)^2
+--R
+--R
+--R 50 4 460 3 389 2 227 4099
+--R - ---- x - ----- x - ----- x - ------ x - -------
+--R 2187 19683 78732 295245 5314410
+--R (2) ----------------------------------------------------
+--R 6 5 20 4 160 3 80 2 64 64
+--R x + 4x + -- x + --- x + -- x + -- x + ---
+--R 3 27 27 81 729
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 167
+
+--S 168 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R - 243000x - 248400x - 52515x - 8172x - 8198
+--R /
+--R 6 5 4 3 2
+--R 10628820x + 42515280x + 70858800x + 62985600x + 31492800x + 8398080x
+--R +
+--R 933120
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 171
+
+--S 172 of 500
+r0:=(-7/243)/(2+3*x)^7+259/729/(2+3*x)^6+(-503/405)/(2+3*x)^5+_
+ 185/243/(2+3*x)^4+(-100/729)/(2+3*x)^3
+--R
+--R
+--R 100 4 245 3 41 2 487 1423
+--R - ----- x - ----- x + ------ x + ------- x - -------
+--R 19683 59049 295245 2657205 7971615
+--R (2) ------------------------------------------------------------
+--R 7 14 6 28 5 280 4 560 3 224 2 448 128
+--R x + -- x + -- x + --- x + --- x + --- x + --- x + ----
+--R 3 3 27 81 81 729 2187
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 172
+
+--S 173 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R - 40500x - 33075x + 1107x + 1461x - 1423
+--R /
+--R 7 6 5 4 3
+--R 7971615x + 37200870x + 74401740x + 82668600x + 55112400x
+--R +
+--R 2
+--R 22044960x + 4898880x + 466560
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(1-2*x)^2*(2+3*x)^10*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 15 14 13 12 11
+--R 29524500x + 220449600x + 734077485x + 1417418757x + 1707104403x
+--R +
+--R 10 9 8 7 6
+--R 1233925083x + 360437040x - 236139300x - 320907744x - 154612896x
+--R +
+--R 5 4 3 2
+--R - 21254656x + 15928960x + 10576640x + 3002112x + 442368x + 27648
+--R Type: Polynomial(Integer)
+--E 176
+
+--S 177 of 500
+r0:=-49/8019*(2+3*x)^11+763/8748*(2+3*x)^12-4099/9477*(2+3*x)^13+_
+ 8285/10206*(2+3*x)^14-760/2187*(2+3*x)^15+125/2916*(2+3*x)^16
+--R
+--R
+--R (2)
+--R 7381125 16 15 734077485 14 1417418757 13 569034801 12
+--R ------- x + 14696640x + --------- x + ---------- x + --------- x
+--R 4 14 13 4
+--R +
+--R 1233925083 11 10 9 8 154612896 7
+--R ---------- x + 36043704x - 26237700x - 40113468x - --------- x
+--R 11 7
+--R +
+--R 10627328 6 5 4 3 2
+--R - -------- x + 3185792x + 2644160x + 1000704x + 221184x + 27648x
+--R 3
+--R +
+--R 3336045568
+--R ----------
+--R 2189187
+--R Type: Polynomial(Fraction(Integer))
+--E 177
+
+--S 178 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7381125 16 15 734077485 14 1417418757 13 569034801 12
+--R ------- x + 14696640x + --------- x + ---------- x + --------- x
+--R 4 14 13 4
+--R +
+--R 1233925083 11 10 9 8 154612896 7
+--R ---------- x + 36043704x - 26237700x - 40113468x - --------- x
+--R 11 7
+--R +
+--R 10627328 6 5 4 3 2
+--R - -------- x + 3185792x + 2644160x + 1000704x + 221184x + 27648x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 178
+
+--S 179 of 500
+m0:=a0-r0
+--R
+--R
+--R 3336045568
+--R (4) - ----------
+--R 2189187
+--R Type: Polynomial(Fraction(Integer))
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(1-2*x)^2*(2+3*x)^9*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 14 13 12 11 10
+--R 9841500x + 66922200x + 200077695x + 339087789x + 342976275x
+--R +
+--R 9 8 7 6 5 4
+--R 182657511x - 1625994x - 77629104x - 55216512x - 14726624x + 2732864x
+--R +
+--R 3 2
+--R 3487744x + 1200384x + 200448x + 13824
+--R Type: Polynomial(Integer)
+--E 181
+
+--S 182 of 500
+r0:=-49/7290*(2+3*x)^10+763/8019*(2+3*x)^11-4099/8748*(2+3*x)^12+_
+ 8285/9477*(2+3*x)^13-1900/5103*(2+3*x)^14+100/2187*(2+3*x)^15
+--R
+--R
+--R (2)
+--R 15 33461100 14 200077695 13 113029263 12 342976275 11
+--R 656100x + -------- x + --------- x + --------- x + --------- x
+--R 7 13 4 11
+--R +
+--R 182657511 10 9 8 55216512 7 7363312 6
+--R --------- x - 180666x - 9703638x - -------- x - ------- x
+--R 10 7 3
+--R +
+--R 2732864 5 4 3 2 9067849216
+--R ------- x + 871936x + 400128x + 100224x + 13824x + ----------
+--R 5 10945935
+--R Type: Polynomial(Fraction(Integer))
+--E 182
+
+--S 183 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 33461100 14 200077695 13 113029263 12 342976275 11
+--R 656100x + -------- x + --------- x + --------- x + --------- x
+--R 7 13 4 11
+--R +
+--R 182657511 10 9 8 55216512 7 7363312 6
+--R --------- x - 180666x - 9703638x - -------- x - ------- x
+--R 10 7 3
+--R +
+--R 2732864 5 4 3 2
+--R ------- x + 871936x + 400128x + 100224x + 13824x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 183
+
+--S 184 of 500
+m0:=a0-r0
+--R
+--R
+--R 9067849216
+--R (4) - ----------
+--R 10945935
+--R Type: Polynomial(Fraction(Integer))
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(1-2*x)^2*(2+3*x)^8*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 13 12 11 10 9
+--R 3280500x + 20120400x + 53278965x + 77509953x + 62652123x
+--R +
+--R 8 7 6 5 4 3
+--R 19117755x - 13287168x - 17018256x - 7060000x - 202208x + 1045760x
+--R +
+--R 2
+--R 465408x + 89856x + 6912
+--R Type: Polynomial(Integer)
+--E 186
+
+--S 187 of 500
+r0:=6912*x+44928*x^2+155136*x^3+261440*x^4-202208/5*x^5-3530000/3*x^6-_
+ 17018256/7*x^7-1660896*x^8+2124195*x^9+62652123/10*x^10+_
+ 77509953/11*x^11+17759655/4*x^12+20120400/13*x^13+1640250/7*x^14
+--R
+--R
+--R (2)
+--R 1640250 14 20120400 13 17759655 12 77509953 11 62652123 10
+--R ------- x + -------- x + -------- x + -------- x + -------- x
+--R 7 13 4 11 10
+--R +
+--R 9 8 17018256 7 3530000 6 202208 5 4
+--R 2124195x - 1660896x - -------- x - ------- x - ------ x + 261440x
+--R 7 3 5
+--R +
+--R 3 2
+--R 155136x + 44928x + 6912x
+--R Type: Polynomial(Fraction(Integer))
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1640250 14 20120400 13 17759655 12 77509953 11 62652123 10
+--R ------- x + -------- x + -------- x + -------- x + -------- x
+--R 7 13 4 11 10
+--R +
+--R 9 8 17018256 7 3530000 6 202208 5 4
+--R 2124195x - 1660896x - -------- x - ------- x - ------ x + 261440x
+--R 7 3 5
+--R +
+--R 3 2
+--R 155136x + 44928x + 6912x
+--R Type: Polynomial(Fraction(Integer))
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(1-2*x)^2*(2+3*x)^7*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 12 11 10 9 8 7
+--R 1093500x + 5977800x + 13774455x + 16653681x + 9781587x - 148473x
+--R +
+--R 6 5 4 3 2
+--R - 4330074x - 2786036x - 495976x + 263248x + 173088x + 39744x + 3456
+--R Type: Polynomial(Integer)
+--E 191
+
+--S 192 of 500
+r0:=3456*x+19872*x^2+57696*x^3+65812*x^4-495976/5*x^5-1393018/3*x^6-_
+ 618582*x^7-148473/8*x^8+1086843*x^9+16653681/10*x^10+_
+ 13774455/11*x^11+498150*x^12+1093500/13*x^13
+--R
+--R
+--R (2)
+--R 1093500 13 12 13774455 11 16653681 10 9
+--R ------- x + 498150x + -------- x + -------- x + 1086843x
+--R 13 11 10
+--R +
+--R 148473 8 7 1393018 6 495976 5 4 3
+--R - ------ x - 618582x - ------- x - ------ x + 65812x + 57696x
+--R 8 3 5
+--R +
+--R 2
+--R 19872x + 3456x
+--R Type: Polynomial(Fraction(Integer))
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1093500 13 12 13774455 11 16653681 10 9
+--R ------- x + 498150x + -------- x + -------- x + 1086843x
+--R 13 11 10
+--R +
+--R 148473 8 7 1393018 6 495976 5 4 3
+--R - ------ x - 618582x - ------- x - ------ x + 65812x + 57696x
+--R 8 3 5
+--R +
+--R 2
+--R 19872x + 3456x
+--R Type: Polynomial(Fraction(Integer))
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(1-2*x)^2*(2+3*x)^6*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 11 10 9 8 7 6
+--R 364500x + 1749600x + 3425085x + 3267837x + 1081971x - 770805x
+--R +
+--R 5 4 3 2
+--R - 929488x - 309020x + 40688x + 60624x + 17280x + 1728
+--R Type: Polynomial(Integer)
+--E 196
+
+--S 197 of 500
+r0:=1728*x+8640*x^2+20208*x^3+10172*x^4-61804*x^5-464744/3*x^6-_
+ 110115*x^7+1081971/8*x^8+363093*x^9+685017/2*x^10+1749600/11*x^11+_
+ 30375*x^12
+--R
+--R
+--R (2)
+--R 12 1749600 11 685017 10 9 1081971 8 7
+--R 30375x + ------- x + ------ x + 363093x + ------- x - 110115x
+--R 11 2 8
+--R +
+--R 464744 6 5 4 3 2
+--R - ------ x - 61804x + 10172x + 20208x + 8640x + 1728x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 1749600 11 685017 10 9 1081971 8 7
+--R 30375x + ------- x + ------ x + 363093x + ------- x - 110115x
+--R 11 2 8
+--R +
+--R 464744 6 5 4 3 2
+--R - ------ x - 61804x + 10172x + 20208x + 8640x + 1728x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(1-2*x)^2*(2+3*x)^5*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5 4
+--R 121500x + 502200x + 806895x + 551349x - 6909x - 252329x - 141610x
+--R +
+--R 3 2
+--R - 8600x + 19296x + 7344x + 864
+--R Type: Polynomial(Integer)
+--E 201
+
+--S 202 of 500
+r0:=864*x+3672*x^2+6432*x^3-2150*x^4-28322*x^5-252329/6*x^6-987*x^7+_
+ 551349/8*x^8+89655*x^9+50220*x^10+121500/11*x^11
+--R
+--R
+--R (2)
+--R 121500 11 10 9 551349 8 7 252329 6 5
+--R ------ x + 50220x + 89655x + ------ x - 987x - ------ x - 28322x
+--R 11 8 6
+--R +
+--R 4 3 2
+--R - 2150x + 6432x + 3672x + 864x
+--R Type: Polynomial(Fraction(Integer))
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 121500 11 10 9 551349 8 7 252329 6 5
+--R ------ x + 50220x + 89655x + ------ x - 987x - ------ x - 28322x
+--R 11 8 6
+--R +
+--R 4 3 2
+--R - 2150x + 6432x + 3672x + 864x
+--R Type: Polynomial(Fraction(Integer))
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(1-2*x)^2*(2+3*x)^4*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3
+--R 40500x + 140400x + 175365x + 66873x - 46885x - 52853x - 11968x
+--R +
+--R 2
+--R 5112x + 3024x + 432
+--R Type: Polynomial(Integer)
+--E 206
+
+--S 207 of 500
+r0:=432*x+1512*x^2+1704*x^3-2992*x^4-52853/5*x^5-46885/6*x^6+66873/7*x^7+_
+ 175365/8*x^8+15600*x^9+4050*x^10
+--R
+--R
+--R (2)
+--R 10 9 175365 8 66873 7 46885 6 52853 5 4
+--R 4050x + 15600x + ------ x + ----- x - ----- x - ----- x - 2992x
+--R 8 7 6 5
+--R +
+--R 3 2
+--R 1704x + 1512x + 432x
+--R Type: Polynomial(Fraction(Integer))
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 175365 8 66873 7 46885 6 52853 5 4
+--R 4050x + 15600x + ------ x + ----- x - ----- x - ----- x - 2992x
+--R 8 7 6 5
+--R +
+--R 3 2
+--R 1704x + 1512x + 432x
+--R Type: Polynomial(Fraction(Integer))
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(1-2*x)^2*(2+3*x)^3*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x + 216
+--R Type: Polynomial(Integer)
+--E 211
+
+--S 212 of 500
+r0:=216*x+594*x^2+258*x^3-7145/4*x^4-15709/5*x^5+121/6*x^6+33255/7*x^7+_
+ 4725*x^8+1500*x^9
+--R
+--R
+--R (2)
+--R 9 8 33255 7 121 6 15709 5 7145 4 3 2
+--R 1500x + 4725x + ----- x + --- x - ----- x - ---- x + 258x + 594x
+--R 7 6 5 4
+--R +
+--R 216x
+--R Type: Polynomial(Fraction(Integer))
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 33255 7 121 6 15709 5 7145 4 3 2
+--R 1500x + 4725x + ----- x + --- x - ----- x - ---- x + 258x + 594x
+--R 7 6 5 4
+--R +
+--R 216x
+--R Type: Polynomial(Fraction(Integer))
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(1-2*x)^2*(2+3*x)^2*(3+5*x)^3
+--R
+--R
+--R 7 6 5 4 3 2
+--R (1) 4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108
+--R Type: Polynomial(Integer)
+--E 216
+
+--S 217 of 500
+r0:=108*x+216*x^2-87*x^3-3181/4*x^4-3083/5*x^5+4685/6*x^6+9600/7*x^7+1125/2*x^8
+--R
+--R
+--R 1125 8 9600 7 4685 6 3083 5 3181 4 3 2
+--R (2) ---- x + ---- x + ---- x - ---- x - ---- x - 87x + 216x + 108x
+--R 2 7 6 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 1125 8 9600 7 4685 6 3083 5 3181 4 3 2
+--R (3) ---- x + ---- x + ---- x - ---- x - ---- x - 87x + 216x + 108x
+--R 2 7 6 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(1-2*x)^2*(2+3*x)*(3+5*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R (1) 1500x + 2200x + 95x - 1091x - 333x + 135x + 54
+--R Type: Polynomial(Integer)
+--E 221
+
+--S 222 of 500
+r0:=54*x+135/2*x^2-111*x^3-1091/4*x^4+19*x^5+1100/3*x^6+1500/7*x^7
+--R
+--R
+--R 1500 7 1100 6 5 1091 4 3 135 2
+--R (2) ---- x + ---- x + 19x - ---- x - 111x + --- x + 54x
+--R 7 3 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 222
+
+--S 223 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 1500 7 1100 6 5 1091 4 3 135 2
+--R (3) ---- x + ---- x + 19x - ---- x - 111x + --- x + 54x
+--R 7 3 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 223
+
+--S 224 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(1-2*x)^2*(3+5*x)^3
+--R
+--R
+--R 5 4 3 2
+--R (1) 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Polynomial(Integer)
+--E 226
+
+--S 227 of 500
+r0:=27*x+27/2*x^2-69*x^3-235/4*x^4+80*x^5+250/3*x^6
+--R
+--R
+--R 250 6 5 235 4 3 27 2
+--R (2) --- x + 80x - --- x - 69x + -- x + 27x
+--R 3 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 227
+
+--S 228 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 250 6 5 235 4 3 27 2
+--R (3) --- x + 80x - --- x - 69x + -- x + 27x
+--R 3 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 228
+
+--S 229 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)
+--R
+--R
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R (1) ----------------------------------------
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 500
+r0:=3305/243*x-559/162*x^2-2515/81*x^3+50/9*x^4+100/3*x^5-49/729*log(2+3*x)
+--R
+--R
+--R 5 4 3 2
+--R - 98log(3x + 2) + 48600x + 8100x - 45270x - 5031x + 19830x
+--R (2) --------------------------------------------------------------
+--R 1458
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R - 98log(3x + 2) + 48600x + 8100x - 45270x - 5031x + 19830x
+--R (3) --------------------------------------------------------------
+--R 1458
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^2
+--R
+--R
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R (1) ----------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 500
+r0:=1271/243*x-305/54*x^2-800/81*x^3+125/9*x^4+49/729/(2+3*x)+_
+ 763/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (4578x + 3052)log(3x + 2) + 60750x - 2700x - 53505x + 6408x + 15252x + 98
+--R -----------------------------------------------------------------------------
+--R 4374x + 2916
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (4578x + 3052)log(3x + 2) + 60750x - 2700x - 53505x + 6408x + 15252x + 98
+--R -----------------------------------------------------------------------------
+--R 4374x + 2916
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^3
+--R
+--R
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R (1) ----------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 500
+r0:=895/81*x-100/9*x^2+500/81*x^3+49/1458/(2+3*x)^2+(-763/729)/(2+3*x)-_
+ 4099/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 5 4 3
+--R (- 73782x - 98376x - 32792)log(3x + 2) + 81000x - 37800x - 13410x
+--R +
+--R 2
+--R 128520x + 59862x - 3003
+--R /
+--R 2
+--R 13122x + 17496x + 5832
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4 3
+--R (- 73782x - 98376x - 32792)log(3x + 2) + 81000x - 37800x - 13410x
+--R +
+--R 2
+--R 128520x + 59862x - 3003
+--R /
+--R 2
+--R 13122x + 17496x + 5832
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^4
+--R
+--R
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R (1) ----------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 500
+r0:=-2800/243*x+250/81*x^2+49/2187/(2+3*x)^3+(-763/1458)/(2+3*x)^2+_
+ 4099/729/(2+3*x)+8285/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 5
+--R (1342170x + 2684340x + 1789560x + 397680)log(3x + 2) + 364500x
+--R +
+--R 4 3 2
+--R - 631800x - 2235600x - 1485054x - 114939x + 93896
+--R /
+--R 3 2
+--R 118098x + 236196x + 157464x + 34992
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 5
+--R (1342170x + 2684340x + 1789560x + 397680)log(3x + 2) + 364500x
+--R +
+--R 4 3 2
+--R - 631800x - 2235600x - 1485054x - 114939x + 93896
+--R /
+--R 3 2
+--R 118098x + 236196x + 157464x + 34992
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^5
+--R
+--R
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 500
+r0:=500/243*x+49/2916/(2+3*x)^4+(-763/2187)/(2+3*x)^3+4099/1458/(2+3*x)^2+_
+ (-8285/729)/(2+3*x)-3800/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 3693600x - 9849600x - 9849600x - 4377600x - 729600)log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 1458000x + 3888000x + 1203660x - 3419334x - 3005148x - 702941
+--R /
+--R 4 3 2
+--R 708588x + 1889568x + 1889568x + 839808x + 139968
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 3693600x - 9849600x - 9849600x - 4377600x - 729600)log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 1458000x + 3888000x + 1203660x - 3419334x - 3005148x - 702941
+--R /
+--R 4 3 2
+--R 708588x + 1889568x + 1889568x + 839808x + 139968
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^6
+--R
+--R
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 500
+r0:=49/3645/(2+3*x)^5+(-763/2916)/(2+3*x)^4+4099/2187/(2+3*x)^3+_
+ (-8285/1458)/(2+3*x)^2+3800/729/(2+3*x)+500/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (7290000x + 24300000x + 32400000x + 21600000x + 7200000x + 960000)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 18468000x + 42537150x + 36564120x + 13889625x + 1965218
+--R /
+--R 5 4 3 2
+--R 10628820x + 35429400x + 47239200x + 31492800x + 10497600x + 1399680
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (7290000x + 24300000x + 32400000x + 21600000x + 7200000x + 960000)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 18468000x + 42537150x + 36564120x + 13889625x + 1965218
+--R /
+--R 5 4 3 2
+--R 10628820x + 35429400x + 47239200x + 31492800x + 10497600x + 1399680
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^7
+--R
+--R
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 500
+r0:=49/4374/(2+3*x)^6+(-763/3645)/(2+3*x)^5+4099/2916/(2+3*x)^4+_
+ (-8285/2187)/(2+3*x)^3+1900/729/(2+3*x)^2+(-500/729)/(2+3*x)
+--R
+--R
+--R 500 5 3100 4 22685 3 39781 2 41968 116741
+--R - ---- x - ---- x - ----- x - ------ x - ------ x - --------
+--R 2187 6561 59049 236196 885735 15943230
+--R (2) ----------------------------------------------------------------
+--R 6 5 20 4 160 3 80 2 64 64
+--R x + 4x + -- x + --- x + -- x + -- x + ---
+--R 3 27 27 81 729
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 262
+
+--S 263 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 7290000x - 15066000x - 12249900x - 5370435x - 1510848x - 233482
+--R /
+--R 6 5 4 3 2
+--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x
+--R +
+--R 25194240x + 2799360
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 266
+
+--S 267 of 500
+r0:=7/729/(2+3*x)^7+(-763/4374)/(2+3*x)^6+4099/3645/(2+3*x)^5+_
+ (-8285/2916)/(2+3*x)^4+3800/2187/(2+3*x)^3+(-250/729)/(2+3*x)^2
+--R
+--R
+--R 250 5 3700 4 23255 3 12077 2 35089 19072
+--R - ---- x - ----- x - ------ x - ------- x - -------- x - --------
+--R 6561 59049 708588 1771470 15943230 23914845
+--R (2) ---------------------------------------------------------------------
+--R 7 14 6 28 5 280 4 560 3 224 2 448 128
+--R x + -- x + -- x + --- x + --- x + --- x + --- x + ----
+--R 3 3 27 81 81 729 2187
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 267
+
+--S 268 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 3645000x - 5994000x - 3139425x - 652158x - 210534x - 76288
+--R /
+--R 7 6 5 4 3
+--R 95659380x + 446410440x + 892820880x + 992023200x + 661348800x
+--R +
+--R 2
+--R 264539520x + 58786560x + 5598720
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(1-2*x)^2*(2+3*x)^7/(3+5*x)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3 2
+--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x
+--R +
+--R 832x + 128
+--R /
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 271
+
+--S 272 of 500
+r0:=83333293/1953125*x+80555569/781250*x^2+1327159/78125*x^3-_
+ 20577159/62500*x^4-7315947/15625*x^5+130383/1250*x^6+_
+ 672867/875*x^7+16767/25*x^8+972/5*x^9+121/9765625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 9 8 7
+--R 3388log(5x + 3) + 53156250000x + 183389062500x + 210270937500x
+--R +
+--R 6 5 4 3
+--R 28521281250x - 128029072500x - 90025070625x + 4645056500x
+--R +
+--R 2
+--R 28194449150x + 11666661020x
+--R /
+--R 273437500
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7
+--R 3388log(5x + 3) + 53156250000x + 183389062500x + 210270937500x
+--R +
+--R 6 5 4 3
+--R 28521281250x - 128029072500x - 90025070625x + 4645056500x
+--R +
+--R 2
+--R 28194449150x + 11666661020x
+--R /
+--R 273437500
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(1-2*x)^2*(2+3*x)^6/(3+5*x)
+--R
+--R
+--R 8 7 6 5 4 3 2
+--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64
+--R (1) ----------------------------------------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 276
+
+--S 277 of 500
+r0:=8333293/390625*x+5555569/156250*x^2-422841/15625*x^3-_
+ 1677159/12500*x^4-228447/3125*x^5+35883/250*x^6+34992/175*x^7+_
+ 729/10*x^8+121/1953125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R 3388log(5x + 3) + 3986718750x + 10935000000x + 7849406250x
+--R +
+--R 5 4 3 2
+--R - 3997822500x - 7337570625x - 1479943500x + 1944449150x + 1166661020x
+--R /
+--R 54687500
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R 3388log(5x + 3) + 3986718750x + 10935000000x + 7849406250x
+--R +
+--R 5 4 3 2
+--R - 3997822500x - 7337570625x - 1479943500x + 1944449150x + 1166661020x
+--R /
+--R 54687500
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(1-2*x)^2*(2+3*x)^5/(3+5*x)
+--R
+--R
+--R 7 6 5 4 3 2
+--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32
+--R (1) -----------------------------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 500
+r0:=833293/78125*x+305569/31250*x^2-72841/3125*x^3-102159/2500*x^4+_
+ 7803/625*x^5+1404/25*x^6+972/35*x^7+121/390625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 3388log(5x + 3) + 303750000x + 614250000x + 136552500x - 446945625x
+--R +
+--R 3 2
+--R - 254943500x + 106949150x + 116661020x
+--R /
+--R 10937500
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 3388log(5x + 3) + 303750000x + 614250000x + 136552500x - 446945625x
+--R +
+--R 3 2
+--R - 254943500x + 106949150x + 116661020x
+--R /
+--R 10937500
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(1-2*x)^2*(2+3*x)^4/(3+5*x)
+--R
+--R
+--R 6 5 4 3 2
+--R 324x + 540x + 81x - 264x - 104x + 32x + 16
+--R (1) -----------------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 500
+r0:=83293/15625*x+5569/6250*x^2-7841/625*x^3-3159/500*x^4+1728/125*x^5+_
+ 54/5*x^6+121/78125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 484log(5x + 3) + 3375000x + 4320000x - 1974375x - 3920500x + 278450x
+--R +
+--R 1665860x
+--R /
+--R 312500
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 484log(5x + 3) + 3375000x + 4320000x - 1974375x - 3920500x + 278450x
+--R +
+--R 1665860x
+--R /
+--R 312500
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(1-2*x)^2*(2+3*x)^3/(3+5*x)
+--R
+--R
+--R 5 4 3 2
+--R 108x + 108x - 45x - 58x + 4x + 8
+--R (1) ------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 500
+r0:=8293/3125*x-1931/1250*x^2-591/125*x^3+54/25*x^4+108/25*x^5+_
+ 121/15625*log(3+5*x)
+--R
+--R
+--R 5 4 3 2
+--R 242log(5x + 3) + 135000x + 67500x - 147750x - 48275x + 82930x
+--R (2) -----------------------------------------------------------------
+--R 31250
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R 242log(5x + 3) + 135000x + 67500x - 147750x - 48275x + 82930x
+--R (3) -----------------------------------------------------------------
+--R 31250
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(1-2*x)^2*(2+3*x)^2/(3+5*x)
+--R
+--R
+--R 4 3 2
+--R 36x + 12x - 23x - 4x + 4
+--R (1) ---------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 296
+
+--S 297 of 500
+r0:=793/625*x-431/250*x^2-16/25*x^3+9/5*x^4+121/3125*log(3+5*x)
+--R
+--R
+--R 4 3 2
+--R 242log(5x + 3) + 11250x - 4000x - 10775x + 7930x
+--R (2) ---------------------------------------------------
+--R 6250
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R 242log(5x + 3) + 11250x - 4000x - 10775x + 7930x
+--R (3) ---------------------------------------------------
+--R 6250
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(1-2*x)^2*(2+3*x)/(3+5*x)
+--R
+--R
+--R 3 2
+--R 12x - 4x - 5x + 2
+--R (1) -------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 301
+
+--S 302 of 500
+r0:=43/125*x-28/25*x^2+4/5*x^3+121/625*log(3+5*x)
+--R
+--R
+--R 3 2
+--R 121log(5x + 3) + 500x - 700x + 215x
+--R (2) -------------------------------------
+--R 625
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 121log(5x + 3) + 500x - 700x + 215x
+--R (3) -------------------------------------
+--R 625
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(1-2*x)^2/(3+5*x)
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 306
+
+--S 307 of 500
+r0:=-32/25*x+2/5*x^2+121/125*log(3+5*x)
+--R
+--R
+--R 2
+--R 121log(5x + 3) + 50x - 160x
+--R (2) ----------------------------
+--R 125
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 121log(5x + 3) + 50x - 160x
+--R (3) ----------------------------
+--R 125
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(1-2*x)^2/((2+3*x)*(3+5*x))
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) --------------
+--R 2
+--R 15x + 19x + 6
+--R Type: Fraction(Polynomial(Integer))
+--E 311
+
+--S 312 of 500
+r0:=4/15*x-49/9*log(2+3*x)+121/25*log(3+5*x)
+--R
+--R
+--R 1089log(5x + 3) - 1225log(3x + 2) + 60x
+--R (2) ---------------------------------------
+--R 225
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 1089log(5x + 3) - 1225log(3x + 2) + 60x
+--R (3) ---------------------------------------
+--R 225
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(1-2*x)^2/((2+3*x)^2*(3+5*x))
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ----------------------
+--R 3 2
+--R 45x + 87x + 56x + 12
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 500
+r0:=49/9/(2+3*x)-217/9*log(2+3*x)+121/5*log(3+5*x)
+--R
+--R
+--R (3267x + 2178)log(5x + 3) + (- 3255x - 2170)log(3x + 2) + 245
+--R (2) -------------------------------------------------------------
+--R 135x + 90
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3267x + 2178)log(5x + 3) + (- 3255x - 2170)log(3x + 2) + 245
+--R (3) -------------------------------------------------------------
+--R 135x + 90
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(1-2*x)^2/((2+3*x)^3*(3+5*x))
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 135x + 351x + 342x + 148x + 24
+--R Type: Fraction(Polynomial(Integer))
+--E 321
+
+--S 322 of 500
+r0:=49/18/(2+3*x)^2+217/9/(2+3*x)-121*log(2+3*x)+121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (19602x + 26136x + 8712)log(5x + 3)
+--R +
+--R 2
+--R (- 19602x - 26136x - 8712)log(3x + 2) + 1302x + 917
+--R /
+--R 2
+--R 162x + 216x + 72
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (19602x + 26136x + 8712)log(5x + 3)
+--R +
+--R 2
+--R (- 19602x - 26136x - 8712)log(3x + 2) + 1302x + 917
+--R /
+--R 2
+--R 162x + 216x + 72
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(1-2*x)^2/((2+3*x)^4*(3+5*x))
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 405x + 1323x + 1728x + 1128x + 368x + 48
+--R Type: Fraction(Polynomial(Integer))
+--E 326
+
+--S 327 of 500
+r0:=49/27/(2+3*x)^3+217/18/(2+3*x)^2+121/(2+3*x)-605*log(2+3*x)+605*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (882090x + 1764180x + 1176120x + 261360)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 882090x - 1764180x - 1176120x - 261360)log(3x + 2) + 58806x
+--R +
+--R 80361x + 27536
+--R /
+--R 3 2
+--R 1458x + 2916x + 1944x + 432
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (882090x + 1764180x + 1176120x + 261360)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 882090x - 1764180x - 1176120x - 261360)log(3x + 2) + 58806x
+--R +
+--R 80361x + 27536
+--R /
+--R 3 2
+--R 1458x + 2916x + 1944x + 432
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(1-2*x)^2/((2+3*x)^5*(3+5*x))
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ------------------------------------------------------
+--R 6 5 4 3 2
+--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96
+--R Type: Fraction(Polynomial(Integer))
+--E 331
+
+--S 332 of 500
+r0:=49/36/(2+3*x)^4+217/27/(2+3*x)^3+121/2/(2+3*x)^2+605/(2+3*x)-_
+ 3025*log(2+3*x)+3025*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (26462700x + 70567200x + 70567200x + 31363200x + 5227200)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 26462700x - 70567200x - 70567200x - 31363200x - 5227200)log(3x + 2)
+--R +
+--R 3 2
+--R 1764180x + 3587166x + 2433252x + 550739
+--R /
+--R 4 3 2
+--R 8748x + 23328x + 23328x + 10368x + 1728
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (26462700x + 70567200x + 70567200x + 31363200x + 5227200)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 26462700x - 70567200x - 70567200x - 31363200x - 5227200)log(3x + 2)
+--R +
+--R 3 2
+--R 1764180x + 3587166x + 2433252x + 550739
+--R /
+--R 4 3 2
+--R 8748x + 23328x + 23328x + 10368x + 1728
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(1-2*x)^2/((2+3*x)^6*(3+5*x))
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192
+--R Type: Fraction(Polynomial(Integer))
+--E 336
+
+--S 337 of 500
+r0:=49/45/(2+3*x)^5+217/36/(2+3*x)^4+121/3/(2+3*x)^3+605/2/(2+3*x)^2+_
+ 3025/(2+3*x)-15125*log(2+3*x)+15125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 661567500x + 2205225000x + 2940300000x + 1960200000x + 653400000x
+--R +
+--R 87120000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 661567500x - 2205225000x - 2940300000x - 1960200000x
+--R +
+--R - 653400000x - 87120000
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 44104500x + 119082150x + 120617640x + 54322575x + 9179006
+--R /
+--R 5 4 3 2
+--R 43740x + 145800x + 194400x + 129600x + 43200x + 5760
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 661567500x + 2205225000x + 2940300000x + 1960200000x + 653400000x
+--R +
+--R 87120000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 661567500x - 2205225000x - 2940300000x - 1960200000x
+--R +
+--R - 653400000x - 87120000
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 44104500x + 119082150x + 120617640x + 54322575x + 9179006
+--R /
+--R 5 4 3 2
+--R 43740x + 145800x + 194400x + 129600x + 43200x + 5760
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(1-2*x)^2/((2+3*x)^7*(3+5*x))
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x
+--R +
+--R 4672x + 384
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 500
+r0:=49/54/(2+3*x)^6+217/45/(2+3*x)^5+121/4/(2+3*x)^4+605/3/(2+3*x)^3+_
+ 3025/2/(2+3*x)^2+15125/(2+3*x)-75625*log(2+3*x)+75625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 29770537500x + 119082150000x + 198470250000x + 176418000000x
+--R +
+--R 2
+--R 88209000000x + 23522400000x + 2613600000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 29770537500x - 119082150000x - 198470250000x - 176418000000x
+--R +
+--R 2
+--R - 88209000000x - 23522400000x - 2613600000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 1984702500x + 6681831750x + 9000258300x + 6063045615x + 2042732232x
+--R +
+--R 275370238
+--R /
+--R 6 5 4 3 2
+--R 393660x + 1574640x + 2624400x + 2332800x + 1166400x + 311040x + 34560
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 29770537500x + 119082150000x + 198470250000x + 176418000000x
+--R +
+--R 2
+--R 88209000000x + 23522400000x + 2613600000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 29770537500x - 119082150000x - 198470250000x - 176418000000x
+--R +
+--R 2
+--R - 88209000000x - 23522400000x - 2613600000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 1984702500x + 6681831750x + 9000258300x + 6063045615x + 2042732232x
+--R +
+--R 275370238
+--R /
+--R 6 5 4 3 2
+--R 393660x + 1574640x + 2624400x + 2332800x + 1166400x + 311040x + 34560
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(1-2*x)^2/((2+3*x)^8*(3+5*x))
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 32805x + 194643x + 513216x + 789264x + 780192x + 514080x + 225792x
+--R +
+--R 2
+--R 63744x + 10496x + 768
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 500
+r0:=7/9/(2+3*x)^7+217/54/(2+3*x)^6+121/5/(2+3*x)^5+605/4/(2+3*x)^4+_
+ 3025/3/(2+3*x)^3+15125/2/(2+3*x)^2+75625/(2+3*x)-378125*log(2+3*x)+_
+ 378125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 446558062500x + 2083937625000x + 4167875250000x + 4630972500000x
+--R +
+--R 3 2
+--R 3087315000000x + 1234926000000x + 274428000000x + 26136000000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 446558062500x - 2083937625000x - 4167875250000x
+--R +
+--R 4 3 2
+--R - 4630972500000x - 3087315000000x - 1234926000000x - 274428000000x
+--R +
+--R - 26136000000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 29770537500x + 120074501250x + 201822192000x + 180948267225x
+--R +
+--R 2
+--R 91271440062x + 24557875626x + 2753702432
+--R /
+--R 7 6 5 4 3 2
+--R 1180980x + 5511240x + 11022480x + 12247200x + 8164800x + 3265920x
+--R +
+--R 725760x + 69120
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 446558062500x + 2083937625000x + 4167875250000x + 4630972500000x
+--R +
+--R 3 2
+--R 3087315000000x + 1234926000000x + 274428000000x + 26136000000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 446558062500x - 2083937625000x - 4167875250000x
+--R +
+--R 4 3 2
+--R - 4630972500000x - 3087315000000x - 1234926000000x - 274428000000x
+--R +
+--R - 26136000000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 29770537500x + 120074501250x + 201822192000x + 180948267225x
+--R +
+--R 2
+--R 91271440062x + 24557875626x + 2753702432
+--R /
+--R 7 6 5 4 3 2
+--R 1180980x + 5511240x + 11022480x + 12247200x + 8164800x + 3265920x
+--R +
+--R 725760x + 69120
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(1-2*x)^2*(2+3*x)^7/(3+5*x)^2
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3 2
+--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x
+--R +
+--R 832x + 128
+--R /
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 351
+
+--S 352 of 500
+r0:=27776932/1953125*x+17592879/781250*x^2-1512378/78125*x^3-_
+ 213867/2500*x^4-656424/15625*x^5+116397/1250*x^6+_
+ 107892/875*x^7+2187/50*x^8+(-121/9765625)/(3+5*x)+2497/9765625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 9 8
+--R (349580x + 209748)log(5x + 3) + 59800781250x + 204461718750x
+--R +
+--R 7 6 5 4
+--R 228457968750x + 18948431250x - 151420775625x - 96641724375x
+--R +
+--R 3 2
+--R 14907569250x + 37916375350x + 11666311440x - 3388
+--R /
+--R 1367187500x + 820312500
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8
+--R (349580x + 209748)log(5x + 3) + 59800781250x + 204461718750x
+--R +
+--R 7 6 5 4
+--R 228457968750x + 18948431250x - 151420775625x - 96641724375x
+--R +
+--R 3 2
+--R 14907569250x + 37916375350x + 11666311440x - 3388
+--R /
+--R 1367187500x + 820312500
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(1-2*x)^2*(2+3*x)^6/(3+5*x)^2
+--R
+--R
+--R 8 7 6 5 4 3 2
+--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64
+--R (1) ----------------------------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 356
+
+--S 357 of 500
+r0:=2777053/390625*x+463086/78125*x^2-48771/3125*x^3-_
+ 157599/6250*x^4+28917/3125*x^5+4374/125*x^6+2916/175*x^7+_
+ (-121/1953125)/(3+5*x)+2134/1953125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R (149380x + 89628)log(5x + 3) + 2278125000x + 6150937500x + 4135556250x
+--R +
+--R 5 4 3 2
+--R - 2688406875x - 4202218125x - 469838250x + 1458208850x + 583181130x
+--R +
+--R - 1694
+--R /
+--R 136718750x + 82031250
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R (149380x + 89628)log(5x + 3) + 2278125000x + 6150937500x + 4135556250x
+--R +
+--R 5 4 3 2
+--R - 2688406875x - 4202218125x - 469838250x + 1458208850x + 583181130x
+--R +
+--R - 1694
+--R /
+--R 136718750x + 82031250
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(1-2*x)^2*(2+3*x)^5/(3+5*x)^2
+--R
+--R
+--R 7 6 5 4 3 2
+--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32
+--R (1) -----------------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 361
+
+--S 362 of 500
+r0:=277174/78125*x+1893/6250*x^2-25332/3125*x^3-8721/2500*x^4+_
+ 5508/625*x^5+162/25*x^6+(-121/390625)/(3+5*x)+1771/390625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R (35420x + 21252)log(5x + 3) + 50625000x + 99225000x + 14056875x
+--R +
+--R 4 3 2
+--R - 79681875x - 35631750x + 29137150x + 16630440x - 484
+--R /
+--R 7812500x + 4687500
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R (35420x + 21252)log(5x + 3) + 50625000x + 99225000x + 14056875x
+--R +
+--R 4 3 2
+--R - 79681875x - 35631750x + 29137150x + 16630440x - 484
+--R /
+--R 7812500x + 4687500
+--R Type: Union(Expression(Integer),...)
+--E 363
+
+--S 364 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(1-2*x)^2*(2+3*x)^4/(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R 324x + 540x + 81x - 264x - 104x + 32x + 16
+--R (1) -----------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 366
+
+--S 367 of 500
+r0:=5459/3125*x-3621/3125*x^2-1809/625*x^3+189/125*x^4+324/125*x^5+_
+ (-121/78125)/(3+5*x)+1408/78125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R (7040x + 4224)log(5x + 3) + 1012500x + 1198125x - 776250x - 1131000x
+--R +
+--R 2
+--R 410800x + 409425x - 121
+--R /
+--R 390625x + 234375
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R (7040x + 4224)log(5x + 3) + 1012500x + 1198125x - 776250x - 1131000x
+--R +
+--R 2
+--R 410800x + 409425x - 121
+--R /
+--R 390625x + 234375
+--R Type: Union(Expression(Integer),...)
+--E 368
+
+--S 369 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(1-2*x)^2*(2+3*x)^3/(3+5*x)^2
+--R
+--R
+--R 5 4 3 2
+--R 108x + 108x - 45x - 58x + 4x + 8
+--R (1) ------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 371
+
+--S 372 of 500
+r0:=2416/3125*x-1449/1250*x^2-36/125*x^3+27/25*x^4+(-121/15625)/(3+5*x)+_
+ 209/3125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (10450x + 6270)log(5x + 3) + 168750x + 56250x - 208125x + 12125x
+--R +
+--R 72480x - 242
+--R /
+--R 156250x + 93750
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (10450x + 6270)log(5x + 3) + 168750x + 56250x - 208125x + 12125x
+--R +
+--R 72480x - 242
+--R /
+--R 156250x + 93750
+--R Type: Union(Expression(Integer),...)
+--E 373
+
+--S 374 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(1-2*x)^2*(2+3*x)^2/(3+5*x)^2
+--R
+--R
+--R 4 3 2
+--R 36x + 12x - 23x - 4x + 4
+--R (1) ---------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 376
+
+--S 377 of 500
+r0:=37/625*x-78/125*x^2+12/25*x^3+(-121/3125)/(3+5*x)+682/3125*log(3+5*x)
+--R
+--R
+--R 4 3 2
+--R (3410x + 2046)log(5x + 3) + 7500x - 5250x - 4925x + 555x - 121
+--R (2) -----------------------------------------------------------------
+--R 15625x + 9375
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R (3410x + 2046)log(5x + 3) + 7500x - 5250x - 4925x + 555x - 121
+--R (3) -----------------------------------------------------------------
+--R 15625x + 9375
+--R Type: Union(Expression(Integer),...)
+--E 378
+
+--S 379 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(1-2*x)^2*(2+3*x)/(3+5*x)^2
+--R
+--R
+--R 3 2
+--R 12x - 4x - 5x + 2
+--R (1) -------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 381
+
+--S 382 of 500
+r0:=-92/125*x+6/25*x^2+(-121/625)/(3+5*x)+319/625*log(3+5*x)
+--R
+--R
+--R 3 2
+--R (1595x + 957)log(5x + 3) + 750x - 1850x - 1380x - 121
+--R (2) -------------------------------------------------------
+--R 3125x + 1875
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R (1595x + 957)log(5x + 3) + 750x - 1850x - 1380x - 121
+--R (3) -------------------------------------------------------
+--R 3125x + 1875
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(1-2*x)^2/(3+5*x)^2
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) --------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 386
+
+--S 387 of 500
+r0:=4/25*x+(-121/125)/(3+5*x)-44/125*log(3+5*x)
+--R
+--R
+--R 2
+--R (- 220x - 132)log(5x + 3) + 100x + 60x - 121
+--R (2) ---------------------------------------------
+--R 625x + 375
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (- 220x - 132)log(5x + 3) + 100x + 60x - 121
+--R (3) ---------------------------------------------
+--R 625x + 375
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(1-2*x)^2/((2+3*x)*(3+5*x)^2)
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) -----------------------
+--R 3 2
+--R 75x + 140x + 87x + 18
+--R Type: Fraction(Polynomial(Integer))
+--E 391
+
+--S 392 of 500
+r0:=(-121/25)/(3+5*x)+49/3*log(2+3*x)-407/25*log(3+5*x)
+--R
+--R
+--R (- 6105x - 3663)log(5x + 3) + (6125x + 3675)log(3x + 2) - 363
+--R (2) -------------------------------------------------------------
+--R 375x + 225
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (- 6105x - 3663)log(5x + 3) + (6125x + 3675)log(3x + 2) - 363
+--R (3) -------------------------------------------------------------
+--R 375x + 225
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(1-2*x)^2/((2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 225x + 570x + 541x + 228x + 36
+--R Type: Fraction(Polynomial(Integer))
+--E 396
+
+--S 397 of 500
+r0:=(-49/3)/(2+3*x)+(-121/5)/(3+5*x)+154*log(2+3*x)-154*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 34650x - 43890x - 13860)log(5x + 3)
+--R +
+--R 2
+--R (34650x + 43890x + 13860)log(3x + 2) - 2314x - 1461
+--R /
+--R 2
+--R 225x + 285x + 90
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (- 34650x - 43890x - 13860)log(5x + 3)
+--R +
+--R 2
+--R (34650x + 43890x + 13860)log(3x + 2) - 2314x - 1461
+--R /
+--R 2
+--R 225x + 285x + 90
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(1-2*x)^2/((2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 675x + 2160x + 2763x + 1766x + 564x + 72
+--R Type: Fraction(Polynomial(Integer))
+--E 401
+
+--S 402 of 500
+r0:=(-49/6)/(2+3*x)^2+(-154)/(2+3*x)+(-121)/(3+5*x)+1133*log(2+3*x)-_
+ 1133*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (- 305910x - 591426x - 380688x - 81576)log(5x + 3)
+--R +
+--R 3 2 2
+--R (305910x + 591426x + 380688x + 81576)log(3x + 2) - 20394x - 26513x
+--R +
+--R - 8595
+--R /
+--R 3 2
+--R 270x + 522x + 336x + 72
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (- 305910x - 591426x - 380688x - 81576)log(5x + 3)
+--R +
+--R 3 2 2
+--R (305910x + 591426x + 380688x + 81576)log(3x + 2) - 20394x - 26513x
+--R +
+--R - 8595
+--R /
+--R 3 2
+--R 270x + 522x + 336x + 72
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(1-2*x)^2/((2+3*x)^4*(3+5*x)^2)
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ----------------------------------------------------------
+--R 6 5 4 3 2
+--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144
+--R Type: Fraction(Polynomial(Integer))
+--E 406
+
+--S 407 of 500
+r0:=(-49/9)/(2+3*x)^3+(-77)/(2+3*x)^2+(-1133)/(2+3*x)+(-605)/(3+5*x)+_
+ 7480*log(2+3*x)-7480*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 9088200x - 23629320x - 23023440x - 9963360x - 1615680)log(5x + 3)
+--R +
+--R 4 3 2
+--R (9088200x + 23629320x + 23023440x + 9963360x + 1615680)log(3x + 2)
+--R +
+--R 3 2
+--R - 605880x - 1191564x - 780464x - 170229
+--R /
+--R 4 3 2
+--R 1215x + 3159x + 3078x + 1332x + 216
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 9088200x - 23629320x - 23023440x - 9963360x - 1615680)log(5x + 3)
+--R +
+--R 4 3 2
+--R (9088200x + 23629320x + 23023440x + 9963360x + 1615680)log(3x + 2)
+--R +
+--R 3 2
+--R - 605880x - 1191564x - 780464x - 170229
+--R /
+--R 4 3 2
+--R 1215x + 3159x + 3078x + 1332x + 216
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(1-2*x)^2/((2+3*x)^5*(3+5*x)^2)
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288
+--R Type: Fraction(Polynomial(Integer))
+--E 411
+
+--S 412 of 500
+r0:=(-49/12)/(2+3*x)^4+(-154/3)/(2+3*x)^3+(-1133/2)/(2+3*x)^2+_
+ (-7480)/(2+3*x)+(-3025)/(3+5*x)+46475*log(2+3*x)-46475*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 75289500x - 245945700x - 321235200x - 209695200x - 68411200x
+--R +
+--R - 8923200
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 75289500x + 245945700x + 321235200x + 209695200x + 68411200x
+--R +
+--R 8923200
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R - 5019300x - 13217490x - 13046462x - 5720639x - 940153
+--R /
+--R 5 4 3 2
+--R 1620x + 5292x + 6912x + 4512x + 1472x + 192
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 75289500x - 245945700x - 321235200x - 209695200x - 68411200x
+--R +
+--R - 8923200
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 75289500x + 245945700x + 321235200x + 209695200x + 68411200x
+--R +
+--R 8923200
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R - 5019300x - 13217490x - 13046462x - 5720639x - 940153
+--R /
+--R 5 4 3 2
+--R 1620x + 5292x + 6912x + 4512x + 1472x + 192
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(1-2*x)^2/((2+3*x)^6*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x
+--R +
+--R 7104x + 576
+--R Type: Fraction(Polynomial(Integer))
+--E 416
+
+--S 417 of 500
+r0:=(-49/15)/(2+3*x)^5+(-77/2)/(2+3*x)^4+(-1133/3)/(2+3*x)^3+_
+ (-3740)/(2+3*x)^2+(-46475)/(2+3*x)+(-15125)/(3+5*x)+_
+ 277750*log(2+3*x)-277750*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R - 10123987500x - 39821017500x - 65243475000x - 56994300000x
+--R +
+--R 2
+--R - 27997200000x - 7332600000x - 799920000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R 10123987500x + 39821017500x + 65243475000x + 56994300000x
+--R +
+--R 2
+--R 27997200000x + 7332600000x + 799920000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 674932500x - 2227277250x - 2939206050x - 1938789435x - 639246515x
+--R +
+--R - 84279984
+--R /
+--R 6 5 4 3 2
+--R 36450x + 143370x + 234900x + 205200x + 100800x + 26400x + 2880
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R - 10123987500x - 39821017500x - 65243475000x - 56994300000x
+--R +
+--R 2
+--R - 27997200000x - 7332600000x - 799920000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R 10123987500x + 39821017500x + 65243475000x + 56994300000x
+--R +
+--R 2
+--R 27997200000x + 7332600000x + 799920000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 674932500x - 2227277250x - 2939206050x - 1938789435x - 639246515x
+--R +
+--R - 84279984
+--R /
+--R 6 5 4 3 2
+--R 36450x + 143370x + 234900x + 205200x + 100800x + 26400x + 2880
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(1-2*x)^2/((2+3*x)^7*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R /
+--R 9 8 7 6 5 4
+--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x
+--R +
+--R 3 2
+--R 351120x + 97952x + 15936x + 1152
+--R Type: Fraction(Polynomial(Integer))
+--E 421
+
+--S 422 of 500
+r0:=(-49/18)/(2+3*x)^6+(-154/5)/(2+3*x)^5+(-1133/4)/(2+3*x)^4+_
+ (-7480/3)/(2+3*x)^3+(-46475/2)/(2+3*x)^2+(-277750)/(2+3*x)+_
+ (-75625)/(3+5*x)+1615625*log(2+3*x)-1615625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R - 1060011562500x - 4876053187500x - 9610771500000x
+--R +
+--R 4 3 2
+--R - 10521596250000x - 6909705000000x - 2722005000000x
+--R +
+--R - 595584000000x - 55836000000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R 1060011562500x + 4876053187500x + 9610771500000x
+--R +
+--R 4 3 2
+--R 10521596250000x + 6909705000000x + 2722005000000x + 595584000000x
+--R +
+--R 55836000000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 70667437500x - 280314168750x - 463211966250x - 408159415125x
+--R +
+--R 2
+--R - 202262350455x - 53445037346x - 5882909754
+--R /
+--R 7 6 5 4 3 2
+--R 656100x + 3018060x + 5948640x + 6512400x + 4276800x + 1684800x
+--R +
+--R 368640x + 34560
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R - 1060011562500x - 4876053187500x - 9610771500000x
+--R +
+--R 4 3 2
+--R - 10521596250000x - 6909705000000x - 2722005000000x
+--R +
+--R - 595584000000x - 55836000000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R 1060011562500x + 4876053187500x + 9610771500000x
+--R +
+--R 4 3 2
+--R 10521596250000x + 6909705000000x + 2722005000000x + 595584000000x
+--R +
+--R 55836000000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 70667437500x - 280314168750x - 463211966250x - 408159415125x
+--R +
+--R 2
+--R - 202262350455x - 53445037346x - 5882909754
+--R /
+--R 7 6 5 4 3 2
+--R 656100x + 3018060x + 5948640x + 6512400x + 4276800x + 1684800x
+--R +
+--R 368640x + 34560
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(1-2*x)^2/((2+3*x)^8*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R /
+--R 10 9 8 7 6 5
+--R 164025x + 1071630x + 3150009x + 5485968x + 6268752x + 4910976x
+--R +
+--R 4 3 2
+--R 2671200x + 996096x + 243712x + 35328x + 2304
+--R Type: Fraction(Polynomial(Integer))
+--E 426
+
+--S 427 of 500
+r0:=(-7/3)/(2+3*x)^7+(-77/3)/(2+3*x)^6+(-1133/5)/(2+3*x)^5+_
+ (-1870)/(2+3*x)^4+(-46475/3)/(2+3*x)^3+(-138875)/(2+3*x)^2+_
+ (-1615625)/(2+3*x)+(-378125)/(3+5*x)+9212500*log(2+3*x)-9212500*log(3+5*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R - 1511080312500x - 7958356312500x - 18334441125000x
+--R +
+--R 5 4 3
+--R - 24132512250000x - 19849252500000x - 10446975000000x
+--R +
+--R 2
+--R - 3435894000000x - 645612000000x - 53064000000
+--R *
+--R log(5x + 3)
+--R +
+--R 8 7 6
+--R 1511080312500x + 7958356312500x + 18334441125000x
+--R +
+--R 5 4 3
+--R 24132512250000x + 19849252500000x + 10446975000000x
+--R +
+--R 2
+--R 3435894000000x + 645612000000x + 53064000000
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 100738687500x - 466755918750x - 926721303750x - 1022059900125x
+--R +
+--R 3 2
+--R - 676227617505x - 268408563588x - 59178013234x - 5590850403
+--R /
+--R 8 7 6 5 4 3
+--R 164025x + 863865x + 1990170x + 2619540x + 2154600x + 1134000x
+--R +
+--R 2
+--R 372960x + 70080x + 5760
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R - 1511080312500x - 7958356312500x - 18334441125000x
+--R +
+--R 5 4 3
+--R - 24132512250000x - 19849252500000x - 10446975000000x
+--R +
+--R 2
+--R - 3435894000000x - 645612000000x - 53064000000
+--R *
+--R log(5x + 3)
+--R +
+--R 8 7 6
+--R 1511080312500x + 7958356312500x + 18334441125000x
+--R +
+--R 5 4 3
+--R 24132512250000x + 19849252500000x + 10446975000000x
+--R +
+--R 2
+--R 3435894000000x + 645612000000x + 53064000000
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 100738687500x - 466755918750x - 926721303750x - 1022059900125x
+--R +
+--R 3 2
+--R - 676227617505x - 268408563588x - 59178013234x - 5590850403
+--R /
+--R 8 7 6 5 4 3
+--R 164025x + 863865x + 1990170x + 2619540x + 2154600x + 1134000x
+--R +
+--R 2
+--R 372960x + 70080x + 5760
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(1-2*x)^2*(2+3*x)^8/(3+5*x)^3
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5 4
+--R 26244x + 113724x + 193185x + 143856x + 9072x - 60480x - 38304x
+--R +
+--R 3 2
+--R - 3840x + 4864x + 2048x + 256
+--R /
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 431
+
+--S 432 of 500
+r0:=92582457/9765625*x+55559043/3906250*x^2-5350194/390625*x^3-_
+ 1700919/31250*x^4-74601/3125*x^5+376407/6250*x^6+332424/4375*x^7+_
+ 6561/250*x^8+(-121/97656250)/(3+5*x)^2+(-572/9765625)/(3+5*x)+_
+ 5888/9765625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 10
+--R (10304000x + 12364800x + 3709440)log(5x + 3) + 448505859375x
+--R +
+--R 9 8 7 6
+--R 1836738281250x + 2748937500000x + 1294582500000x - 1049233500000x
+--R +
+--R 5 4 3 2
+--R - 1497169800000x - 372682800000x + 369438720000x + 281928652425x
+--R +
+--R 58326747710x - 120967
+--R /
+--R 2
+--R 17089843750x + 20507812500x + 6152343750
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 10
+--R (10304000x + 12364800x + 3709440)log(5x + 3) + 448505859375x
+--R +
+--R 9 8 7 6
+--R 1836738281250x + 2748937500000x + 1294582500000x - 1049233500000x
+--R +
+--R 5 4 3 2
+--R - 1497169800000x - 372682800000x + 369438720000x + 281928652425x
+--R +
+--R 58326747710x - 120967
+--R /
+--R 2
+--R 17089843750x + 20507812500x + 6152343750
+--R Type: Union(Expression(Integer),...)
+--E 433
+
+--S 434 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(1-2*x)^2*(2+3*x)^7/(3+5*x)^3
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3 2
+--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x
+--R +
+--R 832x + 128
+--R /
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 436
+
+--S 437 of 500
+r0:=9251661/1953125*x+1390203/390625*x^2-162612/15625*x^3-_
+ 193833/12500*x^4+104247/15625*x^5+13608/625*x^6+8748/875*x^7+_
+ (-121/19531250)/(3+5*x)^2+(-2497/9765625)/(3+5*x)+21949/9765625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 9
+--R (15364300x + 18437160x + 5531148)log(5x + 3) + 68343750000x
+--R +
+--R 8 7 6 5
+--R 230850000000x + 248816812500x + 2308753125x - 181926753750x
+--R +
+--R 4 3 2
+--R - 99203619375x + 35963686500x + 47615255100x + 11656743280x - 211442
+--R /
+--R 2
+--R 6835937500x + 8203125000x + 2460937500
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 9
+--R (15364300x + 18437160x + 5531148)log(5x + 3) + 68343750000x
+--R +
+--R 8 7 6 5
+--R 230850000000x + 248816812500x + 2308753125x - 181926753750x
+--R +
+--R 4 3 2
+--R - 99203619375x + 35963686500x + 47615255100x + 11656743280x - 211442
+--R /
+--R 2
+--R 6835937500x + 8203125000x + 2460937500
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(1-2*x)^2*(2+3*x)^6/(3+5*x)^3
+--R
+--R
+--R 8 7 6 5 4 3 2
+--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64
+--R (1) ----------------------------------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 441
+
+--S 442 of 500
+r0:=920502/390625*x+189/15625*x^2-16299/3125*x^3-23571/12500*x^4+_
+ 17496/3125*x^5+486/125*x^6+(-121/3906250)/(3+5*x)^2+_
+ (-2134/1953125)/(3+5*x)+15547/1953125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 8 7
+--R (1554700x + 1865640x + 559692)log(5x + 3) + 759375000x + 2004750000x
+--R +
+--R 6 5 4 3 2
+--R 1217278125x - 1066983750x - 1352649375x + 96358500x + 553151700x
+--R +
+--R 165647680x - 25850
+--R /
+--R 2
+--R 195312500x + 234375000x + 70312500
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 7
+--R (1554700x + 1865640x + 559692)log(5x + 3) + 759375000x + 2004750000x
+--R +
+--R 6 5 4 3 2
+--R 1217278125x - 1066983750x - 1352649375x + 96358500x + 553151700x
+--R +
+--R 165647680x - 25850
+--R /
+--R 2
+--R 195312500x + 234375000x + 70312500
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(1-2*x)^2*(2+3*x)^5/(3+5*x)^3
+--R
+--R
+--R 7 6 5 4 3 2
+--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32
+--R (1) -----------------------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 446
+
+--S 447 of 500
+r0:=17796/15625*x-5301/6250*x^2-5499/3125*x^3+648/625*x^4+972/625*x^5+_
+ (-121/781250)/(3+5*x)^2+(-1771/390625)/(3+5*x)+10234/390625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 7 6
+--R (511700x + 614040x + 184212)log(5x + 3) + 30375000x + 56700000x
+--R +
+--R 5 4 3 2
+--R 866250x - 50518125x - 10006500x + 20730375x + 7990490x - 10747
+--R /
+--R 2
+--R 19531250x + 23437500x + 7031250
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 6
+--R (511700x + 614040x + 184212)log(5x + 3) + 30375000x + 56700000x
+--R +
+--R 5 4 3 2
+--R 866250x - 50518125x - 10006500x + 20730375x + 7990490x - 10747
+--R /
+--R 2
+--R 19531250x + 23437500x + 7031250
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(1-2*x)^2*(2+3*x)^4/(3+5*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R 324x + 540x + 81x - 264x - 104x + 32x + 16
+--R (1) -----------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 451
+
+--S 452 of 500
+r0:=1419/3125*x-4779/6250*x^2-72/625*x^3+81/125*x^4+(-121/156250)/(3+5*x)^2+_
+ (-1408/78125)/(3+5*x)+1202/15625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 6 5
+--R (300500x + 360600x + 108180)log(5x + 3) + 2531250x + 2587500x
+--R +
+--R 4 3 2
+--R - 2615625x - 1972500x + 1053225x + 624470x - 8569
+--R /
+--R 2
+--R 3906250x + 4687500x + 1406250
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 5
+--R (300500x + 360600x + 108180)log(5x + 3) + 2531250x + 2587500x
+--R +
+--R 4 3 2
+--R - 2615625x - 1972500x + 1053225x + 624470x - 8569
+--R /
+--R 2
+--R 3906250x + 4687500x + 1406250
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(1-2*x)^2*(2+3*x)^3/(3+5*x)^3
+--R
+--R
+--R 5 4 3 2
+--R 108x + 108x - 45x - 58x + 4x + 8
+--R (1) ------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 456
+
+--S 457 of 500
+r0:=-153/3125*x-216/625*x^2+36/125*x^3+(-121/31250)/(3+5*x)^2+_
+ (-209/3125)/(3+5*x)+23/125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 5 3 2
+--R (143750x + 172500x + 51750)log(5x + 3) + 225000x - 281250x - 143100x
+--R +
+--R - 24220x - 6391
+--R /
+--R 2
+--R 781250x + 937500x + 281250
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 3 2
+--R (143750x + 172500x + 51750)log(5x + 3) + 225000x - 281250x - 143100x
+--R +
+--R - 24220x - 6391
+--R /
+--R 2
+--R 781250x + 937500x + 281250
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(1-2*x)^2*(2+3*x)^2/(3+5*x)^3
+--R
+--R
+--R 4 3 2
+--R 36x + 12x - 23x - 4x + 4
+--R (1) ---------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 461
+
+--S 462 of 500
+r0:=-264/625*x+18/125*x^2+(-121/6250)/(3+5*x)^2+(-682/3125)/(3+5*x)+_
+ 829/3125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2
+--R (41450x + 49740x + 14922)log(5x + 3) + 22500x - 39000x - 71100x
+--R +
+--R - 30580x - 4213
+--R /
+--R 2
+--R 156250x + 187500x + 56250
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2
+--R (41450x + 49740x + 14922)log(5x + 3) + 22500x - 39000x - 71100x
+--R +
+--R - 30580x - 4213
+--R /
+--R 2
+--R 156250x + 187500x + 56250
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(1-2*x)^2*(2+3*x)/(3+5*x)^3
+--R
+--R
+--R 3 2
+--R 12x - 4x - 5x + 2
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 466
+
+--S 467 of 500
+r0:=12/125*x+(-121/1250)/(3+5*x)^2+(-319/625)/(3+5*x)-128/625*log(3+5*x)
+--R
+--R
+--R 2 3 2
+--R (- 6400x - 7680x - 2304)log(5x + 3) + 3000x + 3600x - 2110x - 2035
+--R (2) ---------------------------------------------------------------------
+--R 2
+--R 31250x + 37500x + 11250
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2
+--R (- 6400x - 7680x - 2304)log(5x + 3) + 3000x + 3600x - 2110x - 2035
+--R (3) ---------------------------------------------------------------------
+--R 2
+--R 31250x + 37500x + 11250
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(1-2*x)^2/(3+5*x)^3
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 471
+
+--S 472 of 500
+r0:=(-121/250)/(3+5*x)^2+44/125/(3+5*x)+4/125*log(3+5*x)
+--R
+--R
+--R 2
+--R (200x + 240x + 72)log(5x + 3) + 440x + 143
+--R (2) -------------------------------------------
+--R 2
+--R 6250x + 7500x + 2250
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (200x + 240x + 72)log(5x + 3) + 440x + 143
+--R (3) -------------------------------------------
+--R 2
+--R 6250x + 7500x + 2250
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(1-2*x)^2/((2+3*x)*(3+5*x)^3)
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 375x + 925x + 855x + 351x + 54
+--R Type: Fraction(Polynomial(Integer))
+--E 476
+
+--S 477 of 500
+r0:=(-121/50)/(3+5*x)^2+407/25/(3+5*x)-49*log(2+3*x)+49*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (61250x + 73500x + 22050)log(5x + 3)
+--R +
+--R 2
+--R (- 61250x - 73500x - 22050)log(3x + 2) + 4070x + 2321
+--R /
+--R 2
+--R 1250x + 1500x + 450
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (61250x + 73500x + 22050)log(5x + 3)
+--R +
+--R 2
+--R (- 61250x - 73500x - 22050)log(3x + 2) + 4070x + 2321
+--R /
+--R 2
+--R 1250x + 1500x + 450
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(1-2*x)^2/((2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) ----------------------------------------------
+--R 5 4 3 2
+--R 1125x + 3525x + 4415x + 2763x + 864x + 108
+--R Type: Fraction(Polynomial(Integer))
+--E 481
+
+--S 482 of 500
+r0:=49/(2+3*x)+(-121/10)/(3+5*x)^2+154/(3+5*x)-707*log(2+3*x)+707*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (530250x + 989800x + 615090x + 127260)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 530250x - 989800x - 615090x - 127260)log(3x + 2) + 35350x + 43597x
+--R +
+--R 13408
+--R /
+--R 3 2
+--R 750x + 1400x + 870x + 180
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (530250x + 989800x + 615090x + 127260)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 530250x - 989800x - 615090x - 127260)log(3x + 2) + 35350x + 43597x
+--R +
+--R 13408
+--R /
+--R 3 2
+--R 750x + 1400x + 870x + 180
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(1-2*x)^2/((2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R 2
+--R 4x - 4x + 1
+--R (1) -----------------------------------------------------------
+--R 6 5 4 3 2
+--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216
+--R Type: Fraction(Polynomial(Integer))
+--E 486
+
+--S 487 of 500
+r0:=49/2/(2+3*x)^2+707/(2+3*x)+(-121/2)/(3+5*x)^2+1133/(3+5*x)-_
+ 6934*log(2+3*x)+6934*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (3120300x + 7904760x + 7502588x + 3161904x + 499248)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 3120300x - 7904760x - 7502588x - 3161904x - 499248)log(3x + 2)
+--R +
+--R 3 2
+--R 208020x + 395238x + 249932x + 52601
+--R /
+--R 4 3 2
+--R 450x + 1140x + 1082x + 456x + 72
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (3120300x + 7904760x + 7502588x + 3161904x + 499248)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 3120300x - 7904760x - 7502588x - 3161904x - 499248)log(3x + 2)
+--R +
+--R 3 2
+--R 208020x + 395238x + 249932x + 52601
+--R /
+--R 4 3 2
+--R 450x + 1140x + 1082x + 456x + 72
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(1-2*x)^2/((2+3*x)^4*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R -----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432
+--R Type: Fraction(Polynomial(Integer))
+--E 491
+
+--S 492 of 500
+r0:=49/3/(2+3*x)^3+707/2/(2+3*x)^2+6934/(2+3*x)+(-605/2)/(3+5*x)^2+_
+ 7480/(3+5*x)-57110*log(2+3*x)+57110*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 231295500x + 740145600x + 946769580x + 605137560x + 193260240x
+--R +
+--R 24671520
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 231295500x - 740145600x - 946769580x - 605137560x - 193260240x
+--R +
+--R - 24671520
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 15419700x + 39577230x + 38058104x + 16250079x + 2599404
+--R /
+--R 5 4 3 2
+--R 4050x + 12960x + 16578x + 10596x + 3384x + 432
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 231295500x + 740145600x + 946769580x + 605137560x + 193260240x
+--R +
+--R 24671520
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 231295500x - 740145600x - 946769580x - 605137560x - 193260240x
+--R +
+--R - 24671520
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 15419700x + 39577230x + 38058104x + 16250079x + 2599404
+--R /
+--R 5 4 3 2
+--R 4050x + 12960x + 16578x + 10596x + 3384x + 432
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(1-2*x)^2/((2+3*x)^5*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x
+--R +
+--R 10800x + 864
+--R Type: Fraction(Polynomial(Integer))
+--E 496
+
+--S 497 of 500
+r0:=49/4/(2+3*x)^4+707/3/(2+3*x)^3+3467/(2+3*x)^2+57110/(2+3*x)+_
+ (-3025/2)/(3+5*x)^2+46475/(3+5*x)-424975*log(2+3*x)+424975*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 10326892500x + 39930651000x + 64302117300x + 55199152800x
+--R +
+--R 2
+--R 26640832800x + 6853996800x + 734356800
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 10326892500x - 39930651000x - 64302117300x - 55199152800x
+--R +
+--R 2
+--R - 26640832800x - 6853996800x - 734356800
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 688459500x + 2226019050x + 2877250740x + 1858347679x + 599747838x
+--R +
+--R 77372211
+--R /
+--R 6 5 4 3 2
+--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 10326892500x + 39930651000x + 64302117300x + 55199152800x
+--R +
+--R 2
+--R 26640832800x + 6853996800x + 734356800
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 10326892500x - 39930651000x - 64302117300x - 55199152800x
+--R +
+--R 2
+--R - 26640832800x - 6853996800x - 734356800
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 688459500x + 2226019050x + 2877250740x + 1858347679x + 599747838x
+--R +
+--R 77372211
+--R /
+--R 6 5 4 3 2
+--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3e.input.pdf b/src/axiom-website/CATS/rich3e.input.pdf
new file mode 100644
index 0000000..aa0dc30
Binary files /dev/null and b/src/axiom-website/CATS/rich3e.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3f.input.pamphlet b/src/axiom-website/CATS/rich3f.input.pamphlet
new file mode 100644
index 0000000..1311f46
--- /dev/null
+++ b/src/axiom-website/CATS/rich3f.input.pamphlet
@@ -0,0 +1,6798 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3f.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 99 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 1 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3f.output
+)spool rich3f.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(1-2*x)^2/((2+3*x)^6*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R /
+--R 9 8 7 6 5 4
+--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x
+--R +
+--R 3 2
+--R 545840x + 150480x + 24192x + 1728
+--R Type: Fraction(Polynomial(Integer))
+--E 1
+
+--S 2 of 500
+r0:=49/5/(2+3*x)^5+707/4/(2+3*x)^4+6934/3/(2+3*x)^3+28555/(2+3*x)^2+_
+ 424975/(2+3*x)+(-15125/2)/(3+5*x)^2+277750/(3+5*x)-_
+ 2958125*log(2+3*x)+2958125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R 1078236562500x + 4888005750000x + 9493273912500x
+--R +
+--R 4 3 2
+--R 10239253875000x + 6623833500000x + 2570019000000x + 553761000000x
+--R +
+--R 51116400000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 1078236562500x - 4888005750000x - 9493273912500x
+--R +
+--R 4 3 2
+--R - 10239253875000x - 6623833500000x - 2570019000000x
+--R +
+--R - 553761000000x - 51116400000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 71882437500x + 280341506250x + 455361930000x + 394308004875x
+--R +
+--R 2
+--R 191974077080x + 49825144515x + 5385650262
+--R /
+--R 7 6 5 4 3 2
+--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x
+--R +
+--R 187200x + 17280
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R 1078236562500x + 4888005750000x + 9493273912500x
+--R +
+--R 4 3 2
+--R 10239253875000x + 6623833500000x + 2570019000000x + 553761000000x
+--R +
+--R 51116400000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 1078236562500x - 4888005750000x - 9493273912500x
+--R +
+--R 4 3 2
+--R - 10239253875000x - 6623833500000x - 2570019000000x
+--R +
+--R - 553761000000x - 51116400000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 71882437500x + 280341506250x + 455361930000x + 394308004875x
+--R +
+--R 2
+--R 191974077080x + 49825144515x + 5385650262
+--R /
+--R 7 6 5 4 3 2
+--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x
+--R +
+--R 187200x + 17280
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(1-2*x)^2/((2+3*x)^7*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R /
+--R 10 9 8 7 6 5
+--R 273375x + 1767825x + 5143095x + 8864559x + 10024182x + 7770924x
+--R +
+--R 4 3 2
+--R 4182360x + 1543120x + 373536x + 53568x + 3456
+--R Type: Fraction(Polynomial(Integer))
+--E 6
+
+--S 7 of 500
+r0:=49/6/(2+3*x)^6+707/5/(2+3*x)^5+3467/2/(2+3*x)^4+57110/3/(2+3*x)^3+_
+ 424975/2/(2+3*x)^2+2958125/(2+3*x)+(-75625/2)/(3+5*x)^2+_
+ 1615625/(3+5*x)-19637500*log(2+3*x)+19637500*log(3+5*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R 3578934375000x + 18610458750000x + 42326863875000x
+--R +
+--R 5 4 3
+--R 54993640500000x + 44643892500000x + 23187960000000x
+--R +
+--R 2
+--R 7525090000000x + 1395048000000x + 113112000000
+--R *
+--R log(5x + 3)
+--R +
+--R 8 7 6
+--R - 3578934375000x - 18610458750000x - 42326863875000x
+--R +
+--R 5 4 3
+--R - 54993640500000x - 44643892500000x - 23187960000000x
+--R +
+--R 2
+--R - 7525090000000x - 1395048000000x - 113112000000
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R 238595625000x + 1089586687500x + 2131807725000x + 2316445391250x
+--R +
+--R 3 2
+--R 1509746867100x + 590188362770x + 128130976648x + 11917538647
+--R /
+--R 8 7 6 5 4 3
+--R 182250x + 947700x + 2155410x + 2800440x + 2273400x + 1180800x
+--R +
+--R 2
+--R 383200x + 71040x + 5760
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R 3578934375000x + 18610458750000x + 42326863875000x
+--R +
+--R 5 4 3
+--R 54993640500000x + 44643892500000x + 23187960000000x
+--R +
+--R 2
+--R 7525090000000x + 1395048000000x + 113112000000
+--R *
+--R log(5x + 3)
+--R +
+--R 8 7 6
+--R - 3578934375000x - 18610458750000x - 42326863875000x
+--R +
+--R 5 4 3
+--R - 54993640500000x - 44643892500000x - 23187960000000x
+--R +
+--R 2
+--R - 7525090000000x - 1395048000000x - 113112000000
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R 238595625000x + 1089586687500x + 2131807725000x + 2316445391250x
+--R +
+--R 3 2
+--R 1509746867100x + 590188362770x + 128130976648x + 11917538647
+--R /
+--R 8 7 6 5 4 3
+--R 182250x + 947700x + 2155410x + 2800440x + 2273400x + 1180800x
+--R +
+--R 2
+--R 383200x + 71040x + 5760
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(1-2*x)^2/((2+3*x)^8*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 2
+--R 4x - 4x + 1
+--R /
+--R 11 10 9 8 7
+--R 820125x + 5850225x + 18964935x + 36879867x + 47801664x
+--R +
+--R 6 5 4 3 2
+--R 43361136x + 28088928x + 12994080x + 4206848x + 907776x + 117504x
+--R +
+--R 6912
+--R Type: Fraction(Polynomial(Integer))
+--E 11
+
+--S 12 of 500
+r0:=7/(2+3*x)^7+707/6/(2+3*x)^6+6934/5/(2+3*x)^5+28555/2/(2+3*x)^4+_
+ 424975/3/(2+3*x)^3+2958125/2/(2+3*x)^2+19637500/(2+3*x)+_
+ (-378125/2)/(3+5*x)^2+9212500/(3+5*x)-125825000*log(2+3*x)+_
+ 125825000*log(3+5*x)
+--R
+--R
+--R (2)
+--R 9 8 7
+--R 68794818750000x + 403596270000000x + 1052102094750000x
+--R +
+--R 6 5 4
+--R 1599505015500000x + 1562882391000000x + 1017823590000000x
+--R +
+--R 3 2
+--R 441796740000000x + 123248104000000x + 20051472000000x + 1449504000000
+--R *
+--R log(5x + 3)
+--R +
+--R 9 8 7
+--R - 68794818750000x - 403596270000000x - 1052102094750000x
+--R +
+--R 6 5 4
+--R - 1599505015500000x - 1562882391000000x - 1017823590000000x
+--R +
+--R 3 2
+--R - 441796740000000x - 123248104000000x - 20051472000000x
+--R +
+--R - 1449504000000
+--R *
+--R log(3x + 2)
+--R +
+--R 8 7 6 5
+--R 4586321250000x + 24001747875000x + 54940731300000x + 71845684942500x
+--R +
+--R 4 3 2
+--R 58705292494800x + 30691745453460x + 10026079791288x + 1871049429619x
+--R +
+--R 152720488888
+--R /
+--R 9 8 7 6 5 4
+--R 546750x + 3207600x + 8361630x + 12712140x + 12421080x + 8089200x
+--R +
+--R 3 2
+--R 3511200x + 979520x + 159360x + 11520
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7
+--R 68794818750000x + 403596270000000x + 1052102094750000x
+--R +
+--R 6 5 4
+--R 1599505015500000x + 1562882391000000x + 1017823590000000x
+--R +
+--R 3 2
+--R 441796740000000x + 123248104000000x + 20051472000000x + 1449504000000
+--R *
+--R log(5x + 3)
+--R +
+--R 9 8 7
+--R - 68794818750000x - 403596270000000x - 1052102094750000x
+--R +
+--R 6 5 4
+--R - 1599505015500000x - 1562882391000000x - 1017823590000000x
+--R +
+--R 3 2
+--R - 441796740000000x - 123248104000000x - 20051472000000x
+--R +
+--R - 1449504000000
+--R *
+--R log(3x + 2)
+--R +
+--R 8 7 6 5
+--R 4586321250000x + 24001747875000x + 54940731300000x + 71845684942500x
+--R +
+--R 4 3 2
+--R 58705292494800x + 30691745453460x + 10026079791288x + 1871049429619x
+--R +
+--R 152720488888
+--R /
+--R 9 8 7 6 5 4
+--R 546750x + 3207600x + 8361630x + 12712140x + 12421080x + 8089200x
+--R +
+--R 3 2
+--R 3511200x + 979520x + 159360x + 11520
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(1-2*x)^3*(2+3*x)^8*(3+5*x)
+--R
+--R
+--R (1)
+--R 12 11 10 9 8 7
+--R - 262440x - 1163484x - 1966842x - 1290573x + 344979x + 1027296x
+--R +
+--R 6 5 4 3 2
+--R 470736x - 104736x - 159712x - 36864x + 9984x + 5888x + 768
+--R Type: Polynomial(Integer)
+--E 16
+
+--S 17 of 500
+r0:=-343/2187*(2+3*x)^9+2009/2430*(2+3*x)^10-518/891*(2+3*x)^11+_
+ 107/729*(2+3*x)^12-40/3159*(2+3*x)^13
+--R
+--R
+--R (2)
+--R 262440 13 12 1966842 11 1290573 10 9 8
+--R - ------ x - 96957x - ------- x - ------- x + 38331x + 128412x
+--R 13 11 10
+--R +
+--R 7 6 159712 5 4 3 2 114328576
+--R 67248x - 17456x - ------ x - 9216x + 3328x + 2944x + 768x + ---------
+--R 5 1563705
+--R Type: Polynomial(Fraction(Integer))
+--E 17
+
+--S 18 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 262440 13 12 1966842 11 1290573 10 9 8
+--R - ------ x - 96957x - ------- x - ------- x + 38331x + 128412x
+--R 13 11 10
+--R +
+--R 7 6 159712 5 4 3 2
+--R 67248x - 17456x - ------ x - 9216x + 3328x + 2944x + 768x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 18
+
+--S 19 of 500
+m0:=a0-r0
+--R
+--R
+--R 114328576
+--R (4) - ---------
+--R 1563705
+--R Type: Polynomial(Fraction(Integer))
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(1-2*x)^3*(2+3*x)^7*(3+5*x)
+--R
+--R
+--R (1)
+--R 11 10 9 8 7 6
+--R - 87480x - 329508x - 435942x - 139563x + 208035x + 203742x
+--R +
+--R 5 4 3 2
+--R 21084x - 48968x - 20592x + 1440x + 2368x + 384
+--R Type: Polynomial(Integer)
+--E 21
+
+--S 22 of 500
+r0:=384*x+1184*x^2+480*x^3-5148*x^4-48968/5*x^5+3514*x^6+29106*x^7+_
+ 208035/8*x^8-15507*x^9-217971/5*x^10-329508/11*x^11-7290*x^12
+--R
+--R
+--R (2)
+--R 12 329508 11 217971 10 9 208035 8 7
+--R - 7290x - ------ x - ------ x - 15507x + ------ x + 29106x
+--R 11 5 8
+--R +
+--R 6 48968 5 4 3 2
+--R 3514x - ----- x - 5148x + 480x + 1184x + 384x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 22
+
+--S 23 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 329508 11 217971 10 9 208035 8 7
+--R - 7290x - ------ x - ------ x - 15507x + ------ x + 29106x
+--R 11 5 8
+--R +
+--R 6 48968 5 4 3 2
+--R 3514x - ----- x - 5148x + 480x + 1184x + 384x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 23
+
+--S 24 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(1-2*x)^3*(2+3*x)^6*(3+5*x)
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5 4
+--R - 29160x - 90396x - 85050x + 10179x + 62559x + 26208x - 10444x
+--R +
+--R 3 2
+--R - 9360x - 624x + 896x + 192
+--R Type: Polynomial(Integer)
+--E 26
+
+--S 27 of 500
+r0:=192*x+448*x^2-208*x^3-2340*x^4-10444/5*x^5+4368*x^6+8937*x^7+_
+ 10179/8*x^8-9450*x^9-45198/5*x^10-29160/11*x^11
+--R
+--R
+--R (2)
+--R 29160 11 45198 10 9 10179 8 7 6 10444 5
+--R - ----- x - ----- x - 9450x + ----- x + 8937x + 4368x - ----- x
+--R 11 5 8 5
+--R +
+--R 4 3 2
+--R - 2340x - 208x + 448x + 192x
+--R Type: Polynomial(Fraction(Integer))
+--E 27
+
+--S 28 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 29160 11 45198 10 9 10179 8 7 6 10444 5
+--R - ----- x - ----- x - 9450x + ----- x + 8937x + 4368x - ----- x
+--R 11 5 8 5
+--R +
+--R 4 3 2
+--R - 2340x - 208x + 448x + 192x
+--R Type: Polynomial(Fraction(Integer))
+--E 28
+
+--S 29 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(1-2*x)^3*(2+3*x)^5*(3+5*x)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3 2
+--R - 9720x - 23652x - 12582x + 11781x + 12999x + 70x - 3528x - 768x
+--R +
+--R 304x + 96
+--R Type: Polynomial(Integer)
+--E 31
+
+--S 32 of 500
+r0:=96*x+152*x^2-256*x^3-882*x^4+14*x^5+4333/2*x^6+1683*x^7-6291/4*x^8-_
+ 2628*x^9-972*x^10
+--R
+--R
+--R (2)
+--R 10 9 6291 8 7 4333 6 5 4 3
+--R - 972x - 2628x - ---- x + 1683x + ---- x + 14x - 882x - 256x
+--R 4 2
+--R +
+--R 2
+--R 152x + 96x
+--R Type: Polynomial(Fraction(Integer))
+--E 32
+
+--S 33 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 6291 8 7 4333 6 5 4 3
+--R - 972x - 2628x - ---- x + 1683x + ---- x + 14x - 882x - 256x
+--R 4 2
+--R +
+--R 2
+--R 152x + 96x
+--R Type: Polynomial(Fraction(Integer))
+--E 33
+
+--S 34 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(1-2*x)^3*(2+3*x)^4*(3+5*x)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 3240x - 5724x - 378x + 4179x + 1547x - 1008x - 504x + 80x + 48
+--R Type: Polynomial(Integer)
+--E 36
+
+--S 37 of 500
+r0:=48*x+40*x^2-168*x^3-252*x^4+1547/5*x^5+1393/2*x^6-54*x^7-1431/2*x^8-360*x^9
+--R
+--R
+--R (2)
+--R 9 1431 8 7 1393 6 1547 5 4 3 2
+--R - 360x - ---- x - 54x + ---- x + ---- x - 252x - 168x + 40x + 48x
+--R 2 2 5
+--R Type: Polynomial(Fraction(Integer))
+--E 37
+
+--S 38 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 1431 8 7 1393 6 1547 5 4 3 2
+--R - 360x - ---- x - 54x + ---- x + ---- x - 252x - 168x + 40x + 48x
+--R 2 2 5
+--R Type: Polynomial(Fraction(Integer))
+--E 38
+
+--S 39 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(1-2*x)^3*(2+3*x)^3*(3+5*x)
+--R
+--R
+--R 7 6 5 4 3 2
+--R (1) - 1080x - 1188x + 666x + 949x - 117x - 258x + 4x + 24
+--R Type: Polynomial(Integer)
+--E 41
+
+--S 42 of 500
+r0:=24*x+2*x^2-86*x^3-117/4*x^4+949/5*x^5+111*x^6-1188/7*x^7-135*x^8
+--R
+--R
+--R 8 1188 7 6 949 5 117 4 3 2
+--R (2) - 135x - ---- x + 111x + --- x - --- x - 86x + 2x + 24x
+--R 7 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 42
+
+--S 43 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 1188 7 6 949 5 117 4 3 2
+--R (3) - 135x - ---- x + 111x + --- x - --- x - 86x + 2x + 24x
+--R 7 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 43
+
+--S 44 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(1-2*x)^3*(2+3*x)^2*(3+5*x)
+--R
+--R
+--R 6 5 4 3 2
+--R (1) - 360x - 156x + 326x + 99x - 105x - 16x + 12
+--R Type: Polynomial(Integer)
+--E 46
+
+--S 47 of 500
+r0:=12*x-8*x^2-35*x^3+99/4*x^4+326/5*x^5-26*x^6-360/7*x^7
+--R
+--R
+--R 360 7 6 326 5 99 4 3 2
+--R (2) - --- x - 26x + --- x + -- x - 35x - 8x + 12x
+--R 7 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 47
+
+--S 48 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 360 7 6 326 5 99 4 3 2
+--R (3) - --- x - 26x + --- x + -- x - 35x - 8x + 12x
+--R 7 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 48
+
+--S 49 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(1-2*x)^3*(2+3*x)*(3+5*x)
+--R
+--R
+--R 5 4 3 2
+--R (1) - 120x + 28x + 90x - 27x - 17x + 6
+--R Type: Polynomial(Integer)
+--E 51
+
+--S 52 of 500
+r0:=6*x-17/2*x^2-9*x^3+45/2*x^4+28/5*x^5-20*x^6
+--R
+--R
+--R 6 28 5 45 4 3 17 2
+--R (2) - 20x + -- x + -- x - 9x - -- x + 6x
+--R 5 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 52
+
+--S 53 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 28 5 45 4 3 17 2
+--R (3) - 20x + -- x + -- x - 9x - -- x + 6x
+--R 5 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 53
+
+--S 54 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(1-2*x)^3*(3+5*x)
+--R
+--R
+--R 4 3 2
+--R (1) - 40x + 36x + 6x - 13x + 3
+--R Type: Polynomial(Integer)
+--E 56
+
+--S 57 of 500
+r0:=3*x-13/2*x^2+2*x^3+9*x^4-8*x^5
+--R
+--R
+--R 5 4 3 13 2
+--R (2) - 8x + 9x + 2x - -- x + 3x
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 57
+
+--S 58 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 13 2
+--R (3) - 8x + 9x + 2x - -- x + 3x
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 58
+
+--S 59 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(1-2*x)^3*(3+5*x)/(2+3*x)
+--R
+--R
+--R 4 3 2
+--R - 40x + 36x + 6x - 13x + 3
+--R (1) -----------------------------
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 61
+
+--S 62 of 500
+r0:=293/81*x-161/27*x^2+188/27*x^3-10/3*x^4-343/243*log(2+3*x)
+--R
+--R
+--R 4 3 2
+--R - 343log(3x + 2) - 810x + 1692x - 1449x + 879x
+--R (2) -------------------------------------------------
+--R 243
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R - 343log(3x + 2) - 810x + 1692x - 1449x + 879x
+--R (3) -------------------------------------------------
+--R 243
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^2
+--R
+--R
+--R 4 3 2
+--R - 40x + 36x + 6x - 13x + 3
+--R (1) -----------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 66
+
+--S 67 of 500
+r0:=-286/27*x+134/27*x^2-40/27*x^3+343/243/(2+3*x)+2009/243*log(2+3*x)
+--R
+--R
+--R 4 3 2
+--R (6027x + 4018)log(3x + 2) - 1080x + 2898x - 5310x - 5148x + 343
+--R (2) ------------------------------------------------------------------
+--R 729x + 486
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R (6027x + 4018)log(3x + 2) - 1080x + 2898x - 5310x - 5148x + 343
+--R (3) ------------------------------------------------------------------
+--R 729x + 486
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^3
+--R
+--R
+--R 4 3 2
+--R - 40x + 36x + 6x - 13x + 3
+--R (1) -----------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 71
+
+--S 72 of 500
+r0:=116/27*x-20/27*x^2+343/486/(2+3*x)^2+(-2009/243)/(2+3*x)-518/81*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2
+--R (- 27972x - 37296x - 12432)log(3x + 2) - 3240x + 14472x + 23616x
+--R +
+--R - 3702x - 7693
+--R /
+--R 2
+--R 4374x + 5832x + 1944
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2
+--R (- 27972x - 37296x - 12432)log(3x + 2) - 3240x + 14472x + 23616x
+--R +
+--R - 3702x - 7693
+--R /
+--R 2
+--R 4374x + 5832x + 1944
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^4
+--R
+--R
+--R 4 3 2
+--R - 40x + 36x + 6x - 13x + 3
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 76
+
+--S 77 of 500
+r0:=-40/81*x+343/729/(2+3*x)^3+(-2009/486)/(2+3*x)^2+518/81/(2+3*x)+_
+ 428/243*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 4 3
+--R (69336x + 138672x + 92448x + 20544)log(3x + 2) - 19440x - 38880x
+--R +
+--R 2
+--R 57996x + 88047x + 25928
+--R /
+--R 3 2
+--R 39366x + 78732x + 52488x + 11664
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 3
+--R (69336x + 138672x + 92448x + 20544)log(3x + 2) - 19440x - 38880x
+--R +
+--R 2
+--R 57996x + 88047x + 25928
+--R /
+--R 3 2
+--R 39366x + 78732x + 52488x + 11664
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^5
+--R
+--R
+--R 4 3 2
+--R - 40x + 36x + 6x - 13x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 81
+
+--S 82 of 500
+r0:=343/972/(2+3*x)^4+(-2009/729)/(2+3*x)^3+259/81/(2+3*x)^2+_
+ (-428/243)/(2+3*x)-40/243*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 3
+--R (- 38880x - 103680x - 103680x - 46080x - 7680)log(3x + 2) - 138672x
+--R +
+--R 2
+--R - 193428x - 97116x - 18835
+--R /
+--R 4 3 2
+--R 236196x + 629856x + 629856x + 279936x + 46656
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 3
+--R (- 38880x - 103680x - 103680x - 46080x - 7680)log(3x + 2) - 138672x
+--R +
+--R 2
+--R - 193428x - 97116x - 18835
+--R /
+--R 4 3 2
+--R 236196x + 629856x + 629856x + 279936x + 46656
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^6
+--R
+--R
+--R 4 3 2
+--R - 40x + 36x + 6x - 13x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 86
+
+--S 87 of 500
+r0:=1/105*(1-2*x)^4/(2+3*x)^5-173/2940*(1-2*x)^4/(2+3*x)^4
+--R
+--R
+--R 692 5 64 4 38 3 58 2 5 53
+--R - ----- x + ---- x - ----- x - ----- x + ---- x - ------
+--R 59535 3969 11907 11907 1764 119070
+--R (2) ------------------------------------------------------------
+--R 5 10 4 40 3 80 2 80 32
+--R x + -- x + -- x + -- x + -- x + ---
+--R 3 9 27 81 243
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 87
+
+--S 88 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R 64800x + 57240x + 34920x + 16905x + 1282
+--R (3) -----------------------------------------------------------------
+--R 5 4 3 2
+--R 1180980x + 3936600x + 5248800x + 3499200x + 1166400x + 155520
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500
+m0:=a0-r0
+--R
+--R
+--R 692
+--R (4) -----
+--R 59535
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^7
+--R
+--R
+--R 4 3 2
+--R - 40x + 36x + 6x - 13x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 91
+
+--S 92 of 500
+r0:=1/126*(1-2*x)^4/(2+3*x)^6-103/2205*(1-2*x)^4/(2+3*x)^5-_
+ 103/30870*(1-2*x)^4/(2+3*x)^4
+--R
+--R
+--R (2)
+--R 824 6 3296 5 44 4 316 3 659 2 349
+--R - ------- x - ------- x + ---- x - ------ x - ------ x + ------ x
+--R 1250235 1250235 9261 250047 500094 416745
+--R +
+--R 113
+--R - ------
+--R 833490
+--R /
+--R 6 5 20 4 160 3 80 2 64 64
+--R x + 4x + -- x + --- x + -- x + -- x + ---
+--R 3 27 27 81 729
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 92
+
+--S 93 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 48600x + 14040x + 3375x + 7218x - 413
+--R /
+--R 6 5 4 3 2
+--R 5314410x + 21257640x + 35429400x + 31492800x + 15746400x + 4199040x
+--R +
+--R 466560
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500
+m0:=a0-r0
+--R
+--R
+--R 824
+--R (4) -------
+--R 1250235
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 4 3 2
+--R - 40x + 36x + 6x - 13x + 3
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 96
+
+--S 97 of 500
+r0:=49/243/(2+3*x)^7+(-2009/1458)/(2+3*x)^6+518/405/(2+3*x)^5+_
+ (-107/243)/(2+3*x)^4+40/729/(2+3*x)^3
+--R
+--R
+--R 40 4 1 3 56 2 1531 302
+--R ----- x - ----- x - ------ x + ------- x - -------
+--R 19683 59049 295245 5314410 7971615
+--R (2) ------------------------------------------------------------
+--R 7 14 6 28 5 280 4 560 3 224 2 448 128
+--R x + -- x + -- x + --- x + --- x + --- x + --- x + ----
+--R 3 3 27 81 81 729 2187
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 97
+
+--S 98 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 32400x - 270x - 3024x + 4593x - 604
+--R /
+--R 7 6 5 4 3
+--R 15943230x + 74401740x + 148803480x + 165337200x + 110224800x
+--R +
+--R 2
+--R 44089920x + 9797760x + 933120
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(1-2*x)^3*(2+3*x)^8*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 13 12 11 10 9
+--R - 1312200x - 6604740x - 13324662x - 12353391x - 2146824x
+--R +
+--R 8 7 6 5 4 3 2
+--R 6171417x + 5435568x + 888528x - 1112768x - 663456x - 60672x + 59392x
+--R +
+--R 21504x + 2304
+--R Type: Polynomial(Integer)
+--E 101
+
+--S 102 of 500
+r0:=2304*x+10752*x^2+59392/3*x^3-15168*x^4-663456/5*x^5-556384/3*x^6+_
+ 888528/7*x^7+679446*x^8+685713*x^9-1073412/5*x^10-_
+ 12353391/11*x^11-2220777/2*x^12-6604740/13*x^13-656100/7*x^14
+--R
+--R
+--R (2)
+--R 656100 14 6604740 13 2220777 12 12353391 11 1073412 10
+--R - ------ x - ------- x - ------- x - -------- x - ------- x
+--R 7 13 2 11 5
+--R +
+--R 9 8 888528 7 556384 6 663456 5 4
+--R 685713x + 679446x + ------ x - ------ x - ------ x - 15168x
+--R 7 3 5
+--R +
+--R 59392 3 2
+--R ----- x + 10752x + 2304x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 102
+
+--S 103 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 656100 14 6604740 13 2220777 12 12353391 11 1073412 10
+--R - ------ x - ------- x - ------- x - -------- x - ------- x
+--R 7 13 2 11 5
+--R +
+--R 9 8 888528 7 556384 6 663456 5 4
+--R 685713x + 679446x + ------ x - ------ x - ------ x - 15168x
+--R 7 3 5
+--R +
+--R 59392 3 2
+--R ----- x + 10752x + 2304x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 103
+
+--S 104 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(1-2*x)^3*(2+3*x)^7*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 12 11 10 9 8 7
+--R - 437400x - 1909980x - 3168234x - 2005641x + 621486x + 1642815x
+--R +
+--R 6 5 4 3 2
+--R 716646x - 181588x - 249864x - 54576x + 16160x + 9024x + 1152
+--R Type: Polynomial(Integer)
+--E 106
+
+--S 107 of 500
+r0:=1152*x+4512*x^2+16160/3*x^3-13644*x^4-249864/5*x^5-90794/3*x^6+_
+ 102378*x^7+1642815/8*x^8+69054*x^9-2005641/10*x^10-3168234/11*x^11-_
+ 159165*x^12-437400/13*x^13
+--R
+--R
+--R (2)
+--R 437400 13 12 3168234 11 2005641 10 9 1642815 8
+--R - ------ x - 159165x - ------- x - ------- x + 69054x + ------- x
+--R 13 11 10 8
+--R +
+--R 7 90794 6 249864 5 4 16160 3 2
+--R 102378x - ----- x - ------ x - 13644x + ----- x + 4512x + 1152x
+--R 3 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 107
+
+--S 108 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 437400 13 12 3168234 11 2005641 10 9 1642815 8
+--R - ------ x - 159165x - ------- x - ------- x + 69054x + ------- x
+--R 13 11 10 8
+--R +
+--R 7 90794 6 249864 5 4 16160 3 2
+--R 102378x - ----- x - ------ x - 13644x + ----- x + 4512x + 1152x
+--R 3 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 108
+
+--S 109 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(1-2*x)^3*(2+3*x)^6*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 11 10 9 8 7 6
+--R - 145800x - 539460x - 696438x - 204255x + 343332x + 318717x
+--R +
+--R 5 4 3 2
+--R 26404x - 78132x - 31200x + 2608x + 3648x + 576
+--R Type: Polynomial(Integer)
+--E 111
+
+--S 112 of 500
+r0:=576*x+1824*x^2+2608/3*x^3-7800*x^4-78132/5*x^5+13202/3*x^6+45531*x^7+_
+ 85833/2*x^8-22695*x^9-348219/5*x^10-539460/11*x^11-12150*x^12
+--R
+--R
+--R (2)
+--R 12 539460 11 348219 10 9 85833 8 7
+--R - 12150x - ------ x - ------ x - 22695x + ----- x + 45531x
+--R 11 5 2
+--R +
+--R 13202 6 78132 5 4 2608 3 2
+--R ----- x - ----- x - 7800x + ---- x + 1824x + 576x
+--R 3 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 112
+
+--S 113 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 539460 11 348219 10 9 85833 8 7
+--R - 12150x - ------ x - ------ x - 22695x + ----- x + 45531x
+--R 11 5 2
+--R +
+--R 13202 6 78132 5 4 2608 3 2
+--R ----- x - ----- x - 7800x + ---- x + 1824x + 576x
+--R 3 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 113
+
+--S 114 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(1-2*x)^3*(2+3*x)^5*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5 4
+--R - 48600x - 147420x - 133866x + 21159x + 100338x + 39347x - 17430x
+--R +
+--R 3 2
+--R - 14424x - 784x + 1392x + 288
+--R Type: Polynomial(Integer)
+--E 116
+
+--S 117 of 500
+r0:=288*x+696*x^2-784/3*x^3-3606*x^4-3486*x^5+39347/6*x^6+14334*x^7+_
+ 21159/8*x^8-14874*x^9-14742*x^10-48600/11*x^11
+--R
+--R
+--R (2)
+--R 48600 11 10 9 21159 8 7 39347 6 5
+--R - ----- x - 14742x - 14874x + ----- x + 14334x + ----- x - 3486x
+--R 11 8 6
+--R +
+--R 4 784 3 2
+--R - 3606x - --- x + 696x + 288x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 117
+
+--S 118 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 48600 11 10 9 21159 8 7 39347 6 5
+--R - ----- x - 14742x - 14874x + ----- x + 14334x + ----- x - 3486x
+--R 11 8 6
+--R +
+--R 4 784 3 2
+--R - 3606x - --- x + 696x + 288x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 118
+
+--S 119 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(1-2*x)^3*(2+3*x)^4*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3 2
+--R - 16200x - 38340x - 19062x + 19761x + 20272x - 399x - 5544x - 1112x
+--R +
+--R 480x + 144
+--R Type: Polynomial(Integer)
+--E 121
+
+--S 122 of 500
+r0:=144*x+240*x^2-1112/3*x^3-1386*x^4-399/5*x^5+10136/3*x^6+2823*x^7-_
+ 9531/4*x^8-4260*x^9-1620*x^10
+--R
+--R
+--R (2)
+--R 10 9 9531 8 7 10136 6 399 5 4
+--R - 1620x - 4260x - ---- x + 2823x + ----- x - --- x - 1386x
+--R 4 3 5
+--R +
+--R 1112 3 2
+--R - ---- x + 240x + 144x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 122
+
+--S 123 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 9531 8 7 10136 6 399 5 4
+--R - 1620x - 4260x - ---- x + 2823x + ----- x - --- x - 1386x
+--R 4 3 5
+--R +
+--R 1112 3 2
+--R - ---- x + 240x + 144x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 123
+
+--S 124 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(1-2*x)^3*(2+3*x)^3*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 5400x - 9180x - 234x + 6743x + 2262x - 1641x - 754x + 132x + 72
+--R Type: Polynomial(Integer)
+--E 126
+
+--S 127 of 500
+r0:=72*x+66*x^2-754/3*x^3-1641/4*x^4+2262/5*x^5+6743/6*x^6-234/7*x^7-_
+ 2295/2*x^8-600*x^9
+--R
+--R
+--R (2)
+--R 9 2295 8 234 7 6743 6 2262 5 1641 4 754 3 2
+--R - 600x - ---- x - --- x + ---- x + ---- x - ---- x - --- x + 66x
+--R 2 7 6 5 4 3
+--R +
+--R 72x
+--R Type: Polynomial(Fraction(Integer))
+--E 127
+
+--S 128 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 2295 8 234 7 6743 6 2262 5 1641 4 754 3 2
+--R - 600x - ---- x - --- x + ---- x + ---- x - ---- x - --- x + 66x
+--R 2 7 6 5 4 3
+--R +
+--R 72x
+--R Type: Polynomial(Fraction(Integer))
+--E 128
+
+--S 129 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(1-2*x)^3*(2+3*x)^2*(3+5*x)^2
+--R
+--R
+--R 7 6 5 4 3 2
+--R (1) - 1800x - 1860x + 1162x + 1473x - 228x - 395x + 12x + 36
+--R Type: Polynomial(Integer)
+--E 131
+
+--S 132 of 500
+r0:=36*x+6*x^2-395/3*x^3-57*x^4+1473/5*x^5+581/3*x^6-1860/7*x^7-225*x^8
+--R
+--R
+--R 8 1860 7 581 6 1473 5 4 395 3 2
+--R (2) - 225x - ---- x + --- x + ---- x - 57x - --- x + 6x + 36x
+--R 7 3 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 132
+
+--S 133 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 1860 7 581 6 1473 5 4 395 3 2
+--R (3) - 225x - ---- x + --- x + ---- x - 57x - --- x + 6x + 36x
+--R 7 3 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 133
+
+--S 134 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(1-2*x)^3*(2+3*x)*(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R (1) - 600x - 220x + 534x + 135x - 166x - 21x + 18
+--R Type: Polynomial(Integer)
+--E 136
+
+--S 137 of 500
+r0:=18*x-21/2*x^2-166/3*x^3+135/4*x^4+534/5*x^5-110/3*x^6-600/7*x^7
+--R
+--R
+--R 600 7 110 6 534 5 135 4 166 3 21 2
+--R (2) - --- x - --- x + --- x + --- x - --- x - -- x + 18x
+--R 7 3 5 4 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 137
+
+--S 138 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 600 7 110 6 534 5 135 4 166 3 21 2
+--R (3) - --- x - --- x + --- x + --- x - --- x - -- x + 18x
+--R 7 3 5 4 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 138
+
+--S 139 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(1-2*x)^3*(3+5*x)^2
+--R
+--R
+--R 5 4 3 2
+--R (1) - 200x + 60x + 138x - 47x - 24x + 9
+--R Type: Polynomial(Integer)
+--E 141
+
+--S 142 of 500
+r0:=9*x-12*x^2-47/3*x^3+69/2*x^4+12*x^5-100/3*x^6
+--R
+--R
+--R 100 6 5 69 4 47 3 2
+--R (2) - --- x + 12x + -- x - -- x - 12x + 9x
+--R 3 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 142
+
+--S 143 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 100 6 5 69 4 47 3 2
+--R (3) - --- x + 12x + -- x - -- x - 12x + 9x
+--R 3 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 143
+
+--S 144 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)
+--R
+--R
+--R 5 4 3 2
+--R - 200x + 60x + 138x - 47x - 24x + 9
+--R (1) ---------------------------------------
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 500
+r0:=922/243*x-1433/162*x^2+82/81*x^3+145/9*x^4-40/3*x^5+343/729*log(2+3*x)
+--R
+--R
+--R 5 4 3 2
+--R 686log(3x + 2) - 19440x + 23490x + 1476x - 12897x + 5532x
+--R (2) -------------------------------------------------------------
+--R 1458
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R 686log(3x + 2) - 19440x + 23490x + 1476x - 12897x + 5532x
+--R (3) -------------------------------------------------------------
+--R 1458
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^2
+--R
+--R
+--R 5 4 3 2
+--R - 200x + 60x + 138x - 47x - 24x + 9
+--R (1) ---------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 151
+
+--S 152 of 500
+r0:=2323/243*x-313/27*x^2+980/81*x^3-50/9*x^4+(-343/729)/(2+3*x)-_
+ 3724/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (- 11172x - 7448)log(3x + 2) - 12150x + 18360x - 7713x + 4005x
+--R +
+--R 13938x - 343
+--R /
+--R 2187x + 1458
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (- 11172x - 7448)log(3x + 2) - 12150x + 18360x - 7713x + 4005x
+--R +
+--R 13938x - 343
+--R /
+--R 2187x + 1458
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^3
+--R
+--R
+--R 5 4 3 2
+--R - 200x + 60x + 138x - 47x - 24x + 9
+--R (1) ---------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 500
+r0:=-1546/81*x+230/27*x^2-200/81*x^3+(-343/1458)/(2+3*x)^2+3724/729/(2+3*x)+_
+ 11599/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 5 4 3
+--R (208782x + 278376x + 92792)log(3x + 2) - 32400x + 68580x - 115812x
+--R +
+--R 2
+--R - 284256x - 88968x + 14553
+--R /
+--R 2
+--R 13122x + 17496x + 5832
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4 3
+--R (208782x + 278376x + 92792)log(3x + 2) - 32400x + 68580x - 115812x
+--R +
+--R 2
+--R - 284256x - 88968x + 14553
+--R /
+--R 2
+--R 13122x + 17496x + 5832
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^4
+--R
+--R
+--R 5 4 3 2
+--R - 200x + 60x + 138x - 47x - 24x + 9
+--R (1) ---------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 500
+r0:=1780/243*x-100/81*x^2+(-343/2187)/(2+3*x)^3+1862/729/(2+3*x)^2+_
+ (-11599/729)/(2+3*x)-8198/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 5
+--R (- 664038x - 1328076x - 885384x - 196752)log(3x + 2) - 72900x
+--R +
+--R 4 3 2
+--R 286740x + 767880x + 241947x - 272646x - 128359
+--R /
+--R 3 2
+--R 59049x + 118098x + 78732x + 17496
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 5
+--R (- 664038x - 1328076x - 885384x - 196752)log(3x + 2) - 72900x
+--R +
+--R 4 3 2
+--R 286740x + 767880x + 241947x - 272646x - 128359
+--R /
+--R 3 2
+--R 59049x + 118098x + 78732x + 17496
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^5
+--R
+--R
+--R 5 4 3 2
+--R - 200x + 60x + 138x - 47x - 24x + 9
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 166
+
+--S 167 of 500
+r0:=-200/243*x+(-343/2916)/(2+3*x)^4+3724/2187/(2+3*x)^3+_
+ (-11599/1458)/(2+3*x)^2+8198/729/(2+3*x)+2180/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (2118960x + 5650560x + 5650560x + 2511360x + 418560)log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 583200x - 1555200x + 1100952x + 3994758x + 2635896x + 537395
+--R /
+--R 4 3 2
+--R 708588x + 1889568x + 1889568x + 839808x + 139968
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (2118960x + 5650560x + 5650560x + 2511360x + 418560)log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 583200x - 1555200x + 1100952x + 3994758x + 2635896x + 537395
+--R /
+--R 4 3 2
+--R 708588x + 1889568x + 1889568x + 839808x + 139968
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^6
+--R
+--R
+--R 5 4 3 2
+--R - 200x + 60x + 138x - 47x - 24x + 9
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 171
+
+--S 172 of 500
+r0:=(-343/3645)/(2+3*x)^5+931/729/(2+3*x)^4+(-11599/2187)/(2+3*x)^3+_
+ 4099/729/(2+3*x)^2+(-2180/729)/(2+3*x)-200/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (- 729000x - 2430000x - 3240000x - 2160000x - 720000x - 96000)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R - 2648700x - 5403105x - 4264965x - 1579785x - 236399
+--R /
+--R 5 4 3 2
+--R 2657205x + 8857350x + 11809800x + 7873200x + 2624400x + 349920
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (- 729000x - 2430000x - 3240000x - 2160000x - 720000x - 96000)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R - 2648700x - 5403105x - 4264965x - 1579785x - 236399
+--R /
+--R 5 4 3 2
+--R 2657205x + 8857350x + 11809800x + 7873200x + 2624400x + 349920
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^7
+--R
+--R
+--R 5 4 3 2
+--R - 200x + 60x + 138x - 47x - 24x + 9
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 176
+
+--S 177 of 500
+r0:=(-343/4374)/(2+3*x)^6+3724/3645/(2+3*x)^5+(-11599/2916)/(2+3*x)^4+_
+ 8198/2187/(2+3*x)^3+(-1090/729)/(2+3*x)^2+200/729/(2+3*x)
+--R
+--R
+--R 200 5 910 4 6038 3 13345 2 15289 19643
+--R ---- x + ---- x + ----- x + ------ x + ------ x + --------
+--R 2187 6561 59049 236196 885735 15943230
+--R (2) --------------------------------------------------------------
+--R 6 5 20 4 160 3 80 2 64 64
+--R x + 4x + -- x + --- x + -- x + -- x + ---
+--R 3 27 27 81 729
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 177
+
+--S 178 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 2916000x + 4422600x + 3260520x + 1801575x + 550404x + 39286
+--R /
+--R 6 5 4 3 2
+--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x
+--R +
+--R 25194240x + 2799360
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 5 4 3 2
+--R - 200x + 60x + 138x - 47x - 24x + 9
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 500
+r0:=(-49/729)/(2+3*x)^7+1862/2187/(2+3*x)^6+(-11599/3645)/(2+3*x)^5+_
+ 4099/1458/(2+3*x)^4+(-2180/2187)/(2+3*x)^3+100/729/(2+3*x)^2
+--R
+--R
+--R 100 5 820 4 1417 3 2686 2 10232 1763
+--R ---- x + ----- x + ------ x + ------ x + ------- x - --------
+--R 6561 59049 354294 885735 7971615 23914845
+--R (2) -----------------------------------------------------------------
+--R 7 14 6 28 5 280 4 560 3 224 2 448 128
+--R x + -- x + -- x + --- x + --- x + --- x + --- x + ----
+--R 3 3 27 81 81 729 2187
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 182
+
+--S 183 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 729000x + 664200x + 191295x + 145044x + 61392x - 3526
+--R /
+--R 7 6 5 4 3
+--R 47829690x + 223205220x + 446410440x + 496011600x + 330674400x
+--R +
+--R 2
+--R 132269760x + 29393280x + 2799360
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(1-2*x)^3*(2+3*x)^7*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 13 12 11 10 9
+--R - 2187000x - 10862100x - 21571110x - 19532907x - 2909493x
+--R +
+--R 8 7 6 5 4 3
+--R 10078533x + 8511675x + 1241998x - 1794084x - 1022472x - 82928x
+--R +
+--R 2
+--R 93600x + 32832x + 3456
+--R Type: Polynomial(Integer)
+--E 186
+
+--S 187 of 500
+r0:=3456*x+16416*x^2+31200*x^3-20732*x^4-1022472/5*x^5-299014*x^6+_
+ 1241998/7*x^7+8511675/8*x^8+1119837*x^9-2909493/10*x^10-_
+ 19532907/11*x^11-3595185/2*x^12-10862100/13*x^13-1093500/7*x^14
+--R
+--R
+--R (2)
+--R 1093500 14 10862100 13 3595185 12 19532907 11 2909493 10
+--R - ------- x - -------- x - ------- x - -------- x - ------- x
+--R 7 13 2 11 10
+--R +
+--R 9 8511675 8 1241998 7 6 1022472 5 4
+--R 1119837x + ------- x + ------- x - 299014x - ------- x - 20732x
+--R 8 7 5
+--R +
+--R 3 2
+--R 31200x + 16416x + 3456x
+--R Type: Polynomial(Fraction(Integer))
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1093500 14 10862100 13 3595185 12 19532907 11 2909493 10
+--R - ------- x - -------- x - ------- x - -------- x - ------- x
+--R 7 13 2 11 10
+--R +
+--R 9 8511675 8 1241998 7 6 1022472 5 4
+--R 1119837x + ------- x + ------- x - 299014x - ------- x - 20732x
+--R 8 7 5
+--R +
+--R 3 2
+--R 31200x + 16416x + 3456x
+--R Type: Polynomial(Fraction(Integer))
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(1-2*x)^3*(2+3*x)^6*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 12 11 10 9 8 7
+--R - 729000x - 3134700x - 5100570x - 3110589x + 1103895x + 2623581x
+--R +
+--R 6 5 4 3 2
+--R 1088171x - 311448x - 390396x - 80560x + 26064x + 13824x + 1728
+--R Type: Polynomial(Integer)
+--E 191
+
+--S 192 of 500
+r0:=1728*x+6912*x^2+8688*x^3-20140*x^4-390396/5*x^5-51908*x^6+_
+ 155453*x^7+2623581/8*x^8+122655*x^9-3110589/10*x^10-5100570/11*x^11-_
+ 261225*x^12-729000/13*x^13
+--R
+--R
+--R (2)
+--R 729000 13 12 5100570 11 3110589 10 9
+--R - ------ x - 261225x - ------- x - ------- x + 122655x
+--R 13 11 10
+--R +
+--R 2623581 8 7 6 390396 5 4 3 2
+--R ------- x + 155453x - 51908x - ------ x - 20140x + 8688x + 6912x
+--R 8 5
+--R +
+--R 1728x
+--R Type: Polynomial(Fraction(Integer))
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 729000 13 12 5100570 11 3110589 10 9
+--R - ------ x - 261225x - ------- x - ------- x + 122655x
+--R 13 11 10
+--R +
+--R 2623581 8 7 6 390396 5 4 3 2
+--R ------- x + 155453x - 51908x - ------ x - 20140x + 8688x + 6912x
+--R 8 5
+--R +
+--R 1728x
+--R Type: Polynomial(Fraction(Integer))
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(1-2*x)^3*(2+3*x)^5*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 11 10 9 8 7 6
+--R - 243000x - 882900x - 1111590x - 295803x + 565167x + 497749x
+--R +
+--R 5 4 3 2
+--R 30891x - 124410x - 47192x + 4608x + 5616x + 864
+--R Type: Polynomial(Integer)
+--E 196
+
+--S 197 of 500
+r0:=864*x+2808*x^2+1536*x^3-11798*x^4-24882*x^5+10297/2*x^6+_
+ 71107*x^7+565167/8*x^8-32867*x^9-111159*x^10-882900/11*x^11-20250*x^12
+--R
+--R
+--R (2)
+--R 12 882900 11 10 9 565167 8 7
+--R - 20250x - ------ x - 111159x - 32867x + ------ x + 71107x
+--R 11 8
+--R +
+--R 10297 6 5 4 3 2
+--R ----- x - 24882x - 11798x + 1536x + 2808x + 864x
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 882900 11 10 9 565167 8 7
+--R - 20250x - ------ x - 111159x - 32867x + ------ x + 71107x
+--R 11 8
+--R +
+--R 10297 6 5 4 3 2
+--R ----- x - 24882x - 11798x + 1536x + 2808x + 864x
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(1-2*x)^3*(2+3*x)^4*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5 4
+--R - 81000x - 240300x - 210330x + 41619x + 160643x + 58821x - 28917x
+--R +
+--R 3 2
+--R - 22192x - 936x + 2160x + 432
+--R Type: Polynomial(Integer)
+--E 201
+
+--S 202 of 500
+r0:=432*x+1080*x^2-312*x^3-5548*x^4-28917/5*x^5+19607/2*x^6+22949*x^7+_
+ 41619/8*x^8-23370*x^9-24030*x^10-81000/11*x^11
+--R
+--R
+--R (2)
+--R 81000 11 10 9 41619 8 7 19607 6 28917 5
+--R - ----- x - 24030x - 23370x + ----- x + 22949x + ----- x - ----- x
+--R 11 8 2 5
+--R +
+--R 4 3 2
+--R - 5548x - 312x + 1080x + 432x
+--R Type: Polynomial(Fraction(Integer))
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 81000 11 10 9 41619 8 7 19607 6 28917 5
+--R - ----- x - 24030x - 23370x + ----- x + 22949x + ----- x - ----- x
+--R 11 8 2 5
+--R +
+--R 4 3 2
+--R - 5548x - 312x + 1080x + 432x
+--R Type: Polynomial(Fraction(Integer))
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(1-2*x)^3*(2+3*x)^3*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3
+--R - 27000x - 62100x - 28710x + 33013x + 31539x - 1419x - 8693x
+--R +
+--R 2
+--R - 1602x + 756x + 216
+--R Type: Polynomial(Integer)
+--E 206
+
+--S 207 of 500
+r0:=216*x+378*x^2-534*x^3-8693/4*x^4-1419/5*x^5+10513/2*x^6+33013/7*x^7-_
+ 14355/4*x^8-6900*x^9-2700*x^10
+--R
+--R
+--R (2)
+--R 10 9 14355 8 33013 7 10513 6 1419 5 8693 4
+--R - 2700x - 6900x - ----- x + ----- x + ----- x - ---- x - ---- x
+--R 4 7 2 5 4
+--R +
+--R 3 2
+--R - 534x + 378x + 216x
+--R Type: Polynomial(Fraction(Integer))
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 14355 8 33013 7 10513 6 1419 5 8693 4
+--R - 2700x - 6900x - ----- x + ----- x + ----- x - ---- x - ---- x
+--R 4 7 2 5 4
+--R +
+--R 3 2
+--R - 534x + 378x + 216x
+--R Type: Polynomial(Fraction(Integer))
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(1-2*x)^3*(2+3*x)^2*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 9000x - 14700x + 230x + 10851x + 3279x - 2659x - 1125x + 216x + 108
+--R Type: Polynomial(Integer)
+--E 211
+
+--S 212 of 500
+r0:=108*x+108*x^2-375*x^3-2659/4*x^4+3279/5*x^5+3617/2*x^6+230/7*x^7-_
+ 3675/2*x^8-1000*x^9
+--R
+--R
+--R (2)
+--R 9 3675 8 230 7 3617 6 3279 5 2659 4 3 2
+--R - 1000x - ---- x + --- x + ---- x + ---- x - ---- x - 375x + 108x
+--R 2 7 2 5 4
+--R +
+--R 108x
+--R Type: Polynomial(Fraction(Integer))
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 3675 8 230 7 3617 6 3279 5 2659 4 3 2
+--R - 1000x - ---- x + --- x + ---- x + ---- x - ---- x - 375x + 108x
+--R 2 7 2 5 4
+--R +
+--R 108x
+--R Type: Polynomial(Fraction(Integer))
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(1-2*x)^3*(2+3*x)*(3+5*x)^3
+--R
+--R
+--R 7 6 5 4 3 2
+--R (1) - 3000x - 2900x + 2010x + 2277x - 425x - 603x + 27x + 54
+--R Type: Polynomial(Integer)
+--E 216
+
+--S 217 of 500
+r0:=54*x+27/2*x^2-201*x^3-425/4*x^4+2277/5*x^5+335*x^6-2900/7*x^7-375*x^8
+--R
+--R
+--R 8 2900 7 6 2277 5 425 4 3 27 2
+--R (2) - 375x - ---- x + 335x + ---- x - --- x - 201x + -- x + 54x
+--R 7 5 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 2900 7 6 2277 5 425 4 3 27 2
+--R (3) - 375x - ---- x + 335x + ---- x - --- x - 201x + -- x + 54x
+--R 7 5 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(1-2*x)^3*(3+5*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R (1) - 1000x - 300x + 870x + 179x - 261x - 27x + 27
+--R Type: Polynomial(Integer)
+--E 221
+
+--S 222 of 500
+r0:=27*x-27/2*x^2-87*x^3+179/4*x^4+174*x^5-50*x^6-1000/7*x^7
+--R
+--R
+--R 1000 7 6 5 179 4 3 27 2
+--R (2) - ---- x - 50x + 174x + --- x - 87x - -- x + 27x
+--R 7 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 222
+
+--S 223 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 1000 7 6 5 179 4 3 27 2
+--R (3) - ---- x - 50x + 174x + --- x - 87x - -- x + 27x
+--R 7 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 223
+
+--S 224 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)
+--R
+--R
+--R 6 5 4 3 2
+--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27
+--R (1) ---------------------------------------------------
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 226
+
+--S 227 of 500
+r0:=10013/729*x-8287/486*x^2-6427/243*x^3+2815/54*x^4+220/9*x^5-500/9*x^6-_
+ 343/2187*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 686log(3x + 2) - 243000x + 106920x + 228015x - 115686x - 74583x
+--R +
+--R 60078x
+--R /
+--R 4374
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 686log(3x + 2) - 243000x + 106920x + 228015x - 115686x - 74583x
+--R +
+--R 60078x
+--R /
+--R 4374
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27
+--R (1) ---------------------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 500
+r0:=2287/729*x-5287/486*x^2-190/81*x^3+775/27*x^4-200/9*x^5+343/2187/(2+3*x)+_
+ 1813/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R (32634x + 21756)log(3x + 2) - 291600x + 182250x + 220320x - 163269x
+--R +
+--R 2
+--R - 54000x + 27444x + 686
+--R /
+--R 13122x + 8748
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R (32634x + 21756)log(3x + 2) - 291600x + 182250x + 220320x - 163269x
+--R +
+--R 2
+--R - 54000x + 27444x + 686
+--R /
+--R 13122x + 8748
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27
+--R (1) ---------------------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 500
+r0:=16253/729*x-1795/81*x^2+1700/81*x^3-250/27*x^4+343/4374/(2+3*x)^2+_
+ (-1813/729)/(2+3*x)-10073/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 6 5
+--R (- 543942x - 725256x - 241752)log(3x + 2) - 364500x + 340200x
+--R +
+--R 4 3 2
+--R 67230x + 81702x + 782496x + 357438x - 21413
+--R /
+--R 2
+--R 39366x + 52488x + 17496
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 5
+--R (- 543942x - 725256x - 241752)log(3x + 2) - 364500x + 340200x
+--R +
+--R 4 3 2
+--R 67230x + 81702x + 782496x + 357438x - 21413
+--R /
+--R 2
+--R 39366x + 52488x + 17496
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^4
+--R
+--R
+--R 6 5 4 3 2
+--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27
+--R (1) ---------------------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 500
+r0:=-24970/729*x+3550/243*x^2-1000/243*x^3+343/6561/(2+3*x)^3+_
+ (-1813/1458)/(2+3*x)^2+10073/729/(2+3*x)+66193/2187*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 6
+--R (10723266x + 21446532x + 14297688x + 3177264)log(3x + 2) - 1458000x
+--R +
+--R 5 4 3 2
+--R 2259900x - 3727620x - 17801640x - 13015134x - 1468863x + 693308
+--R /
+--R 3 2
+--R 354294x + 708588x + 472392x + 104976
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 6
+--R (10723266x + 21446532x + 14297688x + 3177264)log(3x + 2) - 1458000x
+--R +
+--R 5 4 3 2
+--R 2259900x - 3727620x - 17801640x - 13015134x - 1468863x + 693308
+--R /
+--R 3 2
+--R 354294x + 708588x + 472392x + 104976
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^5
+--R
+--R
+--R 6 5 4 3 2
+--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27
+--R (1) ---------------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 500
+r0:=9100/729*x-500/243*x^2+343/8748/(2+3*x)^4+(-1813/2187)/(2+3*x)^3+_
+ 10073/1458/(2+3*x)^2+(-66193/2187)/(2+3*x)-14390/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 4662360x - 12432960x - 12432960x - 5525760x - 920960)log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 486000x + 1652400x + 6566400x + 4903452x - 1186182x - 2360364x
+--R +
+--R - 630195
+--R /
+--R 4 3 2
+--R 236196x + 629856x + 629856x + 279936x + 46656
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 4662360x - 12432960x - 12432960x - 5525760x - 920960)log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 486000x + 1652400x + 6566400x + 4903452x - 1186182x - 2360364x
+--R +
+--R - 630195
+--R /
+--R 4 3 2
+--R 236196x + 629856x + 629856x + 279936x + 46656
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^6
+--R
+--R
+--R 6 5 4 3 2
+--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 500
+r0:=-1000/729*x+343/10935/(2+3*x)^5+(-1813/2916)/(2+3*x)^4+_
+ 10073/2187/(2+3*x)^3+(-66193/4374)/(2+3*x)^2+14390/729/(2+3*x)+_
+ 3700/729*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 17982000x + 59940000x + 79920000x + 53280000x + 17760000x
+--R +
+--R 2368000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 4860000x - 16200000x + 1711800x + 41807430x + 46054440x
+--R +
+--R 19824285x + 3090594
+--R /
+--R 5 4 3 2
+--R 3542940x + 11809800x + 15746400x + 10497600x + 3499200x + 466560
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 17982000x + 59940000x + 79920000x + 53280000x + 17760000x
+--R +
+--R 2368000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 4860000x - 16200000x + 1711800x + 41807430x + 46054440x
+--R +
+--R 19824285x + 3090594
+--R /
+--R 5 4 3 2
+--R 3542940x + 11809800x + 15746400x + 10497600x + 3499200x + 466560
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^7
+--R
+--R
+--R 6 5 4 3 2
+--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 500
+r0:=343/13122/(2+3*x)^6+(-1813/3645)/(2+3*x)^5+10073/2916/(2+3*x)^4+_
+ (-66193/6561)/(2+3*x)^3+7195/729/(2+3*x)^2+(-3700/729)/(2+3*x)-_
+ 1000/2187*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 14580000x - 58320000x - 97200000x - 86400000x - 43200000x
+--R +
+--R - 11520000x - 1280000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 53946000x - 144852300x - 158427540x - 89062425x - 25975248x - 3165082
+--R /
+--R 6 5 4 3 2
+--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x
+--R +
+--R 25194240x + 2799360
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 14580000x - 58320000x - 97200000x - 86400000x - 43200000x
+--R +
+--R - 11520000x - 1280000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 53946000x - 144852300x - 158427540x - 89062425x - 25975248x - 3165082
+--R /
+--R 6 5 4 3 2
+--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x
+--R +
+--R 25194240x + 2799360
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 6 5 4 3 2
+--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 500
+r0:=49/2187/(2+3*x)^7+(-1813/4374)/(2+3*x)^6+10073/3645/(2+3*x)^5+_
+ (-66193/8748)/(2+3*x)^4+14390/2187/(2+3*x)^3+(-1850/729)/(2+3*x)^2+_
+ 1000/2187/(2+3*x)
+--R
+--R
+--R (2)
+--R 1000 6 2150 5 18890 4 146287 3 160381 2 331697 33326
+--R ---- x + ---- x + ----- x + ------ x + ------- x + -------- x + --------
+--R 6561 6561 59049 708588 1771470 15943230 23914845
+--R -----------------------------------------------------------------------------
+--R 7 14 6 28 5 280 4 560 3 224 2 448 128
+--R x + -- x + -- x + --- x + --- x + --- x + --- x + ----
+--R 3 3 27 81 81 729 2187
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 262
+
+--S 263 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 14580000x + 31347000x + 30601800x + 19748745x + 8660574x + 1990182x
+--R +
+--R 133304
+--R /
+--R 7 6 5 4 3
+--R 95659380x + 446410440x + 892820880x + 992023200x + 661348800x
+--R +
+--R 2
+--R 264539520x + 58786560x + 5598720
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(1-2*x)^3*(2+3*x)^6/(3+5*x)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3 2
+--R - 5832x - 14580x - 8262x + 6993x + 8316x + 252x - 2240x - 528x
+--R +
+--R 192x + 64
+--R /
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 266
+
+--S 267 of 500
+r0:=41666223/1953125*x+11111259/781250*x^2-17453753/234375*x^3-_
+ 5848749/62500*x^4+2212083/15625*x^5+331713/1250*x^6-40338/875*x^7-_
+ 13851/50*x^8-648/5*x^9+1331/9765625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 9 8 7
+--R 111804log(5x + 3) - 106312500000x - 227242968750x - 37816875000x
+--R +
+--R 6 5 4 3
+--R 217686656250x + 116134357500x - 76764830625x - 61088135500x
+--R +
+--R 2
+--R 11666821950x + 17499813660x
+--R /
+--R 820312500
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7
+--R 111804log(5x + 3) - 106312500000x - 227242968750x - 37816875000x
+--R +
+--R 6 5 4 3
+--R 217686656250x + 116134357500x - 76764830625x - 61088135500x
+--R +
+--R 2
+--R 11666821950x + 17499813660x
+--R /
+--R 820312500
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(1-2*x)^3*(2+3*x)^5/(3+5*x)
+--R
+--R
+--R 8 7 6 5 4 3 2
+--R - 1944x - 3564x - 378x + 2583x + 1050x - 616x - 336x + 48x + 32
+--R (1) ----------------------------------------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 271
+
+--S 272 of 500
+r0:=4166223/390625*x-138741/156250*x^2-1703753/46875*x^3-73749/12500*x^4+_
+ 243333/3125*x^5+4419/125*x^6-11988/175*x^7-243/5*x^8+_
+ 1331/1953125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R 111804log(5x + 3) - 7973437500x - 11238750000x + 5799937500x
+--R +
+--R 5 4 3 2
+--R 12774982500x - 967955625x - 5963135500x - 145678050x + 1749813660x
+--R /
+--R 164062500
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R 111804log(5x + 3) - 7973437500x - 11238750000x + 5799937500x
+--R +
+--R 5 4 3 2
+--R 12774982500x - 967955625x - 5963135500x - 145678050x + 1749813660x
+--R /
+--R 164062500
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(1-2*x)^3*(2+3*x)^4/(3+5*x)
+--R
+--R
+--R 7 6 5 4 3 2
+--R - 648x - 756x + 378x + 609x - 56x - 168x + 16
+--R (1) ---------------------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 276
+
+--S 277 of 500
+r0:=416223/78125*x-138741/31250*x^2-128753/9375*x^3+31251/2500*x^4+_
+ 14958/625*x^5-306/25*x^6-648/35*x^7+1331/390625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 111804log(5x + 3) - 607500000x - 401625000x + 785295000x + 410169375x
+--R +
+--R 3 2
+--R - 450635500x - 145678050x + 174813660x
+--R /
+--R 32812500
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 111804log(5x + 3) - 607500000x - 401625000x + 785295000x + 410169375x
+--R +
+--R 3 2
+--R - 450635500x - 145678050x + 174813660x
+--R /
+--R 32812500
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(1-2*x)^3*(2+3*x)^3/(3+5*x)
+--R
+--R
+--R 6 5 4 3 2
+--R - 216x - 108x + 198x + 71x - 66x - 12x + 8
+--R (1) -----------------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 500
+r0:=41223/15625*x-26241/6250*x^2-5003/1875*x^3+2313/250*x^4+_
+ 108/125*x^5-36/5*x^6+1331/78125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 7986log(5x + 3) - 3375000x + 405000x + 4336875x - 1250750x
+--R +
+--R 2
+--R - 1968075x + 1236690x
+--R /
+--R 468750
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 7986log(5x + 3) - 3375000x + 405000x + 4336875x - 1250750x
+--R +
+--R 2
+--R - 1968075x + 1236690x
+--R /
+--R 468750
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(1-2*x)^3*(2+3*x)^2/(3+5*x)
+--R
+--R
+--R 5 4 3 2
+--R - 72x + 12x + 58x - 15x - 12x + 4
+--R (1) -------------------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 500
+r0:=3723/3125*x-3741/1250*x^2+622/375*x^3+69/25*x^4-72/25*x^5+_
+ 1331/15625*log(3+5*x)
+--R
+--R
+--R 5 4 3 2
+--R 7986log(5x + 3) - 270000x + 258750x + 155500x - 280575x + 111690x
+--R (2) ---------------------------------------------------------------------
+--R 93750
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R 7986log(5x + 3) - 270000x + 258750x + 155500x - 280575x + 111690x
+--R (3) ---------------------------------------------------------------------
+--R 93750
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(1-2*x)^3*(2+3*x)/(3+5*x)
+--R
+--R
+--R 4 3 2
+--R - 24x + 20x + 6x - 9x + 2
+--R (1) ----------------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 500
+r0:=-27/625*x-183/125*x^2+172/75*x^3-6/5*x^4+1331/3125*log(3+5*x)
+--R
+--R
+--R 4 3 2
+--R 3993log(5x + 3) - 11250x + 21500x - 13725x - 405x
+--R (2) ----------------------------------------------------
+--R 9375
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R 3993log(5x + 3) - 11250x + 21500x - 13725x - 405x
+--R (3) ----------------------------------------------------
+--R 9375
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(1-2*x)^3/(3+5*x)
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ---------------------
+--R 5x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 296
+
+--S 297 of 500
+r0:=-402/125*x+42/25*x^2-8/15*x^3+1331/625*log(3+5*x)
+--R
+--R
+--R 3 2
+--R 3993log(5x + 3) - 1000x + 3150x - 6030x
+--R (2) -----------------------------------------
+--R 1875
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 3993log(5x + 3) - 1000x + 3150x - 6030x
+--R (3) -----------------------------------------
+--R 1875
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(1-2*x)^3/((2+3*x)*(3+5*x))
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ---------------------
+--R 2
+--R 15x + 19x + 6
+--R Type: Fraction(Polynomial(Integer))
+--E 301
+
+--S 302 of 500
+r0:=332/225*x-4/15*x^2-343/27*log(2+3*x)+1331/125*log(3+5*x)
+--R
+--R
+--R 2
+--R 35937log(5x + 3) - 42875log(3x + 2) - 900x + 4980x
+--R (2) ---------------------------------------------------
+--R 3375
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 35937log(5x + 3) - 42875log(3x + 2) - 900x + 4980x
+--R (3) ---------------------------------------------------
+--R 3375
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(1-2*x)^3/((2+3*x)^2*(3+5*x))
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ----------------------
+--R 3 2
+--R 45x + 87x + 56x + 12
+--R Type: Fraction(Polynomial(Integer))
+--E 306
+
+--S 307 of 500
+r0:=-8/45*x+343/27/(2+3*x)-1421/27*log(2+3*x)+1331/25*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (107811x + 71874)log(5x + 3) + (- 106575x - 71050)log(3x + 2) - 360x
+--R +
+--R - 240x + 8575
+--R /
+--R 2025x + 1350
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (107811x + 71874)log(5x + 3) + (- 106575x - 71050)log(3x + 2) - 360x
+--R +
+--R - 240x + 8575
+--R /
+--R 2025x + 1350
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(1-2*x)^3/((2+3*x)^3*(3+5*x))
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 135x + 351x + 342x + 148x + 24
+--R Type: Fraction(Polynomial(Integer))
+--E 311
+
+--S 312 of 500
+r0:=343/54/(2+3*x)^2+1421/27/(2+3*x)-7189/27*log(2+3*x)+1331/5*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (646866x + 862488x + 287496)log(5x + 3)
+--R +
+--R 2
+--R (- 647010x - 862680x - 287560)log(3x + 2) + 42630x + 30135
+--R /
+--R 2
+--R 2430x + 3240x + 1080
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (646866x + 862488x + 287496)log(5x + 3)
+--R +
+--R 2
+--R (- 647010x - 862680x - 287560)log(3x + 2) + 42630x + 30135
+--R /
+--R 2
+--R 2430x + 3240x + 1080
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(1-2*x)^3/((2+3*x)^4*(3+5*x))
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 405x + 1323x + 1728x + 1128x + 368x + 48
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 500
+r0:=343/81/(2+3*x)^3+1421/54/(2+3*x)^2+7189/27/(2+3*x)-1331*log(2+3*x)+_
+ 1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (5821794x + 11643588x + 7762392x + 1724976)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 5821794x - 11643588x - 7762392x - 1724976)log(3x + 2) + 388206x
+--R +
+--R 530397x + 181748
+--R /
+--R 3 2
+--R 4374x + 8748x + 5832x + 1296
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (5821794x + 11643588x + 7762392x + 1724976)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 5821794x - 11643588x - 7762392x - 1724976)log(3x + 2) + 388206x
+--R +
+--R 530397x + 181748
+--R /
+--R 3 2
+--R 4374x + 8748x + 5832x + 1296
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(1-2*x)^3/((2+3*x)^5*(3+5*x))
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ------------------------------------------------------
+--R 6 5 4 3 2
+--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96
+--R Type: Fraction(Polynomial(Integer))
+--E 321
+
+--S 322 of 500
+r0:=343/108/(2+3*x)^4+1421/81/(2+3*x)^3+7189/54/(2+3*x)^2+1331/(2+3*x)-_
+ 6655*log(2+3*x)+6655*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (174653820x + 465743520x + 465743520x + 206997120x + 34499520)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 174653820x - 465743520x - 465743520x - 206997120x - 34499520)
+--R *
+--R log(3x + 2)
+--R +
+--R 3 2
+--R 11643588x + 23675382x + 16059444x + 3634885
+--R /
+--R 4 3 2
+--R 26244x + 69984x + 69984x + 31104x + 5184
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (174653820x + 465743520x + 465743520x + 206997120x + 34499520)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 174653820x - 465743520x - 465743520x - 206997120x - 34499520)
+--R *
+--R log(3x + 2)
+--R +
+--R 3 2
+--R 11643588x + 23675382x + 16059444x + 3634885
+--R /
+--R 4 3 2
+--R 26244x + 69984x + 69984x + 31104x + 5184
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(1-2*x)^3/((2+3*x)^6*(3+5*x))
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192
+--R Type: Fraction(Polynomial(Integer))
+--E 326
+
+--S 327 of 500
+r0:=343/135/(2+3*x)^5+1421/108/(2+3*x)^4+7189/81/(2+3*x)^3+1331/2/(2+3*x)^2+_
+ 6655/(2+3*x)-33275*log(2+3*x)+33275*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 13099036500x + 43663455000x + 58217940000x + 38811960000x
+--R +
+--R 12937320000x + 1724976000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 13099036500x - 43663455000x - 58217940000x - 38811960000x
+--R +
+--R - 12937320000x - 1724976000
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 873269100x + 2357826570x + 2388229560x + 1075586865x + 181744346
+--R /
+--R 5 4 3 2
+--R 393660x + 1312200x + 1749600x + 1166400x + 388800x + 51840
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 13099036500x + 43663455000x + 58217940000x + 38811960000x
+--R +
+--R 12937320000x + 1724976000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 13099036500x - 43663455000x - 58217940000x - 38811960000x
+--R +
+--R - 12937320000x - 1724976000
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 873269100x + 2357826570x + 2388229560x + 1075586865x + 181744346
+--R /
+--R 5 4 3 2
+--R 393660x + 1312200x + 1749600x + 1166400x + 388800x + 51840
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(1-2*x)^3/((2+3*x)^7*(3+5*x))
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x
+--R +
+--R 4672x + 384
+--R Type: Fraction(Polynomial(Integer))
+--E 331
+
+--S 332 of 500
+r0:=343/162/(2+3*x)^6+1421/135/(2+3*x)^5+7189/108/(2+3*x)^4+_
+ 1331/3/(2+3*x)^3+6655/2/(2+3*x)^2+33275/(2+3*x)-166375*log(2+3*x)+_
+ 166375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 196485547500x + 785942190000x + 1309903650000x + 1164358800000x
+--R +
+--R 2
+--R 582179400000x + 155247840000x + 17249760000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 196485547500x - 785942190000x - 1309903650000x - 1164358800000x
+--R +
+--R 2
+--R - 582179400000x - 155247840000x - 17249760000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 13099036500x + 44100089550x + 59401704780x + 40016101275x
+--R +
+--R 13482032616x + 1817443594
+--R /
+--R 6 5 4 3 2
+--R 1180980x + 4723920x + 7873200x + 6998400x + 3499200x + 933120x
+--R +
+--R 103680
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 196485547500x + 785942190000x + 1309903650000x + 1164358800000x
+--R +
+--R 2
+--R 582179400000x + 155247840000x + 17249760000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 196485547500x - 785942190000x - 1309903650000x - 1164358800000x
+--R +
+--R 2
+--R - 582179400000x - 155247840000x - 17249760000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 13099036500x + 44100089550x + 59401704780x + 40016101275x
+--R +
+--R 13482032616x + 1817443594
+--R /
+--R 6 5 4 3 2
+--R 1180980x + 4723920x + 7873200x + 6998400x + 3499200x + 933120x
+--R +
+--R 103680
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(1-2*x)^3/((2+3*x)^8*(3+5*x))
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 32805x + 194643x + 513216x + 789264x + 780192x + 514080x + 225792x
+--R +
+--R 2
+--R 63744x + 10496x + 768
+--R Type: Fraction(Polynomial(Integer))
+--E 336
+
+--S 337 of 500
+r0:=49/27/(2+3*x)^7+1421/162/(2+3*x)^6+7189/135/(2+3*x)^5+1331/4/(2+3*x)^4+_
+ 6655/3/(2+3*x)^3+33275/2/(2+3*x)^2+166375/(2+3*x)-_
+ 831875*log(2+3*x)+831875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R 2947283212500x + 13753988325000x + 27507976650000x
+--R +
+--R 4 3 2
+--R 30564418500000x + 20376279000000x + 8150511600000x
+--R +
+--R 1811224800000x + 172497600000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 2947283212500x - 13753988325000x - 27507976650000x
+--R +
+--R 4 3 2
+--R - 30564418500000x - 20376279000000x - 8150511600000x
+--R +
+--R - 1811224800000x - 172497600000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 196485547500x + 792491708250x + 1332026467200x + 1194258563685x
+--R +
+--R 2
+--R 602391504582x + 162081979026x + 18174436072
+--R /
+--R 7 6 5 4 3 2
+--R 3542940x + 16533720x + 33067440x + 36741600x + 24494400x + 9797760x
+--R +
+--R 2177280x + 207360
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R 2947283212500x + 13753988325000x + 27507976650000x
+--R +
+--R 4 3 2
+--R 30564418500000x + 20376279000000x + 8150511600000x
+--R +
+--R 1811224800000x + 172497600000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 2947283212500x - 13753988325000x - 27507976650000x
+--R +
+--R 4 3 2
+--R - 30564418500000x - 20376279000000x - 8150511600000x
+--R +
+--R - 1811224800000x - 172497600000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 196485547500x + 792491708250x + 1332026467200x + 1194258563685x
+--R +
+--R 2
+--R 602391504582x + 162081979026x + 18174436072
+--R /
+--R 7 6 5 4 3 2
+--R 3542940x + 16533720x + 33067440x + 36741600x + 24494400x + 9797760x
+--R +
+--R 2177280x + 207360
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(1-2*x)^3*(2+3*x)^6/(3+5*x)^2
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3 2
+--R - 5832x - 14580x - 8262x + 6993x + 8316x + 252x - 2240x - 528x
+--R +
+--R 192x + 64
+--R /
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 500
+r0:=13880997/1953125*x-461623/390625*x^2-1836723/78125*x^3-5643/3125*x^4+_
+ 774981/15625*x^5+12231/625*x^6-37908/875*x^7-729/25*x^8+_
+ (-1331/9765625)/(3+5*x)+23232/9765625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 9 8
+--R (813120x + 487872)log(5x + 3) - 9966796875x - 20787890625x
+--R +
+--R 7 6 5 4
+--R - 2195859375x + 20966006250x + 9554422500x - 8405985000x
+--R +
+--R 3 2
+--R - 5225318000x + 2186822400x + 1457504685x - 9317
+--R /
+--R 341796875x + 205078125
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8
+--R (813120x + 487872)log(5x + 3) - 9966796875x - 20787890625x
+--R +
+--R 7 6 5 4
+--R - 2195859375x + 20966006250x + 9554422500x - 8405985000x
+--R +
+--R 3 2
+--R - 5225318000x + 2186822400x + 1457504685x - 9317
+--R /
+--R 341796875x + 205078125
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(1-2*x)^3*(2+3*x)^5/(3+5*x)^2
+--R
+--R
+--R 8 7 6 5 4 3 2
+--R - 1944x - 3564x - 378x + 2583x + 1050x - 616x - 336x + 48x + 32
+--R (1) ----------------------------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 500
+r0:=1382328/390625*x-507023/156250*x^2-26594/3125*x^3+108387/12500*x^4+_
+ 44982/3125*x^5-1026/125*x^6-1944/175*x^7+(-1331/1953125)/(3+5*x)+_
+ 19239/1953125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 8 7
+--R (2693460x + 1616076)log(5x + 3) - 3037500000x - 4066875000x
+--R +
+--R 6 5 4 3 2
+--R 2589300000x + 4732520625x - 904395625x - 2283475250x + 435255450x
+--R +
+--R 580577760x - 37268
+--R /
+--R 273437500x + 164062500
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7
+--R (2693460x + 1616076)log(5x + 3) - 3037500000x - 4066875000x
+--R +
+--R 6 5 4 3 2
+--R 2589300000x + 4732520625x - 904395625x - 2283475250x + 435255450x
+--R +
+--R 580577760x - 37268
+--R /
+--R 273437500x + 164062500
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(1-2*x)^3*(2+3*x)^4/(3+5*x)^2
+--R
+--R
+--R 7 6 5 4 3 2
+--R - 648x - 756x + 378x + 609x - 56x - 168x + 16
+--R (1) ---------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 351
+
+--S 352 of 500
+r0:=133659/78125*x-1816/625*x^2-4217/3125*x^3+7317/1250*x^4+108/625*x^5-_
+ 108/25*x^6+(-1331/390625)/(3+5*x)+15246/390625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R (152460x + 91476)log(5x + 3) - 16875000x - 9450000x + 23270625x
+--R +
+--R 4 3 2
+--R 8448125x - 14512750x - 127050x + 4009770x - 2662
+--R /
+--R 3906250x + 2343750
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R (152460x + 91476)log(5x + 3) - 16875000x - 9450000x + 23270625x
+--R +
+--R 4 3 2
+--R 8448125x - 14512750x - 127050x + 4009770x - 2662
+--R /
+--R 3906250x + 2343750
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(1-2*x)^3*(2+3*x)^3/(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R - 216x - 108x + 198x + 71x - 66x - 12x + 8
+--R (1) -----------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 356
+
+--S 357 of 500
+r0:=1998/3125*x-12077/6250*x^2+786/625*x^3+189/125*x^4-216/125*x^5+_
+ (-1331/78125)/(3+5*x)+11253/78125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R (112530x + 67518)log(5x + 3) - 1350000x + 371250x + 1691250x
+--R +
+--R 3 2
+--R - 920125x - 406275x + 299700x - 2662
+--R /
+--R 781250x + 468750
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R (112530x + 67518)log(5x + 3) - 1350000x + 371250x + 1691250x
+--R +
+--R 3 2
+--R - 920125x - 406275x + 299700x - 2662
+--R /
+--R 781250x + 468750
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(1-2*x)^3*(2+3*x)^2/(3+5*x)^2
+--R
+--R
+--R 5 4 3 2
+--R - 72x + 12x + 58x - 15x - 12x + 4
+--R (1) -------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 361
+
+--S 362 of 500
+r0:=-1179/3125*x-427/625*x^2+164/125*x^3-18/25*x^4+(-1331/15625)/(3+5*x)+_
+ 1452/3125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (36300x + 21780)log(5x + 3) - 56250x + 68750x + 8125x - 61500x
+--R +
+--R - 17685x - 1331
+--R /
+--R 78125x + 46875
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (36300x + 21780)log(5x + 3) - 56250x + 68750x + 8125x - 61500x
+--R +
+--R - 17685x - 1331
+--R /
+--R 78125x + 46875
+--R Type: Union(Expression(Integer),...)
+--E 363
+
+--S 364 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(1-2*x)^3*(2+3*x)/(3+5*x)^2
+--R
+--R
+--R 4 3 2
+--R - 24x + 20x + 6x - 9x + 2
+--R (1) ----------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 366
+
+--S 367 of 500
+r0:=-1098/625*x+122/125*x^2-8/25*x^3+(-1331/3125)/(3+5*x)+3267/3125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (16335x + 9801)log(5x + 3) - 5000x + 12250x - 18300x - 16470x - 1331
+--R -----------------------------------------------------------------------
+--R 15625x + 9375
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (16335x + 9801)log(5x + 3) - 5000x + 12250x - 18300x - 16470x - 1331
+--R -----------------------------------------------------------------------
+--R 15625x + 9375
+--R Type: Union(Expression(Integer),...)
+--E 368
+
+--S 369 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(1-2*x)^3/(3+5*x)^2
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ---------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 371
+
+--S 372 of 500
+r0:=108/125*x-4/25*x^2+(-1331/625)/(3+5*x)-726/625*log(3+5*x)
+--R
+--R
+--R 3 2
+--R (- 3630x - 2178)log(5x + 3) - 500x + 2400x + 1620x - 1331
+--R (2) -----------------------------------------------------------
+--R 3125x + 1875
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R (- 3630x - 2178)log(5x + 3) - 500x + 2400x + 1620x - 1331
+--R (3) -----------------------------------------------------------
+--R 3125x + 1875
+--R Type: Union(Expression(Integer),...)
+--E 373
+
+--S 374 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(1-2*x)^3/((2+3*x)*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) -----------------------
+--R 3 2
+--R 75x + 140x + 87x + 18
+--R Type: Fraction(Polynomial(Integer))
+--E 376
+
+--S 377 of 500
+r0:=-8/75*x+(-1331/125)/(3+5*x)+343/9*log(2+3*x)-4719/125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 212355x - 127413)log(5x + 3) + (214375x + 128625)log(3x + 2) - 600x
+--R +
+--R - 360x - 11979
+--R /
+--R 5625x + 3375
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (- 212355x - 127413)log(5x + 3) + (214375x + 128625)log(3x + 2) - 600x
+--R +
+--R - 360x - 11979
+--R /
+--R 5625x + 3375
+--R Type: Union(Expression(Integer),...)
+--E 378
+
+--S 379 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(1-2*x)^3/((2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 225x + 570x + 541x + 228x + 36
+--R Type: Fraction(Polynomial(Integer))
+--E 381
+
+--S 382 of 500
+r0:=(-343/9)/(2+3*x)+(-1331/25)/(3+5*x)+3136/9*log(2+3*x)-8712/25*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 1176120x - 1489752x - 470448)log(5x + 3)
+--R +
+--R 2
+--R (1176000x + 1489600x + 470400)log(3x + 2) - 78812x - 49683
+--R /
+--R 2
+--R 3375x + 4275x + 1350
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (- 1176120x - 1489752x - 470448)log(5x + 3)
+--R +
+--R 2
+--R (1176000x + 1489600x + 470400)log(3x + 2) - 78812x - 49683
+--R /
+--R 2
+--R 3375x + 4275x + 1350
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(1-2*x)^3/((2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 675x + 2160x + 2763x + 1766x + 564x + 72
+--R Type: Fraction(Polynomial(Integer))
+--E 386
+
+--S 387 of 500
+r0:=(-343/18)/(2+3*x)^2+(-3136/9)/(2+3*x)+(-1331/5)/(3+5*x)+_
+ 2541*log(2+3*x)-2541*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (- 10291050x - 19896030x - 12806640x - 2744280)log(5x + 3)
+--R +
+--R 3 2 2
+--R (10291050x + 19896030x + 12806640x + 2744280)log(3x + 2) - 686022x
+--R +
+--R - 891911x - 289137
+--R /
+--R 3 2
+--R 4050x + 7830x + 5040x + 1080
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (- 10291050x - 19896030x - 12806640x - 2744280)log(5x + 3)
+--R +
+--R 3 2 2
+--R (10291050x + 19896030x + 12806640x + 2744280)log(3x + 2) - 686022x
+--R +
+--R - 891911x - 289137
+--R /
+--R 3 2
+--R 4050x + 7830x + 5040x + 1080
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(1-2*x)^3/((2+3*x)^4*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ----------------------------------------------------------
+--R 6 5 4 3 2
+--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144
+--R Type: Fraction(Polynomial(Integer))
+--E 391
+
+--S 392 of 500
+r0:=(-343/27)/(2+3*x)^3+(-1568/9)/(2+3*x)^2+(-2541)/(2+3*x)+_
+ (-1331)/(3+5*x)+16698*log(2+3*x)-16698*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 60864210x - 158246946x - 154189332x - 66725208x - 10820304)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (60864210x + 158246946x + 154189332x + 66725208x + 10820304)
+--R *
+--R log(3x + 2)
+--R +
+--R 3 2
+--R - 4057614x - 7979967x - 5226815x - 1140033
+--R /
+--R 4 3 2
+--R 3645x + 9477x + 9234x + 3996x + 648
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 60864210x - 158246946x - 154189332x - 66725208x - 10820304)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (60864210x + 158246946x + 154189332x + 66725208x + 10820304)
+--R *
+--R log(3x + 2)
+--R +
+--R 3 2
+--R - 4057614x - 7979967x - 5226815x - 1140033
+--R /
+--R 4 3 2
+--R 3645x + 9477x + 9234x + 3996x + 648
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(1-2*x)^3/((2+3*x)^5*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288
+--R Type: Fraction(Polynomial(Integer))
+--E 396
+
+--S 397 of 500
+r0:=(-343/36)/(2+3*x)^4+(-3136/27)/(2+3*x)^3+(-2541/2)/(2+3*x)^2+_
+ (-16698)/(2+3*x)+(-6655)/(3+5*x)+103455*log(2+3*x)-103455*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 4525121700x - 14782064220x - 19307185920x - 12603301920x
+--R +
+--R - 4111715520x - 536310720
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 4525121700x + 14782064220x + 19307185920x + 12603301920x
+--R +
+--R 4111715520x + 536310720
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R - 301674780x - 794410254x - 784130946x - 343827337x - 56505975
+--R /
+--R 5 4 3 2
+--R 43740x + 142884x + 186624x + 121824x + 39744x + 5184
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 4525121700x - 14782064220x - 19307185920x - 12603301920x
+--R +
+--R - 4111715520x - 536310720
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 4525121700x + 14782064220x + 19307185920x + 12603301920x
+--R +
+--R 4111715520x + 536310720
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R - 301674780x - 794410254x - 784130946x - 343827337x - 56505975
+--R /
+--R 5 4 3 2
+--R 43740x + 142884x + 186624x + 121824x + 39744x + 5184
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(1-2*x)^3/((2+3*x)^6*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x
+--R +
+--R 7104x + 576
+--R Type: Fraction(Polynomial(Integer))
+--E 401
+
+--S 402 of 500
+r0:=(-343/45)/(2+3*x)^5+(-784/9)/(2+3*x)^4+(-847)/(2+3*x)^3+_
+ (-8349)/(2+3*x)^2+(-103455)/(2+3*x)+(-33275)/(3+5*x)+_
+ 617100*log(2+3*x)-617100*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R - 33739942500x - 132710440500x - 217435185000x - 189943380000x
+--R +
+--R 2
+--R - 93305520000x - 24437160000x - 2665872000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R 33739942500x + 132710440500x + 217435185000x + 189943380000x
+--R +
+--R 2
+--R 93305520000x + 24437160000x + 2665872000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 2249329500x - 7422787350x - 9795413430x - 6461351715x - 2130399775x
+--R +
+--R - 280877649
+--R /
+--R 6 5 4 3 2
+--R 54675x + 215055x + 352350x + 307800x + 151200x + 39600x + 4320
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R - 33739942500x - 132710440500x - 217435185000x - 189943380000x
+--R +
+--R 2
+--R - 93305520000x - 24437160000x - 2665872000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R 33739942500x + 132710440500x + 217435185000x + 189943380000x
+--R +
+--R 2
+--R 93305520000x + 24437160000x + 2665872000
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 2249329500x - 7422787350x - 9795413430x - 6461351715x - 2130399775x
+--R +
+--R - 280877649
+--R /
+--R 6 5 4 3 2
+--R 54675x + 215055x + 352350x + 307800x + 151200x + 39600x + 4320
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(1-2*x)^3/((2+3*x)^7*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R /
+--R 9 8 7 6 5 4
+--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x
+--R +
+--R 3 2
+--R 351120x + 97952x + 15936x + 1152
+--R Type: Fraction(Polynomial(Integer))
+--E 406
+
+--S 407 of 500
+r0:=(-343/54)/(2+3*x)^6+(-3136/45)/(2+3*x)^5+(-2541/4)/(2+3*x)^4+_
+ (-5566)/(2+3*x)^3+(-103455/2)/(2+3*x)^2+(-617100)/(2+3*x)+_
+ (-166375)/(3+5*x)+3584625*log(2+3*x)-3584625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R - 7055617387500x - 32455839982500x - 63970930980000x
+--R +
+--R 4 3 2
+--R - 70033535550000x - 45992172600000x - 18118128600000x
+--R +
+--R - 3964308480000x - 371653920000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R 7055617387500x + 32455839982500x + 63970930980000x
+--R +
+--R 4 3 2
+--R 70033535550000x + 45992172600000x + 18118128600000x
+--R +
+--R 3964308480000x + 371653920000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 470374492500x - 1865818820250x - 3083217691950x - 2716778541015x
+--R +
+--R 2
+--R - 1346292632205x - 355739265638x - 39157648662
+--R /
+--R 7 6 5 4 3 2
+--R 1968300x + 9054180x + 17845920x + 19537200x + 12830400x + 5054400x
+--R +
+--R 1105920x + 103680
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R - 7055617387500x - 32455839982500x - 63970930980000x
+--R +
+--R 4 3 2
+--R - 70033535550000x - 45992172600000x - 18118128600000x
+--R +
+--R - 3964308480000x - 371653920000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R 7055617387500x + 32455839982500x + 63970930980000x
+--R +
+--R 4 3 2
+--R 70033535550000x + 45992172600000x + 18118128600000x
+--R +
+--R 3964308480000x + 371653920000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 470374492500x - 1865818820250x - 3083217691950x - 2716778541015x
+--R +
+--R 2
+--R - 1346292632205x - 355739265638x - 39157648662
+--R /
+--R 7 6 5 4 3 2
+--R 1968300x + 9054180x + 17845920x + 19537200x + 12830400x + 5054400x
+--R +
+--R 1105920x + 103680
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(1-2*x)^3/((2+3*x)^8*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R /
+--R 10 9 8 7 6 5
+--R 164025x + 1071630x + 3150009x + 5485968x + 6268752x + 4910976x
+--R +
+--R 4 3 2
+--R 2671200x + 996096x + 243712x + 35328x + 2304
+--R Type: Fraction(Polynomial(Integer))
+--E 411
+
+--S 412 of 500
+r0:=(-49/9)/(2+3*x)^7+(-1568/27)/(2+3*x)^6+(-2541/5)/(2+3*x)^5+_
+ (-8349/2)/(2+3*x)^4+(-34485)/(2+3*x)^3+(-308550)/(2+3*x)^2+_
+ (-3584625)/(2+3*x)+(-831875)/(3+5*x)+20418750*log(2+3*x)-_
+ 20418750*log(3+5*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R - 60285338437500x - 317502782437500x - 731462106375000x
+--R +
+--R 5 4 3
+--R - 962779182750000x - 791896297500000x - 416787525000000x
+--R +
+--R 2
+--R - 137076786000000x - 25757028000000x - 2117016000000
+--R *
+--R log(5x + 3)
+--R +
+--R 8 7 6
+--R 60285338437500x + 317502782437500x + 731462106375000x
+--R +
+--R 5 4 3
+--R 962779182750000x + 791896297500000x + 416787525000000x
+--R +
+--R 2
+--R 137076786000000x + 25757028000000x + 2117016000000
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5
+--R - 4019022562500x - 18621471206250x - 36972030521250x
+--R +
+--R 4 3 2
+--R - 40775613627375x - 26978454053595x - 10708299857748x - 2360937751874x
+--R +
+--R - 223049897418
+--R /
+--R 8 7 6 5 4
+--R 2952450x + 15549570x + 35823060x + 47151720x + 38782800x
+--R +
+--R 3 2
+--R 20412000x + 6713280x + 1261440x + 103680
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R - 60285338437500x - 317502782437500x - 731462106375000x
+--R +
+--R 5 4 3
+--R - 962779182750000x - 791896297500000x - 416787525000000x
+--R +
+--R 2
+--R - 137076786000000x - 25757028000000x - 2117016000000
+--R *
+--R log(5x + 3)
+--R +
+--R 8 7 6
+--R 60285338437500x + 317502782437500x + 731462106375000x
+--R +
+--R 5 4 3
+--R 962779182750000x + 791896297500000x + 416787525000000x
+--R +
+--R 2
+--R 137076786000000x + 25757028000000x + 2117016000000
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5
+--R - 4019022562500x - 18621471206250x - 36972030521250x
+--R +
+--R 4 3 2
+--R - 40775613627375x - 26978454053595x - 10708299857748x - 2360937751874x
+--R +
+--R - 223049897418
+--R /
+--R 8 7 6 5 4
+--R 2952450x + 15549570x + 35823060x + 47151720x + 38782800x
+--R +
+--R 3 2
+--R 20412000x + 6713280x + 1261440x + 103680
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(1-2*x)^3*(2+3*x)^7/(3+5*x)^3
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5 4
+--R - 17496x - 55404x - 53946x + 4455x + 38934x + 17388x - 6216x
+--R +
+--R 3 2
+--R - 6064x - 480x + 576x + 128
+--R /
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 416
+
+--S 417 of 500
+r0:=46214407/9765625*x-2300646/1953125*x^2-5918904/390625*x^3+_
+ 6507/62500*x^4+491913/15625*x^5+33291/3125*x^6-119556/4375*x^7-_
+ 2187/125*x^8+(-1331/97656250)/(3+5*x)^2+(-1089/1953125)/(3+5*x)+_
+ 47289/9765625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 10
+--R (165511500x + 198613800x + 59584140)log(5x + 3) - 598007812500x
+--R +
+--R 9 8 7 6
+--R - 1651640625000x - 972000000000x + 1176752812500x + 1425913453125x
+--R +
+--R 5 4 3 2
+--R - 126252393750x - 660465159375x - 73008617500x + 179606439600x
+--R +
+--R 58226341320x - 2305534
+--R /
+--R 2
+--R 34179687500x + 41015625000x + 12304687500
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 10
+--R (165511500x + 198613800x + 59584140)log(5x + 3) - 598007812500x
+--R +
+--R 9 8 7 6
+--R - 1651640625000x - 972000000000x + 1176752812500x + 1425913453125x
+--R +
+--R 5 4 3 2
+--R - 126252393750x - 660465159375x - 73008617500x + 179606439600x
+--R +
+--R 58226341320x - 2305534
+--R /
+--R 2
+--R 34179687500x + 41015625000x + 12304687500
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(1-2*x)^3*(2+3*x)^6/(3+5*x)^3
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3 2
+--R - 5832x - 14580x - 8262x + 6993x + 8316x + 252x - 2240x - 528x
+--R +
+--R 192x + 64
+--R /
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 421
+
+--S 422 of 500
+r0:=4571416/1953125*x-915777/390625*x^2-81747/15625*x^3+74223/12500*x^4+_
+ 134622/15625*x^5-3402/625*x^6-5832/875*x^7+(-1331/19531250)/(3+5*x)^2+_
+ (-23232/9765625)/(3+5*x)+166749/9765625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 9
+--R (116724300x + 140069160x + 42020748)log(5x + 3) - 45562500000x
+--R +
+--R 8 7 6 5
+--R - 91884375000x - 2156625000x + 97871878125x + 34147496250x
+--R +
+--R 4 3 2
+--R - 44330619375x - 16106513500x + 13430552100x + 5756731680x - 1970122
+--R /
+--R 2
+--R 6835937500x + 8203125000x + 2460937500
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 9
+--R (116724300x + 140069160x + 42020748)log(5x + 3) - 45562500000x
+--R +
+--R 8 7 6 5
+--R - 91884375000x - 2156625000x + 97871878125x + 34147496250x
+--R +
+--R 4 3 2
+--R - 44330619375x - 16106513500x + 13430552100x + 5756731680x - 1970122
+--R /
+--R 2
+--R 6835937500x + 8203125000x + 2460937500
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(1-2*x)^3*(2+3*x)^5/(3+5*x)^3
+--R
+--R
+--R 8 7 6 5 4 3 2
+--R - 1944x - 3564x - 378x + 2583x + 1050x - 616x - 336x + 48x + 32
+--R (1) ----------------------------------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 426
+
+--S 427 of 500
+r0:=424432/390625*x-62097/31250*x^2-393/625*x^3+22977/6250*x^4-_
+ 324/3125*x^5-324/125*x^6+(-1331/3906250)/(3+5*x)^2+_
+ (-19239/1953125)/(3+5*x)+109032/1953125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 8 7
+--R (5451600x + 6541920x + 1962576)log(5x + 3) - 253125000x - 313875000x
+--R +
+--R 6 5 4 3 2
+--R 255740625x + 365767500x - 138495000x - 148862000x + 57470475x
+--R +
+--R 38006490x - 116765
+--R /
+--R 2
+--R 97656250x + 117187500x + 35156250
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 7
+--R (5451600x + 6541920x + 1962576)log(5x + 3) - 253125000x - 313875000x
+--R +
+--R 6 5 4 3 2
+--R 255740625x + 365767500x - 138495000x - 148862000x + 57470475x
+--R +
+--R 38006490x - 116765
+--R /
+--R 2
+--R 97656250x + 117187500x + 35156250
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(1-2*x)^3*(2+3*x)^4/(3+5*x)^3
+--R
+--R
+--R 7 6 5 4 3 2
+--R - 648x - 756x + 378x + 609x - 56x - 168x + 16
+--R (1) ---------------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 431
+
+--S 432 of 500
+r0:=4691/15625*x-7617/6250*x^2+2826/3125*x^3+513/625*x^4-648/625*x^5+_
+ (-1331/781250)/(3+5*x)^2+(-15246/390625)/(3+5*x)+63294/390625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 7 6
+--R (3164700x + 3797640x + 1139292)log(5x + 3) - 20250000x - 8268750x
+--R +
+--R 5 4 3 2
+--R 29610000x + 3163125x - 16341500x - 1532625x + 1958490x - 92807
+--R /
+--R 2
+--R 19531250x + 23437500x + 7031250
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 6
+--R (3164700x + 3797640x + 1139292)log(5x + 3) - 20250000x - 8268750x
+--R +
+--R 5 4 3 2
+--R 29610000x + 3163125x - 16341500x - 1532625x + 1958490x - 92807
+--R /
+--R 2
+--R 19531250x + 23437500x + 7031250
+--R Type: Union(Expression(Integer),...)
+--E 433
+
+--S 434 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(1-2*x)^3*(2+3*x)^3/(3+5*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R - 216x - 108x + 198x + 71x - 66x - 12x + 8
+--R (1) -----------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 436
+
+--S 437 of 500
+r0:=-1303/3125*x-927/3125*x^2+468/625*x^3-54/125*x^4+_
+ (-1331/156250)/(3+5*x)^2+(-11253/78125)/(3+5*x)+5907/15625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 6 5
+--R (1476750x + 1772100x + 531630)log(5x + 3) - 1687500x + 900000x
+--R +
+--R 4 3 2
+--R 1743750x - 1966250x - 2371650x - 698880x - 68849
+--R /
+--R 2
+--R 3906250x + 4687500x + 1406250
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 5
+--R (1476750x + 1772100x + 531630)log(5x + 3) - 1687500x + 900000x
+--R +
+--R 4 3 2
+--R 1743750x - 1966250x - 2371650x - 698880x - 68849
+--R /
+--R 2
+--R 3906250x + 4687500x + 1406250
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(1-2*x)^3*(2+3*x)^2/(3+5*x)^3
+--R
+--R
+--R 5 4 3 2
+--R - 72x + 12x + 58x - 15x - 12x + 4
+--R (1) -------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 441
+
+--S 442 of 500
+r0:=-2978/3125*x+354/625*x^2-24/125*x^3+(-1331/31250)/(3+5*x)^2+_
+ (-1452/3125)/(3+5*x)+1551/3125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 5 4 3
+--R (387750x + 465300x + 139590)log(5x + 3) - 150000x + 262500x - 267500x
+--R +
+--R 2
+--R - 734100x - 340620x - 44891
+--R /
+--R 2
+--R 781250x + 937500x + 281250
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4 3
+--R (387750x + 465300x + 139590)log(5x + 3) - 150000x + 262500x - 267500x
+--R +
+--R 2
+--R - 734100x - 340620x - 44891
+--R /
+--R 2
+--R 781250x + 937500x + 281250
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(1-2*x)^3*(2+3*x)/(3+5*x)^3
+--R
+--R
+--R 4 3 2
+--R - 24x + 20x + 6x - 9x + 2
+--R (1) ----------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 446
+
+--S 447 of 500
+r0:=316/625*x-12/125*x^2+(-1331/6250)/(3+5*x)^2+(-3267/3125)/(3+5*x)-_
+ 2046/3125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2
+--R (- 102300x - 122760x - 36828)log(5x + 3) - 15000x + 61000x + 89400x
+--R +
+--R - 4230x - 20933
+--R /
+--R 2
+--R 156250x + 187500x + 56250
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2
+--R (- 102300x - 122760x - 36828)log(5x + 3) - 15000x + 61000x + 89400x
+--R +
+--R - 4230x - 20933
+--R /
+--R 2
+--R 156250x + 187500x + 56250
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(1-2*x)^3/(3+5*x)^3
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 451
+
+--S 452 of 500
+r0:=-8/125*x+(-1331/1250)/(3+5*x)^2+726/625/(3+5*x)+132/625*log(3+5*x)
+--R
+--R
+--R 2 3 2
+--R (6600x + 7920x + 2376)log(5x + 3) - 2000x - 2400x + 6540x + 3025
+--R (2) -------------------------------------------------------------------
+--R 2
+--R 31250x + 37500x + 11250
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2
+--R (6600x + 7920x + 2376)log(5x + 3) - 2000x - 2400x + 6540x + 3025
+--R (3) -------------------------------------------------------------------
+--R 2
+--R 31250x + 37500x + 11250
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(1-2*x)^3/((2+3*x)*(3+5*x)^3)
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 375x + 925x + 855x + 351x + 54
+--R Type: Fraction(Polynomial(Integer))
+--E 456
+
+--S 457 of 500
+r0:=(-1331/250)/(3+5*x)^2+4719/125/(3+5*x)-343/3*log(2+3*x)+_
+ 14289/125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (2143350x + 2572020x + 771606)log(5x + 3)
+--R +
+--R 2
+--R (- 2143750x - 2572500x - 771750)log(3x + 2) + 141570x + 80949
+--R /
+--R 2
+--R 18750x + 22500x + 6750
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (2143350x + 2572020x + 771606)log(5x + 3)
+--R +
+--R 2
+--R (- 2143750x - 2572500x - 771750)log(3x + 2) + 141570x + 80949
+--R /
+--R 2
+--R 18750x + 22500x + 6750
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(1-2*x)^3/((2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) ----------------------------------------------
+--R 5 4 3 2
+--R 1125x + 3525x + 4415x + 2763x + 864x + 108
+--R Type: Fraction(Polynomial(Integer))
+--E 461
+
+--S 462 of 500
+r0:=343/3/(2+3*x)+(-1331/50)/(3+5*x)^2+8712/25/(3+5*x)-1617*log(2+3*x)+_
+ 1617*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (18191250x + 33957000x + 21101850x + 4365900)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 18191250x - 33957000x - 21101850x - 4365900)log(3x + 2) + 1212830x
+--R +
+--R 1495689x + 459996
+--R /
+--R 3 2
+--R 11250x + 21000x + 13050x + 2700
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (18191250x + 33957000x + 21101850x + 4365900)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 18191250x - 33957000x - 21101850x - 4365900)log(3x + 2) + 1212830x
+--R +
+--R 1495689x + 459996
+--R /
+--R 3 2
+--R 11250x + 21000x + 13050x + 2700
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(1-2*x)^3/((2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R (1) -----------------------------------------------------------
+--R 6 5 4 3 2
+--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216
+--R Type: Fraction(Polynomial(Integer))
+--E 466
+
+--S 467 of 500
+r0:=343/6/(2+3*x)^2+1617/(2+3*x)+(-1331/10)/(3+5*x)^2+2541/(3+5*x)-_
+ 15708*log(2+3*x)+15708*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (106029000x + 268606800x + 254940840x + 107442720x + 16964640)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 106029000x - 268606800x - 254940840x - 107442720x - 16964640)
+--R *
+--R log(3x + 2)
+--R +
+--R 3 2
+--R 7068600x + 13430348x + 8492784x + 1787403
+--R /
+--R 4 3 2
+--R 6750x + 17100x + 16230x + 6840x + 1080
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (106029000x + 268606800x + 254940840x + 107442720x + 16964640)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 106029000x - 268606800x - 254940840x - 107442720x - 16964640)
+--R *
+--R log(3x + 2)
+--R +
+--R 3 2
+--R 7068600x + 13430348x + 8492784x + 1787403
+--R /
+--R 4 3 2
+--R 6750x + 17100x + 16230x + 6840x + 1080
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(1-2*x)^3/((2+3*x)^4*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R -----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432
+--R Type: Fraction(Polynomial(Integer))
+--E 471
+
+--S 472 of 500
+r0:=343/9/(2+3*x)^3+1617/2/(2+3*x)^2+15708/(2+3*x)+(-1331/2)/(3+5*x)^2+_
+ 16698/(3+5*x)-128634*log(2+3*x)+128634*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 1562903100x + 5001289920x + 6397483356x + 4089017592x
+--R +
+--R 1305892368x + 166709664
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 1562903100x - 5001289920x - 6397483356x - 4089017592x
+--R +
+--R - 1305892368x - 166709664
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 104193540x + 267430086x + 257165096x + 109804551x + 17564616
+--R /
+--R 5 4 3 2
+--R 12150x + 38880x + 49734x + 31788x + 10152x + 1296
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 1562903100x + 5001289920x + 6397483356x + 4089017592x
+--R +
+--R 1305892368x + 166709664
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 1562903100x - 5001289920x - 6397483356x - 4089017592x
+--R +
+--R - 1305892368x - 166709664
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R 104193540x + 267430086x + 257165096x + 109804551x + 17564616
+--R /
+--R 5 4 3 2
+--R 12150x + 38880x + 49734x + 31788x + 10152x + 1296
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(1-2*x)^3/((2+3*x)^5*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x
+--R +
+--R 10800x + 864
+--R Type: Fraction(Polynomial(Integer))
+--E 476
+
+--S 477 of 500
+r0:=343/12/(2+3*x)^4+539/(2+3*x)^3+7854/(2+3*x)^2+128634/(2+3*x)+_
+ (-6655/2)/(3+5*x)^2+103455/(3+5*x)-953535*log(2+3*x)+953535*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 23170900500x + 89594148600x + 144277473780x + 123852754080x
+--R +
+--R 2
+--R 59775202080x + 15378612480x + 1647708480
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 23170900500x - 89594148600x - 144277473780x - 123852754080x
+--R +
+--R 2
+--R - 59775202080x - 15378612480x - 1647708480
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 1544726700x + 4994616330x + 6455813364x + 4169655991x + 1345680462x
+--R +
+--R 173603415
+--R /
+--R 6 5 4 3 2
+--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 23170900500x + 89594148600x + 144277473780x + 123852754080x
+--R +
+--R 2
+--R 59775202080x + 15378612480x + 1647708480
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4 3
+--R - 23170900500x - 89594148600x - 144277473780x - 123852754080x
+--R +
+--R 2
+--R - 59775202080x - 15378612480x - 1647708480
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R 1544726700x + 4994616330x + 6455813364x + 4169655991x + 1345680462x
+--R +
+--R 173603415
+--R /
+--R 6 5 4 3 2
+--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(1-2*x)^3/((2+3*x)^6*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R /
+--R 9 8 7 6 5 4
+--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x
+--R +
+--R 3 2
+--R 545840x + 150480x + 24192x + 1728
+--R Type: Fraction(Polynomial(Integer))
+--E 481
+
+--S 482 of 500
+r0:=343/15/(2+3*x)^5+1617/4/(2+3*x)^4+5236/(2+3*x)^3+64317/(2+3*x)^2+_
+ 953535/(2+3*x)+(-33275/2)/(3+5*x)^2+617100/(3+5*x)-_
+ 6618975*log(2+3*x)+6618975*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R 2412616387500x + 10937194290000x + 21241746949500x
+--R +
+--R 4 3 2
+--R 22910920065000x + 14821208820000x + 5750565480000x
+--R +
+--R 1239072120000x + 114375888000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 2412616387500x - 10937194290000x - 21241746949500x
+--R +
+--R 4 3 2
+--R - 22910920065000x - 14821208820000x - 5750565480000x
+--R +
+--R - 1239072120000x - 114375888000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 160841092500x + 627280260750x + 1018898535600x + 882286862985x
+--R +
+--R 2
+--R 429553050280x + 111486629505x + 12050702538
+--R /
+--R 7 6 5 4 3 2
+--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x
+--R +
+--R 187200x + 17280
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R 2412616387500x + 10937194290000x + 21241746949500x
+--R +
+--R 4 3 2
+--R 22910920065000x + 14821208820000x + 5750565480000x
+--R +
+--R 1239072120000x + 114375888000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 2412616387500x - 10937194290000x - 21241746949500x
+--R +
+--R 4 3 2
+--R - 22910920065000x - 14821208820000x - 5750565480000x
+--R +
+--R - 1239072120000x - 114375888000
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R 160841092500x + 627280260750x + 1018898535600x + 882286862985x
+--R +
+--R 2
+--R 429553050280x + 111486629505x + 12050702538
+--R /
+--R 7 6 5 4 3 2
+--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x
+--R +
+--R 187200x + 17280
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(1-2*x)^3/((2+3*x)^7*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R /
+--R 10 9 8 7 6 5
+--R 273375x + 1767825x + 5143095x + 8864559x + 10024182x + 7770924x
+--R +
+--R 4 3 2
+--R 4182360x + 1543120x + 373536x + 53568x + 3456
+--R Type: Fraction(Polynomial(Integer))
+--E 486
+
+--S 487 of 500
+r0:=343/18/(2+3*x)^6+1617/5/(2+3*x)^5+3927/(2+3*x)^4+42878/(2+3*x)^3+_
+ 953535/2/(2+3*x)^2+6618975/(2+3*x)+(-166375/2)/(3+5*x)^2+_
+ 3584625/(3+5*x)-43848750*log(2+3*x)+43848750*log(3+5*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R 71922912187500x + 373999143375000x + 850608308137500x
+--R +
+--R 5 4 3
+--R 1105162141050000x + 897171734250000x + 465989436000000x
+--R +
+--R 2
+--R 151225569000000x + 28035136800000x + 2273119200000
+--R *
+--R log(5x + 3)
+--R +
+--R 8 7 6
+--R - 71922912187500x - 373999143375000x - 850608308137500x
+--R +
+--R 5 4 3
+--R - 1105162141050000x - 897171734250000x - 465989436000000x
+--R +
+--R 2
+--R - 151225569000000x - 28035136800000x - 2273119200000
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R 4794860812500x + 21896531043750x + 42841193422500x + 46551705341625x
+--R +
+--R 3 2
+--R 30340145968110x + 11860532030465x + 2574943269792x + 239497011063
+--R /
+--R 8 7 6 5 4 3
+--R 1640250x + 8529300x + 19398690x + 25203960x + 20460600x + 10627200x
+--R +
+--R 2
+--R 3448800x + 639360x + 51840
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R 71922912187500x + 373999143375000x + 850608308137500x
+--R +
+--R 5 4 3
+--R 1105162141050000x + 897171734250000x + 465989436000000x
+--R +
+--R 2
+--R 151225569000000x + 28035136800000x + 2273119200000
+--R *
+--R log(5x + 3)
+--R +
+--R 8 7 6
+--R - 71922912187500x - 373999143375000x - 850608308137500x
+--R +
+--R 5 4 3
+--R - 1105162141050000x - 897171734250000x - 465989436000000x
+--R +
+--R 2
+--R - 151225569000000x - 28035136800000x - 2273119200000
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R 4794860812500x + 21896531043750x + 42841193422500x + 46551705341625x
+--R +
+--R 3 2
+--R 30340145968110x + 11860532030465x + 2574943269792x + 239497011063
+--R /
+--R 8 7 6 5 4 3
+--R 1640250x + 8529300x + 19398690x + 25203960x + 20460600x + 10627200x
+--R +
+--R 2
+--R 3448800x + 639360x + 51840
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(1-2*x)^3/((2+3*x)^8*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 8x + 12x - 6x + 1
+--R /
+--R 11 10 9 8 7
+--R 820125x + 5850225x + 18964935x + 36879867x + 47801664x
+--R +
+--R 6 5 4 3 2
+--R 43361136x + 28088928x + 12994080x + 4206848x + 907776x + 117504x
+--R +
+--R 6912
+--R Type: Fraction(Polynomial(Integer))
+--E 491
+
+--S 492 of 500
+r0:=49/3/(2+3*x)^7+539/2/(2+3*x)^6+15708/5/(2+3*x)^5+64317/2/(2+3*x)^4+_
+ 317845/(2+3*x)^3+6618975/2/(2+3*x)^2+43848750/(2+3*x)+_
+ (-831875/2)/(3+5*x)^2+20418750/(3+5*x)-280500000*log(2+3*x)+_
+ 280500000*log(3+5*x)
+--R
+--R
+--R (2)
+--R 9 8 7
+--R 460090125000000x + 2699195400000000x + 7036311645000000x
+--R +
+--R 6 5 4
+--R 10697265810000000x + 10452338820000000x + 6807061800000000x
+--R +
+--R 3 2
+--R 2954674800000000x + 824266080000000x + 134101440000000x
+--R +
+--R 9694080000000
+--R *
+--R log(5x + 3)
+--R +
+--R 9 8 7
+--R - 460090125000000x - 2699195400000000x - 7036311645000000x
+--R +
+--R 6 5 4
+--R - 10697265810000000x - 10452338820000000x - 6807061800000000x
+--R +
+--R 3 2
+--R - 2954674800000000x - 824266080000000x - 134101440000000x
+--R +
+--R - 9694080000000
+--R *
+--R log(3x + 2)
+--R +
+--R 8 7 6
+--R 30672675000000x + 160520332500000x + 367435926000000x
+--R +
+--R 5 4 3
+--R 480493891350000x + 392612784696000x + 205262100529200x
+--R +
+--R 2
+--R 67053019228048x + 12513316868859x + 1021373267628
+--R /
+--R 9 8 7 6 5 4
+--R 1640250x + 9622800x + 25084890x + 38136420x + 37263240x + 24267600x
+--R +
+--R 3 2
+--R 10533600x + 2938560x + 478080x + 34560
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7
+--R 460090125000000x + 2699195400000000x + 7036311645000000x
+--R +
+--R 6 5 4
+--R 10697265810000000x + 10452338820000000x + 6807061800000000x
+--R +
+--R 3 2
+--R 2954674800000000x + 824266080000000x + 134101440000000x
+--R +
+--R 9694080000000
+--R *
+--R log(5x + 3)
+--R +
+--R 9 8 7
+--R - 460090125000000x - 2699195400000000x - 7036311645000000x
+--R +
+--R 6 5 4
+--R - 10697265810000000x - 10452338820000000x - 6807061800000000x
+--R +
+--R 3 2
+--R - 2954674800000000x - 824266080000000x - 134101440000000x
+--R +
+--R - 9694080000000
+--R *
+--R log(3x + 2)
+--R +
+--R 8 7 6
+--R 30672675000000x + 160520332500000x + 367435926000000x
+--R +
+--R 5 4 3
+--R 480493891350000x + 392612784696000x + 205262100529200x
+--R +
+--R 2
+--R 67053019228048x + 12513316868859x + 1021373267628
+--R /
+--R 9 8 7 6 5 4
+--R 1640250x + 9622800x + 25084890x + 38136420x + 37263240x + 24267600x
+--R +
+--R 3 2
+--R 10533600x + 2938560x + 478080x + 34560
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(2+3*x)^m*(3+5*x)/(1-2*x)
+--R
+--R
+--R m
+--R (- 5x - 3)(3x + 2)
+--R (1) -------------------
+--R 2x - 1
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+--r0:=-5/6*(2+3*x)^(1+m)/(1+m)+11/14*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)
+--E 497
+
+--S 498 of 500
+--a0:=integrate(t0,x)
+--E 498
+
+--S 499 of 500
+--m0:=a0-r0
+--E 499
+
+--S 500 of 500
+--d0:=D(m0,x)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3f.input.pdf b/src/axiom-website/CATS/rich3f.input.pdf
new file mode 100644
index 0000000..a20d0ea
Binary files /dev/null and b/src/axiom-website/CATS/rich3f.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3g.input.pamphlet b/src/axiom-website/CATS/rich3g.input.pamphlet
new file mode 100644
index 0000000..fe9418d
--- /dev/null
+++ b/src/axiom-website/CATS/rich3g.input.pamphlet
@@ -0,0 +1,6855 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3g.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 95 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 5 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3g.output
+)spool rich3g.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(2+3*x)^8*(3+5*x)/(1-2*x)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4
+--R - 32805x - 194643x - 513216x - 789264x - 780192x - 514080x
+--R +
+--R 3 2
+--R - 225792x - 63744x - 10496x - 768
+--R /
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1
+
+--S 2 of 500
+r0:=-63019595/512*x-60332619/512*x^2-17391129/128*x^3-37722699/256*x^4-_
+ 21272139/160*x^5-2929689/32*x^6-353565/8*x^7-422091/32*x^8-_
+ 3645/2*x^9-63412811/1024*log(1-2*x)
+--R
+--R
+--R (2)
+--R 9 8 7
+--R - 317064055log(- 2x + 1) - 9331200x - 67534560x - 226281600x
+--R +
+--R 6 5 4 3 2
+--R - 468750240x - 680708448x - 754453980x - 695645160x - 603326190x
+--R +
+--R - 630195950x
+--R /
+--R 5120
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7
+--R - 317064055log(2x - 1) - 9331200x - 67534560x - 226281600x
+--R +
+--R 6 5 4 3 2
+--R - 468750240x - 680708448x - 754453980x - 695645160x - 603326190x
+--R +
+--R - 630195950x
+--R /
+--R 5120
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500
+m0:=a0-r0
+--R
+--R
+--R - 63412811log(2x - 1) + 63412811log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 1024
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(2+3*x)^7*(3+5*x)/(1-2*x)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 10935x - 57591x - 132678x - 174636x - 143640x - 75600x - 24864x
+--R +
+--R - 4672x - 384
+--R /
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 6
+
+--S 7 of 500
+r0:=-8960669/256*x-8362653/256*x^2-2257119/64*x^3-4352157/128*x^4-_
+ 2053917/80*x^5-218943/16*x^6-126117/28*x^7-10935/16*x^8-_
+ 9058973/512*log(1-2*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R - 317064055log(- 2x + 1) - 12247200x - 80714880x - 245216160x
+--R +
+--R 5 4 3 2
+--R - 460077408x - 609301980x - 631993320x - 585385710x - 627246830x
+--R /
+--R 17920
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R - 317064055log(2x - 1) - 12247200x - 80714880x - 245216160x
+--R +
+--R 5 4 3 2
+--R - 460077408x - 609301980x - 631993320x - 585385710x - 627246830x
+--R /
+--R 17920
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 500
+m0:=a0-r0
+--R
+--R
+--R - 9058973log(2x - 1) + 9058973log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 512
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(2+3*x)^6*(3+5*x)/(1-2*x)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 3645x - 16767x - 33048x - 36180x - 23760x - 9360x - 2048x - 192
+--R -----------------------------------------------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 11
+
+--S 12 of 500
+r0:=-1269563/128*x-1138491/128*x^2-279657/32*x^3-458811/64*x^4-_
+ 169371/40*x^5-12393/8*x^6-3645/14*x^7-1294139/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R - 45294865log(- 2x + 1) - 2332800x - 13880160x - 37939104x
+--R +
+--R 4 3 2
+--R - 64233540x - 78303960x - 79694370x - 88869410x
+--R /
+--R 8960
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R - 45294865log(2x - 1) - 2332800x - 13880160x - 37939104x - 64233540x
+--R +
+--R 3 2
+--R - 78303960x - 79694370x - 88869410x
+--R /
+--R 8960
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1294139log(2x - 1) + 1294139log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(2+3*x)^5*(3+5*x)/(1-2*x)
+--R
+--R
+--R 6 5 4 3 2
+--R - 1215x - 4779x - 7830x - 6840x - 3360x - 880x - 96
+--R (1) --------------------------------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 16
+
+--S 17 of 500
+r0:=-178733/64*x-150573/64*x^2-32271/16*x^3-42093/32*x^4-10773/20*x^5-_
+ 405/4*x^6-184877/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R - 924385log(- 2x + 1) - 64800x - 344736x - 841860x - 1290840x
+--R +
+--R 2
+--R - 1505730x - 1787330x
+--R /
+--R 640
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R - 924385log(2x - 1) - 64800x - 344736x - 841860x - 1290840x
+--R +
+--R 2
+--R - 1505730x - 1787330x
+--R /
+--R 640
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 500
+m0:=a0-r0
+--R
+--R
+--R - 184877log(2x - 1) + 184877log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(2+3*x)^4*(3+5*x)/(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R - 405x - 1323x - 1728x - 1128x - 368x - 48
+--R (1) ----------------------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 21
+
+--S 22 of 500
+r0:=-24875/32*x-18987/32*x^2-3321/8*x^3-3051/16*x^4-81/2*x^5-_
+ 26411/64*log(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R - 26411log(- 2x + 1) - 2592x - 12204x - 26568x - 37974x - 49750x
+--R (2) --------------------------------------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R - 26411log(2x - 1) - 2592x - 12204x - 26568x - 37974x - 49750x
+--R (3) ------------------------------------------------------------------
+--R 64
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 500
+m0:=a0-r0
+--R
+--R
+--R - 26411log(2x - 1) + 26411log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(2+3*x)^3*(3+5*x)/(1-2*x)
+--R
+--R
+--R 4 3 2
+--R - 135x - 351x - 342x - 148x - 24
+--R (1) -----------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 26
+
+--S 27 of 500
+r0:=-3389/16*x-2205/16*x^2-279/4*x^3-135/8*x^4-3773/32*log(1-2*x)
+--R
+--R
+--R 4 3 2
+--R - 3773log(- 2x + 1) - 540x - 2232x - 4410x - 6778x
+--R (2) -----------------------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R - 3773log(2x - 1) - 540x - 2232x - 4410x - 6778x
+--R (3) ---------------------------------------------------
+--R 32
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 500
+m0:=a0-r0
+--R
+--R
+--R - 3773log(2x - 1) + 3773log(- 2x + 1)
+--R (4) -------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(2+3*x)^2*(3+5*x)/(1-2*x)
+--R
+--R
+--R 3 2
+--R - 45x - 87x - 56x - 12
+--R (1) ------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 31
+
+--S 32 of 500
+r0:=-443/8*x-219/8*x^2-15/2*x^3-539/16*log(1-2*x)
+--R
+--R
+--R 3 2
+--R - 539log(- 2x + 1) - 120x - 438x - 886x
+--R (2) -----------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R - 539log(2x - 1) - 120x - 438x - 886x
+--R (3) ---------------------------------------
+--R 16
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 500
+m0:=a0-r0
+--R
+--R
+--R - 539log(2x - 1) + 539log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(2+3*x)*(3+5*x)/(1-2*x)
+--R
+--R
+--R 2
+--R - 15x - 19x - 6
+--R (1) ----------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 36
+
+--S 37 of 500
+r0:=-53/4*x-15/4*x^2-77/8*log(1-2*x)
+--R
+--R
+--R 2
+--R - 77log(- 2x + 1) - 30x - 106x
+--R (2) -------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 77log(2x - 1) - 30x - 106x
+--R (3) -----------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 500
+m0:=a0-r0
+--R
+--R
+--R - 77log(2x - 1) + 77log(- 2x + 1)
+--R (4) ---------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(3+5*x)/(1-2*x)
+--R
+--R
+--R - 5x - 3
+--R (1) --------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 41
+
+--S 42 of 500
+r0:=-5/2*x-11/4*log(1-2*x)
+--R
+--R
+--R - 11log(- 2x + 1) - 10x
+--R (2) -----------------------
+--R 4
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R - 11log(2x - 1) - 10x
+--R (3) ---------------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500
+m0:=a0-r0
+--R
+--R
+--R - 11log(2x - 1) + 11log(- 2x + 1)
+--R (4) ---------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(3+5*x)/((1-2*x)*(2+3*x))
+--R
+--R
+--R - 5x - 3
+--R (1) -----------
+--R 2
+--R 6x + x - 2
+--R Type: Fraction(Polynomial(Integer))
+--E 46
+
+--S 47 of 500
+r0:=-11/14*log(1-2*x)-1/21*log(2+3*x)
+--R
+--R
+--R - 2log(3x + 2) - 33log(- 2x + 1)
+--R (2) --------------------------------
+--R 42
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R - 2log(3x + 2) - 33log(2x - 1)
+--R (3) ------------------------------
+--R 42
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500
+m0:=a0-r0
+--R
+--R
+--R - 11log(2x - 1) + 11log(- 2x + 1)
+--R (4) ---------------------------------
+--R 14
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(3+5*x)/((1-2*x)*(2+3*x)^2)
+--R
+--R
+--R - 5x - 3
+--R (1) --------------------
+--R 3 2
+--R 18x + 15x - 4x - 4
+--R Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 500
+r0:=1/21/(2+3*x)-11/49*log(1-2*x)+11/49*log(2+3*x)
+--R
+--R
+--R (99x + 66)log(3x + 2) + (- 99x - 66)log(- 2x + 1) + 7
+--R (2) -----------------------------------------------------
+--R 441x + 294
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (99x + 66)log(3x + 2) + (- 99x - 66)log(2x - 1) + 7
+--R (3) ---------------------------------------------------
+--R 441x + 294
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500
+m0:=a0-r0
+--R
+--R
+--R - 11log(2x - 1) + 11log(- 2x + 1)
+--R (4) ---------------------------------
+--R 49
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(3+5*x)/((1-2*x)*(2+3*x)^3)
+--R
+--R
+--R - 5x - 3
+--R (1) ----------------------------
+--R 4 3 2
+--R 54x + 81x + 18x - 20x - 8
+--R Type: Fraction(Polynomial(Integer))
+--E 56
+
+--S 57 of 500
+r0:=1/42/(2+3*x)^2+(-11/49)/(2+3*x)-22/343*log(1-2*x)+22/343*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (1188x + 1584x + 528)log(3x + 2) + (- 1188x - 1584x - 528)log(- 2x + 1)
+--R +
+--R - 1386x - 875
+--R /
+--R 2
+--R 18522x + 24696x + 8232
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (1188x + 1584x + 528)log(3x + 2) + (- 1188x - 1584x - 528)log(2x - 1)
+--R +
+--R - 1386x - 875
+--R /
+--R 2
+--R 18522x + 24696x + 8232
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 500
+m0:=a0-r0
+--R
+--R
+--R - 22log(2x - 1) + 22log(- 2x + 1)
+--R (4) ---------------------------------
+--R 343
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(3+5*x)/((1-2*x)*(2+3*x)^4)
+--R
+--R
+--R - 5x - 3
+--R (1) ---------------------------------------
+--R 5 4 3 2
+--R 162x + 351x + 216x - 24x - 64x - 16
+--R Type: Fraction(Polynomial(Integer))
+--E 61
+
+--S 62 of 500
+r0:=1/63/(2+3*x)^3+(-11/98)/(2+3*x)^2+(-22/343)/(2+3*x)-_
+ 44/2401*log(1-2*x)+44/2401*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (21384x + 42768x + 28512x + 6336)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 21384x - 42768x - 28512x - 6336)log(- 2x + 1) - 24948x - 47817x
+--R +
+--R - 20104
+--R /
+--R 3 2
+--R 1166886x + 2333772x + 1555848x + 345744
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (21384x + 42768x + 28512x + 6336)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 21384x - 42768x - 28512x - 6336)log(2x - 1) - 24948x - 47817x - 20104
+--R /
+--R 3 2
+--R 1166886x + 2333772x + 1555848x + 345744
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 500
+m0:=a0-r0
+--R
+--R
+--R - 44log(2x - 1) + 44log(- 2x + 1)
+--R (4) ---------------------------------
+--R 2401
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(3+5*x)/((1-2*x)*(2+3*x)^5)
+--R
+--R
+--R - 5x - 3
+--R (1) ---------------------------------------------------
+--R 6 5 4 3 2
+--R 486x + 1377x + 1350x + 360x - 240x - 176x - 32
+--R Type: Fraction(Polynomial(Integer))
+--E 66
+
+--S 67 of 500
+r0:=1/84/(2+3*x)^4+(-11/147)/(2+3*x)^3+(-11/343)/(2+3*x)^2+_
+ (-44/2401)/(2+3*x)-88/16807*log(1-2*x)+88/16807*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (28512x + 76032x + 76032x + 33792x + 5632)log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 28512x - 76032x - 76032x - 33792x - 5632)log(- 2x + 1) - 33264x
+--R +
+--R 2
+--R - 85932x - 85316x - 27741
+--R /
+--R 4 3 2
+--R 5445468x + 14521248x + 14521248x + 6453888x + 1075648
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (28512x + 76032x + 76032x + 33792x + 5632)log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 28512x - 76032x - 76032x - 33792x - 5632)log(2x - 1) - 33264x
+--R +
+--R 2
+--R - 85932x - 85316x - 27741
+--R /
+--R 4 3 2
+--R 5445468x + 14521248x + 14521248x + 6453888x + 1075648
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 500
+m0:=a0-r0
+--R
+--R
+--R - 88log(2x - 1) + 88log(- 2x + 1)
+--R (4) ---------------------------------
+--R 16807
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(3+5*x)/((1-2*x)*(2+3*x)^6)
+--R
+--R
+--R - 5x - 3
+--R (1) ------------------------------------------------------
+--R 7 6 5 4 2
+--R 1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64
+--R Type: Fraction(Polynomial(Integer))
+--E 71
+
+--S 72 of 500
+r0:=1/105/(2+3*x)^5+(-11/196)/(2+3*x)^4+(-22/1029)/(2+3*x)^3+_
+ (-22/2401)/(2+3*x)^2+(-88/16807)/(2+3*x)-176/117649*log(1-2*x)+_
+ 176/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (2566080x + 8553600x + 11404800x + 7603200x + 2534400x + 337920)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 2566080x - 8553600x - 11404800x - 7603200x - 2534400x - 337920)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 2993760x - 9729720x - 12834360x - 8876175x - 2437582
+--R /
+--R 5 4 3 2
+--R 1715322420x + 5717741400x + 7623655200x + 5082436800x + 1694145600x
+--R +
+--R 225886080
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (2566080x + 8553600x + 11404800x + 7603200x + 2534400x + 337920)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 2566080x - 8553600x - 11404800x - 7603200x - 2534400x - 337920)
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 2993760x - 9729720x - 12834360x - 8876175x - 2437582
+--R /
+--R 5 4 3 2
+--R 1715322420x + 5717741400x + 7623655200x + 5082436800x + 1694145600x
+--R +
+--R 225886080
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 500
+m0:=a0-r0
+--R
+--R
+--R - 176log(2x - 1) + 176log(- 2x + 1)
+--R (4) -----------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(3+5*x)/((1-2*x)*(2+3*x)^7)
+--R
+--R
+--R (1)
+--R - 5x - 3
+--R -----------------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 4374x + 18225x + 30618x + 24948x + 7560x - 3024x - 3360x - 1088x - 128
+--R Type: Fraction(Polynomial(Integer))
+--E 76
+
+--S 77 of 500
+r0:=1/126/(2+3*x)^6+(-11/245)/(2+3*x)^5+(-11/686)/(2+3*x)^4+_
+ (-44/7203)/(2+3*x)^3+(-44/16807)/(2+3*x)^2+(-176/117649)/(2+3*x)-_
+ 352/823543*log(1-2*x)+352/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 23094720x + 92378880x + 153964800x + 136857600x + 68428800x
+--R +
+--R 18247680x + 2027520
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 23094720x - 92378880x - 153964800x - 136857600x - 68428800x
+--R +
+--R - 18247680x - 2027520
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 26943840x - 105530040x - 173887560x - 156891735x - 85783698x
+--R +
+--R - 21096187
+--R /
+--R 6 5 4 3
+--R 54032656230x + 216130624920x + 360217708200x + 320193518400x
+--R +
+--R 2
+--R 160096759200x + 42692469120x + 4743607680
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 23094720x + 92378880x + 153964800x + 136857600x + 68428800x
+--R +
+--R 18247680x + 2027520
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 23094720x - 92378880x - 153964800x - 136857600x - 68428800x
+--R +
+--R - 18247680x - 2027520
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 26943840x - 105530040x - 173887560x - 156891735x - 85783698x
+--R +
+--R - 21096187
+--R /
+--R 6 5 4 3
+--R 54032656230x + 216130624920x + 360217708200x + 320193518400x
+--R +
+--R 2
+--R 160096759200x + 42692469120x + 4743607680
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 500
+m0:=a0-r0
+--R
+--R
+--R - 352log(2x - 1) + 352log(- 2x + 1)
+--R (4) -----------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(3+5*x)/((1-2*x)*(2+3*x)^8)
+--R
+--R
+--R (1)
+--R - 5x - 3
+--R /
+--R 9 8 7 6 5 4 3
+--R 13122x + 63423x + 128304x + 136080x + 72576x + 6048x - 16128x
+--R +
+--R 2
+--R - 9984x - 2560x - 256
+--R Type: Fraction(Polynomial(Integer))
+--E 81
+
+--S 82 of 500
+r0:=1/147/(2+3*x)^7+(-11/294)/(2+3*x)^6+(-22/1715)/(2+3*x)^5+_
+ (-11/2401)/(2+3*x)^4+(-88/50421)/(2+3*x)^3+(-88/117649)/(2+3*x)^2+_
+ (-352/823543)/(2+3*x)-704/5764801*log(1-2*x)+704/5764801*log(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3
+--R 46189440x + 215550720x + 431101440x + 479001600x + 319334400x
+--R +
+--R 2
+--R 127733760x + 28385280x + 2703360
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4 3
+--R - 46189440x - 215550720x - 431101440x - 479001600x - 319334400x
+--R +
+--R 2
+--R - 127733760x - 28385280x - 2703360
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3 2
+--R - 53887680x - 246985200x - 488481840x - 545633550x - 380756376x
+--R +
+--R - 177159213x - 40677476
+--R /
+--R 7 6 5 4
+--R 378228593610x + 1765066770180x + 3530133540360x + 3922370600400x
+--R +
+--R 3 2
+--R 2614913733600x + 1045965493440x + 232436776320x + 22136835840
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R 46189440x + 215550720x + 431101440x + 479001600x + 319334400x
+--R +
+--R 2
+--R 127733760x + 28385280x + 2703360
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4 3
+--R - 46189440x - 215550720x - 431101440x - 479001600x - 319334400x
+--R +
+--R 2
+--R - 127733760x - 28385280x - 2703360
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3 2
+--R - 53887680x - 246985200x - 488481840x - 545633550x - 380756376x
+--R +
+--R - 177159213x - 40677476
+--R /
+--R 7 6 5 4
+--R 378228593610x + 1765066770180x + 3530133540360x + 3922370600400x
+--R +
+--R 3 2
+--R 2614913733600x + 1045965493440x + 232436776320x + 22136835840
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500
+m0:=a0-r0
+--R
+--R
+--R - 704log(2x - 1) + 704log(- 2x + 1)
+--R (4) -----------------------------------
+--R 5764801
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(2+3*x)^m*(3+5*x)^2/(1-2*x)
+--R
+--R
+--R 2 m
+--R (- 25x - 30x - 9)(3x + 2)
+--R (1) ---------------------------
+--R 2x - 1
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+--r0:=-5/36*(64+33*m)*(2+3*x)^(1+m)/((1+m)*(2+m))-_
+-- 5/6*(2+3*x)^(1+m)*(3+5*x)/(2+m)+121/28*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)
+--E 87
+
+--S 88 of 500
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 500
+--m0:=a0-r0
+--E 89
+
+--S 90 of 500
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(2+3*x)^8*(3+5*x)^2/(1-2*x)
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5
+--R - 164025x - 1071630x - 3150009x - 5485968x - 6268752x - 4910976x
+--R +
+--R 4 3 2
+--R - 2671200x - 996096x - 243712x - 35328x - 2304
+--R /
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 91
+
+--S 92 of 500
+r0:=-695181625/1024*x-677093689/1024*x^2-204901139/256*x^3-_
+ 487203129/512*x^4-316246329/320*x^5-53031699/64*x^6-8399295/16*x^7-_
+ 14907321/64*x^8-256365/4*x^9-32805/4*x^10-697540921/2048*log(1-2*x)
+--R
+--R
+--R (2)
+--R 10 9 8
+--R - 3487704605log(- 2x + 1) - 83980800x - 656294400x - 2385171360x
+--R +
+--R 7 6 5 4
+--R - 5375548800x - 8485071840x - 10119882528x - 9744062580x
+--R +
+--R 3 2
+--R - 8196045560x - 6770936890x - 6951816250x
+--R /
+--R 10240
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 8
+--R - 3487704605log(2x - 1) - 83980800x - 656294400x - 2385171360x
+--R +
+--R 7 6 5 4
+--R - 5375548800x - 8485071840x - 10119882528x - 9744062580x
+--R +
+--R 3 2
+--R - 8196045560x - 6770936890x - 6951816250x
+--R /
+--R 10240
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500
+m0:=a0-r0
+--R
+--R
+--R - 697540921log(2x - 1) + 697540921log(- 2x + 1)
+--R (4) -----------------------------------------------
+--R 2048
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(2+3*x)^7*(3+5*x)^2/(1-2*x)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4
+--R - 54675x - 320760x - 836163x - 1271214x - 1242108x - 808920x
+--R +
+--R 3 2
+--R - 351120x - 97952x - 15936x - 1152
+--R /
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 96
+
+--S 97 of 500
+r0:=-99058879/512*x-94979263/512*x^2-27480469/128*x^3-59969727/256*x^4-_
+ 34084287/160*x^5-4736853/32*x^6-4040847/56*x^7-696195/32*x^8-_
+ 6075/2*x^9-99648703/1024*log(1-2*x)
+--R
+--R
+--R (2)
+--R 9 8 7
+--R - 3487704605log(- 2x + 1) - 108864000x - 779738400x - 2586142080x
+--R +
+--R 6 5 4 3
+--R - 5305275360x - 7634880288x - 8395761780x - 7694531320x
+--R +
+--R 2
+--R - 6648548410x - 6934121530x
+--R /
+--R 35840
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7
+--R - 3487704605log(2x - 1) - 108864000x - 779738400x - 2586142080x
+--R +
+--R 6 5 4 3
+--R - 5305275360x - 7634880288x - 8395761780x - 7694531320x
+--R +
+--R 2
+--R - 6648548410x - 6934121530x
+--R /
+--R 35840
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500
+m0:=a0-r0
+--R
+--R
+--R - 99648703log(2x - 1) + 99648703log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 1024
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(2+3*x)^6*(3+5*x)^2/(1-2*x)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 18225x - 94770x - 215541x - 280044x - 227340x - 118080x - 38320x
+--R +
+--R - 7104x - 576
+--R /
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 500
+r0:=-14088073/256*x-13178761/256*x^2-3575427/64*x^3-6947721/128*x^4-_
+ 3310281/80*x^5-356643/16*x^6-207765/28*x^7-18225/16*x^8-_
+ 14235529/512*log(1-2*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R - 498243515log(- 2x + 1) - 20412000x - 132969600x - 399440160x
+--R +
+--R 5 4 3 2
+--R - 741502944x - 972680940x - 1001119560x - 922513270x - 986165110x
+--R /
+--R 17920
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R - 498243515log(2x - 1) - 20412000x - 132969600x - 399440160x
+--R +
+--R 5 4 3 2
+--R - 741502944x - 972680940x - 1001119560x - 922513270x - 986165110x
+--R /
+--R 17920
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 500
+m0:=a0-r0
+--R
+--R
+--R - 14235529log(2x - 1) + 14235529log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 512
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 6075x - 27540x - 53487x - 57690x - 37320x - 14480x - 3120x - 288
+--R ------------------------------------------------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 106
+
+--S 107 of 500
+r0:=-1996783/128*x-1797103/128*x^2-444581/32*x^3-736623/64*x^4-_
+ 275103/40*x^5-20385/8*x^6-6075/14*x^7-2033647/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R - 71177645log(- 2x + 1) - 3888000x - 22831200x - 61623072x
+--R +
+--R 4 3 2
+--R - 103127220x - 124482680x - 125797210x - 139774810x
+--R /
+--R 8960
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R - 71177645log(2x - 1) - 3888000x - 22831200x - 61623072x - 103127220x
+--R +
+--R 3 2
+--R - 124482680x - 125797210x - 139774810x
+--R /
+--R 8960
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2033647log(2x - 1) + 2033647log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)
+--R
+--R
+--R 6 5 4 3 2
+--R - 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144
+--R (1) ------------------------------------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 111
+
+--S 112 of 500
+r0:=-281305/64*x-238297/64*x^2-51571/16*x^3-68121/32*x^4-3537/4*x^5-_
+ 675/4*x^6-290521/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R - 290521log(- 2x + 1) - 21600x - 113184x - 272484x - 412568x
+--R +
+--R 2
+--R - 476594x - 562610x
+--R /
+--R 128
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 290521log(2x - 1) - 21600x - 113184x - 272484x - 412568x - 476594x
+--R +
+--R - 562610x
+--R /
+--R 128
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 500
+m0:=a0-r0
+--R
+--R
+--R - 290521log(2x - 1) + 290521log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R - 675x - 2160x - 2763x - 1766x - 564x - 72
+--R (1) ----------------------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 116
+
+--S 117 of 500
+r0:=-39199/32*x-30175/32*x^2-5349/8*x^3-4995/16*x^4-135/2*x^5-_
+ 41503/64*log(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R - 41503log(- 2x + 1) - 4320x - 19980x - 42792x - 60350x - 78398x
+--R (2) --------------------------------------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R - 41503log(2x - 1) - 4320x - 19980x - 42792x - 60350x - 78398x
+--R (3) ------------------------------------------------------------------
+--R 64
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 500
+m0:=a0-r0
+--R
+--R
+--R - 41503log(2x - 1) + 41503log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)
+--R
+--R
+--R 4 3 2
+--R - 225x - 570x - 541x - 228x - 36
+--R (1) -----------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 121
+
+--S 122 of 500
+r0:=-5353/16*x-3529/16*x^2-455/4*x^3-225/8*x^4-5929/32*log(1-2*x)
+--R
+--R
+--R 4 3 2
+--R - 5929log(- 2x + 1) - 900x - 3640x - 7058x - 10706x
+--R (2) ------------------------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R - 5929log(2x - 1) - 900x - 3640x - 7058x - 10706x
+--R (3) ----------------------------------------------------
+--R 32
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 500
+m0:=a0-r0
+--R
+--R
+--R - 5929log(2x - 1) + 5929log(- 2x + 1)
+--R (4) -------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(2+3*x)*(3+5*x)^2/(1-2*x)
+--R
+--R
+--R 3 2
+--R - 75x - 140x - 87x - 18
+--R (1) -------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 126
+
+--S 127 of 500
+r0:=-703/8*x-355/8*x^2-25/2*x^3-847/16*log(1-2*x)
+--R
+--R
+--R 3 2
+--R - 847log(- 2x + 1) - 200x - 710x - 1406x
+--R (2) ------------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R - 847log(2x - 1) - 200x - 710x - 1406x
+--R (3) ----------------------------------------
+--R 16
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 500
+m0:=a0-r0
+--R
+--R
+--R - 847log(2x - 1) + 847log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(3+5*x)^2/(1-2*x)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ----------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 131
+
+--S 132 of 500
+r0:=-85/4*x-25/4*x^2-121/8*log(1-2*x)
+--R
+--R
+--R 2
+--R - 121log(- 2x + 1) - 50x - 170x
+--R (2) --------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 121log(2x - 1) - 50x - 170x
+--R (3) ------------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 500
+m0:=a0-r0
+--R
+--R
+--R - 121log(2x - 1) + 121log(- 2x + 1)
+--R (4) -----------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(3+5*x)^2/((1-2*x)*(2+3*x))
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ----------------
+--R 2
+--R 6x + x - 2
+--R Type: Fraction(Polynomial(Integer))
+--E 136
+
+--S 137 of 500
+r0:=-25/6*x-121/28*log(1-2*x)+1/63*log(2+3*x)
+--R
+--R
+--R 4log(3x + 2) - 1089log(- 2x + 1) - 1050x
+--R (2) ----------------------------------------
+--R 252
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4log(3x + 2) - 1089log(2x - 1) - 1050x
+--R (3) --------------------------------------
+--R 252
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 500
+m0:=a0-r0
+--R
+--R
+--R - 121log(2x - 1) + 121log(- 2x + 1)
+--R (4) -----------------------------------
+--R 28
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^2)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) --------------------
+--R 3 2
+--R 18x + 15x - 4x - 4
+--R Type: Fraction(Polynomial(Integer))
+--E 141
+
+--S 142 of 500
+r0:=(-1/63)/(2+3*x)-121/98*log(1-2*x)-68/441*log(2+3*x)
+--R
+--R
+--R (- 408x - 272)log(3x + 2) + (- 3267x - 2178)log(- 2x + 1) - 14
+--R (2) --------------------------------------------------------------
+--R 2646x + 1764
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (- 408x - 272)log(3x + 2) + (- 3267x - 2178)log(2x - 1) - 14
+--R (3) ------------------------------------------------------------
+--R 2646x + 1764
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500
+m0:=a0-r0
+--R
+--R
+--R - 121log(2x - 1) + 121log(- 2x + 1)
+--R (4) -----------------------------------
+--R 98
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^3)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ----------------------------
+--R 4 3 2
+--R 54x + 81x + 18x - 20x - 8
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 500
+r0:=(-1/126)/(2+3*x)^2+68/441/(2+3*x)-121/343*log(1-2*x)+121/343*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2
+--R (19602x + 26136x + 8712)log(3x + 2)
+--R +
+--R 2
+--R (- 19602x - 26136x - 8712)log(- 2x + 1) + 2856x + 1855
+--R /
+--R 2
+--R 55566x + 74088x + 24696
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (19602x + 26136x + 8712)log(3x + 2)
+--R +
+--R 2
+--R (- 19602x - 26136x - 8712)log(2x - 1) + 2856x + 1855
+--R /
+--R 2
+--R 55566x + 74088x + 24696
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500
+m0:=a0-r0
+--R
+--R
+--R - 121log(2x - 1) + 121log(- 2x + 1)
+--R (4) -----------------------------------
+--R 343
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^4)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ---------------------------------------
+--R 5 4 3 2
+--R 162x + 351x + 216x - 24x - 64x - 16
+--R Type: Fraction(Polynomial(Integer))
+--E 151
+
+--S 152 of 500
+r0:=(-1/189)/(2+3*x)^3+34/441/(2+3*x)^2+(-121/343)/(2+3*x)-_
+ 242/2401*log(1-2*x)+242/2401*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (176418x + 352836x + 235224x + 52272)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 176418x - 352836x - 235224x - 52272)log(- 2x + 1) - 205821x
+--R +
+--R - 259434x - 81823
+--R /
+--R 3 2
+--R 1750329x + 3500658x + 2333772x + 518616
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (176418x + 352836x + 235224x + 52272)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 176418x - 352836x - 235224x - 52272)log(2x - 1) - 205821x - 259434x
+--R +
+--R - 81823
+--R /
+--R 3 2
+--R 1750329x + 3500658x + 2333772x + 518616
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R - 242log(2x - 1) + 242log(- 2x + 1)
+--R (4) -----------------------------------
+--R 2401
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^5)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ---------------------------------------------------
+--R 6 5 4 3 2
+--R 486x + 1377x + 1350x + 360x - 240x - 176x - 32
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 500
+r0:=(-1/252)/(2+3*x)^4+68/1323/(2+3*x)^3+(-121/686)/(2+3*x)^2+(-242/2401)/_
+ (2+3*x)-484/16807*log(1-2*x)+484/16807*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (4234032x + 11290752x + 11290752x + 5018112x + 836352)log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 4234032x - 11290752x - 11290752x - 5018112x - 836352)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 4939704x - 12760902x - 10148376x - 2564891
+--R /
+--R 4 3 2
+--R 147027636x + 392073696x + 392073696x + 174254976x + 29042496
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (4234032x + 11290752x + 11290752x + 5018112x + 836352)log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 4234032x - 11290752x - 11290752x - 5018112x - 836352)log(2x - 1)
+--R +
+--R 3 2
+--R - 4939704x - 12760902x - 10148376x - 2564891
+--R /
+--R 4 3 2
+--R 147027636x + 392073696x + 392073696x + 174254976x + 29042496
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R - 484log(2x - 1) + 484log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16807
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^6)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ------------------------------------------------------
+--R 7 6 5 4 2
+--R 1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64
+--R Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 500
+r0:=(-1/315)/(2+3*x)^5+17/441/(2+3*x)^4+(-121/1029)/(2+3*x)^3+(-121/2401)/_
+ (2+3*x)^2+(-484/16807)/(2+3*x)-968/117649*log(1-2*x)+968/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 10585080x + 35283600x + 47044800x + 31363200x + 10454400x
+--R +
+--R 1393920
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 10585080x - 35283600x - 47044800x - 31363200x - 10454400x
+--R +
+--R - 1393920
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 12349260x - 40135095x - 52941735x - 31099425x - 6672617
+--R /
+--R 5 4 3 2
+--R 1286491815x + 4288306050x + 5717741400x + 3811827600x + 1270609200x
+--R +
+--R 169414560
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 10585080x + 35283600x + 47044800x + 31363200x + 10454400x
+--R +
+--R 1393920
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 10585080x - 35283600x - 47044800x - 31363200x - 10454400x
+--R +
+--R - 1393920
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 12349260x - 40135095x - 52941735x - 31099425x - 6672617
+--R /
+--R 5 4 3 2
+--R 1286491815x + 4288306050x + 5717741400x + 3811827600x + 1270609200x
+--R +
+--R 169414560
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R - 968log(2x - 1) + 968log(- 2x + 1)
+--R (4) -----------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^7)
+--R
+--R
+--R (1)
+--R 2
+--R - 25x - 30x - 9
+--R -----------------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 4374x + 18225x + 30618x + 24948x + 7560x - 3024x - 3360x - 1088x - 128
+--R Type: Fraction(Polynomial(Integer))
+--E 166
+
+--S 167 of 500
+r0:=(-1/378)/(2+3*x)^6+68/2205/(2+3*x)^5+(-121/1372)/(2+3*x)^4+_
+ (-242/7203)/(2+3*x)^3+(-242/16807)/(2+3*x)^2+(-968/117649)/(2+3*x)-_
+ 1936/823543*log(1-2*x)+1936/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 762125760x + 3048503040x + 5080838400x + 4516300800x
+--R +
+--R 2
+--R 2258150400x + 602173440x + 66908160
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 762125760x - 3048503040x - 5080838400x - 4516300800x
+--R +
+--R 2
+--R - 2258150400x - 602173440x - 66908160
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 889146720x - 3482491320x - 5738289480x - 5177427255x - 2460267684x
+--R +
+--R - 469699846
+--R /
+--R 6 5 4 3
+--R 324195937380x + 1296783749520x + 2161306249200x + 1921161110400x
+--R +
+--R 2
+--R 960580555200x + 256154814720x + 28461646080
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 762125760x + 3048503040x + 5080838400x + 4516300800x
+--R +
+--R 2
+--R 2258150400x + 602173440x + 66908160
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 762125760x - 3048503040x - 5080838400x - 4516300800x
+--R +
+--R 2
+--R - 2258150400x - 602173440x - 66908160
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 889146720x - 3482491320x - 5738289480x - 5177427255x - 2460267684x
+--R +
+--R - 469699846
+--R /
+--R 6 5 4 3
+--R 324195937380x + 1296783749520x + 2161306249200x + 1921161110400x
+--R +
+--R 2
+--R 960580555200x + 256154814720x + 28461646080
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1936log(2x - 1) + 1936log(- 2x + 1)
+--R (4) -------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^8)
+--R
+--R
+--R (1)
+--R 2
+--R - 25x - 30x - 9
+--R /
+--R 9 8 7 6 5 4 3
+--R 13122x + 63423x + 128304x + 136080x + 72576x + 6048x - 16128x
+--R +
+--R 2
+--R - 9984x - 2560x - 256
+--R Type: Fraction(Polynomial(Integer))
+--E 171
+
+--S 172 of 500
+r0:=(-1/441)/(2+3*x)^7+34/1323/(2+3*x)^6+(-121/1715)/(2+3*x)^5+_
+ (-121/4802)/(2+3*x)^4+(-484/50421)/(2+3*x)^3+(-484/117649)/(2+3*x)^2+_
+ (-1936/823543)/(2+3*x)-3872/5764801*log(1-2*x)+3872/5764801*log(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 2286377280x + 10669760640x + 21339521280x + 23710579200x
+--R +
+--R 3 2
+--R 15807052800x + 6322821120x + 1405071360x + 133816320
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 2286377280x - 10669760640x - 21339521280x - 23710579200x
+--R +
+--R 3 2
+--R - 15807052800x - 6322821120x - 1405071360x - 133816320
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R - 2667440160x - 12225767400x - 24179851080x - 27008860725x
+--R +
+--R 2
+--R - 18847440612x - 7688480856x - 1354700662
+--R /
+--R 7 6 5 4
+--R 3404057342490x + 15885600931620x + 31771201863240x + 35301335403600x
+--R +
+--R 3 2
+--R 23534223602400x + 9413689440960x + 2091930986880x + 199231522560
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 2286377280x + 10669760640x + 21339521280x + 23710579200x
+--R +
+--R 3 2
+--R 15807052800x + 6322821120x + 1405071360x + 133816320
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 2286377280x - 10669760640x - 21339521280x - 23710579200x
+--R +
+--R 3 2
+--R - 15807052800x - 6322821120x - 1405071360x - 133816320
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3
+--R - 2667440160x - 12225767400x - 24179851080x - 27008860725x
+--R +
+--R 2
+--R - 18847440612x - 7688480856x - 1354700662
+--R /
+--R 7 6 5 4
+--R 3404057342490x + 15885600931620x + 31771201863240x + 35301335403600x
+--R +
+--R 3 2
+--R 23534223602400x + 9413689440960x + 2091930986880x + 199231522560
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500
+m0:=a0-r0
+--R
+--R
+--R - 3872log(2x - 1) + 3872log(- 2x + 1)
+--R (4) -------------------------------------
+--R 5764801
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(2+3*x)^m*(3+5*x)^3/(1-2*x)
+--R
+--R
+--R 3 2 m
+--R (- 125x - 225x - 135x - 27)(3x + 2)
+--R (1) --------------------------------------
+--R 2x - 1
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+--r0:=-5135/216*(2+3*x)^(1+m)/(1+m)-725/108*(2+3*x)^(2+m)/(2+m)-_
+-- 125/54*(2+3*x)^(3+m)/(3+m)+1331/56*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)
+--E 177
+
+--S 178 of 500
+--a0:=integrate(t0,x)
+--E 178
+
+--S 179 of 500
+--m0:=a0-r0
+--E 179
+
+--S 180 of 500
+--d0:=D(m0,x)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(2+3*x)^7*(3+5*x)^3/(1-2*x)
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5
+--R - 273375x - 1767825x - 5143095x - 8864559x - 10024182x - 7770924x
+--R +
+--R 4 3 2
+--R - 4182360x - 1543120x - 373536x - 53568x - 3456
+--R /
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 500
+r0:=-1092596789/1024*x-1065169973/1024*x^2-969544757/768*x^3-_
+ 772025397/512*x^4-504354357/320*x^5-85228263/64*x^6-_
+ 95297877/112*x^7-24381405/64*x^8-423225/4*x^9-54675/4*x^10-_
+ 1096135733/2048*log(1-2*x)
+--R
+--R
+--R (2)
+--R 10 9
+--R - 115094251965log(- 2x + 1) - 2939328000x - 22752576000x
+--R +
+--R 8 7 6 5
+--R - 81921520800x - 182971923840x - 286366963680x - 338926127904x
+--R +
+--R 4 3 2
+--R - 324250666740x - 271472531960x - 223685694330x - 229445325690x
+--R /
+--R 215040
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 8
+--R - 115094251965log(2x - 1) - 2939328000x - 22752576000x - 81921520800x
+--R +
+--R 7 6 5 4
+--R - 182971923840x - 286366963680x - 338926127904x - 324250666740x
+--R +
+--R 3 2
+--R - 271472531960x - 223685694330x - 229445325690x
+--R /
+--R 215040
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1096135733log(2x - 1) + 1096135733log(- 2x + 1)
+--R (4) -------------------------------------------------
+--R 2048
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(2+3*x)^6*(3+5*x)^3/(1-2*x)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4
+--R - 91125x - 528525x - 1362015x - 2046843x - 1976832x - 1272420x
+--R +
+--R 3 2
+--R - 545840x - 150480x - 24192x - 1728
+--R /
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 186
+
+--S 187 of 500
+r0:=-155706083/512*x-149512931/512*x^2-130251491/384*x^3-95317731/256*x^4-_
+ 54600291/160*x^5-7656993/32*x^6-6596235/56*x^7-1148175/32*x^8-_
+ 10125/2*x^9-156590819/1024*log(1-2*x)
+--R
+--R
+--R (2)
+--R 9 8 7
+--R - 16442035995log(- 2x + 1) - 544320000x - 3857868000x - 12664771200x
+--R +
+--R 6 5 4 3
+--R - 25727496480x - 36691395552x - 40033447020x - 36470417480x
+--R +
+--R 2
+--R - 31397715510x - 32698277430x
+--R /
+--R 107520
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7
+--R - 16442035995log(2x - 1) - 544320000x - 3857868000x - 12664771200x
+--R +
+--R 6 5 4 3
+--R - 25727496480x - 36691395552x - 40033447020x - 36470417480x
+--R +
+--R 2
+--R - 31397715510x - 32698277430x
+--R /
+--R 107520
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R - 156590819log(2x - 1) + 156590819log(- 2x + 1)
+--R (4) -----------------------------------------------
+--R 1024
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3
+--R - 30375x - 155925x - 350055x - 448911x - 359670x - 184360x
+--R +
+--R 2
+--R - 59040x - 10800x - 864
+--R /
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 500
+r0:=-22148933/256*x-20766533/256*x^2-16987973/192*x^3-11088453/128*x^4-_
+ 5333733/80*x^5-580815/16*x^6-342225/28*x^7-30375/16*x^8-_
+ 22370117/512*log(1-2*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R - 2348862285log(- 2x + 1) - 102060000x - 657072000x - 1951538400x
+--R +
+--R 5 4 3 2
+--R - 3584268576x - 4657150260x - 4756632440x - 4360971930x - 4651275930x
+--R /
+--R 53760
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R - 2348862285log(2x - 1) - 102060000x - 657072000x - 1951538400x
+--R +
+--R 5 4 3 2
+--R - 3584268576x - 4657150260x - 4756632440x - 4360971930x - 4651275930x
+--R /
+--R 53760
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R - 22370117log(2x - 1) + 22370117log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 512
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 10125x - 45225x - 86535x - 91947x - 58592x - 22392x - 4752x - 432
+--R -------------------------------------------------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 196
+
+--S 197 of 500
+r0:=-3140435/128*x-2836307/128*x^2-2119763/96*x^3-1182291/64*x^4-_
+ 89343/8*x^5-33525/8*x^6-10125/14*x^7-3195731/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R - 67110351log(- 2x + 1) - 3888000x - 22528800x - 60038496x
+--R +
+--R 4 3 2
+--R - 99312444x - 118706728x - 119124894x - 131898270x
+--R /
+--R 5376
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R - 67110351log(2x - 1) - 3888000x - 22528800x - 60038496x - 99312444x
+--R +
+--R 3 2
+--R - 118706728x - 119124894x - 131898270x
+--R /
+--R 5376
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R - 3195731log(2x - 1) + 3195731log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)
+--R
+--R
+--R 6 5 4 3 2
+--R - 3375x - 12825x - 20295x - 17119x - 8118x - 2052x - 216
+--R (1) -------------------------------------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 201
+
+--S 202 of 500
+r0:=-442709/64*x-377045/64*x^2-247157/48*x^3-110205/32*x^4-5805/4*x^5-_
+ 1125/4*x^6-456533/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R - 1369599log(- 2x + 1) - 108000x - 557280x - 1322460x - 1977256x
+--R +
+--R 2
+--R - 2262270x - 2656254x
+--R /
+--R 384
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R - 1369599log(2x - 1) - 108000x - 557280x - 1322460x - 1977256x
+--R +
+--R 2
+--R - 2262270x - 2656254x
+--R /
+--R 384
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R - 456533log(2x - 1) + 456533log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R - 1125x - 3525x - 4415x - 2763x - 864x - 108
+--R (1) ------------------------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 206
+
+--S 207 of 500
+r0:=-61763/32*x-47939/32*x^2-25835/24*x^3-8175/16*x^4-225/2*x^5-_
+ 65219/64*log(1-2*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 195657log(- 2x + 1) - 21600x - 98100x - 206680x - 287634x - 370578x
+--R -------------------------------------------------------------------------
+--R 192
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 195657log(2x - 1) - 21600x - 98100x - 206680x - 287634x - 370578x
+--R -----------------------------------------------------------------------
+--R 192
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R - 65219log(2x - 1) + 65219log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(2+3*x)*(3+5*x)^3/(1-2*x)
+--R
+--R
+--R 4 3 2
+--R - 375x - 925x - 855x - 351x - 54
+--R (1) -----------------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 211
+
+--S 212 of 500
+r0:=-8453/16*x-5645/16*x^2-2225/12*x^3-375/8*x^4-9317/32*log(1-2*x)
+--R
+--R
+--R 4 3 2
+--R - 27951log(- 2x + 1) - 4500x - 17800x - 33870x - 50718x
+--R (2) ----------------------------------------------------------
+--R 96
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R - 27951log(2x - 1) - 4500x - 17800x - 33870x - 50718x
+--R (3) --------------------------------------------------------
+--R 96
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R - 9317log(2x - 1) + 9317log(- 2x + 1)
+--R (4) -------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(3+5*x)^3/(1-2*x)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------
+--R 2x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 216
+
+--S 217 of 500
+r0:=-1115/8*x-575/8*x^2-125/6*x^3-1331/16*log(1-2*x)
+--R
+--R
+--R 3 2
+--R - 3993log(- 2x + 1) - 1000x - 3450x - 6690x
+--R (2) ---------------------------------------------
+--R 48
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R - 3993log(2x - 1) - 1000x - 3450x - 6690x
+--R (3) -------------------------------------------
+--R 48
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1331log(2x - 1) + 1331log(- 2x + 1)
+--R (4) -------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(3+5*x)^3/((1-2*x)*(2+3*x))
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------
+--R 2
+--R 6x + x - 2
+--R Type: Fraction(Polynomial(Integer))
+--E 221
+
+--S 222 of 500
+r0:=-1225/36*x-125/12*x^2-1331/56*log(1-2*x)-1/189*log(2+3*x)
+--R
+--R
+--R 2
+--R - 8log(3x + 2) - 35937log(- 2x + 1) - 15750x - 51450x
+--R (2) ------------------------------------------------------
+--R 1512
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 8log(3x + 2) - 35937log(2x - 1) - 15750x - 51450x
+--R (3) ----------------------------------------------------
+--R 1512
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1331log(2x - 1) + 1331log(- 2x + 1)
+--R (4) -------------------------------------
+--R 56
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^2)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------
+--R 3 2
+--R 18x + 15x - 4x - 4
+--R Type: Fraction(Polynomial(Integer))
+--E 226
+
+--S 227 of 500
+r0:=-125/18*x+1/189/(2+3*x)-1331/196*log(1-2*x)+103/1323*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2
+--R (1236x + 824)log(3x + 2) + (- 107811x - 71874)log(- 2x + 1) - 110250x
+--R +
+--R - 73500x + 28
+--R /
+--R 15876x + 10584
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (1236x + 824)log(3x + 2) + (- 107811x - 71874)log(2x - 1) - 110250x
+--R +
+--R - 73500x + 28
+--R /
+--R 15876x + 10584
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1331log(2x - 1) + 1331log(- 2x + 1)
+--R (4) -------------------------------------
+--R 196
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^3)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ----------------------------
+--R 4 3 2
+--R 54x + 81x + 18x - 20x - 8
+--R Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 500
+r0:=1/378/(2+3*x)^2+(-103/1323)/(2+3*x)-1331/686*log(1-2*x)-_
+ 3469/9261*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 62442x - 83256x - 27752)log(3x + 2)
+--R +
+--R 2
+--R (- 323433x - 431244x - 143748)log(- 2x + 1) - 4326x - 2835
+--R /
+--R 2
+--R 166698x + 222264x + 74088
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (- 62442x - 83256x - 27752)log(3x + 2)
+--R +
+--R 2
+--R (- 323433x - 431244x - 143748)log(2x - 1) - 4326x - 2835
+--R /
+--R 2
+--R 166698x + 222264x + 74088
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1331log(2x - 1) + 1331log(- 2x + 1)
+--R (4) -------------------------------------
+--R 686
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^4)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------------------
+--R 5 4 3 2
+--R 162x + 351x + 216x - 24x - 64x - 16
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 500
+r0:=1/567/(2+3*x)^3+(-103/2646)/(2+3*x)^2+3469/9261/(2+3*x)-_
+ 1331/2401*log(1-2*x)+1331/2401*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (5821794x + 11643588x + 7762392x + 1724976)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 5821794x - 11643588x - 7762392x - 1724976)log(- 2x + 1) + 1311282x
+--R +
+--R 1702953x + 553196
+--R /
+--R 3 2
+--R 10501974x + 21003948x + 14002632x + 3111696
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (5821794x + 11643588x + 7762392x + 1724976)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 5821794x - 11643588x - 7762392x - 1724976)log(2x - 1) + 1311282x
+--R +
+--R 1702953x + 553196
+--R /
+--R 3 2
+--R 10501974x + 21003948x + 14002632x + 3111696
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1331log(2x - 1) + 1331log(- 2x + 1)
+--R (4) -------------------------------------
+--R 2401
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^5)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------------------------------
+--R 6 5 4 3 2
+--R 486x + 1377x + 1350x + 360x - 240x - 176x - 32
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 500
+r0:=1/756/(2+3*x)^4+(-103/3969)/(2+3*x)^3+3469/18522/(2+3*x)^2+_
+ (-1331/2401)/(2+3*x)-2662/16807*log(1-2*x)+2662/16807*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (69861528x + 186297408x + 186297408x + 82798848x + 13799808)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 69861528x - 186297408x - 186297408x - 82798848x - 13799808)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 3 2
+--R - 81505116x - 153831258x - 96858804x - 20345549
+--R /
+--R 4 3 2
+--R 441082908x + 1176221088x + 1176221088x + 522764928x + 87127488
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (69861528x + 186297408x + 186297408x + 82798848x + 13799808)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 69861528x - 186297408x - 186297408x - 82798848x - 13799808)
+--R *
+--R log(2x - 1)
+--R +
+--R 3 2
+--R - 81505116x - 153831258x - 96858804x - 20345549
+--R /
+--R 4 3 2
+--R 441082908x + 1176221088x + 1176221088x + 522764928x + 87127488
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2662log(2x - 1) + 2662log(- 2x + 1)
+--R (4) -------------------------------------
+--R 16807
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^6)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ------------------------------------------------------
+--R 7 6 5 4 2
+--R 1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 500
+r0:=1/945/(2+3*x)^5+(-103/5292)/(2+3*x)^4+3469/27783/(2+3*x)^3+_
+ (-1331/4802)/(2+3*x)^2+(-2662/16807)/(2+3*x)-_
+ 5324/117649*log(1-2*x)+5324/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 2095845840x + 6986152800x + 9314870400x + 6209913600x
+--R +
+--R 2069971200x + 275996160
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 2095845840x - 6986152800x - 9314870400x - 6209913600x
+--R +
+--R - 2069971200x - 275996160
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 2445153480x - 7946748810x - 9158912280x - 4525306275x - 817640446
+--R /
+--R 5 4 3 2
+--R 46313705340x + 154379017800x + 205838690400x + 137225793600x
+--R +
+--R 45741931200x + 6098924160
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 2095845840x + 6986152800x + 9314870400x + 6209913600x
+--R +
+--R 2069971200x + 275996160
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 2095845840x - 6986152800x - 9314870400x - 6209913600x
+--R +
+--R - 2069971200x - 275996160
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 2445153480x - 7946748810x - 9158912280x - 4525306275x - 817640446
+--R /
+--R 5 4 3 2
+--R 46313705340x + 154379017800x + 205838690400x + 137225793600x
+--R +
+--R 45741931200x + 6098924160
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500
+m0:=a0-r0
+--R
+--R
+--R - 5324log(2x - 1) + 5324log(- 2x + 1)
+--R (4) -------------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^7)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R -----------------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 4374x + 18225x + 30618x + 24948x + 7560x - 3024x - 3360x - 1088x - 128
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 500
+r0:=1/1134/(2+3*x)^6+(-103/6615)/(2+3*x)^5+3469/37044/(2+3*x)^4+_
+ (-1331/7203)/(2+3*x)^3+(-1331/16807)/(2+3*x)^2+_
+ (-5324/117649)/(2+3*x)-10648/823543*log(1-2*x)+10648/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 12575075040x + 50300300160x + 83833833600x + 74518963200x
+--R +
+--R 2
+--R 37259481600x + 9935861760x + 1103984640
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 12575075040x - 50300300160x - 83833833600x - 74518963200x
+--R +
+--R 2
+--R - 37259481600x - 9935861760x - 1103984640
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 14670920880x - 57461106780x - 94681776420x - 78478905645x
+--R +
+--R - 32070746736x - 5135298434
+--R /
+--R 6 5 4 3
+--R 972587812140x + 3890351248560x + 6483918747600x + 5763483331200x
+--R +
+--R 2
+--R 2881741665600x + 768464444160x + 85384938240
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 12575075040x + 50300300160x + 83833833600x + 74518963200x
+--R +
+--R 2
+--R 37259481600x + 9935861760x + 1103984640
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 12575075040x - 50300300160x - 83833833600x - 74518963200x
+--R +
+--R 2
+--R - 37259481600x - 9935861760x - 1103984640
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 14670920880x - 57461106780x - 94681776420x - 78478905645x
+--R +
+--R - 32070746736x - 5135298434
+--R /
+--R 6 5 4 3
+--R 972587812140x + 3890351248560x + 6483918747600x + 5763483331200x
+--R +
+--R 2
+--R 2881741665600x + 768464444160x + 85384938240
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500
+m0:=a0-r0
+--R
+--R
+--R - 10648log(2x - 1) + 10648log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^8)
+--R
+--R
+--R (1)
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R /
+--R 9 8 7 6 5 4 3
+--R 13122x + 63423x + 128304x + 136080x + 72576x + 6048x - 16128x
+--R +
+--R 2
+--R - 9984x - 2560x - 256
+--R Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 500
+r0:=1/1323/(2+3*x)^7+(-103/7938)/(2+3*x)^6+3469/46305/(2+3*x)^5+_
+ (-1331/9604)/(2+3*x)^4+(-2662/50421)/(2+3*x)^3+(-2662/117649)/(2+3*x)^2+_
+ (-10648/823543)/(2+3*x)-21296/5764801*log(1-2*x)+21296/5764801*log(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 75450450240x + 352102101120x + 704204202240x + 782449113600x
+--R +
+--R 3 2
+--R 521632742400x + 208653096960x + 46367354880x + 4415938560
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 75450450240x - 352102101120x - 704204202240x - 782449113600x
+--R +
+--R 3 2
+--R - 521632742400x - 208653096960x - 46367354880x - 4415938560
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R - 88025525280x - 403450324200x - 797935085640x - 891292403925x
+--R +
+--R 2
+--R - 583053133446x - 206160259998x - 30169587896
+--R /
+--R 7 6 5
+--R 20424344054940x + 95313605589720x + 190627211179440x
+--R +
+--R 4 3 2
+--R 211808012421600x + 141205341614400x + 56482136645760x
+--R +
+--R 12551585921280x + 1195389135360
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 75450450240x + 352102101120x + 704204202240x + 782449113600x
+--R +
+--R 3 2
+--R 521632742400x + 208653096960x + 46367354880x + 4415938560
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 75450450240x - 352102101120x - 704204202240x - 782449113600x
+--R +
+--R 3 2
+--R - 521632742400x - 208653096960x - 46367354880x - 4415938560
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3
+--R - 88025525280x - 403450324200x - 797935085640x - 891292403925x
+--R +
+--R 2
+--R - 583053133446x - 206160259998x - 30169587896
+--R /
+--R 7 6 5
+--R 20424344054940x + 95313605589720x + 190627211179440x
+--R +
+--R 4 3 2
+--R 211808012421600x + 141205341614400x + 56482136645760x
+--R +
+--R 12551585921280x + 1195389135360
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 500
+m0:=a0-r0
+--R
+--R
+--R - 21296log(2x - 1) + 21296log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 5764801
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(a+b*x)^3/((c+d*x)*(e+f*x))
+--R
+--R
+--R 3 3 2 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) ----------------------------
+--R 2
+--R d f x + (c f + d e)x + c e
+--R Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 500
+r0:=-b^2*(b*d*e+b*c*f-3*a*d*f)*x/(d^2*f^2)+1/2*b^3*x^2/(d*f)-_
+ (b*c-a*d)^3*log(c+d*x)/(d^3*(d*e-c*f))+_
+ (b*e-a*f)^3*log(e+f*x)/(f^3*(d*e-c*f))
+--R
+--R
+--R (2)
+--R 3 3 3 2 3 2 2 3 2 3 3 3
+--R (2a d f - 6a b d e f + 6a b d e f - 2b d e )log(f x + e)
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )f log(d x + c)
+--R +
+--R 3 2 3 3 3 2 2
+--R (b c d f - b d e f )x
+--R +
+--R 2 2 3 2 3 2 3 2 3 3 2
+--R ((6a b c d - 2b c d)f - 6a b d e f + 2b d e f)x
+--R /
+--R 3 4 4 3
+--R 2c d f - 2d e f
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 3 2 3 2 2 3 2 3 3 3
+--R (2a d f - 6a b d e f + 6a b d e f - 2b d e )log(f x + e)
+--R +
+--R 3 3 2 2 2 2 3 3 3
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )f log(d x + c)
+--R +
+--R 3 2 3 3 3 2 2
+--R (b c d f - b d e f )x
+--R +
+--R 2 2 3 2 3 2 3 2 3 3 2
+--R ((6a b c d - 2b c d)f - 6a b d e f + 2b d e f)x
+--R /
+--R 3 4 4 3
+--R 2c d f - 2d e f
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(2+3*x)^m/((1-2*x)*(3+5*x))
+--R
+--R
+--R m
+--R (3x + 2)
+--R (1) - ------------
+--R 2
+--R 10x + x - 3
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+--r0:=2/77*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)-5/11*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)
+--E 267
+
+--S 268 of 500
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 500
+--m0:=a0-r0
+--E 269
+
+--S 270 of 500
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(2+3*x)^8/((1-2*x)*(3+5*x))
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x
+--R +
+--R - 3072x - 256
+--R /
+--R 2
+--R 10x + x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 271
+
+--S 272 of 500
+r0:=-40089855591/10000000*x-7136193339/2000000*x^2-345533877/100000*x^3-_
+ 111146499/40000*x^4-8018271/5000*x^5-114453/200*x^6-6561/70*x^7-_
+ 5764801/2816*log(1-2*x)+1/4296875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7
+--R 1792log(5x + 3) - 15763127734375log(- 2x + 1) - 721710000000x
+--R +
+--R 6 5 4
+--R - 4406440500000x - 12348137340000x - 21395701057500x
+--R +
+--R 3 2
+--R - 26606108529000x - 27474344355150x - 30869188805070x
+--R /
+--R 7700000000
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7
+--R 1792log(5x + 3) - 15763127734375log(2x - 1) - 721710000000x
+--R +
+--R 6 5 4
+--R - 4406440500000x - 12348137340000x - 21395701057500x
+--R +
+--R 3 2
+--R - 26606108529000x - 27474344355150x - 30869188805070x
+--R /
+--R 7700000000
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500
+m0:=a0-r0
+--R
+--R
+--R - 5764801log(2x - 1) + 5764801log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 2816
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(2+3*x)^7/((1-2*x)*(3+5*x))
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128
+--R -----------------------------------------------------------------------
+--R 2
+--R 10x + x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 276
+
+--S 277 of 500
+r0:=-1127138733/1000000*x-187738857/200000*x^2-7889751/10000*x^3-_
+ 2006937/4000*x^4-99873/500*x^5-729/20*x^6-823543/1408*log(1-2*x)+_
+ 1/859375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5
+--R 128log(5x + 3) - 64339296875log(- 2x + 1) - 4009500000x - 21972060000x
+--R +
+--R 4 3 2
+--R - 55190767500x - 86787261000x - 103256371350x - 123985260630x
+--R /
+--R 110000000
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5
+--R 128log(5x + 3) - 64339296875log(2x - 1) - 4009500000x - 21972060000x
+--R +
+--R 4 3 2
+--R - 55190767500x - 86787261000x - 103256371350x - 123985260630x
+--R /
+--R 110000000
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500
+m0:=a0-r0
+--R
+--R
+--R - 823543log(2x - 1) + 823543log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 1408
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(2+3*x)^6/((1-2*x)*(3+5*x))
+--R
+--R
+--R 6 5 4 3 2
+--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64
+--R (1) -------------------------------------------------------
+--R 2
+--R 10x + x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 500
+r0:=-31289679/100000*x-4693491/20000*x^2-159813/1000*x^3-_
+ 28431/400*x^4-729/50*x^5-117649/704*log(1-2*x)+1/171875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4
+--R 64log(5x + 3) - 1838265625log(- 2x + 1) - 160380000x - 781852500x
+--R +
+--R 3 2
+--R - 1757943000x - 2581420050x - 3441864690x
+--R /
+--R 11000000
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4
+--R 64log(5x + 3) - 1838265625log(2x - 1) - 160380000x - 781852500x
+--R +
+--R 3 2
+--R - 1757943000x - 2581420050x - 3441864690x
+--R /
+--R 11000000
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500
+m0:=a0-r0
+--R
+--R
+--R - 117649log(2x - 1) + 117649log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 704
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(2+3*x)^5/((1-2*x)*(3+5*x))
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 2
+--R 10x + x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 500
+r0:=-848277/10000*x-107433/2000*x^2-2619/100*x^3-243/40*x^4-_
+ 16807/352*log(1-2*x)+1/34375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3
+--R 32log(5x + 3) - 52521875log(- 2x + 1) - 6682500x - 28809000x
+--R +
+--R 2
+--R - 59088150x - 93310470x
+--R /
+--R 1100000
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 32log(5x + 3) - 52521875log(2x - 1) - 6682500x - 28809000x - 59088150x
+--R +
+--R - 93310470x
+--R /
+--R 1100000
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500
+m0:=a0-r0
+--R
+--R
+--R - 16807log(2x - 1) + 16807log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 352
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(2+3*x)^4/((1-2*x)*(3+5*x))
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) ---------------------------------
+--R 2
+--R 10x + x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 500
+r0:=-21951/1000*x-2079/200*x^2-27/10*x^3-2401/176*log(1-2*x)+1/6875*log(3+5*x)
+--R
+--R
+--R 3 2
+--R 16log(5x + 3) - 1500625log(- 2x + 1) - 297000x - 1143450x - 2414610x
+--R (2) ----------------------------------------------------------------------
+--R 110000
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 16log(5x + 3) - 1500625log(2x - 1) - 297000x - 1143450x - 2414610x
+--R (3) --------------------------------------------------------------------
+--R 110000
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2401log(2x - 1) + 2401log(- 2x + 1)
+--R (4) -------------------------------------
+--R 176
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(2+3*x)^3/((1-2*x)*(3+5*x))
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) -----------------------
+--R 2
+--R 10x + x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 296
+
+--S 297 of 500
+r0:=-513/100*x-27/20*x^2-343/88*log(1-2*x)+1/1375*log(3+5*x)
+--R
+--R
+--R 2
+--R 8log(5x + 3) - 42875log(- 2x + 1) - 14850x - 56430x
+--R (2) ----------------------------------------------------
+--R 11000
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 8log(5x + 3) - 42875log(2x - 1) - 14850x - 56430x
+--R (3) --------------------------------------------------
+--R 11000
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500
+m0:=a0-r0
+--R
+--R
+--R - 343log(2x - 1) + 343log(- 2x + 1)
+--R (4) -----------------------------------
+--R 88
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(2+3*x)^2/((1-2*x)*(3+5*x))
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) ---------------
+--R 2
+--R 10x + x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 301
+
+--S 302 of 500
+r0:=-9/10*x-49/44*log(1-2*x)+1/275*log(3+5*x)
+--R
+--R
+--R 4log(5x + 3) - 1225log(- 2x + 1) - 990x
+--R (2) ---------------------------------------
+--R 1100
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4log(5x + 3) - 1225log(2x - 1) - 990x
+--R (3) -------------------------------------
+--R 1100
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500
+m0:=a0-r0
+--R
+--R
+--R - 49log(2x - 1) + 49log(- 2x + 1)
+--R (4) ---------------------------------
+--R 44
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(2+3*x)/((1-2*x)*(3+5*x))
+--R
+--R
+--R - 3x - 2
+--R (1) ------------
+--R 2
+--R 10x + x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 306
+
+--S 307 of 500
+r0:=-7/22*log(1-2*x)+1/55*log(3+5*x)
+--R
+--R
+--R 2log(5x + 3) - 35log(- 2x + 1)
+--R (2) ------------------------------
+--R 110
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2log(5x + 3) - 35log(2x - 1)
+--R (3) ----------------------------
+--R 110
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500
+m0:=a0-r0
+--R
+--R
+--R - 7log(2x - 1) + 7log(- 2x + 1)
+--R (4) -------------------------------
+--R 22
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=1/((1-2*x)*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ------------
+--R 2
+--R 10x + x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 311
+
+--S 312 of 500
+r0:=-1/11*log(1-2*x)+1/11*log(3+5*x)
+--R
+--R
+--R log(5x + 3) - log(- 2x + 1)
+--R (2) ---------------------------
+--R 11
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R log(5x + 3) - log(2x - 1)
+--R (3) -------------------------
+--R 11
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500
+m0:=a0-r0
+--R
+--R
+--R - log(2x - 1) + log(- 2x + 1)
+--R (4) -----------------------------
+--R 11
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=1/((1-2*x)*(2+3*x)*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - --------------------
+--R 3 2
+--R 30x + 23x - 7x - 6
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 500
+r0:=-2/77*log(1-2*x)-3/7*log(2+3*x)+5/11*log(3+5*x)
+--R
+--R
+--R 35log(5x + 3) - 33log(3x + 2) - 2log(- 2x + 1)
+--R (2) ----------------------------------------------
+--R 77
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 35log(5x + 3) - 33log(3x + 2) - 2log(2x - 1)
+--R (3) --------------------------------------------
+--R 77
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2log(2x - 1) + 2log(- 2x + 1)
+--R (4) -------------------------------
+--R 77
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=1/((1-2*x)*(2+3*x)^2*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ------------------------------
+--R 4 3 2
+--R 90x + 129x + 25x - 32x - 12
+--R Type: Fraction(Polynomial(Integer))
+--E 321
+
+--S 322 of 500
+r0:=3/7/(2+3*x)-4/539*log(1-2*x)-111/49*log(2+3*x)+25/11*log(3+5*x)
+--R
+--R
+--R (2)
+--R (3675x + 2450)log(5x + 3) + (- 3663x - 2442)log(3x + 2)
+--R +
+--R (- 12x - 8)log(- 2x + 1) + 231
+--R /
+--R 1617x + 1078
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (3675x + 2450)log(5x + 3) + (- 3663x - 2442)log(3x + 2)
+--R +
+--R (- 12x - 8)log(2x - 1) + 231
+--R /
+--R 1617x + 1078
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500
+m0:=a0-r0
+--R
+--R
+--R - 4log(2x - 1) + 4log(- 2x + 1)
+--R (4) -------------------------------
+--R 539
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=1/((1-2*x)*(2+3*x)^3*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ----------------------------------------
+--R 5 4 3 2
+--R 270x + 567x + 333x - 46x - 100x - 24
+--R Type: Fraction(Polynomial(Integer))
+--E 326
+
+--S 327 of 500
+r0:=3/14/(2+3*x)^2+111/49/(2+3*x)-8/3773*log(1-2*x)-3897/343*log(2+3*x)+_
+ 125/11*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (771750x + 1029000x + 343000)log(5x + 3)
+--R +
+--R 2
+--R (- 771606x - 1028808x - 342936)log(3x + 2)
+--R +
+--R 2
+--R (- 144x - 192x - 64)log(- 2x + 1) + 51282x + 35805
+--R /
+--R 2
+--R 67914x + 90552x + 30184
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (771750x + 1029000x + 343000)log(5x + 3)
+--R +
+--R 2
+--R (- 771606x - 1028808x - 342936)log(3x + 2)
+--R +
+--R 2
+--R (- 144x - 192x - 64)log(2x - 1) + 51282x + 35805
+--R /
+--R 2
+--R 67914x + 90552x + 30184
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R - 8log(2x - 1) + 8log(- 2x + 1)
+--R (4) -------------------------------
+--R 3773
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=1/((1-2*x)*(2+3*x)^4*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ---------------------------------------------------
+--R 6 5 4 3 2
+--R 810x + 2241x + 2133x + 528x - 392x - 272x - 48
+--R Type: Fraction(Polynomial(Integer))
+--E 331
+
+--S 332 of 500
+r0:=1/7/(2+3*x)^3+111/98/(2+3*x)^2+3897/343/(2+3*x)-16/26411*log(1-2*x)-_
+ 136419/2401*log(2+3*x)+625/11*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (81033750x + 162067500x + 108045000x + 24010000)log(5x + 3)
+--R +
+--R 3 2
+--R (- 81032886x - 162065772x - 108043848x - 24009744)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 864x - 1728x - 1152x - 256)log(- 2x + 1) + 5401242x + 7381143x
+--R +
+--R 2527756
+--R /
+--R 3 2
+--R 1426194x + 2852388x + 1901592x + 422576
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (81033750x + 162067500x + 108045000x + 24010000)log(5x + 3)
+--R +
+--R 3 2
+--R (- 81032886x - 162065772x - 108043848x - 24009744)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 864x - 1728x - 1152x - 256)log(2x - 1) + 5401242x + 7381143x
+--R +
+--R 2527756
+--R /
+--R 3 2
+--R 1426194x + 2852388x + 1901592x + 422576
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500
+m0:=a0-r0
+--R
+--R
+--R - 16log(2x - 1) + 16log(- 2x + 1)
+--R (4) ---------------------------------
+--R 26411
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=1/((1-2*x)*(2+3*x)^5*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ---------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2430x + 8343x + 10881x + 5850x - 120x - 1600x - 688x - 96
+--R Type: Fraction(Polynomial(Integer))
+--E 336
+
+--S 337 of 500
+r0:=3/28/(2+3*x)^4+37/49/(2+3*x)^3+3897/686/(2+3*x)^2+136419/2401/(2+3*x)-_
+ 32/184877*log(1-2*x)-4774713/16807*log(2+3*x)+3125/11*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 17017087500x + 45378900000x + 45378900000x + 20168400000x
+--R +
+--R 3361400000
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 17017077132x - 45378872352x - 45378872352x - 20168387712x
+--R +
+--R - 3361397952
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 10368x - 27648x - 27648x - 12288x - 2048)log(- 2x + 1)
+--R +
+--R 3 2
+--R 1134460404x + 2306729502x + 1564700676x + 354136321
+--R /
+--R 4 3 2
+--R 59900148x + 159733728x + 159733728x + 70992768x + 11832128
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 17017087500x + 45378900000x + 45378900000x + 20168400000x
+--R +
+--R 3361400000
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 17017077132x - 45378872352x - 45378872352x - 20168387712x
+--R +
+--R - 3361397952
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 10368x - 27648x - 27648x - 12288x - 2048)log(2x - 1) + 1134460404x
+--R +
+--R 2
+--R 2306729502x + 1564700676x + 354136321
+--R /
+--R 4 3 2
+--R 59900148x + 159733728x + 159733728x + 70992768x + 11832128
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500
+m0:=a0-r0
+--R
+--R
+--R - 32log(2x - 1) + 32log(- 2x + 1)
+--R (4) ---------------------------------
+--R 184877
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=1/((1-2*x)*(2+3*x)^6*(3+5*x))
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 7290x + 29889x + 49329x + 39312x + 11340x - 5040x - 5264x
+--R +
+--R - 1664x - 192
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 500
+r0:=3/35/(2+3*x)^5+111/196/(2+3*x)^4+1299/343/(2+3*x)^3+_
+ 136419/4802/(2+3*x)^2+4774713/16807/(2+3*x)-64/1294139*log(1-2*x)-_
+ 167115051/117649*log(2+3*x)+15625/11*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3
+--R 8933970937500x + 29779903125000x + 39706537500000x
+--R +
+--R 2
+--R 26471025000000x + 8823675000000x + 1176490000000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 8933970626460x - 29779902088200x - 39706536117600x
+--R +
+--R 2
+--R - 26471024078400x - 8823674692800x - 1176489959040
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 311040x - 1036800x - 1382400x - 921600x - 307200x - 40960)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R 595597699620x + 1608113589390x + 1628848849320x + 733584557475x
+--R +
+--R 123954940494
+--R /
+--R 5 4 3 2
+--R 6289515540x + 20965051800x + 27953402400x + 18635601600x
+--R +
+--R 6211867200x + 828248960
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R 8933970937500x + 29779903125000x + 39706537500000x
+--R +
+--R 2
+--R 26471025000000x + 8823675000000x + 1176490000000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 8933970626460x - 29779902088200x - 39706536117600x
+--R +
+--R 2
+--R - 26471024078400x - 8823674692800x - 1176489959040
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 311040x - 1036800x - 1382400x - 921600x - 307200x - 40960)
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R 595597699620x + 1608113589390x + 1628848849320x + 733584557475x
+--R +
+--R 123954940494
+--R /
+--R 5 4 3 2
+--R 6289515540x + 20965051800x + 27953402400x + 18635601600x
+--R +
+--R 6211867200x + 828248960
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500
+m0:=a0-r0
+--R
+--R
+--R - 64log(2x - 1) + 64log(- 2x + 1)
+--R (4) ---------------------------------
+--R 1294139
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=1/((1-2*x)*(2+3*x)^7*(3+5*x))
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 21870x + 104247x + 207765x + 216594x + 112644x + 7560x - 25872x
+--R +
+--R 2
+--R - 15520x - 3904x - 384
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 500
+r0:=1/14/(2+3*x)^6+111/245/(2+3*x)^5+3897/1372/(2+3*x)^4+_
+ 45473/2401/(2+3*x)^3+4774713/33614/(2+3*x)^2+_
+ 167115051/117649/(2+3*x)-128/9058973*log(1-2*x)-_
+ 5849026977/823543*log(2+3*x)+78125/11*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R 938066948437500x + 3752267793750000x + 6253779656250000x
+--R +
+--R 3 2
+--R 5558915250000000x + 2779457625000000x + 741188700000000x
+--R +
+--R 82354300000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 938066946571260x - 3752267786285040x - 6253779643808400x
+--R +
+--R 3 2
+--R - 5558915238940800x - 2779457619470400x - 741188698525440x
+--R +
+--R - 82354299836160
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 1866240x - 7464960x - 12441600x - 11059200x - 5529600x
+--R +
+--R - 1474560x - 163840
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3
+--R 62537794385220x + 210543906566070x + 283597312285980x
+--R +
+--R 2
+--R 191046007176255x + 64366302153384x + 8676887688546
+--R /
+--R 6 5 4 3
+--R 132079826340x + 528319305360x + 880532175600x + 782695267200x
+--R +
+--R 2
+--R 391347633600x + 104359368960x + 11595485440
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R 938066948437500x + 3752267793750000x + 6253779656250000x
+--R +
+--R 3 2
+--R 5558915250000000x + 2779457625000000x + 741188700000000x
+--R +
+--R 82354300000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 938066946571260x - 3752267786285040x - 6253779643808400x
+--R +
+--R 3 2
+--R - 5558915238940800x - 2779457619470400x - 741188698525440x
+--R +
+--R - 82354299836160
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 1866240x - 7464960x - 12441600x - 11059200x - 5529600x
+--R +
+--R - 1474560x - 163840
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3
+--R 62537794385220x + 210543906566070x + 283597312285980x
+--R +
+--R 2
+--R 191046007176255x + 64366302153384x + 8676887688546
+--R /
+--R 6 5 4 3
+--R 132079826340x + 528319305360x + 880532175600x + 782695267200x
+--R +
+--R 2
+--R 391347633600x + 104359368960x + 11595485440
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500
+m0:=a0-r0
+--R
+--R
+--R - 128log(2x - 1) + 128log(- 2x + 1)
+--R (4) -----------------------------------
+--R 9058973
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(2+3*x)^m/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R m
+--R (3x + 2)
+--R (1) - ---------------------
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+--r0:=-5/11*(2+3*x)^(1+m)/(3+5*x)+4/847*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)-10/121*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)-15/11*m*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)
+--E 352
+
+--S 353 of 500
+--a0:=integrate(t0,x)
+--E 353
+
+--S 354 of 500
+--m0:=a0-r0
+--E 354
+
+--S 355 of 500
+--d0:=D(m0,x)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(2+3*x)^8/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x
+--R +
+--R - 3072x - 256
+--R /
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 356
+
+--S 357 of 500
+r0:=-3579885909/5000000*x-118543581/200000*x^2-24660207/50000*x^3-_
+ 6194313/20000*x^4-303993/2500*x^5-2187/100*x^6+(-1/4296875)/(3+5*x)-_
+ 5764801/15488*log(1-2*x)+266/47265625*log(3+5*x)
+--R
+--R
+--R (2)
+--R (170240x + 102144)log(5x + 3)
+--R +
+--R 7
+--R (- 11259376953125x - 6755626171875)log(- 2x + 1) - 661567500000x
+--R +
+--R 6 5 4
+--R - 4075255800000x - 11575887592500x - 20540764282500x
+--R +
+--R 3 2
+--R - 26881371767250x - 32416139725200x - 12994985849670x - 1408
+--R /
+--R 30250000000x + 18150000000
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (170240x + 102144)log(5x + 3)
+--R +
+--R 7
+--R (- 11259376953125x - 6755626171875)log(2x - 1) - 661567500000x
+--R +
+--R 6 5 4
+--R - 4075255800000x - 11575887592500x - 20540764282500x
+--R +
+--R 3 2
+--R - 26881371767250x - 32416139725200x - 12994985849670x - 1408
+--R /
+--R 30250000000x + 18150000000
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500
+m0:=a0-r0
+--R
+--R
+--R - 5764801log(2x - 1) + 5764801log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 15488
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(2+3*x)^7/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128
+--R -----------------------------------------------------------------------
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 361
+
+--S 362 of 500
+r0:=-19846971/100000*x-14750667/100000*x^2-495477/5000*x^3-86751/2000*x^4-_
+ 2187/250*x^5+(-1/859375)/(3+5*x)-823543/7744*log(1-2*x)+_
+ 233/9453125*log(3+5*x)
+--R
+--R
+--R (2)
+--R (74560x + 44736)log(5x + 3)
+--R +
+--R 6
+--R (- 321696484375x - 193017890625)log(- 2x + 1) - 26462700000x
+--R +
+--R 5 4 3 2
+--R - 147088507500x - 378490117500x - 626065827750x - 868095478800x
+--R +
+--R - 360222523650x - 704
+--R /
+--R 3025000000x + 1815000000
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (74560x + 44736)log(5x + 3) + (- 321696484375x - 193017890625)log(2x - 1)
+--R +
+--R 6 5 4 3
+--R - 26462700000x - 147088507500x - 378490117500x - 626065827750x
+--R +
+--R 2
+--R - 868095478800x - 360222523650x - 704
+--R /
+--R 3025000000x + 1815000000
+--R Type: Union(Expression(Integer),...)
+--E 363
+
+--S 364 of 500
+m0:=a0-r0
+--R
+--R
+--R - 823543log(2x - 1) + 823543log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 7744
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(2+3*x)^6/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R 6 5 4 3 2
+--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64
+--R (1) -------------------------------------------------------
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 366
+
+--S 367 of 500
+r0:=-2682909/50000*x-335097/10000*x^2-8019/500*x^3-729/200*x^4+_
+ (-1/171875)/(3+5*x)-117649/3872*log(1-2*x)+8/75625*log(3+5*x)
+--R
+--R
+--R (2)
+--R (32000x + 19200)log(5x + 3) + (- 9191328125x - 5514796875)log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 1102612500x - 5513062500x - 13047581250x - 22313610000x
+--R +
+--R - 9738959670x - 352
+--R /
+--R 302500000x + 181500000
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (32000x + 19200)log(5x + 3) + (- 9191328125x - 5514796875)log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 1102612500x - 5513062500x - 13047581250x - 22313610000x
+--R +
+--R - 9738959670x - 352
+--R /
+--R 302500000x + 181500000
+--R Type: Union(Expression(Integer),...)
+--E 368
+
+--S 369 of 500
+m0:=a0-r0
+--R
+--R
+--R - 117649log(2x - 1) + 117649log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 3872
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(2+3*x)^5/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 371
+
+--S 372 of 500
+r0:=-69039/5000*x-6399/1000*x^2-81/50*x^3+(-1/34375)/(3+5*x)-_
+ 16807/1936*log(1-2*x)+167/378125*log(3+5*x)
+--R
+--R
+--R (2)
+--R (13360x + 8016)log(5x + 3) + (- 262609375x - 157565625)log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 49005000x - 222972750x - 533827800x - 250611570x - 176
+--R /
+--R 30250000x + 18150000
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (13360x + 8016)log(5x + 3) + (- 262609375x - 157565625)log(2x - 1)
+--R +
+--R 4 3 2
+--R - 49005000x - 222972750x - 533827800x - 250611570x - 176
+--R /
+--R 30250000x + 18150000
+--R Type: Union(Expression(Integer),...)
+--E 373
+
+--S 374 of 500
+m0:=a0-r0
+--R
+--R
+--R - 16807log(2x - 1) + 16807log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 1936
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(2+3*x)^4/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) ---------------------------------
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 376
+
+--S 377 of 500
+r0:=-1593/500*x-81/100*x^2+(-1/6875)/(3+5*x)-2401/968*log(1-2*x)+_
+ 134/75625*log(3+5*x)
+--R
+--R
+--R (2)
+--R (5360x + 3216)log(5x + 3) + (- 7503125x - 4501875)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 2450250x - 11107800x - 5782590x - 88
+--R /
+--R 3025000x + 1815000
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3
+--R (5360x + 3216)log(5x + 3) + (- 7503125x - 4501875)log(2x - 1) - 2450250x
+--R +
+--R 2
+--R - 11107800x - 5782590x - 88
+--R /
+--R 3025000x + 1815000
+--R Type: Union(Expression(Integer),...)
+--E 378
+
+--S 379 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2401log(2x - 1) + 2401log(- 2x + 1)
+--R (4) -------------------------------------
+--R 968
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(2+3*x)^3/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) -----------------------
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 381
+
+--S 382 of 500
+r0:=-27/50*x+(-1/1375)/(3+5*x)-343/484*log(1-2*x)+101/15125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (2020x + 1212)log(5x + 3) + (- 214375x - 128625)log(- 2x + 1) - 163350x
+--R +
+--R - 98010x - 44
+--R /
+--R 302500x + 181500
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (2020x + 1212)log(5x + 3) + (- 214375x - 128625)log(2x - 1) - 163350x
+--R +
+--R - 98010x - 44
+--R /
+--R 302500x + 181500
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500
+m0:=a0-r0
+--R
+--R
+--R - 343log(2x - 1) + 343log(- 2x + 1)
+--R (4) -----------------------------------
+--R 484
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(2+3*x)^2/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) ---------------------
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 386
+
+--S 387 of 500
+r0:=(-1/275)/(3+5*x)-49/242*log(1-2*x)+68/3025*log(3+5*x)
+--R
+--R
+--R (680x + 408)log(5x + 3) + (- 6125x - 3675)log(- 2x + 1) - 22
+--R (2) ------------------------------------------------------------
+--R 30250x + 18150
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (680x + 408)log(5x + 3) + (- 6125x - 3675)log(2x - 1) - 22
+--R (3) ----------------------------------------------------------
+--R 30250x + 18150
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500
+m0:=a0-r0
+--R
+--R
+--R - 49log(2x - 1) + 49log(- 2x + 1)
+--R (4) ---------------------------------
+--R 242
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(2+3*x)/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R - 3x - 2
+--R (1) ---------------------
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 391
+
+--S 392 of 500
+r0:=(-1/55)/(3+5*x)-7/121*log(1-2*x)+7/121*log(3+5*x)
+--R
+--R
+--R (175x + 105)log(5x + 3) + (- 175x - 105)log(- 2x + 1) - 11
+--R (2) ----------------------------------------------------------
+--R 3025x + 1815
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (175x + 105)log(5x + 3) + (- 175x - 105)log(2x - 1) - 11
+--R (3) --------------------------------------------------------
+--R 3025x + 1815
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500
+m0:=a0-r0
+--R
+--R
+--R - 7log(2x - 1) + 7log(- 2x + 1)
+--R (4) -------------------------------
+--R 121
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=1/((1-2*x)*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - ---------------------
+--R 3 2
+--R 50x + 35x - 12x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 396
+
+--S 397 of 500
+r0:=(-1/11)/(3+5*x)-2/121*log(1-2*x)+2/121*log(3+5*x)
+--R
+--R
+--R (10x + 6)log(5x + 3) + (- 10x - 6)log(- 2x + 1) - 11
+--R (2) ----------------------------------------------------
+--R 605x + 363
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (10x + 6)log(5x + 3) + (- 10x - 6)log(2x - 1) - 11
+--R (3) --------------------------------------------------
+--R 605x + 363
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2log(2x - 1) + 2log(- 2x + 1)
+--R (4) -------------------------------
+--R 121
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=1/((1-2*x)*(2+3*x)*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - -------------------------------
+--R 4 3 2
+--R 150x + 205x + 34x - 51x - 18
+--R Type: Fraction(Polynomial(Integer))
+--E 401
+
+--S 402 of 500
+r0:=(-5/11)/(3+5*x)-4/847*log(1-2*x)+9/7*log(2+3*x)-155/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R (- 5425x - 3255)log(5x + 3) + (5445x + 3267)log(3x + 2)
+--R +
+--R (- 20x - 12)log(- 2x + 1) - 385
+--R /
+--R 4235x + 2541
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (- 5425x - 3255)log(5x + 3) + (5445x + 3267)log(3x + 2)
+--R +
+--R (- 20x - 12)log(2x - 1) - 385
+--R /
+--R 4235x + 2541
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500
+m0:=a0-r0
+--R
+--R
+--R - 4log(2x - 1) + 4log(- 2x + 1)
+--R (4) -------------------------------
+--R 847
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=1/((1-2*x)*(2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - ----------------------------------------
+--R 5 4 3 2
+--R 450x + 915x + 512x - 85x - 156x - 36
+--R Type: Fraction(Polynomial(Integer))
+--E 406
+
+--S 407 of 500
+r0:=(-9/7)/(2+3*x)+(-25/11)/(3+5*x)-8/5929*log(1-2*x)+648/49*log(2+3*x)-_
+ 1600/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 1176000x - 1489600x - 470400)log(5x + 3)
+--R +
+--R 2
+--R (1176120x + 1489752x + 470448)log(3x + 2)
+--R +
+--R 2
+--R (- 120x - 152x - 48)log(- 2x + 1) - 78540x - 49819
+--R /
+--R 2
+--R 88935x + 112651x + 35574
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (- 1176000x - 1489600x - 470400)log(5x + 3)
+--R +
+--R 2
+--R (1176120x + 1489752x + 470448)log(3x + 2)
+--R +
+--R 2
+--R (- 120x - 152x - 48)log(2x - 1) - 78540x - 49819
+--R /
+--R 2
+--R 88935x + 112651x + 35574
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500
+m0:=a0-r0
+--R
+--R
+--R - 8log(2x - 1) + 8log(- 2x + 1)
+--R (4) -------------------------------
+--R 5929
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=1/((1-2*x)*(2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - ----------------------------------------------------
+--R 6 5 4 3 2
+--R 1350x + 3645x + 3366x + 769x - 638x - 420x - 72
+--R Type: Fraction(Polynomial(Integer))
+--E 411
+
+--S 412 of 500
+r0:=(-9/14)/(2+3*x)^2+(-648/49)/(2+3*x)+(-125/11)/(3+5*x)-_
+ 16/41503*log(1-2*x)+34371/343*log(2+3*x)-12125/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (- 374298750x - 723644250x - 465794000x - 99813000)log(5x + 3)
+--R +
+--R 3 2
+--R (374300190x + 723647034x + 465795792x + 99813384)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 1440x - 2784x - 1792x - 384)log(- 2x + 1) - 24954930x - 32442333x
+--R +
+--R - 10519355
+--R /
+--R 3 2
+--R 3735270x + 7221522x + 4648336x + 996072
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (- 374298750x - 723644250x - 465794000x - 99813000)log(5x + 3)
+--R +
+--R 3 2
+--R (374300190x + 723647034x + 465795792x + 99813384)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 1440x - 2784x - 1792x - 384)log(2x - 1) - 24954930x - 32442333x
+--R +
+--R - 10519355
+--R /
+--R 3 2
+--R 3735270x + 7221522x + 4648336x + 996072
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500
+m0:=a0-r0
+--R
+--R
+--R - 16log(2x - 1) + 16log(- 2x + 1)
+--R (4) ---------------------------------
+--R 41503
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=1/((1-2*x)*(2+3*x)^4*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - ------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 4050x + 13635x + 17388x + 9039x - 376x - 2536x - 1056x - 144
+--R Type: Fraction(Polynomial(Integer))
+--E 416
+
+--S 417 of 500
+r0:=(-3/7)/(2+3*x)^3+(-324/49)/(2+3*x)^2+(-34371/343)/(2+3*x)+_
+ (-625/11)/(3+5*x)-32/290521*log(1-2*x)+1612242/2401*log(2+3*x)-_
+ 81250/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R - 26335968750x - 68473518750x - 66717787500x - 28872025000x
+--R +
+--R - 4681950000
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R 26335973070x + 68473529982x + 66717798444x + 28872029736x
+--R +
+--R 4681950768
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 4320x - 11232x - 10944x - 4736x - 768)log(- 2x + 1) - 1755736290x
+--R +
+--R 2
+--R - 3452950809x - 2261654241x - 493301347
+--R /
+--R 4 3 2
+--R 39220335x + 101972871x + 99358182x + 42997108x + 6972504
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R - 26335968750x - 68473518750x - 66717787500x - 28872025000x
+--R +
+--R - 4681950000
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R 26335973070x + 68473529982x + 66717798444x + 28872029736x
+--R +
+--R 4681950768
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 4320x - 11232x - 10944x - 4736x - 768)log(2x - 1) - 1755736290x
+--R +
+--R 2
+--R - 3452950809x - 2261654241x - 493301347
+--R /
+--R 4 3 2
+--R 39220335x + 101972871x + 99358182x + 42997108x + 6972504
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 500
+m0:=a0-r0
+--R
+--R
+--R - 32log(2x - 1) + 32log(- 2x + 1)
+--R (4) ---------------------------------
+--R 290521
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=1/((1-2*x)*(2+3*x)^5*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 12150x + 49005x + 79434x + 61893x + 16950x - 8360x - 8240x
+--R +
+--R - 2544x - 288
+--R Type: Fraction(Polynomial(Integer))
+--E 421
+
+--S 422 of 500
+r0:=(-9/28)/(2+3*x)^4+(-216/49)/(2+3*x)^3+(-34371/686)/(2+3*x)^2+_
+ (-1612242/2401)/(2+3*x)+(-3125/11)/(3+5*x)-64/2033647*log(1-2*x)+_
+ 70752609/16807*log(2+3*x)-509375/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3
+--R - 13868926312500x - 45305159287500x - 59174085600000x
+--R +
+--R 2
+--R - 38627528100000x - 12601888600000x - 1643724600000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R 13868926416180x + 45305159626188x + 59174086042368x
+--R +
+--R 2
+--R 38627528388768x + 12601888694208x + 1643724612288
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 103680x - 338688x - 442368x - 288768x - 94208x - 12288)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 924595208460x - 2434767448806x - 2403262839978x - 1053787613109x
+--R +
+--R - 173183872939
+--R /
+--R 5 4 3 2
+--R 3294508140x + 10762059924x + 14056568064x + 9175815264x + 2993528384x
+--R +
+--R 390460224
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R - 13868926312500x - 45305159287500x - 59174085600000x
+--R +
+--R 2
+--R - 38627528100000x - 12601888600000x - 1643724600000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R 13868926416180x + 45305159626188x + 59174086042368x
+--R +
+--R 2
+--R 38627528388768x + 12601888694208x + 1643724612288
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 103680x - 338688x - 442368x - 288768x - 94208x - 12288)log(2x - 1)
+--R +
+--R 4 3 2
+--R - 924595208460x - 2434767448806x - 2403262839978x - 1053787613109x
+--R +
+--R - 173183872939
+--R /
+--R 5 4 3 2
+--R 3294508140x + 10762059924x + 14056568064x + 9175815264x + 2993528384x
+--R +
+--R 390460224
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 500
+m0:=a0-r0
+--R
+--R
+--R - 64log(2x - 1) + 64log(- 2x + 1)
+--R (4) ---------------------------------
+--R 2033647
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=1/((1-2*x)*(2+3*x)^6*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 36450x + 171315x + 336312x + 344547x + 174636x + 8820x - 41440x
+--R +
+--R 2
+--R - 24112x - 5952x - 576
+--R Type: Fraction(Polynomial(Integer))
+--E 426
+
+--S 427 of 500
+r0:=(-9/35)/(2+3*x)^5+(-162/49)/(2+3*x)^4+(-11457/343)/(2+3*x)^3+_
+ (-806121/2401)/(2+3*x)^2+(-70752609/16807)/(2+3*x)+_
+ (-15625/11)/(3+5*x)-128/14235529*log(1-2*x)+2977686468/117649*_
+ log(2+3*x)-3062500/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R - 2188822879687500x - 8609369993437500x - 14105747446875000x
+--R +
+--R 3 2
+--R - 12322262137500000x - 6053041050000000x - 1585320275000000x
+--R +
+--R - 172944030000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R 2188822880465100x + 8609369996496060x + 14105747451886200x
+--R +
+--R 3 2
+--R 12322262141877600x + 6053041052150400x + 1585320275563200x
+--R +
+--R 172944030061440
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 777600x - 3058560x - 5011200x - 4377600x - 2150400x - 563200x
+--R +
+--R - 61440
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3
+--R - 145921526219700x - 481541037023970x - 635461225889490x
+--R +
+--R 2
+--R - 419169494735145x - 138206158563165x - 18221473659389
+--R /
+--R 6 5 4 3
+--R 86480838675x + 340157965455x + 557320960350x + 486855091800x
+--R +
+--R 2
+--R 239156887200x + 62636327600x + 6833053920
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R - 2188822879687500x - 8609369993437500x - 14105747446875000x
+--R +
+--R 3 2
+--R - 12322262137500000x - 6053041050000000x - 1585320275000000x
+--R +
+--R - 172944030000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R 2188822880465100x + 8609369996496060x + 14105747451886200x
+--R +
+--R 3 2
+--R 12322262141877600x + 6053041052150400x + 1585320275563200x
+--R +
+--R 172944030061440
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 777600x - 3058560x - 5011200x - 4377600x - 2150400x - 563200x
+--R +
+--R - 61440
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3
+--R - 145921526219700x - 481541037023970x - 635461225889490x
+--R +
+--R 2
+--R - 419169494735145x - 138206158563165x - 18221473659389
+--R /
+--R 6 5 4 3
+--R 86480838675x + 340157965455x + 557320960350x + 486855091800x
+--R +
+--R 2
+--R 239156887200x + 62636327600x + 6833053920
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 500
+m0:=a0-r0
+--R
+--R
+--R - 128log(2x - 1) + 128log(- 2x + 1)
+--R (4) -----------------------------------
+--R 14235529
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(2+3*x)^m/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R m
+--R (3x + 2)
+--R (1) - -------------------------------
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+--r0:=-5/22*(2+3*x)^(1+m)/(3+5*x)^2-10/121*(2+3*x)^(1+m)/(3+5*x)+_
+-- 15/22*(1-m)*(2+3*x)^(1+m)/(3+5*x)+8/9317*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)-20/1331*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)-30/121*m*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)+45/22*(1-m)*m*(2+3*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)
+--E 432
+
+--S 433 of 500
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 500
+--m0:=a0-r0
+--E 434
+
+--S 435 of 500
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(2+3*x)^8/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x
+--R +
+--R - 3072x - 256
+--R /
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 436
+
+--S 437 of 500
+r0:=-62934003/500000*x-9268263/100000*x^2-1535517/25000*x^3-_
+ 264627/10000*x^4-6561/1250*x^5+(-1/8593750)/(3+5*x)^2+_
+ (-266/47265625)/(3+5*x)-5764801/85184*log(1-2*x)+_
+ 31024/519921875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (49638400x + 59566080x + 17869824)log(5x + 3)
+--R +
+--R 2
+--R (- 56296884765625x - 67556261718750x - 20266878515625)log(- 2x + 1)
+--R +
+--R 7 6 5
+--R - 4366345500000x - 27253273162500x - 79082602830000x
+--R +
+--R 4 3 2
+--R - 146338473723750x - 215620841031750x - 153403867608750x
+--R +
+--R - 37694322033170x - 565664
+--R /
+--R 2
+--R 831875000000x + 998250000000x + 299475000000
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (49638400x + 59566080x + 17869824)log(5x + 3)
+--R +
+--R 2
+--R (- 56296884765625x - 67556261718750x - 20266878515625)log(2x - 1)
+--R +
+--R 7 6 5
+--R - 4366345500000x - 27253273162500x - 79082602830000x
+--R +
+--R 4 3 2
+--R - 146338473723750x - 215620841031750x - 153403867608750x
+--R +
+--R - 37694322033170x - 565664
+--R /
+--R 2
+--R 831875000000x + 998250000000x + 299475000000
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500
+m0:=a0-r0
+--R
+--R
+--R - 5764801log(2x - 1) + 5764801log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 85184
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(2+3*x)^7/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128
+--R -----------------------------------------------------------------------
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 441
+
+--S 442 of 500
+r0:=-339309/10000*x-1044657/50000*x^2-24543/2500*x^3-2187/1000*x^4+_
+ (-1/1718750)/(3+5*x)^2+(-233/9453125)/(3+5*x)-_
+ 823543/42592*log(1-2*x)+4667/20796875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (18668000x + 22401600x + 6720480)log(5x + 3)
+--R +
+--R 2
+--R (- 1608482421875x - 1930178906250x - 579053671875)log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R - 181931062500x - 1034985600000x - 2783545256250x - 5202285041250x
+--R +
+--R 2
+--R - 4012849402650x - 1016146037830x - 247984
+--R /
+--R 2
+--R 83187500000x + 99825000000x + 29947500000
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (18668000x + 22401600x + 6720480)log(5x + 3)
+--R +
+--R 2
+--R (- 1608482421875x - 1930178906250x - 579053671875)log(2x - 1)
+--R +
+--R 6 5 4 3
+--R - 181931062500x - 1034985600000x - 2783545256250x - 5202285041250x
+--R +
+--R 2
+--R - 4012849402650x - 1016146037830x - 247984
+--R /
+--R 2
+--R 83187500000x + 99825000000x + 29947500000
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500
+m0:=a0-r0
+--R
+--R
+--R - 823543log(2x - 1) + 823543log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 42592
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(2+3*x)^6/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R 6 5 4 3 2
+--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64
+--R (1) -------------------------------------------------------
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 446
+
+--S 447 of 500
+r0:=-216999/25000*x-19683/5000*x^2-243/250*x^3+(-1/343750)/(3+5*x)^2+_
+ (-8/75625)/(3+5*x)-117649/21296*log(1-2*x)+3347/4159375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (6694000x + 8032800x + 2409840)log(5x + 3)
+--R +
+--R 2
+--R (- 45956640625x - 55147968750x - 16544390625)log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 8085825000x - 42450581250x - 114414423750x - 98436833550x
+--R +
+--R - 25994486210x - 106568
+--R /
+--R 2
+--R 8318750000x + 9982500000x + 2994750000
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (6694000x + 8032800x + 2409840)log(5x + 3)
+--R +
+--R 2 5
+--R (- 45956640625x - 55147968750x - 16544390625)log(2x - 1) - 8085825000x
+--R +
+--R 4 3 2
+--R - 42450581250x - 114414423750x - 98436833550x - 25994486210x - 106568
+--R /
+--R 2
+--R 8318750000x + 9982500000x + 2994750000
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500
+m0:=a0-r0
+--R
+--R
+--R - 117649log(2x - 1) + 117649log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 21296
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(2+3*x)^5/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 451
+
+--S 452 of 500
+r0:=-4941/2500*x-243/500*x^2+(-1/68750)/(3+5*x)^2+(-167/378125)/(3+5*x)-_
+ 16807/10648*log(1-2*x)+11224/4159375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (2244800x + 2693760x + 808128)log(5x + 3)
+--R +
+--R 2 4
+--R (- 1313046875x - 1575656250x - 472696875)log(- 2x + 1) - 404291250x
+--R +
+--R 3 2
+--R - 2129267250x - 2118486150x - 591955870x - 44572
+--R /
+--R 2
+--R 831875000x + 998250000x + 299475000
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (2244800x + 2693760x + 808128)log(5x + 3)
+--R +
+--R 2 4
+--R (- 1313046875x - 1575656250x - 472696875)log(2x - 1) - 404291250x
+--R +
+--R 3 2
+--R - 2129267250x - 2118486150x - 591955870x - 44572
+--R /
+--R 2
+--R 831875000x + 998250000x + 299475000
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500
+m0:=a0-r0
+--R
+--R
+--R - 16807log(2x - 1) + 16807log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 10648
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(2+3*x)^4/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) ---------------------------------
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 456
+
+--S 457 of 500
+r0:=-81/250*x+(-1/13750)/(3+5*x)^2+(-134/75625)/(3+5*x)-_
+ 2401/5324*log(1-2*x)+6802/831875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (680200x + 816240x + 244872)log(5x + 3)
+--R +
+--R 2 3
+--R (- 37515625x - 45018750x - 13505625)log(- 2x + 1) - 26952750x
+--R +
+--R 2
+--R - 32343300x - 9732470x - 17930
+--R /
+--R 2
+--R 83187500x + 99825000x + 29947500
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (680200x + 816240x + 244872)log(5x + 3)
+--R +
+--R 2 3
+--R (- 37515625x - 45018750x - 13505625)log(2x - 1) - 26952750x
+--R +
+--R 2
+--R - 32343300x - 9732470x - 17930
+--R /
+--R 2
+--R 83187500x + 99825000x + 29947500
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2401log(2x - 1) + 2401log(- 2x + 1)
+--R (4) -------------------------------------
+--R 5324
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(2+3*x)^3/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) -------------------------------
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 461
+
+--S 462 of 500
+r0:=(-1/2750)/(3+5*x)^2+(-101/15125)/(3+5*x)-343/2662*log(1-2*x)+_
+ 3469/166375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (173450x + 208140x + 62442)log(5x + 3)
+--R +
+--R 2
+--R (- 1071875x - 1286250x - 385875)log(- 2x + 1) - 11110x - 6787
+--R /
+--R 2
+--R 8318750x + 9982500x + 2994750
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (173450x + 208140x + 62442)log(5x + 3)
+--R +
+--R 2
+--R (- 1071875x - 1286250x - 385875)log(2x - 1) - 11110x - 6787
+--R /
+--R 2
+--R 8318750x + 9982500x + 2994750
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500
+m0:=a0-r0
+--R
+--R
+--R - 343log(2x - 1) + 343log(- 2x + 1)
+--R (4) -----------------------------------
+--R 2662
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(2+3*x)^2/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) -------------------------------
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 466
+
+--S 467 of 500
+r0:=(-1/550)/(3+5*x)^2+(-68/3025)/(3+5*x)-49/1331*log(1-2*x)+49/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (61250x + 73500x + 22050)log(5x + 3)
+--R +
+--R 2
+--R (- 61250x - 73500x - 22050)log(- 2x + 1) - 7480x - 4609
+--R /
+--R 2
+--R 1663750x + 1996500x + 598950
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (61250x + 73500x + 22050)log(5x + 3)
+--R +
+--R 2
+--R (- 61250x - 73500x - 22050)log(2x - 1) - 7480x - 4609
+--R /
+--R 2
+--R 1663750x + 1996500x + 598950
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 500
+m0:=a0-r0
+--R
+--R
+--R - 49log(2x - 1) + 49log(- 2x + 1)
+--R (4) ---------------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(2+3*x)/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R - 3x - 2
+--R (1) -------------------------------
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 471
+
+--S 472 of 500
+r0:=(-1/110)/(3+5*x)^2+(-7/121)/(3+5*x)-14/1331*log(1-2*x)+14/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (3500x + 4200x + 1260)log(5x + 3)
+--R +
+--R 2
+--R (- 3500x - 4200x - 1260)log(- 2x + 1) - 3850x - 2431
+--R /
+--R 2
+--R 332750x + 399300x + 119790
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (3500x + 4200x + 1260)log(5x + 3) + (- 3500x - 4200x - 1260)log(2x - 1)
+--R +
+--R - 3850x - 2431
+--R /
+--R 2
+--R 332750x + 399300x + 119790
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 500
+m0:=a0-r0
+--R
+--R
+--R - 14log(2x - 1) + 14log(- 2x + 1)
+--R (4) ---------------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=1/((1-2*x)*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) - -------------------------------
+--R 4 3 2
+--R 250x + 325x + 45x - 81x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 476
+
+--S 477 of 500
+r0:=(-1/22)/(3+5*x)^2+(-2/121)/(3+5*x)-4/1331*log(1-2*x)+4/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (200x + 240x + 72)log(5x + 3) + (- 200x - 240x - 72)log(- 2x + 1)
+--R +
+--R - 220x - 253
+--R /
+--R 2
+--R 66550x + 79860x + 23958
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (200x + 240x + 72)log(5x + 3) + (- 200x - 240x - 72)log(2x - 1) - 220x
+--R +
+--R - 253
+--R /
+--R 2
+--R 66550x + 79860x + 23958
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 500
+m0:=a0-r0
+--R
+--R
+--R - 4log(2x - 1) + 4log(- 2x + 1)
+--R (4) -------------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=1/((1-2*x)*(2+3*x)*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) - ------------------------------------------
+--R 5 4 3 2
+--R 750x + 1475x + 785x - 153x - 243x - 54
+--R Type: Fraction(Polynomial(Integer))
+--E 481
+
+--S 482 of 500
+r0:=(-5/22)/(3+5*x)^2+155/121/(3+5*x)-8/9317*log(1-2*x)-27/7*log(2+3*x)+_
+ 5135/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (1797250x + 2156700x + 647010)log(5x + 3)
+--R +
+--R 2
+--R (- 1796850x - 2156220x - 646866)log(3x + 2)
+--R +
+--R 2
+--R (- 400x - 480x - 144)log(- 2x + 1) + 119350x + 67375
+--R /
+--R 2
+--R 465850x + 559020x + 167706
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (1797250x + 2156700x + 647010)log(5x + 3)
+--R +
+--R 2
+--R (- 1796850x - 2156220x - 646866)log(3x + 2)
+--R +
+--R 2
+--R (- 400x - 480x - 144)log(2x - 1) + 119350x + 67375
+--R /
+--R 2
+--R 465850x + 559020x + 167706
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500
+m0:=a0-r0
+--R
+--R
+--R - 8log(2x - 1) + 8log(- 2x + 1)
+--R (4) -------------------------------
+--R 9317
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=1/((1-2*x)*(2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------------------
+--R 6 5 4 3 2
+--R 2250x + 5925x + 5305x + 1111x - 1035x - 648x - 108
+--R Type: Fraction(Polynomial(Integer))
+--E 486
+
+--S 487 of 500
+r0:=27/7/(2+3*x)+(-25/22)/(3+5*x)^2+1600/121/(3+5*x)-16/65219*log(1-2*x)-_
+ 2889/49*log(2+3*x)+78475/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (576791250x + 1076677000x + 669077850x + 138429900)log(5x + 3)
+--R +
+--R 3 2
+--R (- 576788850x - 1076672520x - 669075066x - 138429324)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 2400x - 4480x - 2784x - 576)log(- 2x + 1) + 38449950x + 47420065x
+--R +
+--R 14580412
+--R /
+--R 3 2
+--R 9782850x + 18261320x + 11348106x + 2347884
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (576791250x + 1076677000x + 669077850x + 138429900)log(5x + 3)
+--R +
+--R 3 2
+--R (- 576788850x - 1076672520x - 669075066x - 138429324)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 2400x - 4480x - 2784x - 576)log(2x - 1) + 38449950x + 47420065x
+--R +
+--R 14580412
+--R /
+--R 3 2
+--R 9782850x + 18261320x + 11348106x + 2347884
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500
+m0:=a0-r0
+--R
+--R
+--R - 16log(2x - 1) + 16log(- 2x + 1)
+--R (4) ---------------------------------
+--R 65219
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=1/((1-2*x)*(2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 6750x + 22275x + 27765x + 13943x - 883x - 4014x - 1620x - 216
+--R Type: Fraction(Polynomial(Integer))
+--E 491
+
+--S 492 of 500
+r0:=27/14/(2+3*x)^2+2889/49/(2+3*x)+(-125/22)/(3+5*x)^2+12125/121/(3+5*x)-_
+ 32/456533*log(1-2*x)-204228/343*log(2+3*x)+792500/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 122322375000x + 309883350000x + 294117355000x + 123953340000x
+--R +
+--R 19571580000
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 122322360600x - 309883313520x - 294117320376x - 123953325408x
+--R +
+--R - 19571577696
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 14400x - 36480x - 34624x - 14592x - 2304)log(- 2x + 1)
+--R +
+--R 3 2
+--R 8154808200x + 15494126340x + 9797832352x + 2062044985
+--R /
+--R 4 3 2
+--R 205439850x + 520447620x + 493968706x + 208179048x + 32870376
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 122322375000x + 309883350000x + 294117355000x + 123953340000x
+--R +
+--R 19571580000
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 122322360600x - 309883313520x - 294117320376x - 123953325408x
+--R +
+--R - 19571577696
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 14400x - 36480x - 34624x - 14592x - 2304)log(2x - 1) + 8154808200x
+--R +
+--R 2
+--R 15494126340x + 9797832352x + 2062044985
+--R /
+--R 4 3 2
+--R 205439850x + 520447620x + 493968706x + 208179048x + 32870376
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500
+m0:=a0-r0
+--R
+--R
+--R - 32log(2x - 1) + 32log(- 2x + 1)
+--R (4) ---------------------------------
+--R 456533
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=1/((1-2*x)*(2+3*x)^4*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 20250x + 80325x + 127845x + 97359x + 25237x - 13808x - 12888x
+--R +
+--R - 3888x - 432
+--R Type: Fraction(Polynomial(Integer))
+--E 496
+
+--S 497 of 500
+r0:=9/7/(2+3*x)^3+2889/98/(2+3*x)^2+204228/343/(2+3*x)+(-625/22)/(3+5*x)^2+_
+ 81250/121/(3+5*x)-64/3195731*log(1-2*x)-11984706/2401*log(2+3*x)+_
+ 6643750/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3
+--R 21534719062500x + 68911101000000x + 88148783362500x
+--R +
+--R 2
+--R 56341205725000x + 17993454150000x + 2297036700000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 21534718976100x - 68911100723520x - 88148783008836x
+--R +
+--R 2
+--R - 56341205498952x - 17993454077808x - 2297036690784
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 86400x - 276480x - 353664x - 226048x - 72192x - 9216)log(- 2x + 1)
+--R +
+--R 4 3 2
+--R 1435647836700x + 3684829392090x + 3543391400472x + 1512959972293x
+--R +
+--R 242016815656
+--R /
+--R 5 4 3 2
+--R 4314236850x + 13805557920x + 17659609506x + 11287321892x
+--R +
+--R 3604784568x + 460185264
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R 21534719062500x + 68911101000000x + 88148783362500x
+--R +
+--R 2
+--R 56341205725000x + 17993454150000x + 2297036700000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 21534718976100x - 68911100723520x - 88148783008836x
+--R +
+--R 2
+--R - 56341205498952x - 17993454077808x - 2297036690784
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 86400x - 276480x - 353664x - 226048x - 72192x - 9216)log(2x - 1)
+--R +
+--R 4 3 2
+--R 1435647836700x + 3684829392090x + 3543391400472x + 1512959972293x
+--R +
+--R 242016815656
+--R /
+--R 5 4 3 2
+--R 4314236850x + 13805557920x + 17659609506x + 11287321892x
+--R +
+--R 3604784568x + 460185264
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500
+m0:=a0-r0
+--R
+--R
+--R - 64log(2x - 1) + 64log(- 2x + 1)
+--R (4) ---------------------------------
+--R 3195731
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3g.input.pdf b/src/axiom-website/CATS/rich3g.input.pdf
new file mode 100644
index 0000000..7f8f6b9
Binary files /dev/null and b/src/axiom-website/CATS/rich3g.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3h.input.pamphlet b/src/axiom-website/CATS/rich3h.input.pamphlet
new file mode 100644
index 0000000..147824c
--- /dev/null
+++ b/src/axiom-website/CATS/rich3h.input.pamphlet
@@ -0,0 +1,7356 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3h.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 97 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 3 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3h.output
+)spool rich3h.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=1/((1-2*x)*(2+3*x)^5*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 60750x + 281475x + 544185x + 547767x + 270429x + 9050x - 66280x
+--R +
+--R 2
+--R - 37440x - 9072x - 864
+--R Type: Fraction(Polynomial(Integer))
+--E 1
+
+--S 2 of 500
+r0:=27/28/(2+3*x)^4+963/49/(2+3*x)^3+102114/343/(2+3*x)^2+_
+ 11984706/2401/(2+3*x)+(-3125/22)/(3+5*x)^2+509375/121/(3+5*x)-_
+ 128/22370117*log(1-2*x)-631722537/16807*log(2+3*x)+_
+ 50028125/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R 6810663844687500x + 26334566866125000x + 42407733539587500x
+--R +
+--R 3 2
+--R 36404259483900000x + 17569831073900000x + 4520262818400000x
+--R +
+--R 484313873400000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 6810663843650700x - 26334566862116040x - 42407733533131692x
+--R +
+--R 3 2
+--R - 36404259478358112x - 17569831071225312x - 4520262817711872x
+--R +
+--R - 484313873326272
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 1036800x - 4008960x - 6455808x - 5541888x - 2674688x - 688128x
+--R +
+--R - 73728
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3
+--R 454044255102900x + 1468076424167430x + 1897568655019884x
+--R +
+--R 2
+--R 1225594367568417x + 395538240141506x + 51027557612801
+--R /
+--R 6 5 4 3
+--R 181197947700x + 700632064440x + 1128259221012x + 968536585632x
+--R +
+--R 2
+--R 467445964832x + 120261748992x + 12885187392
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R 6810663844687500x + 26334566866125000x + 42407733539587500x
+--R +
+--R 3 2
+--R 36404259483900000x + 17569831073900000x + 4520262818400000x
+--R +
+--R 484313873400000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 6810663843650700x - 26334566862116040x - 42407733533131692x
+--R +
+--R 3 2
+--R - 36404259478358112x - 17569831071225312x - 4520262817711872x
+--R +
+--R - 484313873326272
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 1036800x - 4008960x - 6455808x - 5541888x - 2674688x - 688128x
+--R +
+--R - 73728
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3
+--R 454044255102900x + 1468076424167430x + 1897568655019884x
+--R +
+--R 2
+--R 1225594367568417x + 395538240141506x + 51027557612801
+--R /
+--R 6 5 4 3
+--R 181197947700x + 700632064440x + 1128259221012x + 968536585632x
+--R +
+--R 2
+--R 467445964832x + 120261748992x + 12885187392
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500
+m0:=a0-r0
+--R
+--R
+--R - 128log(2x - 1) + 128log(- 2x + 1)
+--R (4) -----------------------------------
+--R 22370117
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(2+3*x)^8*(3+5*x)/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3
+--R 32805x + 194643x + 513216x + 789264x + 780192x + 514080x + 225792x
+--R +
+--R 2
+--R 63744x + 10496x + 768
+--R /
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 6
+
+--S 7 of 500
+r0:=63412811/1024/(1-2*x)+91609881/256*x+122887143/512*x^2+5892813/32*x^3+_
+ 32991057/256*x^4+5859459/80*x^5+976617/32*x^6+56862/7*x^7+_
+ 32805/32*x^8+246239357/1024*log(1-2*x)
+--R
+--R
+--R (2)
+--R 9 8
+--R (17236754990x - 8618377495)log(- 2x + 1) + 73483200x + 545525280x
+--R +
+--R 7 6 5 4 3
+--R 1896488640x + 4156264224x + 6612458328x + 8581153140x + 10604249460x
+--R +
+--R 2
+--R 17048666670x - 12825383340x - 2219448385
+--R /
+--R 71680x - 35840
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8
+--R (17236754990x - 8618377495)log(2x - 1) + 73483200x + 545525280x
+--R +
+--R 7 6 5 4 3
+--R 1896488640x + 4156264224x + 6612458328x + 8581153140x + 10604249460x
+--R +
+--R 2
+--R 17048666670x - 12825383340x - 2219448385
+--R /
+--R 71680x - 35840
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 500
+m0:=a0-r0
+--R
+--R
+--R 246239357log(2x - 1) - 246239357log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 1024
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(2+3*x)^7*(3+5*x)/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x
+--R +
+--R 4672x + 384
+--R /
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 11
+
+--S 12 of 500
+r0:=9058973/512/(1-2*x)+22333965/256*x+873207/16*x^2+2399985/64*x^3+_
+ 1423899/64*x^4+793881/80*x^5+11421/4*x^6+10935/28*x^7+_
+ 15647317/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 8 7
+--R (2190624380x - 1095312190)log(- 2x + 1) + 13996800x + 95333760x
+--R +
+--R 6 5 4 3 2
+--R 304492608x + 619554096x + 945299880x + 1283987880x + 2148763260x
+--R +
+--R - 1563377550x - 317064055
+--R /
+--R 35840x - 17920
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7
+--R (2190624380x - 1095312190)log(2x - 1) + 13996800x + 95333760x
+--R +
+--R 6 5 4 3 2
+--R 304492608x + 619554096x + 945299880x + 1283987880x + 2148763260x
+--R +
+--R - 1563377550x - 317064055
+--R /
+--R 35840x - 17920
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 500
+m0:=a0-r0
+--R
+--R
+--R 15647317log(2x - 1) - 15647317log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(2+3*x)^6*(3+5*x)/(1-2*x)^2
+--R
+--R
+--R 7 6 5 4 3 2
+--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192
+--R (1) ---------------------------------------------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 16
+
+--S 17 of 500
+r0:=1294139/256/(1-2*x)+661617/32*x+1507977/128*x^2+111501/16*x^3+_
+ 210195/64*x^4+5103/5*x^5+1215/8*x^6+3916031/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R (39160310x - 19580155)log(- 2x + 1) + 388800x + 2418336x + 7101432x
+--R +
+--R 4 3 2
+--R 13636260x + 21239460x + 37849590x - 26464680x - 6470695
+--R /
+--R 2560x - 1280
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R (39160310x - 19580155)log(2x - 1) + 388800x + 2418336x + 7101432x
+--R +
+--R 4 3 2
+--R 13636260x + 21239460x + 37849590x - 26464680x - 6470695
+--R /
+--R 2560x - 1280
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 500
+m0:=a0-r0
+--R
+--R
+--R 3916031log(2x - 1) - 3916031log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96
+--R (1) ------------------------------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 21
+
+--S 22 of 500
+r0:=184877/128/(1-2*x)+301467/64*x+75447/32*x^2+18027/16*x^3+2997/8*x^4+_
+ 243/4*x^5+60025/16*log(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R (960400x - 480200)log(- 2x + 1) + 15552x + 88128x + 240480x + 459360x
+--R +
+--R 2
+--R 904080x - 602934x - 184877
+--R /
+--R 256x - 128
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R (960400x - 480200)log(2x - 1) + 15552x + 88128x + 240480x + 459360x
+--R +
+--R 2
+--R 904080x - 602934x - 184877
+--R /
+--R 256x - 128
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 500
+m0:=a0-r0
+--R
+--R
+--R 60025log(2x - 1) - 60025log(- 2x + 1)
+--R (4) -------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^2
+--R
+--R
+--R 5 4 3 2
+--R 405x + 1323x + 1728x + 1128x + 368x + 48
+--R (1) --------------------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 26
+
+--S 27 of 500
+r0:=26411/64/(1-2*x)+16203/16*x+13419/32*x^2+144*x^3+405/16*x^4+_
+ 57281/64*log(1-2*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (114562x - 57281)log(- 2x + 1) + 3240x + 16812x + 44460x + 102786x
+--R +
+--R - 64812x - 26411
+--R /
+--R 128x - 64
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (114562x - 57281)log(2x - 1) + 3240x + 16812x + 44460x + 102786x
+--R +
+--R - 64812x - 26411
+--R /
+--R 128x - 64
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 500
+m0:=a0-r0
+--R
+--R
+--R 57281log(2x - 1) - 57281log(- 2x + 1)
+--R (4) -------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^2
+--R
+--R
+--R 4 3 2
+--R 135x + 351x + 342x + 148x + 24
+--R (1) ---------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 31
+
+--S 32 of 500
+r0:=3773/32/(1-2*x)+3177/16*x+243/4*x^2+45/4*x^3+3283/16*log(1-2*x)
+--R
+--R
+--R 4 3 2
+--R (13132x - 6566)log(- 2x + 1) + 720x + 3528x + 10764x - 6354x - 3773
+--R (2) ----------------------------------------------------------------------
+--R 64x - 32
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R (13132x - 6566)log(2x - 1) + 720x + 3528x + 10764x - 6354x - 3773
+--R (3) --------------------------------------------------------------------
+--R 64x - 32
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 500
+m0:=a0-r0
+--R
+--R
+--R 3283log(2x - 1) - 3283log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^2
+--R
+--R
+--R 3 2
+--R 45x + 87x + 56x + 12
+--R (1) ----------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 36
+
+--S 37 of 500
+r0:=539/16/(1-2*x)+33*x+45/8*x^2+707/16*log(1-2*x)
+--R
+--R
+--R 3 2
+--R (1414x - 707)log(- 2x + 1) + 180x + 966x - 528x - 539
+--R (2) -------------------------------------------------------
+--R 32x - 16
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R (1414x - 707)log(2x - 1) + 180x + 966x - 528x - 539
+--R (3) -----------------------------------------------------
+--R 32x - 16
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 500
+m0:=a0-r0
+--R
+--R
+--R 707log(2x - 1) - 707log(- 2x + 1)
+--R (4) ---------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(2+3*x)*(3+5*x)/(1-2*x)^2
+--R
+--R
+--R 2
+--R 15x + 19x + 6
+--R (1) --------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 41
+
+--S 42 of 500
+r0:=77/8/(1-2*x)+15/4*x+17/2*log(1-2*x)
+--R
+--R
+--R 2
+--R (136x - 68)log(- 2x + 1) + 60x - 30x - 77
+--R (2) ------------------------------------------
+--R 16x - 8
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (136x - 68)log(2x - 1) + 60x - 30x - 77
+--R (3) ----------------------------------------
+--R 16x - 8
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500
+m0:=a0-r0
+--R
+--R
+--R 17log(2x - 1) - 17log(- 2x + 1)
+--R (4) -------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(3+5*x)/(1-2*x)^2
+--R
+--R
+--R 5x + 3
+--R (1) ------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 46
+
+--S 47 of 500
+r0:=11/4/(1-2*x)+5/4*log(1-2*x)
+--R
+--R
+--R (10x - 5)log(- 2x + 1) - 11
+--R (2) ---------------------------
+--R 8x - 4
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (10x - 5)log(2x - 1) - 11
+--R (3) -------------------------
+--R 8x - 4
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500
+m0:=a0-r0
+--R
+--R
+--R 5log(2x - 1) - 5log(- 2x + 1)
+--R (4) -----------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(3+5*x)/((1-2*x)^2*(2+3*x))
+--R
+--R
+--R 5x + 3
+--R (1) -------------------
+--R 3 2
+--R 12x - 4x - 5x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 500
+r0:=11/14/(1-2*x)+1/49*log(1-2*x)-1/49*log(2+3*x)
+--R
+--R
+--R (- 4x + 2)log(3x + 2) + (4x - 2)log(- 2x + 1) - 77
+--R (2) --------------------------------------------------
+--R 196x - 98
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (- 4x + 2)log(3x + 2) + (4x - 2)log(2x - 1) - 77
+--R (3) ------------------------------------------------
+--R 196x - 98
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500
+m0:=a0-r0
+--R
+--R
+--R log(2x - 1) - log(- 2x + 1)
+--R (4) ---------------------------
+--R 49
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^2)
+--R
+--R
+--R 5x + 3
+--R (1) ---------------------------
+--R 4 3 2
+--R 36x + 12x - 23x - 4x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 56
+
+--S 57 of 500
+r0:=11/49/(1-2*x)+1/49/(2+3*x)-31/343*log(1-2*x)+31/343*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (186x + 31x - 62)log(3x + 2) + (- 186x - 31x + 62)log(- 2x + 1) - 217x
+--R +
+--R - 161
+--R /
+--R 2
+--R 2058x + 343x - 686
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (186x + 31x - 62)log(3x + 2) + (- 186x - 31x + 62)log(2x - 1) - 217x - 161
+--R ----------------------------------------------------------------------------
+--R 2
+--R 2058x + 343x - 686
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 500
+m0:=a0-r0
+--R
+--R
+--R - 31log(2x - 1) + 31log(- 2x + 1)
+--R (4) ---------------------------------
+--R 343
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^3)
+--R
+--R
+--R 5x + 3
+--R (1) ------------------------------------
+--R 5 4 3 2
+--R 108x + 108x - 45x - 58x + 4x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 61
+
+--S 62 of 500
+r0:=22/343/(1-2*x)+1/98/(2+3*x)^2+(-31/343)/(2+3*x)-128/2401*log(1-2*x)+_
+ 128/2401*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (4608x + 3840x - 1024x - 1024)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 4608x - 3840x + 1024x + 1024)log(- 2x + 1) - 5376x - 4032x - 413
+--R /
+--R 3 2
+--R 86436x + 72030x - 19208x - 19208
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (4608x + 3840x - 1024x - 1024)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 4608x - 3840x + 1024x + 1024)log(2x - 1) - 5376x - 4032x - 413
+--R /
+--R 3 2
+--R 86436x + 72030x - 19208x - 19208
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 500
+m0:=a0-r0
+--R
+--R
+--R - 128log(2x - 1) + 128log(- 2x + 1)
+--R (4) -----------------------------------
+--R 2401
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^4)
+--R
+--R
+--R 5x + 3
+--R (1) -----------------------------------------------
+--R 6 5 4 3 2
+--R 324x + 540x + 81x - 264x - 104x + 32x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 66
+
+--S 67 of 500
+r0:=44/2401/(1-2*x)+1/147/(2+3*x)^3+(-31/686)/(2+3*x)^2+(-128/2401)/(2+3*x)-_
+ 388/16807*log(1-2*x)+388/16807*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (125712x + 188568x + 41904x - 46560x - 18624)log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 125712x - 188568x - 41904x + 46560x + 18624)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 146664x - 207774x - 48209x + 15148
+--R /
+--R 4 3 2
+--R 5445468x + 8168202x + 1815156x - 2016840x - 806736
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (125712x + 188568x + 41904x - 46560x - 18624)log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 125712x - 188568x - 41904x + 46560x + 18624)log(2x - 1) - 146664x
+--R +
+--R 2
+--R - 207774x - 48209x + 15148
+--R /
+--R 4 3 2
+--R 5445468x + 8168202x + 1815156x - 2016840x - 806736
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 500
+m0:=a0-r0
+--R
+--R
+--R - 388log(2x - 1) + 388log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16807
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^5)
+--R
+--R
+--R 5x + 3
+--R (1) -----------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 71
+
+--S 72 of 500
+r0:=88/16807/(1-2*x)+1/196/(2+3*x)^4+(-31/1029)/(2+3*x)^3+_
+ (-64/2401)/(2+3*x)^2+(-388/16807)/(2+3*x)-1040/117649*log(1-2*x)+_
+ 1040/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (2021760x + 4380480x + 2695680x - 299520x - 798720x - 199680)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 2021760x - 4380480x - 2695680x + 299520x + 798720x + 199680)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 2358720x - 4914000x - 3003000x + 64610x + 370853
+--R /
+--R 5 4 3 2
+--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (2021760x + 4380480x + 2695680x - 299520x - 798720x - 199680)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 2021760x - 4380480x - 2695680x + 299520x + 798720x + 199680)
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 2358720x - 4914000x - 3003000x + 64610x + 370853
+--R /
+--R 5 4 3 2
+--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1040log(2x - 1) + 1040log(- 2x + 1)
+--R (4) -------------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^6)
+--R
+--R
+--R 5x + 3
+--R (1) ----------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 76
+
+--S 77 of 500
+r0:=176/117649/(1-2*x)+1/245/(2+3*x)^5+(-31/1372)/(2+3*x)^4+_
+ (-128/7203)/(2+3*x)^3+(-194/16807)/(2+3*x)^2+_
+ (-1040/117649)/(2+3*x)-2608/823543*log(1-2*x)+2608/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 76049280x + 215472960x + 211248000x + 56332800x - 37555200x
+--R +
+--R - 27540480x - 5007360
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 76049280x - 215472960x - 211248000x - 56332800x + 37555200x
+--R +
+--R 27540480x + 5007360
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 88724160x - 243991440x - 236187000x - 72875670x + 24420823x
+--R +
+--R 14729806
+--R /
+--R 6 5 4 3
+--R 24014513880x + 68041122660x + 66706983000x + 17788528800x
+--R +
+--R 2
+--R - 11859019200x - 8696614080x - 1581202560
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 76049280x + 215472960x + 211248000x + 56332800x - 37555200x
+--R +
+--R - 27540480x - 5007360
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 76049280x - 215472960x - 211248000x - 56332800x + 37555200x
+--R +
+--R 27540480x + 5007360
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 88724160x - 243991440x - 236187000x - 72875670x + 24420823x
+--R +
+--R 14729806
+--R /
+--R 6 5 4 3
+--R 24014513880x + 68041122660x + 66706983000x + 17788528800x
+--R +
+--R 2
+--R - 11859019200x - 8696614080x - 1581202560
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2608log(2x - 1) + 2608log(- 2x + 1)
+--R (4) -------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^7)
+--R
+--R
+--R (1)
+--R 5x + 3
+--R /
+--R 9 8 7 6 5 4 3 2
+--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x
+--R +
+--R 832x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 81
+
+--S 82 of 500
+r0:=352/823543/(1-2*x)+1/294/(2+3*x)^6+(-31/1715)/(2+3*x)^5+_
+ (-32/2401)/(2+3*x)^4+(-388/50421)/(2+3*x)^3+_
+ (-520/117649)/(2+3*x)^2+(-2608/823543)/(2+3*x)-_
+ 128/117649*log(1-2*x)+128/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 2
+--R 1866240x + 6531840x + 8709120x + 4838400x - 1290240x - 573440x
+--R +
+--R - 81920
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4 2
+--R - 1866240x - 6531840x - 8709120x - 4838400x + 1290240x + 573440x
+--R +
+--R 81920
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3 2
+--R - 2177280x - 7439040x - 9787680x - 5652360x - 592956x + 929404x
+--R +
+--R 343917
+--R /
+--R 7 6 5 4 2
+--R 1715322420x + 6003628470x + 8004837960x + 4447132200x - 1185901920x
+--R +
+--R - 527067520x - 75295360
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 2
+--R 1866240x + 6531840x + 8709120x + 4838400x - 1290240x - 573440x
+--R +
+--R - 81920
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4 2
+--R - 1866240x - 6531840x - 8709120x - 4838400x + 1290240x + 573440x
+--R +
+--R 81920
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3 2
+--R - 2177280x - 7439040x - 9787680x - 5652360x - 592956x + 929404x
+--R +
+--R 343917
+--R /
+--R 7 6 5 4 2
+--R 1715322420x + 6003628470x + 8004837960x + 4447132200x - 1185901920x
+--R +
+--R - 527067520x - 75295360
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500
+m0:=a0-r0
+--R
+--R
+--R - 128log(2x - 1) + 128log(- 2x + 1)
+--R (4) -----------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(2+3*x)^8*(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5
+--R 164025x + 1071630x + 3150009x + 5485968x + 6268752x + 4910976x
+--R +
+--R 4 3 2
+--R 2671200x + 996096x + 243712x + 35328x + 2304
+--R /
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 86
+
+--S 87 of 500
+r0:=697540921/2048/(1-2*x)+2330515357/1024*x+413355417/256*x^2+_
+ 346239417/256*x^3+275757561/256*x^4+235268793/320*x^5+_
+ 396738*x^6+17378631/112*x^7+1235655/32*x^8+18225/4*x^9+_
+ 1512848491/1024*log(1-2*x)
+--R
+--R
+--R (2)
+--R 10 9
+--R (211798788740x - 105899394370)log(- 2x + 1) + 653184000x + 5209142400x
+--R +
+--R 8 7 6 5
+--R 19476780480x + 45754035840x + 76962239424x + 101724024528x
+--R +
+--R 4 3 2
+--R 116681956440x + 134531996760x + 210532633220x - 163136074990x
+--R +
+--R - 24413932235
+--R /
+--R 143360x - 71680
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9
+--R (211798788740x - 105899394370)log(2x - 1) + 653184000x + 5209142400x
+--R +
+--R 8 7 6 5
+--R 19476780480x + 45754035840x + 76962239424x + 101724024528x
+--R +
+--R 4 3 2
+--R 116681956440x + 134531996760x + 210532633220x - 163136074990x
+--R +
+--R - 24413932235
+--R /
+--R 143360x - 71680
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500
+m0:=a0-r0
+--R
+--R
+--R 1512848491log(2x - 1) - 1512848491log(- 2x + 1)
+--R (4) -----------------------------------------------
+--R 1024
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(2+3*x)^7*(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4
+--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x
+--R +
+--R 3 2
+--R 351120x + 97952x + 15936x + 1152
+--R /
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 91
+
+--S 92 of 500
+r0:=99648703/1024/(1-2*x)+9077405/16*x+195497697/512*x^2+18842715/64*x^3+_
+ 53086563/256*x^4+4750569/40*x^5+1597239/32*x^6+375435/28*x^7+_
+ 54675/32*x^8+389535839/1024*log(1-2*x)
+--R
+--R
+--R (2)
+--R 9 8
+--R (27267508730x - 13633754365)log(- 2x + 1) + 122472000x + 899877600x
+--R +
+--R 7 6 5 4
+--R 3097258560x + 6724111968x + 10607727816x + 13671721980x
+--R +
+--R 3 2
+--R 16817757180x + 26981935610x - 20333387200x - 3487704605
+--R /
+--R 71680x - 35840
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8
+--R (27267508730x - 13633754365)log(2x - 1) + 122472000x + 899877600x
+--R +
+--R 7 6 5 4
+--R 3097258560x + 6724111968x + 10607727816x + 13671721980x
+--R +
+--R 3 2
+--R 16817757180x + 26981935610x - 20333387200x - 3487704605
+--R /
+--R 71680x - 35840
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500
+m0:=a0-r0
+--R
+--R
+--R 389535839log(2x - 1) - 389535839log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 1024
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(2+3*x)^6*(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x
+--R +
+--R 7104x + 576
+--R /
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 96
+
+--S 97 of 500
+r0:=14235529/512/(1-2*x)+35458963/256*x+11140101/128*x^2+3851307/64*x^3+_
+ 575775/16*x^4+1295919/80*x^5+37665/8*x^6+18225/28*x^7+_
+ 12386759/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 8 7
+--R (3468292520x - 1734146260)log(- 2x + 1) + 23328000x + 157075200x
+--R +
+--R 6 5 4 3 2
+--R 496202112x + 999450144x + 1511863920x + 2040862320x + 3404640680x
+--R +
+--R - 2482127410x - 498243515
+--R /
+--R 35840x - 17920
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7
+--R (3468292520x - 1734146260)log(2x - 1) + 23328000x + 157075200x
+--R +
+--R 6 5 4 3 2
+--R 496202112x + 999450144x + 1511863920x + 2040862320x + 3404640680x
+--R +
+--R - 2482127410x - 498243515
+--R /
+--R 35840x - 17920
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500
+m0:=a0-r0
+--R
+--R
+--R 12386759log(2x - 1) - 12386759log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R 7 6 5 4 3 2
+--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288
+--R (1) ----------------------------------------------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 500
+r0:=2033647/256/(1-2*x)+2104901/64*x+2412699/128*x^2+89913/8*x^3+_
+ 342333/64*x^4+6723/4*x^5+2025/8*x^6+6206585/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R (12413170x - 6206585)log(- 2x + 1) + 129600x + 795744x + 2308392x
+--R +
+--R 4 3 2
+--R 4385100x + 6773580x + 12013810x - 8419604x - 2033647
+--R /
+--R 512x - 256
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R (12413170x - 6206585)log(2x - 1) + 129600x + 795744x + 2308392x
+--R +
+--R 4 3 2
+--R 4385100x + 6773580x + 12013810x - 8419604x - 2033647
+--R /
+--R 512x - 256
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 500
+m0:=a0-r0
+--R
+--R
+--R 6206585log(2x - 1) - 6206585log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144
+--R (1) ----------------------------------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 106
+
+--S 107 of 500
+r0:=290521/128/(1-2*x)+480841/64*x+15159/4*x^2+29277/16*x^3+9855/16*x^4+_
+ 405/4*x^5+381073/64*log(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R (1524292x - 762146)log(- 2x + 1) + 25920x + 144720x + 389592x
+--R +
+--R 3 2
+--R 735960x + 1438276x - 961682x - 290521
+--R /
+--R 256x - 128
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R (1524292x - 762146)log(2x - 1) + 25920x + 144720x + 389592x + 735960x
+--R +
+--R 2
+--R 1438276x - 961682x - 290521
+--R /
+--R 256x - 128
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 500
+m0:=a0-r0
+--R
+--R
+--R 381073log(2x - 1) - 381073log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R 5 4 3 2
+--R 675x + 2160x + 2763x + 1766x + 564x + 72
+--R (1) --------------------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 111
+
+--S 112 of 500
+r0:=41503/64/(1-2*x)+12973/8*x+21717/32*x^2+945/4*x^3+675/16*x^4+_
+ 91091/64*log(1-2*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (182182x - 91091)log(- 2x + 1) + 5400x + 27540x + 71748x + 164134x
+--R +
+--R - 103784x - 41503
+--R /
+--R 128x - 64
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (182182x - 91091)log(2x - 1) + 5400x + 27540x + 71748x + 164134x
+--R +
+--R - 103784x - 41503
+--R /
+--R 128x - 64
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 500
+m0:=a0-r0
+--R
+--R
+--R 91091log(2x - 1) - 91091log(- 2x + 1)
+--R (4) -------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R 4 3 2
+--R 225x + 570x + 541x + 228x + 36
+--R (1) ---------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 116
+
+--S 117 of 500
+r0:=5929/32/(1-2*x)+5119/16*x+795/8*x^2+75/4*x^3+1309/4*log(1-2*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (20944x - 10472)log(- 2x + 1) + 1200x + 5760x + 17296x - 10238x - 5929
+--R -------------------------------------------------------------------------
+--R 64x - 32
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (20944x - 10472)log(2x - 1) + 1200x + 5760x + 17296x - 10238x - 5929
+--R -----------------------------------------------------------------------
+--R 64x - 32
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 500
+m0:=a0-r0
+--R
+--R
+--R 1309log(2x - 1) - 1309log(- 2x + 1)
+--R (4) -----------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R 3 2
+--R 75x + 140x + 87x + 18
+--R (1) -----------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 121
+
+--S 122 of 500
+r0:=847/16/(1-2*x)+215/4*x+75/8*x^2+1133/16*log(1-2*x)
+--R
+--R
+--R 3 2
+--R (2266x - 1133)log(- 2x + 1) + 300x + 1570x - 860x - 847
+--R (2) ---------------------------------------------------------
+--R 32x - 16
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R (2266x - 1133)log(2x - 1) + 300x + 1570x - 860x - 847
+--R (3) -------------------------------------------------------
+--R 32x - 16
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 500
+m0:=a0-r0
+--R
+--R
+--R 1133log(2x - 1) - 1133log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) --------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 126
+
+--S 127 of 500
+r0:=121/8/(1-2*x)+25/4*x+55/4*log(1-2*x)
+--R
+--R
+--R 2
+--R (220x - 110)log(- 2x + 1) + 100x - 50x - 121
+--R (2) ---------------------------------------------
+--R 16x - 8
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (220x - 110)log(2x - 1) + 100x - 50x - 121
+--R (3) -------------------------------------------
+--R 16x - 8
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 500
+m0:=a0-r0
+--R
+--R
+--R 55log(2x - 1) - 55log(- 2x + 1)
+--R (4) -------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x))
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) -------------------
+--R 3 2
+--R 12x - 4x - 5x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 131
+
+--S 132 of 500
+r0:=121/28/(1-2*x)+407/196*log(1-2*x)+1/147*log(2+3*x)
+--R
+--R
+--R (8x - 4)log(3x + 2) + (2442x - 1221)log(- 2x + 1) - 2541
+--R (2) --------------------------------------------------------
+--R 1176x - 588
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (8x - 4)log(3x + 2) + (2442x - 1221)log(2x - 1) - 2541
+--R (3) ------------------------------------------------------
+--R 1176x - 588
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 500
+m0:=a0-r0
+--R
+--R
+--R 407log(2x - 1) - 407log(- 2x + 1)
+--R (4) ---------------------------------
+--R 196
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^2)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) ---------------------------
+--R 4 3 2
+--R 36x + 12x - 23x - 4x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 136
+
+--S 137 of 500
+r0:=121/98/(1-2*x)+(-1/147)/(2+3*x)+22/343*log(1-2*x)-22/343*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (- 792x - 132x + 264)log(3x + 2) + (792x + 132x - 264)log(- 2x + 1)
+--R +
+--R - 7651x - 5068
+--R /
+--R 2
+--R 12348x + 2058x - 4116
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (- 792x - 132x + 264)log(3x + 2) + (792x + 132x - 264)log(2x - 1)
+--R +
+--R - 7651x - 5068
+--R /
+--R 2
+--R 12348x + 2058x - 4116
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 500
+m0:=a0-r0
+--R
+--R
+--R 22log(2x - 1) - 22log(- 2x + 1)
+--R (4) -------------------------------
+--R 343
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^3)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) ------------------------------------
+--R 5 4 3 2
+--R 108x + 108x - 45x - 58x + 4x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 141
+
+--S 142 of 500
+r0:=121/343/(1-2*x)+(-1/294)/(2+3*x)^2+22/343/(2+3*x)-319/2401*log(1-2*x)+_
+ 319/2401*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (34452x + 28710x - 7656x - 7656)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 34452x - 28710x + 7656x + 7656)log(- 2x + 1) - 40194x - 60158x
+--R +
+--R - 22127
+--R /
+--R 3 2
+--R 259308x + 216090x - 57624x - 57624
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (34452x + 28710x - 7656x - 7656)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 34452x - 28710x + 7656x + 7656)log(2x - 1) - 40194x - 60158x - 22127
+--R /
+--R 3 2
+--R 259308x + 216090x - 57624x - 57624
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500
+m0:=a0-r0
+--R
+--R
+--R - 319log(2x - 1) + 319log(- 2x + 1)
+--R (4) -----------------------------------
+--R 2401
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^4)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) -----------------------------------------------
+--R 6 5 4 3 2
+--R 324x + 540x + 81x - 264x - 104x + 32x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 500
+r0:=242/2401/(1-2*x)+(-1/441)/(2+3*x)^3+11/343/(2+3*x)^2+_
+ (-319/2401)/(2+3*x)-1364/16807*log(1-2*x)+1364/16807*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (662904x + 994356x + 220968x - 245520x - 98208)log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 662904x - 994356x - 220968x + 245520x + 98208)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 773388x - 1095633x - 464303x - 50939
+--R /
+--R 4 3 2
+--R 8168202x + 12252303x + 2722734x - 3025260x - 1210104
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (662904x + 994356x + 220968x - 245520x - 98208)log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 662904x - 994356x - 220968x + 245520x + 98208)log(2x - 1)
+--R +
+--R 3 2
+--R - 773388x - 1095633x - 464303x - 50939
+--R /
+--R 4 3 2
+--R 8168202x + 12252303x + 2722734x - 3025260x - 1210104
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1364log(2x - 1) + 1364log(- 2x + 1)
+--R (4) -------------------------------------
+--R 16807
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^5)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) -----------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 151
+
+--S 152 of 500
+r0:=484/16807/(1-2*x)+(-1/588)/(2+3*x)^4+22/1029/(2+3*x)^3+_
+ (-319/4802)/(2+3*x)^2+(-1364/16807)/(2+3*x)-4180/117649*log(1-2*x)+_
+ 4180/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (8125920x + 17606160x + 10834560x - 1203840x - 3210240x - 802560)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 8125920x - 17606160x - 10834560x + 1203840x + 3210240x + 802560)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 9480240x - 19750500x - 12069750x - 1210930x + 583289
+--R /
+--R 5 4 3 2
+--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (8125920x + 17606160x + 10834560x - 1203840x - 3210240x - 802560)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 8125920x - 17606160x - 10834560x + 1203840x + 3210240x + 802560)
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 9480240x - 19750500x - 12069750x - 1210930x + 583289
+--R /
+--R 5 4 3 2
+--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R - 4180log(2x - 1) + 4180log(- 2x + 1)
+--R (4) -------------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^6)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) ----------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 500
+r0:=968/117649/(1-2*x)+(-1/735)/(2+3*x)^5+11/686/(2+3*x)^4+_
+ (-319/7203)/(2+3*x)^3+(-682/16807)/(2+3*x)^2+(-4180/117649)/(2+3*x)-_
+ 11264/823543*log(1-2*x)+11264/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 54743040x + 155105280x + 152064000x + 40550400x - 27033600x
+--R +
+--R - 19824640x - 3604480
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 54743040x - 155105280x - 152064000x - 40550400x + 27033600x
+--R +
+--R 19824640x + 3604480
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 63866880x - 175633920x - 170016000x - 52458560x + 10716139x + 6392708
+--R /
+--R 6 5 4 3
+--R 4002418980x + 11340187110x + 11117830500x + 2964754800x
+--R +
+--R 2
+--R - 1976503200x - 1449435680x - 263533760
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 54743040x + 155105280x + 152064000x + 40550400x - 27033600x
+--R +
+--R - 19824640x - 3604480
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 54743040x - 155105280x - 152064000x - 40550400x + 27033600x
+--R +
+--R 19824640x + 3604480
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 63866880x - 175633920x - 170016000x - 52458560x + 10716139x + 6392708
+--R /
+--R 6 5 4 3
+--R 4002418980x + 11340187110x + 11117830500x + 2964754800x
+--R +
+--R 2
+--R - 1976503200x - 1449435680x - 263533760
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R - 11264log(2x - 1) + 11264log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^7)
+--R
+--R
+--R (1)
+--R 2
+--R 25x + 30x + 9
+--R /
+--R 9 8 7 6 5 4 3 2
+--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x
+--R +
+--R 832x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 500
+r0:=1936/823543/(1-2*x)+(-1/882)/(2+3*x)^6+22/1715/(2+3*x)^5+_
+ (-319/9604)/(2+3*x)^4+(-1364/50421)/(2+3*x)^3+(-2090/117649)/(2+3*x)^2+_
+ (-11264/823543)/(2+3*x)-4048/823543*log(1-2*x)+4048/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 1062357120x + 3718249920x + 4957666560x + 2754259200x
+--R +
+--R 2
+--R - 734469120x - 326430720x - 46632960
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 1062357120x - 3718249920x - 4957666560x - 2754259200x
+--R +
+--R 2
+--R 734469120x + 326430720x + 46632960
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3 2
+--R - 1239416640x - 4234673520x - 5571636840x - 3217605930x - 337540203x
+--R +
+--R 426120352x + 132853546
+--R /
+--R 7 6 5 4
+--R 216130624920x + 756457187220x + 1008609582960x + 560338657200x
+--R +
+--R 2
+--R - 149423641920x - 66410507520x - 9487215360
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 1062357120x + 3718249920x + 4957666560x + 2754259200x
+--R +
+--R 2
+--R - 734469120x - 326430720x - 46632960
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 1062357120x - 3718249920x - 4957666560x - 2754259200x
+--R +
+--R 2
+--R 734469120x + 326430720x + 46632960
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3 2
+--R - 1239416640x - 4234673520x - 5571636840x - 3217605930x - 337540203x
+--R +
+--R 426120352x + 132853546
+--R /
+--R 7 6 5 4
+--R 216130624920x + 756457187220x + 1008609582960x + 560338657200x
+--R +
+--R 2
+--R - 149423641920x - 66410507520x - 9487215360
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R - 4048log(2x - 1) + 4048log(- 2x + 1)
+--R (4) -------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^8)
+--R
+--R
+--R (1)
+--R 2
+--R 25x + 30x + 9
+--R /
+--R 10 9 8 7 6 5 4
+--R 26244x + 113724x + 193185x + 143856x + 9072x - 60480x - 38304x
+--R +
+--R 3 2
+--R - 3840x + 4864x + 2048x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 166
+
+--S 167 of 500
+r0:=3872/5764801/(1-2*x)+(-1/1029)/(2+3*x)^7+11/1029/(2+3*x)^6+_
+ (-319/12005)/(2+3*x)^5+(-341/16807)/(2+3*x)^4+(-4180/352947)/(2+3*x)^3+_
+ (-5632/823543)/(2+3*x)^2+(-4048/823543)/(2+3*x)-_
+ 68288/40353607*log(1-2*x)+68288/40353607*log(2+3*x)
+--R
+--R
+--R (2)
+--R 8 7 6 5
+--R 4480375680x + 18668232000x + 31362629760x + 25554735360x
+--R +
+--R 4 3 2
+--R 7743859200x - 3097543680x - 3441715200x - 1114460160x - 131112960
+--R *
+--R log(3x + 2)
+--R +
+--R 8 7 6 5
+--R - 4480375680x - 18668232000x - 31362629760x - 25554735360x
+--R +
+--R 4 3 2
+--R - 7743859200x + 3097543680x + 3441715200x + 1114460160x + 131112960
+--R *
+--R log(- 2x + 1)
+--R +
+--R 7 6 5 4
+--R - 5227104960x - 21344011920x - 35403956280x - 29235085110x
+--R +
+--R 3 2
+--R - 10470141297x + 1282240575x + 2289114821x + 535775051
+--R /
+--R 8 7 6 5
+--R 2647600155270x + 11031667313625x + 18533201086890x + 15101126811540x
+--R +
+--R 4 3 2
+--R 4576099033800x - 1830439613520x - 2033821792800x - 658570866240x
+--R +
+--R - 77478925440
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5
+--R 4480375680x + 18668232000x + 31362629760x + 25554735360x
+--R +
+--R 4 3 2
+--R 7743859200x - 3097543680x - 3441715200x - 1114460160x - 131112960
+--R *
+--R log(3x + 2)
+--R +
+--R 8 7 6 5
+--R - 4480375680x - 18668232000x - 31362629760x - 25554735360x
+--R +
+--R 4 3 2
+--R - 7743859200x + 3097543680x + 3441715200x + 1114460160x + 131112960
+--R *
+--R log(2x - 1)
+--R +
+--R 7 6 5 4
+--R - 5227104960x - 21344011920x - 35403956280x - 29235085110x
+--R +
+--R 3 2
+--R - 10470141297x + 1282240575x + 2289114821x + 535775051
+--R /
+--R 8 7 6 5
+--R 2647600155270x + 11031667313625x + 18533201086890x + 15101126811540x
+--R +
+--R 4 3 2
+--R 4576099033800x - 1830439613520x - 2033821792800x - 658570866240x
+--R +
+--R - 77478925440
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500
+m0:=a0-r0
+--R
+--R
+--R - 68288log(2x - 1) + 68288log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 40353607
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(2+3*x)^8*(3+5*x)^3/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 11 10 9 8 7
+--R 820125x + 5850225x + 18964935x + 36879867x + 47801664x
+--R +
+--R 6 5 4 3 2
+--R 43361136x + 28088928x + 12994080x + 4206848x + 907776x + 117504x
+--R +
+--R 6912
+--R /
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 171
+
+--S 172 of 500
+r0:=7672950131/4096/(1-2*x)+7277894263/512*x+21573106793/2048*x^2+_
+ 2416569641/256*x^3+8502681987/1024*x^4+260574273/40*x^5+_
+ 544462047/128*x^6+242570133/112*x^7+101721015/128*x^8+_
+ 370575/2*x^9+164025/8*x^10+36770371407/4096*log(1-2*x)
+--R
+--R
+--R (2)
+--R 11
+--R (2573925998490x - 1286962999245)log(- 2x + 1) + 5878656000x
+--R +
+--R 10 9 8 7
+--R 50186304000x + 201292257600x + 507052003680x + 909105215040x
+--R +
+--R 6 5 4 3
+--R 1257998896224x + 1446852761928x + 1516182519740x + 1666955952060x
+--R +
+--R 2
+--R 2565503311770x - 2037810393640x - 268553254585
+--R /
+--R 286720x - 143360
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 11
+--R (2573925998490x - 1286962999245)log(2x - 1) + 5878656000x
+--R +
+--R 10 9 8 7
+--R 50186304000x + 201292257600x + 507052003680x + 909105215040x
+--R +
+--R 6 5 4 3
+--R 1257998896224x + 1446852761928x + 1516182519740x + 1666955952060x
+--R +
+--R 2
+--R 2565503311770x - 2037810393640x - 268553254585
+--R /
+--R 286720x - 143360
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500
+m0:=a0-r0
+--R
+--R
+--R 36770371407log(2x - 1) - 36770371407log(- 2x + 1)
+--R (4) -------------------------------------------------
+--R 4096
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(2+3*x)^7*(3+5*x)^3/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 10 9 8 7 6 5
+--R 273375x + 1767825x + 5143095x + 8864559x + 10024182x + 7770924x
+--R +
+--R 4 3 2
+--R 4182360x + 1543120x + 373536x + 53568x + 3456
+--R /
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 176
+
+--S 177 of 500
+r0:=1096135733/2048/(1-2*x)+3690540955/1024*x+1312685491/512*x^2+_
+ 551942075/256*x^3+220950207/128*x^4+379446471/320*x^5+_
+ 20626947/32*x^6+28463805/112*x^7+127575/2*x^8+30375/4*x^9+_
+ 298946109/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 10
+--R (334819642080x - 167409821040)log(- 2x + 1) + 1088640000x
+--R +
+--R 9 8 7 6
+--R 8600256000x + 31861382400x + 74191887360x + 123787657728x
+--R +
+--R 5 4 3 2
+--R 162468222336x + 185355446080x + 213008156480x + 332899764960x
+--R +
+--R - 258337866850x - 38364750655
+--R /
+--R 143360x - 71680
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9
+--R (334819642080x - 167409821040)log(2x - 1) + 1088640000x + 8600256000x
+--R +
+--R 8 7 6 5
+--R 31861382400x + 74191887360x + 123787657728x + 162468222336x
+--R +
+--R 4 3 2
+--R 185355446080x + 213008156480x + 332899764960x - 258337866850x
+--R +
+--R - 38364750655
+--R /
+--R 143360x - 71680
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500
+m0:=a0-r0
+--R
+--R
+--R 298946109log(2x - 1) - 298946109log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(2+3*x)^6*(3+5*x)^3/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4
+--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x
+--R +
+--R 3 2
+--R 545840x + 150480x + 24192x + 1728
+--R /
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 500
+r0:=156590819/1024/(1-2*x)+230244479/256*x+310976027/512*x^2+7530189/16*x^3+_
+ 85406805/256*x^4+15403257/80*x^5+2611845/32*x^6+309825/14*x^7+_
+ 91125/32*x^8+616195041/1024*log(1-2*x)
+--R
+--R
+--R (2)
+--R 9 8
+--R (43133652870x - 21566826435)log(- 2x + 1) + 204120000x + 1484244000x
+--R +
+--R 7 6 5 4
+--R 5057380800x + 10876051872x + 17013246264x + 21778294020x
+--R +
+--R 3 2
+--R 26669020420x + 42700132230x - 32234227060x - 5480678665
+--R /
+--R 71680x - 35840
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8
+--R (43133652870x - 21566826435)log(2x - 1) + 204120000x + 1484244000x
+--R +
+--R 7 6 5 4
+--R 5057380800x + 10876051872x + 17013246264x + 21778294020x
+--R +
+--R 3 2
+--R 26669020420x + 42700132230x - 32234227060x - 5480678665
+--R /
+--R 71680x - 35840
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500
+m0:=a0-r0
+--R
+--R
+--R 616195041log(2x - 1) - 616195041log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 1024
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x
+--R +
+--R 10800x + 864
+--R /
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 186
+
+--S 187 of 500
+r0:=22370117/512/(1-2*x)+56291737/256*x+8881301/64*x^2+6179077/64*x^3+_
+ 3724389/64*x^4+423009/16*x^5+15525/2*x^6+30375/28*x^7+_
+ 39220335/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 8 7
+--R (1098169380x - 549084690)log(- 2x + 1) + 7776000x + 51753600x
+--R +
+--R 6 5 4 3 2
+--R 161687232x + 322377552x + 483490840x + 648677400x + 1078815780x
+--R +
+--R - 788084318x - 156590819
+--R /
+--R 7168x - 3584
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7
+--R (1098169380x - 549084690)log(2x - 1) + 7776000x + 51753600x
+--R +
+--R 6 5 4 3 2
+--R 161687232x + 322377552x + 483490840x + 648677400x + 1078815780x
+--R +
+--R - 788084318x - 156590819
+--R /
+--R 7168x - 3584
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R 39220335log(2x - 1) - 39220335log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^2
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432
+--R -----------------------------------------------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 500
+r0:=3195731/256/(1-2*x)+209243/4*x+3859469/128*x^2+289951/16*x^3+_
+ 557415/64*x^4+5535/2*x^5+3375/8*x^6+9836211/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R (19672422x - 9836211)log(- 2x + 1) + 216000x + 1308960x + 3750840x
+--R +
+--R 4 3 2
+--R 7048772x + 10798660x + 19064166x - 13391552x - 3195731
+--R /
+--R 512x - 256
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R (19672422x - 9836211)log(2x - 1) + 216000x + 1308960x + 3750840x
+--R +
+--R 4 3 2
+--R 7048772x + 10798660x + 19064166x - 13391552x - 3195731
+--R /
+--R 512x - 256
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R 9836211log(2x - 1) - 9836211log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^2
+--R
+--R
+--R 6 5 4 3 2
+--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216
+--R (1) -----------------------------------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 196
+
+--S 197 of 500
+r0:=456533/128/(1-2*x)+766807/64*x+194881/32*x^2+47535/16*x^3+_
+ 2025/2*x^4+675/4*x^5+302379/32*log(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R (2419032x - 1209516)log(- 2x + 1) + 43200x + 237600x + 630960x
+--R +
+--R 3 2
+--R 1178768x + 2287704x - 1533614x - 456533
+--R /
+--R 256x - 128
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R (2419032x - 1209516)log(2x - 1) + 43200x + 237600x + 630960x
+--R +
+--R 3 2
+--R 1178768x + 2287704x - 1533614x - 456533
+--R /
+--R 256x - 128
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R 302379log(2x - 1) - 302379log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^2
+--R
+--R
+--R 5 4 3 2
+--R 1125x + 3525x + 4415x + 2763x + 864x + 108
+--R (1) ----------------------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 201
+
+--S 202 of 500
+r0:=65219/64/(1-2*x)+41537/16*x+35135/32*x^2+775/2*x^3+1125/16*x^4+_
+ 144837/64*log(1-2*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (289674x - 144837)log(- 2x + 1) + 9000x + 45100x + 115740x + 262026x
+--R +
+--R - 166148x - 65219
+--R /
+--R 128x - 64
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (289674x - 144837)log(2x - 1) + 9000x + 45100x + 115740x + 262026x
+--R +
+--R - 166148x - 65219
+--R /
+--R 128x - 64
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R 144837log(2x - 1) - 144837log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^2
+--R
+--R
+--R 4 3 2
+--R 375x + 925x + 855x + 351x + 54
+--R (1) ---------------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 206
+
+--S 207 of 500
+r0:=9317/32/(1-2*x)+8245/16*x+325/2*x^2+125/4*x^3+8349/16*log(1-2*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (33396x - 16698)log(- 2x + 1) + 2000x + 9400x + 27780x - 16490x - 9317
+--R -------------------------------------------------------------------------
+--R 64x - 32
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (33396x - 16698)log(2x - 1) + 2000x + 9400x + 27780x - 16490x - 9317
+--R -----------------------------------------------------------------------
+--R 64x - 32
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R 8349log(2x - 1) - 8349log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(3+5*x)^3/(1-2*x)^2
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) -------------------------
+--R 2
+--R 4x - 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 211
+
+--S 212 of 500
+r0:=1331/16/(1-2*x)+175/2*x+125/8*x^2+1815/16*log(1-2*x)
+--R
+--R
+--R 3 2
+--R (3630x - 1815)log(- 2x + 1) + 500x + 2550x - 1400x - 1331
+--R (2) -----------------------------------------------------------
+--R 32x - 16
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R (3630x - 1815)log(2x - 1) + 500x + 2550x - 1400x - 1331
+--R (3) ---------------------------------------------------------
+--R 32x - 16
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R 1815log(2x - 1) - 1815log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x))
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) -------------------------
+--R 3 2
+--R 12x - 4x - 5x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 216
+
+--S 217 of 500
+r0:=1331/56/(1-2*x)+125/12*x+1089/49*log(1-2*x)-1/441*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 16x + 8)log(3x + 2) + (156816x - 78408)log(- 2x + 1) + 73500x
+--R +
+--R - 36750x - 83853
+--R /
+--R 7056x - 3528
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (- 16x + 8)log(3x + 2) + (156816x - 78408)log(2x - 1) + 73500x - 36750x
+--R +
+--R - 83853
+--R /
+--R 7056x - 3528
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R 1089log(2x - 1) - 1089log(- 2x + 1)
+--R (4) -----------------------------------
+--R 49
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^2)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) ---------------------------
+--R 4 3 2
+--R 36x + 12x - 23x - 4x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 221
+
+--S 222 of 500
+r0:=1331/196/(1-2*x)+1/441/(2+3*x)+4719/1372*log(1-2*x)+101/3087*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2
+--R (2424x + 404x - 808)log(3x + 2)
+--R +
+--R 2
+--R (254826x + 42471x - 84942)log(- 2x + 1) - 251503x - 167734
+--R /
+--R 2
+--R 74088x + 12348x - 24696
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (2424x + 404x - 808)log(3x + 2) + (254826x + 42471x - 84942)log(2x - 1)
+--R +
+--R - 251503x - 167734
+--R /
+--R 2
+--R 74088x + 12348x - 24696
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 500
+m0:=a0-r0
+--R
+--R
+--R 4719log(2x - 1) - 4719log(- 2x + 1)
+--R (4) -----------------------------------
+--R 1372
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^3)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) ------------------------------------
+--R 5 4 3 2
+--R 108x + 108x - 45x - 58x + 4x + 8
+--R Type: Fraction(Polynomial(Integer))
+--E 226
+
+--S 227 of 500
+r0:=1331/686/(1-2*x)+1/882/(2+3*x)^2+(-101/3087)/(2+3*x)+_
+ 363/2401*log(1-2*x)-363/2401*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (- 117612x - 98010x + 26136x + 26136)log(3x + 2)
+--R +
+--R 3 2 2
+--R (117612x + 98010x - 26136x - 26136)log(- 2x + 1) - 763161x - 1007552x
+--R +
+--R - 332633
+--R /
+--R 3 2
+--R 777924x + 648270x - 172872x - 172872
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (- 117612x - 98010x + 26136x + 26136)log(3x + 2)
+--R +
+--R 3 2 2
+--R (117612x + 98010x - 26136x - 26136)log(2x - 1) - 763161x - 1007552x
+--R +
+--R - 332633
+--R /
+--R 3 2
+--R 777924x + 648270x - 172872x - 172872
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500
+m0:=a0-r0
+--R
+--R
+--R 363log(2x - 1) - 363log(- 2x + 1)
+--R (4) ---------------------------------
+--R 2401
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^4)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) -----------------------------------------------
+--R 6 5 4 3 2
+--R 324x + 540x + 81x - 264x - 104x + 32x + 16
+--R Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 500
+r0:=1331/2401/(1-2*x)+1/1323/(2+3*x)^3+(-101/6174)/(2+3*x)^2+_
+ 363/2401/(2+3*x)-3267/16807*log(1-2*x)+3267/16807*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (9526572x + 14289858x + 3175524x - 3528360x - 1411344)log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 9526572x - 14289858x - 3175524x + 3528360x + 1411344)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 11114334x - 25199244x - 18674579x - 4544792
+--R /
+--R 4 3 2
+--R 49009212x + 73513818x + 16336404x - 18151560x - 7260624
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (9526572x + 14289858x + 3175524x - 3528360x - 1411344)log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 9526572x - 14289858x - 3175524x + 3528360x + 1411344)log(2x - 1)
+--R +
+--R 3 2
+--R - 11114334x - 25199244x - 18674579x - 4544792
+--R /
+--R 4 3 2
+--R 49009212x + 73513818x + 16336404x - 18151560x - 7260624
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500
+m0:=a0-r0
+--R
+--R
+--R - 3267log(2x - 1) + 3267log(- 2x + 1)
+--R (4) -------------------------------------
+--R 16807
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^5)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) -----------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 500
+r0:=2662/16807/(1-2*x)+1/1764/(2+3*x)^4+(-101/9261)/(2+3*x)^3+_
+ 363/4802/(2+3*x)^2+(-3267/16807)/(2+3*x)-14520/117649*log(1-2*x)+_
+ 14520/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 254041920x + 550424160x + 338722560x - 37635840x - 100362240x
+--R +
+--R - 25090560
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 254041920x - 550424160x - 338722560x + 37635840x + 100362240x
+--R +
+--R 25090560
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 296382240x - 617463000x - 465575250x - 147766430x - 16012787
+--R /
+--R 5 4 3 2
+--R 2058386904x + 4459838292x + 2744515872x - 304946208x - 813189888x
+--R +
+--R - 203297472
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 254041920x + 550424160x + 338722560x - 37635840x - 100362240x
+--R +
+--R - 25090560
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 254041920x - 550424160x - 338722560x + 37635840x + 100362240x
+--R +
+--R 25090560
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 296382240x - 617463000x - 465575250x - 147766430x - 16012787
+--R /
+--R 5 4 3 2
+--R 2058386904x + 4459838292x + 2744515872x - 304946208x - 813189888x
+--R +
+--R - 203297472
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500
+m0:=a0-r0
+--R
+--R
+--R - 14520log(2x - 1) + 14520log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^6)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) ----------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 500
+r0:=5324/117649/(1-2*x)+1/2205/(2+3*x)^5+(-101/12348)/(2+3*x)^4+_
+ 121/2401/(2+3*x)^3+(-3267/33614)/(2+3*x)^2+(-14520/117649)/(2+3*x)-_
+ 45012/823543*log(1-2*x)+45012/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 3937649760x + 11156674320x + 10937916000x + 2916777600x
+--R +
+--R 2
+--R - 1944518400x - 1425980160x - 259269120
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 3937649760x - 11156674320x - 10937916000x - 2916777600x
+--R +
+--R 2
+--R 1944518400x + 1425980160x + 259269120
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 4593924720x - 12633292980x - 12229197750x - 4545399390x
+--R +
+--R - 181895609x + 165794902
+--R /
+--R 6 5 4 3
+--R 72043541640x + 204123367980x + 200120949000x + 53365586400x
+--R +
+--R 2
+--R - 35577057600x - 26089842240x - 4743607680
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 3937649760x + 11156674320x + 10937916000x + 2916777600x
+--R +
+--R 2
+--R - 1944518400x - 1425980160x - 259269120
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 3937649760x - 11156674320x - 10937916000x - 2916777600x
+--R +
+--R 2
+--R 1944518400x + 1425980160x + 259269120
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 4593924720x - 12633292980x - 12229197750x - 4545399390x
+--R +
+--R - 181895609x + 165794902
+--R /
+--R 6 5 4 3
+--R 72043541640x + 204123367980x + 200120949000x + 53365586400x
+--R +
+--R 2
+--R - 35577057600x - 26089842240x - 4743607680
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500
+m0:=a0-r0
+--R
+--R
+--R - 45012log(2x - 1) + 45012log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^7)
+--R
+--R
+--R (1)
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R /
+--R 9 8 7 6 5 4 3 2
+--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x
+--R +
+--R 832x + 128
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 500
+r0:=10648/823543/(1-2*x)+1/2646/(2+3*x)^6+(-101/15435)/(2+3*x)^5+_
+ 363/9604/(2+3*x)^4+(-1089/16807)/(2+3*x)^3+(-7260/117649)/(2+3*x)^2+_
+ (-45012/823543)/(2+3*x)-17424/823543*log(1-2*x)+17424/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 13718263680x + 48013922880x + 64018563840x + 35565868800x
+--R +
+--R 2
+--R - 9484231680x - 4215214080x - 602173440
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 13718263680x - 48013922880x - 64018563840x - 35565868800x
+--R +
+--R 2
+--R 9484231680x + 4215214080x + 602173440
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R - 16004640960x - 54682523280x - 71946788760x - 41549085270x
+--R +
+--R 2
+--R - 6211643067x + 3228815828x + 1017833894
+--R /
+--R 7 6 5 4
+--R 648391874760x + 2269371561660x + 3025828748880x + 1681015971600x
+--R +
+--R 2
+--R - 448270925760x - 199231522560x - 28461646080
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 13718263680x + 48013922880x + 64018563840x + 35565868800x
+--R +
+--R 2
+--R - 9484231680x - 4215214080x - 602173440
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 13718263680x - 48013922880x - 64018563840x - 35565868800x
+--R +
+--R 2
+--R 9484231680x + 4215214080x + 602173440
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3
+--R - 16004640960x - 54682523280x - 71946788760x - 41549085270x
+--R +
+--R 2
+--R - 6211643067x + 3228815828x + 1017833894
+--R /
+--R 7 6 5 4
+--R 648391874760x + 2269371561660x + 3025828748880x + 1681015971600x
+--R +
+--R 2
+--R - 448270925760x - 199231522560x - 28461646080
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500
+m0:=a0-r0
+--R
+--R
+--R - 17424log(2x - 1) + 17424log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^8)
+--R
+--R
+--R (1)
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R /
+--R 10 9 8 7 6 5 4
+--R 26244x + 113724x + 193185x + 143856x + 9072x - 60480x - 38304x
+--R +
+--R 3 2
+--R - 3840x + 4864x + 2048x + 256
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 500
+r0:=21296/5764801/(1-2*x)+1/3087/(2+3*x)^7+(-101/18522)/(2+3*x)^6+_
+ 363/12005/(2+3*x)^5+(-3267/67228)/(2+3*x)^4+(-4840/117649)/(2+3*x)^3+_
+ (-22506/823543)/(2+3*x)^2+(-17424/823543)/(2+3*x)-_
+ 307824/40353607*log(1-2*x)+307824/40353607*log(2+3*x)
+--R
+--R
+--R (2)
+--R 8 7 6 5
+--R 727067975040x + 3029449896000x + 5089475825280x + 4146980302080x
+--R +
+--R 4 3 2
+--R 1256660697600x - 502664279040x - 558515865600x - 180852756480x
+--R +
+--R - 21276794880
+--R *
+--R log(3x + 2)
+--R +
+--R 8 7 6
+--R - 727067975040x - 3029449896000x - 5089475825280x
+--R +
+--R 5 4 3 2
+--R - 4146980302080x - 1256660697600x + 502664279040x + 558515865600x
+--R +
+--R 180852756480x + 21276794880
+--R *
+--R log(- 2x + 1)
+--R +
+--R 7 6 5 4
+--R - 848245970880x - 3463671047760x - 5745295626840x - 4744221388830x
+--R +
+--R 3 2
+--R - 1699077259341x + 132416872350x + 278976950938x + 58668936928
+--R /
+--R 8 7 6
+--R 95313605589720x + 397140023290500x + 667195239128040x
+--R +
+--R 5 4 3
+--R 543640565215440x + 164739565216800x - 65895826086720x
+--R +
+--R 2
+--R - 73217584540800x - 23708551184640x - 2789241315840
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5
+--R 727067975040x + 3029449896000x + 5089475825280x + 4146980302080x
+--R +
+--R 4 3 2
+--R 1256660697600x - 502664279040x - 558515865600x - 180852756480x
+--R +
+--R - 21276794880
+--R *
+--R log(3x + 2)
+--R +
+--R 8 7 6
+--R - 727067975040x - 3029449896000x - 5089475825280x
+--R +
+--R 5 4 3 2
+--R - 4146980302080x - 1256660697600x + 502664279040x + 558515865600x
+--R +
+--R 180852756480x + 21276794880
+--R *
+--R log(2x - 1)
+--R +
+--R 7 6 5 4
+--R - 848245970880x - 3463671047760x - 5745295626840x - 4744221388830x
+--R +
+--R 3 2
+--R - 1699077259341x + 132416872350x + 278976950938x + 58668936928
+--R /
+--R 8 7 6
+--R 95313605589720x + 397140023290500x + 667195239128040x
+--R +
+--R 5 4 3
+--R 543640565215440x + 164739565216800x - 65895826086720x
+--R +
+--R 2
+--R - 73217584540800x - 23708551184640x - 2789241315840
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500
+m0:=a0-r0
+--R
+--R
+--R - 307824log(2x - 1) + 307824log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 40353607
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(a+b*x)^m/(e+f*x)^2
+--R
+--R
+--R m
+--R (b x + a)
+--R (1) ------------------
+--R 2 2 2
+--R f x + 2e f x + e
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+--r0:=(a+b*x)^(1+m)/((b*e-a*f)*(e+f*x))-b*m*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)^2*(1+m))
+--E 257
+
+--S 258 of 500
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 500
+--m0:=a0-r0
+--E 259
+
+--S 260 of 500
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(a+b*x)^m/((c+d*x)*(e+f*x)^2)
+--R
+--R
+--R m
+--R (b x + a)
+--R (1) ----------------------------------------------------
+--R 2 3 2 2 2 2
+--R d f x + (c f + 2d e f)x + (2c e f + d e )x + c e
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+--r0:=-f*(a+b*x)^(1+m)/((b*e-a*f)*(d*e-c*f)*(e+f*x))+d^2*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*_
+-- (d*e-c*f)^2*(1+m))-d*f*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_
+-- ((b*e-a*f)*(d*e-c*f)^2*(1+m))+b*f*m*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_
+-- ((b*e-a*f)^2*(d*e-c*f)*(1+m))
+--E 262
+
+--S 263 of 500
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 500
+--m0:=a0-r0
+--E 264
+
+--S 265 of 500
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(a+b*x)^m/((c+d*x)^2*(e+f*x)^2)
+--R
+--R
+--R (1)
+--R m
+--R (b x + a)
+--R /
+--R 2 2 4 2 2 3 2 2 2 2 2
+--R d f x + (2c d f + 2d e f)x + (c f + 4c d e f + d e )x
+--R +
+--R 2 2 2 2
+--R (2c e f + 2c d e )x + c e
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+--r0:=d^2*(a+b*x)^(1+m)/((b*c-a*d)*(d*e-c*f)^2*(c+d*x))+_
+-- f^2*(a+b*x)^(1+m)/((b*e-a*f)*(d*e-c*f)^2*(e+f*x))-_
+-- 2*d^2*f*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_
+-- ((b*c-a*d)*(d*e-c*f)^3*(1+m))-b*d^2*m*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_
+-- ((b*c-a*d)^2*(d*e-c*f)^2*(1+m))+2*d*f^2*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_
+-- ((b*e-a*f)*(d*e-c*f)^3*(1+m))-b*f^2*m*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_
+-- ((b*e-a*f)^2*(d*e-c*f)^2*(1+m))
+--E 267
+
+--S 268 of 500
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 500
+--m0:=a0-r0
+--E 269
+
+--S 270 of 500
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(2+3*x)^8/((1-2*x)^2*(3+5*x))
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R /
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 271
+
+--S 272 of 500
+r0:=5764801/2816/(1-2*x)+2041906293/250000*x+1839811401/400000*x^2+_
+ 26773659/10000*x^3+9899091/8000*x^4+94041/250*x^5+2187/40*x^6+_
+ 188591347/30976*log(1-2*x)+1/9453125*log(3+5*x)
+--R
+--R
+--R (2)
+--R (512x - 256)log(5x + 3) + (29467397968750x - 14733698984375)log(- 2x + 1)
+--R +
+--R 7 6 5 4
+--R 264627000000x + 1688320260000x + 5078633175000x + 9963975928500x
+--R +
+--R 3 2
+--R 15782492474100x + 28400446856430x - 19765652916240x - 4954125859375
+--R /
+--R 4840000000x - 2420000000
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (512x - 256)log(5x + 3) + (29467397968750x - 14733698984375)log(2x - 1)
+--R +
+--R 7 6 5 4
+--R 264627000000x + 1688320260000x + 5078633175000x + 9963975928500x
+--R +
+--R 3 2
+--R 15782492474100x + 28400446856430x - 19765652916240x - 4954125859375
+--R /
+--R 4840000000x - 2420000000
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500
+m0:=a0-r0
+--R
+--R
+--R 188591347log(2x - 1) - 188591347log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 30976
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(2+3*x)^7/((1-2*x)^2*(3+5*x))
+--R
+--R
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R (1) ---------------------------------------------------------------------
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 276
+
+--S 277 of 500
+r0:=823543/1408/(1-2*x)+370109547/200000*x+18237069/20000*x^2+_
+ 853659/2000*x^3+13851/100*x^4+2187/100*x^5+5764801/3872*log(1-2*x)+_
+ 1/1890625*log(3+5*x)
+--R
+--R
+--R (2)
+--R (256x - 128)log(5x + 3) + (720600125000x - 360300062500)log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R 10585080000x + 61746300000x + 173066058000x + 338044330800x
+--R +
+--R 2
+--R 674996568840x - 447832551870x - 141546453125
+--R /
+--R 484000000x - 242000000
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (256x - 128)log(5x + 3) + (720600125000x - 360300062500)log(2x - 1)
+--R +
+--R 6 5 4 3
+--R 10585080000x + 61746300000x + 173066058000x + 338044330800x
+--R +
+--R 2
+--R 674996568840x - 447832551870x - 141546453125
+--R /
+--R 484000000x - 242000000
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500
+m0:=a0-r0
+--R
+--R
+--R 5764801log(2x - 1) - 5764801log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 3872
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(2+3*x)^6/((1-2*x)^2*(3+5*x))
+--R
+--R
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R (1) -----------------------------------------------------
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 500
+r0:=117649/704/(1-2*x)+3946293/10000*x+639819/4000*x^2+2673/50*x^3+_
+ 729/80*x^4+2739541/7744*log(1-2*x)+1/378125*log(3+5*x)
+--R
+--R
+--R (2)
+--R (128x - 64)log(5x + 3) + (17122131250x - 8561065625)log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R 441045000x + 2366941500x + 6448077900x + 15229153170x - 9550029060x
+--R +
+--R - 4044184375
+--R /
+--R 48400000x - 24200000
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (128x - 64)log(5x + 3) + (17122131250x - 8561065625)log(2x - 1)
+--R +
+--R 5 4 3 2
+--R 441045000x + 2366941500x + 6448077900x + 15229153170x - 9550029060x
+--R +
+--R - 4044184375
+--R /
+--R 48400000x - 24200000
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500
+m0:=a0-r0
+--R
+--R
+--R 2739541log(2x - 1) - 2739541log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 7744
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(2+3*x)^5/((1-2*x)^2*(3+5*x))
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 500
+r0:=16807/352/(1-2*x)+152793/2000*x+567/25*x^2+81/20*x^3+_
+ 156065/1936*log(1-2*x)+1/75625*log(3+5*x)
+--R
+--R
+--R (2)
+--R (64x - 32)log(5x + 3) + (390162500x - 195081250)log(- 2x + 1)
+--R +
+--R 4 3 2
+--R 19602000x + 99970200x + 314873460x - 184879530x - 115548125
+--R /
+--R 4840000x - 2420000
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4
+--R (64x - 32)log(5x + 3) + (390162500x - 195081250)log(2x - 1) + 19602000x
+--R +
+--R 3 2
+--R 99970200x + 314873460x - 184879530x - 115548125
+--R /
+--R 4840000x - 2420000
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500
+m0:=a0-r0
+--R
+--R
+--R 156065log(2x - 1) - 156065log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 1936
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(2+3*x)^4/((1-2*x)^2*(3+5*x))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) -------------------------------
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 500
+r0:=2401/176/(1-2*x)+621/50*x+81/40*x^2+33271/1936*log(1-2*x)+_
+ 1/15125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3
+--R (32x - 16)log(5x + 3) + (8317750x - 4158875)log(- 2x + 1) + 980100x
+--R +
+--R 2
+--R 5521230x - 3005640x - 3301375
+--R /
+--R 484000x - 242000
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3
+--R (32x - 16)log(5x + 3) + (8317750x - 4158875)log(2x - 1) + 980100x
+--R +
+--R 2
+--R 5521230x - 3005640x - 3301375
+--R /
+--R 484000x - 242000
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500
+m0:=a0-r0
+--R
+--R
+--R 33271log(2x - 1) - 33271log(- 2x + 1)
+--R (4) -------------------------------------
+--R 1936
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(2+3*x)^3/((1-2*x)^2*(3+5*x))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) ---------------------
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 296
+
+--S 297 of 500
+r0:=343/88/(1-2*x)+27/20*x+392/121*log(1-2*x)+1/3025*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (16x - 8)log(5x + 3) + (156800x - 78400)log(- 2x + 1) + 65340x - 32670x
+--R +
+--R - 94325
+--R /
+--R 48400x - 24200
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (16x - 8)log(5x + 3) + (156800x - 78400)log(2x - 1) + 65340x - 32670x
+--R +
+--R - 94325
+--R /
+--R 48400x - 24200
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500
+m0:=a0-r0
+--R
+--R
+--R 392log(2x - 1) - 392log(- 2x + 1)
+--R (4) ---------------------------------
+--R 121
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(2+3*x)^2/((1-2*x)^2*(3+5*x))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) -------------------
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 301
+
+--S 302 of 500
+r0:=49/44/(1-2*x)+217/484*log(1-2*x)+1/605*log(3+5*x)
+--R
+--R
+--R (8x - 4)log(5x + 3) + (2170x - 1085)log(- 2x + 1) - 2695
+--R (2) --------------------------------------------------------
+--R 4840x - 2420
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (8x - 4)log(5x + 3) + (2170x - 1085)log(2x - 1) - 2695
+--R (3) ------------------------------------------------------
+--R 4840x - 2420
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500
+m0:=a0-r0
+--R
+--R
+--R 217log(2x - 1) - 217log(- 2x + 1)
+--R (4) ---------------------------------
+--R 484
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(2+3*x)/((1-2*x)^2*(3+5*x))
+--R
+--R
+--R 3x + 2
+--R (1) -------------------
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 306
+
+--S 307 of 500
+r0:=7/22/(1-2*x)-1/121*log(1-2*x)+1/121*log(3+5*x)
+--R
+--R
+--R (4x - 2)log(5x + 3) + (- 4x + 2)log(- 2x + 1) - 77
+--R (2) --------------------------------------------------
+--R 484x - 242
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (4x - 2)log(5x + 3) + (- 4x + 2)log(2x - 1) - 77
+--R (3) ------------------------------------------------
+--R 484x - 242
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500
+m0:=a0-r0
+--R
+--R
+--R - log(2x - 1) + log(- 2x + 1)
+--R (4) -----------------------------
+--R 121
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=1/((1-2*x)^2*(3+5*x))
+--R
+--R
+--R 1
+--R (1) -------------------
+--R 3 2
+--R 20x - 8x - 7x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 311
+
+--S 312 of 500
+r0:=1/11/(1-2*x)-5/121*log(1-2*x)+5/121*log(3+5*x)
+--R
+--R
+--R (10x - 5)log(5x + 3) + (- 10x + 5)log(- 2x + 1) - 11
+--R (2) ----------------------------------------------------
+--R 242x - 121
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (10x - 5)log(5x + 3) + (- 10x + 5)log(2x - 1) - 11
+--R (3) --------------------------------------------------
+--R 242x - 121
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500
+m0:=a0-r0
+--R
+--R
+--R - 5log(2x - 1) + 5log(- 2x + 1)
+--R (4) -------------------------------
+--R 121
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=1/((1-2*x)^2*(2+3*x)*(3+5*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R 4 3 2
+--R 60x + 16x - 37x - 5x + 6
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 500
+r0:=2/77/(1-2*x)-136/5929*log(1-2*x)-9/49*log(2+3*x)+25/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R (2450x - 1225)log(5x + 3) + (- 2178x + 1089)log(3x + 2)
+--R +
+--R (- 272x + 136)log(- 2x + 1) - 154
+--R /
+--R 11858x - 5929
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R (2450x - 1225)log(5x + 3) + (- 2178x + 1089)log(3x + 2)
+--R +
+--R (- 272x + 136)log(2x - 1) - 154
+--R /
+--R 11858x - 5929
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500
+m0:=a0-r0
+--R
+--R
+--R - 136log(2x - 1) + 136log(- 2x + 1)
+--R (4) -----------------------------------
+--R 5929
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^2*(3+5*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R 5 4 3 2
+--R 180x + 168x - 79x - 89x + 8x + 12
+--R Type: Fraction(Polynomial(Integer))
+--E 321
+
+--S 322 of 500
+r0:=4/539/(1-2*x)+9/49/(2+3*x)-404/41503*log(1-2*x)-_
+ 351/343*log(2+3*x)+125/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (257250x + 42875x - 85750)log(5x + 3)
+--R +
+--R 2
+--R (- 254826x - 42471x + 84942)log(3x + 2)
+--R +
+--R 2
+--R (- 2424x - 404x + 808)log(- 2x + 1) + 14322x - 8239
+--R /
+--R 2
+--R 249018x + 41503x - 83006
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (257250x + 42875x - 85750)log(5x + 3)
+--R +
+--R 2
+--R (- 254826x - 42471x + 84942)log(3x + 2)
+--R +
+--R 2
+--R (- 2424x - 404x + 808)log(2x - 1) + 14322x - 8239
+--R /
+--R 2
+--R 249018x + 41503x - 83006
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500
+m0:=a0-r0
+--R
+--R
+--R - 404log(2x - 1) + 404log(- 2x + 1)
+--R (4) -----------------------------------
+--R 41503
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^3*(3+5*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------
+--R 6 5 4 3 2
+--R 540x + 864x + 99x - 425x - 154x + 52x + 24
+--R Type: Fraction(Polynomial(Integer))
+--E 326
+
+--S 327 of 500
+r0:=8/3773/(1-2*x)+9/98/(2+3*x)^2+351/343/(2+3*x)-1072/290521*log(1-2*x)-_
+ 12393/2401*log(2+3*x)+625/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (54022500x + 45018750x - 12005000x - 12005000)log(5x + 3)
+--R +
+--R 3 2
+--R (- 53983908x - 44986590x + 11996424x + 11996424)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 38592x - 32160x + 8576x + 8576)log(- 2x + 1) + 3556476x + 686532x
+--R +
+--R - 1247477
+--R /
+--R 3 2
+--R 10458756x + 8715630x - 2324168x - 2324168
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (54022500x + 45018750x - 12005000x - 12005000)log(5x + 3)
+--R +
+--R 3 2
+--R (- 53983908x - 44986590x + 11996424x + 11996424)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 38592x - 32160x + 8576x + 8576)log(2x - 1) + 3556476x + 686532x
+--R +
+--R - 1247477
+--R /
+--R 3 2
+--R 10458756x + 8715630x - 2324168x - 2324168
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1072log(2x - 1) + 1072log(- 2x + 1)
+--R (4) -------------------------------------
+--R 290521
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^4*(3+5*x))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48
+--R Type: Fraction(Polynomial(Integer))
+--E 331
+
+--S 332 of 500
+r0:=16/26411/(1-2*x)+3/49/(2+3*x)^3+351/686/(2+3*x)^2+12393/2401/(2+3*x)-_
+ 2672/2033647*log(1-2*x)-434043/16807*log(2+3*x)+3125/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (5672362500x + 8508543750x + 1890787500x - 2100875000x - 840350000)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 5672073924x - 8508110886x - 1890691308x + 2100768120x
+--R +
+--R 840307248
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 288576x - 432864x - 96192x + 106880x + 42752)log(- 2x + 1)
+--R +
+--R 3 2
+--R 377820828x + 327259548x - 81484557x - 88405856
+--R /
+--R 4 3 2
+--R 219633876x + 329450814x + 73211292x - 81345880x - 32538352
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (5672362500x + 8508543750x + 1890787500x - 2100875000x - 840350000)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 5672073924x - 8508110886x - 1890691308x + 2100768120x
+--R +
+--R 840307248
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 288576x - 432864x - 96192x + 106880x + 42752)log(2x - 1)
+--R +
+--R 3 2
+--R 377820828x + 327259548x - 81484557x - 88405856
+--R /
+--R 4 3 2
+--R 219633876x + 329450814x + 73211292x - 81345880x - 32538352
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2672log(2x - 1) + 2672log(- 2x + 1)
+--R (4) -------------------------------------
+--R 2033647
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^5*(3+5*x))
+--R
+--R
+--R (1)
+--R 1
+--R ------------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 4860x + 14256x + 13419x + 819x - 6090x - 3080x + 224x + 496x + 96
+--R Type: Fraction(Polynomial(Integer))
+--E 336
+
+--S 337 of 500
+r0:=32/184877/(1-2*x)+9/196/(2+3*x)^4+117/343/(2+3*x)^3+_
+ 12393/4802/(2+3*x)^2+434043/16807/(2+3*x)-6400/14235529*log(1-2*x)-_
+ 15192225/117649*log(2+3*x)+15625/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 1191196125000x + 2580924937500x + 1588261500000x - 176473500000x
+--R +
+--R - 470596000000x - 117649000000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 1191191977800x - 2580915951900x - 1588255970400x
+--R +
+--R 2
+--R 176472885600x + 470594361600x + 117648590400
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 4147200x - 8985600x - 5529600x + 614400x + 1638400x + 409600)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R 79408236600x + 121756635000x + 28788432750x - 29974871850x - 12393745441
+--R /
+--R 5 4 3 2
+--R 9224622792x + 19986682716x + 12299497056x - 1366610784x - 3644295424x
+--R +
+--R - 911073856
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 1191196125000x + 2580924937500x + 1588261500000x - 176473500000x
+--R +
+--R - 470596000000x - 117649000000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 1191191977800x - 2580915951900x - 1588255970400x
+--R +
+--R 2
+--R 176472885600x + 470594361600x + 117648590400
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 4147200x - 8985600x - 5529600x + 614400x + 1638400x + 409600)
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R 79408236600x + 121756635000x + 28788432750x - 29974871850x - 12393745441
+--R /
+--R 5 4 3 2
+--R 9224622792x + 19986682716x + 12299497056x - 1366610784x - 3644295424x
+--R +
+--R - 911073856
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500
+m0:=a0-r0
+--R
+--R
+--R - 6400log(2x - 1) + 6400log(- 2x + 1)
+--R (4) -------------------------------------
+--R 14235529
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^6*(3+5*x))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 14580x + 52488x + 68769x + 29295x - 16632x - 21420x - 5488x
+--R +
+--R 2
+--R 1936x + 1280x + 192
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 500
+r0:=64/1294139/(1-2*x)+9/245/(2+3*x)^5+351/1372/(2+3*x)^4+_
+ 4131/2401/(2+3*x)^3+434043/33614/(2+3*x)^2+15192225/117649/(2+3*x)-_
+ 14912/99648703*log(1-2*x)-531729603/823543*log(2+3*x)+78125/121*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R 625377965625000x + 1771904235937500x + 1737161015625000x
+--R +
+--R 3 2
+--R 463242937500000x - 308828625000000x - 226474325000000x
+--R +
+--R - 41177150000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 625377820680360x - 1771903825261020x - 1737160613001000x
+--R +
+--R 3 2
+--R - 463242830133600x + 308828553422400x + 226474272509760x
+--R +
+--R 41177140456320
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 144944640x - 410676480x - 402624000x - 107366400x + 71577600x
+--R +
+--R 52490240x + 9543680
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R 41691695272920x + 91721636594280x + 57735061287750x - 5658908734710x
+--R +
+--R - 16998574124301x - 4338387945122
+--R /
+--R 6 5 4 3
+--R 968585393160x + 2744325280620x + 2690514981000x + 717470661600x
+--R +
+--R 2
+--R - 478313774400x - 350763434560x - 63775169920
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R 625377965625000x + 1771904235937500x + 1737161015625000x
+--R +
+--R 3 2
+--R 463242937500000x - 308828625000000x - 226474325000000x
+--R +
+--R - 41177150000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 625377820680360x - 1771903825261020x - 1737160613001000x
+--R +
+--R 3 2
+--R - 463242830133600x + 308828553422400x + 226474272509760x
+--R +
+--R 41177140456320
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 144944640x - 410676480x - 402624000x - 107366400x + 71577600x
+--R +
+--R 52490240x + 9543680
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R 41691695272920x + 91721636594280x + 57735061287750x - 5658908734710x
+--R +
+--R - 16998574124301x - 4338387945122
+--R /
+--R 6 5 4 3
+--R 968585393160x + 2744325280620x + 2690514981000x + 717470661600x
+--R +
+--R 2
+--R - 478313774400x - 350763434560x - 63775169920
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500
+m0:=a0-r0
+--R
+--R
+--R - 14912log(2x - 1) + 14912log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 99648703
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(2+3*x)^8/((1-2*x)^2*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R /
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 500
+r0:=5764801/15488/(1-2*x)+231915717/200000*x+14171517/25000*x^2+_
+ 2626101/10000*x^3+168399/2000*x^4+6561/500*x^5+(-1/9453125)/(3+5*x)+_
+ 79883671/85184*log(1-2*x)+268/103984375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (343040x + 34304x - 102912)log(5x + 3)
+--R +
+--R 2
+--R (124818235937500x + 12481823593750x - 37445470781250)log(- 2x + 1)
+--R +
+--R 7 6 5 4
+--R 1746538200000x + 11381607270000x + 35550138195000x + 75582410904000x
+--R +
+--R 3 2
+--R 151398804021300x - 7200755986050x - 71072602198741x - 14862377576717
+--R /
+--R 2
+--R 133100000000x + 13310000000x - 39930000000
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (343040x + 34304x - 102912)log(5x + 3)
+--R +
+--R 2
+--R (124818235937500x + 12481823593750x - 37445470781250)log(2x - 1)
+--R +
+--R 7 6 5 4
+--R 1746538200000x + 11381607270000x + 35550138195000x + 75582410904000x
+--R +
+--R 3 2
+--R 151398804021300x - 7200755986050x - 71072602198741x - 14862377576717
+--R /
+--R 2
+--R 133100000000x + 13310000000x - 39930000000
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500
+m0:=a0-r0
+--R
+--R
+--R 79883671log(2x - 1) - 79883671log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 85184
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(2+3*x)^7/((1-2*x)^2*(3+5*x)^2)
+--R
+--R
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R (1) ---------------------------------------------------------------------
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 351
+
+--S 352 of 500
+r0:=823543/7744/(1-2*x)+6156243/25000*x+1974861/20000*x^2+16281/500*x^3+_
+ 2187/400*x^4+(-1/1890625)/(3+5*x)+18941489/85184*log(1-2*x)+_
+ 47/4159375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (150400x + 15040x - 45120)log(5x + 3)
+--R +
+--R 2
+--R (2959607656250x + 295960765625x - 887882296875)log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R 72772425000x + 440677462500x + 1335778290000x + 3278990706750x
+--R +
+--R 2
+--R - 66522621330x - 1691007398993x - 424639358671
+--R /
+--R 2
+--R 13310000000x + 1331000000x - 3993000000
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (150400x + 15040x - 45120)log(5x + 3)
+--R +
+--R 2
+--R (2959607656250x + 295960765625x - 887882296875)log(2x - 1)
+--R +
+--R 6 5 4 3
+--R 72772425000x + 440677462500x + 1335778290000x + 3278990706750x
+--R +
+--R 2
+--R - 66522621330x - 1691007398993x - 424639358671
+--R /
+--R 2
+--R 13310000000x + 1331000000x - 3993000000
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 500
+m0:=a0-r0
+--R
+--R
+--R 18941489log(2x - 1) - 18941489log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 85184
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(2+3*x)^6/((1-2*x)^2*(3+5*x)^2)
+--R
+--R
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R (1) -----------------------------------------------------
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 356
+
+--S 357 of 500
+r0:=117649/3872/(1-2*x)+473607/10000*x+13851/1000*x^2+243/100*x^3+_
+ (-1/378125)/(3+5*x)+67228/1331*log(1-2*x)+202/4159375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (64640x + 6464x - 19392)log(5x + 3)
+--R +
+--R 2 5
+--R (67228000000x + 6722800000x - 20168400000)log(- 2x + 1) + 3234330000x
+--R +
+--R 4 3 2
+--R 18759114000x + 63910360800x + 773004870x - 39132050089x - 12132552773
+--R /
+--R 2
+--R 1331000000x + 133100000x - 399300000
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (64640x + 6464x - 19392)log(5x + 3)
+--R +
+--R 2 5
+--R (67228000000x + 6722800000x - 20168400000)log(2x - 1) + 3234330000x
+--R +
+--R 4 3 2
+--R 18759114000x + 63910360800x + 773004870x - 39132050089x - 12132552773
+--R /
+--R 2
+--R 1331000000x + 133100000x - 399300000
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500
+m0:=a0-r0
+--R
+--R
+--R 67228log(2x - 1) - 67228log(- 2x + 1)
+--R (4) -------------------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(2+3*x)^5/((1-2*x)^2*(3+5*x)^2)
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 361
+
+--S 362 of 500
+r0:=16807/1936/(1-2*x)+3807/500*x+243/200*x^2+(-1/75625)/(3+5*x)+_
+ 228095/21296*log(1-2*x)+169/831875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (27040x + 2704x - 8112)log(5x + 3)
+--R +
+--R 2 4
+--R (1425593750x + 142559375x - 427678125)log(- 2x + 1) + 161716500x
+--R +
+--R 3 2
+--R 1029595050x + 52827390x - 881767997x - 346644199
+--R /
+--R 2
+--R 133100000x + 13310000x - 39930000
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (27040x + 2704x - 8112)log(5x + 3)
+--R +
+--R 2 4
+--R (1425593750x + 142559375x - 427678125)log(2x - 1) + 161716500x
+--R +
+--R 3 2
+--R 1029595050x + 52827390x - 881767997x - 346644199
+--R /
+--R 2
+--R 133100000x + 13310000x - 39930000
+--R Type: Union(Expression(Integer),...)
+--E 363
+
+--S 364 of 500
+m0:=a0-r0
+--R
+--R
+--R 228095log(2x - 1) - 228095log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 21296
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(2+3*x)^4/((1-2*x)^2*(3+5*x)^2)
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) -------------------------------
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 366
+
+--S 367 of 500
+r0:=2401/968/(1-2*x)+81/100*x+(-1/15125)/(3+5*x)+10633/5324*log(1-2*x)+_
+ 136/166375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (10880x + 1088x - 3264)log(5x + 3)
+--R +
+--R 2 3 2
+--R (26582500x + 2658250x - 7974750)log(- 2x + 1) + 10781100x + 1078110x
+--R +
+--R - 19741381x - 9904037
+--R /
+--R 2
+--R 13310000x + 1331000x - 3993000
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (10880x + 1088x - 3264)log(5x + 3)
+--R +
+--R 2 3 2
+--R (26582500x + 2658250x - 7974750)log(2x - 1) + 10781100x + 1078110x
+--R +
+--R - 19741381x - 9904037
+--R /
+--R 2
+--R 13310000x + 1331000x - 3993000
+--R Type: Union(Expression(Integer),...)
+--E 368
+
+--S 369 of 500
+m0:=a0-r0
+--R
+--R
+--R 10633log(2x - 1) - 10633log(- 2x + 1)
+--R (4) -------------------------------------
+--R 5324
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(2+3*x)^3/((1-2*x)^2*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) ----------------------------
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 371
+
+--S 372 of 500
+r0:=343/484/(1-2*x)+(-1/3025)/(3+5*x)+1421/5324*log(1-2*x)+103/33275*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (4120x + 412x - 1236)log(5x + 3)
+--R +
+--R 2
+--R (355250x + 35525x - 106575)log(- 2x + 1) - 471713x - 282931
+--R /
+--R 2
+--R 1331000x + 133100x - 399300
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (4120x + 412x - 1236)log(5x + 3)
+--R +
+--R 2
+--R (355250x + 35525x - 106575)log(2x - 1) - 471713x - 282931
+--R /
+--R 2
+--R 1331000x + 133100x - 399300
+--R Type: Union(Expression(Integer),...)
+--E 373
+
+--S 374 of 500
+m0:=a0-r0
+--R
+--R
+--R 1421log(2x - 1) - 1421log(- 2x + 1)
+--R (4) -----------------------------------
+--R 5324
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(2+3*x)^2/((1-2*x)^2*(3+5*x)^2)
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) ----------------------------
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 376
+
+--S 377 of 500
+r0:=49/242/(1-2*x)+(-1/605)/(3+5*x)-14/1331*log(1-2*x)+14/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (1400x + 140x - 420)log(5x + 3) + (- 1400x - 140x + 420)log(- 2x + 1)
+--R +
+--R - 13519x - 8063
+--R /
+--R 2
+--R 133100x + 13310x - 39930
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (1400x + 140x - 420)log(5x + 3) + (- 1400x - 140x + 420)log(2x - 1)
+--R +
+--R - 13519x - 8063
+--R /
+--R 2
+--R 133100x + 13310x - 39930
+--R Type: Union(Expression(Integer),...)
+--E 378
+
+--S 379 of 500
+m0:=a0-r0
+--R
+--R
+--R - 14log(2x - 1) + 14log(- 2x + 1)
+--R (4) ---------------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(2+3*x)/((1-2*x)^2*(3+5*x)^2)
+--R
+--R
+--R 3x + 2
+--R (1) ----------------------------
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 381
+
+--S 382 of 500
+r0:=7/121/(1-2*x)+(-1/121)/(3+5*x)-37/1331*log(1-2*x)+37/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (370x + 37x - 111)log(5x + 3) + (- 370x - 37x + 111)log(- 2x + 1)
+--R +
+--R - 407x - 220
+--R /
+--R 2
+--R 13310x + 1331x - 3993
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (370x + 37x - 111)log(5x + 3) + (- 370x - 37x + 111)log(2x - 1) - 407x
+--R +
+--R - 220
+--R /
+--R 2
+--R 13310x + 1331x - 3993
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500
+m0:=a0-r0
+--R
+--R
+--R - 37log(2x - 1) + 37log(- 2x + 1)
+--R (4) ---------------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=1/((1-2*x)^2*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R 4 3 2
+--R 100x + 20x - 59x - 6x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 386
+
+--S 387 of 500
+r0:=2/121/(1-2*x)+(-5/121)/(3+5*x)-20/1331*log(1-2*x)+20/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (200x + 20x - 60)log(5x + 3) + (- 200x - 20x + 60)log(- 2x + 1) - 220x - 11
+--R -----------------------------------------------------------------------------
+--R 2
+--R 13310x + 1331x - 3993
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (200x + 20x - 60)log(5x + 3) + (- 200x - 20x + 60)log(2x - 1) - 220x - 11
+--R ---------------------------------------------------------------------------
+--R 2
+--R 13310x + 1331x - 3993
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500
+m0:=a0-r0
+--R
+--R
+--R - 20log(2x - 1) + 20log(- 2x + 1)
+--R (4) ---------------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=1/((1-2*x)^2*(2+3*x)*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------------------------
+--R 5 4 3 2
+--R 300x + 260x - 137x - 136x + 15x + 18
+--R Type: Fraction(Polynomial(Integer))
+--E 391
+
+--S 392 of 500
+r0:=4/847/(1-2*x)+(-25/121)/(3+5*x)-412/65219*log(1-2*x)+27/49*log(2+3*x)-_
+ 725/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 355250x - 35525x + 106575)log(5x + 3)
+--R +
+--R 2
+--R (359370x + 35937x - 107811)log(3x + 2)
+--R +
+--R 2
+--R (- 4120x - 412x + 1236)log(- 2x + 1) - 28490x + 12551
+--R /
+--R 2
+--R 652190x + 65219x - 195657
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (- 355250x - 35525x + 106575)log(5x + 3)
+--R +
+--R 2
+--R (359370x + 35937x - 107811)log(3x + 2)
+--R +
+--R 2
+--R (- 4120x - 412x + 1236)log(2x - 1) - 28490x + 12551
+--R /
+--R 2
+--R 652190x + 65219x - 195657
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500
+m0:=a0-r0
+--R
+--R
+--R - 412log(2x - 1) + 412log(- 2x + 1)
+--R (4) -----------------------------------
+--R 65219
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------
+--R 6 5 4 3 2
+--R 900x + 1380x + 109x - 682x - 227x + 84x + 36
+--R Type: Fraction(Polynomial(Integer))
+--E 396
+
+--S 397 of 500
+r0:=8/5929/(1-2*x)+(-27/49)/(2+3*x)+(-125/121)/(3+5*x)-_
+ 1088/456533*log(1-2*x)+1998/343*log(2+3*x)-7750/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (- 79747500x - 61139750x + 18607750x + 15949500)log(5x + 3)
+--R +
+--R 3 2
+--R (79780140x + 61164774x - 18615366x - 15956028)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 32640x - 25024x + 7616x + 6528)log(- 2x + 1) - 5354580x - 734888x
+--R +
+--R 1694231
+--R /
+--R 3 2
+--R 13695990x + 10500259x - 3195731x - 2739198
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (- 79747500x - 61139750x + 18607750x + 15949500)log(5x + 3)
+--R +
+--R 3 2
+--R (79780140x + 61164774x - 18615366x - 15956028)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 32640x - 25024x + 7616x + 6528)log(2x - 1) - 5354580x - 734888x
+--R +
+--R 1694231
+--R /
+--R 3 2
+--R 13695990x + 10500259x - 3195731x - 2739198
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1088log(2x - 1) + 1088log(- 2x + 1)
+--R (4) -------------------------------------
+--R 456533
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72
+--R Type: Fraction(Polynomial(Integer))
+--E 401
+
+--S 402 of 500
+r0:=16/41503/(1-2*x)+(-27/98)/(2+3*x)^2+(-1998/343)/(2+3*x)+_
+ (-625/121)/(3+5*x)-2704/3195731*log(1-2*x)+107109/2401*log(2+3*x)-_
+ 59375/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R - 25660687500x - 36780318750x - 7127968750x + 9123800000x
+--R +
+--R 3421425000
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R 25661174220x + 36781016382x + 7128103950x - 9123973056x
+--R +
+--R - 3421489896
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 486720x - 697632x - 135200x + 173056x + 64896)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 1711280340x - 1369336584x + 390771227x + 360692563
+--R /
+--R 4 3 2
+--R 575231580x + 824498598x + 159786550x - 204526784x - 76697544
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R - 25660687500x - 36780318750x - 7127968750x + 9123800000x
+--R +
+--R 3421425000
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R 25661174220x + 36781016382x + 7128103950x - 9123973056x
+--R +
+--R - 3421489896
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 486720x - 697632x - 135200x + 173056x + 64896)log(2x - 1)
+--R +
+--R 3 2
+--R - 1711280340x - 1369336584x + 390771227x + 360692563
+--R /
+--R 4 3 2
+--R 575231580x + 824498598x + 159786550x - 204526784x - 76697544
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2704log(2x - 1) + 2704log(- 2x + 1)
+--R (4) -------------------------------------
+--R 3195731
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^4*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 1
+--R -------------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 8100x + 23220x + 21141x + 690x - 9791x - 4696x + 424x + 768x + 144
+--R Type: Fraction(Polynomial(Integer))
+--E 406
+
+--S 407 of 500
+r0:=32/290521/(1-2*x)+(-9/49)/(2+3*x)^3+(-999/343)/(2+3*x)^2+_
+ (-107109/2401)/(2+3*x)+(-3125/121)/(3+5*x)-6464/22370117*log(1-2*x)+_
+ 5050944/16807*log(2+3*x)-400000/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3
+--R - 1815156000000x - 3811827600000x - 2238692400000x
+--R +
+--R 2
+--R 309248800000x + 672280000000x + 161347200000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 1815157745280x + 3811831265088x + 2238694552512x - 309249097344x
+--R +
+--R - 672280646400x - 161347355136
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 1745280x - 3665088x - 2152512x + 297344x + 646400x + 155136)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 121012436160x - 177486026256x - 36888162696x + 43940321194x
+--R +
+--R 17000329577
+--R /
+--R 5 4 3 2
+--R 6039931590x + 12683856339x + 7449248961x - 1029025382x - 2237011700x
+--R +
+--R - 536882808
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R - 1815156000000x - 3811827600000x - 2238692400000x
+--R +
+--R 2
+--R 309248800000x + 672280000000x + 161347200000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 1815157745280x + 3811831265088x + 2238694552512x - 309249097344x
+--R +
+--R - 672280646400x - 161347355136
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 1745280x - 3665088x - 2152512x + 297344x + 646400x + 155136)
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 121012436160x - 177486026256x - 36888162696x + 43940321194x
+--R +
+--R 17000329577
+--R /
+--R 5 4 3 2
+--R 6039931590x + 12683856339x + 7449248961x - 1029025382x - 2237011700x
+--R +
+--R - 536882808
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500
+m0:=a0-r0
+--R
+--R
+--R - 6464log(2x - 1) + 6464log(- 2x + 1)
+--R (4) -------------------------------------
+--R 22370117
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^5*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 24300x + 85860x + 109863x + 44352x - 27993x - 33670x - 8120x
+--R +
+--R 2
+--R 3152x + 1968x + 288
+--R Type: Fraction(Polynomial(Integer))
+--E 411
+
+--S 412 of 500
+r0:=64/2033647/(1-2*x)+(-27/196)/(2+3*x)^4+(-666/343)/(2+3*x)^3+_
+ (-107109/4802)/(2+3*x)^2+(-5050944/16807)/(2+3*x)+(-15625/121)/(3+5*x)-_
+ 15040/156590819*log(1-2*x)+222359715/117649*log(2+3*x)-_
+ 2515625/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R - 958912880625000x - 2652992303062500x - 2525137252312500x
+--R +
+--R 3 2
+--R - 625069137000000x + 464066480500000x + 322005313000000x
+--R +
+--R 56824467000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R 958912929354600x + 2652992437881060x + 2525137380633780x
+--R +
+--R 3 2
+--R 625069168764480x - 464066504082720x - 322005329363520x
+--R +
+--R - 56824469887680
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 48729600x - 134818560x - 128321280x - 31764480x + 23582720x
+--R +
+--R 16363520x + 2887680
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3
+--R - 63927582226200x - 136378873350720x - 81993113952750x
+--R +
+--R 2
+--R 10222048359600x + 24455908667575x + 5987073080219
+--R /
+--R 6 5 4 3
+--R 507354253560x + 1403680101516x + 1336032867708x + 330719809728x
+--R +
+--R 2
+--R - 245534404192x - 170370811072x - 30065437248
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R - 958912880625000x - 2652992303062500x - 2525137252312500x
+--R +
+--R 3 2
+--R - 625069137000000x + 464066480500000x + 322005313000000x
+--R +
+--R 56824467000000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R 958912929354600x + 2652992437881060x + 2525137380633780x
+--R +
+--R 3 2
+--R 625069168764480x - 464066504082720x - 322005329363520x
+--R +
+--R - 56824469887680
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 48729600x - 134818560x - 128321280x - 31764480x + 23582720x
+--R +
+--R 16363520x + 2887680
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3
+--R - 63927582226200x - 136378873350720x - 81993113952750x
+--R +
+--R 2
+--R 10222048359600x + 24455908667575x + 5987073080219
+--R /
+--R 6 5 4 3
+--R 507354253560x + 1403680101516x + 1336032867708x + 330719809728x
+--R +
+--R 2
+--R - 245534404192x - 170370811072x - 30065437248
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500
+m0:=a0-r0
+--R
+--R
+--R - 15040log(2x - 1) + 15040log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 156590819
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(2+3*x)^8/((1-2*x)^2*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R /
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 416
+
+--S 417 of 500
+r0:=5764801/85184/(1-2*x)+7680987/50000*x+6093711/100000*x^2+12393/625*x^3+_
+ 6561/2000*x^4+(-1/18906250)/(3+5*x)^2+(-268/103984375)/(3+5*x)+_
+ 130943337/937024*log(1-2*x)+6312/228765625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (100992000x + 70694400x - 24238080x - 18178560)log(5x + 3)
+--R +
+--R 3 2
+--R 511497410156250x + 358048187109375x - 122759378437500x
+--R +
+--R - 92069533828125
+--R *
+--R log(- 2x + 1)
+--R +
+--R 7 6 5
+--R 12007450125000x + 80983580287500x + 270968124487500x
+--R +
+--R 4 3 2
+--R 698838044478750x + 327005737947900x - 298950055409445x
+--R +
+--R - 249835373577966x - 44587132164487
+--R /
+--R 3 2
+--R 3660250000000x + 2562175000000x - 878460000000x - 658845000000
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (100992000x + 70694400x - 24238080x - 18178560)log(5x + 3)
+--R +
+--R 3 2
+--R 511497410156250x + 358048187109375x - 122759378437500x
+--R +
+--R - 92069533828125
+--R *
+--R log(2x - 1)
+--R +
+--R 7 6 5
+--R 12007450125000x + 80983580287500x + 270968124487500x
+--R +
+--R 4 3 2
+--R 698838044478750x + 327005737947900x - 298950055409445x
+--R +
+--R - 249835373577966x - 44587132164487
+--R /
+--R 3 2
+--R 3660250000000x + 2562175000000x - 878460000000x - 658845000000
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 500
+m0:=a0-r0
+--R
+--R
+--R 130943337log(2x - 1) - 130943337log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 937024
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(2+3*x)^7/((1-2*x)^2*(3+5*x)^3)
+--R
+--R
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R (1) ---------------------------------------------------------------------
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 421
+
+--S 422 of 500
+r0:=823543/42592/(1-2*x)+1467477/50000*x+21141/2500*x^2+729/500*x^3+_
+ (-1/3781250)/(3+5*x)^2+(-47/4159375)/(3+5*x)+7411887/234256*log(1-2*x)+_
+ 4761/45753125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (38088000x + 26661600x - 9141120x - 6855840)log(5x + 3)
+--R +
+--R 3 2
+--R (11581073437500x + 8106751406250x - 2779457625000x - 2084593218750)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R 533664450000x + 3468818925000x + 12781263577500x + 6680945249550x
+--R +
+--R 2
+--R - 6674047531965x - 6180073448472x - 1273917828029
+--R /
+--R 3 2
+--R 366025000000x + 256217500000x - 87846000000x - 65884500000
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (38088000x + 26661600x - 9141120x - 6855840)log(5x + 3)
+--R +
+--R 3 2
+--R (11581073437500x + 8106751406250x - 2779457625000x - 2084593218750)
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3
+--R 533664450000x + 3468818925000x + 12781263577500x + 6680945249550x
+--R +
+--R 2
+--R - 6674047531965x - 6180073448472x - 1273917828029
+--R /
+--R 3 2
+--R 366025000000x + 256217500000x - 87846000000x - 65884500000
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 500
+m0:=a0-r0
+--R
+--R
+--R 7411887log(2x - 1) - 7411887log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 234256
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(2+3*x)^6/((1-2*x)^2*(3+5*x)^3)
+--R
+--R
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R (1) -----------------------------------------------------
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 426
+
+--S 427 of 500
+r0:=117649/21296/(1-2*x)+2916/625*x+729/1000*x^2+(-1/756250)/(3+5*x)^2+_
+ (-202/4159375)/(3+5*x)+1563051/234256*log(1-2*x)+17139/45753125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (13711200x + 9597840x - 3290688x - 2468016)log(5x + 3)
+--R +
+--R 3 2
+--R (244226718750x + 170958703125x - 58614412500x - 43960809375)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R 26683222500x + 189450879750x + 113136863400x - 146893374705x
+--R +
+--R - 152064641058x - 36397551751
+--R /
+--R 3 2
+--R 36602500000x + 25621750000x - 8784600000x - 6588450000
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (13711200x + 9597840x - 3290688x - 2468016)log(5x + 3)
+--R +
+--R 3 2
+--R (244226718750x + 170958703125x - 58614412500x - 43960809375)log(2x - 1)
+--R +
+--R 5 4 3 2
+--R 26683222500x + 189450879750x + 113136863400x - 146893374705x
+--R +
+--R - 152064641058x - 36397551751
+--R /
+--R 3 2
+--R 36602500000x + 25621750000x - 8784600000x - 6588450000
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 500
+m0:=a0-r0
+--R
+--R
+--R 1563051log(2x - 1) - 1563051log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 234256
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(2+3*x)^5/((1-2*x)^2*(3+5*x)^3)
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 431
+
+--S 432 of 500
+r0:=16807/10648/(1-2*x)+243/500*x+(-1/151250)/(3+5*x)^2+_
+ (-169/831875)/(3+5*x)+36015/29282*log(1-2*x)+11562/9150625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (4624800x + 3237360x - 1109952x - 832464)log(5x + 3)
+--R +
+--R 3 2
+--R (4501875000x + 3151312500x - 1080450000x - 810337500)log(- 2x + 1)
+--R +
+--R 4 3 2
+--R 1778881500x + 1245217050x - 3315783405x - 3786658260x - 1039888025
+--R /
+--R 3 2
+--R 3660250000x + 2562175000x - 878460000x - 658845000
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (4624800x + 3237360x - 1109952x - 832464)log(5x + 3)
+--R +
+--R 3 2
+--R (4501875000x + 3151312500x - 1080450000x - 810337500)log(2x - 1)
+--R +
+--R 4 3 2
+--R 1778881500x + 1245217050x - 3315783405x - 3786658260x - 1039888025
+--R /
+--R 3 2
+--R 3660250000x + 2562175000x - 878460000x - 658845000
+--R Type: Union(Expression(Integer),...)
+--E 433
+
+--S 434 of 500
+m0:=a0-r0
+--R
+--R
+--R 36015log(2x - 1) - 36015log(- 2x + 1)
+--R (4) -------------------------------------
+--R 29282
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(2+3*x)^4/((1-2*x)^2*(3+5*x)^3)
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) ----------------------------------------
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 436
+
+--S 437 of 500
+r0:=2401/5324/(1-2*x)+(-1/30250)/(3+5*x)^2+(-136/166375)/(3+5*x)+_
+ 9261/58564*log(1-2*x)+7074/1830125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (1414800x + 990360x - 339552x - 254664)log(5x + 3)
+--R +
+--R 3 2
+--R (57881250x + 40516875x - 13891500x - 10418625)log(- 2x + 1)
+--R +
+--R 2
+--R - 82594215x - 99047718x - 29694181
+--R /
+--R 3 2
+--R 366025000x + 256217500x - 87846000x - 65884500
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (1414800x + 990360x - 339552x - 254664)log(5x + 3)
+--R +
+--R 3 2 2
+--R (57881250x + 40516875x - 13891500x - 10418625)log(2x - 1) - 82594215x
+--R +
+--R - 99047718x - 29694181
+--R /
+--R 3 2
+--R 366025000x + 256217500x - 87846000x - 65884500
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500
+m0:=a0-r0
+--R
+--R
+--R 9261log(2x - 1) - 9261log(- 2x + 1)
+--R (4) -----------------------------------
+--R 58564
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(2+3*x)^3/((1-2*x)^2*(3+5*x)^3)
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) ----------------------------------------
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 441
+
+--S 442 of 500
+r0:=343/2662/(1-2*x)+(-1/6050)/(3+5*x)^2+(-103/33275)/(3+5*x)-_
+ 147/14641*log(1-2*x)+147/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (367500x + 257250x - 88200x - 66150)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 367500x - 257250x + 88200x + 66150)log(- 2x + 1) - 2380785x
+--R +
+--R - 2832258x - 842006
+--R /
+--R 3 2
+--R 36602500x + 25621750x - 8784600x - 6588450
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (367500x + 257250x - 88200x - 66150)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 367500x - 257250x + 88200x + 66150)log(2x - 1) - 2380785x
+--R +
+--R - 2832258x - 842006
+--R /
+--R 3 2
+--R 36602500x + 25621750x - 8784600x - 6588450
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500
+m0:=a0-r0
+--R
+--R
+--R - 147log(2x - 1) + 147log(- 2x + 1)
+--R (4) -----------------------------------
+--R 14641
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(2+3*x)^2/((1-2*x)^2*(3+5*x)^3)
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) ----------------------------------------
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 446
+
+--S 447 of 500
+r0:=49/1331/(1-2*x)+(-1/1210)/(3+5*x)^2+(-14/1331)/(3+5*x)-_
+ 273/14641*log(1-2*x)+273/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (136500x + 95550x - 32760x - 24570)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 136500x - 95550x + 32760x + 24570)log(- 2x + 1) - 150150x - 163482x
+--R +
+--R - 43769
+--R /
+--R 3 2
+--R 7320500x + 5124350x - 1756920x - 1317690
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (136500x + 95550x - 32760x - 24570)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 136500x - 95550x + 32760x + 24570)log(2x - 1) - 150150x - 163482x
+--R +
+--R - 43769
+--R /
+--R 3 2
+--R 7320500x + 5124350x - 1756920x - 1317690
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500
+m0:=a0-r0
+--R
+--R
+--R - 273log(2x - 1) + 273log(- 2x + 1)
+--R (4) -----------------------------------
+--R 14641
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(2+3*x)/((1-2*x)^2*(3+5*x)^3)
+--R
+--R
+--R 3x + 2
+--R (1) ----------------------------------------
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 451
+
+--S 452 of 500
+r0:=14/1331/(1-2*x)+(-1/242)/(3+5*x)^2+(-37/1331)/(3+5*x)-_
+ 144/14641*log(1-2*x)+144/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (14400x + 10080x - 3456x - 2592)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 14400x - 10080x + 3456x + 2592)log(- 2x + 1) - 15840x - 10296x - 209
+--R /
+--R 3 2
+--R 1464100x + 1024870x - 351384x - 263538
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (14400x + 10080x - 3456x - 2592)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 14400x - 10080x + 3456x + 2592)log(2x - 1) - 15840x - 10296x - 209
+--R /
+--R 3 2
+--R 1464100x + 1024870x - 351384x - 263538
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500
+m0:=a0-r0
+--R
+--R
+--R - 144log(2x - 1) + 144log(- 2x + 1)
+--R (4) -----------------------------------
+--R 14641
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=1/((1-2*x)^2*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) ----------------------------------------
+--R 5 4 3 2
+--R 500x + 400x - 235x - 207x + 27x + 27
+--R Type: Fraction(Polynomial(Integer))
+--E 456
+
+--S 457 of 500
+r0:=4/1331/(1-2*x)+(-5/242)/(3+5*x)^2+(-20/1331)/(3+5*x)-_
+ 60/14641*log(1-2*x)+60/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (6000x + 4200x - 1440x - 1080)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 6000x - 4200x + 1440x + 1080)log(- 2x + 1) - 6600x - 4290x + 1133
+--R /
+--R 3 2
+--R 1464100x + 1024870x - 351384x - 263538
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (6000x + 4200x - 1440x - 1080)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 6000x - 4200x + 1440x + 1080)log(2x - 1) - 6600x - 4290x + 1133
+--R /
+--R 3 2
+--R 1464100x + 1024870x - 351384x - 263538
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500
+m0:=a0-r0
+--R
+--R
+--R - 60log(2x - 1) + 60log(- 2x + 1)
+--R (4) ---------------------------------
+--R 14641
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=1/((1-2*x)^2*(2+3*x)*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------------
+--R 6 5 4 3 2
+--R 1500x + 2200x + 95x - 1091x - 333x + 135x + 54
+--R Type: Fraction(Polynomial(Integer))
+--E 461
+
+--S 462 of 500
+r0:=8/9317/(1-2*x)+(-25/242)/(3+5*x)^2+725/1331/(3+5*x)-_
+ 1104/717409*log(1-2*x)-81/49*log(2+3*x)+24225/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (118702500x + 83091750x - 28488600x - 21366450)log(5x + 3)
+--R +
+--R 3 2
+--R (- 118592100x - 83014470x + 28462104x + 21346578)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 110400x - 77280x + 26496x + 19872)log(- 2x + 1) + 7784700x
+--R +
+--R 448140x - 2207513
+--R /
+--R 3 2
+--R 71740900x + 50218630x - 17217816x - 12913362
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (118702500x + 83091750x - 28488600x - 21366450)log(5x + 3)
+--R +
+--R 3 2
+--R (- 118592100x - 83014470x + 28462104x + 21346578)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 110400x - 77280x + 26496x + 19872)log(2x - 1) + 7784700x + 448140x
+--R +
+--R - 2207513
+--R /
+--R 3 2
+--R 71740900x + 50218630x - 17217816x - 12913362
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1104log(2x - 1) + 1104log(- 2x + 1)
+--R (4) -------------------------------------
+--R 717409
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108
+--R Type: Fraction(Polynomial(Integer))
+--E 466
+
+--S 467 of 500
+r0:=16/65219/(1-2*x)+81/49/(2+3*x)+(-125/242)/(3+5*x)^2+7750/1331/(3+5*x)-_
+ 2736/5021863*log(1-2*x)-8829/343*log(2+3*x)+376875/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 38780437500x + 52999931250x + 8790232500x - 13185348750x
+--R +
+--R - 4653652500
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 38779616700x - 52998809490x - 8790046452x + 13185069678x
+--R +
+--R 4653554004
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 820800x - 1121760x - 186048x + 279072x + 98496)log(- 2x + 1)
+--R +
+--R 3 2
+--R 2584404900x + 1894703580x - 614007471x - 489983648
+--R /
+--R 4 3 2
+--R 1506558900x + 2058963830x + 341486684x - 512230026x - 180787068
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 38780437500x + 52999931250x + 8790232500x - 13185348750x
+--R +
+--R - 4653652500
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 38779616700x - 52998809490x - 8790046452x + 13185069678x
+--R +
+--R 4653554004
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 820800x - 1121760x - 186048x + 279072x + 98496)log(2x - 1)
+--R +
+--R 3 2
+--R 2584404900x + 1894703580x - 614007471x - 489983648
+--R /
+--R 4 3 2
+--R 1506558900x + 2058963830x + 341486684x - 512230026x - 180787068
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2736log(2x - 1) + 2736log(- 2x + 1)
+--R (4) -------------------------------------
+--R 5021863
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 1
+--R ----------------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x + 216
+--R Type: Fraction(Polynomial(Integer))
+--E 471
+
+--S 472 of 500
+r0:=32/456533/(1-2*x)+81/98/(2+3*x)^2+8829/343/(2+3*x)+(-625/242)/(3+5*x)^2+_
+ 59375/1331/(3+5*x)-6528/35153041*log(1-2*x)-_
+ 630342/2401*log(2+3*x)+3843750/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3
+--R 8305959375000x + 16888784062500x + 9450336000000x
+--R +
+--R 2
+--R - 1568903437500x - 2879399250000x - 664476750000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 8305953499800x - 16888772116260x - 9450329315328x
+--R +
+--R 2
+--R 1568902327740x + 2879397213264x + 664476279984
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 5875200x - 11946240x - 6684672x + 1109760x + 2036736x + 470016)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R 553723770600x + 775209508920x + 139245535506x - 192629430378x
+--R +
+--R - 70007419097
+--R /
+--R 5 4 3 2
+--R 31637736900x + 64330065030x + 35996713984x - 5976016970x
+--R +
+--R - 10967748792x - 2531018952
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R 8305959375000x + 16888784062500x + 9450336000000x
+--R +
+--R 2
+--R - 1568903437500x - 2879399250000x - 664476750000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 8305953499800x - 16888772116260x - 9450329315328x
+--R +
+--R 2
+--R 1568902327740x + 2879397213264x + 664476279984
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 5875200x - 11946240x - 6684672x + 1109760x + 2036736x + 470016)
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R 553723770600x + 775209508920x + 139245535506x - 192629430378x
+--R +
+--R - 70007419097
+--R /
+--R 5 4 3 2
+--R 31637736900x + 64330065030x + 35996713984x - 5976016970x
+--R +
+--R - 10967748792x - 2531018952
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 500
+m0:=a0-r0
+--R
+--R
+--R - 6528log(2x - 1) + 6528log(- 2x + 1)
+--R (4) -------------------------------------
+--R 35153041
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=1/((1-2*x)^2*(2+3*x)^4*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 40500x + 140400x + 175365x + 66873x - 46885x - 52853x - 11968x
+--R +
+--R 2
+--R 5112x + 3024x + 432
+--R Type: Fraction(Polynomial(Integer))
+--E 476
+
+--S 477 of 500
+r0:=64/3195731/(1-2*x)+27/49/(2+3*x)^3+8829/686/(2+3*x)^2+_
+ 630342/2401/(2+3*x)+(-3125/242)/(3+5*x)^2+400000/1331/(3+5*x)-_
+ 15168/246071287*log(1-2*x)-37214802/16807*log(2+3*x)+_
+ 32418750/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R 1471127214375000x + 3972043478812500x + 3668010521175000x
+--R +
+--R 3 2
+--R 837997650262500x - 695243824275000x - 457684022250000x
+--R +
+--R - 78460118100000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 1471127173421400x - 3972043368237780x - 3668010419064024x
+--R +
+--R 3 2
+--R - 837997626934116x + 695243804920632x + 457684009508880x
+--R +
+--R 78460115915808
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 40953600x - 110574720x - 102110976x - 23328384x + 19354368x
+--R +
+--R 12741120x + 2184192
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3
+--R 98075099845800x + 202688513402760x + 116200773740898x
+--R +
+--R 2
+--R - 17675352484482x - 35145131488467x - 8266584593036
+--R /
+--R 6 5 4 3
+--R 664392474900x + 1793859682230x + 1656551904084x + 378457639406x
+--R +
+--R 2
+--R - 313986962212x - 206699881080x - 35434265328
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R 1471127214375000x + 3972043478812500x + 3668010521175000x
+--R +
+--R 3 2
+--R 837997650262500x - 695243824275000x - 457684022250000x
+--R +
+--R - 78460118100000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 1471127173421400x - 3972043368237780x - 3668010419064024x
+--R +
+--R 3 2
+--R - 837997626934116x + 695243804920632x + 457684009508880x
+--R +
+--R 78460115915808
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 40953600x - 110574720x - 102110976x - 23328384x + 19354368x
+--R +
+--R 12741120x + 2184192
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3
+--R 98075099845800x + 202688513402760x + 116200773740898x
+--R +
+--R 2
+--R - 17675352484482x - 35145131488467x - 8266584593036
+--R /
+--R 6 5 4 3
+--R 664392474900x + 1793859682230x + 1656551904084x + 378457639406x
+--R +
+--R 2
+--R - 313986962212x - 206699881080x - 35434265328
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 500
+m0:=a0-r0
+--R
+--R
+--R - 15168log(2x - 1) + 15168log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 246071287
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(2+3*x)^8*(3+5*x)/(1-2*x)^3
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4
+--R - 32805x - 194643x - 513216x - 789264x - 780192x - 514080x
+--R +
+--R 3 2
+--R - 225792x - 63744x - 10496x - 768
+--R /
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 481
+
+--S 482 of 500
+r0:=63412811/2048/(1-2*x)^2+(-246239357/1024)/(1-2*x)-120864213/256*x-_
+ 118841283/512*x^2-16042509/128*x^3-7568235/128*x^4-213597/10*x^5-_
+ 162567/32*x^6-32805/56*x^7-106237047/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 118985492640x + 118985492640x - 29746373160)log(- 2x + 1)
+--R +
+--R 9 8 7 6
+--R - 167961600x - 1288638720x - 4709643264x - 11192743296x
+--R +
+--R 5 4 3 2
+--R - 20513437056x - 34854109920x - 77800605120x + 118730138940x
+--R +
+--R 631530340x - 15017306605
+--R /
+--R 2
+--R 286720x - 286720x + 71680
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 9
+--R (- 118985492640x + 118985492640x - 29746373160)log(2x - 1) - 167961600x
+--R +
+--R 8 7 6 5
+--R - 1288638720x - 4709643264x - 11192743296x - 20513437056x
+--R +
+--R 4 3 2
+--R - 34854109920x - 77800605120x + 118730138940x + 631530340x - 15017306605
+--R /
+--R 2
+--R 286720x - 286720x + 71680
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500
+m0:=a0-r0
+--R
+--R
+--R - 106237047log(2x - 1) + 106237047log(- 2x + 1)
+--R (4) -----------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(2+3*x)^7*(3+5*x)/(1-2*x)^3
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 10935x - 57591x - 132678x - 174636x - 143640x - 75600x - 24864x
+--R +
+--R - 4672x - 384
+--R /
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 486
+
+--S 487 of 500
+r0:=9058973/1024/(1-2*x)^2+(-15647317/256)/(1-2*x)-24960933/256*x-_
+ 10989621/256*x^2-631611/32*x^3-235467/32*x^4-147987/80*x^5-_
+ 3645/16*x^6-23647449/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 8
+--R (- 1891795920x + 1891795920x - 472948980)log(- 2x + 1) - 4665600x
+--R +
+--R 7 6 5 4 3
+--R - 33219072x - 113980608x - 263003328x - 512613360x - 1218762720x
+--R +
+--R 2
+--R 1777082220x + 126674020x - 267651475
+--R /
+--R 2
+--R 20480x - 20480x + 5120
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8
+--R (- 1891795920x + 1891795920x - 472948980)log(2x - 1) - 4665600x
+--R +
+--R 7 6 5 4 3
+--R - 33219072x - 113980608x - 263003328x - 512613360x - 1218762720x
+--R +
+--R 2
+--R 1777082220x + 126674020x - 267651475
+--R /
+--R 2
+--R 20480x - 20480x + 5120
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500
+m0:=a0-r0
+--R
+--R
+--R - 23647449log(2x - 1) + 23647449log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(2+3*x)^6*(3+5*x)/(1-2*x)^3
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 3645x - 16767x - 33048x - 36180x - 23760x - 9360x - 2048x - 192
+--R -----------------------------------------------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 491
+
+--S 492 of 500
+r0:=1294139/512/(1-2*x)^2+(-3916031/256)/(1-2*x)-2431647/128*x-_
+ 461835/64*x^2-10611/4*x^3-44469/64*x^4-729/8*x^5-5078115/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 7 6
+--R (- 40624920x + 40624920x - 10156230)log(- 2x + 1) - 186624x - 1236384x
+--R +
+--R 5 4 3 2
+--R - 4056480x - 9701640x - 25485840x + 35211672x + 5937536x - 6537923
+--R /
+--R 2
+--R 2048x - 2048x + 512
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 6
+--R (- 40624920x + 40624920x - 10156230)log(2x - 1) - 186624x - 1236384x
+--R +
+--R 5 4 3 2
+--R - 4056480x - 9701640x - 25485840x + 35211672x + 5937536x - 6537923
+--R /
+--R 2
+--R 2048x - 2048x + 512
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500
+m0:=a0-r0
+--R
+--R
+--R - 5078115log(2x - 1) + 5078115log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R - 1215x - 4779x - 7830x - 6840x - 3360x - 880x - 96
+--R (1) --------------------------------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 496
+
+--S 497 of 500
+r0:=184877/256/(1-2*x)^2+(-60025/16)/(1-2*x)-109089/32*x-16821/16*x^2-_
+ 4401/16*x^3-1215/32*x^4-519645/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 6 5
+--R (- 4157160x + 4157160x - 1039290)log(- 2x + 1) - 38880x - 242784x
+--R +
+--R 4 3 2
+--R - 804600x - 2484720x + 3221712x + 1048088x - 775523
+--R /
+--R 2
+--R 1024x - 1024x + 256
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 5
+--R (- 4157160x + 4157160x - 1039290)log(2x - 1) - 38880x - 242784x
+--R +
+--R 4 3 2
+--R - 804600x - 2484720x + 3221712x + 1048088x - 775523
+--R /
+--R 2
+--R 1024x - 1024x + 256
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500
+m0:=a0-r0
+--R
+--R
+--R - 519645log(2x - 1) + 519645log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
+
diff --git a/src/axiom-website/CATS/rich3h.input.pdf b/src/axiom-website/CATS/rich3h.input.pdf
new file mode 100644
index 0000000..74ea9fe
Binary files /dev/null and b/src/axiom-website/CATS/rich3h.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3i.input.pamphlet b/src/axiom-website/CATS/rich3i.input.pamphlet
new file mode 100644
index 0000000..8e4ecb1
--- /dev/null
+++ b/src/axiom-website/CATS/rich3i.input.pamphlet
@@ -0,0 +1,7464 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3i.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 92 matching answers.
+\item 8 cases where Axiom differed from Rubi
+\item 0 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 rich3i.output
+)spool rich3i.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^3
+--R
+--R
+--R 5 4 3 2
+--R - 405x - 1323x - 1728x - 1128x - 368x - 48
+--R (1) ----------------------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1
+
+--S 2 of 500
+r0:=26411/128/(1-2*x)^2+(-57281/64)/(1-2*x)-540*x-3861/32*x^2-_
+ 135/8*x^3-24843/32*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 5 4 3
+--R (- 397488x + 397488x - 99372)log(- 2x + 1) - 8640x - 53136x - 216864x
+--R +
+--R 2
+--R 261036x + 160004x - 88151
+--R /
+--R 2
+--R 512x - 512x + 128
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4 3
+--R (- 397488x + 397488x - 99372)log(2x - 1) - 8640x - 53136x - 216864x
+--R +
+--R 2
+--R 261036x + 160004x - 88151
+--R /
+--R 2
+--R 512x - 512x + 128
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500
+m0:=a0-r0
+--R
+--R
+--R - 24843log(2x - 1) + 24843log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^3
+--R
+--R
+--R 4 3 2
+--R - 135x - 351x - 342x - 148x - 24
+--R (1) -----------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 6
+
+--S 7 of 500
+r0:=3773/64/(1-2*x)^2+(-3283/16)/(1-2*x)-1107/16*x-135/16*x^2-1071/8*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2
+--R (- 34272x + 34272x - 8568)log(- 2x + 1) - 2160x - 15552x + 17172x
+--R +
+--R 21836x - 9359
+--R /
+--R 2
+--R 256x - 256x + 64
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2
+--R (- 34272x + 34272x - 8568)log(2x - 1) - 2160x - 15552x + 17172x
+--R +
+--R 21836x - 9359
+--R /
+--R 2
+--R 256x - 256x + 64
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1071log(2x - 1) + 1071log(- 2x + 1)
+--R (4) -------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^3
+--R
+--R
+--R 3 2
+--R - 45x - 87x - 56x - 12
+--R (1) ------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 11
+
+--S 12 of 500
+r0:=539/32/(1-2*x)^2+(-707/16)/(1-2*x)-45/8*x-309/16*log(1-2*x)
+--R
+--R
+--R 2 3 2
+--R (- 2472x + 2472x - 618)log(- 2x + 1) - 720x + 720x + 2648x - 875
+--R (2) -------------------------------------------------------------------
+--R 2
+--R 128x - 128x + 32
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2
+--R (- 2472x + 2472x - 618)log(2x - 1) - 720x + 720x + 2648x - 875
+--R (3) -----------------------------------------------------------------
+--R 2
+--R 128x - 128x + 32
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 500
+m0:=a0-r0
+--R
+--R
+--R - 309log(2x - 1) + 309log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(2+3*x)*(3+5*x)/(1-2*x)^3
+--R
+--R
+--R 2
+--R - 15x - 19x - 6
+--R (1) -------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 16
+
+--S 17 of 500
+r0:=77/16/(1-2*x)^2+(-17/2)/(1-2*x)-15/8*log(1-2*x)
+--R
+--R
+--R 2
+--R (- 120x + 120x - 30)log(- 2x + 1) + 272x - 59
+--R (2) ----------------------------------------------
+--R 2
+--R 64x - 64x + 16
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (- 120x + 120x - 30)log(2x - 1) + 272x - 59
+--R (3) --------------------------------------------
+--R 2
+--R 64x - 64x + 16
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 500
+m0:=a0-r0
+--R
+--R
+--R - 15log(2x - 1) + 15log(- 2x + 1)
+--R (4) ---------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(3+5*x)/(1-2*x)^3
+--R
+--R
+--R - 5x - 3
+--R (1) -------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 21
+
+--S 22 of 500
+r0:=1/22*(3+5*x)^2/(1-2*x)^2
+--R
+--R
+--R 25 2 15 9
+--R -- x + -- x + --
+--R 88 44 88
+--R (2) -----------------
+--R 2 1
+--R x - x + -
+--R 4
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 22
+
+--S 23 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 20x + 1
+--R (3) --------------
+--R 2
+--R 32x - 32x + 8
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 500
+m0:=a0-r0
+--R
+--R
+--R 25
+--R (4) - --
+--R 88
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(3+5*x)/((1-2*x)^3*(2+3*x))
+--R
+--R
+--R - 5x - 3
+--R (1) --------------------------
+--R 4 3 2
+--R 24x - 20x - 6x + 9x - 2
+--R Type: Fraction(Polynomial(Integer))
+--E 26
+
+--S 27 of 500
+r0:=11/28/(1-2*x)^2+(-1/49)/(1-2*x)+3/343*log(1-2*x)-3/343*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (- 48x + 48x - 12)log(3x + 2) + (48x - 48x + 12)log(- 2x + 1) + 56x + 511
+--R ---------------------------------------------------------------------------
+--R 2
+--R 5488x - 5488x + 1372
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (- 48x + 48x - 12)log(3x + 2) + (48x - 48x + 12)log(2x - 1) + 56x + 511
+--R -------------------------------------------------------------------------
+--R 2
+--R 5488x - 5488x + 1372
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 500
+m0:=a0-r0
+--R
+--R
+--R 3log(2x - 1) - 3log(- 2x + 1)
+--R (4) -----------------------------
+--R 343
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^2)
+--R
+--R
+--R - 5x - 3
+--R (1) -----------------------------------
+--R 5 4 3 2
+--R 72x - 12x - 58x + 15x + 12x - 4
+--R Type: Fraction(Polynomial(Integer))
+--E 31
+
+--S 32 of 500
+r0:=11/98/(1-2*x)^2+31/343/(1-2*x)+3/343/(2+3*x)-87/2401*log(1-2*x)+_
+ 87/2401*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (2088x - 696x - 870x + 348)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 2088x + 696x + 870x - 348)log(- 2x + 1) - 2436x + 1015x + 1988
+--R /
+--R 3 2
+--R 57624x - 19208x - 24010x + 9604
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (2088x - 696x - 870x + 348)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 2088x + 696x + 870x - 348)log(2x - 1) - 2436x + 1015x + 1988
+--R /
+--R 3 2
+--R 57624x - 19208x - 24010x + 9604
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 500
+m0:=a0-r0
+--R
+--R
+--R - 87log(2x - 1) + 87log(- 2x + 1)
+--R (4) ---------------------------------
+--R 2401
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^3)
+--R
+--R
+--R - 5x - 3
+--R (1) ---------------------------------------------
+--R 6 5 4 3 2
+--R 216x + 108x - 198x - 71x + 66x + 12x - 8
+--R Type: Fraction(Polynomial(Integer))
+--E 36
+
+--S 37 of 500
+r0:=11/343/(1-2*x)^2+128/2401/(1-2*x)+3/686/(2+3*x)^2+(-87/2401)/(2+3*x)-_
+ 558/16807*log(1-2*x)+558/16807*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (40176x + 13392x - 25668x - 4464x + 4464)log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 40176x - 13392x + 25668x + 4464x - 4464)log(- 2x + 1) - 46872x
+--R +
+--R 2
+--R - 11718x + 25606x + 9191
+--R /
+--R 4 3 2
+--R 1210104x + 403368x - 773122x - 134456x + 134456
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (40176x + 13392x - 25668x - 4464x + 4464)log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 40176x - 13392x + 25668x + 4464x - 4464)log(2x - 1) - 46872x
+--R +
+--R 2
+--R - 11718x + 25606x + 9191
+--R /
+--R 4 3 2
+--R 1210104x + 403368x - 773122x - 134456x + 134456
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 500
+m0:=a0-r0
+--R
+--R
+--R - 558log(2x - 1) + 558log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16807
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^4)
+--R
+--R
+--R - 5x - 3
+--R (1) -------------------------------------------------
+--R 7 6 5 4 3 2
+--R 648x + 756x - 378x - 609x + 56x + 168x - 16
+--R Type: Fraction(Polynomial(Integer))
+--E 41
+
+--S 42 of 500
+r0:=22/2401/(1-2*x)^2+388/16807/(1-2*x)+1/343/(2+3*x)^3+_
+ (-87/4802)/(2+3*x)^2+(-558/16807)/(2+3*x)-2280/117649*log(1-2*x)+_
+ 2280/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (492480x + 492480x - 205200x - 264480x + 18240x + 36480)log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 492480x - 492480x + 205200x + 264480x - 18240x - 36480)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 574560x - 526680x + 218120x + 236075x + 21616
+--R /
+--R 5 4 3 2
+--R 25412184x + 25412184x - 10588410x - 13647284x + 941192x + 1882384
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (492480x + 492480x - 205200x - 264480x + 18240x + 36480)log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 492480x - 492480x + 205200x + 264480x - 18240x - 36480)log(2x - 1)
+--R +
+--R 4 3 2
+--R - 574560x - 526680x + 218120x + 236075x + 21616
+--R /
+--R 5 4 3 2
+--R 25412184x + 25412184x - 10588410x - 13647284x + 941192x + 1882384
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2280log(2x - 1) + 2280log(- 2x + 1)
+--R (4) -------------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^5)
+--R
+--R
+--R - 5x - 3
+--R (1) --------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 1944x + 3564x + 378x - 2583x - 1050x + 616x + 336x - 48x - 32
+--R Type: Fraction(Polynomial(Integer))
+--E 46
+
+--S 47 of 500
+r0:=44/16807/(1-2*x)^2+1040/117649/(1-2*x)+3/1372/(2+3*x)^4+_
+ (-29/2401)/(2+3*x)^3+(-279/16807)/(2+3*x)^2+(-2280/117649)/(2+3*x)-_
+ 7680/823543*log(1-2*x)+7680/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 9953280x + 16588800x + 2488320x - 8110080x - 3194880x + 983040x
+--R +
+--R 491520
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 9953280x - 16588800x - 2488320x + 8110080x + 3194880x
+--R +
+--R - 983040x - 491520
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 11612160x - 18385920x - 2688000x + 7710080x + 2825088x - 197925
+--R /
+--R 6 5 4 3 2
+--R 1067311728x + 1778852880x + 266827932x - 869661408x - 342593888x
+--R +
+--R 105413504x + 52706752
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 9953280x + 16588800x + 2488320x - 8110080x - 3194880x + 983040x
+--R +
+--R 491520
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 9953280x - 16588800x - 2488320x + 8110080x + 3194880x
+--R +
+--R - 983040x - 491520
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 11612160x - 18385920x - 2688000x + 7710080x + 2825088x - 197925
+--R /
+--R 6 5 4 3 2
+--R 1067311728x + 1778852880x + 266827932x - 869661408x - 342593888x
+--R +
+--R 105413504x + 52706752
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500
+m0:=a0-r0
+--R
+--R
+--R - 7680log(2x - 1) + 7680log(- 2x + 1)
+--R (4) -------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^6)
+--R
+--R
+--R (1)
+--R - 5x - 3
+--R /
+--R 9 8 7 6 5 4 3 2
+--R 5832x + 14580x + 8262x - 6993x - 8316x - 252x + 2240x + 528x
+--R +
+--R - 192x - 64
+--R Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 500
+r0:=88/117649/(1-2*x)^2+2608/823543/(1-2*x)+3/1715/(2+3*x)^5+_
+ (-87/9604)/(2+3*x)^4+(-186/16807)/(2+3*x)^3+(-1140/117649)/(2+3*x)^2+_
+ (-7680/823543)/(2+3*x)-3312/823543*log(1-2*x)+3312/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3
+--R 64385280x + 150232320x + 87635520x - 41731200x - 55641600x
+--R +
+--R 2
+--R - 7418880x + 7418880x + 2119680
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4 3
+--R - 64385280x - 150232320x - 87635520x + 41731200x + 55641600x
+--R +
+--R 2
+--R 7418880x - 7418880x - 2119680
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3 2
+--R - 75116160x - 169011360x - 96677280x + 38282580x + 51524508x
+--R +
+--R 7943257x - 2669758
+--R /
+--R 7 6 5 4
+--R 16009675920x + 37355910480x + 21790947780x - 10376641800x
+--R +
+--R 3 2
+--R - 13835522400x - 1844736320x + 1844736320x + 527067520
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R 64385280x + 150232320x + 87635520x - 41731200x - 55641600x
+--R +
+--R 2
+--R - 7418880x + 7418880x + 2119680
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4 3
+--R - 64385280x - 150232320x - 87635520x + 41731200x + 55641600x
+--R +
+--R 2
+--R 7418880x - 7418880x - 2119680
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3 2
+--R - 75116160x - 169011360x - 96677280x + 38282580x + 51524508x
+--R +
+--R 7943257x - 2669758
+--R /
+--R 7 6 5 4
+--R 16009675920x + 37355910480x + 21790947780x - 10376641800x
+--R +
+--R 3 2
+--R - 13835522400x - 1844736320x + 1844736320x + 527067520
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500
+m0:=a0-r0
+--R
+--R
+--R - 3312log(2x - 1) + 3312log(- 2x + 1)
+--R (4) -------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(2+3*x)^7*(3+5*x)^2/(1-2*x)^3
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4
+--R - 54675x - 320760x - 836163x - 1271214x - 1242108x - 808920x
+--R +
+--R 3 2
+--R - 351120x - 97952x - 15936x - 1152
+--R /
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 56
+
+--S 57 of 500
+r0:=99648703/2048/(1-2*x)^2+(-389535839/1024)/(1-2*x)-48280011/64*x-_
+ 190742391/512*x^2-25895367/128*x^3-12299769/128*x^4-2798631/80*x^5-_
+ 268515/32*x^6-54675/56*x^7-84589631/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 189480773440x + 189480773440x - 47370193360)log(- 2x + 1)
+--R +
+--R 9 8 7 6
+--R - 279936000x - 2125958400x - 7694383104x - 18122662656x
+--R +
+--R 5 4 3 2
+--R - 32961712896x - 55697987520x - 123980115840x + 189590514540x
+--R +
+--R 461405140x - 23779804125
+--R /
+--R 2
+--R 286720x - 286720x + 71680
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 9
+--R (- 189480773440x + 189480773440x - 47370193360)log(2x - 1) - 279936000x
+--R +
+--R 8 7 6 5
+--R - 2125958400x - 7694383104x - 18122662656x - 32961712896x
+--R +
+--R 4 3 2
+--R - 55697987520x - 123980115840x + 189590514540x + 461405140x
+--R +
+--R - 23779804125
+--R /
+--R 2
+--R 286720x - 286720x + 71680
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 500
+m0:=a0-r0
+--R
+--R
+--R - 84589631log(2x - 1) + 84589631log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(2+3*x)^6*(3+5*x)^2/(1-2*x)^3
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 18225x - 94770x - 215541x - 280044x - 227340x - 118080x - 38320x
+--R +
+--R - 7104x - 576
+--R /
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 61
+
+--S 62 of 500
+r0:=14235529/1024/(1-2*x)^2+(-12386759/128)/(1-2*x)-39980457/256*x-_
+ 17700255/256*x^2-1024389/32*x^3-770067/64*x^4-48843/16*x^5-_
+ 6075/16*x^6-18859855/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 8
+--R (- 603515360x + 603515360x - 150878840)log(- 2x + 1) - 1555200x
+--R +
+--R 7 6 5 4 3
+--R - 10948608x - 37169280x - 84963456x - 164403360x - 389263680x
+--R +
+--R 2
+--R 568886292x + 38266316x - 84858543
+--R /
+--R 2
+--R 4096x - 4096x + 1024
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8
+--R (- 603515360x + 603515360x - 150878840)log(2x - 1) - 1555200x
+--R +
+--R 7 6 5 4 3
+--R - 10948608x - 37169280x - 84963456x - 164403360x - 389263680x
+--R +
+--R 2
+--R 568886292x + 38266316x - 84858543
+--R /
+--R 2
+--R 4096x - 4096x + 1024
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 500
+m0:=a0-r0
+--R
+--R
+--R - 18859855log(2x - 1) + 18859855log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^3
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 6075x - 27540x - 53487x - 57690x - 37320x - 14480x - 3120x - 288
+--R ------------------------------------------------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 66
+
+--S 67 of 500
+r0:=2033647/512/(1-2*x)^2+(-6206585/256)/(1-2*x)-3907293/128*x-_
+ 747297/64*x^2-69273/16*x^3-73305/64*x^4-1215/8*x^5-8117095/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 7 6
+--R (- 64936760x + 64936760x - 16234190)log(- 2x + 1) - 311040x - 2034720x
+--R +
+--R 5 4 3 2
+--R - 6598944x - 15633000x - 40819920x + 56538312x + 9197168x - 10379523
+--R /
+--R 2
+--R 2048x - 2048x + 512
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 6
+--R (- 64936760x + 64936760x - 16234190)log(2x - 1) - 311040x - 2034720x
+--R +
+--R 5 4 3 2
+--R - 6598944x - 15633000x - 40819920x + 56538312x + 9197168x - 10379523
+--R /
+--R 2
+--R 2048x - 2048x + 512
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 500
+m0:=a0-r0
+--R
+--R
+--R - 8117095log(2x - 1) + 8117095log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R - 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144
+--R (1) ------------------------------------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 71
+
+--S 72 of 500
+r0:=290521/256/(1-2*x)^2+(-381073/64)/(1-2*x)-176055/32*x-_
+ 54783/32*x^2-7245/16*x^3-2025/32*x^4-832951/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 6 5
+--R (- 6663608x + 6663608x - 1665902)log(- 2x + 1) - 64800x - 398880x
+--R +
+--R 4 3 2
+--R - 1305576x - 3996624x + 5195496x + 1640144x - 1233771
+--R /
+--R 2
+--R 1024x - 1024x + 256
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 5
+--R (- 6663608x + 6663608x - 1665902)log(2x - 1) - 64800x - 398880x
+--R +
+--R 4 3 2
+--R - 1305576x - 3996624x + 5195496x + 1640144x - 1233771
+--R /
+--R 2
+--R 1024x - 1024x + 256
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 500
+m0:=a0-r0
+--R
+--R
+--R - 832951log(2x - 1) + 832951log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^3
+--R
+--R
+--R 5 4 3 2
+--R - 675x - 2160x - 2763x - 1766x - 564x - 72
+--R (1) ----------------------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 76
+
+--S 77 of 500
+r0:=41503/128/(1-2*x)^2+(-91091/64)/(1-2*x)-14031/16*x-6345/32*x^2-_
+ 225/8*x^3-39977/32*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 5 4
+--R (- 639632x + 639632x - 159908)log(- 2x + 1) - 14400x - 87120x
+--R +
+--R 3 2
+--R - 351072x + 423612x + 252116x - 140679
+--R /
+--R 2
+--R 512x - 512x + 128
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4 3
+--R (- 639632x + 639632x - 159908)log(2x - 1) - 14400x - 87120x - 351072x
+--R +
+--R 2
+--R 423612x + 252116x - 140679
+--R /
+--R 2
+--R 512x - 512x + 128
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 500
+m0:=a0-r0
+--R
+--R
+--R - 39977log(2x - 1) + 39977log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^3
+--R
+--R
+--R 4 3 2
+--R - 225x - 570x - 541x - 228x - 36
+--R (1) -----------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 81
+
+--S 82 of 500
+r0:=5929/64/(1-2*x)^2+(-1309/4)/(1-2*x)-1815/16*x-225/16*x^2-3467/16*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2
+--R (- 55472x + 55472x - 13868)log(- 2x + 1) - 3600x - 25440x + 28140x
+--R +
+--R 34628x - 15015
+--R /
+--R 2
+--R 256x - 256x + 64
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2
+--R (- 55472x + 55472x - 13868)log(2x - 1) - 3600x - 25440x + 28140x
+--R +
+--R 34628x - 15015
+--R /
+--R 2
+--R 256x - 256x + 64
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500
+m0:=a0-r0
+--R
+--R
+--R - 3467log(2x - 1) + 3467log(- 2x + 1)
+--R (4) -------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^3
+--R
+--R
+--R 3 2
+--R - 75x - 140x - 87x - 18
+--R (1) -------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 86
+
+--S 87 of 500
+r0:=847/32/(1-2*x)^2+(-1133/16)/(1-2*x)-75/8*x-505/16*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 3 2
+--R (- 4040x + 4040x - 1010)log(- 2x + 1) - 1200x + 1200x + 4232x - 1419
+--R -----------------------------------------------------------------------
+--R 2
+--R 128x - 128x + 32
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2
+--R (- 4040x + 4040x - 1010)log(2x - 1) - 1200x + 1200x + 4232x - 1419
+--R (3) ---------------------------------------------------------------------
+--R 2
+--R 128x - 128x + 32
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500
+m0:=a0-r0
+--R
+--R
+--R - 505log(2x - 1) + 505log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(3+5*x)^2/(1-2*x)^3
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) -------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 91
+
+--S 92 of 500
+r0:=121/16/(1-2*x)^2+(-55/4)/(1-2*x)-25/8*log(1-2*x)
+--R
+--R
+--R 2
+--R (- 200x + 200x - 50)log(- 2x + 1) + 440x - 99
+--R (2) ----------------------------------------------
+--R 2
+--R 64x - 64x + 16
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (- 200x + 200x - 50)log(2x - 1) + 440x - 99
+--R (3) --------------------------------------------
+--R 2
+--R 64x - 64x + 16
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500
+m0:=a0-r0
+--R
+--R
+--R - 25log(2x - 1) + 25log(- 2x + 1)
+--R (4) ---------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x))
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) --------------------------
+--R 4 3 2
+--R 24x - 20x - 6x + 9x - 2
+--R Type: Fraction(Polynomial(Integer))
+--E 96
+
+--S 97 of 500
+r0:=121/56/(1-2*x)^2+(-407/196)/(1-2*x)-1/343*log(1-2*x)+1/343*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (32x - 32x + 8)log(3x + 2) + (- 32x + 32x - 8)log(- 2x + 1) + 11396x + 231
+--R ----------------------------------------------------------------------------
+--R 2
+--R 10976x - 10976x + 2744
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (32x - 32x + 8)log(3x + 2) + (- 32x + 32x - 8)log(2x - 1) + 11396x + 231
+--R --------------------------------------------------------------------------
+--R 2
+--R 10976x - 10976x + 2744
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500
+m0:=a0-r0
+--R
+--R
+--R - log(2x - 1) + log(- 2x + 1)
+--R (4) -----------------------------
+--R 343
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^2)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) -----------------------------------
+--R 5 4 3 2
+--R 72x - 12x - 58x + 15x + 12x - 4
+--R Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 500
+r0:=121/196/(1-2*x)^2+(-22/343)/(1-2*x)+(-1/343)/(2+3*x)+_
+ 64/2401*log(1-2*x)-64/2401*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (- 3072x + 1024x + 1280x - 512)log(3x + 2)
+--R +
+--R 3 2 2
+--R (3072x - 1024x - 1280x + 512)log(- 2x + 1) + 3584x + 18515x + 10598
+--R /
+--R 3 2
+--R 115248x - 38416x - 48020x + 19208
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (- 3072x + 1024x + 1280x - 512)log(3x + 2)
+--R +
+--R 3 2 2
+--R (3072x - 1024x - 1280x + 512)log(2x - 1) + 3584x + 18515x + 10598
+--R /
+--R 3 2
+--R 115248x - 38416x - 48020x + 19208
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 500
+m0:=a0-r0
+--R
+--R
+--R 64log(2x - 1) - 64log(- 2x + 1)
+--R (4) -------------------------------
+--R 2401
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^3)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ---------------------------------------------
+--R 6 5 4 3 2
+--R 216x + 108x - 198x - 71x + 66x + 12x - 8
+--R Type: Fraction(Polynomial(Integer))
+--E 106
+
+--S 107 of 500
+r0:=121/686/(1-2*x)^2+319/2401/(1-2*x)+(-1/686)/(2+3*x)^2+_
+ 64/2401/(2+3*x)-829/16807*log(1-2*x)+829/16807*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (59688x + 19896x - 38134x - 6632x + 6632)log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 59688x - 19896x + 38134x + 6632x - 6632)log(- 2x + 1) - 69636x
+--R +
+--R 2
+--R - 17409x + 84728x + 43323
+--R /
+--R 4 3 2
+--R 1210104x + 403368x - 773122x - 134456x + 134456
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (59688x + 19896x - 38134x - 6632x + 6632)log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (- 59688x - 19896x + 38134x + 6632x - 6632)log(2x - 1) - 69636x
+--R +
+--R 2
+--R - 17409x + 84728x + 43323
+--R /
+--R 4 3 2
+--R 1210104x + 403368x - 773122x - 134456x + 134456
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 500
+m0:=a0-r0
+--R
+--R
+--R - 829log(2x - 1) + 829log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16807
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^4)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) -------------------------------------------------
+--R 7 6 5 4 3 2
+--R 648x + 756x - 378x - 609x + 56x + 168x - 16
+--R Type: Fraction(Polynomial(Integer))
+--E 111
+
+--S 112 of 500
+r0:=121/2401/(1-2*x)^2+1364/16807/(1-2*x)+(-1/1029)/(2+3*x)^3+_
+ 32/2401/(2+3*x)^2+(-829/16807)/(2+3*x)-5750/117649*log(1-2*x)+_
+ 5750/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (1863000x + 1863000x - 776250x - 1000500x + 69000x + 138000)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 1863000x - 1863000x + 776250x + 1000500x - 69000x - 138000)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 2173500x - 1992375x + 825125x + 1260700x + 310877
+--R /
+--R 5 4 3 2
+--R 38118276x + 38118276x - 15882615x - 20470926x + 1411788x + 2823576
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (1863000x + 1863000x - 776250x - 1000500x + 69000x + 138000)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 1863000x - 1863000x + 776250x + 1000500x - 69000x - 138000)
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 2173500x - 1992375x + 825125x + 1260700x + 310877
+--R /
+--R 5 4 3 2
+--R 38118276x + 38118276x - 15882615x - 20470926x + 1411788x + 2823576
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 500
+m0:=a0-r0
+--R
+--R
+--R - 5750log(2x - 1) + 5750log(- 2x + 1)
+--R (4) -------------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^5)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) --------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 1944x + 3564x + 378x - 2583x - 1050x + 616x + 336x - 48x - 32
+--R Type: Fraction(Polynomial(Integer))
+--E 116
+
+--S 117 of 500
+r0:=242/16807/(1-2*x)^2+4180/117649/(1-2*x)+(-1/1372)/(2+3*x)^4+_
+ 64/7203/(2+3*x)^3+(-829/33614)/(2+3*x)^2+(-5750/117649)/(2+3*x)-_
+ 24040/823543*log(1-2*x)+24040/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 93467520x + 155779200x + 23366880x - 76158720x - 30001920x
+--R +
+--R 9231360x + 4615680
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 93467520x - 155779200x - 23366880x + 76158720x + 30001920x
+--R +
+--R - 9231360x - 4615680
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 109045440x - 172655280x - 25242000x + 72402470x + 34764772x + 3224165
+--R /
+--R 6 5 4 3 2
+--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x
+--R +
+--R 316240512x + 158120256
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 93467520x + 155779200x + 23366880x - 76158720x - 30001920x
+--R +
+--R 9231360x + 4615680
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 93467520x - 155779200x - 23366880x + 76158720x + 30001920x
+--R +
+--R - 9231360x - 4615680
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 109045440x - 172655280x - 25242000x + 72402470x + 34764772x + 3224165
+--R /
+--R 6 5 4 3 2
+--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x
+--R +
+--R 316240512x + 158120256
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 500
+m0:=a0-r0
+--R
+--R
+--R - 24040log(2x - 1) + 24040log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^6)
+--R
+--R
+--R (1)
+--R 2
+--R - 25x - 30x - 9
+--R /
+--R 9 8 7 6 5 4 3 2
+--R 5832x + 14580x + 8262x - 6993x - 8316x - 252x + 2240x + 528x
+--R +
+--R - 192x - 64
+--R Type: Fraction(Polynomial(Integer))
+--E 121
+
+--S 122 of 500
+r0:=484/117649/(1-2*x)^2+11264/823543/(1-2*x)+(-1/1715)/(2+3*x)^5+_
+ 16/2401/(2+3*x)^4+(-829/50421)/(2+3*x)^3+(-2875/117649)/(2+3*x)^2+_
+ (-24040/823543)/(2+3*x)-11696/823543*log(1-2*x)+11696/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3
+--R 170527680x + 397897920x + 232107120x - 110527200x - 147369600x
+--R +
+--R 2
+--R - 19649280x + 19649280x + 5614080
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4 3
+--R - 170527680x - 397897920x - 232107120x + 110527200x + 147369600x
+--R +
+--R 2
+--R 19649280x - 19649280x - 5614080
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3 2
+--R - 198948960x - 447635160x - 256054680x + 101393355x + 136465273x
+--R +
+--R 29616692x - 1806623
+--R /
+--R 7 6 5 4
+--R 12007256940x + 28016932860x + 16343210835x - 7782481350x
+--R +
+--R 3 2
+--R - 10376641800x - 1383552240x + 1383552240x + 395300640
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R 170527680x + 397897920x + 232107120x - 110527200x - 147369600x
+--R +
+--R 2
+--R - 19649280x + 19649280x + 5614080
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4 3
+--R - 170527680x - 397897920x - 232107120x + 110527200x + 147369600x
+--R +
+--R 2
+--R 19649280x - 19649280x - 5614080
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3 2
+--R - 198948960x - 447635160x - 256054680x + 101393355x + 136465273x
+--R +
+--R 29616692x - 1806623
+--R /
+--R 7 6 5 4
+--R 12007256940x + 28016932860x + 16343210835x - 7782481350x
+--R +
+--R 3 2
+--R - 10376641800x - 1383552240x + 1383552240x + 395300640
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 500
+m0:=a0-r0
+--R
+--R
+--R - 11696log(2x - 1) + 11696log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(2+3*x)^6*(3+5*x)^3/(1-2*x)^3
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4
+--R - 91125x - 528525x - 1362015x - 2046843x - 1976832x - 1272420x
+--R +
+--R 3 2
+--R - 545840x - 150480x - 24192x - 1728
+--R /
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 126
+
+--S 127 of 500
+r0:=156590819/2048/(1-2*x)^2+(-616195041/1024)/(1-2*x)-308539921/256*x-_
+ 306103815/512*x^2-41793093/128*x^3-19986237/128*x^4-_
+ 229149/4*x^5-443475/32*x^6-91125/56*x^7-33674025/32*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 9
+--R (- 60343852800x + 60343852800x - 15085963200)log(- 2x + 1) - 93312000x
+--R +
+--R 8 7 6 5
+--R - 701395200x - 2513700864x - 5867430912x - 10590741504x
+--R +
+--R 4 3 2
+--R - 17798780160x - 39510141440x + 60542035484x - 24774428x - 7530594841
+--R /
+--R 2
+--R 57344x - 57344x + 14336
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 9
+--R (- 60343852800x + 60343852800x - 15085963200)log(2x - 1) - 93312000x
+--R +
+--R 8 7 6 5
+--R - 701395200x - 2513700864x - 5867430912x - 10590741504x
+--R +
+--R 4 3 2
+--R - 17798780160x - 39510141440x + 60542035484x - 24774428x - 7530594841
+--R /
+--R 2
+--R 57344x - 57344x + 14336
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 500
+m0:=a0-r0
+--R
+--R
+--R - 33674025log(2x - 1) + 33674025log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)^3
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3
+--R - 30375x - 155925x - 350055x - 448911x - 359670x - 184360x
+--R +
+--R 2
+--R - 59040x - 10800x - 864
+--R /
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 131
+
+--S 132 of 500
+r0:=22370117/1024/(1-2*x)^2+(-39220335/256)/(1-2*x)-64029233/256*x-_
+ 28504029/256*x^2-1661133/32*x^3-629505/32*x^4-80595/16*x^5-_
+ 10125/16*x^6-60160485/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 8
+--R (- 962567760x + 962567760x - 240641940)log(- 2x + 1) - 2592000x
+--R +
+--R 7 6 5 4 3
+--R - 18040320x - 60592320x - 137206464x - 263583600x - 621559520x
+--R +
+--R 2
+--R 910451612x + 57645748x - 134511223
+--R /
+--R 2
+--R 4096x - 4096x + 1024
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8
+--R (- 962567760x + 962567760x - 240641940)log(2x - 1) - 2592000x
+--R +
+--R 7 6 5 4 3
+--R - 18040320x - 60592320x - 137206464x - 263583600x - 621559520x
+--R +
+--R 2
+--R 910451612x + 57645748x - 134511223
+--R /
+--R 2
+--R 4096x - 4096x + 1024
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 500
+m0:=a0-r0
+--R
+--R
+--R - 60160485log(2x - 1) + 60160485log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^3
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 10125x - 45225x - 86535x - 91947x - 58592x - 22392x - 4752x - 432
+--R -------------------------------------------------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 136
+
+--S 137 of 500
+r0:=3195731/512/(1-2*x)^2+(-9836211/256)/(1-2*x)-6277415/128*x-_
+ 1208973/64*x^2-7065*x^3-120825/64*x^4-2025/8*x^5-12973191/256*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 7
+--R (- 103785528x + 103785528x - 25946382)log(- 2x + 1) - 518400x
+--R +
+--R 6 5 4 3 2
+--R - 3348000x - 10732320x - 25184616x - 65368784x + 90766856x
+--R +
+--R 14235184x - 16476691
+--R /
+--R 2
+--R 2048x - 2048x + 512
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 6
+--R (- 103785528x + 103785528x - 25946382)log(2x - 1) - 518400x - 3348000x
+--R +
+--R 5 4 3 2
+--R - 10732320x - 25184616x - 65368784x + 90766856x + 14235184x - 16476691
+--R /
+--R 2
+--R 2048x - 2048x + 512
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 500
+m0:=a0-r0
+--R
+--R
+--R - 12973191log(2x - 1) + 12973191log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^3
+--R
+--R
+--R 6 5 4 3 2
+--R - 3375x - 12825x - 20295x - 17119x - 8118x - 2052x - 216
+--R (1) -------------------------------------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 141
+
+--S 142 of 500
+r0:=456533/256/(1-2*x)^2+(-302379/32)/(1-2*x)-284071/32*x-44595/16*x^2-_
+ 11925/16*x^3-3375/32*x^4-1334949/128*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 6 5
+--R (- 10679592x + 10679592x - 2669898)log(- 2x + 1) - 108000x - 655200x
+--R +
+--R 4 3 2
+--R - 2117880x - 6426992x + 8376752x + 2565496x - 1962499
+--R /
+--R 2
+--R 1024x - 1024x + 256
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 5
+--R (- 10679592x + 10679592x - 2669898)log(2x - 1) - 108000x - 655200x
+--R +
+--R 4 3 2
+--R - 2117880x - 6426992x + 8376752x + 2565496x - 1962499
+--R /
+--R 2
+--R 1024x - 1024x + 256
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1334949log(2x - 1) + 1334949log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^3
+--R
+--R
+--R 5 4 3 2
+--R - 1125x - 3525x - 4415x - 2763x - 864x - 108
+--R (1) ------------------------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 500
+r0:=65219/128/(1-2*x)^2+(-144837/64)/(1-2*x)-5695/4*x-10425/32*x^2-_
+ 375/8*x^3-64317/32*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 5 4
+--R (- 1029072x + 1029072x - 257268)log(- 2x + 1) - 24000x - 142800x
+--R +
+--R 3 2
+--R - 568160x + 687260x + 397108x - 224455
+--R /
+--R 2
+--R 512x - 512x + 128
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 4
+--R (- 1029072x + 1029072x - 257268)log(2x - 1) - 24000x - 142800x
+--R +
+--R 3 2
+--R - 568160x + 687260x + 397108x - 224455
+--R /
+--R 2
+--R 512x - 512x + 128
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500
+m0:=a0-r0
+--R
+--R
+--R - 64317log(2x - 1) + 64317log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 32
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^3
+--R
+--R
+--R 4 3 2
+--R - 375x - 925x - 855x - 351x - 54
+--R (1) -----------------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 151
+
+--S 152 of 500
+r0:=9317/64/(1-2*x)^2+(-8349/16)/(1-2*x)-2975/16*x-375/16*x^2-2805/8*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 4 3 2
+--R (- 89760x + 89760x - 22440)log(- 2x + 1) - 6000x - 41600x + 46100x
+--R +
+--R 54892x - 24079
+--R /
+--R 2
+--R 256x - 256x + 64
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2
+--R (- 89760x + 89760x - 22440)log(2x - 1) - 6000x - 41600x + 46100x
+--R +
+--R 54892x - 24079
+--R /
+--R 2
+--R 256x - 256x + 64
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2805log(2x - 1) + 2805log(- 2x + 1)
+--R (4) -------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(3+5*x)^3/(1-2*x)^3
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------
+--R 3 2
+--R 8x - 12x + 6x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 500
+r0:=1331/32/(1-2*x)^2+(-1815/16)/(1-2*x)-125/8*x-825/16*log(1-2*x)
+--R
+--R
+--R (2)
+--R 2 3 2
+--R (- 6600x + 6600x - 1650)log(- 2x + 1) - 2000x + 2000x + 6760x - 2299
+--R -----------------------------------------------------------------------
+--R 2
+--R 128x - 128x + 32
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2
+--R (- 6600x + 6600x - 1650)log(2x - 1) - 2000x + 2000x + 6760x - 2299
+--R (3) ---------------------------------------------------------------------
+--R 2
+--R 128x - 128x + 32
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R - 825log(2x - 1) + 825log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x))
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------
+--R 4 3 2
+--R 24x - 20x - 6x + 9x - 2
+--R Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 500
+r0:=1331/112/(1-2*x)^2+(-1089/49)/(1-2*x)-14289/2744*log(1-2*x)-_
+ 1/1029*log(2+3*x)
+--R
+--R
+--R (2)
+--R 2
+--R (- 64x + 64x - 16)log(3x + 2)
+--R +
+--R 2
+--R (- 342936x + 342936x - 85734)log(- 2x + 1) + 731808x - 170247
+--R /
+--R 2
+--R 65856x - 65856x + 16464
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (- 64x + 64x - 16)log(3x + 2)
+--R +
+--R 2
+--R (- 342936x + 342936x - 85734)log(2x - 1) + 731808x - 170247
+--R /
+--R 2
+--R 65856x - 65856x + 16464
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R - 14289log(2x - 1) + 14289log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 2744
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^2)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) -----------------------------------
+--R 5 4 3 2
+--R 72x - 12x - 58x + 15x + 12x - 4
+--R Type: Fraction(Polynomial(Integer))
+--E 166
+
+--S 167 of 500
+r0:=1331/392/(1-2*x)^2+(-4719/1372)/(1-2*x)+1/1029/(2+3*x)-_
+ 33/2401*log(1-2*x)+33/2401*log(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (9504x - 3168x - 3960x + 1584)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 9504x + 3168x + 3960x - 1584)log(- 2x + 1) + 1189412x + 784945x
+--R +
+--R - 5026
+--R /
+--R 3 2
+--R 691488x - 230496x - 288120x + 115248
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (9504x - 3168x - 3960x + 1584)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 9504x + 3168x + 3960x - 1584)log(2x - 1) + 1189412x + 784945x - 5026
+--R /
+--R 3 2
+--R 691488x - 230496x - 288120x + 115248
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500
+m0:=a0-r0
+--R
+--R
+--R - 33log(2x - 1) + 33log(- 2x + 1)
+--R (4) ---------------------------------
+--R 2401
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^3)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------------------------
+--R 6 5 4 3 2
+--R 216x + 108x - 198x - 71x + 66x + 12x - 8
+--R Type: Fraction(Polynomial(Integer))
+--E 171
+
+--S 172 of 500
+r0:=1331/1372/(1-2*x)^2+(-363/2401)/(1-2*x)+1/2058/(2+3*x)^2+_
+ (-33/2401)/(2+3*x)+1023/16807*log(1-2*x)-1023/16807*log(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 441936x - 147312x + 282348x + 49104x - 49104)log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (441936x + 147312x - 282348x - 49104x + 49104)log(- 2x + 1) + 515592x
+--R +
+--R 2
+--R 2229773x + 2239384x + 655214
+--R /
+--R 4 3 2
+--R 7260624x + 2420208x - 4638732x - 806736x + 806736
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 441936x - 147312x + 282348x + 49104x - 49104)log(3x + 2)
+--R +
+--R 4 3 2 3
+--R (441936x + 147312x - 282348x - 49104x + 49104)log(2x - 1) + 515592x
+--R +
+--R 2
+--R 2229773x + 2239384x + 655214
+--R /
+--R 4 3 2
+--R 7260624x + 2420208x - 4638732x - 806736x + 806736
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500
+m0:=a0-r0
+--R
+--R
+--R 1023log(2x - 1) - 1023log(- 2x + 1)
+--R (4) -----------------------------------
+--R 16807
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^4)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) -------------------------------------------------
+--R 7 6 5 4 3 2
+--R 648x + 756x - 378x - 609x + 56x + 168x - 16
+--R Type: Fraction(Polynomial(Integer))
+--E 176
+
+--S 177 of 500
+r0:=1331/4802/(1-2*x)^2+3267/16807/(1-2*x)+1/3087/(2+3*x)^3+_
+ (-33/4802)/(2+3*x)^2+1023/16807/(2+3*x)-7755/117649*log(1-2*x)+_
+ 7755/117649*log(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (15075720x + 15075720x - 6281550x - 8096220x + 558360x + 1116720)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 15075720x - 15075720x + 6281550x + 8096220x - 558360x - 1116720)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 17588340x - 16122645x + 21383180x + 28918225x + 8476076
+--R /
+--R 5 4 3 2
+--R 228709656x + 228709656x - 95295690x - 122825556x + 8470728x + 16941456
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (15075720x + 15075720x - 6281550x - 8096220x + 558360x + 1116720)
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R (- 15075720x - 15075720x + 6281550x + 8096220x - 558360x - 1116720)
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 17588340x - 16122645x + 21383180x + 28918225x + 8476076
+--R /
+--R 5 4 3 2
+--R 228709656x + 228709656x - 95295690x - 122825556x + 8470728x + 16941456
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500
+m0:=a0-r0
+--R
+--R
+--R - 7755log(2x - 1) + 7755log(- 2x + 1)
+--R (4) -------------------------------------
+--R 117649
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^5)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) --------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 1944x + 3564x + 378x - 2583x - 1050x + 616x + 336x - 48x - 32
+--R Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 500
+r0:=1331/16807/(1-2*x)^2+14520/117649/(1-2*x)+1/4116/(2+3*x)^4+_
+ (-11/2401)/(2+3*x)^3+1023/33614/(2+3*x)^2+(-7755/117649)/(2+3*x)-_
+ 59070/823543*log(1-2*x)+59070/823543*log(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 229664160x + 382773600x + 57416040x - 187133760x - 73719360x
+--R +
+--R 22682880x + 11341440
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 229664160x - 382773600x - 57416040x + 187133760x + 73719360x
+--R +
+--R - 22682880x - 11341440
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 267941520x - 424240740x - 62023500x + 229375510x + 149599856x
+--R +
+--R 27940465
+--R /
+--R 6 5 4 3 2
+--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x
+--R +
+--R 316240512x + 158120256
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 229664160x + 382773600x + 57416040x - 187133760x - 73719360x
+--R +
+--R 22682880x + 11341440
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 229664160x - 382773600x - 57416040x + 187133760x + 73719360x
+--R +
+--R - 22682880x - 11341440
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 267941520x - 424240740x - 62023500x + 229375510x + 149599856x
+--R +
+--R 27940465
+--R /
+--R 6 5 4 3 2
+--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x
+--R +
+--R 316240512x + 158120256
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500
+m0:=a0-r0
+--R
+--R
+--R - 59070log(2x - 1) + 59070log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 823543
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(2+3*x)^8/((1-2*x)^3*(3+5*x))
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x
+--R +
+--R - 3072x - 256
+--R /
+--R 4 3 2
+--R 40x - 36x - 6x + 13x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 186
+
+--S 187 of 500
+r0:=5764801/5632/(1-2*x)^2+(-188591347/30976)/(1-2*x)-2941619571/400000*x-_
+ 110180817/40000*x^2-124416/125*x^3-408969/1600*x^4-6561/200*x^5-_
+ 2644396573/340736*log(1-2*x)+1/20796875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (2048x - 2048x + 512)log(5x + 3)
+--R +
+--R 2
+--R (- 330549571625000x + 330549571625000x - 82637392906250)log(- 2x + 1)
+--R +
+--R 7 6 5 4
+--R - 1397230560000x - 9489524220000x - 31855563036000x - 77649212460600x
+--R +
+--R 3 2
+--R - 206501370522480x + 283893518434680x + 51350638082480x - 53929198640625
+--R /
+--R 2
+--R 42592000000x - 42592000000x + 10648000000
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (2048x - 2048x + 512)log(5x + 3)
+--R +
+--R 2
+--R (- 330549571625000x + 330549571625000x - 82637392906250)log(2x - 1)
+--R +
+--R 7 6 5 4
+--R - 1397230560000x - 9489524220000x - 31855563036000x - 77649212460600x
+--R +
+--R 3 2
+--R - 206501370522480x + 283893518434680x + 51350638082480x - 53929198640625
+--R /
+--R 2
+--R 42592000000x - 42592000000x + 10648000000
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2644396573log(2x - 1) + 2644396573log(- 2x + 1)
+--R (4) -------------------------------------------------
+--R 340736
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(2+3*x)^7/((1-2*x)^3*(3+5*x))
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128
+--R -----------------------------------------------------------------------
+--R 4 3 2
+--R 40x - 36x - 6x + 13x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 500
+r0:=823543/2816/(1-2*x)^2+(-5764801/3872)/(1-2*x)-26161299/20000*x-_
+ 792423/2000*x^2-40581/400*x^3-2187/160*x^4-269063263/170368*_
+ log(1-2*x)+1/4159375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (1024x - 1024x + 256)log(5x + 3)
+--R +
+--R 2
+--R (- 6726581575000x + 6726581575000x - 1681645393750)log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R - 58217940000x - 373888548000x - 1269992017800x - 3991792836240x
+--R +
+--R 2
+--R 5149424229840x + 1777812991240x - 1273918078125
+--R /
+--R 2
+--R 4259200000x - 4259200000x + 1064800000
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (1024x - 1024x + 256)log(5x + 3)
+--R +
+--R 2
+--R (- 6726581575000x + 6726581575000x - 1681645393750)log(2x - 1)
+--R +
+--R 6 5 4 3
+--R - 58217940000x - 373888548000x - 1269992017800x - 3991792836240x
+--R +
+--R 2
+--R 5149424229840x + 1777812991240x - 1273918078125
+--R /
+--R 2
+--R 4259200000x - 4259200000x + 1064800000
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R - 269063263log(2x - 1) + 269063263log(- 2x + 1)
+--R (4) -----------------------------------------------
+--R 170368
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(2+3*x)^6/((1-2*x)^3*(3+5*x))
+--R
+--R
+--R 6 5 4 3 2
+--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64
+--R (1) -------------------------------------------------------
+--R 4 3 2
+--R 40x - 36x - 6x + 13x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 196
+
+--S 197 of 500
+r0:=117649/1408/(1-2*x)^2+(-2739541/7744)/(1-2*x)-102303/500*x-35721/800*x^2-_
+ 243/40*x^3-12761315/42592*log(1-2*x)+1/831875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (512x - 512x + 128)log(5x + 3)
+--R +
+--R 2
+--R (- 127613150000x + 127613150000x - 31903287500)log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 2587464000x - 16430396400x - 68774793120x + 82391322420x
+--R +
+--R 53550930620x - 28771483125
+--R /
+--R 2
+--R 425920000x - 425920000x + 106480000
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (512x - 512x + 128)log(5x + 3)
+--R +
+--R 2
+--R (- 127613150000x + 127613150000x - 31903287500)log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 2587464000x - 16430396400x - 68774793120x + 82391322420x
+--R +
+--R 53550930620x - 28771483125
+--R /
+--R 2
+--R 425920000x - 425920000x + 106480000
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R - 12761315log(2x - 1) + 12761315log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 42592
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(2+3*x)^5/((1-2*x)^3*(3+5*x))
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 4 3 2
+--R 40x - 36x - 6x + 13x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 201
+
+--S 202 of 500
+r0:=16807/704/(1-2*x)^2+(-156065/1936)/(1-2*x)-10287/400*x-243/80*x^2-_
+ 543655/10648*log(1-2*x)+1/166375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (256x - 256x + 64)log(5x + 3)
+--R +
+--R 2 4
+--R (- 2174620000x + 2174620000x - 543655000)log(- 2x + 1) - 129373200x
+--R +
+--R 3 2
+--R - 965986560x + 1063016460x + 1442875060x - 604151625
+--R /
+--R 2
+--R 42592000x - 42592000x + 10648000
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (256x - 256x + 64)log(5x + 3)
+--R +
+--R 2 4
+--R (- 2174620000x + 2174620000x - 543655000)log(2x - 1) - 129373200x
+--R +
+--R 3 2
+--R - 965986560x + 1063016460x + 1442875060x - 604151625
+--R /
+--R 2
+--R 42592000x - 42592000x + 10648000
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R - 543655log(2x - 1) + 543655log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 10648
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(2+3*x)^4/((1-2*x)^3*(3+5*x))
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) ---------------------------------
+--R 4 3 2
+--R 40x - 36x - 6x + 13x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 206
+
+--S 207 of 500
+r0:=2401/352/(1-2*x)^2+(-33271/1936)/(1-2*x)-81/40*x-_
+ 153811/21296*log(1-2*x)+1/33275*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (128x - 128x + 32)log(5x + 3)
+--R +
+--R 2 3 2
+--R (- 30762200x + 30762200x - 7690550)log(- 2x + 1) - 8624880x + 8624880x
+--R +
+--R 34441880x - 11036025
+--R /
+--R 2
+--R 4259200x - 4259200x + 1064800
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (128x - 128x + 32)log(5x + 3)
+--R +
+--R 2 3 2
+--R (- 30762200x + 30762200x - 7690550)log(2x - 1) - 8624880x + 8624880x
+--R +
+--R 34441880x - 11036025
+--R /
+--R 2
+--R 4259200x - 4259200x + 1064800
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R - 153811log(2x - 1) + 153811log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 21296
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(2+3*x)^3/((1-2*x)^3*(3+5*x))
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) ---------------------------
+--R 4 3 2
+--R 40x - 36x - 6x + 13x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 211
+
+--S 212 of 500
+r0:=343/176/(1-2*x)^2+(-392/121)/(1-2*x)-7189/10648*log(1-2*x)+_
+ 1/6655*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (64x - 64x + 16)log(5x + 3)
+--R +
+--R 2
+--R (- 287560x + 287560x - 71890)log(- 2x + 1) + 689920x - 137445
+--R /
+--R 2
+--R 425920x - 425920x + 106480
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (64x - 64x + 16)log(5x + 3) + (- 287560x + 287560x - 71890)log(2x - 1)
+--R +
+--R 689920x - 137445
+--R /
+--R 2
+--R 425920x - 425920x + 106480
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R - 7189log(2x - 1) + 7189log(- 2x + 1)
+--R (4) -------------------------------------
+--R 10648
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(2+3*x)^2/((1-2*x)^3*(3+5*x))
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) ---------------------------
+--R 4 3 2
+--R 40x - 36x - 6x + 13x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 216
+
+--S 217 of 500
+r0:=49/88/(1-2*x)^2+(-217/484)/(1-2*x)-1/1331*log(1-2*x)+1/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (32x - 32x + 8)log(5x + 3) + (- 32x + 32x - 8)log(- 2x + 1) + 9548x + 1155
+--R ----------------------------------------------------------------------------
+--R 2
+--R 42592x - 42592x + 10648
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (32x - 32x + 8)log(5x + 3) + (- 32x + 32x - 8)log(2x - 1) + 9548x + 1155
+--R --------------------------------------------------------------------------
+--R 2
+--R 42592x - 42592x + 10648
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R - log(2x - 1) + log(- 2x + 1)
+--R (4) -----------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(2+3*x)/((1-2*x)^3*(3+5*x))
+--R
+--R
+--R - 3x - 2
+--R (1) ---------------------------
+--R 4 3 2
+--R 40x - 36x - 6x + 13x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 221
+
+--S 222 of 500
+r0:=7/44/(1-2*x)^2+1/121/(1-2*x)-5/1331*log(1-2*x)+5/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (80x - 80x + 20)log(5x + 3) + (- 80x + 80x - 20)log(- 2x + 1) - 88x + 891
+--R ---------------------------------------------------------------------------
+--R 2
+--R 21296x - 21296x + 5324
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (80x - 80x + 20)log(5x + 3) + (- 80x + 80x - 20)log(2x - 1) - 88x + 891
+--R -------------------------------------------------------------------------
+--R 2
+--R 21296x - 21296x + 5324
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 500
+m0:=a0-r0
+--R
+--R
+--R - 5log(2x - 1) + 5log(- 2x + 1)
+--R (4) -------------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=1/((1-2*x)^3*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ---------------------------
+--R 4 3 2
+--R 40x - 36x - 6x + 13x - 3
+--R Type: Fraction(Polynomial(Integer))
+--E 226
+
+--S 227 of 500
+r0:=1/22/(1-2*x)^2+5/121/(1-2*x)-25/1331*log(1-2*x)+25/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2 2
+--R (200x - 200x + 50)log(5x + 3) + (- 200x + 200x - 50)log(- 2x + 1)
+--R +
+--R - 220x + 231
+--R /
+--R 2
+--R 10648x - 10648x + 2662
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2
+--R (200x - 200x + 50)log(5x + 3) + (- 200x + 200x - 50)log(2x - 1) - 220x
+--R +
+--R 231
+--R /
+--R 2
+--R 10648x - 10648x + 2662
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500
+m0:=a0-r0
+--R
+--R
+--R - 25log(2x - 1) + 25log(- 2x + 1)
+--R (4) ---------------------------------
+--R 1331
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=1/((1-2*x)^3*(2+3*x)*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ------------------------------------
+--R 5 4 3 2
+--R 120x - 28x - 90x + 27x + 17x - 6
+--R Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 500
+r0:=1/77/(1-2*x)^2+136/5929/(1-2*x)-6938/456533*log(1-2*x)-_
+ 27/343*log(2+3*x)+125/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (171500x - 171500x + 42875)log(5x + 3)
+--R +
+--R 2
+--R (- 143748x + 143748x - 35937)log(3x + 2)
+--R +
+--R 2
+--R (- 27752x + 27752x - 6938)log(- 2x + 1) - 20944x + 16401
+--R /
+--R 2
+--R 1826132x - 1826132x + 456533
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (171500x - 171500x + 42875)log(5x + 3)
+--R +
+--R 2
+--R (- 143748x + 143748x - 35937)log(3x + 2)
+--R +
+--R 2
+--R (- 27752x + 27752x - 6938)log(2x - 1) - 20944x + 16401
+--R /
+--R 2
+--R 1826132x - 1826132x + 456533
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500
+m0:=a0-r0
+--R
+--R
+--R - 6938log(2x - 1) + 6938log(- 2x + 1)
+--R (4) -------------------------------------
+--R 456533
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=1/((1-2*x)^3*(2+3*x)^2*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - -----------------------------------------------
+--R 6 5 4 3 2
+--R 360x + 156x - 326x - 99x + 105x + 16x - 12
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 500
+r0:=2/539/(1-2*x)^2+404/41503/(1-2*x)+27/343/(2+3*x)-_
+ 27208/3195731*log(1-2*x)-1107/2401*log(2+3*x)+625/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (18007500x - 6002500x - 7503125x + 3001250)log(5x + 3)
+--R +
+--R 3 2
+--R (- 17681004x + 5893668x + 7367085x - 2946834)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 326496x + 108832x + 136040x - 54416)log(- 2x + 1) + 819588x
+--R +
+--R - 1001770x + 337491
+--R /
+--R 3 2
+--R 38348772x - 12782924x - 15978655x + 6391462
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (18007500x - 6002500x - 7503125x + 3001250)log(5x + 3)
+--R +
+--R 3 2
+--R (- 17681004x + 5893668x + 7367085x - 2946834)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 326496x + 108832x + 136040x - 54416)log(2x - 1) + 819588x
+--R +
+--R - 1001770x + 337491
+--R /
+--R 3 2
+--R 38348772x - 12782924x - 15978655x + 6391462
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500
+m0:=a0-r0
+--R
+--R
+--R - 27208log(2x - 1) + 27208log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 3195731
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=1/((1-2*x)^3*(2+3*x)^3*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ---------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 1080x + 1188x - 666x - 949x + 117x + 258x - 4x - 24
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 500
+r0:=4/3773/(1-2*x)^2+1072/290521/(1-2*x)+27/686/(2+3*x)^2+1107/2401/(2+3*x)-_
+ 89792/22370117*log(1-2*x)-39393/16807*log(2+3*x)+3125/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (3781575000x + 1260525000x - 2416006250x - 420175000x + 420175000)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 3775109976x - 1258369992x + 2411875818x + 419456664x - 419456664)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 6465024x - 2155008x + 4130432x + 718336x - 718336)log(- 2x + 1)
+--R +
+--R 3 2
+--R 244562472x - 77517132x - 108953306x + 43866669
+--R /
+--R 4 3 2
+--R 1610648424x + 536882808x - 1029025382x - 178960936x + 178960936
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (3781575000x + 1260525000x - 2416006250x - 420175000x + 420175000)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 3775109976x - 1258369992x + 2411875818x + 419456664x - 419456664)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 6465024x - 2155008x + 4130432x + 718336x - 718336)log(2x - 1)
+--R +
+--R 3 2
+--R 244562472x - 77517132x - 108953306x + 43866669
+--R /
+--R 4 3 2
+--R 1610648424x + 536882808x - 1029025382x - 178960936x + 178960936
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500
+m0:=a0-r0
+--R
+--R
+--R - 89792log(2x - 1) + 89792log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 22370117
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=1/((1-2*x)^3*(2+3*x)^4*(3+5*x))
+--R
+--R
+--R (1)
+--R 1
+--R - ---------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 3240x + 5724x + 378x - 4179x - 1547x + 1008x + 504x - 80x - 48
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 500
+r0:=8/26411/(1-2*x)^2+2672/2033647/(1-2*x)+9/343/(2+3*x)^3+_
+ 1107/4802/(2+3*x)^2+39393/16807/(2+3*x)-267760/156590819*log(1-2*x)-_
+ 1380915/117649*log(2+3*x)+15625/1331*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 397065375000x + 397065375000x - 165443906250x - 213238812500x
+--R +
+--R 14706125000x + 29412250000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 397007538840x - 397007538840x + 165419807850x + 213207752340x
+--R +
+--R - 14703982920x - 29407965840
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 57836160x - 57836160x + 24098400x + 31060160x - 2142080x
+--R +
+--R - 4284160
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R 26403549480x + 9644189940x - 17141334210x - 3318409325x + 3092859924
+--R /
+--R 5 4 3 2
+--R 33823616904x + 33823616904x - 14093173710x - 18164535004x
+--R +
+--R 1252726552x + 2505453104
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 397065375000x + 397065375000x - 165443906250x - 213238812500x
+--R +
+--R 14706125000x + 29412250000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R - 397007538840x - 397007538840x + 165419807850x + 213207752340x
+--R +
+--R - 14703982920x - 29407965840
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 57836160x - 57836160x + 24098400x + 31060160x - 2142080x
+--R +
+--R - 4284160
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R 26403549480x + 9644189940x - 17141334210x - 3318409325x + 3092859924
+--R /
+--R 5 4 3 2
+--R 33823616904x + 33823616904x - 14093173710x - 18164535004x
+--R +
+--R 1252726552x + 2505453104
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500
+m0:=a0-r0
+--R
+--R
+--R - 267760log(2x - 1) + 267760log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 156590819
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(2+3*x)^8/((1-2*x)^3*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x
+--R +
+--R - 3072x - 256
+--R /
+--R 5 4 3 2
+--R 200x - 60x - 138x + 47x + 24x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 500
+r0:=5764801/30976/(1-2*x)^2+(-79883671/85184)/(1-2*x)-81001863/100000*x-_
+ 4863159/20000*x^2-123201/2000*x^3-6561/800*x^4+(-1/20796875)/(3+5*x)-_
+ 1845559863/1874048*log(1-2*x)+54/45753125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (1382400x - 552960x - 483840x + 207360)log(5x + 3)
+--R +
+--R 3 2
+--R - 1153474914375000x + 461389965750000x + 403716220031250x
+--R +
+--R - 173021237156250
+--R *
+--R log(- 2x + 1)
+--R +
+--R 7 6 5
+--R - 9605960100000x - 68309049600000x - 252583384185000x
+--R +
+--R 4 3 2
+--R - 811024095717000x + 468362848619160x + 838544848893576x
+--R +
+--R - 32898384865071x - 132062840768441
+--R /
+--R 3 2
+--R 1171280000000x - 468512000000x - 409948000000x + 175692000000
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (1382400x - 552960x - 483840x + 207360)log(5x + 3)
+--R +
+--R 3 2
+--R - 1153474914375000x + 461389965750000x + 403716220031250x
+--R +
+--R - 173021237156250
+--R *
+--R log(2x - 1)
+--R +
+--R 7 6 5
+--R - 9605960100000x - 68309049600000x - 252583384185000x
+--R +
+--R 4 3 2
+--R - 811024095717000x + 468362848619160x + 838544848893576x
+--R +
+--R - 32898384865071x - 132062840768441
+--R /
+--R 3 2
+--R 1171280000000x - 468512000000x - 409948000000x + 175692000000
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1845559863log(2x - 1) + 1845559863log(- 2x + 1)
+--R (4) -------------------------------------------------
+--R 1874048
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(2+3*x)^7/((1-2*x)^3*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128
+--R -----------------------------------------------------------------------
+--R 5 4 3 2
+--R 200x - 60x - 138x + 47x + 24x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 500
+r0:=823543/15488/(1-2*x)^2+(-18941489/85184)/(1-2*x)-1258983/10000*x-_
+ 108621/4000*x^2-729/200*x^3+(-1/4159375)/(3+5*x)-_
+ 87177909/468512*log(1-2*x)+237/45753125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (606720x - 242688x - 212352x + 91008)log(5x + 3)
+--R +
+--R 3 2
+--R (- 21794477250000x + 8717790900000x + 7628067037500x - 3269171587500)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R - 426931560000x - 3009867498000x - 13324533987600x + 6947670741660x
+--R +
+--R 2
+--R 17706353292408x + 647305946397x - 2972475517033
+--R /
+--R 3 2
+--R 117128000000x - 46851200000x - 40994800000x + 17569200000
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (606720x - 242688x - 212352x + 91008)log(5x + 3)
+--R +
+--R 3 2
+--R (- 21794477250000x + 8717790900000x + 7628067037500x - 3269171587500)
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3
+--R - 426931560000x - 3009867498000x - 13324533987600x + 6947670741660x
+--R +
+--R 2
+--R 17706353292408x + 647305946397x - 2972475517033
+--R /
+--R 3 2
+--R 117128000000x - 46851200000x - 40994800000x + 17569200000
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 500
+m0:=a0-r0
+--R
+--R
+--R - 87177909log(2x - 1) + 87177909log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 468512
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(2+3*x)^6/((1-2*x)^3*(3+5*x)^2)
+--R
+--R
+--R 6 5 4 3 2
+--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64
+--R (1) -------------------------------------------------------
+--R 5 4 3 2
+--R 200x - 60x - 138x + 47x + 24x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 500
+r0:=117649/7744/(1-2*x)^2+(-67228/1331)/(1-2*x)-31347/2000*x-729/400*x^2+_
+ (-1/831875)/(3+5*x)-7383075/234256*log(1-2*x)+204/9150625*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (261120x - 104448x - 91392x + 39168)log(5x + 3)
+--R +
+--R 3 2
+--R (- 369153750000x + 147661500000x + 129203812500x - 55373062500)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 21346578000x - 175041939600x + 80903530620x + 356854410264x
+--R +
+--R 46529265321x - 62049343829
+--R /
+--R 3 2
+--R 11712800000x - 4685120000x - 4099480000x + 1756920000
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (261120x - 104448x - 91392x + 39168)log(5x + 3)
+--R +
+--R 3 2
+--R (- 369153750000x + 147661500000x + 129203812500x - 55373062500)
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 21346578000x - 175041939600x + 80903530620x + 356854410264x
+--R +
+--R 46529265321x - 62049343829
+--R /
+--R 3 2
+--R 11712800000x - 4685120000x - 4099480000x + 1756920000
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500
+m0:=a0-r0
+--R
+--R
+--R - 7383075log(2x - 1) + 7383075log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 234256
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(2+3*x)^5/((1-2*x)^3*(3+5*x)^2)
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 200x - 60x - 138x + 47x + 24x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 266
+
+--S 267 of 500
+r0:=16807/3872/(1-2*x)^2+(-228095/21296)/(1-2*x)-243/200*x+_
+ (-1/166375)/(3+5*x)-1034145/234256*log(1-2*x)+171/1830125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (109440x - 43776x - 38304x + 16416)log(5x + 3)
+--R +
+--R 3 2
+--R (- 5170725000x + 2068290000x + 1809753750x - 775608750)log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 1423105200x + 569242080x + 6770697912x + 1684826253x - 1119166477
+--R /
+--R 3 2
+--R 1171280000x - 468512000x - 409948000x + 175692000
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (109440x - 43776x - 38304x + 16416)log(5x + 3)
+--R +
+--R 3 2
+--R (- 5170725000x + 2068290000x + 1809753750x - 775608750)log(2x - 1)
+--R +
+--R 4 3 2
+--R - 1423105200x + 569242080x + 6770697912x + 1684826253x - 1119166477
+--R /
+--R 3 2
+--R 1171280000x - 468512000x - 409948000x + 175692000
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1034145log(2x - 1) + 1034145log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 234256
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(2+3*x)^4/((1-2*x)^3*(3+5*x)^2)
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) -------------------------------------
+--R 5 4 3 2
+--R 200x - 60x - 138x + 47x + 24x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 271
+
+--S 272 of 500
+r0:=2401/1936/(1-2*x)^2+(-10633/5324)/(1-2*x)+(-1/33275)/(3+5*x)-_
+ 47481/117128*log(1-2*x)+138/366025*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (44160x - 17664x - 15456x + 6624)log(5x + 3)
+--R +
+--R 3 2
+--R (- 47481000x + 18992400x + 16618350x - 7122150)log(- 2x + 1)
+--R +
+--R 2
+--R 116962296x + 48012129x - 13300001
+--R /
+--R 3 2
+--R 117128000x - 46851200x - 40994800x + 17569200
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (44160x - 17664x - 15456x + 6624)log(5x + 3)
+--R +
+--R 3 2
+--R (- 47481000x + 18992400x + 16618350x - 7122150)log(2x - 1)
+--R +
+--R 2
+--R 116962296x + 48012129x - 13300001
+--R /
+--R 3 2
+--R 117128000x - 46851200x - 40994800x + 17569200
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500
+m0:=a0-r0
+--R
+--R
+--R - 47481log(2x - 1) + 47481log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 117128
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(2+3*x)^3/((1-2*x)^3*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) -------------------------------------
+--R 5 4 3 2
+--R 200x - 60x - 138x + 47x + 24x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 276
+
+--S 277 of 500
+r0:=343/968/(1-2*x)^2+(-1421/5324)/(1-2*x)+(-1/6655)/(3+5*x)-_
+ 21/14641*log(1-2*x)+21/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (16800x - 6720x - 5880x + 2520)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 16800x + 6720x + 5880x - 2520)log(- 2x + 1) + 1562748x + 1194237x
+--R +
+--R 153527
+--R /
+--R 3 2
+--R 11712800x - 4685120x - 4099480x + 1756920
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (16800x - 6720x - 5880x + 2520)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 16800x + 6720x + 5880x - 2520)log(2x - 1) + 1562748x + 1194237x
+--R +
+--R 153527
+--R /
+--R 3 2
+--R 11712800x - 4685120x - 4099480x + 1756920
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500
+m0:=a0-r0
+--R
+--R
+--R - 21log(2x - 1) + 21log(- 2x + 1)
+--R (4) ---------------------------------
+--R 14641
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(2+3*x)^2/((1-2*x)^3*(3+5*x)^2)
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) -------------------------------------
+--R 5 4 3 2
+--R 200x - 60x - 138x + 47x + 24x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 500
+r0:=49/484/(1-2*x)^2+14/1331/(1-2*x)+(-1/1331)/(3+5*x)-_
+ 72/14641*log(1-2*x)+72/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (5760x - 2304x - 2016x + 864)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 5760x + 2304x + 2016x - 864)log(- 2x + 1) - 6336x + 29205x + 19591
+--R /
+--R 3 2
+--R 1171280x - 468512x - 409948x + 175692
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (5760x - 2304x - 2016x + 864)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 5760x + 2304x + 2016x - 864)log(2x - 1) - 6336x + 29205x + 19591
+--R /
+--R 3 2
+--R 1171280x - 468512x - 409948x + 175692
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500
+m0:=a0-r0
+--R
+--R
+--R - 72log(2x - 1) + 72log(- 2x + 1)
+--R (4) ---------------------------------
+--R 14641
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(2+3*x)/((1-2*x)^3*(3+5*x)^2)
+--R
+--R
+--R - 3x - 2
+--R (1) -------------------------------------
+--R 5 4 3 2
+--R 200x - 60x - 138x + 47x + 24x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 500
+r0:=7/242/(1-2*x)^2+37/1331/(1-2*x)+(-5/1331)/(3+5*x)-_
+ 195/14641*log(1-2*x)+195/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (7800x - 3120x - 2730x + 1170)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 7800x + 3120x + 2730x - 1170)log(- 2x + 1) - 8580x + 3861x + 4873
+--R /
+--R 3 2
+--R 585640x - 234256x - 204974x + 87846
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (7800x - 3120x - 2730x + 1170)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 7800x + 3120x + 2730x - 1170)log(2x - 1) - 8580x + 3861x + 4873
+--R /
+--R 3 2
+--R 585640x - 234256x - 204974x + 87846
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500
+m0:=a0-r0
+--R
+--R
+--R - 195log(2x - 1) + 195log(- 2x + 1)
+--R (4) -----------------------------------
+--R 14641
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=1/((1-2*x)^3*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - -------------------------------------
+--R 5 4 3 2
+--R 200x - 60x - 138x + 47x + 24x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 500
+r0:=1/121/(1-2*x)^2+20/1331/(1-2*x)+(-25/1331)/(3+5*x)-_
+ 150/14641*log(1-2*x)+150/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (3000x - 1200x - 1050x + 450)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 3000x + 1200x + 1050x - 450)log(- 2x + 1) - 3300x + 1485x + 748
+--R /
+--R 3 2
+--R 292820x - 117128x - 102487x + 43923
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (3000x - 1200x - 1050x + 450)log(5x + 3)
+--R +
+--R 3 2 2
+--R (- 3000x + 1200x + 1050x - 450)log(2x - 1) - 3300x + 1485x + 748
+--R /
+--R 3 2
+--R 292820x - 117128x - 102487x + 43923
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500
+m0:=a0-r0
+--R
+--R
+--R - 150log(2x - 1) + 150log(- 2x + 1)
+--R (4) -----------------------------------
+--R 14641
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=1/((1-2*x)^3*(2+3*x)*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - ------------------------------------------------
+--R 6 5 4 3 2
+--R 600x + 220x - 534x - 135x + 166x + 21x - 18
+--R Type: Fraction(Polynomial(Integer))
+--E 296
+
+--S 297 of 500
+r0:=2/847/(1-2*x)^2+412/65219/(1-2*x)+(-125/1331)/(3+5*x)-_
+ 28296/5021863*log(1-2*x)+81/343*log(2+3*x)-3375/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (- 23152500x + 9261000x + 8103375x - 3472875)log(5x + 3)
+--R +
+--R 3 2
+--R (23718420x - 9487368x - 8301447x + 3557763)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 565920x + 226368x + 198072x - 84888)log(- 2x + 1) - 2203740x
+--R +
+--R 1914066x - 340879
+--R /
+--R 3 2
+--R 100437260x - 40174904x - 35153041x + 15065589
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (- 23152500x + 9261000x + 8103375x - 3472875)log(5x + 3)
+--R +
+--R 3 2
+--R (23718420x - 9487368x - 8301447x + 3557763)log(3x + 2)
+--R +
+--R 3 2 2
+--R (- 565920x + 226368x + 198072x - 84888)log(2x - 1) - 2203740x
+--R +
+--R 1914066x - 340879
+--R /
+--R 3 2
+--R 100437260x - 40174904x - 35153041x + 15065589
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500
+m0:=a0-r0
+--R
+--R
+--R - 28296log(2x - 1) + 28296log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 5021863
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=1/((1-2*x)^3*(2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - ------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 1800x + 1860x - 1162x - 1473x + 228x + 395x - 12x - 36
+--R Type: Fraction(Polynomial(Integer))
+--E 301
+
+--S 302 of 500
+r0:=4/5929/(1-2*x)^2+1088/456533/(1-2*x)+(-81/343)/(2+3*x)+_
+ (-625/1331)/(3+5*x)-92496/35153041*log(1-2*x)+_
+ 6156/2401*log(2+3*x)-37500/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 5402250000x - 1440600000x + 3331387500x + 450187500x - 540225000)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (5407799760x + 1442079936x - 3334809852x - 450649980x + 540779976)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 5549760x - 1479936x + 3422352x + 462480x - 554976)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 366624720x + 130867968x + 141681540x - 57273139
+--R /
+--R 4 3 2
+--R 2109182460x + 562448656x - 1300662517x - 175765205x + 210918246
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 5402250000x - 1440600000x + 3331387500x + 450187500x - 540225000)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (5407799760x + 1442079936x - 3334809852x - 450649980x + 540779976)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 5549760x - 1479936x + 3422352x + 462480x - 554976)log(2x - 1)
+--R +
+--R 3 2
+--R - 366624720x + 130867968x + 141681540x - 57273139
+--R /
+--R 4 3 2
+--R 2109182460x + 562448656x - 1300662517x - 175765205x + 210918246
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500
+m0:=a0-r0
+--R
+--R
+--R - 92496log(2x - 1) + 92496log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 35153041
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=1/((1-2*x)^3*(2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 1
+--R - ----------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 5400x + 9180x + 234x - 6743x - 2262x + 1641x + 754x - 132x - 72
+--R Type: Fraction(Polynomial(Integer))
+--E 306
+
+--S 307 of 500
+r0:=8/41503/(1-2*x)^2+2704/3195731/(1-2*x)+(-81/686)/(2+3*x)^2+_
+ (-6156/2401)/(2+3*x)+(-3125/1331)/(3+5*x)-_
+ 274224/246071287*log(1-2*x)+333639/16807*log(2+3*x)-_
+ 290625/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 1758432375000x - 1641203550000x + 771756431250x + 869447118750x
+--R +
+--R - 78152550000x - 117228825000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 1758531095640x + 1641295689264x - 771799758642x - 869495930622x
+--R +
+--R 78156937584x + 117235406376
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 98720640x - 92139264x + 43327392x + 48811872x - 4387584x
+--R +
+--R - 6581376
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R - 117343999080x - 35266545468x + 73726130478x + 11356433319x
+--R +
+--R - 12361039691
+--R /
+--R 5 4 3 2
+--R 88585663320x + 82679952432x - 38879263346x - 43800689086x
+--R +
+--R 3937140592x + 5905710888
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 1758432375000x - 1641203550000x + 771756431250x + 869447118750x
+--R +
+--R - 78152550000x - 117228825000
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3 2
+--R 1758531095640x + 1641295689264x - 771799758642x - 869495930622x
+--R +
+--R 78156937584x + 117235406376
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 98720640x - 92139264x + 43327392x + 48811872x - 4387584x
+--R +
+--R - 6581376
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R - 117343999080x - 35266545468x + 73726130478x + 11356433319x
+--R +
+--R - 12361039691
+--R /
+--R 5 4 3 2
+--R 88585663320x + 82679952432x - 38879263346x - 43800689086x
+--R +
+--R 3937140592x + 5905710888
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500
+m0:=a0-r0
+--R
+--R
+--R - 274224log(2x - 1) + 274224log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 246071287
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=1/((1-2*x)^3*(2+3*x)^4*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 16200x + 38340x + 19062x - 19761x - 20272x + 399x + 5544x
+--R +
+--R 2
+--R 1112x - 480x - 144
+--R Type: Fraction(Polynomial(Integer))
+--E 311
+
+--S 312 of 500
+r0:=16/290521/(1-2*x)^2+6464/22370117/(1-2*x)+(-27/343)/(2+3*x)^3+_
+ (-3078/2401)/(2+3*x)^2+(-333639/16807)/(2+3*x)+_
+ (-15625/1331)/(3+5*x)-761760/1722499009*log(1-2*x)+_
+ 15820110/117649*log(2+3*x)-1968750/14641*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R - 125075593125000x - 200120949000000x - 22930525406250x
+--R +
+--R 3 2
+--R 98439124218750x + 35669706187500x - 12044316375000x - 5558915250000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R 125076004475400x + 200121607160640x + 22930600820490x
+--R +
+--R 3 2
+--R - 98439447966750x - 35669823498540x + 12044355986520x + 5558933532240
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 411350400x - 658160640x - 75414240x + 323748000x + 117311040x
+--R +
+--R - 39611520x - 18282240
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 8338852783800x - 8061154974180x + 3573065429010x + 4298892128685x
+--R +
+--R - 342379099755x - 585732955423
+--R /
+--R 6 5 4 3
+--R 930149464860x + 1488239143776x + 170527401891x - 732062078825x
+--R +
+--R 2
+--R - 265264847386x + 89569948468x + 41339976216
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R - 125075593125000x - 200120949000000x - 22930525406250x
+--R +
+--R 3 2
+--R 98439124218750x + 35669706187500x - 12044316375000x - 5558915250000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R 125076004475400x + 200121607160640x + 22930600820490x
+--R +
+--R 3 2
+--R - 98439447966750x - 35669823498540x + 12044355986520x + 5558933532240
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3 2
+--R - 411350400x - 658160640x - 75414240x + 323748000x + 117311040x
+--R +
+--R - 39611520x - 18282240
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 8338852783800x - 8061154974180x + 3573065429010x + 4298892128685x
+--R +
+--R - 342379099755x - 585732955423
+--R /
+--R 6 5 4 3
+--R 930149464860x + 1488239143776x + 170527401891x - 732062078825x
+--R +
+--R 2
+--R - 265264847386x + 89569948468x + 41339976216
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500
+m0:=a0-r0
+--R
+--R
+--R - 761760log(2x - 1) + 761760log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 1722499009
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(2+3*x)^9/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4
+--R - 19683x - 118098x - 314928x - 489888x - 489888x - 326592x
+--R +
+--R 3 2
+--R - 145152x - 41472x - 6912x - 512
+--R /
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 500
+r0:=40353607/340736/(1-2*x)^2+(-17294403/29282)/(1-2*x)-_
+ 50150097/100000*x-7459857/50000*x^2-373977/10000*x^3-_
+ 19683/4000*x^4+(-1/207968750)/(3+5*x)^2+(-303/1143828125)/(3+5*x)-_
+ 12657032367/20614528*log(1-2*x)+8202/2516421875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (1049856000x + 209971200x - 619415040x - 62991360x + 94487040)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 197766130734375000x - 39553226146875000x + 116682017133281250x
+--R +
+--R 11865967844062500x - 17798951766093750
+--R *
+--R log(- 2x + 1)
+--R +
+--R 8 7 6
+--R - 1584983416500000x - 12362870648700000x - 49530731765625000x
+--R +
+--R 5 4 3
+--R - 163943640232020000x - 3373337816263800x + 192223824266320440x
+--R +
+--R 2
+--R 81487109015452107x - 25922683108313662x - 13688249752028357
+--R /
+--R 4 3 2
+--R 322102000000000x + 64420400000000x - 190040180000000x
+--R +
+--R - 19326120000000x + 28989180000000
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (1049856000x + 209971200x - 619415040x - 62991360x + 94487040)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 197766130734375000x - 39553226146875000x + 116682017133281250x
+--R +
+--R 11865967844062500x - 17798951766093750
+--R *
+--R log(2x - 1)
+--R +
+--R 8 7 6
+--R - 1584983416500000x - 12362870648700000x - 49530731765625000x
+--R +
+--R 5 4 3
+--R - 163943640232020000x - 3373337816263800x + 192223824266320440x
+--R +
+--R 2
+--R 81487109015452107x - 25922683108313662x - 13688249752028357
+--R /
+--R 4 3 2
+--R 322102000000000x + 64420400000000x - 190040180000000x
+--R +
+--R - 19326120000000x + 28989180000000
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500
+m0:=a0-r0
+--R
+--R
+--R - 12657032367log(2x - 1) + 12657032367log(- 2x + 1)
+--R (4) ---------------------------------------------------
+--R 20614528
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(2+3*x)^8/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x
+--R +
+--R - 3072x - 256
+--R /
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 321
+
+--S 322 of 500
+r0:=5764801/170368/(1-2*x)^2+(-130943337/937024)/(1-2*x)-242028/3125*x-_
+ 330237/20000*x^2-2187/1000*x^3+(-1/41593750)/(3+5*x)^2+_
+ (-54/45753125)/(3+5*x)-595421589/5153632*log(1-2*x)+_
+ 1284/100656875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (410880000x + 82176000x - 242419200x - 24652800x + 36979200)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 3721384931250000x - 744276986250000x + 2195617109437500x
+--R +
+--R 223283095875000x - 334924643812500
+--R *
+--R log(- 2x + 1)
+--R +
+--R 7 6 5
+--R - 70443707400000x - 545938732350000x - 2559454702200000x
+--R +
+--R 4 3 2
+--R - 180911181221100x + 3748001092791780x + 1949701238862399x
+--R +
+--R - 437687139939434x - 307014257976349
+--R /
+--R 4 3 2
+--R 32210200000000x + 6442040000000x - 19004018000000x - 1932612000000x
+--R +
+--R 2898918000000
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (410880000x + 82176000x - 242419200x - 24652800x + 36979200)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R - 3721384931250000x - 744276986250000x + 2195617109437500x
+--R +
+--R 223283095875000x - 334924643812500
+--R *
+--R log(2x - 1)
+--R +
+--R 7 6 5
+--R - 70443707400000x - 545938732350000x - 2559454702200000x
+--R +
+--R 4 3 2
+--R - 180911181221100x + 3748001092791780x + 1949701238862399x
+--R +
+--R - 437687139939434x - 307014257976349
+--R /
+--R 4 3 2
+--R 32210200000000x + 6442040000000x - 19004018000000x - 1932612000000x
+--R +
+--R 2898918000000
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500
+m0:=a0-r0
+--R
+--R
+--R - 595421589log(2x - 1) + 595421589log(- 2x + 1)
+--R (4) -----------------------------------------------
+--R 5153632
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(2+3*x)^7/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128
+--R -----------------------------------------------------------------------
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 326
+
+--S 327 of 500
+r0:=823543/85184/(1-2*x)^2+(-7411887/234256)/(1-2*x)-95499/10000*x-_
+ 2187/2000*x^2+(-1/8318750)/(3+5*x)^2+(-237/45753125)/(3+5*x)-_
+ 25059237/1288408*log(1-2*x)+24279/503284375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (155385600x + 31077120x - 91677504x - 9323136x + 13984704)log(5x + 3)
+--R +
+--R 4 3 2
+--R - 62648092500000x - 12529618500000x + 36962374575000x
+--R +
+--R 3758885550000x - 5638328325000
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4 3
+--R - 3522185370000x - 31464855972000x - 4073994411300x + 69316698060060x
+--R +
+--R 2
+--R 44983390879251x - 5655984161146x - 6369590895041
+--R /
+--R 4 3 2
+--R 3221020000000x + 644204000000x - 1900401800000x - 193261200000x
+--R +
+--R 289891800000
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (155385600x + 31077120x - 91677504x - 9323136x + 13984704)log(5x + 3)
+--R +
+--R 4 3 2
+--R - 62648092500000x - 12529618500000x + 36962374575000x
+--R +
+--R 3758885550000x - 5638328325000
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4 3
+--R - 3522185370000x - 31464855972000x - 4073994411300x + 69316698060060x
+--R +
+--R 2
+--R 44983390879251x - 5655984161146x - 6369590895041
+--R /
+--R 4 3 2
+--R 3221020000000x + 644204000000x - 1900401800000x - 193261200000x
+--R +
+--R 289891800000
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R - 25059237log(2x - 1) + 25059237log(- 2x + 1)
+--R (4) ---------------------------------------------
+--R 1288408
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(2+3*x)^6/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R 6 5 4 3 2
+--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64
+--R (1) -------------------------------------------------------
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 331
+
+--S 332 of 500
+r0:=117649/42592/(1-2*x)^2+(-1563051/234256)/(1-2*x)-729/1000*x+_
+ (-1/1663750)/(3+5*x)^2+(-204/9150625)/(3+5*x)-_
+ 6950895/2576816*log(1-2*x)+17547/100656875*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (56150400x + 11230080x - 33128736x - 3369024x + 5053536)log(5x + 3)
+--R +
+--R 4 3 2
+--R - 868861875000x - 173772375000x + 512628506250x + 52131712500x
+--R +
+--R - 78197568750
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R - 234812358000x - 46962471600x + 1213135417560x + 988737742575x
+--R +
+--R - 12119848070x - 113352927985
+--R /
+--R 4 3 2
+--R 322102000000x + 64420400000x - 190040180000x - 19326120000x
+--R +
+--R 28989180000
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (56150400x + 11230080x - 33128736x - 3369024x + 5053536)log(5x + 3)
+--R +
+--R 4 3 2
+--R - 868861875000x - 173772375000x + 512628506250x + 52131712500x
+--R +
+--R - 78197568750
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R - 234812358000x - 46962471600x + 1213135417560x + 988737742575x
+--R +
+--R - 12119848070x - 113352927985
+--R /
+--R 4 3 2
+--R 322102000000x + 64420400000x - 190040180000x - 19326120000x
+--R +
+--R 28989180000
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500
+m0:=a0-r0
+--R
+--R
+--R - 6950895log(2x - 1) + 6950895log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 2576816
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(2+3*x)^5/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) -------------------------------------------------
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 336
+
+--S 337 of 500
+r0:=16807/21296/(1-2*x)^2+(-36015/29282)/(1-2*x)+(-1/332750)/(3+5*x)^2+_
+ (-171/1830125)/(3+5*x)-313845/1288408*log(1-2*x)+11904/20131375*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (19046400x + 3809280x - 11237376x - 1142784x + 1714176)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 7846125000x - 1569225000x + 4629213750x + 470767500x - 706151250)
+--R *
+--R log(- 2x + 1)
+--R +
+--R 3 2
+--R 19807648080x + 20221158771x + 2872410794x - 1277723381
+--R /
+--R 4 3 2
+--R 32210200000x + 6442040000x - 19004018000x - 1932612000x + 2898918000
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (19046400x + 3809280x - 11237376x - 1142784x + 1714176)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 7846125000x - 1569225000x + 4629213750x + 470767500x - 706151250)
+--R *
+--R log(2x - 1)
+--R +
+--R 3 2
+--R 19807648080x + 20221158771x + 2872410794x - 1277723381
+--R /
+--R 4 3 2
+--R 32210200000x + 6442040000x - 19004018000x - 1932612000x + 2898918000
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500
+m0:=a0-r0
+--R
+--R
+--R - 313845log(2x - 1) + 313845log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 1288408
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(2+3*x)^4/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) -------------------------------------------------
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 500
+r0:=2401/10648/(1-2*x)^2+(-9261/58564)/(1-2*x)+(-1/66550)/(3+5*x)^2+_
+ (-138/366025)/(3+5*x)-294/161051*log(1-2*x)+294/161051*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (5880000x + 1176000x - 3469200x - 352800x + 529200)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 5880000x - 1176000x + 3469200x + 352800x - 529200)log(- 2x + 1)
+--R +
+--R 3 2
+--R 254434620x + 359945091x + 156855094x + 19488359
+--R /
+--R 4 3 2
+--R 3221020000x + 644204000x - 1900401800x - 193261200x + 289891800
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (5880000x + 1176000x - 3469200x - 352800x + 529200)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 5880000x - 1176000x + 3469200x + 352800x - 529200)log(2x - 1)
+--R +
+--R 3 2
+--R 254434620x + 359945091x + 156855094x + 19488359
+--R /
+--R 4 3 2
+--R 3221020000x + 644204000x - 1900401800x - 193261200x + 289891800
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500
+m0:=a0-r0
+--R
+--R
+--R - 294log(2x - 1) + 294log(- 2x + 1)
+--R (4) -----------------------------------
+--R 161051
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(2+3*x)^3/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) -------------------------------------------------
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 500
+r0:=343/5324/(1-2*x)^2+147/14641/(1-2*x)+(-1/13310)/(3+5*x)^2+_
+ (-21/14641)/(3+5*x)-777/161051*log(1-2*x)+777/161051*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (1554000x + 310800x - 916860x - 93240x + 139860)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 1554000x - 310800x + 916860x + 93240x - 139860)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 1709400x + 4091967x + 6646838x + 2144593
+--R /
+--R 4 3 2
+--R 322102000x + 64420400x - 190040180x - 19326120x + 28989180
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (1554000x + 310800x - 916860x - 93240x + 139860)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 1554000x - 310800x + 916860x + 93240x - 139860)log(2x - 1)
+--R +
+--R 3 2
+--R - 1709400x + 4091967x + 6646838x + 2144593
+--R /
+--R 4 3 2
+--R 322102000x + 64420400x - 190040180x - 19326120x + 28989180
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500
+m0:=a0-r0
+--R
+--R
+--R - 777log(2x - 1) + 777log(- 2x + 1)
+--R (4) -----------------------------------
+--R 161051
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(2+3*x)^2/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) -------------------------------------------------
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 351
+
+--S 352 of 500
+r0:=49/2662/(1-2*x)^2+273/14641/(1-2*x)+(-1/2662)/(3+5*x)^2+_
+ (-72/14641)/(3+5*x)-1509/161051*log(1-2*x)+1509/161051*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (301800x + 60360x - 178062x - 18108x + 27162)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 301800x - 60360x + 178062x + 18108x - 27162)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 331980x - 49797x + 261514x + 102542
+--R /
+--R 4 3 2
+--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (301800x + 60360x - 178062x - 18108x + 27162)log(5x + 3)
+--R +
+--R 4 3 2 3
+--R (- 301800x - 60360x + 178062x + 18108x - 27162)log(2x - 1) - 331980x
+--R +
+--R 2
+--R - 49797x + 261514x + 102542
+--R /
+--R 4 3 2
+--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1509log(2x - 1) + 1509log(- 2x + 1)
+--R (4) -------------------------------------
+--R 161051
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(2+3*x)/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R - 3x - 2
+--R (1) -------------------------------------------------
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 356
+
+--S 357 of 500
+r0:=7/1331/(1-2*x)^2+144/14641/(1-2*x)+(-5/2662)/(3+5*x)^2+_
+ (-195/14641)/(3+5*x)-1110/161051*log(1-2*x)+1110/161051*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (222000x + 44400x - 130980x - 13320x + 19980)log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 222000x - 44400x + 130980x + 13320x - 19980)log(- 2x + 1)
+--R +
+--R 3 2
+--R - 244200x - 36630x + 121286x + 30283
+--R /
+--R 4 3 2
+--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (222000x + 44400x - 130980x - 13320x + 19980)log(5x + 3)
+--R +
+--R 4 3 2 3
+--R (- 222000x - 44400x + 130980x + 13320x - 19980)log(2x - 1) - 244200x
+--R +
+--R 2
+--R - 36630x + 121286x + 30283
+--R /
+--R 4 3 2
+--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500
+m0:=a0-r0
+--R
+--R
+--R - 1110log(2x - 1) + 1110log(- 2x + 1)
+--R (4) -------------------------------------
+--R 161051
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=1/((1-2*x)^3*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------------
+--R 6 5 4 3 2
+--R 1000x + 300x - 870x - 179x + 261x + 27x - 27
+--R Type: Fraction(Polynomial(Integer))
+--E 361
+
+--S 362 of 500
+r0:=2/1331/(1-2*x)^2+60/14641/(1-2*x)+(-25/2662)/(3+5*x)^2+_
+ (-150/14641)/(3+5*x)-600/161051*log(1-2*x)+600/161051*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (120000x + 24000x - 70800x - 7200x + 10800)log(5x + 3)
+--R +
+--R 4 3 2 3
+--R (- 120000x - 24000x + 70800x + 7200x - 10800)log(- 2x + 1) - 132000x
+--R +
+--R 2
+--R - 19800x + 65560x + 3311
+--R /
+--R 4 3 2
+--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (120000x + 24000x - 70800x - 7200x + 10800)log(5x + 3)
+--R +
+--R 4 3 2 3
+--R (- 120000x - 24000x + 70800x + 7200x - 10800)log(2x - 1) - 132000x
+--R +
+--R 2
+--R - 19800x + 65560x + 3311
+--R /
+--R 4 3 2
+--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918
+--R Type: Union(Expression(Integer),...)
+--E 363
+
+--S 364 of 500
+m0:=a0-r0
+--R
+--R
+--R - 600log(2x - 1) + 600log(- 2x + 1)
+--R (4) -----------------------------------
+--R 161051
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=1/((1-2*x)^3*(2+3*x)*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) - ------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 3000x + 2900x - 2010x - 2277x + 425x + 603x - 27x - 54
+--R Type: Fraction(Polynomial(Integer))
+--E 366
+
+--S 367 of 500
+r0:=4/9317/(1-2*x)^2+1104/717409/(1-2*x)+(-125/2662)/(3+5*x)^2+_
+ 3375/14641/(3+5*x)-95232/55240493*log(1-2*x)-243/343*log(2+3*x)+_
+ 114375/161051*log(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (7846125000x + 1569225000x - 4629213750x - 470767500x + 706151250)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 7827078600x - 1565415720x + 4617976374x + 469624716x - 704437074)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 19046400x - 3809280x + 11237376x + 1142784x - 1714176)log(- 2x + 1)
+--R +
+--R 3 2
+--R 500854200x - 229258260x - 154059598x + 73172407
+--R /
+--R 4 3 2
+--R 11048098600x + 2209619720x - 6518378174x - 662885916x + 994328874
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (7846125000x + 1569225000x - 4629213750x - 470767500x + 706151250)
+--R *
+--R log(5x + 3)
+--R +
+--R 4 3 2
+--R (- 7827078600x - 1565415720x + 4617976374x + 469624716x - 704437074)
+--R *
+--R log(3x + 2)
+--R +
+--R 4 3 2
+--R (- 19046400x - 3809280x + 11237376x + 1142784x - 1714176)log(2x - 1)
+--R +
+--R 3 2
+--R 500854200x - 229258260x - 154059598x + 73172407
+--R /
+--R 4 3 2
+--R 11048098600x + 2209619720x - 6518378174x - 662885916x + 994328874
+--R Type: Union(Expression(Integer),...)
+--E 368
+
+--S 369 of 500
+m0:=a0-r0
+--R
+--R
+--R - 95232log(2x - 1) + 95232log(- 2x + 1)
+--R (4) ---------------------------------------
+--R 55240493
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=1/((1-2*x)^3*(2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 1
+--R - --------------------------------------------------------------------------
+--R 8 7 6 5 4 3 2
+--R 9000x + 14700x - 230x - 10851x - 3279x + 2659x + 1125x - 216x - 108
+--R Type: Fraction(Polynomial(Integer))
+--E 371
+
+--S 372 of 500
+r0:=8/65219/(1-2*x)^2+2736/5021863/(1-2*x)+243/343/(2+3*x)+_
+ (-625/2662)/(3+5*x)^2+37500/14641/(3+5*x)-280752/386683451*log(1-2*x)-_
+ 26973/2401*log(2+3*x)+1809375/161051*log(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 2606585625000x + 2259040875000x - 1190340768750x - 1181652150000x
+--R +
+--R 130329281250x + 156395137500
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 2606417173800x - 2258894883960x + 1190263842702x
+--R +
+--R 2
+--R 1181575785456x - 130320858690x - 156385030428
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 168451200x - 145991040x + 76926048x + 76364544x - 8422560x
+--R +
+--R - 10107072
+--R *
+--R log(- 2x + 1)
+--R +
+--R 4 3 2
+--R 173575848600x + 40392941820x - 104891101854x - 12253878175x
+--R +
+--R 16462150012
+--R /
+--R 5 4 3 2
+--R 232010070600x + 201075394520x - 105951265574x - 105177898672x
+--R +
+--R 11600503530x + 13920604236
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 2606585625000x + 2259040875000x - 1190340768750x - 1181652150000x
+--R +
+--R 130329281250x + 156395137500
+--R *
+--R log(5x + 3)
+--R +
+--R 5 4 3
+--R - 2606417173800x - 2258894883960x + 1190263842702x
+--R +
+--R 2
+--R 1181575785456x - 130320858690x - 156385030428
+--R *
+--R log(3x + 2)
+--R +
+--R 5 4 3 2
+--R - 168451200x - 145991040x + 76926048x + 76364544x - 8422560x
+--R +
+--R - 10107072
+--R *
+--R log(2x - 1)
+--R +
+--R 4 3 2
+--R 173575848600x + 40392941820x - 104891101854x - 12253878175x
+--R +
+--R 16462150012
+--R /
+--R 5 4 3 2
+--R 232010070600x + 201075394520x - 105951265574x - 105177898672x
+--R +
+--R 11600503530x + 13920604236
+--R Type: Union(Expression(Integer),...)
+--E 373
+
+--S 374 of 500
+m0:=a0-r0
+--R
+--R
+--R - 280752log(2x - 1) + 280752log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 386683451
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=1/((1-2*x)^3*(2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 9 8 7 6 5 4 3
+--R 27000x + 62100x + 28710x - 33013x - 31539x + 1419x + 8693x
+--R +
+--R 2
+--R 1602x - 756x - 216
+--R Type: Fraction(Polynomial(Integer))
+--E 376
+
+--S 377 of 500
+r0:=16/456533/(1-2*x)^2+6528/35153041/(1-2*x)+243/686/(2+3*x)^2+_
+ 26973/2401/(2+3*x)+(-3125/2662)/(3+5*x)^2+290625/14641/(3+5*x)-_
+ 776928/2706784157*log(1-2*x)-1944972/16807*log(2+3*x)+_
+ 18637500/161051*log(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R 563832832500000x + 864543676500000x + 68286420825000x
+--R +
+--R 3 2
+--R - 427259990850000x - 142211169975000x + 52624397700000x
+--R +
+--R 22553313300000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 563831434029600x - 864541532178720x - 68286251454696x
+--R +
+--R 3 2
+--R 427258931120208x + 142210817249688x - 52624267176096x
+--R +
+--R - 22553257361184
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 1398470400x - 2144321280x - 169370304x + 1059729792x
+--R +
+--R 2
+--R 352725312x - 130523904x - 55938816
+--R *
+--R log(- 2x + 1)
+--R +
+--R 5 4 3 2
+--R 37587223951200x + 33827604204240x - 16859483294808x - 17801732753112x
+--R +
+--R 1786038929444x + 2376093430249
+--R /
+--R 6 5 4 3
+--R 4872211482600x + 7470724273320x + 590078946226x - 3692053590148x
+--R +
+--R 2
+--R - 1228880007278x + 454739738376x + 194888459304
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R 563832832500000x + 864543676500000x + 68286420825000x
+--R +
+--R 3 2
+--R - 427259990850000x - 142211169975000x + 52624397700000x
+--R +
+--R 22553313300000
+--R *
+--R log(5x + 3)
+--R +
+--R 6 5 4
+--R - 563831434029600x - 864541532178720x - 68286251454696x
+--R +
+--R 3 2
+--R 427258931120208x + 142210817249688x - 52624267176096x
+--R +
+--R - 22553257361184
+--R *
+--R log(3x + 2)
+--R +
+--R 6 5 4 3
+--R - 1398470400x - 2144321280x - 169370304x + 1059729792x
+--R +
+--R 2
+--R 352725312x - 130523904x - 55938816
+--R *
+--R log(2x - 1)
+--R +
+--R 5 4 3 2
+--R 37587223951200x + 33827604204240x - 16859483294808x - 17801732753112x
+--R +
+--R 1786038929444x + 2376093430249
+--R /
+--R 6 5 4 3
+--R 4872211482600x + 7470724273320x + 590078946226x - 3692053590148x
+--R +
+--R 2
+--R - 1228880007278x + 454739738376x + 194888459304
+--R Type: Union(Expression(Integer),...)
+--E 378
+
+--S 379 of 500
+m0:=a0-r0
+--R
+--R
+--R - 776928log(2x - 1) + 776928log(- 2x + 1)
+--R (4) -----------------------------------------
+--R 2706784157
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=1/((1-2*x)^3*(2+3*x)^4*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 10 9 8 7 6 5
+--R 81000x + 240300x + 210330x - 41619x - 160643x - 58821x
+--R +
+--R 4 3 2
+--R 28917x + 22192x + 936x - 2160x - 432
+--R Type: Fraction(Polynomial(Integer))
+--E 381
+
+--S 382 of 500
+r0:=32/3195731/(1-2*x)^2+15168/246071287/(1-2*x)+81/343/(2+3*x)^3+_
+ 26973/4802/(2+3*x)^2+1944972/16807/(2+3*x)+(-15625/2662)/(3+5*x)^2+_
+ 1968750/14641/(3+5*x)-2054400/18947489099*log(1-2*x)-_
+ 115534350/117649*log(2+3*x)+158156250/161051*log(3+5*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R 100477393143750000x + 221050264916250000x + 114879152827687500x
+--R +
+--R 4 3 2
+--R - 68026916543250000x - 76102321844062500x - 7517197561125000x
+--R +
+--R 10271022410250000x + 2679397150500000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 100477382049990000x - 221050240509978000x - 114879140143821900x
+--R +
+--R 4 3 2
+--R 68026909032363600x + 76102313441566500x + 7517196731147400x
+--R +
+--R - 10271021276221200x - 2679396854666400
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 11093760000x - 24406272000x - 12683865600x + 7510886400x
+--R +
+--R 3 2
+--R 8402496000x + 829977600x - 1134028800x - 295833600
+--R *
+--R log(- 2x + 1)
+--R +
+--R 6 5 4
+--R 6698479933530000x + 10494278110701000x + 1014683641656300x
+--R +
+--R 3 2
+--R - 5175447127123350x - 1796782743686700x + 635595472278305x
+--R +
+--R 282301665291184
+--R /
+--R 7 6 5
+--R 102316441134600x + 225096170496120x + 116981797697226x
+--R +
+--R 4 3 2
+--R - 69272020145944x - 77495230414910x - 7654785595996x + 10459013982648x
+--R +
+--R 2728438430256
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R 100477393143750000x + 221050264916250000x + 114879152827687500x
+--R +
+--R 4 3 2
+--R - 68026916543250000x - 76102321844062500x - 7517197561125000x
+--R +
+--R 10271022410250000x + 2679397150500000
+--R *
+--R log(5x + 3)
+--R +
+--R 7 6 5
+--R - 100477382049990000x - 221050240509978000x - 114879140143821900x
+--R +
+--R 4 3 2
+--R 68026909032363600x + 76102313441566500x + 7517196731147400x
+--R +
+--R - 10271021276221200x - 2679396854666400
+--R *
+--R log(3x + 2)
+--R +
+--R 7 6 5 4
+--R - 11093760000x - 24406272000x - 12683865600x + 7510886400x
+--R +
+--R 3 2
+--R 8402496000x + 829977600x - 1134028800x - 295833600
+--R *
+--R log(2x - 1)
+--R +
+--R 6 5 4
+--R 6698479933530000x + 10494278110701000x + 1014683641656300x
+--R +
+--R 3 2
+--R - 5175447127123350x - 1796782743686700x + 635595472278305x
+--R +
+--R 282301665291184
+--R /
+--R 7 6 5
+--R 102316441134600x + 225096170496120x + 116981797697226x
+--R +
+--R 4 3 2
+--R - 69272020145944x - 77495230414910x - 7654785595996x + 10459013982648x
+--R +
+--R 2728438430256
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500
+m0:=a0-r0
+--R
+--R
+--R - 2054400log(2x - 1) + 2054400log(- 2x + 1)
+--R (4) -------------------------------------------
+--R 18947489099
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(2+3*x)^6*(3+5*x)*sqrt(1-2*x)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R (3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+r0:=-1294139/384*(1-2*x)^(3/2)+3916031/640*(1-2*x)^(5/2)-_
+ 725445/128*(1-2*x)^(7/2)+406455/128*(1-2*x)^(9/2)-_
+ 1580985/1408*(1-2*x)^(11/2)+409941/1664*(1-2*x)^(13/2)-_
+ 19683/640*(1-2*x)^(15/2)+3645/2176*(1-2*x)^(17/2)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4
+--R 15637050x + 80999919x + 181983186x + 229582836x + 173491920x
+--R +
+--R 3 2
+--R 72883440x + 5339712x - 16666112x - 23667392
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 36465
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4
+--R 15637050x + 80999919x + 181983186x + 229582836x + 173491920x
+--R +
+--R 3 2
+--R 72883440x + 5339712x - 16666112x - 23667392
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 36465
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(2+3*x)^5*(3+5*x)*sqrt(1-2*x)
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (1) (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+r0:=-184877/192*(1-2*x)^(3/2)+12005/8*(1-2*x)^(5/2)-74235/64*(1-2*x)^(7/2)+_
+ 4165/8*(1-2*x)^(9/2)-97335/704*(1-2*x)^(11/2)+81/4*(1-2*x)^(13/2)-_
+ 81/64*(1-2*x)^(15/2)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R (5346x + 24057x + 45765x + 46875x + 26220x + 5172x - 4120x - 7288)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 33
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R (5346x + 24057x + 45765x + 46875x + 26220x + 5172x - 4120x - 7288)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 33
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(2+3*x)^4*(3+5*x)*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1) (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+r0:=-26411/96*(1-2*x)^(3/2)+57281/160*(1-2*x)^(5/2)-3549/16*(1-2*x)^(7/2)+_
+ 1197/16*(1-2*x)^(9/2)-4671/352*(1-2*x)^(11/2)+405/416*(1-2*x)^(13/2)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R (133650x + 509895x + 791640x + 614160x + 200328x - 60928x - 163888)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R (133650x + 509895x + 791640x + 614160x + 200328x - 60928x - 163888)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(2+3*x)^3*(3+5*x)*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1) (135x + 351x + 342x + 148x + 24)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+r0:=-3773/48*(1-2*x)^(3/2)+3283/40*(1-2*x)^(5/2)-153/4*(1-2*x)^(7/2)+_
+ 69/8*(1-2*x)^(9/2)-135/176*(1-2*x)^(11/2)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (4050x + 12645x + 15075x + 7527x - 482x - 4442)\|- 2x + 1
+--R (2) --------------------------------------------------------------
+--R 165
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (4050x + 12645x + 15075x + 7527x - 482x - 4442)\|- 2x + 1
+--R (3) --------------------------------------------------------------
+--R 165
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(2+3*x)^2*(3+5*x)*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+
+--R (1) (45x + 87x + 56x + 12)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+r0:=-539/24*(1-2*x)^(3/2)+707/40*(1-2*x)^(5/2)-309/56*(1-2*x)^(7/2)+_
+ 5/8*(1-2*x)^(9/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1050x + 2535x + 2046x + 244x - 1016)\|- 2x + 1
+--R (2) ---------------------------------------------------
+--R 105
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1050x + 2535x + 2046x + 244x - 1016)\|- 2x + 1
+--R (3) ---------------------------------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(2+3*x)*(3+5*x)*sqrt(1-2*x)
+--R
+--R
+--R 2 +--------+
+--R (1) (15x + 19x + 6)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+r0:=-77/12*(1-2*x)^(3/2)+17/5*(1-2*x)^(5/2)-15/28*(1-2*x)^(7/2)
+--R
+--R
+--R 3 2 +--------+
+--R (450x + 753x + 257x - 373)\|- 2x + 1
+--R (2) ---------------------------------------
+--R 105
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +--------+
+--R (450x + 753x + 257x - 373)\|- 2x + 1
+--R (3) ---------------------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(3+5*x)*sqrt(1-2*x)
+--R
+--R
+--R +--------+
+--R (1) (5x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+r0:=-11/6*(1-2*x)^(3/2)+1/2*(1-2*x)^(5/2)
+--R
+--R
+--R 2 +--------+
+--R (6x + 5x - 4)\|- 2x + 1
+--R (2) -------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +--------+
+--R (6x + 5x - 4)\|- 2x + 1
+--R (3) -------------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R (1) -------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+r0:=-5/9*(1-2*x)^(3/2)+2/9*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_
+ 2/9*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1 +-+ +--------+
+--R 2\|7 atanh(---------------) + (10x - 7)\|3 \|- 2x + 1
+--R +-+
+--R \|7
+--R (2) ------------------------------------------------------
+--R +-+
+--R 9\|3
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +--------+ +-+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ +--------+
+--R \|7 log(---------------------------------) + (10x - 7)\|3 \|- 2x + 1
+--R 3x + 2
+--R (3) ---------------------------------------------------------------------
+--R +-+
+--R 9\|3
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R \|7 log(---------------------------------) - 2\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ------------------------------------------------------------------------
+--R +-+
+--R 9\|3
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R (1) -------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+r0:=1/21*(1-2*x)^(3/2)/(2+3*x)-8*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ 8/7*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--------+
+--R (- 72x - 48)atanh(---------------) + (10x + 7)\|21 \|- 2x + 1
+--R +-+
+--R \|7
+--R (2) --------------------------------------------------------------
+--R +--+
+--R (9x + 6)\|21
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+
+--R (36x + 24)log(-----------------------------) + (10x + 7)\|21 \|- 2x + 1
+--R 3x + 2
+--R ------------------------------------------------------------------------
+--R +--+
+--R (9x + 6)\|21
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 4log(-----------------------------) + 8atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 12x + 20)\|21 + (12x - 20)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 8x + 4)\|3 \|7 \|21 + 168x - 84
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (126x + 21x - 42)\|- 2x + 1 + (18x - 27x - 11x + 10)\|21
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R (1) ---------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+r0:=1/42*(1-2*x)^(3/2)/(2+3*x)^2+23/21*_
+ atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-23/42*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1 +--+ +--------+
+--R (414x + 552x + 184)atanh(---------------) + (- 71x - 45)\|21 \|- 2x + 1
+--R +-+
+--R \|7
+--R -------------------------------------------------------------------------
+--R 2 +--+
+--R (378x + 504x + 168)\|21
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 - 21\|- 2x + 1 + (3x - 5)\|21
+--R (207x + 276x + 92)log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R (- 71x - 45)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (378x + 504x + 168)\|21
+--R Type: Union(Expression(Integer),...)
+--E 433
+
+--S 434 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 23log(-------------------------------) - 46atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 42\|21
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 69x + 115)\|21 + (69x - 115)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (46x - 23)\|3 \|7 \|21 - 966x + 483
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (5292x + 882x - 1764)\|- 2x + 1 + (- 756x + 1134x + 462x - 420)\|21
+--R Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^4
+--R
+--R
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+r0:=1/63*(1-2*x)^(3/2)/(2+3*x)^3+34/441*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)-17/63*sqrt(1-2*x)/(2+3*x)^2+17/441*_
+ sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (918x + 1836x + 1224x + 272)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (153x - 167x - 163)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (11907x + 23814x + 15876x + 3528)\|21
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 3 2 - 21\|- 2x + 1 + (3x - 5)\|21
+--R (459x + 918x + 612x + 136)log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (153x - 167x - 163)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (11907x + 23814x + 15876x + 3528)\|21
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 17log(-------------------------------) - 34atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 441\|21
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 51x + 85)\|21 + (51x - 85)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (34x - 17)\|3 \|7 \|21 - 714x + 357
+--R /
+--R 2 +--------+
+--R (55566x + 9261x - 18522)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 7938x + 11907x + 4851x - 4410)\|21
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^5
+--R
+--R
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+r0:=1/84*(1-2*x)^(3/2)/(2+3*x)^4+5/1372*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(3/7)-5/28*sqrt(1-2*x)/(2+3*x)^3+5/392*sqrt(1-2*x)/(2+3*x)^2+_
+ 15/2744*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 4 3 2 +-+ \|3 \|- 2x + 1
+--R (2430x + 6480x + 6480x + 2880x + 480)\|3 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +--------+
+--R (1215x + 3375x - 1726x - 2062)\|7 \|- 2x + 1
+--R /
+--R 4 3 2 +-+
+--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|7
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (1215x + 3240x + 3240x + 1440x + 240)\|3
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--------+
+--R (1215x + 3375x - 1726x - 2062)\|7 \|- 2x + 1
+--R /
+--R 4 3 2 +-+
+--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|7
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R 5\|3 log(---------------------------------) - 10\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R --------------------------------------------------------------------------
+--R +-+
+--R 2744\|7
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^6
+--R
+--R
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+r0:=1/105*(1-2*x)^(3/2)/(2+3*x)^5+2/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/_
+ sqrt(21)-2/15*sqrt(1-2*x)/(2+3*x)^4+2/315*sqrt(1-2*x)/(2+3*x)^3+_
+ 1/441*sqrt(1-2*x)/(2+3*x)^2+1/1029*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 5 4 3 2 \|3 \|- 2x + 1
+--R (2430x + 8100x + 10800x + 7200x + 2400x + 320)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (405x + 1395x + 2004x - 864x - 1019)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (1250235x + 4167450x + 5556600x + 3704400x + 1234800x + 164640)\|21
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (1215x + 4050x + 5400x + 3600x + 1200x + 160)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (405x + 1395x + 2004x - 864x - 1019)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (1250235x + 4167450x + 5556600x + 3704400x + 1234800x + 164640)\|21
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R log(-------------------------------) - 2atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------
+--R +--+
+--R 1029\|21
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+
+--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21
+--R +
+--R - 42x + 21
+--R /
+--R 2 +--------+
+--R (129654x + 21609x - 43218)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 18522x + 27783x + 11319x - 10290)\|21
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(2+3*x)^4*(3+5*x)^2*sqrt(1-2*x)
+--R
+--R
+--R (1)
+--R 6 5 4 3 2 +--------+
+--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+r0:=-290521/192*(1-2*x)^(3/2)+381073/160*(1-2*x)^(5/2)-118993/64*_
+ (1-2*x)^(7/2)+40453/48*(1-2*x)^(9/2)-159111/704*(1-2*x)^(11/2)+_
+ 13905/416*(1-2*x)^(13/2)-135/64*(1-2*x)^(15/2)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R 579150x + 2561625x + 4787910x + 4814245x + 2635780x + 493524x
+--R +
+--R - 426024x - 734904
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R 579150x + 2561625x + 4787910x + 4814245x + 2635780x + 493524x
+--R +
+--R - 426024x - 734904
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(2+3*x)^3*(3+5*x)^2*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1) (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+r0:=-41503/96*(1-2*x)^(3/2)+91091/160*(1-2*x)^(5/2)-5711/16*(1-2*x)^(7/2)+_
+ 1949/16*(1-2*x)^(9/2)-7695/352*(1-2*x)^(11/2)+675/416*(1-2*x)^(13/2)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R (222750x + 832275x + 1264605x + 958275x + 301263x - 99458x - 253898)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R (222750x + 832275x + 1264605x + 958275x + 301263x - 99458x - 253898)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(2+3*x)^2*(3+5*x)^2*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1) (225x + 570x + 541x + 228x + 36)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+r0:=-5929/48*(1-2*x)^(3/2)+1309/10*(1-2*x)^(5/2)-3467/56*(1-2*x)^(7/2)+_
+ 85/6*(1-2*x)^(9/2)-225/176*(1-2*x)^(11/2)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (47250x + 143675x + 166580x + 80313x - 6518x - 48098)\|- 2x + 1
+--R (2) --------------------------------------------------------------------
+--R 1155
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (47250x + 143675x + 166580x + 80313x - 6518x - 48098)\|- 2x + 1
+--R (3) --------------------------------------------------------------------
+--R 1155
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(2+3*x)*(3+5*x)^2*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+
+--R (1) (75x + 140x + 87x + 18)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+r0:=-847/24*(1-2*x)^(3/2)+1133/40*(1-2*x)^(5/2)-505/56*(1-2*x)^(7/2)+_
+ 25/24*(1-2*x)^(9/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1750x + 4075x + 3159x + 321x - 1569)\|- 2x + 1
+--R (2) ---------------------------------------------------
+--R 105
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1750x + 4075x + 3159x + 321x - 1569)\|- 2x + 1
+--R (3) ---------------------------------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(3+5*x)^2*sqrt(1-2*x)
+--R
+--R
+--R 2 +--------+
+--R (1) (25x + 30x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+r0:=-121/12*(1-2*x)^(3/2)+11/2*(1-2*x)^(5/2)-25/28*(1-2*x)^(7/2)
+--R
+--R
+--R 3 2 +--------+
+--R (150x + 237x + 74x - 115)\|- 2x + 1
+--R (2) --------------------------------------
+--R 21
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +--------+
+--R (150x + 237x + 74x - 115)\|- 2x + 1
+--R (3) --------------------------------------
+--R 21
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R (1) ---------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+r0:=-28/27*(1-2*x)^(3/2)-1/3*(1-2*x)^(3/2)*(3+5*x)-2/27*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(7/3)+2/27*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1 2 +-+ +--------+
+--R - 2\|7 atanh(---------------) + (90x + 65x - 53)\|3 \|- 2x + 1
+--R +-+
+--R \|7
+--R (2) ----------------------------------------------------------------
+--R +-+
+--R 27\|3
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 2 +-+ +--------+
+--R \|7 log(-------------------------------) + (90x + 65x - 53)\|3 \|- 2x + 1
+--R 3x + 2
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 27\|3
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 500
+m0:=a0-r0
+--R
+--R
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R \|7 log(-------------------------------) + 2\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ----------------------------------------------------------------------
+--R +-+
+--R 27\|3
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R (1) ---------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+r0:=-25/27*(1-2*x)^(3/2)-1/63*(1-2*x)^(3/2)/(2+3*x)+142/27*_
+ atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-142/189*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|3 \|- 2x + 1 2 +--+ +--------+
+--R (426x + 284)atanh(---------------) + (150x - 35x - 91)\|21 \|- 2x + 1
+--R +-+
+--R \|7
+--R -----------------------------------------------------------------------
+--R +--+
+--R (81x + 54)\|21
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R (213x + 142)log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (150x - 35x - 91)\|21 \|- 2x + 1
+--R /
+--R +--+
+--R (81x + 54)\|21
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 71log(-------------------------------) - 142atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 27\|21
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 213x + 355)\|21 + (213x - 355)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (142x - 71)\|3 \|7 \|21 - 2982x + 1491
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (3402x + 567x - 1134)\|- 2x + 1 + (- 486x + 729x + 297x - 270)\|21
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R (1) ---------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+r0:=-1/126*(1-2*x)^(3/2)/(2+3*x)^2+139/882*(1-2*x)^(3/2)/(2+3*x)-_
+ 863/63*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+863/441*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1
+--R (- 15534x - 20712x - 6904)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (2100x + 2941x + 1025)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (1134x + 1512x + 504)\|21
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 21\|- 2x + 1 + (3x - 5)\|21
+--R (7767x + 10356x + 3452)log(-----------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (2100x + 2941x + 1025)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (1134x + 1512x + 504)\|21
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 863log(-----------------------------) + 1726atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 126\|21
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 2589x + 4315)\|21 + (2589x - 4315)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 1726x + 863)\|3 \|7 \|21 + 36246x - 18123
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (15876x + 2646x - 5292)\|- 2x + 1 + (2268x - 3402x - 1386x + 1260)\|21
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4
+--R
+--R
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+r0:=-1/189*(1-2*x)^(3/2)/(2+3*x)^3+23/294*(1-2*x)^(3/2)/(2+3*x)^2+_
+ 2381/1323*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 2381/2646*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (128574x + 257148x + 171432x + 38096)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (- 22671x - 28751x - 9124)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (71442x + 142884x + 95256x + 21168)\|21
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 3 2 - 21\|- 2x + 1 + (3x - 5)\|21
+--R (64287x + 128574x + 85716x + 19048)log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (- 22671x - 28751x - 9124)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (71442x + 142884x + 95256x + 21168)\|21
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 2381log(-------------------------------) - 4762atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 2646\|21
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 7143x + 11905)\|21 + (7143x - 11905)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (4762x - 2381)\|3 \|7 \|21 - 100002x + 50001
+--R /
+--R 2 +--------+
+--R (333396x + 55566x - 111132)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 47628x + 71442x + 29106x - 26460)\|21
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5
+--R
+--R
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+r0:=-1/252*(1-2*x)^(3/2)/(2+3*x)^4+275/5292*(1-2*x)^(3/2)/(2+3*x)^3+_
+ 4625/37044*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 4625/10584*sqrt(1-2*x)/(2+3*x)^2+4625/74088*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (749250x + 1998000x + 1998000x + 888000x + 148000)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (124875x - 64725x - 225262x - 85094)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (374625x + 999000x + 999000x + 444000x + 74000)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (124875x - 64725x - 225262x - 85094)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 4625log(-------------------------------) - 9250atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 74088\|21
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 13875x + 23125)\|21 + (13875x - 23125)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (9250x - 4625)\|3 \|7 \|21 - 194250x + 97125
+--R /
+--R 2 +--------+
+--R (9335088x + 1555848x - 3111696)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 1333584x + 2000376x + 814968x - 740880)\|21
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3i.input.pdf b/src/axiom-website/CATS/rich3i.input.pdf
new file mode 100644
index 0000000..a5d5df8
Binary files /dev/null and b/src/axiom-website/CATS/rich3i.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3j.input.pamphlet b/src/axiom-website/CATS/rich3j.input.pamphlet
new file mode 100644
index 0000000..7bfb8f5
--- /dev/null
+++ b/src/axiom-website/CATS/rich3j.input.pamphlet
@@ -0,0 +1,9134 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3j.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 55 matching answers.
+\item 45 cases where Axiom differs from Rubi
+\item 0 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 rich3j.output
+)spool rich3j.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^6
+--R
+--R
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+r0:=-1/315*(1-2*x)^(3/2)/(2+3*x)^5+7/180*(1-2*x)^(3/2)/(2+3*x)^4+_
+ 31/1764*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 31/108*sqrt(1-2*x)/(2+3*x)^3+31/1512*sqrt(1-2*x)/(2+3*x)^2+_
+ 31/3528*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (75330x + 251100x + 334800x + 223200x + 74400x + 9920)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (12555x + 43245x + 3324x - 33434x - 13564)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (4286520x + 14288400x + 19051200x + 12700800x + 4233600x + 564480)\|21
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (37665x + 125550x + 167400x + 111600x + 37200x + 4960)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (12555x + 43245x + 3324x - 33434x - 13564)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (4286520x + 14288400x + 19051200x + 12700800x + 4233600x + 564480)\|21
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 31log(-------------------------------) - 62atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 3528\|21
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 93x + 155)\|21 + (93x - 155)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (62x - 31)\|3 \|7 \|21 - 1302x + 651
+--R /
+--R 2 +--------+
+--R (444528x + 74088x - 148176)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 63504x + 95256x + 38808x - 35280)\|21
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^7
+--R
+--R
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+r0:=-1/378*(1-2*x)^(3/2)/(2+3*x)^6+137/4410*(1-2*x)^(3/2)/(2+3*x)^5+_
+ 1613/518616*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 1613/7560*sqrt(1-2*x)/(2+3*x)^4+1613/158760*sqrt(1-2*x)/(2+3*x)^3+_
+ 1613/444528*sqrt(1-2*x)/(2+3*x)^2+1613/1037232*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 11758770x + 47035080x + 78391800x + 69681600x + 34840800x
+--R +
+--R 9290880x + 1032320
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R (1959795x + 8056935x + 14197626x + 1791558x - 7772840x - 3136864)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3
+--R 3780710640x + 15122842560x + 25204737600x + 22404211200x
+--R +
+--R 2
+--R 11202105600x + 2987228160x + 331914240
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 5879385x + 23517540x + 39195900x + 34840800x + 17420400x
+--R +
+--R 4645440x + 516160
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R (1959795x + 8056935x + 14197626x + 1791558x - 7772840x - 3136864)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3
+--R 3780710640x + 15122842560x + 25204737600x + 22404211200x
+--R +
+--R 2
+--R 11202105600x + 2987228160x + 331914240
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 1613log(-------------------------------) - 3226atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 1037232\|21
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 4839x + 8065)\|21 + (4839x - 8065)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (3226x - 1613)\|3 \|7 \|21 - 67746x + 33873
+--R /
+--R 2 +--------+
+--R (130691232x + 21781872x - 43563744)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 18670176x + 28005264x + 11409552x - 10372320)\|21
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(2+3*x)^4*(3+5*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R (10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+r0:=-3195731/384*(1-2*x)^(3/2)+9836211/640*(1-2*x)^(5/2)-_
+ 1853313/128*(1-2*x)^(7/2)+9504551/1152*(1-2*x)^(9/2)-_
+ 4177401/1408*(1-2*x)^(11/2)+1101465/1664*(1-2*x)^(13/2)-_
+ 10755/128*(1-2*x)^(15/2)+10125/2176*(1-2*x)^(17/2)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4
+--R 130308750x + 655308225x + 1428673950x + 1747511955x + 1277595710x
+--R +
+--R 3 2
+--R 514265240x + 26582592x - 124054192x - 171312832
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 109395
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4
+--R 130308750x + 655308225x + 1428673950x + 1747511955x + 1277595710x
+--R +
+--R 3 2
+--R 514265240x + 26582592x - 124054192x - 171312832
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 109395
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(2+3*x)^3*(3+5*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (1)
+--R 6 5 4 3 2 +--------+
+--R (3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+r0:=-456533/192*(1-2*x)^(3/2)+302379/80*(1-2*x)^(5/2)-_
+ 190707/64*(1-2*x)^(7/2)+98209/72*(1-2*x)^(9/2)-_
+ 260055/704*(1-2*x)^(11/2)+11475/208*(1-2*x)^(13/2)-225/64*(1-2*x)^(15/2)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3
+--R 2895750x + 12585375x + 23107275x + 22806620x + 12220625x
+--R +
+--R 2
+--R 2166357x - 2030662x - 3420622
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6435
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R 2895750x + 12585375x + 23107275x + 22806620x + 12220625x
+--R +
+--R 2
+--R 2166357x - 2030662x - 3420622
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6435
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(2+3*x)^2*(3+5*x)^3*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1) (1125x + 3525x + 4415x + 2763x + 864x + 108)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+r0:=-65219/96*(1-2*x)^(3/2)+144837/160*(1-2*x)^(5/2)-_
+ 64317/112*(1-2*x)^(7/2)+28555/144*(1-2*x)^(9/2)-_
+ 12675/352*(1-2*x)^(11/2)+1125/416*(1-2*x)^(13/2)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 7796250x + 28515375x + 42393400x + 31374085x + 9500136x - 3396296x
+--R +
+--R - 8261156
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 45045
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 7796250x + 28515375x + 42393400x + 31374085x + 9500136x - 3396296x
+--R +
+--R - 8261156
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 45045
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(2+3*x)*(3+5*x)^3*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1) (375x + 925x + 855x + 351x + 54)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+r0:=-9317/48*(1-2*x)^(3/2)+8349/40*(1-2*x)^(5/2)-2805/28*(1-2*x)^(7/2)+_
+ 1675/72*(1-2*x)^(9/2)-375/176*(1-2*x)^(11/2)
+--R
+--R
+--R (2)
+--R 5 4 3 2 +--------+
+--R (236250x + 699125x + 788075x + 366816x - 36121x - 223231)\|- 2x + 1
+--R ------------------------------------------------------------------------
+--R 3465
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2 +--------+
+--R (236250x + 699125x + 788075x + 366816x - 36121x - 223231)\|- 2x + 1
+--R ------------------------------------------------------------------------
+--R 3465
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(3+5*x)^3*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+
+--R (1) (125x + 225x + 135x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+r0:=-1331/24*(1-2*x)^(3/2)+363/8*(1-2*x)^(5/2)-825/56*(1-2*x)^(7/2)+_
+ 125/72*(1-2*x)^(9/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1750x + 3925x + 2922x + 247x - 1454)\|- 2x + 1
+--R (2) ---------------------------------------------------
+--R 63
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1750x + 3925x + 2922x + 247x - 1454)\|- 2x + 1
+--R (3) ---------------------------------------------------
+--R 63
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R (1) --------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+r0:=2/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-6946/945*sqrt(1-2*x)-_
+ 47/315*(3+5*x)^2*sqrt(1-2*x)+2/21*(3+5*x)^3*sqrt(1-2*x)-_
+ 1/567*(1333+1877*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R 14\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +--------+
+--R (6750x + 10035x + 2875x - 4804)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 567\|3
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 7\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--------+
+--R (6750x + 10035x + 2875x - 4804)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 567\|3
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R \|7 log(---------------------------------) - 2\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ------------------------------------------------------------------------
+--R +-+
+--R 81\|3
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R (1) --------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+r0:=-212/81*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-124/27*sqrt(1-2*x)+_
+ 7/9*(3+5*x)^2*sqrt(1-2*x)-1/3*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)-_
+ 10/81*(5+34*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R (- 636x - 424)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (1350x + 1725x - 110x - 439)\|21 \|- 2x + 1
+--R /
+--R +--+
+--R (243x + 162)\|21
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R (318x + 212)log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (1350x + 1725x - 110x - 439)\|21 \|- 2x + 1
+--R /
+--R +--+
+--R (243x + 162)\|21
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 106log(-----------------------------) + 212atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 81\|21
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 318x + 530)\|21 + (318x - 530)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 212x + 106)\|3 \|7 \|21 + 4452x - 2226
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (10206x + 1701x - 3402)\|- 2x + 1 + (1458x - 2187x - 891x + 810)\|21
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R (1) --------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+r0:=7559/567*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+115/27*sqrt(1-2*x)-_
+ 5/1134*(643-2815*x)*sqrt(1-2*x)-53/63*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)-_
+ 1/6*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1
+--R (136062x + 181416x + 60472)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (31500x + 7350x - 32833x - 15815)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (10206x + 13608x + 4536)\|21
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 - 21\|- 2x + 1 + (3x - 5)\|21
+--R (68031x + 90708x + 30236)log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (31500x + 7350x - 32833x - 15815)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (10206x + 13608x + 4536)\|21
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 7559log(-------------------------------) - 15118atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ----------------------------------------------------------------------
+--R +--+
+--R 1134\|21
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 22677x + 37795)\|21 + (22677x - 37795)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (15118x - 7559)\|3 \|7 \|21 - 317478x + 158739
+--R /
+--R 2 +--------+
+--R (142884x + 23814x - 47628)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 20412x + 30618x + 12474x - 11340)\|21
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4
+--R
+--R
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R (1) --------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+r0:=-92996/3969*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+23710/3969*sqrt(1-2*x)-_
+ 3796/3969*(3+5*x)*sqrt(1-2*x)/(2+3*x)-53/189*(3+5*x)^2*_
+ sqrt(1-2*x)/(2+3*x)^2-1/9*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (- 2510892x - 5021784x - 3347856x - 743968)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (330750x + 695043x + 484618x + 112187)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (107163x + 214326x + 142884x + 31752)\|21
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (1255446x + 2510892x + 1673928x + 371984)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (330750x + 695043x + 484618x + 112187)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (107163x + 214326x + 142884x + 31752)\|21
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 46498log(-----------------------------) + 92996atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 3969\|21
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 139494x + 232490)\|21 + (139494x - 232490)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 92996x + 46498)\|3 \|7 \|21 + 1952916x - 976458
+--R /
+--R 2 +--------+
+--R (500094x + 83349x - 166698)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (71442x - 107163x - 43659x + 39690)\|21
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5
+--R
+--R
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+r0:=328715/111132*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-48005/111132*_
+ sqrt(1-2*x)/(2+3*x)-7625/31752*(3+5*x)*sqrt(1-2*x)/(2+3*x)^2-_
+ 53/378*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3-1/12*(3+5*x)^3*_
+ sqrt(1-2*x)/(2+3*x)^4
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (53251830x + 142004880x + 142004880x + 63113280x + 10518880)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (- 9646695x - 18358575x - 11657098x - 2469626)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (18003384x + 48009024x + 48009024x + 21337344x + 3556224)\|21
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (26625915x + 71002440x + 71002440x + 31556640x + 5259440)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (- 9646695x - 18358575x - 11657098x - 2469626)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (18003384x + 48009024x + 48009024x + 21337344x + 3556224)\|21
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 328715log(-------------------------------) - 657430atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -------------------------------------------------------------------------
+--R +--+
+--R 222264\|21
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 986145x + 1643575)\|21 + (986145x - 1643575)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (657430x - 328715)\|3 \|7 \|21 - 13806030x + 6903015
+--R /
+--R 2 +--------+
+--R (28005264x + 4667544x - 9335088)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 4000752x + 6001128x + 2444904x - 2222640)\|21
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^6
+--R
+--R
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+r0:=11237/55566*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 475/5292*sqrt(1-2*x)/(2+3*x)^2+11237/111132*sqrt(1-2*x)/(2+3*x)-_
+ 547/5670*(3+5*x)*sqrt(1-2*x)/(2+3*x)^3-53/630*(3+5*x)^2*_
+ sqrt(1-2*x)/(2+3*x)^4-1/15*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 27305910x + 91019700x + 121359600x + 80906400x + 26968800x
+--R +
+--R 3595840
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (4550985x + 240615x - 10100352x - 8471518x - 1984928)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 135025380x + 450084600x + 600112800x + 400075200x + 133358400x
+--R +
+--R 17781120
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 13652955x + 45509850x + 60679800x + 40453200x + 13484400x
+--R +
+--R 1797920
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (4550985x + 240615x - 10100352x - 8471518x - 1984928)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 135025380x + 450084600x + 600112800x + 400075200x + 133358400x
+--R +
+--R 17781120
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 11237log(-------------------------------) - 22474atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------
+--R +--+
+--R 111132\|21
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 33711x + 56185)\|21 + (33711x - 56185)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (22474x - 11237)\|3 \|7 \|21 - 471954x + 235977
+--R /
+--R 2 +--------+
+--R (14002632x + 2333772x - 4667544)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 2000376x + 3000564x + 1222452x - 1111320)\|21
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^7
+--R
+--R
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+r0:=43957/1555848*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 1861/59535*sqrt(1-2*x)/(2+3*x)^3+43957/1333584*sqrt(1-2*x)/(2+_
+ 3*x)^2+43957/3111696*sqrt(1-2*x)/(2+3*x)-7691/158760*(3+5*x)*_
+ sqrt(1-2*x)/(2+3*x)^4-53/945*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5-_
+ 1/18*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^6
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 320446530x + 1281786120x + 2136310200x + 1898942400x
+--R +
+--R 2
+--R 949471200x + 253192320x + 28132480
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R 53407755x + 219565215x + 127601514x - 139462938x - 150340360x
+--R +
+--R - 36741296
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3
+--R 11342131920x + 45368527680x + 75614212800x + 67212633600x
+--R +
+--R 2
+--R 33606316800x + 8961684480x + 995742720
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 160223265x + 640893060x + 1068155100x + 949471200x + 474735600x
+--R +
+--R 126596160x + 14066240
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R 53407755x + 219565215x + 127601514x - 139462938x - 150340360x
+--R +
+--R - 36741296
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3
+--R 11342131920x + 45368527680x + 75614212800x + 67212633600x
+--R +
+--R 2
+--R 33606316800x + 8961684480x + 995742720
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 43957log(-------------------------------) - 87914atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------
+--R +--+
+--R 3111696\|21
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 131871x + 219785)\|21 + (131871x - 219785)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (87914x - 43957)\|3 \|7 \|21 - 1846194x + 923097
+--R /
+--R 2 +--------+
+--R (392073696x + 65345616x - 130691232)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 56010528x + 84015792x + 34228656x - 31116960)\|21
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+r0:=47434/9529569*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 13676/972405*sqrt(1-2*x)/(2+3*x)^4+47434/2917215*_
+ sqrt(1-2*x)/(2+3*x)^3+23717/4084101*sqrt(1-2*x)/(2+3*x)^2+_
+ 23717/9529569*sqrt(1-2*x)/(2+3*x)-3862/138915*(3+5*x)*_
+ sqrt(1-2*x)/(2+3*x)^5-53/1323*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^6-_
+ 1/21*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^7
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 518690790x + 2420557020x + 4841114040x + 5379015600x
+--R +
+--R 3 2
+--R 3586010400x + 1434404160x + 318756480x + 30357760
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 6 5 4 3 2
+--R 86448465x + 413031555x + 863203932x + 473987484x - 306463011x
+--R +
+--R - 361589428x - 88036937
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 7 6 5 4
+--R 104205837015x + 486293906070x + 972587812140x + 1080653124600x
+--R +
+--R 3 2
+--R 720435416400x + 288174166560x + 64038703680x + 6098924160
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4
+--R 259345395x + 1210278510x + 2420557020x + 2689507800x
+--R +
+--R 3 2
+--R 1793005200x + 717202080x + 159378240x + 15178880
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 6 5 4 3 2
+--R 86448465x + 413031555x + 863203932x + 473987484x - 306463011x
+--R +
+--R - 361589428x - 88036937
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 7 6 5 4
+--R 104205837015x + 486293906070x + 972587812140x + 1080653124600x
+--R +
+--R 3 2
+--R 720435416400x + 288174166560x + 64038703680x + 6098924160
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 23717log(-------------------------------) - 47434atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------
+--R +--+
+--R 9529569\|21
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 71151x + 118585)\|21 + (71151x - 118585)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (47434x - 23717)\|3 \|7 \|21 - 996114x + 498057
+--R /
+--R 2 +--------+
+--R (1200725694x + 200120949x - 400241898)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 171532242x + 257298363x + 104825259x - 95295690)\|21
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+r0:=-2/3125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-93922/28125*_
+ sqrt(1-2*x)-107/225*(2+3*x)*sqrt(1-2*x)-184/1875*(2+3*x)^2*_
+ sqrt(1-2*x)-17/1575*(2+3*x)^3*sqrt(1-2*x)+2/45*(2+3*x)^4*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 14\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--------+
+--R (78750x + 203625x + 177930x + 27865x - 88776)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 21875\|5
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 7\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--------+
+--R (78750x + 203625x + 177930x + 27865x - 88776)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 21875\|5
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R \|11 log(--------------------------------) + 2\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -------------------------------------------------------------------------
+--R +-+
+--R 3125\|5
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R (1) ----------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+r0:=-2/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_
+ 922/625*sqrt(1-2*x)-3/125*(2+3*x)^2*sqrt(1-2*x)+2/35*(2+3*x)^3*_
+ sqrt(1-2*x)-1/625*(236+375*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 14\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+
+--R (6750x + 12555x + 5115x - 6526)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 4375\|5
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 7\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--------+
+--R (6750x + 12555x + 5115x - 6526)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 4375\|5
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R \|11 log(--------------------------------) + 2\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -------------------------------------------------------------------------
+--R +-+
+--R 625\|5
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R (1) --------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+r0:=-8/25*(1-2*x)^(3/2)-3/25*(1-2*x)^(3/2)*(2+3*x)-2/125*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)+2/125*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+
+--R - 2\|11 atanh(---------------) + (90x + 95x - 68)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) -----------------------------------------------------------------
+--R +-+
+--R 125\|5
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 2 +-+ +--------+
+--R \|11 log(--------------------------------) + (90x + 95x - 68)\|5 \|- 2x + 1
+--R 5x + 3
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 125\|5
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R \|11 log(--------------------------------) + 2\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -------------------------------------------------------------------------
+--R +-+
+--R 125\|5
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R (1) -------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+r0:=-1/5*(1-2*x)^(3/2)-2/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/25*_
+ sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1 +-+ +--------+
+--R - 2\|11 atanh(---------------) + (10x - 3)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ---------------------------------------------------------
+--R +-+
+--R 25\|5
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +-+ +--------+
+--R \|11 log(--------------------------------) + (10x - 3)\|5 \|- 2x + 1
+--R 5x + 3
+--R (3) ---------------------------------------------------------------------
+--R +-+
+--R 25\|5
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R \|11 log(--------------------------------) + 2\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -------------------------------------------------------------------------
+--R +-+
+--R 25\|5
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+r0:=-2/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/5*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1 +-+ +--------+
+--R - 2\|11 atanh(---------------) + 2\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) -------------------------------------------------
+--R +-+
+--R 5\|5
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +-+ +--------+
+--R \|11 log(--------------------------------) + 2\|5 \|- 2x + 1
+--R 5x + 3
+--R (3) -------------------------------------------------------------
+--R +-+
+--R 5\|5
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R \|11 log(--------------------------------) + 2\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -------------------------------------------------------------------------
+--R +-+
+--R 5\|5
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) --------------
+--R 2
+--R 15x + 19x + 6
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+r0:=-2*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(7/3)
+--R
+--R
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R 2\|5 \|7 atanh(---------------) - 2\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R (2) ------------------------------------------------------------------
+--R +-+ +-+
+--R \|3 \|5
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R \|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R \|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R /
+--R +-+ +-+
+--R \|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R \|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R \|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R - 2\|5 \|7 atanh(---------------) + 2\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R \|3 \|5
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ----------------------
+--R 3 2
+--R 45x + 87x + 56x + 12
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+r0:=68*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-2*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(55)+sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R (204x + 136)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1 +--+ +--------+
+--R (- 6x - 4)\|21 \|55 atanh(---------------) + \|21 \|- 2x + 1
+--R +--+
+--R \|11
+--R /
+--R +--+
+--R (3x + 2)\|21
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R (3x + 2)\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+
+--R (102x + 68)log(-------------------------------) + \|21 \|- 2x + 1
+--R 3x + 2
+--R /
+--R +--+
+--R (3x + 2)\|21
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R \|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 34log(-------------------------------) - 68atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R 2\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (45x - 117x + 22x + 80)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 340x - 34x + 102)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 210x - 441x + 168
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+ 2 +-+ +--+
+--R (75x - 365x + 592x - 320)\|21 + (6930x + 1155x - 2310)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 2550x + 6800x - 1802x - 4080)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 30x + 113x - 129x + 40)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (630x - 903x - 378x + 336)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (1020x - 1598x - 476x + 510)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 990x + 1485x + 605x - 550)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 1700x + 2550x + 782x - 816)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 1050x - 3885x + 4368x - 1344
+--R /
+--R 4 3 2 +--+ +--+ 4 3 2
+--R (90x - 81x - 136x + 17x + 30)\|21 \|55 - 3150x + 2625x + 4599x
+--R +
+--R - 546x - 1008
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (1260x + 336x - 777x - 105x + 126)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (450x - 1125x - 32x + 1173x + 14x - 240)\|21
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 135x + 351x + 342x + 148x + 24
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+r0:=793/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(55)+1/2*sqrt(1-2*x)/(2+3*x)^2+69/14*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ \|3 \|- 2x + 1
+--R (14274x + 19032x + 6344)\|3 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +--+ \|5 \|- 2x + 1
+--R (- 1260x - 1680x - 560)\|7 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+
+--R (207x + 145)\|7 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (126x + 168x + 56)\|7
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+
+--R 2 +-+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R (630x + 840x + 280)\|7 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R 2 +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (7137x + 9516x + 3172)\|3 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R (207x + 145)\|7 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (126x + 168x + 56)\|7
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +-+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 70\|7 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 793\|3 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R - 1586\|3 atanh(---------------) + 140\|7 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+
+--R 14\|7
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 +-+ +-+ +--+ +-+ +--+
+--R ((75x - 245x + 200)\|5 \|7 \|11 + (- 3850x + 1925)\|3 )\|55
+--R +
+--R +-+ +-+ +--+ 2 +-+
+--R (3850x - 1925)\|3 \|5 \|11 + (- 4125x + 13475x - 11000)\|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +-+ +--+ 2 +-+ +--+
+--R ((350x - 735x + 280)\|3 \|5 \|11 + (1650x - 3575x + 1375)\|7 )\|55
+--R +
+--R 2 +-+ +-+ +--+ 2 +-+
+--R (- 1650x + 3575x - 1375)\|5 \|7 \|11 + (- 19250x + 40425x - 15400)\|3
+--R /
+--R 3 2 +-+ +--+
+--R (30x - 47x - 14x + 15)\|7 \|55
+--R +
+--R 3 2 +-+
+--R (- 350x + 525x + 161x - 168)\|3
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--+
+--R (140x - 56x - 49x + 21)\|3 \|55
+--R +
+--R 4 3 2 +-+
+--R (150x - 475x + 306x + 187x - 120)\|7
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 405x + 1323x + 1728x + 1128x + 368x + 48
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+r0:=83264/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-50*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(55)+1/3*sqrt(1-2*x)/(2+3*x)^3+52/21*_
+ sqrt(1-2*x)/(2+3*x)^2+1207/49*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (2248128x + 4496256x + 2997504x + 666112)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 3 2 +--+ +--+ \|5 \|- 2x + 1
+--R (- 66150x - 132300x - 88200x - 19600)\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (10863x + 14848x + 5087)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (1323x + 2646x + 1764x + 392)\|21
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--+ +--+
+--R (33075x + 66150x + 44100x + 9800)\|21 \|55
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1 + 5x - 8
+--R log(-------------------------)
+--R 5x + 3
+--R +
+--R 3 2
+--R (1124064x + 2248128x + 1498752x + 333056)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (10863x + 14848x + 5087)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (1323x + 2646x + 1764x + 392)\|21
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 1225\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 41632log(-------------------------------) - 83264atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R 2450\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +--+
+--R 49\|21
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (55125x - 143325x + 26950x + 98000)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 416320x - 41632x + 124896)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 253470x - 540603x + 206934
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (90525x - 443525x + 724246x - 394160)\|21
+--R +
+--R 2 +-+ +--+
+--R (8489250x + 1414875x - 2829750)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 3122400x + 8326400x - 2206496x - 4995840)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 36210x + 137579x - 158277x + 49270)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (771750x - 1106175x - 463050x + 411600)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (1248960x - 1956704x - 582848x + 624480)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 1212750x + 1819125x + 741125x - 673750)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 2081600x + 3122400x + 957536x - 999168)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 1267350x - 4730775x + 5359494x - 1655472
+--R /
+--R 4 3 2 +--+ +--+ 4
+--R (4410x - 3969x - 6664x + 833x + 1470)\|21 \|55 - 154350x
+--R +
+--R 3 2
+--R 128625x + 225351x - 26754x - 49392
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (61740x + 16464x - 38073x - 5145x + 6174)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (22050x - 55125x - 1568x + 57477x + 686x - 11760)\|21
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^5*(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ------------------------------------------------------
+--R 6 5 4 3 2
+--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+r0:=11656955/1372*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-250*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+1/4*sqrt(1-2*x)/(2+3*x)^4+_
+ 139/84*sqrt(1-2*x)/(2+3*x)^3+14555/1176*sqrt(1-2*x)/(2+3*x)^2+_
+ 337955/2744*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (1888426710x + 5035804560x + 5035804560x + 2238135360x + 373022560)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+
+--R (- 55566000x - 148176000x - 148176000x - 65856000x - 10976000)\|21
+--R *
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (9124785x + 18555225x + 12587542x + 2849254)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (222264x + 592704x + 592704x + 263424x + 43904)\|21
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +--+ +--+
+--R (27783000x + 74088000x + 74088000x + 32928000x + 5488000)\|21 \|55
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1 + 5x - 8
+--R log(-------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2
+--R (944213355x + 2517902280x + 2517902280x + 1119067680x + 186511280)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (9124785x + 18555225x + 12587542x + 2849254)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (222264x + 592704x + 592704x + 263424x + 43904)\|21
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 343000\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R 11656955log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R - 23313910atanh(---------------) + 686000\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 2744\|21
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (15435000x - 40131000x + 7546000x + 27440000)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 116569550x - 11656955x + 34970865)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 70970550x - 151368945x + 57941835
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (25346625x - 124186000x + 202788615x - 110365400)\|21
+--R +
+--R 2 +-+ +--+
+--R (2376990000x + 396165000x - 792330000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 874271625x + 2331391000x - 617818615x - 1398834600)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 10138650x + 38521885x - 44317630x + 13795675)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (216090000x - 309729000x - 129654000x + 115248000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (349708650x - 547876885x - 163197370x + 174854325)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 339570000x + 509355000x + 207515000x - 188650000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 582847750x + 874271625x + 268109965x - 279766920)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 354852750x - 1324609125x + 1500660735x - 463534680
+--R /
+--R 4 3 2 +--+ +--+
+--R (246960x - 222264x - 373184x + 46648x + 82320)\|21 \|55
+--R +
+--R 4 3 2
+--R - 8643600x + 7203000x + 12619656x - 1498224x - 2765952
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (3457440x + 921984x - 2132088x - 288120x + 345744)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (1234800x - 3087000x - 87808x + 3218712x + 38416x - 658560)\|21
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(2+3*x)^5*sqrt(1-2*x)/(3+5*x)^2
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1
+--R (1) -------------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+r0:=-328/15625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-35128/15625*_
+ sqrt(1-2*x)-172/3125*(2+3*x)^2*sqrt(1-2*x)+64/2625*(2+3*x)^3*_
+ sqrt(1-2*x)+11/75*(2+3*x)^4*sqrt(1-2*x)-1/5*(2+3*x)^5*_
+ sqrt(1-2*x)/(3+5*x)-4/15625*(2216+3625*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R (- 11480x - 6888)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R (1181250x + 3864375x + 4760100x + 2225760x - 1133340x - 862072)
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1
+--R /
+--R +--+
+--R (546875x + 328125)\|55
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R (5740x + 3444)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R (1181250x + 3864375x + 4760100x + 2225760x - 1133340x - 862072)
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1
+--R /
+--R +--+
+--R (546875x + 328125)\|55
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 164log(-----------------------------) + 328atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 15625\|55
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 820x + 1312)\|55 + (820x - 1312)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 328x + 164)\|5 \|11 \|55 + 18040x - 9020
+--R /
+--R 2 +--------+
+--R (8593750x + 859375x - 2578125)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (781250x - 1171875x - 359375x + 375000)\|55
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2
+--R
+--R
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+r0:=-262/3125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3018/3125*sqrt(1-2*x)-_
+ 3/25*(2+3*x)*sqrt(1-2*x)+12/625*(2+3*x)^2*sqrt(1-2*x)+_
+ 27/175*(2+3*x)^3*sqrt(1-2*x)-1/5*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R (- 9170x - 5502)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (101250x + 258525x + 206415x - 52485x - 63088)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R (109375x + 65625)\|55
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R (4585x + 2751)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+ +--------+
+--R (101250x + 258525x + 206415x - 52485x - 63088)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R (109375x + 65625)\|55
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 131log(-----------------------------) + 262atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 3125\|55
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 655x + 1048)\|55 + (655x - 1048)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 262x + 131)\|5 \|11 \|55 + 14410x - 7205
+--R /
+--R 2 +--------+
+--R (1718750x + 171875x - 515625)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (156250x - 234375x - 71875x + 75000)\|55
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2
+--R
+--R
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R (1) ----------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+r0:=-196/625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-294/625*sqrt(1-2*x)+_
+ 21/125*(2+3*x)^2*sqrt(1-2*x)-1/5*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R (- 980x - 588)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (1350x + 2385x - 90x - 622)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R (3125x + 1875)\|55
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R (490x + 294)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+ +--------+
+--R (1350x + 2385x - 90x - 622)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R (3125x + 1875)\|55
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 98log(-----------------------------) + 196atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ----------------------------------------------------------------
+--R +--+
+--R 625\|55
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 490x + 784)\|55 + (490x - 784)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 196x + 98)\|5 \|11 \|55 + 10780x - 5390
+--R /
+--R 2 +--------+
+--R (343750x + 34375x - 103125)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (31250x - 46875x - 14375x + 15000)\|55
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2
+--R
+--R
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R (1) --------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+r0:=-3/25*(1-2*x)^(3/2)-1/275*(1-2*x)^(3/2)/(3+5*x)-_
+ 26/25*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+26/275*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 2 +--+ +--------+
+--R (- 130x - 78)atanh(---------------) + (30x + 15x - 2)\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------------------------
+--R +--+
+--R (125x + 75)\|55
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R (65x + 39)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+ +--------+
+--R (30x + 15x - 2)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R (125x + 75)\|55
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 13log(-----------------------------) + 26atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 25\|55
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 65x + 104)\|55 + (65x - 104)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 26x + 13)\|5 \|11 \|55 + 1430x - 715
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (13750x + 1375x - 4125)\|- 2x + 1 + (1250x - 1875x - 575x + 600)\|55
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^2
+--R
+--R
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R (1) -------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+r0:=-1/55*(1-2*x)^(3/2)/(3+5*x)-64/25*atanh(sqrt(5/11)*sqrt(1-2*x))/_
+ sqrt(55)+64/275*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 +--+ +--------+
+--R (- 320x - 192)atanh(---------------) + (30x + 17)\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) -----------------------------------------------------------------
+--R +--+
+--R (125x + 75)\|55
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+
+--R (160x + 96)log(-----------------------------) + (30x + 17)\|55 \|- 2x + 1
+--R 5x + 3
+--R --------------------------------------------------------------------------
+--R +--+
+--R (125x + 75)\|55
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 32log(-----------------------------) + 64atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 25\|55
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 160x + 256)\|55 + (160x - 256)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 64x + 32)\|5 \|11 \|55 + 3520x - 1760
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (13750x + 1375x - 4125)\|- 2x + 1 + (1250x - 1875x - 575x + 600)\|55
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=sqrt(1-2*x)/(3+5*x)^2
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) --------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+r0:=2/5*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/5*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 +--+ +--------+
+--R (10x + 6)atanh(---------------) - \|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) --------------------------------------------------
+--R +--+
+--R (25x + 15)\|55
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R - 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+
+--R (5x + 3)log(-------------------------------) - \|55 \|- 2x + 1
+--R 5x + 3
+--R (3) ---------------------------------------------------------------
+--R +--+
+--R (25x + 15)\|55
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-------------------------------) - 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) --------------------------------------------------------------
+--R +--+
+--R 5\|55
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+ +-+ +--+ +--+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 + (2x - 1)\|5 \|11 \|55
+--R +
+--R - 110x + 55
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (2750x + 275x - 825)\|- 2x + 1 + (- 250x + 375x + 115x - 120)\|55
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------------------
+--R 3 2
+--R 75x + 140x + 87x + 18
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+r0:=-2*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)+68*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))/sqrt(55)-sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ +--+ \|3 \|- 2x + 1
+--R (- 10x - 6)\|21 \|55 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 +--+ +--------+
+--R (340x + 204)atanh(---------------) - \|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R /
+--R +--+
+--R (5x + 3)\|55
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+
+--R +--+ +--+ \|21 \|- 2x + 1 + 3x - 5
+--R (5x + 3)\|21 \|55 log(-------------------------)
+--R 3x + 2
+--R +
+--R +--------+ +--+
+--R - 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+
+--R (170x + 102)log(-------------------------------) - \|55 \|- 2x + 1
+--R 5x + 3
+--R /
+--R +--+
+--R (5x + 3)\|55
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|21 \|- 2x + 1 + 3x - 5
+--R \|21 \|55 log(-------------------------)
+--R 3x + 2
+--R +
+--R +--------+ +--+
+--R - 55\|- 2x + 1 + (5x - 8)\|55
+--R 34log(-------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1
+--R 2\|21 \|55 atanh(---------------) - 68atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R \|55
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 +-+ +--+
+--R (- 204x - 34x + 68)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (75x - 200x + 53x + 120)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 45x + 222x - 365x + 200
+--R *
+--R +--+
+--R \|55
+--R +
+--R 2 +--+
+--R (- 330x + 715x - 275)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (- 1530x + 3978x - 748x - 2720)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (11550x + 1155x - 3465)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (30x - 113x + 129x - 40)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (- 612x + 918x + 374x - 340)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 1050x + 1575x + 483x - 504)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (1020x - 1462x - 612x + 544)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (1650x - 2585x - 770x + 825)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 990x + 3795x - 4400x + 1375
+--R /
+--R 4 3 2 +--+ +--+ 4 3
+--R (150x - 125x - 219x + 26x + 48)\|21 \|55 - 4950x + 4455x
+--R +
+--R 2
+--R 7480x - 935x - 1650
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2 +--+
+--R (450x - 1125x - 32x + 1173x + 14x - 240)\|55
+--R +
+--R 4 3 2 +--+
+--R (3300x + 880x - 2035x - 275x + 330)\|21
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 225x + 570x + 541x + 228x + 36
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+r0:=-138*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+134*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(5/11)-10*sqrt(1-2*x)/(3+5*x)+sqrt(1-2*x)/_
+ ((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--+ \|3 \|- 2x + 1
+--R (- 2070x - 2622x - 828)\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +-+ \|5 \|- 2x + 1
+--R (2010x + 2546x + 804)\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--+ +--------+
+--R (- 30x - 19)\|7 \|11 \|- 2x + 1
+--R /
+--R 2 +-+ +--+
+--R (15x + 19x + 6)\|7 \|11
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R 2 +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (1035x + 1311x + 414)\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R 2 +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (1005x + 1273x + 402)\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--+ +--------+
+--R (- 30x - 19)\|7 \|11 \|- 2x + 1
+--R /
+--R 2 +-+ +--+
+--R (15x + 19x + 6)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 69\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 67\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R 138\|3 \|11 atanh(---------------) - 134\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R \|7 \|11
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 675x + 2160x + 2763x + 1766x + 564x + 72
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+r0:=-7209/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1000*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(5/11)-1045/14*sqrt(1-2*x)/(3+5*x)+_
+ 1/2*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+52/7*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+
+--R (- 648810x - 1254366x - 807408x - 173016)\|3 \|11
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 3 2 +-+ +-+ \|5 \|- 2x + 1
+--R (630000x + 1218000x + 784000x + 168000)\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+ +--------+
+--R (- 9405x - 12228x - 3965)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (630x + 1218x + 784x + 168)\|7 \|11
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +--+
+--R (324405x + 627183x + 403704x + 86508)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +-+
+--R (315000x + 609000x + 392000x + 84000)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(-----------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--+ +--------+
+--R (- 9405x - 12228x - 3965)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (630x + 1218x + 784x + 168)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 7209\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 7000\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R 14418\|3 \|11 atanh(---------------) - 14000\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 14\|7 \|11
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^2)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ----------------------------------------------------------
+--R 6 5 4 3 2
+--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+r0:=-335579/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+6650*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-48645/98*sqrt(1-2*x)/_
+ (3+5*x)+1/3*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+139/42*sqrt(1-2*x)/_
+ ((2+3*x)^2*(3+5*x))+7261/147*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 4 3 2 +-+
+--R (- 90606330x - 235576458x - 229536036x - 99331384x - 16107792)\|3
+--R *
+--R +-+ +--------+
+--R +--+ \|3 \|- 2x + 1
+--R \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+ +-+
+--R (87979500x + 228746700x + 222881400x + 96451600x + 15640800)\|5 \|7
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (- 1313415x - 2583264x - 1692159x - 369116)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (13230x + 34398x + 33516x + 14504x + 2352)\|7 \|11
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+ +--+
+--R (45303165x + 117788229x + 114768018x + 49665692x + 8053896)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+ +-+
+--R (43989750x + 114373350x + 111440700x + 48225800x + 7820400)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(-----------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (- 1313415x - 2583264x - 1692159x - 369116)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (13230x + 34398x + 33516x + 14504x + 2352)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 335579\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 325850\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R 671158\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R - 651700\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 98\|7 \|11
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^3
+--R
+--R
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+r0:=-12803/34375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-10017/34375*_
+ sqrt(1-2*x)+21/550*(2+3*x)*sqrt(1-2*x)+1428/6875*(2+3*x)^2*_
+ sqrt(1-2*x)-1/10*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2-131/550*_
+ (2+3*x)^3*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 640150x - 768180x - 230454)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (445500x + 1103850x + 506880x - 200305x - 121976)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (1718750x + 2062500x + 618750)\|55
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (320075x + 384090x + 115227)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+ +--------+
+--R (445500x + 1103850x + 506880x - 200305x - 121976)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (1718750x + 2062500x + 618750)\|55
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 12803log(-----------------------------) + 25606atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 68750\|55
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 64015x + 102424)\|55 + (64015x - 102424)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 25606x + 12803)\|5 \|11 \|55 + 1408330x - 704165
+--R /
+--R 2 +--------+
+--R (37812500x + 3781250x - 11343750)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (3437500x - 5156250x - 1581250x + 1650000)\|55
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^3
+--R
+--R
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R (1) ----------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+r0:=-1267/1375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+623/1375*sqrt(1-2*x)-_
+ 7/2750*(46-225*x)*sqrt(1-2*x)-1/10*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-_
+ 49/275*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 63350x - 76020x - 22806)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (9900x + 12870x + 4555x + 236)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (68750x + 82500x + 24750)\|55
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (31675x + 38010x + 11403)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+ +--------+
+--R (9900x + 12870x + 4555x + 236)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (68750x + 82500x + 24750)\|55
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 1267log(-----------------------------) + 2534atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 2750\|55
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 6335x + 10136)\|55 + (6335x - 10136)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2534x + 1267)\|5 \|11 \|55 + 139370x - 69685
+--R /
+--R 2 +--------+
+--R (1512500x + 151250x - 453750)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (137500x - 206250x - 63250x + 66000)\|55
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^3
+--R
+--R
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R (1) --------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+r0:=-1/550*(1-2*x)^(3/2)/(3+5*x)^2-133/6050*(1-2*x)^(3/2)/(3+5*x)-_
+ 409/275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+409/3025*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 20450x - 24540x - 7362)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (1980x + 2245x + 632)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (13750x + 16500x + 4950)\|55
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (10225x + 12270x + 3681)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+ +--------+
+--R (1980x + 2245x + 632)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (13750x + 16500x + 4950)\|55
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 409log(-----------------------------) + 818atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 550\|55
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 2045x + 3272)\|55 + (2045x - 3272)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 818x + 409)\|5 \|11 \|55 + 44990x - 22495
+--R /
+--R 2 +--------+
+--R (302500x + 30250x - 90750)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (27500x - 41250x - 12650x + 13200)\|55
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^3
+--R
+--R
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+r0:=-1/110*(1-2*x)^(3/2)/(3+5*x)^2+67/275*atanh(sqrt(5/11)*sqrt(1-2*x))/_
+ sqrt(55)-67/550*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (3350x + 4020x + 1206)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +--+ +--------+
+--R (- 325x - 206)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (13750x + 16500x + 4950)\|55
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 - 55\|- 2x + 1 + (5x - 8)\|55
+--R (1675x + 2010x + 603)log(-------------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R (- 325x - 206)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (13750x + 16500x + 4950)\|55
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 67log(-------------------------------) - 134atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 550\|55
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 335x + 536)\|55 + (335x - 536)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (134x - 67)\|5 \|11 \|55 - 7370x + 3685
+--R /
+--R 2 +--------+
+--R (302500x + 30250x - 90750)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 27500x + 41250x + 12650x - 13200)\|55
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=sqrt(1-2*x)/(3+5*x)^3
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+r0:=1/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/10*sqrt(1-2*x)/(3+5*x)^2+_
+ 1/110*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1 +--+ +--------+
+--R (50x + 60x + 18)atanh(---------------) + (5x - 8)\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ------------------------------------------------------------------
+--R 2 +--+
+--R (2750x + 3300x + 990)\|55
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 - 55\|- 2x + 1 + (5x - 8)\|55
+--R (25x + 30x + 9)log(-------------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R (5x - 8)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (2750x + 3300x + 990)\|55
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-------------------------------) - 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) --------------------------------------------------------------
+--R +--+
+--R 110\|55
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+ +-+ +--+ +--+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 + (2x - 1)\|5 \|11 \|55
+--R +
+--R - 110x + 55
+--R /
+--R 2 +--------+
+--R (60500x + 6050x - 18150)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 5500x + 8250x + 2530x - 2640)\|55
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^3)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 375x + 925x + 855x + 351x + 54
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+r0:=6*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-2243/11*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))/sqrt(55)-1/2*sqrt(1-2*x)/(3+5*x)^2+67/22*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--+ +--+ \|3 \|- 2x + 1
+--R (3300x + 3960x + 1188)\|21 \|55 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 112150x - 134580x - 40374)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +--+ +--------+
+--R (335x + 190)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (550x + 660x + 198)\|55
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (56075x + 67290x + 20187)log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R 2 +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5
+--R (1650x + 1980x + 594)\|21 \|55 log(---------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R (335x + 190)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (550x + 660x + 198)\|55
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R 2243log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5
+--R 66\|21 \|55 log(---------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1
+--R - 132\|21 \|55 atanh(---------------) + 4486atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 22\|55
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 +-+ +--+
+--R (- 13458x - 2243x + 4486)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (4950x - 13200x + 3498x + 7920)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 3015x + 14769x - 24112x + 13120
+--R *
+--R +--+
+--R \|55
+--R +
+--R 2 +--+
+--R (- 22110x + 47135x - 18040)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (- 100935x + 262431x - 49346x - 179440)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (762300x + 76230x - 228690)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 2010x + 7501x - 8496x + 2624)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (40374x - 60561x - 24673x + 22430)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (69300x - 103950x - 31878x + 33264)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 67290x + 96449x + 40374x - 35888)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 108900x + 170610x + 50820x - 54450)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 66330x - 251955x + 289795x - 90200
+--R /
+--R 4 3 2 +--+ +--+ 4
+--R (3300x - 2750x - 4818x + 572x + 1056)\|21 \|55 - 108900x
+--R +
+--R 3 2
+--R 98010x + 164560x - 20570x - 36300
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2 +--+
+--R (- 9900x + 24750x + 704x - 25806x - 308x + 5280)\|55
+--R +
+--R 4 3 2 +--+
+--R (- 72600x - 19360x + 44770x + 6050x - 7260)\|21
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ----------------------------------------------
+--R 5 4 3 2
+--R 1125x + 3525x + 4415x + 2763x + 864x + 108
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+r0:=624*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-6665/11*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-15/2*sqrt(1-2*x)/_
+ (3+5*x)^2+sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+995/22*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+
+--R (1029600x + 1921920x + 1194336x + 247104)\|3 \|11
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+
+--R (- 999750x - 1866200x - 1159710x - 239940)\|5 \|7
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+ +--------+
+--R (14925x + 18410x + 5662)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (1650x + 3080x + 1914x + 396)\|7 \|11
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +-+
+--R (499875x + 933100x + 579855x + 119970)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+
+--R (514800x + 960960x + 597168x + 123552)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +--+ +--------+
+--R (14925x + 18410x + 5662)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (1650x + 3080x + 1914x + 396)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 6665\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 6864\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 13728\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 13330\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 22\|7 \|11
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------------------------------------------------------
+--R 6 5 4 3 2
+--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+r0:=43467/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-66325/11*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1045/14*_
+ sqrt(1-2*x)/(3+5*x)^2+1/2*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_
+ 139/14*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+34655/77*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +-+
+--R (215161650x + 545076180x + 517344234x + 218030472x + 34425864)\|3
+--R *
+--R +-+ +--------+
+--R +--+ \|3 \|- 2x + 1
+--R \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+
+--R (- 208923750x - 529273500x - 502345550x - 211709400x - 33427800)\|5
+--R *
+--R +-+ +--------+
+--R +-+ \|5 \|- 2x + 1
+--R \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (3118950x + 5926515x + 3748007x + 788875)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (34650x + 87780x + 83314x + 35112x + 5544)\|7 \|11
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (104461875x + 264636750x + 251172775x + 105854700x + 16713900)\|5
+--R *
+--R +-+ +--------+ +--+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+
+--R (107580825x + 272538090x + 258672117x + 109015236x + 17212932)\|3
+--R *
+--R +-+ +--------+ +-+
+--R +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (3118950x + 5926515x + 3748007x + 788875)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (34650x + 87780x + 83314x + 35112x + 5544)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 464275\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 478137\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 956274\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 928550\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 154\|7 \|11
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R +--------+
+--R \|- 2x + 1
+--R -----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+r0:=2528082/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_
+ 551075/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-_
+ 182335/294*sqrt(1-2*x)/(3+5*x)^2+1/3*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2)+_
+ 29/7*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+4042/49*sqrt(1-2*x)/((2+3*x)*_
+ (3+5*x)^2)+4031135/1078*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 37542017700x + 120134456640x + 153671992452x + 98221041864x
+--R +
+--R 31368441456x + 4004481888
+--R *
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R \|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R - 36453611250x - 116651556000x - 149216782050x - 95373448100x
+--R +
+--R - 30459017400x - 3888385200
+--R *
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R \|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+
+--R (544203225x + 1396877220x + 1343346156x + 573620246x + 91763734)\|7
+--R *
+--R +--+ +--------+
+--R \|11 \|- 2x + 1
+--R /
+--R 5 4 3 2 +-+ +--+
+--R (727650x + 2328480x + 2978514x + 1903748x + 607992x + 77616)\|7 \|11
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 18226805625x + 58325778000x + 74608391025x + 47686724050x
+--R +
+--R 15229508700x + 1944192600
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 18771008850x + 60067228320x + 76835996226x + 49110520932x
+--R +
+--R 15684220728x + 2002240944
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+
+--R (544203225x + 1396877220x + 1343346156x + 573620246x + 91763734)\|7
+--R *
+--R +--+ +--------+
+--R \|11 \|- 2x + 1
+--R /
+--R 5 4 3 2 +-+ +--+
+--R (727650x + 2328480x + 2978514x + 1903748x + 607992x + 77616)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 27002675\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 27808902\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 55617804\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 54005350\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 1078\|7 \|11
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^6*(3+5*x)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 7290x - 29889x - 49329x - 39312x - 11340x + 5040x + 5264x
+--R +
+--R 1664x + 192
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+r0:=-1294139/640*(1-2*x)^(5/2)+559433/128*(1-2*x)^(7/2)-_
+ 564235/128*(1-2*x)^(9/2)+3658095/1408*(1-2*x)^(11/2)-_
+ 1580985/1664*(1-2*x)^(13/2)+136647/640*(1-2*x)^(15/2)-_
+ 59049/2176*(1-2*x)^(17/2)+3645/2432*(1-2*x)^(19/2)
+--R
+--R
+--R (2)
+--R 9 8 7 6 5
+--R - 177219900x - 806871780x - 1489122063x - 1322260632x - 372044232x
+--R +
+--R 4 3 2
+--R 342957860x + 377036800x + 136800176x - 7336416x - 51677856
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 230945
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7 6 5
+--R - 177219900x - 806871780x - 1489122063x - 1322260632x - 372044232x
+--R +
+--R 4 3 2
+--R 342957860x + 377036800x + 136800176x - 7336416x - 51677856
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 230945
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^5*(3+5*x)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R (- 2430x - 8343x - 10881x - 5850x + 120x + 1600x + 688x + 96)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+r0:=-184877/320*(1-2*x)^(5/2)+8575/8*(1-2*x)^(7/2)-173215/192*(1-2*x)^(9/2)+_
+ 37485/88*(1-2*x)^(11/2)-97335/832*(1-2*x)^(13/2)+_
+ 351/20*(1-2*x)^(15/2)-1215/1088*(1-2*x)^(17/2)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4
+--R - 10424700x - 40216176x - 59295159x - 35057799x + 5198095x
+--R +
+--R 3 2
+--R 19014940x + 9775332x + 488008x - 3012632
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 36465
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4
+--R - 10424700x - 40216176x - 59295159x - 35057799x + 5198095x
+--R +
+--R 3 2
+--R 19014940x + 9775332x + 488008x - 3012632
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 36465
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (1) (- 810x - 2241x - 2133x - 528x + 392x + 272x + 48)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+r0:=-26411/160*(1-2*x)^(5/2)+8183/32*(1-2*x)^(7/2)-8281/48*(1-2*x)^(9/2)+_
+ 10773/176*(1-2*x)^(11/2)-4671/416*(1-2*x)^(13/2)+27/32*(1-2*x)^(15/2)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R - 231660x - 730620x - 793395x - 184090x + 296840x + 243312x
+--R +
+--R 36368x - 66592
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R - 231660x - 730620x - 793395x - 184090x + 296840x + 243312x
+--R +
+--R 36368x - 66592
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1) (- 270x - 567x - 333x + 46x + 100x + 24)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+r0:=-3773/80*(1-2*x)^(5/2)+469/8*(1-2*x)^(7/2)-119/4*(1-2*x)^(9/2)+_
+ 621/88*(1-2*x)^(11/2)-135/208*(1-2*x)^(13/2)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2 +--------+
+--R (- 29700x - 72360x - 48065x + 15945x + 31589x + 8666x - 8494)\|- 2x + 1
+--R -----------------------------------------------------------------------------
+--R 715
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2 +--------+
+--R (- 29700x - 72360x - 48065x + 15945x + 31589x + 8666x - 8494)\|- 2x + 1
+--R -----------------------------------------------------------------------------
+--R 715
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1) (- 90x - 129x - 25x + 32x + 12)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+r0:=-539/40*(1-2*x)^(5/2)+101/8*(1-2*x)^(7/2)-103/24*(1-2*x)^(9/2)+_
+ 45/88*(1-2*x)^(11/2)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 2700x - 4580x - 755x + 2484x + 1216x - 764)\|- 2x + 1
+--R (2) -------------------------------------------------------------
+--R 165
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 2700x - 4580x - 755x + 2484x + 1216x - 764)\|- 2x + 1
+--R (3) -------------------------------------------------------------
+--R 165
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)
+--R
+--R
+--R 3 2 +--------+
+--R (1) (- 30x - 23x + 7x + 6)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+r0:=-77/20*(1-2*x)^(5/2)+17/7*(1-2*x)^(7/2)-5/12*(1-2*x)^(9/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 700x - 640x + 393x + 437x - 193)\|- 2x + 1
+--R (2) -------------------------------------------------
+--R 105
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 700x - 640x + 393x + 437x - 193)\|- 2x + 1
+--R (3) -------------------------------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)
+--R
+--R
+--R 2 +--------+
+--R (1) (- 10x - x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+r0:=-11/10*(1-2*x)^(5/2)+5/14*(1-2*x)^(7/2)
+--R
+--R
+--R 3 2 +--------+
+--R (- 100x - 4x + 79x - 26)\|- 2x + 1
+--R (2) -------------------------------------
+--R 35
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 100x - 4x + 79x - 26)\|- 2x + 1
+--R (3) -------------------------------------
+--R 35
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)
+--R
+--R
+--R 2 +--------+
+--R (- 10x - x + 3)\|- 2x + 1
+--R (1) ---------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+r0:=-2/27*(1-2*x)^(3/2)-1/3*(1-2*x)^(5/2)+14/27*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(7/3)-14/27*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1 2 +-+ +--------+
+--R 14\|7 atanh(---------------) + (- 36x + 40x - 25)\|3 \|- 2x + 1
+--R +-+
+--R \|7
+--R (2) -----------------------------------------------------------------
+--R +-+
+--R 27\|3
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 7\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +--------+
+--R (- 36x + 40x - 25)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 27\|3
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 7\|7 log(---------------------------------) - 14\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R --------------------------------------------------------------------------
+--R +-+
+--R 27\|3
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^2
+--R
+--R
+--R 2 +--------+
+--R (- 10x - x + 3)\|- 2x + 1
+--R (1) ---------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+r0:=76/189*(1-2*x)^(3/2)+1/21*(1-2*x)^(5/2)/(2+3*x)-76/27*_
+ atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+76/27*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R (- 228x - 152)\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +-+ +--------+
+--R (- 60x + 212x + 175)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (81x + 54)\|3
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (114x + 76)\|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +--------+
+--R (- 60x + 212x + 175)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (81x + 54)\|3
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 38\|7 log(-------------------------------) + 76\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -------------------------------------------------------------------------
+--R +-+
+--R 27\|3
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^3
+--R
+--R
+--R 2 +--------+
+--R (- 10x - x + 3)\|- 2x + 1
+--R (1) ---------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+r0:=1/42*(1-2*x)^(5/2)/(2+3*x)^2-71/126*(1-2*x)^(3/2)/(2+3*x)+_
+ 71/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-71/63*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1
+--R (1278x + 1704x + 568)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (- 120x - 235x - 101)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (162x + 216x + 72)\|21
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 - 21\|- 2x + 1 + (3x - 5)\|21
+--R (639x + 852x + 284)log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (- 120x - 235x - 101)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (162x + 216x + 72)\|21
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 71log(-------------------------------) - 142atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 18\|21
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 213x + 355)\|21 + (213x - 355)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (142x - 71)\|3 \|7 \|21 - 2982x + 1491
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (2268x + 378x - 756)\|- 2x + 1 + (- 324x + 486x + 198x - 180)\|21
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^4
+--R
+--R
+--R 2 +--------+
+--R (- 10x - x + 3)\|- 2x + 1
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+r0:=1/63*(1-2*x)^(5/2)/(2+3*x)^3-52/189*(1-2*x)^(3/2)/(2+3*x)^2-_
+ 104/189*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+52/189*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (- 2808x - 5616x - 3744x - 832)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (792x + 664x + 107)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (5103x + 10206x + 6804x + 1512)\|21
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 3 2 21\|- 2x + 1 + (3x - 5)\|21
+--R (1404x + 2808x + 1872x + 416)log(-----------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (792x + 664x + 107)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (5103x + 10206x + 6804x + 1512)\|21
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 52log(-----------------------------) + 104atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ----------------------------------------------------------------
+--R +--+
+--R 189\|21
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 156x + 260)\|21 + (156x - 260)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 104x + 52)\|3 \|7 \|21 + 2184x - 1092
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (23814x + 3969x - 7938)\|- 2x + 1 + (3402x - 5103x - 2079x + 1890)\|21
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^5
+--R
+--R
+--R 2 +--------+
+--R (- 10x - x + 3)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+r0:=1/84*(1-2*x)^(5/2)/(2+3*x)^4-137/756*(1-2*x)^(3/2)/(2+3*x)^3-_
+ 137/5292*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+137/1512*_
+ sqrt(1-2*x)/(2+3*x)^2-137/10584*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 4 3 2 \|3 \|- 2x + 1
+--R (- 22194x - 59184x - 59184x - 26304x - 4384)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (- 3699x + 13245x + 7990x - 970)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (857304x + 2286144x + 2286144x + 1016064x + 169344)\|21
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (11097x + 29592x + 29592x + 13152x + 2192)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (- 3699x + 13245x + 7990x - 970)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (857304x + 2286144x + 2286144x + 1016064x + 169344)\|21
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 137log(-----------------------------) + 274atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 10584\|21
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 411x + 685)\|21 + (411x - 685)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 274x + 137)\|3 \|7 \|21 + 5754x - 2877
+--R /
+--R 2 +--------+
+--R (1333584x + 222264x - 444528)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (190512x - 285768x - 116424x + 105840)\|21
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^6
+--R
+--R
+--R 2 +--------+
+--R (- 10x - x + 3)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+r0:=1/105*(1-2*x)^(5/2)/(2+3*x)^5-17/126*(1-2*x)^(3/2)/(2+3*x)^4-_
+ 17/6174*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+17/378*_
+ sqrt(1-2*x)/(2+3*x)^3-17/5292*sqrt(1-2*x)/(2+3*x)^2-17/12348*_
+ sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (- 41310x - 137700x - 183600x - 122400x - 40800x - 5440)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 6885x - 23715x + 48252x + 23998x - 7912)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R (15002820x + 50009400x + 66679200x + 44452800x + 14817600x + 1975680)
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (20655x + 68850x + 91800x + 61200x + 20400x + 2720)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 6885x - 23715x + 48252x + 23998x - 7912)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R (15002820x + 50009400x + 66679200x + 44452800x + 14817600x + 1975680)
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 17log(-----------------------------) + 34atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 12348\|21
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 51x + 85)\|21 + (51x - 85)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 34x + 17)\|3 \|7 \|21 + 714x - 357
+--R /
+--R 2 +--------+
+--R (1555848x + 259308x - 518616)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (222264x - 333396x - 135828x + 123480)\|21
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R (- 4050x - 13635x - 17388x - 9039x + 376x + 2536x + 1056x + 144)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+r0:=-290521/320*(1-2*x)^(5/2)+54439/32*(1-2*x)^(7/2)-832951/576*_
+ (1-2*x)^(9/2)+121359/176*(1-2*x)^(11/2)-159111/832*(1-2*x)^(13/2)+_
+ 927/32*(1-2*x)^(15/2)-2025/1088*(1-2*x)^(17/2)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4
+--R - 52123500x - 197142660x - 284055255x - 161801280x + 29120005x
+--R +
+--R 3 2
+--R 90028420x + 44740356x + 1821784x - 13931096
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 109395
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4
+--R - 52123500x - 197142660x - 284055255x - 161801280x + 29120005x
+--R +
+--R 3 2
+--R 90028420x + 44740356x + 1821784x - 13931096
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 109395
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (1) (- 1350x - 3645x - 3366x - 769x + 638x + 420x + 72)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+r0:=-41503/160*(1-2*x)^(5/2)+13013/32*(1-2*x)^(7/2)-39977/144*(1-2*x)^(9/2)+_
+ 17541/176*(1-2*x)^(11/2)-7695/416*(1-2*x)^(13/2)+45/32*(1-2*x)^(15/2)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R - 1158300x - 3564000x - 3749895x - 776255x + 1436365x + 1121793x
+--R +
+--R 155842x - 307478
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6435
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R - 1158300x - 3564000x - 3749895x - 776255x + 1436365x + 1121793x
+--R +
+--R 155842x - 307478
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6435
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1) (- 450x - 915x - 512x + 85x + 156x + 36)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+r0:=-5929/80*(1-2*x)^(5/2)+187/2*(1-2*x)^(7/2)-3467/72*(1-2*x)^(9/2)+_
+ 255/22*(1-2*x)^(11/2)-225/208*(1-2*x)^(13/2)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 445500x - 1050300x - 661435x + 248990x + 441543x + 114182x
+--R +
+--R - 117478
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6435
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 445500x - 1050300x - 661435x + 248990x + 441543x + 114182x
+--R +
+--R - 117478
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6435
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2
+--R
+--R
+--R 4 3 2 +--------+
+--R (1) (- 150x - 205x - 34x + 51x + 18)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+r0:=-847/40*(1-2*x)^(5/2)+1133/56*(1-2*x)^(7/2)-505/72*(1-2*x)^(9/2)+_
+ 75/88*(1-2*x)^(11/2)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 94500x - 152600x - 19385x + 82617x + 37753x - 24617)\|- 2x + 1
+--R (2) ----------------------------------------------------------------------
+--R 3465
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 94500x - 152600x - 19385x + 82617x + 37753x - 24617)\|- 2x + 1
+--R (3) ----------------------------------------------------------------------
+--R 3465
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^2
+--R
+--R
+--R 3 2 +--------+
+--R (1) (- 50x - 35x + 12x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+r0:=-121/20*(1-2*x)^(5/2)+55/14*(1-2*x)^(7/2)-25/36*(1-2*x)^(9/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 3500x - 2900x + 1977x + 1948x - 887)\|- 2x + 1
+--R (2) -----------------------------------------------------
+--R 315
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 3500x - 2900x + 1977x + 1948x - 887)\|- 2x + 1
+--R (3) -----------------------------------------------------
+--R 315
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1
+--R (1) ------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+r0:=2/81*(1-2*x)^(3/2)-26/63*(1-2*x)^(5/2)-5/21*(1-2*x)^(5/2)*(3+5*x)-_
+ 14/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+14/81*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R - 98\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +--------+
+--R (- 2700x + 144x + 1853x - 527)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 567\|3
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 49\|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--------+
+--R (- 2700x + 144x + 1853x - 527)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 567\|3
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 7\|7 log(-------------------------------) + 14\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ------------------------------------------------------------------------
+--R +-+
+--R 81\|3
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^2
+--R
+--R
+--R 3 2 +--------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1
+--R (1) ------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+r0:=-146/567*(1-2*x)^(3/2)-5/9*(1-2*x)^(5/2)-1/63*(1-2*x)^(5/2)/(2+3*x)+_
+ 146/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-146/81*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R (438x + 292)\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +--------+
+--R (- 540x + 300x - 187x - 425)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (243x + 162)\|3
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (219x + 146)\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--------+
+--R (- 540x + 300x - 187x - 425)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (243x + 162)\|3
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 73\|7 log(---------------------------------) - 146\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 81\|3
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^3
+--R
+--R
+--R 3 2 +--------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1
+--R (1) ------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+r0:=2873/3969*(1-2*x)^(3/2)-1/126*(1-2*x)^(5/2)/(2+3*x)^2+_
+ 47/294*(1-2*x)^(5/2)/(2+3*x)-2873/81*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+2873/567*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1
+--R (- 51714x - 68952x - 22984)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (- 1800x + 5520x + 10195x + 3803)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (1458x + 1944x + 648)\|21
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 21\|- 2x + 1 + (3x - 5)\|21
+--R (25857x + 34476x + 11492)log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (- 1800x + 5520x + 10195x + 3803)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (1458x + 1944x + 648)\|21
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 2873log(-----------------------------) + 5746atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 162\|21
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 8619x + 14365)\|21 + (8619x - 14365)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 5746x + 2873)\|3 \|7 \|21 + 120666x - 60333
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (20412x + 3402x - 6804)\|- 2x + 1 + (2916x - 4374x - 1782x + 1620)\|21
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^4
+--R
+--R
+--R 3 2 +--------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1
+--R (1) ------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+r0:=-1/189*(1-2*x)^(5/2)/(2+3*x)^3+209/2646*(1-2*x)^(5/2)/(2+3*x)^2-_
+ 7559/7938*(1-2*x)^(3/2)/(2+3*x)+7559/567*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)-7559/3969*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (408186x + 816372x + 544248x + 120944)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (- 37800x - 100809x - 82493x - 21424)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (30618x + 61236x + 40824x + 9072)\|21
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (204093x + 408186x + 272124x + 60472)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (- 37800x - 100809x - 82493x - 21424)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (30618x + 61236x + 40824x + 9072)\|21
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 7559log(-------------------------------) - 15118atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ----------------------------------------------------------------------
+--R +--+
+--R 1134\|21
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 22677x + 37795)\|21 + (22677x - 37795)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (15118x - 7559)\|3 \|7 \|21 - 317478x + 158739
+--R /
+--R 2 +--------+
+--R (142884x + 23814x - 47628)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 20412x + 30618x + 12474x - 11340)\|21
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^5
+--R
+--R
+--R 3 2 +--------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+r0:=-1/252*(1-2*x)^(5/2)/(2+3*x)^4+277/5292*(1-2*x)^(5/2)/(2+3*x)^3-_
+ 14423/31752*(1-2*x)^(3/2)/(2+3*x)^2-14423/15876*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+14423/31752*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 2336526x - 6230736x - 6230736x - 2769216x - 461536)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (668979x + 988035x + 453730x + 60890)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (2571912x + 6858432x + 6858432x + 3048192x + 508032)\|21
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (1168263x + 3115368x + 3115368x + 1384608x + 230768)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (668979x + 988035x + 453730x + 60890)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (2571912x + 6858432x + 6858432x + 3048192x + 508032)\|21
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 14423log(-----------------------------) + 28846atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 31752\|21
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 43269x + 72115)\|21 + (43269x - 72115)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 28846x + 14423)\|3 \|7 \|21 + 605766x - 302883
+--R /
+--R 2 +--------+
+--R (4000752x + 666792x - 1333584)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (571536x - 857304x - 349272x + 317520)\|21
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^6
+--R
+--R
+--R 3 2 +--------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+r0:=-1/315*(1-2*x)^(5/2)/(2+3*x)^5+23/588*(1-2*x)^(5/2)/(2+3*x)^4-_
+ 4693/15876*(1-2*x)^(3/2)/(2+3*x)^3-4693/111132*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+4693/31752*sqrt(1-2*x)/(2+3*x)^2-_
+ 4693/222264*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 11403990x - 38013300x - 50684400x - 33789600x - 11263200x
+--R +
+--R - 1501760
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 1900665x + 5801265x + 8540988x + 2143262x - 292028)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 270050760x + 900169200x + 1200225600x + 800150400x + 266716800x
+--R +
+--R 35562240
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (5701995x + 19006650x + 25342200x + 16894800x + 5631600x + 750880)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 1900665x + 5801265x + 8540988x + 2143262x - 292028)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 270050760x + 900169200x + 1200225600x + 800150400x + 266716800x
+--R +
+--R 35562240
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 4693log(-----------------------------) + 9386atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 222264\|21
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 14079x + 23465)\|21 + (14079x - 23465)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 9386x + 4693)\|3 \|7 \|21 + 197106x - 98553
+--R /
+--R 2 +--------+
+--R (28005264x + 4667544x - 9335088)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (4000752x - 6001128x - 2444904x + 2222640)\|21
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^7
+--R
+--R
+--R 3 2 +--------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+r0:=-1/378*(1-2*x)^(5/2)/(2+3*x)^6+59/1890*(1-2*x)^(5/2)/(2+3*x)^5-_
+ 991/4536*(1-2*x)^(3/2)/(2+3*x)^4-991/222264*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+991/13608*sqrt(1-2*x)/(2+3*x)^3-_
+ 991/190512*sqrt(1-2*x)/(2+3*x)^2-991/444528*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 7224390x - 28897560x - 48162600x - 42811200x - 21405600x
+--R +
+--R - 5708160x - 634240
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R (- 1204065x - 4950045x + 6094818x + 9658494x + 1262200x - 858112)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3
+--R 1620304560x + 6481218240x + 10802030400x + 9601804800x
+--R +
+--R 2
+--R 4800902400x + 1280240640x + 142248960
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 3612195x + 14448780x + 24081300x + 21405600x + 10702800x
+--R +
+--R 2854080x + 317120
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R (- 1204065x - 4950045x + 6094818x + 9658494x + 1262200x - 858112)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3
+--R 1620304560x + 6481218240x + 10802030400x + 9601804800x
+--R +
+--R 2
+--R 4800902400x + 1280240640x + 142248960
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 991log(-----------------------------) + 1982atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 444528\|21
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 2973x + 4955)\|21 + (2973x - 4955)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 1982x + 991)\|3 \|7 \|21 + 41622x - 20811
+--R /
+--R 2 +--------+
+--R (56010528x + 9335088x - 18670176)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (8001504x - 12002256x - 4889808x + 4445280)\|21
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 20250x - 80325x - 127845x - 97359x - 25237x + 13808x + 12888x
+--R +
+--R 3888x + 432
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+r0:=-3195731/640*(1-2*x)^(5/2)+1405173/128*(1-2*x)^(7/2)-_
+ 4324397/384*(1-2*x)^(9/2)+9504551/1408*(1-2*x)^(11/2)-_
+ 4177401/1664*(1-2*x)^(13/2)+73431/128*(1-2*x)^(15/2)-_
+ 161325/2176*(1-2*x)^(17/2)+10125/2432*(1-2*x)^(19/2)
+--R
+--R
+--R (2)
+--R 9 8 7 6
+--R - 1476832500x - 6503854500x - 11568656385x - 9793273050x
+--R +
+--R 5 4 3 2
+--R - 2388733575x + 2741637820x + 2751200080x + 942365544x - 70133984x
+--R +
+--R - 369438704
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 692835
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7 6
+--R - 1476832500x - 6503854500x - 11568656385x - 9793273050x
+--R +
+--R 5 4 3 2
+--R - 2388733575x + 2741637820x + 2751200080x + 942365544x - 70133984x
+--R +
+--R - 369438704
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 692835
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R (- 6750x - 22275x - 27765x - 13943x + 883x + 4014x + 1620x + 216)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+r0:=-456533/320*(1-2*x)^(5/2)+43197/16*(1-2*x)^(7/2)-_
+ 444983/192*(1-2*x)^(9/2)+98209/88*(1-2*x)^(11/2)-_
+ 260055/832*(1-2*x)^(13/2)+765/16*(1-2*x)^(15/2)-3375/1088*(1-2*x)^(17/2)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4
+--R - 28957500x - 107335800x - 151076475x - 82806465x + 17644040x
+--R +
+--R 3 2
+--R 47302655x + 22736811x + 717734x - 7158706
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 36465
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4
+--R - 28957500x - 107335800x - 151076475x - 82806465x + 17644040x
+--R +
+--R 3 2
+--R 47302655x + 22736811x + 717734x - 7158706
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 36465
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^3
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (1) (- 2250x - 5925x - 5305x - 1111x + 1035x + 648x + 108)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+r0:=-65219/160*(1-2*x)^(5/2)+20691/32*(1-2*x)^(7/2)-_
+ 21439/48*(1-2*x)^(9/2)+28555/176*(1-2*x)^(11/2)-975/32*(1-2*x)^(13/2)+_
+ 75/32*(1-2*x)^(15/2)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R - 49500x - 148500x - 151275x - 27520x + 59255x + 44166x + 5684x
+--R +
+--R - 12136
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 165
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R - 49500x - 148500x - 151275x - 27520x + 59255x + 44166x + 5684x
+--R +
+--R - 12136
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 165
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^3
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1) (- 750x - 1475x - 785x + 153x + 243x + 54)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 500
+r0:=-9317/80*(1-2*x)^(5/2)+8349/56*(1-2*x)^(7/2)-935/12*(1-2*x)^(9/2)+_
+ 1675/88*(1-2*x)^(11/2)-375/208*(1-2*x)^(13/2)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 1732500x - 3948000x - 2351825x + 996295x + 1597776x + 389509x
+--R +
+--R - 421301
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 15015
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 1732500x - 3948000x - 2351825x + 996295x + 1597776x + 389509x
+--R +
+--R - 421301
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 15015
+--R Type: Union(Expression(Integer),...)
+--E 363
+
+--S 364 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^3
+--R
+--R
+--R 4 3 2 +--------+
+--R (1) (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+r0:=-1331/40*(1-2*x)^(5/2)+1815/56*(1-2*x)^(7/2)-275/24*(1-2*x)^(9/2)+_
+ 125/88*(1-2*x)^(11/2)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 52500x - 80500x - 7225x + 43482x + 18593x - 12592)\|- 2x + 1
+--R (2) --------------------------------------------------------------------
+--R 1155
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 52500x - 80500x - 7225x + 43482x + 18593x - 12592)\|- 2x + 1
+--R (3) --------------------------------------------------------------------
+--R 1155
+--R Type: Union(Expression(Integer),...)
+--E 368
+
+--S 369 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1
+--R (1) ----------------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+r0:=2/27*(1-2*x)^(3/2)*(3+5*x)^3+14/243*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(7/3)-72742/14175*sqrt(1-2*x)-919/4725*(3+5*x)^2*_
+ sqrt(1-2*x)+26/315*(3+5*x)^3*sqrt(1-2*x)-1/8505*(14711+17779*x)*_
+ sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R 98\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 31500x - 23400x + 17649x + 15679x - 7456)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 1701\|3
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 49\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 31500x - 23400x + 17649x + 15679x - 7456)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 1701\|3
+--R Type: Union(Expression(Integer),...)
+--E 373
+
+--S 374 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 7\|7 log(---------------------------------) - 14\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R --------------------------------------------------------------------------
+--R +-+
+--R 243\|3
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1
+--R (1) ----------------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+r0:=-1/3*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)-8/9*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(7/3)-1832/315*sqrt(1-2*x)+2/63*(4-239*x)*sqrt(1-2*x)+_
+ 67/35*(3+5*x)^2*sqrt(1-2*x)-2/7*(3+5*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R (- 168x - 112)\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 1500x - 780x + 1005x + 442x - 85)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (189x + 126)\|3
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (84x + 56)\|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 1500x - 780x + 1005x + 442x - 85)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (189x + 126)\|3
+--R Type: Union(Expression(Integer),...)
+--E 378
+
+--S 379 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 4\|7 log(-------------------------------) + 8\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------
+--R +-+
+--R 9\|3
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1
+--R (1) ----------------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2+887/27*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+13*sqrt(1-2*x)-5/54*(67-343*x)*sqrt(1-2*x)-_
+ 31/3*(3+5*x)^2*sqrt(1-2*x)+6*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1
+--R (15966x + 21288x + 7096)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 2 +--+ +--------+
+--R (- 1800x - 570x - 2965x - 1367)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (486x + 648x + 216)\|21
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 - 21\|- 2x + 1 + (3x - 5)\|21
+--R (7983x + 10644x + 3548)log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 2 +--+ +--------+
+--R (- 1800x - 570x - 2965x - 1367)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (486x + 648x + 216)\|21
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 887log(-------------------------------) - 1774atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 54\|21
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 2661x + 4435)\|21 + (2661x - 4435)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (1774x - 887)\|3 \|7 \|21 - 37254x + 18627
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (6804x + 1134x - 2268)\|- 2x + 1 + (- 972x + 1458x + 594x - 540)\|21
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1
+--R (1) ----------------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+r0:=-1/9*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3-36038/567*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)-830/27*sqrt(1-2*x)+5/567*(1163-7265*x)*_
+ sqrt(1-2*x)+251/63*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)+2*(3+5*x)^3*_
+ sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (- 973026x - 1946052x - 1297368x - 288304)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 31500x + 81900x + 259614x + 199243x + 47939)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (15309x + 30618x + 20412x + 4536)\|21
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (486513x + 973026x + 648684x + 144152)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 31500x + 81900x + 259614x + 199243x + 47939)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (15309x + 30618x + 20412x + 4536)\|21
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 18019log(-----------------------------) + 36038atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 567\|21
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 54057x + 90095)\|21 + (54057x - 90095)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 36038x + 18019)\|3 \|7 \|21 + 756798x - 378399
+--R /
+--R 2 +--------+
+--R (71442x + 11907x - 23814)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (10206x - 15309x - 6237x + 5670)\|21
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1
+--R (1) ----------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+r0:=-1/12*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4+13243/588*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)-5305/588*sqrt(1-2*x)+337/392*(3+5*x)*_
+ sqrt(1-2*x)/(2+3*x)+13/56*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2+_
+ (3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (2145366x + 5720976x + 5720976x + 2542656x + 423776)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 196000x - 661639x - 788415x - 401850x - 74810)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (95256x + 254016x + 254016x + 112896x + 18816)\|21
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (1072683x + 2860488x + 2860488x + 1271328x + 211888)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 196000x - 661639x - 788415x - 401850x - 74810)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (95256x + 254016x + 254016x + 112896x + 18816)\|21
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 13243log(-------------------------------) - 26486atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------
+--R +--+
+--R 1176\|21
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 39729x + 66215)\|21 + (39729x - 66215)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (26486x - 13243)\|3 \|7 \|21 - 556206x + 278103
+--R /
+--R 2 +--------+
+--R (148176x + 24696x - 49392)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 21168x + 31752x + 12936x - 11760)\|21
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+r0:=-1/15*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5-13892/9261*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+1/1323*(136-19*x)*sqrt(1-2*x)/(2+3*x)^2-_
+ 3335/3087*sqrt(1-2*x)/(2+3*x)-67/315*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3+_
+ 3/5*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 16878780x - 56262600x - 75016800x - 50011200x - 16670400x
+--R +
+--R - 2222720
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (4904370x + 10375830x + 7992771x + 2619854x + 300049)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R (11252115x + 37507050x + 50009400x + 33339600x + 11113200x + 1481760)
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (8439390x + 28131300x + 37508400x + 25005600x + 8335200x + 1111360)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (4904370x + 10375830x + 7992771x + 2619854x + 300049)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R (11252115x + 37507050x + 50009400x + 33339600x + 11113200x + 1481760)
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 6946log(-----------------------------) + 13892atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 9261\|21
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 20838x + 34730)\|21 + (20838x - 34730)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 13892x + 6946)\|3 \|7 \|21 + 291732x - 145866
+--R /
+--R 2 +--------+
+--R (1166886x + 194481x - 388962)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (166698x - 250047x - 101871x + 92610)\|21
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^7
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+r0:=-1/18*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6-15313/222264*_
+ atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/158760*(9323-8405*x)*_
+ sqrt(1-2*x)/(2+3*x)^3-43207/63504*sqrt(1-2*x)/(2+3*x)^2-_
+ 15313/444528*sqrt(1-2*x)/(2+3*x)-653/2520*(3+5*x)^2*_
+ sqrt(1-2*x)/(2+3*x)^4+2/5*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 111631770x - 446527080x - 744211800x - 661521600x - 330760800x
+--R +
+--R - 88202880x - 9800320
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R - 18605295x + 46991565x + 122053374x + 75153042x + 10947400x
+--R +
+--R - 1660816
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3
+--R 1620304560x + 6481218240x + 10802030400x + 9601804800x
+--R +
+--R 2
+--R 4800902400x + 1280240640x + 142248960
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 55815885x + 223263540x + 372105900x + 330760800x + 165380400x
+--R +
+--R 44101440x + 4900160
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R - 18605295x + 46991565x + 122053374x + 75153042x + 10947400x
+--R +
+--R - 1660816
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3
+--R 1620304560x + 6481218240x + 10802030400x + 9601804800x
+--R +
+--R 2
+--R 4800902400x + 1280240640x + 142248960
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 15313log(-----------------------------) + 30626atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 444528\|21
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 45939x + 76565)\|21 + (45939x - 76565)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 30626x + 15313)\|3 \|7 \|21 + 643146x - 321573
+--R /
+--R 2 +--------+
+--R (56010528x + 9335088x - 18670176)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (8001504x - 12002256x - 4889808x + 4445280)\|21
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 4 3 2 +--------+
+--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+r0:=-1/21*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^7-4369/605052*_
+ atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/61740*(2201-2675*x)*_
+ sqrt(1-2*x)/(2+3*x)^4-5471/13230*sqrt(1-2*x)/(2+3*x)^3-_
+ 4369/518616*sqrt(1-2*x)/(2+3*x)^2-4369/1210104*sqrt(1-2*x)/_
+ (2+3*x)-173/735*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5+2/7*(3+5*x)^3*_
+ sqrt(1-2*x)/(2+3*x)^6
+--R
+--R
+--R (2)
+--R 7 6 5 4 3
+--R - 95550030x - 445900140x - 891800280x - 990889200x - 660592800x
+--R +
+--R 2
+--R - 264237120x - 58719360x - 5592320
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 6 5 4 3 2
+--R - 15925005x - 76086135x + 42669876x + 182748162x + 98441652x
+--R +
+--R - 606784x - 7033976
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 7 6 5 4
+--R 13232487240x + 61751607120x + 123503214240x + 137225793600x
+--R +
+--R 3 2
+--R 91483862400x + 36593544960x + 8131898880x + 774466560
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R 47775015x + 222950070x + 445900140x + 495444600x + 330296400x
+--R +
+--R 2
+--R 132118560x + 29359680x + 2796160
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 6 5 4 3 2
+--R - 15925005x - 76086135x + 42669876x + 182748162x + 98441652x
+--R +
+--R - 606784x - 7033976
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 7 6 5 4
+--R 13232487240x + 61751607120x + 123503214240x + 137225793600x
+--R +
+--R 3 2
+--R 91483862400x + 36593544960x + 8131898880x + 774466560
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 4369log(-----------------------------) + 8738atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 1210104\|21
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 13107x + 21845)\|21 + (13107x - 21845)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 8738x + 4369)\|3 \|7 \|21 + 183498x - 91749
+--R /
+--R 2 +--------+
+--R (152473104x + 25412184x - 50824368)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (21781872x - 32672808x - 13311144x + 12101040)\|21
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^6/(3+5*x)
+--R
+--R
+--R 7 6 5 4 2 +--------+
+--R (- 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+r0:=2/75*(1-2*x)^(3/2)*(2+3*x)^6-22/390625*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(11/5)-16097737918/1508203125*sqrt(1-2*x)-18395813/12065625*(2+3*x)*_
+ sqrt(1-2*x)-32816296/100546875*(2+3*x)^2*sqrt(1-2*x)-_
+ 6469823/84459375*(2+3*x)^3*sqrt(1-2*x)-36202/2413125*(2+3*x)^4*_
+ sqrt(1-2*x)+683/53625*(2+3*x)^5*sqrt(1-2*x)+2/195*(2+3*x)^6*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 66066\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 7 6 5 4
+--R - 45608062500x - 150857437500x - 174123928125x - 49094797500x
+--R +
+--R 3 2
+--R 61883481375x + 56176961670x + 9645684935x - 15379193944
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 1173046875\|5
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 33033\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 7 6 5 4
+--R - 45608062500x - 150857437500x - 174123928125x - 49094797500x
+--R +
+--R 3 2
+--R 61883481375x + 56176961670x + 9645684935x - 15379193944
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 1173046875\|5
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 390625\|5
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (- 486x - 1377x - 1350x - 360x + 240x + 176x + 32)\|- 2x + 1
+--R (1) ------------------------------------------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^5-22/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(11/5)-158985118/33515625*sqrt(1-2*x)-2803796/20109375*(2+3*x)^2*_
+ sqrt(1-2*x)-467323/16891875*(2+3*x)^3*sqrt(1-2*x)+_
+ 6673/482625*(2+3*x)^4*sqrt(1-2*x)+158/10725*(2+3*x)^5*sqrt(1-2*x)-_
+ 1/100546875*(119316702+198601625*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 66066\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R - 3508312500x - 9100350000x - 6683000625x + 1659418875x
+--R +
+--R 2
+--R 4276774170x + 1321809935x - 1180568944
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 234609375\|5
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 33033\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 6 5 4 3
+--R - 3508312500x - 9100350000x - 6683000625x + 1659418875x
+--R +
+--R 2
+--R 4276774170x + 1321809935x - 1180568944
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 234609375\|5
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 78125\|5
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 162x - 351x - 216x + 24x + 64x + 16)\|- 2x + 1
+--R (1) ------------------------------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^4-22/15625*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(11/5)-10083686/4640625*sqrt(1-2*x)-11401/37125*(2+3*x)*_
+ sqrt(1-2*x)-17792/309375*(2+3*x)^2*sqrt(1-2*x)+3629/259875*(2+3*x)^3*_
+ sqrt(1-2*x)+166/7425*(2+3*x)^4*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 5082\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 21262500x - 39532500x - 9559125x + 21433590x + 12144995x
+--R +
+--R - 7095688
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 3609375\|5
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 2541\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R - 21262500x - 39532500x - 9559125x + 21433590x + 12144995x
+--R +
+--R - 7095688
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 3609375\|5
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 15625\|5
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1
+--R (1) -------------------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+r0:=2/45*(1-2*x)^(3/2)*(2+3*x)^3-22/3125*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(11/5)-10826/9375*sqrt(1-2*x)+53/5625*(2+3*x)^2*sqrt(1-2*x)+_
+ 58/1575*(2+3*x)^3*sqrt(1-2*x)-1/28125*(8664+12625*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 462\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 157500x - 171000x + 83565x + 123295x - 50858)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 65625\|5
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 231\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 157500x - 171000x + 83565x + 123295x - 50858)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 65625\|5
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 3125\|5
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 18x - 15x + 4x + 4)\|- 2x + 1
+--R (1) -----------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+r0:=2/375*(1-2*x)^(3/2)-18/125*(1-2*x)^(5/2)-3/35*(1-2*x)^(5/2)*(2+3*x)-_
+ 22/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/625*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 462\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+
+--R (- 13500x - 3060x + 13045x - 3608)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 13125\|5
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 231\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--------+
+--R (- 13500x - 3060x + 13045x - 3608)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 13125\|5
+--R Type: Union(Expression(Integer),...)
+--E 433
+
+--S 434 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 625\|5
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)
+--R
+--R
+--R 2 +--------+
+--R (- 6x - x + 2)\|- 2x + 1
+--R (1) --------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+r0:=2/75*(1-2*x)^(3/2)-3/25*(1-2*x)^(5/2)-22/125*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)+22/125*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+
+--R - 66\|11 atanh(---------------) + (- 180x + 160x + 31)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------------------------
+--R +-+
+--R 375\|5
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 33\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--------+
+--R (- 180x + 160x + 31)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 375\|5
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 125\|5
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(1-2*x)^(3/2)/(3+5*x)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+r0:=2/15*(1-2*x)^(3/2)-22/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_
+ 22/25*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1 +-+ +--------+
+--R - 66\|11 atanh(---------------) + (- 20x + 76)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) -------------------------------------------------------------
+--R +-+
+--R 75\|5
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +-+ +--------+
+--R 33\|11 log(--------------------------------) + (- 20x + 76)\|5 \|- 2x + 1
+--R 5x + 3
+--R --------------------------------------------------------------------------
+--R +-+
+--R 75\|5
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 25\|5
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------
+--R 2
+--R 15x + 19x + 6
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+r0:=-22/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+14/3*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(7/3)-4/15*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R 70\|5 \|7 atanh(---------------) - 66\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R +
+--R +-+ +-+ +--------+
+--R - 4\|3 \|5 \|- 2x + 1
+--R /
+--R +-+ +-+
+--R 15\|3 \|5
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 33\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ +-+ +--------+
+--R 35\|5 \|7 log(---------------------------------) - 4\|3 \|5 \|- 2x + 1
+--R 3x + 2
+--R /
+--R +-+ +-+
+--R 15\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 33\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 35\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R - 70\|5 \|7 atanh(---------------) + 66\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 15\|3 \|5
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------
+--R 3 2
+--R 45x + 87x + 56x + 12
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+r0:=-22*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+64/3*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(7/3)+7*sqrt(1-2*x)/(6+9*x),(1-2*x)^(3/2)/(2+3*x)-_
+ 22*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+64/3*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(7/3)+2/3*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R [
+--R +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1
+--R (192x + 128)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|5 \|- 2x + 1 +-+ +-+ +--------+
+--R (- 198x - 132)\|3 \|11 atanh(---------------) + 7\|3 \|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R /
+--R +-+ +-+
+--R (9x + 6)\|3 \|5
+--R ,
+--R
+--R +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1
+--R (192x + 128)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|5 \|- 2x + 1 +-+ +-+ +--------+
+--R (- 198x - 132)\|3 \|11 atanh(---------------) + 7\|3 \|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R /
+--R +-+ +-+
+--R (9x + 6)\|3 \|5
+--R ]
+--R Type: Tuple(Expression(Integer))
+--E 452
+
+--S 453 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (99x + 66)\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (96x + 64)\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +-+ +--------+
+--R 7\|3 \|5 \|- 2x + 1
+--R /
+--R +-+ +-+
+--R (9x + 6)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 33\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 32\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R - 64\|5 \|7 atanh(---------------) + 66\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 3\|3 \|5
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 135x + 351x + 342x + 148x + 24
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+r0:=1/2*(1-2*x)^(3/2)/(2+3*x)^2+2243/3*atanh(sqrt(3/7)*sqrt(1-2*x))/_
+ sqrt(21)-22*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+67/6*_
+ sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1
+--R (40374x + 53832x + 17944)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +--+ +--+ \|5 \|- 2x + 1
+--R (- 1188x - 1584x - 528)\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +--+ +--------+
+--R (195x + 137)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (54x + 72x + 24)\|21
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+
+--R 2 +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R (594x + 792x + 264)\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R 2 - 21\|- 2x + 1 + (3x - 5)\|21
+--R (20187x + 26916x + 8972)log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R (195x + 137)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (54x + 72x + 24)\|21
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 66\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 2243log(-------------------------------) - 4486atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R 132\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +--+
+--R 6\|21
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (2970x - 7722x + 1452x + 5280)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 22430x - 2243x + 6729)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 13650x - 29127x + 11151
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (4875x - 23890x + 39019x - 21240)\|21
+--R +
+--R 2 +-+ +--+
+--R (457380x + 76230x - 152460)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 168225x + 448600x - 118879x - 269160)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 1950x + 7411x - 8528x + 2655)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (41580x - 59598x - 24948x + 22176)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (67290x - 105421x - 31402x + 33645)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 65340x + 98010x + 39930x - 36300)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 112150x + 168225x + 51589x - 53832)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 68250x - 254835x + 288771x - 89208
+--R /
+--R 4 3 2 +--+ +--+ 4 3
+--R (540x - 486x - 816x + 102x + 180)\|21 \|55 - 18900x + 15750x
+--R +
+--R 2
+--R 27594x - 3276x - 6048
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (7560x + 2016x - 4662x - 630x + 756)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (2700x - 6750x - 192x + 7038x + 84x - 1440)\|21
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 405x + 1323x + 1728x + 1128x + 368x + 48
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+r0:=1/3*(1-2*x)^(3/2)/(2+3*x)^3+78506/21*atanh(sqrt(3/7)*sqrt(1-2*x))/_
+ sqrt(21)-110*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+17/3*_
+ sqrt(1-2*x)/(2+3*x)^2+1138/21*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (2119662x + 4239324x + 2826216x + 628048)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 3 2 +--+ +--+ \|5 \|- 2x + 1
+--R (- 62370x - 124740x - 83160x - 18480)\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (10242x + 13999x + 4797)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (567x + 1134x + 756x + 168)\|21
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--+ +--+
+--R (31185x + 62370x + 41580x + 9240)\|21 \|55
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1 + 5x - 8
+--R log(-------------------------)
+--R 5x + 3
+--R +
+--R 3 2
+--R (1059831x + 2119662x + 1413108x + 314024)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (10242x + 13999x + 4797)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (567x + 1134x + 756x + 168)\|21
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 1155\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 39253log(-------------------------------) - 78506atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R 2310\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +--+
+--R 21\|21
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (51975x - 135135x + 25410x + 92400)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 392530x - 39253x + 117759)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 238980x - 509712x + 195111
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (85350x - 418175x + 682859x - 371640)\|21
+--R +
+--R 2 +-+ +--+
+--R (8004150x + 1334025x - 2668050)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 2943975x + 7850600x - 2080409x - 4710360)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 34140x + 129716x - 149233x + 46455)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (727650x - 1042965x - 436590x + 388080)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (1177590x - 1844891x - 549542x + 588795)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 1143450x + 1715175x + 698775x - 635250)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 1962650x + 2943975x + 902819x - 942072)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 1194900x - 4460400x + 5053251x - 1560888
+--R /
+--R 4 3 2 +--+ +--+ 4 3
+--R (1890x - 1701x - 2856x + 357x + 630)\|21 \|55 - 66150x + 55125x
+--R +
+--R 2
+--R 96579x - 11466x - 21168
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (26460x + 7056x - 16317x - 2205x + 2646)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (9450x - 23625x - 672x + 24633x + 294x - 5040)\|21
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ------------------------------------------------------
+--R 6 5 4 3 2
+--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+r0:=1/4*(1-2*x)^(3/2)/(2+3*x)^4+10990843/588*atanh(sqrt(3/7)*sqrt(1-2*x))/_
+ sqrt(21)-550*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+137/36*_
+ sqrt(1-2*x)/(2+3*x)^3+13723/504*sqrt(1-2*x)/(2+3*x)^2+_
+ 318643/1176*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (1780516566x + 4748044176x + 4748044176x + 2110241856x + 351706976)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+
+--R (- 52390800x - 139708800x - 139708800x - 62092800x - 10348800)\|21
+--R *
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (8603361x + 17494905x + 11868230x + 2686470)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (95256x + 254016x + 254016x + 112896x + 18816)\|21
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +--+ +--+
+--R (26195400x + 69854400x + 69854400x + 31046400x + 5174400)\|21 \|55
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1 + 5x - 8
+--R log(-------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2
+--R (890258283x + 2374022088x + 2374022088x + 1055120928x + 175853488)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (8603361x + 17494905x + 11868230x + 2686470)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (95256x + 254016x + 254016x + 112896x + 18816)\|21
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 323400\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R 10990843log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R - 21981686atanh(---------------) + 646800\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 1176\|21
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (14553000x - 37837800x + 7114800x + 25872000)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 109908430x - 10990843x + 32972529)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 66915030x - 142719297x + 54630891
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (23898225x - 117089600x + 191200679x - 104058840)\|21
+--R +
+--R 2 +-+ +--+
+--R (2241162000x + 373527000x - 747054000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 824313225x + 2198168600x - 582514679x - 1318901160)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 9559290x + 36320621x - 41785198x + 13007355)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (203742000x - 292030200x - 122245200x + 108662400)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (329725290x - 516569621x - 153871802x + 164862645)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 320166000x + 480249000x + 195657000x - 177870000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 549542150x + 824313225x + 252789389x - 263780232)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 334575150x - 1248916725x + 1414908831x - 437047128
+--R /
+--R 4 3 2 +--+ +--+
+--R (105840x - 95256x - 159936x + 19992x + 35280)\|21 \|55
+--R +
+--R 4 3 2
+--R - 3704400x + 3087000x + 5408424x - 642096x - 1185408
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (1481760x + 395136x - 913752x - 123480x + 148176)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (529200x - 1323000x - 37632x + 1379448x + 16464x - 282240)\|21
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^6*(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+r0:=1/5*(1-2*x)^(3/2)/(2+3*x)^5+96169877/1029*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)-2750*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(55)+43/15*sqrt(1-2*x)/(2+3*x)^4+5732/315*sqrt(1-2*x)/_
+ (2+3*x)^3+120077/882*sqrt(1-2*x)/(2+3*x)^2+2788127/2058*_
+ sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 233692801110x + 778976003700x + 1038634671600x + 692423114400x
+--R +
+--R 230807704800x + 30774360640
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R - 6876292500x - 22920975000x - 30561300000x - 20374200000x
+--R +
+--R - 6791400000x - 905520000
+--R *
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R \|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2
+--R (1129191435x + 3049001415x + 3088510878x + 1391064622x + 235067382)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (2500470x + 8334900x + 11113200x + 7408800x + 2469600x + 329280)\|21
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 3438146250x + 11460487500x + 15280650000x + 10187100000x
+--R +
+--R 3395700000x + 452760000
+--R *
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R \|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 116846400555x + 389488001850x + 519317335800x + 346211557200x
+--R +
+--R 115403852400x + 15387180320
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2
+--R (1129191435x + 3049001415x + 3088510878x + 1391064622x + 235067382)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (2500470x + 8334900x + 11113200x + 7408800x + 2469600x + 329280)\|21
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 2829750\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R 96169877log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R - 192339754atanh(---------------) + 5659500\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 2058\|21
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (127338750x - 331080750x + 62254500x + 226380000)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 961698770x - 96169877x + 288509631)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 585506670x - 1248793833x + 478020249
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (209109525x - 1024534150x + 1673005981x - 910514760)\|21
+--R +
+--R 2 +-+ +--+
+--R (19610167500x + 3268361250x - 6536722500)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 7212740775x + 19233975400x - 5097003481x - 11540385240)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 83643810x + 317805469x - 365620472x + 113814345)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (1782742500x - 2555264250x - 1069645500x + 950796000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (2885096310x - 4519984219x - 1346378278x + 1442548155)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 2801452500x + 4202178750x + 1711998750x - 1556362500)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 4808493850x + 7212740775x + 2211907171x - 2308077048)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 2927533350x - 10928022525x + 12380451909x - 3824161992
+--R /
+--R 4 3 2 +--+ +--+
+--R (185220x - 166698x - 279888x + 34986x + 61740)\|21 \|55
+--R +
+--R 4 3 2
+--R - 6482700x + 5402250x + 9464742x - 1123668x - 2074464
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (2593080x + 691488x - 1599066x - 216090x + 259308)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (926100x - 2315250x - 65856x + 2414034x + 28812x - 493920)\|21
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (- 486x - 1377x - 1350x - 360x + 240x + 176x + 32)\|- 2x + 1
+--R (1) ------------------------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+r0:=-1/5*(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)-324/78125*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)-1270604/859375*sqrt(1-2*x)-9388/515625*_
+ (2+3*x)^2*sqrt(1-2*x)+33406/433125*(2+3*x)^3*sqrt(1-2*x)+_
+ 4019/12375*(2+3*x)^4*sqrt(1-2*x)-26/275*(2+3*x)^5*sqrt(1-2*x)-_
+ 2/2578125*(491178+769625*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R (- 124740x - 74844)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3 2
+--R - 106312500x - 270112500x - 181738125x + 76760550x + 135193430x
+--R +
+--R 2532130x - 23061496
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R (30078125x + 18046875)\|5
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (62370x + 37422)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 6 5 4 3 2
+--R - 106312500x - 270112500x - 181738125x + 76760550x + 135193430x
+--R +
+--R 2532130x - 23061496
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R (30078125x + 18046875)\|5
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 162\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 324\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 78125\|5
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^2
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 162x - 351x - 216x + 24x + 64x + 16)\|- 2x + 1
+--R (1) ------------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+r0:=-1/5*(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)-258/15625*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)-110938/140625*sqrt(1-2*x)-83/1125*(2+3*x)*_
+ sqrt(1-2*x)+764/9375*(2+3*x)^2*sqrt(1-2*x)+2707/7875*(2+3*x)^3*_
+ sqrt(1-2*x)-22/225*(2+3*x)^4*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R (- 9030x - 5418)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2 +-+
+--R (- 787500x - 1395000x - 157275x + 924335x + 143235x - 161312)\|5
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R +-+
+--R (546875x + 328125)\|5
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (4515x + 2709)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2 +-+
+--R (- 787500x - 1395000x - 157275x + 924335x + 143235x - 161312)\|5
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R +-+
+--R (546875x + 328125)\|5
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 129\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 258\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 15625\|5
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^2
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1
+--R (1) -------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+r0:=-1/5*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)-192/3125*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)-1418/3125*sqrt(1-2*x)+2/25*(2+3*x)*_
+ sqrt(1-2*x)+237/625*(2+3*x)^2*sqrt(1-2*x)-18/175*(2+3*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R (- 6720x - 4032)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 67500x - 62100x + 57165x + 27640x - 8738)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (109375x + 65625)\|5
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (3360x + 2016)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 67500x - 62100x + 57165x + 27640x - 8738)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (109375x + 65625)\|5
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 96\|11 log(--------------------------------) + 192\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 3125\|5
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^2
+--R
+--R
+--R 3 2 +--------+
+--R (- 18x - 15x + 4x + 4)\|- 2x + 1
+--R (1) -----------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+r0:=42/1375*(1-2*x)^(3/2)-9/125*(1-2*x)^(5/2)-1/275*(1-2*x)^(5/2)/(3+5*x)-_
+ 126/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+126/625*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R (- 630x - 378)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+
+--R (- 900x + 160x + 935x + 298)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (3125x + 1875)\|5
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (315x + 189)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--------+
+--R (- 900x + 160x + 935x + 298)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (3125x + 1875)\|5
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 63\|11 log(--------------------------------) + 126\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 625\|5
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^2
+--R
+--R
+--R 2 +--------+
+--R (- 6x - x + 2)\|- 2x + 1
+--R (1) --------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+r0:=4/55*(1-2*x)^(3/2)-1/55*(1-2*x)^(5/2)/(3+5*x)-12/25*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)+12/25*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+
+--R (- 60x - 36)\|11 atanh(---------------) + (- 20x + 60x + 41)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R (125x + 75)\|5
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (30x + 18)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--------+
+--R (- 20x + 60x + 41)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (125x + 75)\|5
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 6\|11 log(--------------------------------) + 12\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 25\|5
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
+
diff --git a/src/axiom-website/CATS/rich3j.input.pdf b/src/axiom-website/CATS/rich3j.input.pdf
new file mode 100644
index 0000000..adf65d6
Binary files /dev/null and b/src/axiom-website/CATS/rich3j.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3k.input.pamphlet b/src/axiom-website/CATS/rich3k.input.pamphlet
new file mode 100644
index 0000000..5349e5c
--- /dev/null
+++ b/src/axiom-website/CATS/rich3k.input.pamphlet
@@ -0,0 +1,9833 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3k.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 61 matching answers.
+\item 39 results where Axiom differs from Rubi
+\item 0 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 rich3k.output
+)spool rich3k.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(1-2*x)^(3/2)/(3+5*x)^2
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+r0:=-1/5*(1-2*x)^(3/2)/(3+5*x)+6/25*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(11/5)-6/25*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1 +-+ +--------+
+--R (30x + 18)\|11 atanh(---------------) + (- 20x - 23)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) -------------------------------------------------------------------
+--R +-+
+--R (125x + 75)\|5
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (15x + 9)\|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R (- 20x - 23)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (125x + 75)\|5
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 3\|11 log(----------------------------------) - 6\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 25\|5
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^2)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -----------------------
+--R 3 2
+--R 75x + 140x + 87x + 18
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+r0:=-(1-2*x)^(3/2)/(3+5*x)+72/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)_
+ -14*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-2/5*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1
+--R (- 350x - 210)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|5 \|- 2x + 1 +-+ +-+ +--------+
+--R (360x + 216)\|3 \|11 atanh(---------------) - 11\|3 \|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R /
+--R +-+ +-+
+--R (25x + 15)\|3 \|5
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (175x + 105)\|5 \|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+ +-+
+--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (180x + 108)\|3 \|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +-+ +--------+
+--R - 11\|3 \|5 \|- 2x + 1
+--R /
+--R +-+ +-+
+--R (25x + 15)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 35\|5 \|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+ +-+
+--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 36\|3 \|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R 70\|5 \|7 atanh(---------------) - 72\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 5\|3 \|5
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 225x + 570x + 541x + 228x + 36
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+r0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x))+138*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(11/5)-134*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_
+ 22*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +-+ \|3 \|- 2x + 1
+--R (- 2010x - 2546x - 804)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +--+ \|5 \|- 2x + 1
+--R (2070x + 2622x + 828)\|3 \|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +--------+
+--R (- 68x - 43)\|3 \|5 \|- 2x + 1
+--R /
+--R 2 +-+ +-+
+--R (15x + 19x + 6)\|3 \|5
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R 2 +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (1005x + 1273x + 402)\|5 \|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+ +-+
+--R 2 +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (1035x + 1311x + 414)\|3 \|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +-+ +--------+
+--R (- 68x - 43)\|3 \|5 \|- 2x + 1
+--R /
+--R 2 +-+ +-+
+--R (15x + 19x + 6)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 67\|5 \|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+ +-+
+--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 69\|3 \|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R 134\|5 \|7 atanh(---------------) - 138\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R \|3 \|5
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 675x + 2160x + 2763x + 1766x + 564x + 72
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+r0:=1/2*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x))-2311*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(3/7)+204*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-335/2*_
+ sqrt(1-2*x)/(3+5*x)+17*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 +-+ \|3 \|- 2x + 1
+--R (- 207990x - 402114x - 258832x - 55464)\|3 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 3 2 +-+ +--+ \|5 \|- 2x + 1
+--R (18360x + 35496x + 22848x + 4896)\|7 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+
+--R (- 3015x - 3920x - 1271)\|7 \|- 2x + 1
+--R /
+--R 3 2 +-+
+--R (90x + 174x + 112x + 24)\|7
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (103995x + 201057x + 129416x + 27732)\|3
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+
+--R (9180x + 17748x + 11424x + 2448)\|7 \|55
+--R *
+--R +--+ +--------+
+--R - \|55 \|- 2x + 1 + 5x - 8
+--R log(---------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--------+
+--R (- 3015x - 3920x - 1271)\|7 \|- 2x + 1
+--R /
+--R 3 2 +-+
+--R (90x + 174x + 112x + 24)\|7
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 2311\|3 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R +-+ +--+ - \|55 \|- 2x + 1 + 5x - 8
+--R 204\|7 \|55 log(---------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R 4622\|3 atanh(---------------) - 408\|7 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+
+--R 2\|7
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 +-+ +-+ +--+ +-+ +--+
+--R ((1530x - 4998x + 4080)\|5 \|7 \|11 + (- 78540x + 39270)\|3 )\|55
+--R +
+--R +-+ +-+ +--+ 2 +-+
+--R (78540x - 39270)\|3 \|5 \|11 + (- 84150x + 274890x - 224400)\|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +-+ +--+
+--R (- 7140x + 14994x - 5712)\|3 \|5 \|11
+--R +
+--R 2 +-+
+--R (- 33660x + 72930x - 28050)\|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 2 +-+ +-+ +--+ 2 +-+
+--R (33660x - 72930x + 28050)\|5 \|7 \|11 + (392700x - 824670x + 314160)\|3
+--R /
+--R 3 2 +-+ +--+
+--R (30x - 47x - 14x + 15)\|7 \|55
+--R +
+--R 3 2 +-+
+--R (- 350x + 525x + 161x - 168)\|3
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--+
+--R (- 140x + 56x + 49x - 21)\|3 \|55
+--R +
+--R 4 3 2 +-+
+--R (- 150x + 475x - 306x - 187x + 120)\|7
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^2)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------
+--R 6 5 4 3 2
+--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+r0:=1/3*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x))-321161/7*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+1350*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_
+ 46555/42*sqrt(1-2*x)/(3+5*x)+137/18*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_
+ 6949/63*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 86713470x - 225455022x - 219674124x - 95063656x - 15415728)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--+
+--R (2551500x + 6633900x + 6463800x + 2797200x + 453600)\|21 \|55
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 418995x - 824092x - 539819x - 117752)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (1890x + 4914x + 4788x + 2072x + 336)\|21
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (43356735x + 112727511x + 109837062x + 47531828x + 7707864)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--+
+--R (1275750x + 3316950x + 3231900x + 1398600x + 226800)\|21 \|55
+--R *
+--R +--+ +--------+
+--R - \|55 \|- 2x + 1 + 5x - 8
+--R log(---------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+ +--------+
+--R (- 418995x - 824092x - 539819x - 117752)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (1890x + 4914x + 4788x + 2072x + 336)\|21
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R 321161log(-----------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8
+--R 9450\|21 \|55 log(---------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R 642322atanh(---------------) - 18900\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 14\|21
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (425250x - 1105650x + 207900x + 756000)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 3211610x - 321161x + 963483)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 1955310x - 4170369x + 1596357
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (698325x - 3421450x + 5587033x - 3040680)\|21
+--R +
+--R 2 +-+ +--+
+--R (65488500x + 10914750x - 21829500)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 24087075x + 64232200x - 17021533x - 38539320)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (279330x - 1061317x + 1220996x - 380085)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (- 5953500x + 8533350x + 3572100x - 3175200)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 9634830x + 15094567x + 4496254x - 4817415)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (9355500x - 14033250x - 5717250x + 5197500)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (16058050x - 24087075x - 7386703x + 7707864)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 9776550x + 36494325x - 41344737x + 12770856
+--R /
+--R 4 3 2 +--+ +--+ 4 3
+--R (1260x - 1134x - 1904x + 238x + 420)\|21 \|55 - 44100x + 36750x
+--R +
+--R 2
+--R 64386x - 7644x - 14112
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (- 17640x - 4704x + 10878x + 1470x - 1764)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (- 6300x + 15750x + 448x - 16422x - 196x + 3360)\|21
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)^2)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+r0:=1/4*(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x))-55953383/196*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+8400*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(55)-8110915/1176*sqrt(1-2*x)/(3+5*x)+43/9*sqrt(1-2*x)/_
+ ((2+3*x)^3*(3+5*x))+23173/504*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_
+ 302668/441*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 45322240230x - 148052651418x - 193374891648x - 126230832048x
+--R +
+--R - 41181689888x - 5371524768
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R 1333584000x + 4356374400x + 5689958400x + 3714278400x
+--R +
+--R 1211750400x + 158054400
+--R *
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R \|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2
+--R (- 218994705x - 576721848x - 569295605x - 249642200x - 41029970)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (158760x + 518616x + 677376x + 442176x + 144256x + 18816)\|21
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 22661120115x + 74026325709x + 96687445824x + 63115416024x
+--R +
+--R 20590844944x + 2685762384
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R 666792000x + 2178187200x + 2844979200x + 1857139200x + 605875200x
+--R +
+--R 79027200
+--R *
+--R +--+ +--------+
+--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8
+--R \|21 \|55 log(---------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2
+--R (- 218994705x - 576721848x - 569295605x - 249642200x - 41029970)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (158760x + 518616x + 677376x + 442176x + 144256x + 18816)\|21
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R 55953383log(-----------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8
+--R 1646400\|21 \|55 log(---------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R 111906766atanh(---------------) - 3292800\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 392\|21
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (74088000x - 192628800x + 36220800x + 131712000)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 559533830x - 55953383x + 167860149)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 340658430x - 726570957x + 278120871
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (121663725x - 596092600x + 973385299x - 529754040)\|21
+--R +
+--R 2 +-+ +--+
+--R (11409552000x + 1901592000x - 3803184000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 4196503725x + 11190676600x - 2965529299x - 6714405960)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (48665490x - 184905001x + 212724638x - 66219255)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (- 1037232000x + 1486699200x + 622339200x - 553190400)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 1678601490x + 2629809001x + 783347362x - 839300745)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (1629936000x - 2444904000x - 996072000x + 905520000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (2797669150x - 4196503725x - 1286927809x + 1342881192)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 1703292150x + 6358122225x - 7203172011x + 2224966968
+--R /
+--R 4 3 2 +--+ +--+ 4
+--R (35280x - 31752x - 53312x + 6664x + 11760)\|21 \|55 - 1234800x
+--R +
+--R 3 2
+--R 1029000x + 1802808x - 214032x - 395136
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (- 493920x - 131712x + 304584x + 41160x - 49392)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (- 176400x + 441000x + 12544x - 459816x - 5488x + 94080)\|21
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^3
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 162x - 351x - 216x + 24x + 64x + 16)\|- 2x + 1
+--R (1) ------------------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+r0:=-1/10*(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^2-12279/15625*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))/sqrt(55)+2571/15625*sqrt(1-2*x)-3/31250*(1618-4125*x)*_
+ sqrt(1-2*x)+1404/3125*(2+3*x)^2*sqrt(1-2*x)+2643/1750*(2+3*x)^3*_
+ sqrt(1-2*x)-129/50*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 4297650x - 5157180x - 1547154)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2 +--+
+--R (- 2025000x - 3267000x + 496350x + 2120880x + 489445x - 96776)\|55
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2 +--+
+--R (5468750x + 6562500x + 1968750)\|55
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (2148825x + 2578590x + 773577)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2 +--+
+--R (- 2025000x - 3267000x + 496350x + 2120880x + 489445x - 96776)\|55
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2 +--+
+--R (5468750x + 6562500x + 1968750)\|55
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 12279log(-----------------------------) + 24558atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 31250\|55
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 61395x + 98232)\|55 + (61395x - 98232)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 24558x + 12279)\|5 \|11 \|55 + 1350690x - 675345
+--R /
+--R 2 +--------+
+--R (17187500x + 1718750x - 5156250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1562500x - 2343750x - 718750x + 750000)\|55
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^3
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1
+--R (1) -------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+r0:=-1/10*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^2-5943/3125*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))/sqrt(55)+273/3125*sqrt(1-2*x)+21/50*(2+3*x)*_
+ sqrt(1-2*x)+693/625*(2+3*x)^2*sqrt(1-2*x)-48/25*(2+3*x)^3*_
+ sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 297150x - 356580x - 106974)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 27000x - 14400x + 37530x + 36295x + 8644)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (156250x + 187500x + 56250)\|55
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (148575x + 178290x + 53487)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 27000x - 14400x + 37530x + 36295x + 8644)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (156250x + 187500x + 56250)\|55
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 5943log(-----------------------------) + 11886atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 6250\|55
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 29715x + 47544)\|55 + (29715x - 47544)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 11886x + 5943)\|5 \|11 \|55 + 653730x - 326865
+--R /
+--R 2 +--------+
+--R (3437500x + 343750x - 1031250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (312500x - 468750x - 143750x + 150000)\|55
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^3
+--R
+--R
+--R 3 2 +--------+
+--R (- 18x - 15x + 4x + 4)\|- 2x + 1
+--R (1) -----------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+r0:=119/3025*(1-2*x)^(3/2)-1/550*(1-2*x)^(5/2)/(3+5*x)^2-131/6050*_
+ (1-2*x)^(5/2)/(3+5*x)-357/125*atanh(sqrt(5/11)*sqrt(1-2*x))/_
+ sqrt(55)+357/1375*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 17850x - 21420x - 6426)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 600x + 1320x + 2105x + 656)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (6250x + 7500x + 2250)\|55
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (8925x + 10710x + 3213)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+ +--------+
+--R (- 600x + 1320x + 2105x + 656)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (6250x + 7500x + 2250)\|55
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 357log(-----------------------------) + 714atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 250\|55
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 1785x + 2856)\|55 + (1785x - 2856)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 714x + 357)\|5 \|11 \|55 + 39270x - 19635
+--R /
+--R 2 +--------+
+--R (137500x + 13750x - 41250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (12500x - 18750x - 5750x + 6000)\|55
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^3
+--R
+--R
+--R 2 +--------+
+--R (- 6x - x + 2)\|- 2x + 1
+--R (1) --------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+r0:=-1/110*(1-2*x)^(5/2)/(3+5*x)^2-13/110*(1-2*x)^(3/2)/(3+5*x)+_
+ 39/25*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-39/275*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (1950x + 2340x + 702)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (- 120x - 205x - 82)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (1250x + 1500x + 450)\|55
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 - 55\|- 2x + 1 + (5x - 8)\|55
+--R (975x + 1170x + 351)log(-------------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+ +--------+
+--R (- 120x - 205x - 82)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (1250x + 1500x + 450)\|55
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 39log(-------------------------------) - 78atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 50\|55
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 195x + 312)\|55 + (195x - 312)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (78x - 39)\|5 \|11 \|55 - 4290x + 2145
+--R /
+--R 2 +--------+
+--R (27500x + 2750x - 8250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 2500x + 3750x + 1150x - 1200)\|55
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(1-2*x)^(3/2)/(3+5*x)^3
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+r0:=-1/10*(1-2*x)^(3/2)/(3+5*x)^2-3/25*atanh(sqrt(5/11)*sqrt(1-2*x))/_
+ sqrt(55)+3/50*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1 +--+ +--------+
+--R (- 150x - 180x - 54)atanh(---------------) + (25x + 4)\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R -----------------------------------------------------------------------
+--R 2 +--+
+--R (1250x + 1500x + 450)\|55
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (75x + 90x + 27)log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R (25x + 4)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (1250x + 1500x + 450)\|55
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 3log(-----------------------------) + 6atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------
+--R +--+
+--R 50\|55
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 15x + 24)\|55 + (15x - 24)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 6x + 3)\|5 \|11 \|55 + 330x - 165
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (27500x + 2750x - 8250)\|- 2x + 1 + (2500x - 3750x - 1150x + 1200)\|55
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^3)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 375x + 925x + 855x + 351x + 54
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+r0:=-1/2*(1-2*x)^(3/2)/(3+5*x)^2+14*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-_
+ 2379/5*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+69/10*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--+ +--+ \|3 \|- 2x + 1
+--R (3500x + 4200x + 1260)\|21 \|55 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 118950x - 142740x - 42822)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +--+ +--------+
+--R (355x + 202)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (250x + 300x + 90)\|55
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (59475x + 71370x + 21411)log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R 2 +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5
+--R (1750x + 2100x + 630)\|21 \|55 log(---------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R (355x + 202)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (250x + 300x + 90)\|55
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R 2379log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5
+--R 70\|21 \|55 log(---------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1
+--R - 140\|21 \|55 atanh(---------------) + 4758atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 10\|55
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 +-+ +--+
+--R (- 14274x - 2379x + 4758)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (5250x - 14000x + 3710x + 8400)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 3195x + 15657x - 25572x + 13920
+--R *
+--R +--+
+--R \|55
+--R +
+--R 2 +--+
+--R (- 23430x + 49995x - 19140)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (- 107055x + 278343x - 52338x - 190320)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (808500x + 80850x - 242550)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 2130x + 7953x - 9012x + 2784)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (42822x - 64233x - 26169x + 23790)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (73500x - 110250x - 33810x + 35280)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 71370x + 102297x + 42822x - 38064)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 115500x + 180950x + 53900x - 57750)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 70290x - 267135x + 307395x - 95700
+--R /
+--R 4 3 2 +--+ +--+ 4 3
+--R (1500x - 1250x - 2190x + 260x + 480)\|21 \|55 - 49500x + 44550x
+--R +
+--R 2
+--R 74800x - 9350x - 16500
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2 +--+
+--R (- 4500x + 11250x + 320x - 11730x - 140x + 2400)\|55
+--R +
+--R 4 3 2 +--+
+--R (- 33000x - 8800x + 20350x + 2750x - 3300)\|21
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------
+--R 5 4 3 2
+--R 1125x + 3525x + 4415x + 2763x + 864x + 108
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+r0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^2)+204*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(21)-6933*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 33/2*sqrt(1-2*x)/(3+5*x)^2+207/2*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 +--+ +--+ \|3 \|- 2x + 1
+--R (30600x + 57120x + 35496x + 7344)\|21 \|55 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 3 2 \|5 \|- 2x + 1
+--R (- 1039950x - 1941240x - 1206342x - 249588)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (3105x + 3830x + 1178)\|55 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (150x + 280x + 174x + 36)\|55
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (519975x + 970620x + 603171x + 124794)
+--R *
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+ +--+
+--R (15300x + 28560x + 17748x + 3672)\|21 \|55
+--R *
+--R +--+ +--------+
+--R - \|21 \|- 2x + 1 + 3x - 5
+--R log(---------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (3105x + 3830x + 1178)\|55 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (150x + 280x + 174x + 36)\|55
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R 6933log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5
+--R 204\|21 \|55 log(---------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1
+--R - 408\|21 \|55 atanh(---------------) + 13866atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 2\|55
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 +-+ +--+
+--R (- 41598x - 6933x + 13866)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (15300x - 40800x + 10812x + 24480)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 9315x + 45639x - 74526x + 40560
+--R *
+--R +--+
+--R \|55
+--R +
+--R 2 +--+
+--R (- 68310x + 145695x - 55770)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (- 311985x + 811161x - 152526x - 554640)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (2356200x + 235620x - 706860)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 6210x + 23181x - 26262x + 8112)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (124794x - 187191x - 76263x + 69330)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (214200x - 321300x - 98532x + 102816)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 207990x + 298119x + 124794x - 110928)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 336600x + 527340x + 157080x - 168300)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 204930x - 778635x + 895785x - 278850
+--R /
+--R 4 3 2 +--+ +--+ 4 3
+--R (300x - 250x - 438x + 52x + 96)\|21 \|55 - 9900x + 8910x
+--R +
+--R 2
+--R 14960x - 1870x - 3300
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2 +--+
+--R (- 900x + 2250x + 64x - 2346x - 28x + 480)\|55
+--R +
+--R 4 3 2 +--+
+--R (- 6600x - 1760x + 4070x + 550x - 660)\|21
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------------
+--R 6 5 4 3 2
+--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+r0:=1/2*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^2)+14073*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(3/7)-13665*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(5/11)-1015/6*sqrt(1-2*x)/(3+5*x)^2+137/6*sqrt(1-2*x)/((2+3*x)*_
+ (3+5*x)^2)+1020*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +-+ +--+
+--R (6332850x + 16043220x + 15226986x + 6417288x + 1013256)\|3 \|11
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+ +-+
+--R (- 6149250x - 15578100x - 14785530x - 6231240x - 983880)\|5 \|7
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (91800x + 174435x + 110315x + 23219)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (450x + 1140x + 1082x + 456x + 72)\|7 \|11
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+ +-+
+--R (3074625x + 7789050x + 7392765x + 3115620x + 491940)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--+
+--R (3166425x + 8021610x + 7613493x + 3208644x + 506628)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (91800x + 174435x + 110315x + 23219)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (450x + 1140x + 1082x + 456x + 72)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 13665\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 14073\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 28146\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 27330\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 2\|7 \|11
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R -----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+r0:=1/3*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^2)+813716/7*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(3/7)-112875*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(5/11)-176065/126*sqrt(1-2*x)/(3+5*x)^2+86/9*sqrt(1-2*x)/_
+ ((2+3*x)^2*(3+5*x)^2)+1301/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_
+ 117955/14*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 1098516600x + 3515253120x + 4496594616x + 2874044912x
+--R +
+--R 917871648x + 117175104
+--R *
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R \|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R - 1066668750x - 3413340000x - 4366230750x - 2790721500x
+--R +
+--R - 891261000x - 113778000
+--R *
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R \|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--+
+--R (15923925x + 40874010x + 39307638x + 16784696x + 2685098)\|7 \|11
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 5 4 3 2 +-+ +--+
+--R (9450x + 30240x + 38682x + 24724x + 7896x + 1008)\|7 \|11
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 533334375x + 1706670000x + 2183115375x + 1395360750x + 445630500x
+--R +
+--R 56889000
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 549258300x + 1757626560x + 2248297308x + 1437022456x + 458935824x
+--R +
+--R 58587552
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+ +--+
+--R (15923925x + 40874010x + 39307638x + 16784696x + 2685098)\|7 \|11
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 5 4 3 2 +-+ +--+
+--R (9450x + 30240x + 38682x + 24724x + 7896x + 1008)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 790125\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 813716\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 1627432\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 1580250\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 14\|7 \|11
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^6*(3+5*x)
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3
+--R 14580x + 52488x + 68769x + 29295x - 16632x - 21420x - 5488x
+--R +
+--R 2
+--R 1936x + 1280x + 192
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+r0:=-184877/128*(1-2*x)^(7/2)+3916031/1152*(1-2*x)^(9/2)-_
+ 5078115/1408*(1-2*x)^(11/2)+3658095/1664*(1-2*x)^(13/2)-_
+ 105399/128*(1-2*x)^(15/2)+409941/2176*(1-2*x)^(17/2)-_
+ 59049/2432*(1-2*x)^(19/2)+1215/896*(1-2*x)^(21/2)
+--R
+--R
+--R (2)
+--R 10 9 8 7
+--R 4040613720x + 15971057388x + 23013359226x + 10299128697x
+--R +
+--R 6 5 4 3
+--R - 8457459318x - 11546145324x - 3037739768x + 2155110064x
+--R +
+--R 2
+--R 1656222432x + 235056064x - 323646080
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2909907
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 8 7
+--R 4040613720x + 15971057388x + 23013359226x + 10299128697x
+--R +
+--R 6 5 4 3
+--R - 8457459318x - 11546145324x - 3037739768x + 2155110064x
+--R +
+--R 2
+--R 1656222432x + 235056064x - 323646080
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2909907
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^5*(3+5*x)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R (4860x + 14256x + 13419x + 819x - 6090x - 3080x + 224x + 496x + 96)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+r0:=-26411/64*(1-2*x)^(7/2)+60025/72*(1-2*x)^(9/2)-519645/704*(1-2*x)^(11/2)+_
+ 37485/104*(1-2*x)^(13/2)-6489/64*(1-2*x)^(15/2)+1053/68*(1-2*x)^(17/2)-_
+ 1215/1216*(1-2*x)^(19/2)
+--R
+--R
+--R (2)
+--R 9 8 7 6 5
+--R 212663880x + 690949116x + 717196194x + 9461529x - 486084375x
+--R +
+--R 4 3 2
+--R - 273280105x + 53353244x + 95863620x + 21784712x - 18122584
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 415701
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7 6 5
+--R 212663880x + 690949116x + 717196194x + 9461529x - 486084375x
+--R +
+--R 4 3 2
+--R - 273280105x + 53353244x + 95863620x + 21784712x - 18122584
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 415701
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2 +--------+
+--R (1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+r0:=-3773/32*(1-2*x)^(7/2)+57281/288*(1-2*x)^(9/2)-24843/176*(1-2*x)^(11/2)+_
+ 10773/208*(1-2*x)^(13/2)-1557/160*(1-2*x)^(15/2)+405/544*(1-2*x)^(17/2)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4
+--R 20849400x + 52864812x + 31646538x - 24298407x - 32302900x
+--R +
+--R 3 2
+--R - 2705920x + 9403464x + 3351776x - 1899184
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 109395
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4
+--R 20849400x + 52864812x + 31646538x - 24298407x - 32302900x
+--R +
+--R 3 2
+--R - 2705920x + 9403464x + 3351776x - 1899184
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 109395
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (1) (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+r0:=-539/16*(1-2*x)^(7/2)+3283/72*(1-2*x)^(9/2)-1071/44*(1-2*x)^(11/2)+_
+ 621/104*(1-2*x)^(13/2)-9/16*(1-2*x)^(15/2)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R 92664x + 167508x + 13446x - 128237x - 51767x + 35349x + 21850x
+--R +
+--R - 9038
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 1287
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R 92664x + 167508x + 13446x - 128237x - 51767x + 35349x + 21850x
+--R +
+--R - 9038
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 1287
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1) (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+r0:=-77/8*(1-2*x)^(7/2)+707/72*(1-2*x)^(9/2)-309/88*(1-2*x)^(11/2)+_
+ 45/104*(1-2*x)^(13/2)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2 +--------+
+--R (35640x + 37692x - 25678x - 32875x + 7302x + 11732x - 3712)\|- 2x + 1
+--R ---------------------------------------------------------------------------
+--R 1287
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2 +--------+
+--R (35640x + 37692x - 25678x - 32875x + 7302x + 11732x - 3712)\|- 2x + 1
+--R ---------------------------------------------------------------------------
+--R 1287
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (1) (60x + 16x - 37x - 5x + 6)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+r0:=-11/4*(1-2*x)^(7/2)+17/9*(1-2*x)^(9/2)-15/44*(1-2*x)^(11/2)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1080x + 292x - 1106x - 129x + 475x - 119)\|- 2x + 1
+--R (2) ---------------------------------------------------------
+--R 99
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1080x + 292x - 1106x - 129x + 475x - 119)\|- 2x + 1
+--R (3) ---------------------------------------------------------
+--R 99
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)
+--R
+--R
+--R 3 2 +--------+
+--R (1) (20x - 8x - 7x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+r0:=-11/14*(1-2*x)^(7/2)+5/18*(1-2*x)^(9/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (280x - 164x - 174x + 157x - 32)\|- 2x + 1
+--R (2) ----------------------------------------------
+--R 63
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (280x - 164x - 174x + 157x - 32)\|- 2x + 1
+--R (3) ----------------------------------------------
+--R 63
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)
+--R
+--R
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R (1) --------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+r0:=-14/81*(1-2*x)^(3/2)-2/45*(1-2*x)^(5/2)-5/21*(1-2*x)^(7/2)+_
+ 98/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-98/81*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R 3430\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +--------+
+--R (5400x - 8604x + 5534x - 4721)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 2835\|3
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 1715\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--------+
+--R (5400x - 8604x + 5534x - 4721)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 2835\|3
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 49\|7 log(---------------------------------) - 98\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 81\|3
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^2
+--R
+--R
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R (1) --------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+r0:=80/81*(1-2*x)^(3/2)+16/63*(1-2*x)^(5/2)+1/21*(1-2*x)^(7/2)/(2+3*x)-_
+ 560/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+560/81*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R (- 1680x - 1120)\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +--------+
+--R (216x - 516x + 1474x + 1325)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (243x + 162)\|3
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (840x + 560)\|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--------+
+--R (216x - 516x + 1474x + 1325)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (243x + 162)\|3
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 280\|7 log(-------------------------------) + 560\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 81\|3
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^3
+--R
+--R
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R (1) --------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+r0:=-365/567*(1-2*x)^(3/2)+1/42*(1-2*x)^(7/2)/(2+3*x)^2-_
+ 73/126*(1-2*x)^(5/2)/(2+3*x)+365/81*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(7/3)-365/81*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ \|3 \|- 2x + 1
+--R (6570x + 8760x + 2920)\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +--------+
+--R (720x - 4584x - 8731x - 3521)\|3 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (1458x + 1944x + 648)\|3
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R 2 +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (3285x + 4380x + 1460)\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--------+
+--R (720x - 4584x - 8731x - 3521)\|3 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (1458x + 1944x + 648)\|3
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 365\|7 log(---------------------------------) - 730\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 162\|3
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^4
+--R
+--R
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R (1) --------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+r0:=1/63*(1-2*x)^(7/2)/(2+3*x)^3-53/189*(1-2*x)^(5/2)/(2+3*x)^2+_
+ 265/567*(1-2*x)^(3/2)/(2+3*x)-530/81*atanh(sqrt(3/7)*sqrt(1-2*x))/_
+ sqrt(21)+530/567*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (- 14310x - 28620x - 19080x - 4240)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (1080x + 3627x + 2983x + 713)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (2187x + 4374x + 2916x + 648)\|21
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 3 2 21\|- 2x + 1 + (3x - 5)\|21
+--R (7155x + 14310x + 9540x + 2120)log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (1080x + 3627x + 2983x + 713)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (2187x + 4374x + 2916x + 648)\|21
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 265log(-----------------------------) + 530atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 81\|21
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 795x + 1325)\|21 + (795x - 1325)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 530x + 265)\|3 \|7 \|21 + 11130x - 5565
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (10206x + 1701x - 3402)\|- 2x + 1 + (1458x - 2187x - 891x + 810)\|21
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^5
+--R
+--R
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+r0:=1/84*(1-2*x)^(7/2)/(2+3*x)^4-139/756*(1-2*x)^(5/2)/(2+3*x)^3+_
+ 695/4536*(1-2*x)^(3/2)/(2+3*x)^2+695/2268*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)-695/4536*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 4 3 2 \|3 \|- 2x + 1
+--R (112590x + 300240x + 300240x + 133440x + 22240)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (- 41715x - 43971x - 18394x - 4394)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (367416x + 979776x + 979776x + 435456x + 72576)\|21
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (56295x + 150120x + 150120x + 66720x + 11120)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (- 41715x - 43971x - 18394x - 4394)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (367416x + 979776x + 979776x + 435456x + 72576)\|21
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 695log(-------------------------------) - 1390atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 4536\|21
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 2085x + 3475)\|21 + (2085x - 3475)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (1390x - 695)\|3 \|7 \|21 - 29190x + 14595
+--R /
+--R 2 +--------+
+--R (571536x + 95256x - 190512)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 81648x + 122472x + 49896x - 45360)\|21
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^6
+--R
+--R
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+r0:=1/105*(1-2*x)^(7/2)/(2+3*x)^5-43/315*(1-2*x)^(5/2)/(2+3*x)^4+_
+ 43/567*(1-2*x)^(3/2)/(2+3*x)^3+43/3969*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)-43/1134*sqrt(1-2*x)/(2+3*x)^2+43/7938*_
+ sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (104490x + 348300x + 464400x + 309600x + 103200x + 13760)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (17415x - 116415x - 53772x + 3322x - 7018)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R (9644670x + 32148900x + 42865200x + 28576800x + 9525600x + 1270080)
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (52245x + 174150x + 232200x + 154800x + 51600x + 6880)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (17415x - 116415x - 53772x + 3322x - 7018)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R (9644670x + 32148900x + 42865200x + 28576800x + 9525600x + 1270080)
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 43log(-------------------------------) - 86atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 7938\|21
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 129x + 215)\|21 + (129x - 215)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (86x - 43)\|3 \|7 \|21 - 1806x + 903
+--R /
+--R 2 +--------+
+--R (1000188x + 166698x - 333396)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 142884x + 214326x + 87318x - 79380)\|21
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^7
+--R
+--R
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+r0:=1/126*(1-2*x)^(7/2)/(2+3*x)^6-41/378*(1-2*x)^(5/2)/(2+3*x)^5+_
+ 205/4536*(1-2*x)^(3/2)/(2+3*x)^4+205/222264*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)-205/13608*sqrt(1-2*x)/(2+3*x)^3+_
+ 205/190512*sqrt(1-2*x)/(2+3*x)^2+205/444528*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 298890x + 1195560x + 1992600x + 1771200x + 885600x + 236160x
+--R +
+--R 26240
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2 +--+
+--R (49815x + 204795x - 824526x - 176850x + 154312x - 51904)\|21
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 324060912x + 1296243648x + 2160406080x + 1920360960x + 960180480x
+--R +
+--R 256048128x + 28449792
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 149445x + 597780x + 996300x + 885600x + 442800x + 118080x
+--R +
+--R 13120
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2 +--+
+--R (49815x + 204795x - 824526x - 176850x + 154312x - 51904)\|21
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 324060912x + 1296243648x + 2160406080x + 1920360960x + 960180480x
+--R +
+--R 256048128x + 28449792
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 205log(-------------------------------) - 410atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 444528\|21
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 615x + 1025)\|21 + (615x - 1025)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (410x - 205)\|3 \|7 \|21 - 8610x + 4305
+--R /
+--R 2 +--------+
+--R (56010528x + 9335088x - 18670176)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 8001504x + 12002256x + 4889808x - 4445280)\|21
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R (8100x + 23220x + 21141x + 690x - 9791x - 4696x + 424x + 768x + 144)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+r0:=-41503/64*(1-2*x)^(7/2)+381073/288*(1-2*x)^(9/2)-_
+ 832951/704*(1-2*x)^(11/2)+121359/208*(1-2*x)^(13/2)-_
+ 53037/320*(1-2*x)^(15/2)+13905/544*(1-2*x)^(17/2)-2025/1216*(1-2*x)^(19/2)
+--R
+--R
+--R (2)
+--R 9 8 7 6 5
+--R 1772199000x + 5625863100x + 5641824474x - 121581999x - 3896813214x
+--R +
+--R 4 3 2
+--R - 2072749175x + 461747860x + 739308228x + 160311352x - 138993368
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2078505
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7 6 5
+--R 1772199000x + 5625863100x + 5641824474x - 121581999x - 3896813214x
+--R +
+--R 4 3 2
+--R - 2072749175x + 461747860x + 739308228x + 160311352x - 138993368
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2078505
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^2
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2 +--------+
+--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+r0:=-5929/32*(1-2*x)^(7/2)+91091/288*(1-2*x)^(9/2)-_
+ 39977/176*(1-2*x)^(11/2)+17541/208*(1-2*x)^(13/2)-_
+ 513/32*(1-2*x)^(15/2)+675/544*(1-2*x)^(17/2)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4 3
+--R 6949800x + 17096508x + 9599634x - 8175663x - 10040957x - 608627x
+--R +
+--R 2
+--R 2934177x + 993442x - 581846
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 21879
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4 3
+--R 6949800x + 17096508x + 9599634x - 8175663x - 10040957x - 608627x
+--R +
+--R 2
+--R 2934177x + 993442x - 581846
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 21879
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (1) (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+r0:=-847/16*(1-2*x)^(7/2)+1309/18*(1-2*x)^(9/2)-3467/88*(1-2*x)^(11/2)+_
+ 255/26*(1-2*x)^(13/2)-15/16*(1-2*x)^(15/2)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R 154440x + 267300x + 9846x - 205169x - 75320x + 56481x + 32506x
+--R +
+--R - 13826
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 1287
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R 154440x + 267300x + 9846x - 205169x - 75320x + 56481x + 32506x
+--R +
+--R - 13826
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 1287
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^2
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1) (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+r0:=-121/8*(1-2*x)^(7/2)+1133/72*(1-2*x)^(9/2)-505/88*(1-2*x)^(11/2)+_
+ 75/104*(1-2*x)^(13/2)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2 +--------+
+--R (59400x + 58140x - 44062x - 49999x + 12729x + 17495x - 5671)\|- 2x + 1
+--R ----------------------------------------------------------------------------
+--R 1287
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2 +--------+
+--R (59400x + 58140x - 44062x - 49999x + 12729x + 17495x - 5671)\|- 2x + 1
+--R ----------------------------------------------------------------------------
+--R 1287
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^2
+--R
+--R
+--R 4 3 2 +--------+
+--R (1) (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+r0:=-121/28*(1-2*x)^(7/2)+55/18*(1-2*x)^(9/2)-25/44*(1-2*x)^(11/2)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (12600x + 2380x - 12302x - 867x + 4966x - 1271)\|- 2x + 1
+--R (2) --------------------------------------------------------------
+--R 693
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (12600x + 2380x - 12302x - 867x + 4966x - 1271)\|- 2x + 1
+--R (3) --------------------------------------------------------------
+--R 693
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R (1) -----------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+r0:=14/243*(1-2*x)^(3/2)+2/135*(1-2*x)^(5/2)-40/189*(1-2*x)^(7/2)-_
+ 5/27*(1-2*x)^(7/2)*(3+5*x)-98/243*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(7/3)+98/243*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R - 3430\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+ +--------+
+--R (63000x - 42300x - 30546x + 29791x - 2479)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 8505\|3
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 1715\|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+ +--------+
+--R (63000x - 42300x - 30546x + 29791x - 2479)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R 8505\|3
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 49\|7 log(-------------------------------) + 98\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -------------------------------------------------------------------------
+--R +-+
+--R 243\|3
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^2
+--R
+--R
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R (1) -----------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+r0:=-50/81*(1-2*x)^(3/2)-10/63*(1-2*x)^(5/2)-25/63*(1-2*x)^(7/2)-_
+ 1/63*(1-2*x)^(7/2)/(2+3*x)+350/81*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(7/3)-350/81*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R (7350x + 4900)\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+ +--------+
+--R (5400x - 5508x + 1002x - 4471x - 6239)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (1701x + 1134)\|3
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (3675x + 2450)\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+ +--------+
+--R (5400x - 5508x + 1002x - 4471x - 6239)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (1701x + 1134)\|3
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 175\|7 log(---------------------------------) - 350\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 81\|3
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^3
+--R
+--R
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R (1) -----------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+r0:=1055/567*(1-2*x)^(3/2)+211/441*(1-2*x)^(5/2)-1/126*(1-2*x)^(7/2)/_
+ (2+3*x)^2+143/882*(1-2*x)^(7/2)/(2+3*x)-1055/81*_
+ atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+1055/81*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ \|3 \|- 2x + 1
+--R (- 18990x - 25320x - 8440)\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+ +--------+
+--R (2160x - 3960x + 12828x + 25987x + 10007)\|3 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (1458x + 1944x + 648)\|3
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R 2 +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (9495x + 12660x + 4220)\|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+ +--------+
+--R (2160x - 3960x + 12828x + 25987x + 10007)\|3 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (1458x + 1944x + 648)\|3
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 1055\|7 log(-------------------------------) + 2110\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 162\|3
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^4
+--R
+--R
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R (1) -----------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+r0:=-4435/3969*(1-2*x)^(3/2)-1/189*(1-2*x)^(7/2)/(2+3*x)^3+_
+ 211/2646*(1-2*x)^(7/2)/(2+3*x)^2-887/882*(1-2*x)^(5/2)/(2+3*x)+_
+ 4435/81*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-4435/567*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (239490x + 478980x + 319320x + 70960)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (3600x - 21240x - 61353x - 48697x - 12212)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (4374x + 8748x + 5832x + 1296)\|21
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (119745x + 239490x + 159660x + 35480)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (3600x - 21240x - 61353x - 48697x - 12212)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (4374x + 8748x + 5832x + 1296)\|21
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 4435log(-------------------------------) - 8870atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 162\|21
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 13305x + 22175)\|21 + (13305x - 22175)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (8870x - 4435)\|3 \|7 \|21 - 186270x + 93135
+--R /
+--R 2 +--------+
+--R (20412x + 3402x - 6804)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 2916x + 4374x + 1782x - 1620)\|21
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^5
+--R
+--R
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+r0:=-1/252*(1-2*x)^(7/2)/(2+3*x)^4+31/588*(1-2*x)^(7/2)/(2+3*x)^3-_
+ 4993/10584*(1-2*x)^(5/2)/(2+3*x)^2+24965/31752*(1-2*x)^(3/2)/(2+3*x)-_
+ 24965/2268*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+24965/15876*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 4044330x - 10784880x - 10784880x - 4793280x - 798880)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (302400x + 1231065x + 1526937x + 762598x + 134558)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (367416x + 979776x + 979776x + 435456x + 72576)\|21
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (2022165x + 5392440x + 5392440x + 2396640x + 399440)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (302400x + 1231065x + 1526937x + 762598x + 134558)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (367416x + 979776x + 979776x + 435456x + 72576)\|21
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 24965log(-----------------------------) + 49930atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 4536\|21
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 74895x + 124825)\|21 + (74895x - 124825)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 49930x + 24965)\|3 \|7 \|21 + 1048530x - 524265
+--R /
+--R 2 +--------+
+--R (571536x + 95256x - 190512)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (81648x - 122472x - 49896x + 45360)\|21
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^6
+--R
+--R
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+r0:=-1/315*(1-2*x)^(7/2)/(2+3*x)^5+347/8820*(1-2*x)^(7/2)/(2+3*x)^4-_
+ 8051/26460*(1-2*x)^(5/2)/(2+3*x)^3+8051/31752*(1-2*x)^(3/2)/(2+3*x)^2+_
+ 8051/15876*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 8051/31752*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 19563930x + 65213100x + 86950800x + 57967200x + 19322400x
+--R +
+--R 2576320
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 7323345x - 12406455x - 8277204x - 2919346x - 503276)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 38578680x + 128595600x + 171460800x + 114307200x + 38102400x
+--R +
+--R 5080320
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (9781965x + 32606550x + 43475400x + 28983600x + 9661200x + 1288160)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 7323345x - 12406455x - 8277204x - 2919346x - 503276)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 38578680x + 128595600x + 171460800x + 114307200x + 38102400x
+--R +
+--R 5080320
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 8051log(-------------------------------) - 16102atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ----------------------------------------------------------------------
+--R +--+
+--R 31752\|21
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 24153x + 40255)\|21 + (24153x - 40255)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (16102x - 8051)\|3 \|7 \|21 - 338142x + 169071
+--R /
+--R 2 +--------+
+--R (4000752x + 666792x - 1333584)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 571536x + 857304x + 349272x - 317520)\|21
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^7
+--R
+--R
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+r0:=-1/378*(1-2*x)^(7/2)/(2+3*x)^6+83/2646*(1-2*x)^(7/2)/(2+3*x)^5-_
+ 263/1176*(1-2*x)^(5/2)/(2+3*x)^4+1315/10584*(1-2*x)^(3/2)/(2+3*x)^3+_
+ 1315/74088*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 1315/21168*sqrt(1-2*x)/(2+3*x)^2+1315/148176*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 1917270x + 7669080x + 12781800x + 11361600x + 5680800x
+--R +
+--R 1514880x + 168320
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2 +--+
+--R (319545x - 1979115x - 2360850x - 587502x - 106808x - 81568)\|21
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 108020304x + 432081216x + 720135360x + 640120320x + 320060160x
+--R +
+--R 85349376x + 9483264
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 958635x + 3834540x + 6390900x + 5680800x + 2840400x + 757440x
+--R +
+--R 84160
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2 +--+
+--R (319545x - 1979115x - 2360850x - 587502x - 106808x - 81568)\|21
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 108020304x + 432081216x + 720135360x + 640120320x + 320060160x
+--R +
+--R 85349376x + 9483264
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 1315log(-------------------------------) - 2630atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 148176\|21
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 3945x + 6575)\|21 + (3945x - 6575)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (2630x - 1315)\|3 \|7 \|21 - 55230x + 27615
+--R /
+--R 2 +--------+
+--R (18670176x + 3111696x - 6223392)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 2667168x + 4000752x + 1629936x - 1481760)\|21
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+r0:=-1/441*(1-2*x)^(7/2)/(2+3*x)^7+23/882*(1-2*x)^(7/2)/(2+3*x)^6-_
+ 467/2646*(1-2*x)^(5/2)/(2+3*x)^5+2335/31752*(1-2*x)^(3/2)/(2+3*x)^4+_
+ 2335/1555848*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 2335/95256*sqrt(1-2*x)/(2+3*x)^3+2335/1333584*sqrt(1-2*x)/(2+3*x)^2+_
+ 2335/3111696*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3
+--R 10213290x + 47662020x + 95324040x + 105915600x + 70610400x
+--R +
+--R 2
+--R 28244160x + 6276480x + 597760
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 6 5 4 3 2
+--R 1702215x + 8132805x - 24492348x - 23950566x + 1405308x
+--R +
+--R 1415408x - 1107536
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 7 6 5 4
+--R 6805279152x + 31757969376x + 63515938752x + 70573265280x
+--R +
+--R 3 2
+--R 47048843520x + 18819537408x + 4182119424x + 398297088
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R 5106645x + 23831010x + 47662020x + 52957800x + 35305200x
+--R +
+--R 2
+--R 14122080x + 3138240x + 298880
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 6 5 4 3 2
+--R 1702215x + 8132805x - 24492348x - 23950566x + 1405308x
+--R +
+--R 1415408x - 1107536
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 7 6 5 4
+--R 6805279152x + 31757969376x + 63515938752x + 70573265280x
+--R +
+--R 3 2
+--R 47048843520x + 18819537408x + 4182119424x + 398297088
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 2335log(-------------------------------) - 4670atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 3111696\|21
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 7005x + 11675)\|21 + (7005x - 11675)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (4670x - 2335)\|3 \|7 \|21 - 98070x + 49035
+--R /
+--R 2 +--------+
+--R (392073696x + 65345616x - 130691232)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 56010528x + 84015792x + 34228656x - 31116960)\|21
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 9 8 7 6 5 4 3
+--R 40500x + 140400x + 175365x + 66873x - 46885x - 52853x - 11968x
+--R +
+--R 2
+--R 5112x + 3024x + 432
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+r0:=-456533/128*(1-2*x)^(7/2)+3278737/384*(1-2*x)^(9/2)-_
+ 1179381/128*(1-2*x)^(11/2)+9504551/1664*(1-2*x)^(13/2)-_
+ 1392467/640*(1-2*x)^(15/2)+1101465/2176*(1-2*x)^(17/2)-_
+ 161325/2432*(1-2*x)^(19/2)+3375/896*(1-2*x)^(21/2)
+--R
+--R
+--R (2)
+--R 10 9 8 7
+--R 1700595000x + 6471211500x + 8880844050x + 3513142893x
+--R +
+--R 6 5 4 3 2
+--R - 3556515018x - 4297543173x - 970928350x + 842946920x + 588303696x
+--R +
+--R 74758064x - 115708576
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 440895
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 9 8 7
+--R 1700595000x + 6471211500x + 8880844050x + 3513142893x
+--R +
+--R 6 5 4 3 2
+--R - 3556515018x - 4297543173x - 970928350x + 842946920x + 588303696x
+--R +
+--R 74758064x - 115708576
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 440895
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x
+--R +
+--R 216
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+r0:=-65219/64*(1-2*x)^(7/2)+100793/48*(1-2*x)^(9/2)-_
+ 121359/64*(1-2*x)^(11/2)+98209/104*(1-2*x)^(13/2)-_
+ 17337/64*(1-2*x)^(15/2)+675/16*(1-2*x)^(17/2)-3375/1216*(1-2*x)^(19/2)
+--R
+--R
+--R (2)
+--R 9 8 7 6 5 4
+--R 1053000x + 3264300x + 3159234x - 180615x - 2223099x - 1118224x
+--R +
+--R 3 2
+--R 281231x + 406155x + 84038x - 76018
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 741
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 7 6 5 4
+--R 1053000x + 3264300x + 3159234x - 180615x - 2223099x - 1118224x
+--R +
+--R 3 2
+--R 281231x + 406155x + 84038x - 76018
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 741
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^3
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2 +--------+
+--R (4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+r0:=-9317/32*(1-2*x)^(7/2)+16093/32*(1-2*x)^(9/2)-5847/16*(1-2*x)^(11/2)+_
+ 28555/208*(1-2*x)^(13/2)-845/32*(1-2*x)^(15/2)+1125/544*(1-2*x)^(17/2)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4 3 2
+--R 117000x + 278980x + 146310x - 138201x - 157296x - 5935x + 46164x
+--R +
+--R 14864x - 9004
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 221
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4 3 2
+--R 117000x + 278980x + 146310x - 138201x - 157296x - 5935x + 46164x
+--R +
+--R 14864x - 9004
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 221
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^3
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (1) (1500x + 2200x + 95x - 1091x - 333x + 135x + 54)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+r0:=-1331/16*(1-2*x)^(7/2)+2783/24*(1-2*x)^(9/2)-255/4*(1-2*x)^(11/2)+_
+ 1675/104*(1-2*x)^(13/2)-25/16*(1-2*x)^(15/2)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2 +--------+
+--R (7800x + 12900x - 90x - 9917x - 3299x + 2724x + 1465x - 641)\|- 2x + 1
+--R -----------------------------------------------------------------------------
+--R 39
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2 +--------+
+--R (7800x + 12900x - 90x - 9917x - 3299x + 2724x + 1465x - 641)\|- 2x + 1
+--R -----------------------------------------------------------------------------
+--R 39
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^3
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (1) (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+r0:=-1331/56*(1-2*x)^(7/2)+605/24*(1-2*x)^(9/2)-75/8*(1-2*x)^(11/2)+_
+ 125/104*(1-2*x)^(13/2)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2 +--------+
+--R (21000x + 18900x - 15890x - 16061x + 4614x + 5533x - 1838)\|- 2x + 1
+--R --------------------------------------------------------------------------
+--R 273
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2 +--------+
+--R (21000x + 18900x - 15890x - 16061x + 4614x + 5533x - 1838)\|- 2x + 1
+--R --------------------------------------------------------------------------
+--R 273
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+r0:=34/405*(1-2*x)^(3/2)*(3+5*x)^3+2/33*(1-2*x)^(5/2)*(3+5*x)^3+_
+ 98/729*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_
+ 1012658/212625*sqrt(1-2*x)-25631/70875*(3+5*x)^2*sqrt(1-2*x)+_
+ 514/4725*(3+5*x)^3*sqrt(1-2*x)-1/127575*(227389+191021*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R 37730\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2 +-+
+--R (8505000x + 913500x - 7838550x - 249219x + 3024349x - 830656)\|3
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R +-+
+--R 280665\|3
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 18865\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2 +-+
+--R (8505000x + 913500x - 7838550x - 249219x + 3024349x - 830656)\|3
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R +-+
+--R 280665\|3
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 49\|7 log(---------------------------------) - 98\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 729\|3
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^2
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+r0:=-22/81*(1-2*x)^(3/2)*(3+5*x)^3-1/3*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)-_
+ 1540/729*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+_
+ 138578/127575*sqrt(1-2*x)-416152/127575*(3+5*x)*sqrt(1-2*x)+_
+ 65153/14175*(3+5*x)^2*sqrt(1-2*x)-682/945*(3+5*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R (- 32340x - 21560)\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2 +-+ +--------+
+--R (189000x - 17100x - 159714x + 25275x + 65558x + 13759)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (15309x + 10206)\|3
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (16170x + 10780)\|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2 +-+ +--------+
+--R (189000x - 17100x - 159714x + 25275x + 65558x + 13759)\|3 \|- 2x + 1
+--R /
+--R +-+
+--R (15309x + 10206)\|3
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1
+--R 770\|7 log(-------------------------------) + 1540\|7 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 729\|3
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+r0:=-1/6*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^2+55/9*(1-2*x)^(3/2)*_
+ (3+5*x)^3/(2+3*x)+935/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_
+ 78947/2835*sqrt(1-2*x)+89771/5670*(3+5*x)*sqrt(1-2*x)-_
+ 7997/315*(3+5*x)^2*sqrt(1-2*x)+88/21*(3+5*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ \|3 \|- 2x + 1
+--R (117810x + 157080x + 52360)\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2 +-+ +--------+
+--R (54000x - 24120x - 17460x - 67962x - 152833x - 64943)\|3 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (10206x + 13608x + 4536)\|3
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R 2 +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (58905x + 78540x + 26180)\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2 +-+ +--------+
+--R (54000x - 24120x - 17460x - 67962x - 152833x - 64943)\|3 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (10206x + 13608x + 4536)\|3
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 935\|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ \|3 \|- 2x + 1
+--R - 1870\|7 atanh(---------------)
+--R +-+
+--R \|7
+--R /
+--R +-+
+--R 162\|3
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+r0:=-1/9*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3+55/27*(1-2*x)^(3/2)*(3+5*x)^3/_
+ (2+3*x)^2-41360/243*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ 12166/243*sqrt(1-2*x)-8294/243*(3+5*x)*sqrt(1-2*x)+_
+ 1441/27*(3+5*x)^2*sqrt(1-2*x)-275/9*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (- 1116720x - 2233440x - 1488960x - 330880)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2 +--+ +--------+
+--R (16200x - 20700x + 87030x + 289719x + 229336x + 56141)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (6561x + 13122x + 8748x + 1944)\|21
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (558360x + 1116720x + 744480x + 165440)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2 +--+ +--------+
+--R (16200x - 20700x + 87030x + 289719x + 229336x + 56141)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (6561x + 13122x + 8748x + 1944)\|21
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 20680log(-----------------------------) + 41360atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 243\|21
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 62040x + 103400)\|21 + (62040x - 103400)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 41360x + 20680)\|3 \|7 \|21 + 868560x - 434280
+--R /
+--R 2 +--------+
+--R (30618x + 5103x - 10206)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (4374x - 6561x - 2673x + 2430)\|21
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^5
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+r0:=-1/12*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4+55/54*(1-2*x)^(3/2)*(3+5*x)^3/_
+ (2+3*x)^3+645865/6804*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 224675/6804*sqrt(1-2*x)+252725/13608*(3+5*x)*sqrt(1-2*x)-_
+ 2255/378*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)-55/24*(3+5*x)^3*_
+ sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (104630130x + 279013680x + 279013680x + 124006080x + 20667680)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R (1512000x - 8215200x - 32946525x - 39158517x - 19526798x - 3553918)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (1102248x + 2939328x + 2939328x + 1306368x + 217728)\|21
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (52315065x + 139506840x + 139506840x + 62003040x + 10333840)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R (1512000x - 8215200x - 32946525x - 39158517x - 19526798x - 3553918)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (1102248x + 2939328x + 2939328x + 1306368x + 217728)\|21
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 645865log(-------------------------------) - 1291730atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R --------------------------------------------------------------------------
+--R +--+
+--R 13608\|21
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 1937595x + 3229325)\|21 + (1937595x - 3229325)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (1291730x - 645865)\|3 \|7 \|21 - 27126330x + 13563165
+--R /
+--R 2 +--------+
+--R (1714608x + 285768x - 571536)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 244944x + 367416x + 149688x - 136080)\|21
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^6
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+r0:=-1/15*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^5+11/18*(1-2*x)^(3/2)*(3+5*x)^3/_
+ (2+3*x)^4-146971/7938*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 715/7938*sqrt(1-2*x)-13387/15876*(3+5*x)*sqrt(1-2*x)/(2+3*x)-_
+ 209/756*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2+11/9*(3+5*x)^3*_
+ sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 357139530x - 1190465100x - 1587286800x - 1058191200x
+--R +
+--R - 352730400x - 47030720
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R 26460000x + 126578745x + 207486855x + 157178184x + 56745266x
+--R +
+--R 7933096
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R (19289340x + 64297800x + 85730400x + 57153600x + 19051200x + 2540160)
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 178569765x + 595232550x + 793643400x + 529095600x + 176365200x
+--R +
+--R 23515360
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R 26460000x + 126578745x + 207486855x + 157178184x + 56745266x
+--R +
+--R 7933096
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R (19289340x + 64297800x + 85730400x + 57153600x + 19051200x + 2540160)
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 146971log(-----------------------------) + 293942atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------
+--R +--+
+--R 15876\|21
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 440913x + 734855)\|21 + (440913x - 734855)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 293942x + 146971)\|3 \|7 \|21 + 6172782x - 3086391
+--R /
+--R 2 +--------+
+--R (2000376x + 333396x - 666792)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (285768x - 428652x - 174636x + 158760)\|21
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^7
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+r0:=-121/4536*(1-2*x)^(3/2)/(2+3*x)^4+33275/95256*(1-2*x)^(3/2)/(2+3*x)^3-_
+ 1/18*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^6+11/27*(1-2*x)^(3/2)*_
+ (3+5*x)^3/(2+3*x)^5+559625/666792*atanh(sqrt(3/7)*sqrt(1-2*x))/_
+ sqrt(21)-559625/190512*sqrt(1-2*x)/(2+3*x)^2+559625/1333584*_
+ sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 815933250x + 3263733000x + 5439555000x + 4835160000x
+--R +
+--R 2
+--R 2417580000x + 644688000x + 71632000
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R - 308539125x - 720187425x - 687940758x - 352611738x - 102558856x
+--R +
+--R - 13847024
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 972182736x + 3888730944x + 6481218240x + 5761082880x + 2880541440x
+--R +
+--R 768144384x + 85349376
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 407966625x + 1631866500x + 2719777500x + 2417580000x
+--R +
+--R 2
+--R 1208790000x + 322344000x + 35816000
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R - 308539125x - 720187425x - 687940758x - 352611738x - 102558856x
+--R +
+--R - 13847024
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 972182736x + 3888730944x + 6481218240x + 5761082880x + 2880541440x
+--R +
+--R 768144384x + 85349376
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 559625log(-------------------------------) - 1119250atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R --------------------------------------------------------------------------
+--R +--+
+--R 1333584\|21
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 1678875x + 2798125)\|21 + (1678875x - 2798125)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (1119250x - 559625)\|3 \|7 \|21 - 23504250x + 11752125
+--R /
+--R 2 +--------+
+--R (168031584x + 28005264x - 56010528)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 24004512x + 36006768x + 14669424x - 13335840)\|21
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+r0:=-1/21*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^7+55/189*(1-2*x)^(3/2)*(3+5*x)^3/_
+ (2+3*x)^6+33935/1166886*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ 11/166698*(3833-4355*x)*sqrt(1-2*x)/(2+3*x)^3-153505/47628*_
+ sqrt(1-2*x)/(2+3*x)^2+33935/2333772*sqrt(1-2*x)/(2+3*x)-_
+ 3223/2646*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4+11/7*(3+5*x)^3*_
+ sqrt(1-2*x)/(2+3*x)^5
+--R
+--R
+--R (2)
+--R 7 6 5 4
+--R 148431690x + 692681220x + 1385362440x + 1539291600x
+--R +
+--R 3 2
+--R 1026194400x + 410477760x + 91217280x + 8687360
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 6 5 4 3 2
+--R 24738615x - 141112395x - 283697388x - 164222766x - 39606312x
+--R +
+--R - 12384752x - 4005436
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 7 6 5 4
+--R 5103959364x + 23818477032x + 47636954064x + 52929948960x
+--R +
+--R 3 2
+--R 35286632640x + 14114653056x + 3136589568x + 298722816
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R 74215845x + 346340610x + 692681220x + 769645800x + 513097200x
+--R +
+--R 2
+--R 205238880x + 45608640x + 4343680
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 6 5 4 3 2
+--R 24738615x - 141112395x - 283697388x - 164222766x - 39606312x
+--R +
+--R - 12384752x - 4005436
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 7 6 5 4
+--R 5103959364x + 23818477032x + 47636954064x + 52929948960x
+--R +
+--R 3 2
+--R 35286632640x + 14114653056x + 3136589568x + 298722816
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 33935log(-------------------------------) - 67870atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------
+--R +--+
+--R 2333772\|21
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 101805x + 169675)\|21 + (101805x - 169675)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (67870x - 33935)\|3 \|7 \|21 - 1425270x + 712635
+--R /
+--R 2 +--------+
+--R (294055272x + 49009212x - 98018424)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 42007896x + 63011844x + 25671492x - 23337720)\|21
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R (1) ------------------------------------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+r0:=298/10725*(1-2*x)^(3/2)*(2+3*x)^4+2/65*(1-2*x)^(5/2)*(2+3*x)^4-_
+ 242/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_
+ 601617098/301640625*sqrt(1-2*x)-669943/2413125*(2+3*x)*_
+ sqrt(1-2*x)-829256/20109375*(2+3*x)^2*sqrt(1-2*x)+_
+ 861947/16891875*(2+3*x)^3*sqrt(1-2*x)+4138/482625*(2+3*x)^4*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 726726\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 2338875000x + 2842087500x - 1540428750x - 2556079875x
+--R +
+--R 2
+--R 399578370x + 960784285x - 289133384
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 234609375\|5
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 363363\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 6 5 4 3
+--R 2338875000x + 2842087500x - 1540428750x - 2556079875x
+--R +
+--R 2
+--R 399578370x + 960784285x - 289133384
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 234609375\|5
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 121\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 242\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 78125\|5
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R (1) -------------------------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+r0:=34/825*(1-2*x)^(3/2)*(2+3*x)^3+2/55*(1-2*x)^(5/2)*(2+3*x)^3-242/15625*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-207982/171875*_
+ sqrt(1-2*x)+6221/103125*(2+3*x)^2*sqrt(1-2*x)+706/28875*_
+ (2+3*x)^3*sqrt(1-2*x)-1/515625*(177948+223375*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 55902\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R (14175000x + 6142500x - 15572250x - 3564885x + 7726195x - 1796318)
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 3609375\|5
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 27951\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R (14175000x + 6142500x - 15572250x - 3564885x + 7726195x - 1796318)
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R 3609375\|5
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 121\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 242\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 15625\|5
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R (1) ----------------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+r0:=22/1875*(1-2*x)^(3/2)+2/625*(1-2*x)^(5/2)-44/525*(1-2*x)^(7/2)-_
+ 1/15*(1-2*x)^(7/2)*(2+3*x)-242/3125*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)+242/3125*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 5082\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--------+
+--R (105000x - 43500x - 91410x + 69995x - 8188)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 65625\|5
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 2541\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--------+
+--R (105000x - 43500x - 91410x + 69995x - 8188)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 65625\|5
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 121\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 242\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 3125\|5
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)
+--R
+--R
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R (1) --------------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+r0:=22/375*(1-2*x)^(3/2)+2/125*(1-2*x)^(5/2)-3/35*(1-2*x)^(7/2)-_
+ 242/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/625*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 5082\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+
+--R (9000x - 12660x + 4370x + 4937)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 13125\|5
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 2541\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--------+
+--R (9000x - 12660x + 4370x + 4937)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 13125\|5
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 121\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 242\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 625\|5
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(1-2*x)^(5/2)/(3+5*x)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 5x + 3
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+r0:=22/75*(1-2*x)^(3/2)+2/25*(1-2*x)^(5/2)-242/125*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/125*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+
+--R - 726\|11 atanh(---------------) + (120x - 340x + 866)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------------------------
+--R +-+
+--R 375\|5
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 363\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--------+
+--R (120x - 340x + 866)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R 375\|5
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 121\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 242\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 125\|5
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 2
+--R 15x + 19x + 6
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+r0:=-4/45*(1-2*x)^(3/2)-242/25*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(11/5)+98/9*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-272/225*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R 2450\|5 \|7 atanh(---------------) - 2178\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R +
+--R +-+ +-+ +--------+
+--R (40x - 292)\|3 \|5 \|- 2x + 1
+--R /
+--R +-+ +-+
+--R 225\|3 \|5
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 1089\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 1225\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +-+ +--------+
+--R (40x - 292)\|3 \|5 \|- 2x + 1
+--R /
+--R +-+ +-+
+--R 225\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 1089\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 1225\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R - 2450\|5 \|7 atanh(---------------) + 2178\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 225\|3 \|5
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 3 2
+--R 45x + 87x + 56x + 12
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+r0:=2/3*(1-2*x)^(3/2)+(1-2*x)^(5/2)/(2+3*x)-242/5*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)+140/3*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(7/3)+26/15*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1
+--R (2100x + 1400)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|5 \|- 2x + 1
+--R (- 2178x - 1452)\|3 \|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +--------+
+--R (8x + 87)\|3 \|5 \|- 2x + 1
+--R /
+--R +-+ +-+
+--R (45x + 30)\|3 \|5
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (1089x + 726)\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (1050x + 700)\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +-+ +--------+
+--R (8x + 87)\|3 \|5 \|- 2x + 1
+--R /
+--R +-+ +-+
+--R (45x + 30)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 363\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 350\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R - 700\|5 \|7 atanh(---------------) + 726\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 15\|3 \|5
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 135x + 351x + 342x + 148x + 24
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+r0:=1/2*(1-2*x)^(5/2)/(2+3*x)^2+65/6*(1-2*x)^(3/2)/(2+3*x)-_
+ 242*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_
+ 235*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+7*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +-+ \|3 \|- 2x + 1
+--R (12690x + 16920x + 5640)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +--+ \|5 \|- 2x + 1
+--R (- 13068x - 17424x - 5808)\|3 \|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +--------+
+--R (427x + 301)\|3 \|5 \|- 2x + 1
+--R /
+--R 2 +-+ +-+
+--R (54x + 72x + 24)\|3 \|5
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R 2 +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (6534x + 8712x + 2904)\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R 2 +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (6345x + 8460x + 2820)\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +-+ +--------+
+--R (427x + 301)\|3 \|5 \|- 2x + 1
+--R /
+--R 2 +-+ +-+
+--R (54x + 72x + 24)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 242\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 235\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R - 470\|5 \|7 atanh(---------------) + 484\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 2\|3 \|5
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 405x + 1323x + 1728x + 1128x + 368x + 48
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+r0:=1/3*(1-2*x)^(5/2)/(2+3*x)^3+50/9*(1-2*x)^(3/2)/(2+3*x)^2+_
+ 74020/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 242*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+1105/9*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (1998540x + 3997080x + 2664720x + 592160)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 3 2 +--+ +--+ \|5 \|- 2x + 1
+--R (- 58806x - 117612x - 78408x - 17424)\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (9657x + 13198x + 4523)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (243x + 486x + 324x + 72)\|21
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--+ +--+
+--R (29403x + 58806x + 39204x + 8712)\|21 \|55
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1 + 5x - 8
+--R log(-------------------------)
+--R 5x + 3
+--R +
+--R 3 2
+--R (999270x + 1998540x + 1332360x + 296080)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (9657x + 13198x + 4523)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (243x + 486x + 324x + 72)\|21
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 1089\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 37010log(-------------------------------) - 74020atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R 2178\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +--+
+--R 9\|21
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (49005x - 127413x + 23958x + 87120)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 370100x - 37010x + 111030)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 225330x - 480585x + 183960
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (80475x - 394285x + 643840x - 350400)\|21
+--R +
+--R 2 +-+ +--+
+--R (7546770x + 1257795x - 2515590)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 2775750x + 7402000x - 1961530x - 4441200)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 32190x + 122305x - 140705x + 43800)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (686070x - 983367x - 411642x + 365904)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (1110300x - 1739470x - 518140x + 555150)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 1078110x + 1617165x + 658845x - 598950)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 1850500x + 2775750x + 851230x - 888240)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 1126650x - 4205565x + 4764480x - 1471680
+--R /
+--R 4 3 2 +--+ +--+ 4 3
+--R (810x - 729x - 1224x + 153x + 270)\|21 \|55 - 28350x + 23625x
+--R +
+--R 2
+--R 41391x - 4914x - 9072
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (11340x + 3024x - 6993x - 945x + 1134)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (4050x - 10125x - 288x + 10557x + 126x - 2160)\|21
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ------------------------------------------------------
+--R 6 5 4 3 2
+--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+r0:=1/4*(1-2*x)^(5/2)/(2+3*x)^4+15/4*(1-2*x)^(3/2)/(2+3*x)^3+_
+ 3454265/84*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 1210*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+_
+ 1495/24*sqrt(1-2*x)/(2+3*x)^2+100145/168*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (559590930x + 1492242480x + 1492242480x + 663218880x + 110536480)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+
+--R (- 16465680x - 43908480x - 43908480x - 19514880x - 3252480)\|21
+--R *
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (2703915x + 5498403x + 3730002x + 844322)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (13608x + 36288x + 36288x + 16128x + 2688)\|21
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +--+ +--+
+--R (8232840x + 21954240x + 21954240x + 9757440x + 1626240)\|21 \|55
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1 + 5x - 8
+--R log(-------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2
+--R (279795465x + 746121240x + 746121240x + 331609440x + 55268240)
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (2703915x + 5498403x + 3730002x + 844322)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (13608x + 36288x + 36288x + 16128x + 2688)\|21
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 101640\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R 3454265log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R - 6908530atanh(---------------) + 203280\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 168\|21
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (4573800x - 11891880x + 2236080x + 8131200)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 34542650x - 3454265x + 10362795)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 21030450x - 44854635x + 17169705
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (7510875x - 36799600x + 60091645x - 32704200)\|21
+--R +
+--R 2 +-+ +--+
+--R (704365200x + 117394200x - 234788400)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 259069875x + 690853000x - 183076045x - 414511800)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 3004350x + 11415055x - 13132490x + 4088025)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (64033200x - 91780920x - 38419920x + 34151040)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (103627950x - 162350455x - 48359710x + 51813975)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 100623600x + 150935400x + 61492200x - 55902000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 172713250x + 259069875x + 79448095x - 82902360)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 105152250x - 392516775x + 444685605x - 137357640
+--R /
+--R 4 3 2 +--+ +--+ 4
+--R (15120x - 13608x - 22848x + 2856x + 5040)\|21 \|55 - 529200x
+--R +
+--R 3 2
+--R 441000x + 772632x - 91728x - 169344
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (211680x + 56448x - 130536x - 17640x + 21168)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (75600x - 189000x - 5376x + 197064x + 2352x - 40320)\|21
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+r0:=1/5*(1-2*x)^(5/2)/(2+3*x)^5+17/6*(1-2*x)^(3/2)/(2+3*x)^4+_
+ 20149879/98*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 6050*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+251/6*sqrt(1-2*x)/(2+3*x)^3+_
+ 25159/84*sqrt(1-2*x)/(2+3*x)^2+584179/196*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 146892617910x + 489642059700x + 652856079600x + 435237386400x
+--R +
+--R 145079128800x + 19343883840
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R - 4322241000x - 14407470000x - 19209960000x - 12806640000x
+--R +
+--R - 4268880000x - 569184000
+--R *
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R \|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2
+--R (709777485x + 1916515215x + 1941349752x + 874383298x + 147756688)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (714420x + 2381400x + 3175200x + 2116800x + 705600x + 94080)\|21
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 2161120500x + 7203735000x + 9604980000x + 6403320000x
+--R +
+--R 2134440000x + 284592000
+--R *
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R \|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 73446308955x + 244821029850x + 326428039800x + 217618693200x
+--R +
+--R 72539564400x + 9671941920
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2
+--R (709777485x + 1916515215x + 1941349752x + 874383298x + 147756688)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (714420x + 2381400x + 3175200x + 2116800x + 705600x + 94080)\|21
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 592900\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R 20149879log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R - 40299758atanh(---------------) + 1185800\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 196\|21
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (26680500x - 69369300x + 13043800x + 47432000)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 201498790x - 20149879x + 60449637)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 122677590x - 261652041x + 100156623
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (43813425x - 214664300x + 350534587x - 190774520)\|21
+--R +
+--R 2 +-+ +--+
+--R (4108797000x + 684799500x - 1369599000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 1511240925x + 4029975800x - 1067943587x - 2417985480)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 17525370x + 66587813x - 76606194x + 23846815)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (373527000x - 535388700x - 224116200x + 199214400)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (604496370x - 947044313x - 282098306x + 302248185)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 586971000x + 880456500x + 358704500x - 326095000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 1007493950x + 1511240925x + 463447217x - 483597096)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 613387950x - 2289680925x + 2593999443x - 801252984
+--R /
+--R 4 3 2 +--+ +--+ 4
+--R (17640x - 15876x - 26656x + 3332x + 5880)\|21 \|55 - 617400x
+--R +
+--R 3 2
+--R 514500x + 901404x - 107016x - 197568
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (246960x + 65856x - 152292x - 20580x + 24696)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (88200x - 220500x - 6272x + 229908x + 2744x - 47040)\|21
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^7*(3+5*x))
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x
+--R +
+--R 4672x + 384
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+r0:=1/6*(1-2*x)^(5/2)/(2+3*x)^6+41/18*(1-2*x)^(3/2)/(2+3*x)^5+_
+ 25388847535/24696*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 30250*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+_
+ 2269/72*sqrt(1-2*x)/(2+3*x)^4+302651/1512*sqrt(1-2*x)/(2+3*x)^3+_
+ 31700335/21168*sqrt(1-2*x)/(2+3*x)^2+736065535/49392*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R 37016939706030x + 148067758824120x + 246779598040200x
+--R +
+--R 3 2
+--R 219359642702400x + 109679821351200x + 29247952360320x + 3249772484480
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 6 5 4
+--R - 1089204732000x - 4356818928000x - 7261364880000x
+--R +
+--R 3 2
+--R - 6454546560000x - 3227273280000x - 860606208000x - 95622912000
+--R *
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R \|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 178863925005x + 602204446665x + 811194684822x + 546491397114x
+--R +
+--R 184131053992x + 24823128464
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 36006768x + 144027072x + 240045120x + 213373440x + 106686720x
+--R +
+--R 28449792x + 3161088
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 544602366000x + 2178409464000x + 3630682440000x + 3227273280000x
+--R +
+--R 2
+--R 1613636640000x + 430303104000x + 47811456000
+--R *
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R \|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R 6 5 4
+--R 18508469853015x + 74033879412060x + 123389799020100x
+--R +
+--R 3 2
+--R 109679821351200x + 54839910675600x + 14623976180160x + 1624886242240
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R 178863925005x + 602204446665x + 811194684822x + 546491397114x
+--R +
+--R 184131053992x + 24823128464
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 36006768x + 144027072x + 240045120x + 213373440x + 106686720x
+--R +
+--R 28449792x + 3161088
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 747054000\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R 25388847535log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R - 50777695070atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R 1494108000\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +--+
+--R 49392\|21
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2
+--R 33617430000x - 87405318000x + 16435188000x
+--R +
+--R 59764320000
+--R *
+--R +-+ +--+
+--R \|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 253888475350x - 25388847535x + 76166542605)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 154573762350x - 329681571765x + 126197345295
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (55204915125x - 270477017000x + 441673579355x - 240375895800)\|21
+--R +
+--R 2 +-+ +--+
+--R (5177084220000x + 862847370000x - 1725694740000)\|5 \|11
+--R +
+--R 3 2
+--R - 1904163565125x + 5077769507000x - 1345608919355x
+--R +
+--R - 3046661704200
+--R *
+--R +-+ +-+
+--R \|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 22081966050x + 83900644145x - 96523804510x + 30046986975)\|21
+--R +
+--R 3 2
+--R (470644020000x - 674589762000x - 282386412000x + 251010144000)
+--R *
+--R +-+ +--+
+--R \|5 \|11
+--R +
+--R 3 2
+--R (761665426050x - 1193275834145x - 355443865490x + 380832713025)
+--R *
+--R +-+ +-+
+--R \|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2
+--R (- 739583460000x + 1109375190000x + 451967670000x - 410879700000)
+--R *
+--R +-+ +--+
+--R \|5 \|11
+--R +
+--R 3 2
+--R - 1269442376750x + 1904163565125x + 583943493305x
+--R +
+--R - 609332340840
+--R *
+--R +-+ +-+
+--R \|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 772868811750x - 2884997957625x + 3268439300595x - 1009578762360
+--R /
+--R 4 3 2 +--+ +--+
+--R (4445280x - 4000752x - 6717312x + 839664x + 1481760)\|21 \|55
+--R +
+--R 4 3 2
+--R - 155584800x + 129654000x + 227153808x - 26968032x - 49787136
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (62233920x + 16595712x - 38377584x - 5186160x + 6223392)\|55
+--R +
+--R 5 4 3 2
+--R (22226400x - 55566000x - 1580544x + 57936816x + 691488x - 11854080)
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^2
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R (1) ------------------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+r0:=-26/275*(1-2*x)^(3/2)*(2+3*x)^4-1/5*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)-_
+ 2794/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_
+ 20103122/23203125*sqrt(1-2*x)-7327/185625*(2+3*x)*sqrt(1-2*x)+_
+ 312916/1546875*(2+3*x)^2*sqrt(1-2*x)+975383/1299375*(2+3*x)^3*_
+ sqrt(1-2*x)-8318/37125*(2+3*x)^4*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R (- 3227070x - 1936242)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3 2
+--R 212625000x + 237037500x - 173598750x - 214071975x + 85482115x
+--R +
+--R 50081215x - 15982128
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R (90234375x + 54140625)\|5
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (1613535x + 968121)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 6 5 4 3 2
+--R 212625000x + 237037500x - 173598750x - 214071975x + 85482115x
+--R +
+--R 50081215x - 15982128
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R +-+
+--R (90234375x + 54140625)\|5
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 1397\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 2794\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 78125\|5
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R (1) -------------------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+r0:=-22/225*(1-2*x)^(3/2)*(2+3*x)^3-1/5*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)-_
+ 2068/15625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_
+ 224794/421875*sqrt(1-2*x)+796/3375*(2+3*x)*sqrt(1-2*x)+_
+ 23357/28125*(2+3*x)^2*sqrt(1-2*x)-1898/7875*(2+3*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R (- 217140x - 130284)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2 +-+
+--R (1575000x + 427500x - 1858950x + 152105x + 680930x + 16794)\|5
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R +-+
+--R (1640625x + 984375)\|5
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (108570x + 65142)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2 +-+
+--R (1575000x + 427500x - 1858950x + 152105x + 680930x + 16794)\|5
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R +-+
+--R (1640625x + 984375)\|5
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 1034\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 2068\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 15625\|5
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^2
+--R
+--R
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R (1) ----------------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+r0:=122/1875*(1-2*x)^(3/2)+122/6875*(1-2*x)^(5/2)-9/175*(1-2*x)^(7/2)-_
+ 1/275*(1-2*x)^(7/2)/(3+5*x)-1342/3125*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(11/5)+1342/3125*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R (- 140910x - 84546)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--------+
+--R (135000x - 96300x - 75130x + 173795x + 90486)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (328125x + 196875)\|5
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (70455x + 42273)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--------+
+--R (135000x - 96300x - 75130x + 173795x + 90486)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (328125x + 196875)\|5
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 671\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 1342\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 3125\|5
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^2
+--R
+--R
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R (1) --------------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+r0:=56/375*(1-2*x)^(3/2)+56/1375*(1-2*x)^(5/2)-1/55*(1-2*x)^(7/2)/(3+5*x)-_
+ 616/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+616/625*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R (- 9240x - 5544)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+
+--R (1800x - 3820x + 8630x + 6579)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (9375x + 5625)\|5
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (4620x + 2772)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--------+
+--R (1800x - 3820x + 8630x + 6579)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (9375x + 5625)\|5
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 308\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 616\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 625\|5
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(1-2*x)^(5/2)/(3+5*x)^2
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 2
+--R 25x + 30x + 9
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+r0:=-2/15*(1-2*x)^(3/2)-1/5*(1-2*x)^(5/2)/(3+5*x)+22/25*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)-22/25*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+
+--R (330x + 198)\|11 atanh(---------------) + (40x - 260x - 243)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +-+
+--R (375x + 225)\|5
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (165x + 99)\|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--------+
+--R (40x - 260x - 243)\|5 \|- 2x + 1
+--R /
+--R +-+
+--R (375x + 225)\|5
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 11\|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 22\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 25\|5
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^2)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 3 2
+--R 75x + 140x + 87x + 18
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 500
+r0:=-2/5*(1-2*x)^(3/2)-(1-2*x)^(5/2)/(3+5*x)+836/25*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)-98/3*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(7/3)-58/75*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1
+--R (- 12250x - 7350)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|5 \|- 2x + 1
+--R (12540x + 7524)\|3 \|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +--------+
+--R (40x - 339)\|3 \|5 \|- 2x + 1
+--R /
+--R +-+ +-+
+--R (375x + 225)\|3 \|5
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (6125x + 3675)\|5 \|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+ +-+
+--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (6270x + 3762)\|3 \|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +-+ +--------+
+--R (40x - 339)\|3 \|5 \|- 2x + 1
+--R /
+--R +-+ +-+
+--R (375x + 225)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 363
+
+--S 364 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 1225\|5 \|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+ +-+
+--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 1254\|3 \|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R 2450\|5 \|7 atanh(---------------) - 2508\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 75\|3 \|5
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 225x + 570x + 541x + 228x + 36
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+r0:=-22*(1-2*x)^(3/2)/(3+5*x)+(1-2*x)^(5/2)/((2+3*x)*(3+5*x))+_
+ 1562/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_
+ 910/3*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-136/15*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +-+ \|3 \|- 2x + 1
+--R (- 68250x - 86450x - 27300)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +--+ \|5 \|- 2x + 1
+--R (70290x + 89034x + 28116)\|3 \|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +--------+
+--R (- 2314x - 1461)\|3 \|5 \|- 2x + 1
+--R /
+--R 2 +-+ +-+
+--R (225x + 285x + 90)\|3 \|5
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R 2 +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (34125x + 43225x + 13650)\|5 \|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +--+
+--R (35145x + 44517x + 14058)\|3 \|11
+--R *
+--R +--+ +--------+ +-+
+--R - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +-+ +--------+
+--R (- 2314x - 1461)\|3 \|5 \|- 2x + 1
+--R /
+--R 2 +-+ +-+
+--R (225x + 285x + 90)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 368
+
+--S 369 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 2275\|5 \|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+ +-+
+--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 2343\|3 \|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R 4550\|5 \|7 atanh(---------------) - 4686\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 15\|3 \|5
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 5 4 3 2
+--R 675x + 2160x + 2763x + 1766x + 564x + 72
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+r0:=1/2*(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x))+50/3*(1-2*x)^(3/2)/((2+3*x)*_
+ (3+5*x))+2288*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_
+ 6665/3*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-2189/6*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 +-+ +-+ \|3 \|- 2x + 1
+--R (- 599850x - 1159710x - 746480x - 159960)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 3 2 +-+ +--+ \|5 \|- 2x + 1
+--R (617760x + 1194336x + 768768x + 164736)\|3 \|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +-+ +--------+
+--R (- 20289x - 26380x - 8553)\|3 \|5 \|- 2x + 1
+--R /
+--R 3 2 +-+ +-+
+--R (270x + 522x + 336x + 72)\|3 \|5
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +-+
+--R (299925x + 579855x + 373240x + 79980)\|5 \|7
+--R *
+--R +-+ +--------+ +-+
+--R 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+
+--R (308880x + 597168x + 384384x + 82368)\|3 \|11
+--R *
+--R +--+ +--------+ +-+
+--R - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R log(----------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +-+ +--------+
+--R (- 20289x - 26380x - 8553)\|3 \|5 \|- 2x + 1
+--R /
+--R 3 2 +-+ +-+
+--R (270x + 522x + 336x + 72)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 373
+
+--S 374 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 6665\|5 \|7 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+ +-+
+--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 6864\|3 \|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R 13330\|5 \|7 atanh(---------------) - 13728\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 6\|3 \|5
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^2)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------
+--R 6 5 4 3 2
+--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+r0:=1/3*(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x))+15/2*(1-2*x)^(3/2)/((2+3*x)^2*_
+ (3+5*x))-307295/3*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ 3014*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_
+ 44545/18*sqrt(1-2*x)/(3+5*x)+2260/9*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 82969650x - 215721090x - 210189780x - 90959320x - 14750160)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--+
+--R (2441340x + 6347484x + 6184728x + 2676432x + 434016)\|21 \|55
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 400905x - 788512x - 516513x - 112668)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (810x + 2106x + 2052x + 888x + 144)\|21
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (41484825x + 107860545x + 105094890x + 45479660x + 7375080)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--+
+--R (1220670x + 3173742x + 3092364x + 1338216x + 217008)\|21 \|55
+--R *
+--R +--+ +--------+
+--R - \|55 \|- 2x + 1 + 5x - 8
+--R log(---------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+ +--------+
+--R (- 400905x - 788512x - 516513x - 112668)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (810x + 2106x + 2052x + 888x + 144)\|21
+--R Type: Union(Expression(Integer),...)
+--E 378
+
+--S 379 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R 307295log(-----------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8
+--R 9042\|21 \|55 log(---------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R 614590atanh(---------------) - 18084\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 6\|21
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (406890x - 1057914x + 198924x + 723360)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 3072950x - 307295x + 921885)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 1870890x - 3990315x + 1527435
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (668175x - 3273730x + 5345815x - 2909400)\|21
+--R +
+--R 2 +-+ +--+
+--R (62661060x + 10443510x - 20887020)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 23047125x + 61459000x - 16286635x - 36875400)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (267270x - 1015495x + 1168280x - 363675)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (- 5696460x + 8164926x + 3417876x - 3038112)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 9218850x + 14442865x + 4302130x - 4609425)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (8951580x - 13427370x - 5470410x + 4973100)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (15364750x - 23047125x - 7067785x + 7375080)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 9354450x + 34918695x - 39559695x + 12219480
+--R /
+--R 4 3 2 +--+ +--+ 4 3
+--R (540x - 486x - 816x + 102x + 180)\|21 \|55 - 18900x + 15750x
+--R +
+--R 2
+--R 27594x - 3276x - 6048
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (- 7560x - 2016x + 4662x + 630x - 756)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (- 2700x + 6750x + 192x - 7038x - 84x + 1440)\|21
+--R Type: Expression(Integer)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^2)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+r0:=1/4*(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x))+85/18*(1-2*x)^(3/2)/((2+3*x)^3*_
+ (3+5*x))-53384095/84*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ 18700*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_
+ 7738475/504*sqrt(1-2*x)/(3+5*x)+22765/216*sqrt(1-2*x)/_
+ ((2+3*x)^2*(3+5*x))+288770/189*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 43241116950x - 141254315370x - 184495432320x - 120434518320x
+--R +
+--R - 39290693920x - 5124873120
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R 1272348000x + 4156336800x + 5428684800x + 3543724800x
+--R +
+--R 1156108800x + 150796800
+--R *
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R \|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2
+--R (- 208938825x - 550239720x - 543154477x - 238179048x - 39145938)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (68040x + 222264x + 290304x + 189504x + 61824x + 8064)\|21
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 21620558475x + 70627157685x + 92247716160x + 60217259160x
+--R +
+--R 19645346960x + 2562436560
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R 636174000x + 2078168400x + 2714342400x + 1771862400x + 578054400x
+--R +
+--R 75398400
+--R *
+--R +--+ +--------+
+--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8
+--R \|21 \|55 log(---------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2
+--R (- 208938825x - 550239720x - 543154477x - 238179048x - 39145938)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (68040x + 222264x + 290304x + 189504x + 61824x + 8064)\|21
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R 53384095log(-----------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8
+--R 1570800\|21 \|55 log(---------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R 106768190atanh(---------------) - 3141600\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 168\|21
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (70686000x - 183783600x + 34557600x + 125664000)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 533840950x - 53384095x + 160152285)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 325015950x - 693208005x + 265350015
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (116077125x - 568721000x + 928689035x - 505428600)\|21
+--R +
+--R 2 +-+ +--+
+--R (10885644000x + 1814274000x - 3628548000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 4003807125x + 10676819000x - 2829357035x - 6406091400)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (46430850x - 176414465x + 202956670x - 63178575)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (- 989604000x + 1418432400x + 593762400x - 527788800)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 1601522850x + 2509052465x + 747377330x - 800761425)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (1555092000x - 2332638000x - 950334000x + 863940000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (2669204750x - 4003807125x - 1227834185x + 1281218280)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 1625079750x + 6066167625x - 6872414115x + 2122800120
+--R /
+--R 4 3 2 +--+ +--+ 4
+--R (15120x - 13608x - 22848x + 2856x + 5040)\|21 \|55 - 529200x
+--R +
+--R 3 2
+--R 441000x + 772632x - 91728x - 169344
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (- 211680x - 56448x + 130536x + 17640x - 21168)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (- 75600x + 189000x + 5376x - 197064x - 2352x + 40320)\|21
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x
+--R +
+--R 7104x + 576
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+r0:=1/5*(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x))+41/12*(1-2*x)^(3/2)/((2+3*x)^4*_
+ (3+5*x))-2231141147/588*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ 111650*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-323422735/3528*_
+ sqrt(1-2*x)/(3+5*x)+1714/27*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+_
+ 924025/1512*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+12068887/1323*_
+ sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 6 5 4
+--R - 27108364936050x - 106626235415130x - 174698351810100x
+--R +
+--R 3 2
+--R - 152610054454800x - 74966342539200x - 19634042093600x
+--R +
+--R - 2141895501120
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 6 5 4 3
+--R 797649930000x + 3137423058000x + 5140410660000x + 4490473680000x
+--R +
+--R 2
+--R 2205846720000x + 577721760000x + 63024192000
+--R *
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R \|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 130986207675x - 432275892930x - 570477768855x - 376323861626x
+--R +
+--R - 124085884254x - 16360698684
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 7144200x + 28100520x + 46040400x + 40219200x + 19756800x
+--R +
+--R 5174400x + 564480
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R 13554182468025x + 53313117707565x + 87349175905050x
+--R +
+--R 3 2
+--R 76305027227400x + 37483171269600x + 9817021046800x + 1070947750560
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 6 5 4 3
+--R 398824965000x + 1568711529000x + 2570205330000x + 2245236840000x
+--R +
+--R 2
+--R 1102923360000x + 288860880000x + 31512096000
+--R *
+--R +--+ +--------+
+--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8
+--R \|21 \|55 log(---------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R - 130986207675x - 432275892930x - 570477768855x - 376323861626x
+--R +
+--R - 124085884254x - 16360698684
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 7144200x + 28100520x + 46040400x + 40219200x + 19756800x
+--R +
+--R 5174400x + 564480
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R 2231141147log(-----------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8
+--R 65650200\|21 \|55 log(---------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R 4462282294atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R - 131300400\|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +--+
+--R 1176\|21
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2
+--R (2954259000x - 7681073400x + 1444304400x + 5252016000)
+--R *
+--R +-+ +--+
+--R \|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 22311411470x - 2231141147x + 6693423441)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 13583754870x - 28972016913x + 11090069739
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (4851341025x - 23769192400x + 38813738791x - 21123942360)\|21
+--R +
+--R 2 +-+ +--+
+--R (454955886000x + 75825981000x - 151651962000)\|5 \|11
+--R +
+--R 3 2
+--R (- 167335586025x + 446228229400x - 118250480791x - 267736937640)
+--R *
+--R +-+ +-+
+--R \|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1940536410x - 7373086909x + 8482394942x - 2640492795)\|21
+--R +
+--R 3 2 +-+
+--R (- 41359626000x + 59282130600x + 24815775600x - 22058467200)\|5
+--R *
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 66934234410x + 104863633909x + 31235976058x - 33467117205)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (64993698000x - 97490547000x - 39718371000x + 36107610000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (111557057350x - 167335586025x - 51316246381x + 53547387528)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R - 67918774350x + 253530123525x - 287226483999x + 88720557912
+--R /
+--R 4 3 2 +--+ +--+
+--R (105840x - 95256x - 159936x + 19992x + 35280)\|21 \|55
+--R +
+--R 4 3 2
+--R - 3704400x + 3087000x + 5408424x - 642096x - 1185408
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (- 1481760x - 395136x + 913752x + 123480x - 148176)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (- 529200x + 1323000x + 37632x - 1379448x - 16464x + 282240)\|21
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^3
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R (1) ------------------------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+r0:=-1/10*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^2-127/50*(1-2*x)^(3/2)*(2+3*x)^4/_
+ (3+5*x)-11763/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_
+ 50557/78125*sqrt(1-2*x)-1/468750*(118254-449875*x)*sqrt(1-2*x)+_
+ 44804/46875*(2+3*x)^2*sqrt(1-2*x)+250829/78750*(2+3*x)^3*_
+ sqrt(1-2*x)-1117/1125*(2+3*x)^4*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--+ \|5 \|- 2x + 1
+--R (- 4117050x - 4940460x - 1482138)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3 2
+--R 15750000x + 15075000x - 16051500x - 11139550x + 9372960x
+--R +
+--R 6891315x + 871208
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (27343750x + 32812500x + 9843750)\|5
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (2058525x + 2470230x + 741069)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 6 5 4 3 2
+--R 15750000x + 15075000x - 16051500x - 11139550x + 9372960x
+--R +
+--R 6891315x + 871208
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (27343750x + 32812500x + 9843750)\|5
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 11763\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 23526\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 156250\|5
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^3
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R (1) -------------------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+r0:=-1/10*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2-47/25*(1-2*x)^(3/2)*(2+3*x)^3/_
+ (3+5*x)-5559/15625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_
+ 5839/15625*sqrt(1-2*x)+223/250*(2+3*x)*sqrt(1-2*x)+_
+ 7149/3125*(2+3*x)^2*sqrt(1-2*x)-636/875*(2+3*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--+ \|5 \|- 2x + 1
+--R (- 1945650x - 2334780x - 700434)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2 +-+
+--R (1350000x - 27000x - 1506900x + 1651030x + 2637795x + 770444)\|5
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2 +-+
+--R (5468750x + 6562500x + 1968750)\|5
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (972825x + 1167390x + 350217)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2 +-+
+--R (1350000x - 27000x - 1506900x + 1651030x + 2637795x + 770444)\|5
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2 +-+
+--R (5468750x + 6562500x + 1968750)\|5
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 5559\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 11118\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 31250\|5
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^3
+--R
+--R
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R (1) ----------------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+r0:=511/6875*(1-2*x)^(3/2)+1533/75625*(1-2*x)^(5/2)-1/550*(1-2*x)^(7/2)/_
+ (3+5*x)^2-129/6050*(1-2*x)^(7/2)/(3+5*x)-1533/3125*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+1533/3125*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--+ \|5 \|- 2x + 1
+--R (- 76650x - 91980x - 27594)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--------+
+--R (18000x - 25400x + 51980x + 98595x + 32504)\|5 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (156250x + 187500x + 56250)\|5
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (38325x + 45990x + 13797)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--------+
+--R (18000x - 25400x + 51980x + 98595x + 32504)\|5 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (156250x + 187500x + 56250)\|5
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 1533\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R 3066\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 6250\|5
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^3
+--R
+--R
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R (1) --------------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+r0:=-21/275*(1-2*x)^(3/2)-1/110*(1-2*x)^(7/2)/(3+5*x)^2-_
+ 63/550*(1-2*x)^(5/2)/(3+5*x)+63/125*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(11/5)-63/125*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--+ \|5 \|- 2x + 1
+--R (3150x + 3780x + 1134)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+
+--R (400x - 2280x - 3795x - 1394)\|5 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (6250x + 7500x + 2250)\|5
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R 2 +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (1575x + 1890x + 567)\|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--------+
+--R (400x - 2280x - 3795x - 1394)\|5 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (6250x + 7500x + 2250)\|5
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 63\|11 log(----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +--+ \|5 \|- 2x + 1
+--R - 126\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R 250\|5
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(1-2*x)^(5/2)/(3+5*x)^3
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+r0:=-1/10*(1-2*x)^(5/2)/(3+5*x)^2+1/10*(1-2*x)^(3/2)/(3+5*x)-_
+ 3/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+3/25*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--+ \|5 \|- 2x + 1
+--R (- 150x - 180x - 54)\|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+
+--R (80x + 195x + 64)\|5 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (1250x + 1500x + 450)\|5
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (75x + 90x + 27)\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--------+
+--R (80x + 195x + 64)\|5 \|- 2x + 1
+--R /
+--R 2 +-+
+--R (1250x + 1500x + 450)\|5
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+ +-+ +--------+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1
+--R 3\|11 log(--------------------------------) + 6\|11 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R --------------------------------------------------------------------------
+--R +-+
+--R 50\|5
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^3)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 4 3 2
+--R 375x + 925x + 855x + 351x + 54
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+r0:=-1/2*(1-2*x)^(5/2)/(3+5*x)^2+71/10*(1-2*x)^(3/2)/(3+5*x)-_
+ 2523/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_
+ 98*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+73/25*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +-+ \|3 \|- 2x + 1
+--R (122500x + 147000x + 44100)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +--+ \|5 \|- 2x + 1
+--R (- 126150x - 151380x - 45414)\|3 \|11 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +--------+
+--R (4125x + 2354)\|3 \|5 \|- 2x + 1
+--R /
+--R 2 +-+ +-+
+--R (1250x + 1500x + 450)\|3 \|5
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+ +-+
+--R 2 +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R (63075x + 75690x + 22707)\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R 2 +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R (61250x + 73500x + 22050)\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +-+ +--------+
+--R (4125x + 2354)\|3 \|5 \|- 2x + 1
+--R /
+--R 2 +-+ +-+
+--R (1250x + 1500x + 450)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 2523\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 2450\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1
+--R - 4900\|5 \|7 atanh(---------------) + 5046\|3 \|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +-+
+--R 50\|3 \|5
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------
+--R 5 4 3 2
+--R 1125x + 3525x + 4415x + 2763x + 864x + 108
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+r0:=-33/2*(1-2*x)^(3/2)/(3+5*x)^2+(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^2)-_
+ 7209/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_
+ 1400*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+2299/10*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 +-+ +-+ \|3 \|- 2x + 1
+--R (1050000x + 1960000x + 1218000x + 252000)\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +--+
+--R (- 1081350x - 2018520x - 1254366x - 259524)\|3 \|11
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +-+ +--------+
+--R (35515x + 43806x + 13474)\|3 \|5 \|- 2x + 1
+--R /
+--R 3 2 +-+ +-+
+--R (750x + 1400x + 870x + 180)\|3 \|5
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +--+
+--R (540675x + 1009260x + 627183x + 129762)\|3 \|11
+--R *
+--R +--+ +--------+ +-+
+--R 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R log(--------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +-+
+--R (525000x + 980000x + 609000x + 126000)\|5 \|7
+--R *
+--R +-+ +--------+ +-+
+--R - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +-+ +--------+
+--R (35515x + 43806x + 13474)\|3 \|5 \|- 2x + 1
+--R /
+--R 3 2 +-+ +-+
+--R (750x + 1400x + 870x + 180)\|3 \|5
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 7209\|3 \|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3
+--R 7000\|5 \|7 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|3 \|- 2x + 1
+--R - 14000\|5 \|7 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|5 \|- 2x + 1
+--R 14418\|3 \|11 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +-+
+--R 10\|3 \|5
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------------
+--R 6 5 4 3 2
+--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+r0:=1/2*(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^2)+45/2*(1-2*x)^(3/2)/((2+3*x)*_
+ (3+5*x)^2)-14073*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_
+ 4555*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-737/2*sqrt(1-2*x)/_
+ (3+5*x)^2+2311*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +-+ +--+
+--R (2049750x + 5192700x + 4928510x + 2077080x + 327960)\|5 \|21
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+
+--R (- 6332850x - 16043220x - 15226986x - 6417288x - 1013256)\|11
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+
+--R (207990x + 395215x + 249939x + 52607)\|5 \|- 2x + 1
+--R /
+--R 4 3 2 +-+
+--R (450x + 1140x + 1082x + 456x + 72)\|5
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +--+
+--R (3166425x + 8021610x + 7613493x + 3208644x + 506628)\|11
+--R *
+--R +--+ +--------+ +-+
+--R 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R log(--------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--+
+--R (1024875x + 2596350x + 2464255x + 1038540x + 163980)\|5 \|21
+--R *
+--R +--+ +--------+
+--R - \|21 \|- 2x + 1 + 3x - 5
+--R log(---------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--------+
+--R (207990x + 395215x + 249939x + 52607)\|5 \|- 2x + 1
+--R /
+--R 4 3 2 +-+
+--R (450x + 1140x + 1082x + 456x + 72)\|5
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+ +-+
+--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5
+--R 14073\|11 log(--------------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R +-+ +--+ - \|21 \|- 2x + 1 + 3x - 5
+--R 4555\|5 \|21 log(---------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +--+ \|5 \|- 2x + 1
+--R - 9110\|5 \|21 atanh(---------------) + 28146\|11 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+
+--R 2\|5
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+
+--R (- 956550x + 478275)\|11
+--R +
+--R 2 +-+ +-+ +-+
+--R (68325x - 223195x + 182200)\|3 \|5 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R +-+ +-+ +--+
+--R (956550x - 478275)\|3 \|7 \|11
+--R +
+--R 2 +-+
+--R (- 1434825x + 4687095x - 3826200)\|5
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +-+ +--+
+--R (- 136650x + 296075x - 113875)\|3 \|7 \|11
+--R +
+--R 2 +-+
+--R (- 956550x + 2008755x - 765240)\|5
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2 +--+
+--R (2869650x - 6217575x + 2391375)\|11
+--R +
+--R 2 +-+ +-+ +-+
+--R (956550x - 2008755x + 765240)\|3 \|5 \|7
+--R /
+--R 3 2 +-+ +--+
+--R (60x - 86x - 36x + 32)\|5 \|21
+--R +
+--R 3 2 +--+
+--R (- 180x + 270x + 110x - 100)\|11
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+ +--+
+--R (- 120x + 40x + 50x - 20)\|11 \|21
+--R +
+--R 4 3 2 +-+
+--R (- 180x + 558x - 322x - 276x + 160)\|5
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R -----------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+r0:=1/3*(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^2)+85/9*(1-2*x)^(3/2)/((2+3*x)^2*_
+ (3+5*x)^2)+785570*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 23115*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-169975/54*_
+ sqrt(1-2*x)/(3+5*x)^2+11470/27*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_
+ 113875/6*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 1060519500x + 3393662400x + 4341059820x + 2774633240x
+--R +
+--R 886122960x + 113122080
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R - 31205250x - 99856800x - 127733490x - 81642180x - 26073720x
+--R +
+--R - 3328560
+--R *
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R \|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (5124375x + 13153400x + 12649336x + 5401374x + 864074)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (1350x + 4320x + 5526x + 3532x + 1128x + 144)\|21
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 15602625x + 49928400x + 63866745x + 40821090x + 13036860x
+--R +
+--R 1664280
+--R *
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R \|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 530259750x + 1696831200x + 2170529910x + 1387316620x + 443061480x
+--R +
+--R 56561040
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (5124375x + 13153400x + 12649336x + 5401374x + 864074)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2 +--+
+--R (1350x + 4320x + 5526x + 3532x + 1128x + 144)\|21
+--R Type: Union(Expression(Integer),...)
+--E 433
+
+--S 434 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 23115\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R 785570log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R - 1571140atanh(---------------) + 46230\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 2\|21
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (1040175x - 2704455x + 508530x + 1849200)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 7855700x - 785570x + 2356710)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 4782750x - 10200855x + 3904740
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (1708125x - 8368975x + 13666060x - 7437600)\|21
+--R +
+--R 2 +-+ +--+
+--R (160186950x + 26697825x - 53395650)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 58917750x + 157114000x - 41635210x - 94268400)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 683250x + 2596015x - 2986595x + 929700)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (14562450x - 20872845x - 8737470x + 7766640)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (23567100x - 36921790x - 10997980x + 11783550)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 22883850x + 34325775x + 13984575x - 12713250)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 39278500x + 58917750x + 18068110x - 18853680)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 23913750x - 89266275x + 101130540x - 31237920
+--R /
+--R 4 3 2 +--+ +--+ 4 3
+--R (180x - 162x - 272x + 34x + 60)\|21 \|55 - 6300x + 5250x
+--R +
+--R 2
+--R 9198x - 1092x - 2016
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (2520x + 672x - 1554x - 210x + 252)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (900x - 2250x - 64x + 2346x + 28x - 480)\|21
+--R Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x
+--R +
+--R 10800x + 864
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+r0:=1/4*(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^2)+205/36*(1-2*x)^(3/2)/((2+3*x)^3*_
+ (3+5*x)^2)+163363895/28*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 171675*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_
+ 8836825/378*sqrt(1-2*x)/(3+5*x)^2+34525/216*sqrt(1-2*x)/_
+ ((2+3*x)^2*(3+5*x)^2)+522385/168*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_
+ 23680975/168*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 661623774750x + 2558278595700x + 4119710704110x + 3536501598960x
+--R +
+--R 2
+--R 1706825974960x + 439122149760x + 47048801760
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 6 5 4 3
+--R - 19467945000x - 75276054000x - 121220404200x - 104059771200x
+--R +
+--R 2
+--R - 50222491200x - 12920947200x - 1384387200
+--R *
+--R +-+ +--------+
+--R +--+ +--+ \|5 \|- 2x + 1
+--R \|21 \|55 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 3196931625x + 10337268075x + 13362164665x + 8630749831x
+--R +
+--R 2785562634x + 359378534
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3 2 +--+
+--R (113400x + 438480x + 706104x + 606144x + 292544x + 75264x + 8064)\|21
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 9733972500x + 37638027000x + 60610202100x + 52029885600x
+--R +
+--R 2
+--R 25111245600x + 6460473600x + 692193600
+--R *
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R \|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R 6 5 4 3
+--R 330811887375x + 1279139297850x + 2059855352055x + 1768250799480x
+--R +
+--R 2
+--R 853412987480x + 219561074880x + 23524400880
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R 3196931625x + 10337268075x + 13362164665x + 8630749831x
+--R +
+--R 2785562634x + 359378534
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R /
+--R 6 5 4 3 2 +--+
+--R (113400x + 438480x + 706104x + 606144x + 292544x + 75264x + 8064)\|21
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+
+--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8
+--R 4806900\|21 \|55 log(-------------------------)
+--R 5x + 3
+--R +
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R 163363895log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1
+--R - 326727790atanh(---------------) + 9613800\|21 \|55 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +--+
+--R 56\|21
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 2 +-+ +--+
+--R (216310500x - 562407300x + 105751800x + 384552000)\|5 \|11
+--R +
+--R 2 +-+ +-+
+--R (- 1633638950x - 163363895x + 490091685)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 2
+--R 994600950x - 2121327705x + 812013615
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +--+
+--R (355214625x - 1740377500x + 2841937435x - 1546692600)\|21
+--R +
+--R 2 +-+ +--+
+--R (33311817000x + 5551969500x - 11103939000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 12252292125x + 32672779000x - 8658286435x - 19603667400)\|3 \|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 142085850x + 539856565x - 621079970x + 193336575)\|21
+--R +
+--R 3 2 +-+ +--+
+--R (3028347000x - 4340630700x - 1817008200x + 1615118400)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (4900916850x - 7678103065x - 2287094530x + 2450458425)\|3 \|7
+--R *
+--R +--+
+--R \|55
+--R +
+--R 3 2 +-+ +--+
+--R (- 4758831000x + 7138246500x + 2908174500x - 2643795000)\|5 \|11
+--R +
+--R 3 2 +-+ +-+
+--R (- 8168194750x + 12252292125x + 3757369585x - 3920733480)\|3 \|7
+--R *
+--R +--+
+--R \|21
+--R +
+--R 3 2
+--R 4973004750x - 18563446125x + 21030689715x - 6496108920
+--R /
+--R 4 3 2 +--+ +--+ 4
+--R (5040x - 4536x - 7616x + 952x + 1680)\|21 \|55 - 176400x
+--R +
+--R 3 2
+--R 147000x + 257544x - 30576x - 56448
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +--+
+--R (70560x + 18816x - 43512x - 5880x + 7056)\|55
+--R +
+--R 5 4 3 2 +--+
+--R (25200x - 63000x - 1792x + 65688x + 784x - 13440)\|21
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(2+3*x)^5*(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 6 5 4 3 2
+--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96
+--R (1) ------------------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+r0:=60025/24*(1-2*x)^(3/2)-103929/64*(1-2*x)^(5/2)+5355/8*(1-2*x)^(7/2)-_
+ 10815/64*(1-2*x)^(9/2)+1053/44*(1-2*x)^(11/2)-_
+ 1215/832*(1-2*x)^(13/2)-184877/64*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 40095x - 208251x - 488925x - 698580x - 707436x - 597464x
+--R +
+--R - 638648
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 429
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 40095x - 208251x - 488925x - 698580x - 707436x - 597464x
+--R +
+--R - 638648
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 429
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(2+3*x)^4*(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R 405x + 1323x + 1728x + 1128x + 368x + 48
+--R (1) --------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+r0:=57281/96*(1-2*x)^(3/2)-24843/80*(1-2*x)^(5/2)+1539/16*(1-2*x)^(7/2)-_
+ 519/32*(1-2*x)^(9/2)+405/352*(1-2*x)^(11/2)-26411/32*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 6075x - 27630x - 56520x - 71136x - 67664x - 75584)\|- 2x + 1
+--R (2) --------------------------------------------------------------------
+--R 165
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (- 6075x - 27630x - 56520x - 71136x - 67664x - 75584)\|- 2x + 1
+--R (3) --------------------------------------------------------------------
+--R 165
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(2+3*x)^3*(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 4 3 2
+--R 135x + 351x + 342x + 148x + 24
+--R (1) ---------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+r0:=3283/24*(1-2*x)^(3/2)-1071/20*(1-2*x)^(5/2)+621/56*(1-2*x)^(7/2)-_
+ 15/16*(1-2*x)^(9/2)-3773/16*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 1575x - 6165x - 10881x - 12434x - 14954)\|- 2x + 1
+--R (2) ---------------------------------------------------------
+--R 105
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 1575x - 6165x - 10881x - 12434x - 14954)\|- 2x + 1
+--R (3) ---------------------------------------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(2+3*x)^2*(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 3 2
+--R 45x + 87x + 56x + 12
+--R (1) ----------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+r0:=707/24*(1-2*x)^(3/2)-309/40*(1-2*x)^(5/2)+45/56*(1-2*x)^(7/2)-_
+ 539/8*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 675x - 2232x - 3448x - 4708)\|- 2x + 1
+--R (2) --------------------------------------------
+--R 105
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 675x - 2232x - 3448x - 4708)\|- 2x + 1
+--R (3) --------------------------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(2+3*x)*(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 2
+--R 15x + 19x + 6
+--R (1) --------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+r0:=17/3*(1-2*x)^(3/2)-3/4*(1-2*x)^(5/2)-77/4*sqrt(1-2*x)
+--R
+--R
+--R 2 +--------+
+--R (- 9x - 25x - 43)\|- 2x + 1
+--R (2) -----------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +--------+
+--R (- 9x - 25x - 43)\|- 2x + 1
+--R (3) -----------------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 5x + 3
+--R (1) -----------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+r0:=5/6*(1-2*x)^(3/2)-11/2*sqrt(1-2*x)
+--R
+--R
+--R +--------+
+--R (- 5x - 14)\|- 2x + 1
+--R (2) ----------------------
+--R 3
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R (- 5x - 14)\|- 2x + 1
+--R (3) ----------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(3+5*x)/((2+3*x)*sqrt(1-2*x))
+--R
+--R
+--R 5x + 3
+--R (1) -------------------
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+r0:=2/3*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-5/3*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--------+
+--R 2atanh(---------------) - 5\|21 \|- 2x + 1
+--R +-+
+--R \|7
+--R (2) -------------------------------------------
+--R +--+
+--R 3\|21
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+
+--R log(-------------------------------) - 5\|21 \|- 2x + 1
+--R 3x + 2
+--R (3) --------------------------------------------------------
+--R +--+
+--R 3\|21
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R log(-------------------------------) - 2atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------
+--R +--+
+--R 3\|21
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+
+--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21
+--R +
+--R - 42x + 21
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (378x + 63x - 126)\|- 2x + 1 + (- 54x + 81x + 33x - 30)\|21
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(3+5*x)/((2+3*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 5x + 3
+--R (1) --------------------------
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+r0:=-68/21*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/21*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--------+
+--R (- 204x - 136)atanh(---------------) + \|21 \|- 2x + 1
+--R +-+
+--R \|7
+--R (2) -------------------------------------------------------
+--R +--+
+--R (63x + 42)\|21
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+
+--R (102x + 68)log(-----------------------------) + \|21 \|- 2x + 1
+--R 3x + 2
+--R (3) ----------------------------------------------------------------
+--R +--+
+--R (63x + 42)\|21
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 34log(-----------------------------) + 68atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 21\|21
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 102x + 170)\|21 + (102x - 170)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 68x + 34)\|3 \|7 \|21 + 1428x - 714
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (2646x + 441x - 882)\|- 2x + 1 + (378x - 567x - 231x + 210)\|21
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(3+5*x)/((2+3*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 5x + 3
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+r0:=-67/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/42*sqrt(1-2*x)/(2+3*x)^2-_
+ 67/294*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1
+--R (- 1206x - 1608x - 536)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +--+ +--------+
+--R (- 201x - 127)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (2646x + 3528x + 1176)\|21
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 21\|- 2x + 1 + (3x - 5)\|21
+--R (603x + 804x + 268)log(-----------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R (- 201x - 127)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (2646x + 3528x + 1176)\|21
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 67log(-----------------------------) + 134atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ----------------------------------------------------------------
+--R +--+
+--R 294\|21
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 201x + 335)\|21 + (201x - 335)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 134x + 67)\|3 \|7 \|21 + 2814x - 1407
+--R /
+--R 2 +--------+
+--R (37044x + 6174x - 12348)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (5292x - 7938x - 3234x + 2940)\|21
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(3+5*x)/((2+3*x)^4*sqrt(1-2*x))
+--R
+--R
+--R 5x + 3
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+r0:=-100/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ 1/63*sqrt(1-2*x)/(2+3*x)^3-50/441*sqrt(1-2*x)/(2+3*x)^2-_
+ 50/1029*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (- 2700x - 5400x - 3600x - 800)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (- 450x - 950x - 417)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (27783x + 55566x + 37044x + 8232)\|21
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 3 2 21\|- 2x + 1 + (3x - 5)\|21
+--R (1350x + 2700x + 1800x + 400)log(-----------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (- 450x - 950x - 417)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (27783x + 55566x + 37044x + 8232)\|21
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 50log(-----------------------------) + 100atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ----------------------------------------------------------------
+--R +--+
+--R 1029\|21
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 150x + 250)\|21 + (150x - 250)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 100x + 50)\|3 \|7 \|21 + 2100x - 1050
+--R /
+--R 2 +--------+
+--R (129654x + 21609x - 43218)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (18522x - 27783x - 11319x + 10290)\|21
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(3+5*x)/((2+3*x)^5*sqrt(1-2*x))
+--R
+--R
+--R 5x + 3
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+r0:=-95/4116*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ 1/84*sqrt(1-2*x)/(2+3*x)^4-19/252*sqrt(1-2*x)/(2+3*x)^3-_
+ 95/3528*sqrt(1-2*x)/(2+3*x)^2-95/8232*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 4 3 2 \|3 \|- 2x + 1
+--R (- 15390x - 41040x - 41040x - 18240x - 3040)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (- 2565x - 7125x - 7942x - 2790)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (7695x + 20520x + 20520x + 9120x + 1520)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (- 2565x - 7125x - 7942x - 2790)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 95log(-----------------------------) + 190atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ----------------------------------------------------------------
+--R +--+
+--R 8232\|21
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 285x + 475)\|21 + (285x - 475)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 190x + 95)\|3 \|7 \|21 + 3990x - 1995
+--R /
+--R 2 +--------+
+--R (1037232x + 172872x - 345744)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (148176x - 222264x - 90552x + 82320)\|21
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(2+3*x)^5*(3+5*x)^2/sqrt(1-2*x)
+--R
+--R
+--R 7 6 5 4 3 2
+--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288
+--R (1) ----------------------------------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+r0:=6206585/384*(1-2*x)^(3/2)-1623419/128*(1-2*x)^(5/2)+_
+ 842415/128*(1-2*x)^(7/2)-285565/128*(1-2*x)^(9/2)+_
+ 672003/1408*(1-2*x)^(11/2)-97605/1664*(1-2*x)^(13/2)+_
+ 405/128*(1-2*x)^(15/2)-2033647/128*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R - 173745x - 1002375x - 2632743x - 4212525x - 4694340x - 4058988x
+--R +
+--R - 3152152x - 3275704
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 429
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R - 173745x - 1002375x - 2632743x - 4212525x - 4694340x - 4058988x
+--R +
+--R - 3152152x - 3275704
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 429
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3k.input.pdf b/src/axiom-website/CATS/rich3k.input.pdf
new file mode 100644
index 0000000..9354f79
Binary files /dev/null and b/src/axiom-website/CATS/rich3k.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3l.input.pamphlet b/src/axiom-website/CATS/rich3l.input.pamphlet
new file mode 100644
index 0000000..86bc6fd
--- /dev/null
+++ b/src/axiom-website/CATS/rich3l.input.pamphlet
@@ -0,0 +1,8152 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3l.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 50 matching answers.
+\item 51 cases where the Axiom result differs from Rubi
+\item 1 case 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 rich3l.output
+)spool rich3l.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 502
+t0:=(2+3*x)^4*(3+5*x)^2/sqrt(1-2*x)
+--R
+--R
+--R 6 5 4 3 2
+--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144
+--R (1) ----------------------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 502
+r0:=381073/96*(1-2*x)^(3/2)-832951/320*(1-2*x)^(5/2)+17337/16*(1-2*x)^(7/2)-_
+ 17679/64*(1-2*x)^(9/2)+13905/352*(1-2*x)^(11/2)-2025/832*(1-2*x)^(13/2)-_
+ 290521/64*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 334125x - 1709100x - 3954645x - 5576580x - 5587044x - 4685656x
+--R +
+--R - 4994536
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 334125x - 1709100x - 3954645x - 5576580x - 5587044x - 4685656x
+--R +
+--R - 4994536
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 502
+t0:=(2+3*x)^3*(3+5*x)^2/sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R 675x + 2160x + 2763x + 1766x + 564x + 72
+--R (1) --------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 502
+r0:=91091/96*(1-2*x)^(3/2)-39977/80*(1-2*x)^(5/2)+17541/112*(1-2*x)^(7/2)-_
+ 855/32*(1-2*x)^(9/2)+675/352*(1-2*x)^(11/2)-41503/32*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2 +--------+
+--R (- 70875x - 316575x - 636795x - 790023x - 743822x - 826982)\|- 2x + 1
+--R --------------------------------------------------------------------------
+--R 1155
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2 +--------+
+--R (- 70875x - 316575x - 636795x - 790023x - 743822x - 826982)\|- 2x + 1
+--R --------------------------------------------------------------------------
+--R 1155
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 502
+t0:=(2+3*x)^2*(3+5*x)^2/sqrt(1-2*x)
+--R
+--R
+--R 4 3 2
+--R 225x + 570x + 541x + 228x + 36
+--R (1) ---------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 502
+r0:=1309/6*(1-2*x)^(3/2)-3467/40*(1-2*x)^(5/2)+255/14*(1-2*x)^(7/2)-_
+ 25/16*(1-2*x)^(9/2)-5929/16*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 2625x - 10050x - 17391x - 19574x - 23354)\|- 2x + 1
+--R (2) ----------------------------------------------------------
+--R 105
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 2625x - 10050x - 17391x - 19574x - 23354)\|- 2x + 1
+--R (3) ----------------------------------------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 502
+t0:=(2+3*x)*(3+5*x)^2/sqrt(1-2*x)
+--R
+--R
+--R 3 2
+--R 75x + 140x + 87x + 18
+--R (1) -----------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 502
+r0:=1133/24*(1-2*x)^(3/2)-101/8*(1-2*x)^(5/2)+75/56*(1-2*x)^(7/2)-_
+ 847/8*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 225x - 723x - 1091x - 1469)\|- 2x + 1
+--R (2) -------------------------------------------
+--R 21
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 225x - 723x - 1091x - 1469)\|- 2x + 1
+--R (3) -------------------------------------------
+--R 21
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 502
+t0:=(3+5*x)^2/sqrt(1-2*x)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) --------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 502
+r0:=55/6*(1-2*x)^(3/2)-5/4*(1-2*x)^(5/2)-121/4*sqrt(1-2*x)
+--R
+--R
+--R 2 +--------+
+--R (- 15x - 40x - 67)\|- 2x + 1
+--R (2) ------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +--------+
+--R (- 15x - 40x - 67)\|- 2x + 1
+--R (3) ------------------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 502
+t0:=(3+5*x)^2/((2+3*x)*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) -------------------
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 502
+r0:=-2/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-5/9*(13+5*x)*sqrt(1-2*x),_
+ -2/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-50/9*sqrt(1-2*x)-_
+ 5/9*(3+5*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--------+
+--R - 2atanh(---------------) + (- 25x - 65)\|21 \|- 2x + 1
+--R +-+
+--R \|7
+--R [--------------------------------------------------------,
+--R +--+
+--R 9\|21
+--R +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--------+
+--R - 2atanh(---------------) + (- 25x - 65)\|21 \|- 2x + 1
+--R +-+
+--R \|7
+--R --------------------------------------------------------]
+--R +--+
+--R 9\|21
+--R Type: Tuple(Expression(Integer))
+--E 27
+
+--S 28 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+
+--R log(-----------------------------) + (- 25x - 65)\|21 \|- 2x + 1
+--R 3x + 2
+--R (3) -----------------------------------------------------------------
+--R +--+
+--R 9\|21
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 9\|21
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+
+--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (- 2x + 1)\|3 \|7 \|21
+--R +
+--R 42x - 21
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (1134x + 189x - 378)\|- 2x + 1 + (162x - 243x - 99x + 90)\|21
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 502
+t0:=(3+5*x)^2/((2+3*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) --------------------------
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 502
+r0:=46/21*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-25/9*sqrt(1-2*x)-_
+ 1/63*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R +-+ +--------+
+--R \|3 \|- 2x + 1 +--+ +--------+
+--R (138x + 92)atanh(---------------) + (- 175x - 117)\|21 \|- 2x + 1
+--R +-+
+--R \|7
+--R (2) ------------------------------------------------------------------
+--R +--+
+--R (63x + 42)\|21
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R (69x + 46)log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R (- 175x - 117)\|21 \|- 2x + 1
+--R /
+--R +--+
+--R (63x + 42)\|21
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 23log(-------------------------------) - 46atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 21\|21
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 69x + 115)\|21 + (69x - 115)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (46x - 23)\|3 \|7 \|21 - 966x + 483
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (2646x + 441x - 882)\|- 2x + 1 + (- 378x + 567x + 231x - 210)\|21
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 502
+t0:=(3+5*x)^2/((2+3*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 502
+r0:=-257/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 1/126*sqrt(1-2*x)/(2+3*x)^2+137/882*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1
+--R (- 13878x - 18504x - 6168)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +--+ +--------+
+--R (137x + 89)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (2646x + 3528x + 1176)\|21
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 21\|- 2x + 1 + (3x - 5)\|21
+--R (6939x + 9252x + 3084)log(-----------------------------)
+--R 3x + 2
+--R +
+--R +--+ +--------+
+--R (137x + 89)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (2646x + 3528x + 1176)\|21
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 257log(-----------------------------) + 514atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 98\|21
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 771x + 1285)\|21 + (771x - 1285)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 514x + 257)\|3 \|7 \|21 + 10794x - 5397
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (12348x + 2058x - 4116)\|- 2x + 1 + (1764x - 2646x - 1078x + 980)\|21
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 502
+t0:=(3+5*x)^2/((2+3*x)^4*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 502
+r0:=-2245/3087*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 1/189*sqrt(1-2*x)/(2+3*x)^3+205/2646*sqrt(1-2*x)/(2+3*x)^2-_
+ 2245/6174*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (- 121230x - 242460x - 161640x - 35920)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (- 20205x - 25505x - 8056)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (166698x + 333396x + 222264x + 49392)\|21
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 3 2 21\|- 2x + 1 + (3x - 5)\|21
+--R (60615x + 121230x + 80820x + 17960)log(-----------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (- 20205x - 25505x - 8056)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (166698x + 333396x + 222264x + 49392)\|21
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 2245log(-----------------------------) + 4490atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 6174\|21
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 6735x + 11225)\|21 + (6735x - 11225)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 4490x + 2245)\|3 \|7 \|21 + 94290x - 47145
+--R /
+--R 2 +--------+
+--R (777924x + 129654x - 259308)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (111132x - 166698x - 67914x + 61740)\|21
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 502
+t0:=(3+5*x)^2/((2+3*x)^5*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 502
+r0:=-635/4116*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 1/252*sqrt(1-2*x)/(2+3*x)^4+13/252*sqrt(1-2*x)/(2+3*x)^3-_
+ 635/3528*sqrt(1-2*x)/(2+3*x)^2-635/8232*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 102870x - 274320x - 274320x - 121920x - 20320)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (- 17145x - 47625x - 39366x - 10190)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (51435x + 137160x + 137160x + 60960x + 10160)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (- 17145x - 47625x - 39366x - 10190)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 635log(-----------------------------) + 1270atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 8232\|21
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 1905x + 3175)\|21 + (1905x - 3175)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 1270x + 635)\|3 \|7 \|21 + 26670x - 13335
+--R /
+--R 2 +--------+
+--R (1037232x + 172872x - 345744)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (148176x - 222264x - 90552x + 82320)\|21
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 502
+t0:=(3+5*x)^2/((2+3*x)^6*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) ------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 502
+r0:=-117/9604*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_
+ 1/315*sqrt(1-2*x)/(2+3*x)^5+341/8820*sqrt(1-2*x)/(2+3*x)^4-_
+ 117/980*sqrt(1-2*x)/(2+3*x)^3-117/2744*sqrt(1-2*x)/(2+3*x)^2-_
+ 351/19208*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2 +-+
+--R (- 852930x - 2843100x - 3790800x - 2527200x - 842400x - 112320)\|3
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 426465x - 1468935x - 2110212x - 1327058x - 298748)\|7 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 70013160x + 233377200x + 311169600x + 207446400x + 69148800x
+--R +
+--R 9219840
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2 +-+
+--R (426465x + 1421550x + 1895400x + 1263600x + 421200x + 56160)\|3
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+ +--------+
+--R (- 426465x - 1468935x - 2110212x - 1327058x - 298748)\|7 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 70013160x + 233377200x + 311169600x + 207446400x + 69148800x
+--R +
+--R 9219840
+--R *
+--R +-+
+--R \|7
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R 117\|3 log(-------------------------------) + 234\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 19208\|7
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 502
+t0:=(2+3*x)^4*(3+5*x)^3/sqrt(1-2*x)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432
+--R -----------------------------------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 502
+r0:=3278737/128*(1-2*x)^(3/2)-12973191/640*(1-2*x)^(5/2)+_
+ 1357793/128*(1-2*x)^(7/2)-1392467/384*(1-2*x)^(9/2)+_
+ 1101465/1408*(1-2*x)^(11/2)-161325/1664*(1-2*x)^(13/2)+_
+ 675/128*(1-2*x)^(15/2)-3195731/128*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3
+--R - 1447875x - 8241750x - 21369825x - 33786160x - 37260640x
+--R +
+--R 2
+--R - 31962552x - 24706048x - 25632688
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R - 1447875x - 8241750x - 21369825x - 33786160x - 37260640x
+--R +
+--R 2
+--R - 31962552x - 24706048x - 25632688
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2145
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 502
+t0:=(2+3*x)^3*(3+5*x)^3/sqrt(1-2*x)
+--R
+--R
+--R 6 5 4 3 2
+--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216
+--R (1) -----------------------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 502
+r0:=100793/16*(1-2*x)^(3/2)-1334949/320*(1-2*x)^(5/2)+_
+ 98209/56*(1-2*x)^(7/2)-28895/64*(1-2*x)^(9/2)+_
+ 11475/176*(1-2*x)^(11/2)-3375/832*(1-2*x)^(13/2)-456533/64*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 1299375x - 6544125x - 14921900x - 20766885x - 20586249x
+--R +
+--R - 17147586x - 18228666
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 5005
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 1299375x - 6544125x - 14921900x - 20766885x - 20586249x
+--R +
+--R - 17147586x - 18228666
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 5005
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 502
+t0:=(2+3*x)^2*(3+5*x)^3/sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R 1125x + 3525x + 4415x + 2763x + 864x + 108
+--R (1) ----------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 502
+r0:=48279/32*(1-2*x)^(3/2)-64317/80*(1-2*x)^(5/2)+28555/112*(1-2*x)^(7/2)-_
+ 4225/96*(1-2*x)^(9/2)+1125/352*(1-2*x)^(11/2)-65219/32*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R (- 118125x - 518000x - 1024475x - 1252938x - 1167932x - 1292672)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 1155
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (- 118125x - 518000x - 1024475x - 1252938x - 1167932x - 1292672)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 1155
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 502
+t0:=(2+3*x)*(3+5*x)^3/sqrt(1-2*x)
+--R
+--R
+--R 4 3 2
+--R 375x + 925x + 855x + 351x + 54
+--R (1) ---------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 502
+r0:=2783/8*(1-2*x)^(3/2)-561/4*(1-2*x)^(5/2)+1675/56*(1-2*x)^(7/2)-_
+ 125/48*(1-2*x)^(9/2)-9317/16*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 875x - 3275x - 5556x - 6161x - 7295)\|- 2x + 1
+--R (2) -----------------------------------------------------
+--R 21
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 875x - 3275x - 5556x - 6161x - 7295)\|- 2x + 1
+--R (3) -----------------------------------------------------
+--R 21
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 502
+t0:=(3+5*x)^3/sqrt(1-2*x)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) -------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 502
+r0:=605/8*(1-2*x)^(3/2)-165/8*(1-2*x)^(5/2)+125/56*(1-2*x)^(7/2)-_
+ 1331/8*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 125x - 390x - 575x - 764)\|- 2x + 1
+--R (2) -----------------------------------------
+--R 7
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 125x - 390x - 575x - 764)\|- 2x + 1
+--R (3) -----------------------------------------
+--R 7
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 502
+t0:=(3+5*x)^3/((2+3*x)*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) -------------------------
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 502
+r0:=2/27*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-218/9*sqrt(1-2*x)-_
+ 1/3*(3+5*x)^2*sqrt(1-2*x)-5/27*(41+61*x)*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R \|3 \|- 2x + 1 2 +--+ +--------+
+--R 2atanh(---------------) + (- 225x - 575x - 940)\|21 \|- 2x + 1
+--R +-+
+--R \|7
+--R (2) ----------------------------------------------------------------
+--R +--+
+--R 27\|21
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 2 +--+ +--------+
+--R log(-------------------------------) + (- 225x - 575x - 940)\|21 \|- 2x + 1
+--R 3x + 2
+--R -----------------------------------------------------------------------------
+--R +--+
+--R 27\|21
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R log(-------------------------------) - 2atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------
+--R +--+
+--R 27\|21
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+
+--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21
+--R +
+--R - 42x + 21
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (3402x + 567x - 1134)\|- 2x + 1 + (- 486x + 729x + 297x - 270)\|21
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 502
+t0:=(3+5*x)^3/((2+3*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) --------------------------
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 502
+r0:=-208/189*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-1570/189*sqrt(1-2*x)-_
+ 38/189*(3+5*x)*sqrt(1-2*x)/(2+3*x)-5/9*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R (- 624x - 416)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (- 2625x - 8050x - 4199)\|21 \|- 2x + 1
+--R /
+--R +--+
+--R (567x + 378)\|21
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R (312x + 208)log(-----------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (- 2625x - 8050x - 4199)\|21 \|- 2x + 1
+--R /
+--R +--+
+--R (567x + 378)\|21
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 104log(-----------------------------) + 208atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 189\|21
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 312x + 520)\|21 + (312x - 520)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 208x + 104)\|3 \|7 \|21 + 4368x - 2184
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (23814x + 3969x - 7938)\|- 2x + 1 + (3402x - 5103x - 2079x + 1890)\|21
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 502
+t0:=(3+5*x)^3/((2+3*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 502
+r0:=2381/441*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/126*(7-25*x)*_
+ sqrt(1-2*x)/(2+3*x)^2-274/147*sqrt(1-2*x)/(2+3*x)-_
+ 5/3*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|3 \|- 2x + 1
+--R (42858x + 57144x + 19048)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (- 36750x - 49207x - 16469)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (7938x + 10584x + 3528)\|21
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 - 21\|- 2x + 1 + (3x - 5)\|21
+--R (21429x + 28572x + 9524)log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (- 36750x - 49207x - 16469)\|21 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (7938x + 10584x + 3528)\|21
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 2381log(-------------------------------) - 4762atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 882\|21
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 7143x + 11905)\|21 + (7143x - 11905)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (4762x - 2381)\|3 \|7 \|21 - 100002x + 50001
+--R /
+--R 2 +--------+
+--R (111132x + 18522x - 37044)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 15876x + 23814x + 9702x - 8820)\|21
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 502
+t0:=(3+5*x)^3/((2+3*x)^4*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 502
+r0:=-78710/9261*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+10600/9261*_
+ sqrt(1-2*x)-3385/9261*(3+5*x)*sqrt(1-2*x)/(2+3*x)-50/441*(3+5*x)^2*_
+ sqrt(1-2*x)/(2+3*x)^2-1/21*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 \|3 \|- 2x + 1
+--R (- 2125170x - 4250340x - 2833560x - 629680)atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+ +--------+
+--R (31680x + 41155x + 13373)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (250047x + 500094x + 333396x + 74088)\|21
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R (1062585x + 2125170x + 1416780x + 314840)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+ +--------+
+--R (31680x + 41155x + 13373)\|21 \|- 2x + 1
+--R /
+--R 3 2 +--+
+--R (250047x + 500094x + 333396x + 74088)\|21
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 39355log(-----------------------------) + 78710atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 9261\|21
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 118065x + 196775)\|21 + (118065x - 196775)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 78710x + 39355)\|3 \|7 \|21 + 1652910x - 826455
+--R /
+--R 2 +--------+
+--R (1166886x + 194481x - 388962)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (166698x - 250047x - 101871x + 92610)\|21
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 502
+t0:=(3+5*x)^3/((2+3*x)^5*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 502
+r0:=-42995/37044*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 3275/12348*sqrt(1-2*x)/(2+3*x)-1/18*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3-_
+ 1/28*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4+5/10584*(79+29*x)*_
+ sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 6965190x - 18573840x - 18573840x - 8255040x - 1375840)
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+ +--------+
+--R (- 1160865x - 2195625x - 1385462x - 291670)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (3482595x + 9286920x + 9286920x + 4127520x + 687920)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+ +--------+
+--R (- 1160865x - 2195625x - 1385462x - 291670)\|21 \|- 2x + 1
+--R /
+--R 4 3 2 +--+
+--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 42995log(-----------------------------) + 85990atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 74088\|21
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 128985x + 214975)\|21 + (128985x - 214975)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 85990x + 42995)\|3 \|7 \|21 + 1805790x - 902895
+--R /
+--R 2 +--------+
+--R (9335088x + 1555848x - 3111696)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1333584x - 2000376x - 814968x + 740880)\|21
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 502
+t0:=(3+5*x)^3/((2+3*x)^6*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) ------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 502
+r0:=-5293/21609*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_
+ 61/882*sqrt(1-2*x)/(2+3*x)^2-5293/43218*sqrt(1-2*x)/(2+3*x)-_
+ 8/245*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4-1/35*(3+5*x)^3*_
+ sqrt(1-2*x)/(2+3*x)^5+1/15435*(353+295*x)*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 12861990x - 42873300x - 57164400x - 38109600x - 12703200x
+--R +
+--R - 1693760
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 2143665x - 7383735x - 8806422x - 4450198x - 816938)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 52509870x + 175032900x + 233377200x + 155584800x + 51861600x
+--R +
+--R 6914880
+--R *
+--R +--+
+--R \|21
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (6430995x + 21436650x + 28582200x + 19054800x + 6351600x + 846880)
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 2143665x - 7383735x - 8806422x - 4450198x - 816938)\|21 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 52509870x + 175032900x + 233377200x + 155584800x + 51861600x
+--R +
+--R 6914880
+--R *
+--R +--+
+--R \|21
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 5293log(-----------------------------) + 10586atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 43218\|21
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 15879x + 26465)\|21 + (15879x - 26465)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 10586x + 5293)\|3 \|7 \|21 + 222306x - 111153
+--R /
+--R 2 +--------+
+--R (5445468x + 907578x - 1815156)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (777924x - 1166886x - 475398x + 432180)\|21
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 502
+t0:=(a+b*x)^2/((c+d*x)^2*sqrt(e+f*x))
+--R
+--R
+--R 2 2 2
+--R b x + 2a b x + a
+--R (1) ------------------------------
+--R 2 2 2 +-------+
+--R (d x + 2c d x + c )\|f x + e
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 502
+r0:=(b*c-a*d)*(4*b*d*e-3*b*c*f-a*d*f)*atanh(sqrt(d)*sqrt(e+f*x)/_
+ sqrt(d*e-c*f))/(d^(5/2)*(d*e-c*f)^(3/2))+2*b^2*sqrt(e+f*x)/_
+ (d^2*f)-(b*c-a*d)^2*sqrt(e+f*x)/(d^2*(d*e-c*f)*(c+d*x))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 3 2 2
+--R ((- a d - 2a b c d + 3b c d)f + (4a b d - 4b c d )e f)x
+--R +
+--R 2 2 2 2 3 2 2 2 2
+--R (- a c d - 2a b c d + 3b c )f + (4a b c d - 4b c d)e f
+--R *
+--R +-+ +-------+
+--R \|d \|f x + e
+--R atanh(--------------)
+--R +-----------+
+--R \|- c f + d e
+--R +
+--R 2 2 2 2 2 2 2 2
+--R ((2b c d f - 2b d e)x + (a d - 2a b c d + 3b c )f - 2b c d e)
+--R *
+--R +-----------+ +-+ +-------+
+--R \|- c f + d e \|d \|f x + e
+--R /
+--R 3 2 4 2 2 2 3 +-----------+ +-+
+--R ((c d f - d e f)x + c d f - c d e f)\|- c f + d e \|d
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 2 3 2 2
+--R ((a d + 2a b c d - 3b c d)f + (- 4a b d + 4b c d )e f)x
+--R +
+--R 2 2 2 2 3 2 2 2 2
+--R (a c d + 2a b c d - 3b c )f + (- 4a b c d + 4b c d)e f
+--R *
+--R +-------------+
+--R 2 +-------+ | 2
+--R (2c d f - 2d e)\|f x + e + (d f x - c f + 2d e)\|- c d f + d e
+--R log(----------------------------------------------------------------)
+--R d x + c
+--R +
+--R 2 2 2 2 2 2 2 2
+--R ((4b c d f - 4b d e)x + (2a d - 4a b c d + 6b c )f - 4b c d e)
+--R *
+--R +-------------+
+--R | 2 +-------+
+--R \|- c d f + d e \|f x + e
+--R /
+--R +-------------+
+--R 3 2 4 2 2 2 3 | 2
+--R ((2c d f - 2d e f)x + 2c d f - 2c d e f)\|- c d f + d e
+--R ,
+--R
+--R 2 3 2 2 2 2 3 2 2
+--R ((a d + 2a b c d - 3b c d)f + (- 4a b d + 4b c d )e f)x
+--R +
+--R 2 2 2 2 3 2 2 2 2
+--R (a c d + 2a b c d - 3b c )f + (- 4a b c d + 4b c d)e f
+--R *
+--R +-----------+
+--R | 2 +-------+
+--R \|c d f - d e \|f x + e
+--R atan(------------------------)
+--R c f - d e
+--R +
+--R 2 2 2 2 2 2 2 2
+--R ((2b c d f - 2b d e)x + (a d - 2a b c d + 3b c )f - 2b c d e)
+--R *
+--R +-----------+
+--R | 2 +-------+
+--R \|c d f - d e \|f x + e
+--R /
+--R +-----------+
+--R 3 2 4 2 2 2 3 | 2
+--R ((c d f - d e f)x + c d f - c d e f)\|c d f - d e
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 113
+
+--S 114 of 502
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 2 2 +-----------+ +-+
+--R ((a d + 2a b c d - 3b c )f + (- 4a b d + 4b c d)e)\|- c f + d e \|d
+--R *
+--R +-------------+
+--R 2 +-------+ | 2
+--R (2c d f - 2d e)\|f x + e + (d f x - c f + 2d e)\|- c d f + d e
+--R log(----------------------------------------------------------------)
+--R d x + c
+--R +
+--R +-------------+
+--R 2 2 2 2 2 2 | 2
+--R ((2a d + 4a b c d - 6b c )f + (- 8a b d + 8b c d)e)\|- c d f + d e
+--R *
+--R +-+ +-------+
+--R \|d \|f x + e
+--R atanh(--------------)
+--R +-----------+
+--R \|- c f + d e
+--R /
+--R +-------------+
+--R 2 3 | 2 +-----------+ +-+
+--R (2c d f - 2d e)\|- c d f + d e \|- c f + d e \|d
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 502
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+--S 116 of 502
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-----------+
+--R 2 2 2 2 2 2 | 2
+--R ((a d + 2a b c d - 3b c )f + (- 4a b d + 4b c d)e)\|c d f - d e
+--R *
+--R +-+ +-------+
+--R \|d \|f x + e
+--R atanh(--------------)
+--R +-----------+
+--R \|- c f + d e
+--R +
+--R 2 2 2 2 2 2 +-----------+ +-+
+--R ((a d + 2a b c d - 3b c )f + (- 4a b d + 4b c d)e)\|- c f + d e \|d
+--R *
+--R +-----------+
+--R | 2 +-------+
+--R \|c d f - d e \|f x + e
+--R atan(------------------------)
+--R c f - d e
+--R /
+--R +-----------+
+--R 2 3 +-----------+ +-+ | 2
+--R (c d f - d e)\|- c f + d e \|d \|c d f - d e
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 502
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 117
+
+)clear all
+
+--S 118 of 502
+t0:=(2+3*x)^5/((3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 118
+
+--S 119 of 502
+r0:=-2/3125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 125702/3125*sqrt(1-2*x)-748/625*(2+3*x)^2*sqrt(1-2*x)-_
+ 149/525*(2+3*x)^3*sqrt(1-2*x)-1/15*(2+3*x)^4*sqrt(1-2*x)-_
+ 1/3125*(31426+52375*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R - 14atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 118125x - 482625x - 885870x - 1044285x - 1277616)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R 21875\|55
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R 7log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 118125x - 482625x - 885870x - 1044285x - 1277616)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R 21875\|55
+--R Type: Union(Expression(Integer),...)
+--E 120
+
+--S 121 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 3125\|55
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (1718750x + 171875x - 515625)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (156250x - 234375x - 71875x + 75000)\|55
+--R Type: Expression(Integer)
+--E 122
+
+)clear all
+
+--S 123 of 502
+t0:=(2+3*x)^4/((3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) -------------------------------
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 123
+
+--S 124 of 502
+r0:=-2/625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-7878/625*sqrt(1-2*x)-_
+ 9/5*(2+3*x)*sqrt(1-2*x)-48/125*(2+3*x)^2*sqrt(1-2*x)-_
+ 3/35*(2+3*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R - 14atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 10125x - 35370x - 57285x - 80616)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R 4375\|55
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R 7log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+ +--------+
+--R (- 10125x - 35370x - 57285x - 80616)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R 4375\|55
+--R Type: Union(Expression(Integer),...)
+--E 125
+
+--S 126 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 625\|55
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (343750x + 34375x - 103125)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (31250x - 46875x - 14375x + 15000)\|55
+--R Type: Expression(Integer)
+--E 127
+
+)clear all
+
+--S 128 of 502
+t0:=(2+3*x)^3/((3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) ---------------------
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 128
+
+--S 129 of 502
+r0:=-2/125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-542/125*sqrt(1-2*x)-_
+ 3/25*(2+3*x)^2*sqrt(1-2*x)-1/125*(136+225*x)*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 2 +--+ +--------+
+--R - 2atanh(---------------) + (- 135x - 405x - 738)\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ------------------------------------------------------------------
+--R +--+
+--R 125\|55
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55 2 +--+ +--------+
+--R log(-----------------------------) + (- 135x - 405x - 738)\|55 \|- 2x + 1
+--R 5x + 3
+--R ---------------------------------------------------------------------------
+--R +--+
+--R 125\|55
+--R Type: Union(Expression(Integer),...)
+--E 130
+
+--S 131 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 125\|55
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (68750x + 6875x - 20625)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (6250x - 9375x - 2875x + 3000)\|55
+--R Type: Expression(Integer)
+--E 132
+
+)clear all
+
+--S 133 of 502
+t0:=(2+3*x)^2/((3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) -------------------
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 133
+
+--S 134 of 502
+r0:=-2/25*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-38/25*sqrt(1-2*x)-_
+ 1/5*(2+3*x)*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 +--+ +--------+
+--R - 2atanh(---------------) + (- 15x - 48)\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) --------------------------------------------------------
+--R +--+
+--R 25\|55
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+
+--R log(-----------------------------) + (- 15x - 48)\|55 \|- 2x + 1
+--R 5x + 3
+--R (3) -----------------------------------------------------------------
+--R +--+
+--R 25\|55
+--R Type: Union(Expression(Integer),...)
+--E 135
+
+--S 136 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 25\|55
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (13750x + 1375x - 4125)\|- 2x + 1 + (1250x - 1875x - 575x + 600)\|55
+--R Type: Expression(Integer)
+--E 137
+
+)clear all
+
+--S 138 of 502
+t0:=(2+3*x)/((3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 3x + 2
+--R (1) -------------------
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 138
+
+--S 139 of 502
+r0:=-2/5*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3/5*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 +--+ +--------+
+--R - 2atanh(---------------) - 3\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ---------------------------------------------
+--R +--+
+--R 5\|55
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+
+--R log(-----------------------------) - 3\|55 \|- 2x + 1
+--R 5x + 3
+--R (3) ------------------------------------------------------
+--R +--+
+--R 5\|55
+--R Type: Union(Expression(Integer),...)
+--E 140
+
+--S 141 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 5\|55
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (2750x + 275x - 825)\|- 2x + 1 + (250x - 375x - 115x + 120)\|55
+--R Type: Expression(Integer)
+--E 142
+
+)clear all
+
+--S 143 of 502
+t0:=1/((3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +--------+
+--R (5x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 143
+
+--S 144 of 502
+r0:=-2*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R 2atanh(---------------)
+--R +--+
+--R \|11
+--R (2) - -----------------------
+--R +--+
+--R \|55
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R log(-----------------------------)
+--R 5x + 3
+--R (3) ----------------------------------
+--R +--+
+--R \|55
+--R Type: Union(Expression(Integer),...)
+--E 145
+
+--S 146 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R \|55
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (550x + 55x - 165)\|- 2x + 1 + (50x - 75x - 23x + 24)\|55
+--R Type: Expression(Integer)
+--E 147
+
+)clear all
+
+--S 148 of 502
+t0:=1/((2+3*x)*(3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R 2 +--------+
+--R (15x + 19x + 6)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 148
+
+--S 149 of 502
+r0:=2*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-2*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(5/11)
+--R
+--R
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R 2\|3 \|11 atanh(---------------) - 2\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R (2) ------------------------------------------------------------------
+--R +-+ +--+
+--R \|7 \|11
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R /
+--R +-+ +--+
+--R \|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 150
+
+--S 151 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R - 2\|3 \|11 atanh(---------------) + 2\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R \|7 \|11
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 152
+
+)clear all
+
+--S 153 of 502
+t0:=1/((2+3*x)^2*(3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------
+--R 3 2 +--------+
+--R (45x + 87x + 56x + 12)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 153
+
+--S 154 of 502
+r0:=72/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(5/11)+3/7*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R (216x + 144)\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1 +-+ +--+ +--------+
+--R (- 210x - 140)\|5 \|7 atanh(---------------) + 3\|7 \|11 \|- 2x + 1
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R (21x + 14)\|7 \|11
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (105x + 70)\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (108x + 72)\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--+ +--------+
+--R 3\|7 \|11 \|- 2x + 1
+--R /
+--R +-+ +--+
+--R (21x + 14)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 155
+
+--S 156 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 35\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 36\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R - 72\|3 \|11 atanh(---------------) + 70\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 7\|7 \|11
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 157
+
+)clear all
+
+--S 158 of 502
+t0:=1/((2+3*x)^3*(3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------
+--R 4 3 2 +--------+
+--R (135x + 351x + 342x + 148x + 24)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 158
+
+--S 159 of 502
+r0:=2523/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-50*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(5/11)+3/14*sqrt(1-2*x)/(2+3*x)^2+_
+ 219/98*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--+ \|3 \|- 2x + 1
+--R (45414x + 60552x + 20184)\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +-+ \|5 \|- 2x + 1
+--R (- 44100x - 58800x - 19600)\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--+ +--------+
+--R (657x + 459)\|7 \|11 \|- 2x + 1
+--R /
+--R 2 +-+ +--+
+--R (882x + 1176x + 392)\|7 \|11
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R 2 +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (22050x + 29400x + 9800)\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R 2 +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (22707x + 30276x + 10092)\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--+ +--------+
+--R (657x + 459)\|7 \|11 \|- 2x + 1
+--R /
+--R 2 +-+ +--+
+--R (882x + 1176x + 392)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 160
+
+--S 161 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 2450\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 2523\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R - 5046\|3 \|11 atanh(---------------) + 4900\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 98\|7 \|11
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 162
+
+)clear all
+
+--S 163 of 502
+t0:=1/((2+3*x)^4*(3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 163
+
+--S 164 of 502
+r0:=88310/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-250*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+1/7*sqrt(1-2*x)/(2+3*x)^3+_
+ 55/49*sqrt(1-2*x)/(2+3*x)^2+3840/343*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+
+--R (2384370x + 4768740x + 3179160x + 706480)\|3 \|11
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+
+--R (- 2315250x - 4630500x - 3087000x - 686000)\|5 \|7
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+ +--------+
+--R (34560x + 47235x + 16179)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (9261x + 18522x + 12348x + 2744)\|7 \|11
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +-+
+--R (1157625x + 2315250x + 1543500x + 343000)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+
+--R (1192185x + 2384370x + 1589580x + 353240)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +--+ +--------+
+--R (34560x + 47235x + 16179)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (9261x + 18522x + 12348x + 2744)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 165
+
+--S 166 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 42875\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 44155\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 88310\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 85750\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 343\|7 \|11
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 167
+
+)clear all
+
+--S 168 of 502
+t0:=1/((2+3*x)^5*(3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 168
+
+--S 169 of 502
+r0:=36045/28*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_
+ 1250*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 3/28*sqrt(1-2*x)/(2+3*x)^4+3/4*sqrt(1-2*x)/(2+3*x)^3+_
+ 45/8*sqrt(1-2*x)/(2+3*x)^2+3135/56*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +-+ +--+
+--R (5839290x + 15571440x + 15571440x + 6920640x + 1153440)\|3 \|11
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+ +-+
+--R (- 5670000x - 15120000x - 15120000x - 6720000x - 1120000)\|5 \|7
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (84645x + 172125x + 116766x + 26430)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (4536x + 12096x + 12096x + 5376x + 896)\|7 \|11
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+ +-+
+--R (2835000x + 7560000x + 7560000x + 3360000x + 560000)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--+
+--R (2919645x + 7785720x + 7785720x + 3460320x + 576720)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (84645x + 172125x + 116766x + 26430)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (4536x + 12096x + 12096x + 5376x + 896)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 170
+
+--S 171 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 35000\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 36045\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 72090\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 70000\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 56\|7 \|11
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 172
+
+)clear all
+
+--S 173 of 502
+t0:=(2+3*x)^6/((3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R (1) -----------------------------------------------------
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 173
+
+--S 174 of 502
+r0:=-398/171875*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 4434698/171875*sqrt(1-2*x)-26352/34375*(2+3*x)^2*sqrt(1-2*x)-_
+ 1717/9625*(2+3*x)^3*sqrt(1-2*x)+8/825*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)-_
+ 1/15*(2+3*x)^5*sqrt(1-2*x)/(3+5*x)-1/171875*(1108774+_
+ 1847625*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R (- 13930x - 8358)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 19490625x - 92998125x - 200942775x - 273540465x - 334366065x
+--R +
+--R - 135011752
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1
+--R /
+--R +--+
+--R (6015625x + 3609375)\|55
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R (6965x + 4179)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R - 19490625x - 92998125x - 200942775x - 273540465x - 334366065x
+--R +
+--R - 135011752
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1
+--R /
+--R +--+
+--R (6015625x + 3609375)\|55
+--R Type: Union(Expression(Integer),...)
+--E 175
+
+--S 176 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 199log(-----------------------------) + 398atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 171875\|55
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 995x + 1592)\|55 + (995x - 1592)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 398x + 199)\|5 \|11 \|55 + 21890x - 10945
+--R /
+--R 2 +--------+
+--R (94531250x + 9453125x - 28359375)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (8593750x - 12890625x - 3953125x + 4125000)\|55
+--R Type: Expression(Integer)
+--E 177
+
+)clear all
+
+--S 178 of 502
+t0:=(2+3*x)^5/((3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 178
+
+--S 179 of 502
+r0:=-332/34375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 278748/34375*sqrt(1-2*x)-318/275*(2+3*x)*sqrt(1-2*x)-_
+ 1668/6875*(2+3*x)^2*sqrt(1-2*x)+26/1925*(2+3*x)^3*_
+ sqrt(1-2*x)/(3+5*x)-3/35*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R (- 11620x - 6972)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 1670625x - 6994350x - 13532310x - 20175210x - 8527768)\|55
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R +--+
+--R (1203125x + 721875)\|55
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R (5810x + 3486)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+
+--R (- 1670625x - 6994350x - 13532310x - 20175210x - 8527768)\|55
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R +--+
+--R (1203125x + 721875)\|55
+--R Type: Union(Expression(Integer),...)
+--E 180
+
+--S 181 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 166log(-----------------------------) + 332atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 34375\|55
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 830x + 1328)\|55 + (830x - 1328)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 332x + 166)\|5 \|11 \|55 + 18260x - 9130
+--R /
+--R 2 +--------+
+--R (18906250x + 1890625x - 5671875)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1718750x - 2578125x - 790625x + 825000)\|55
+--R Type: Expression(Integer)
+--E 182
+
+)clear all
+
+--S 183 of 502
+t0:=(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) -------------------------------
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 183
+
+--S 184 of 502
+r0:=-266/6875*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 19166/6875*sqrt(1-2*x)+28/1375*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)-_
+ 3/25*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)-7/6875*(694+1125*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R (- 1330x - 798)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 22275x - 82665x - 171765x - 78112)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R (34375x + 20625)\|55
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R (665x + 399)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+ +--------+
+--R (- 22275x - 82665x - 171765x - 78112)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R (34375x + 20625)\|55
+--R Type: Union(Expression(Integer),...)
+--E 185
+
+--S 186 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 133log(-----------------------------) + 266atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 6875\|55
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 665x + 1064)\|55 + (665x - 1064)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 266x + 133)\|5 \|11 \|55 + 14630x - 7315
+--R /
+--R 2 +--------+
+--R (3781250x + 378125x - 1134375)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (343750x - 515625x - 158125x + 165000)\|55
+--R Type: Expression(Integer)
+--E 187
+
+)clear all
+
+--S 188 of 502
+t0:=(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) ---------------------------
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 188
+
+--S 189 of 502
+r0:=-8/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-54/55*sqrt(1-2*x)+_
+ 2/55*(2+3*x)*sqrt(1-2*x)/(3+5*x)-1/5*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 2 +--+ +--------+
+--R (- 40x - 24)atanh(---------------) + (- 99x - 396x - 202)\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R --------------------------------------------------------------------------
+--R +--+
+--R (275x + 165)\|55
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R (20x + 12)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+ +--------+
+--R (- 99x - 396x - 202)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R (275x + 165)\|55
+--R Type: Union(Expression(Integer),...)
+--E 190
+
+--S 191 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 4log(-----------------------------) + 8atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------
+--R +--+
+--R 55\|55
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 20x + 32)\|55 + (20x - 32)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 8x + 4)\|5 \|11 \|55 + 440x - 220
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (30250x + 3025x - 9075)\|- 2x + 1 + (2750x - 4125x - 1265x + 1320)\|55
+--R Type: Expression(Integer)
+--E 192
+
+)clear all
+
+--S 193 of 502
+t0:=(2+3*x)^2/((3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) ---------------------------
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 193
+
+--S 194 of 502
+r0:=-134/275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-9/25*sqrt(1-2*x)-_
+ 1/275*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 +--+ +--------+
+--R (- 670x - 402)atanh(---------------) + (- 495x - 298)\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ---------------------------------------------------------------------
+--R +--+
+--R (1375x + 825)\|55
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R (335x + 201)log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R (- 495x - 298)\|55 \|- 2x + 1
+--R /
+--R +--+
+--R (1375x + 825)\|55
+--R Type: Union(Expression(Integer),...)
+--E 195
+
+--S 196 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 67log(-----------------------------) + 134atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ----------------------------------------------------------------
+--R +--+
+--R 275\|55
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 335x + 536)\|55 + (335x - 536)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 134x + 67)\|5 \|11 \|55 + 7370x - 3685
+--R /
+--R 2 +--------+
+--R (151250x + 15125x - 45375)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (13750x - 20625x - 6325x + 6600)\|55
+--R Type: Expression(Integer)
+--E 197
+
+)clear all
+
+--S 198 of 502
+t0:=(2+3*x)/((3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 3x + 2
+--R (1) ---------------------------
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 198
+
+--S 199 of 502
+r0:=-68/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/55*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 +--+ +--------+
+--R (- 340x - 204)atanh(---------------) - \|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) -------------------------------------------------------
+--R +--+
+--R (275x + 165)\|55
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+
+--R (170x + 102)log(-----------------------------) - \|55 \|- 2x + 1
+--R 5x + 3
+--R (3) -----------------------------------------------------------------
+--R +--+
+--R (275x + 165)\|55
+--R Type: Union(Expression(Integer),...)
+--E 200
+
+--S 201 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 34log(-----------------------------) + 68atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 55\|55
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 170x + 272)\|55 + (170x - 272)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 68x + 34)\|5 \|11 \|55 + 3740x - 1870
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (30250x + 3025x - 9075)\|- 2x + 1 + (2750x - 4125x - 1265x + 1320)\|55
+--R Type: Expression(Integer)
+--E 202
+
+)clear all
+
+--S 203 of 502
+t0:=1/((3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R 2 +--------+
+--R (25x + 30x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 203
+
+--S 204 of 502
+r0:=-2/11*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/11*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R +-+ +--------+
+--R \|5 \|- 2x + 1 +--+ +--------+
+--R (- 10x - 6)atanh(---------------) - \|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------
+--R +--+
+--R (55x + 33)\|55
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+
+--R (5x + 3)log(-----------------------------) - \|55 \|- 2x + 1
+--R 5x + 3
+--R (3) -------------------------------------------------------------
+--R +--+
+--R (55x + 33)\|55
+--R Type: Union(Expression(Integer),...)
+--E 205
+
+--S 206 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 11\|55
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (6050x + 605x - 1815)\|- 2x + 1 + (550x - 825x - 253x + 264)\|55
+--R Type: Expression(Integer)
+--E 207
+
+)clear all
+
+--S 208 of 502
+t0:=1/((2+3*x)*(3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R 3 2 +--------+
+--R (75x + 140x + 87x + 18)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 208
+
+--S 209 of 502
+r0:=-6*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+64/11*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(5/11)-5/11*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R (- 330x - 198)\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1 +-+ +--+ +--------+
+--R (320x + 192)\|5 \|7 atanh(---------------) - 5\|7 \|11 \|- 2x + 1
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R (55x + 33)\|7 \|11
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (165x + 99)\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (160x + 96)\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--+ +--------+
+--R - 5\|7 \|11 \|- 2x + 1
+--R /
+--R +-+ +--+
+--R (55x + 33)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 210
+
+--S 211 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 33\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 32\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R 66\|3 \|11 atanh(---------------) - 64\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 11\|7 \|11
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 212
+
+)clear all
+
+--S 213 of 502
+t0:=1/((2+3*x)^2*(3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------
+--R 4 3 2 +--------+
+--R (225x + 570x + 541x + 228x + 36)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 213
+
+--S 214 of 502
+r0:=-426/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+650/11*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(5/11)-340/77*sqrt(1-2*x)/(3+5*x)+3/7*_
+ sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--+ \|3 \|- 2x + 1
+--R (- 70290x - 89034x - 28116)\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +-+ \|5 \|- 2x + 1
+--R (68250x + 86450x + 27300)\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--+ +--------+
+--R (- 1020x - 647)\|7 \|11 \|- 2x + 1
+--R /
+--R 2 +-+ +--+
+--R (1155x + 1463x + 462)\|7 \|11
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R 2 +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (35145x + 44517x + 14058)\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +-+
+--R (34125x + 43225x + 13650)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--+ +--------+
+--R (- 1020x - 647)\|7 \|11 \|- 2x + 1
+--R /
+--R 2 +-+ +--+
+--R (1155x + 1463x + 462)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 215
+
+--S 216 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 2343\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 2275\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R 4686\|3 \|11 atanh(---------------) - 4550\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 77\|7 \|11
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 217
+
+)clear all
+
+--S 218 of 502
+t0:=1/((2+3*x)^3*(3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 218
+
+--S 219 of 502
+r0:=-22479/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+4900/11*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-35845/1078*_
+ sqrt(1-2*x)/(3+5*x)+3/14*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_
+ 162/49*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+
+--R (- 22254210x - 43024806x - 27694128x - 5934456)\|3 \|11
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+
+--R (21609000x + 41777400x + 26891200x + 5762400)\|5 \|7
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+ +--------+
+--R (- 322605x - 419448x - 136021)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (48510x + 93786x + 60368x + 12936)\|7 \|11
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +--+
+--R (11127105x + 21512403x + 13847064x + 2967228)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +-+
+--R (10804500x + 20888700x + 13445600x + 2881200)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(-----------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--+ +--------+
+--R (- 322605x - 419448x - 136021)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (48510x + 93786x + 60368x + 12936)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 220
+
+--S 221 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 247269\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 240100\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R 494538\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R - 480200\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 1078\|7 \|11
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 222
+
+)clear all
+
+--S 223 of 502
+t0:=1/((2+3*x)^4*(3+5*x)^2*sqrt(1-2*x))
+--R
+--R
+--R (1)
+--R 1
+--R -----------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 223
+
+--S 224 of 502
+r0:=-1051695/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+32750/11*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1676975/7546*_
+ sqrt(1-2*x)/(3+5*x)+1/7*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+_
+ 145/98*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+7585/343*sqrt(1-2*x)/_
+ ((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 4 3 2
+--R - 3123534150x - 8121188790x - 7912953180x - 3424318920x
+--R +
+--R - 555294960
+--R *
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R \|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2
+--R (3032977500x + 7885741500x + 7683543000x + 3325042000x + 539196000)
+--R *
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R \|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (- 45278325x - 89054820x - 58335165x - 12724912)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (1018710x + 2648646x + 2580732x + 1116808x + 181104)\|7 \|11
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (1561767075x + 4060594395x + 3956476590x + 1712159460x + 277647480)
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2
+--R (1516488750x + 3942870750x + 3841771500x + 1662521000x + 269598000)
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (- 45278325x - 89054820x - 58335165x - 12724912)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (1018710x + 2648646x + 2580732x + 1116808x + 181104)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 225
+
+--S 226 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 11568645\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 11233250\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R 23137290\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R - 22466500\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 7546\|7 \|11
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 227
+
+)clear all
+
+--S 228 of 502
+t0:=(2+3*x)^6/((3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R (1) -----------------------------------------------------
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 228
+
+--S 229 of 502
+r0:=-33069/1890625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 9865791/1890625*sqrt(1-2*x)-22437/30250*(2+3*x)*sqrt(1-2*x)-_
+ 56556/378125*(2+3*x)^2*sqrt(1-2*x)+59/3850*(2+3*x)^4*_
+ sqrt(1-2*x)/(3+5*x)^2-3/35*(2+3*x)^5*sqrt(1-2*x)/(3+5*x)^2+_
+ 309/211750*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 11574150x - 13888980x - 4166694)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 551306250x - 2690374500x - 6078090150x - 9876010320x
+--R +
+--R - 7254126105x - 1804176536
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (661718750x + 794062500x + 238218750)\|55
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (5787075x + 6944490x + 2083347)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R - 551306250x - 2690374500x - 6078090150x - 9876010320x
+--R +
+--R - 7254126105x - 1804176536
+--R *
+--R +--+ +--------+
+--R \|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (661718750x + 794062500x + 238218750)\|55
+--R Type: Union(Expression(Integer),...)
+--E 230
+
+--S 231 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 33069log(-----------------------------) + 66138atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 3781250\|55
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 165345x + 264552)\|55 + (165345x - 264552)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 66138x + 33069)\|5 \|11 \|55 + 3637590x - 1818795
+--R /
+--R 2 +--------+
+--R (2079687500x + 207968750x - 623906250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (189062500x - 283593750x - 86968750x + 90750000)\|55
+--R Type: Expression(Integer)
+--E 232
+
+)clear all
+
+--S 233 of 502
+t0:=(2+3*x)^5/((3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 233
+
+--S 234 of 502
+r0:=-22113/378125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 674163/378125*sqrt(1-2*x)+61/2750*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-_
+ 3/25*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2+504/75625*(2+3*x)^2*_
+ sqrt(1-2*x)/(3+5*x)-189/756250*(1842+2875*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 1105650x - 1326780x - 398034)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 7350750x - 32506650x - 76970520x - 63610155x - 16525496)\|55
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2 +--+
+--R (18906250x + 22687500x + 6806250)\|55
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (552825x + 663390x + 199017)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+
+--R (- 7350750x - 32506650x - 76970520x - 63610155x - 16525496)\|55
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 2 +--+
+--R (18906250x + 22687500x + 6806250)\|55
+--R Type: Union(Expression(Integer),...)
+--E 235
+
+--S 236 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 22113log(-----------------------------) + 44226atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 756250\|55
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 110565x + 176904)\|55 + (110565x - 176904)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 44226x + 22113)\|5 \|11 \|55 + 2432430x - 1216215
+--R /
+--R 2 +--------+
+--R (415937500x + 41593750x - 124781250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (37812500x - 56718750x - 17393750x + 18150000)\|55
+--R Type: Expression(Integer)
+--E 237
+
+)clear all
+
+--S 238 of 502
+t0:=(2+3*x)^4/((3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) --------------------------------------
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 238
+
+--S 239 of 502
+r0:=-2667/15125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 9513/15125*sqrt(1-2*x)+21/550*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2-_
+ 1/5*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2+21/1210*(2+3*x)*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 133350x - 160020x - 48006)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 163350x - 784080x - 764745x - 211864)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (756250x + 907500x + 272250)\|55
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (66675x + 80010x + 24003)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+ +--------+
+--R (- 163350x - 784080x - 764745x - 211864)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (756250x + 907500x + 272250)\|55
+--R Type: Union(Expression(Integer),...)
+--E 240
+
+--S 241 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 2667log(-----------------------------) + 5334atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 30250\|55
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 13335x + 21336)\|55 + (13335x - 21336)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 5334x + 2667)\|5 \|11 \|55 + 293370x - 146685
+--R /
+--R 2 +--------+
+--R (16637500x + 1663750x - 4991250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1512500x - 2268750x - 695750x + 726000)\|55
+--R Type: Expression(Integer)
+--E 242
+
+)clear all
+
+--S 243 of 502
+t0:=(2+3*x)^3/((3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) --------------------------------------
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 243
+
+--S 244 of 502
+r0:=-1347/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+13/110*(2+3*x)*_
+ sqrt(1-2*x)/(3+5*x)^2-3/5*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+_
+ 201/3025*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 67350x - 80820x - 24246)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (- 32670x - 39405x - 11884)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (151250x + 181500x + 54450)\|55
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (33675x + 40410x + 12123)log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+ +--------+
+--R (- 32670x - 39405x - 11884)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (151250x + 181500x + 54450)\|55
+--R Type: Union(Expression(Integer),...)
+--E 245
+
+--S 246 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 1347log(-----------------------------) + 2694atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 6050\|55
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 6735x + 10776)\|55 + (6735x - 10776)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2694x + 1347)\|5 \|11 \|55 + 148170x - 74085
+--R /
+--R 2 +--------+
+--R (3327500x + 332750x - 998250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (302500x - 453750x - 139150x + 145200)\|55
+--R Type: Expression(Integer)
+--E 247
+
+)clear all
+
+--S 248 of 502
+t0:=(2+3*x)^2/((3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) --------------------------------------
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 248
+
+--S 249 of 502
+r0:=-2313/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/550*sqrt(1-2*x)/_
+ (3+5*x)^2-27/1210*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 115650x - 138780x - 41634)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +--+ +--------+
+--R (- 675x - 416)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (151250x + 181500x + 54450)\|55
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (57825x + 69390x + 20817)log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R (- 675x - 416)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (151250x + 181500x + 54450)\|55
+--R Type: Union(Expression(Integer),...)
+--E 250
+
+--S 251 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 2313log(-----------------------------) + 4626atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 6050\|55
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 11565x + 18504)\|55 + (11565x - 18504)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 4626x + 2313)\|5 \|11 \|55 + 254430x - 127215
+--R /
+--R 2 +--------+
+--R (3327500x + 332750x - 998250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (302500x - 453750x - 139150x + 145200)\|55
+--R Type: Expression(Integer)
+--E 252
+
+)clear all
+
+--S 253 of 502
+t0:=(2+3*x)/((3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 3x + 2
+--R (1) --------------------------------------
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 253
+
+--S 254 of 502
+r0:=-69/605*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/110*sqrt(1-2*x)/_
+ (3+5*x)^2-69/1210*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1
+--R (- 3450x - 4140x - 1242)atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +--+ +--------+
+--R (- 345x - 218)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (30250x + 36300x + 10890)\|55
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (1725x + 2070x + 621)log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R (- 345x - 218)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (30250x + 36300x + 10890)\|55
+--R Type: Union(Expression(Integer),...)
+--E 255
+
+--S 256 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 69log(-----------------------------) + 138atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ----------------------------------------------------------------
+--R +--+
+--R 1210\|55
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 345x + 552)\|55 + (345x - 552)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 138x + 69)\|5 \|11 \|55 + 7590x - 3795
+--R /
+--R 2 +--------+
+--R (665500x + 66550x - 199650)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (60500x - 90750x - 27830x + 29040)\|55
+--R Type: Expression(Integer)
+--E 257
+
+)clear all
+
+--S 258 of 502
+t0:=1/((3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) --------------------------------------
+--R 3 2 +--------+
+--R (125x + 225x + 135x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 258
+
+--S 259 of 502
+r0:=-3/121*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/22*sqrt(1-2*x)/_
+ (3+5*x)^2-3/242*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 \|5 \|- 2x + 1 +--+ +--------+
+--R (- 150x - 180x - 54)atanh(---------------) + (- 15x - 20)\|55 \|- 2x + 1
+--R +--+
+--R \|11
+--R --------------------------------------------------------------------------
+--R 2 +--+
+--R (6050x + 7260x + 2178)\|55
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 55\|- 2x + 1 + (5x - 8)\|55
+--R (75x + 90x + 27)log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+ +--------+
+--R (- 15x - 20)\|55 \|- 2x + 1
+--R /
+--R 2 +--+
+--R (6050x + 7260x + 2178)\|55
+--R Type: Union(Expression(Integer),...)
+--E 260
+
+--S 261 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 3log(-----------------------------) + 6atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------
+--R +--+
+--R 242\|55
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 15x + 24)\|55 + (15x - 24)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 6x + 3)\|5 \|11 \|55 + 330x - 165
+--R /
+--R 2 +--------+
+--R (133100x + 13310x - 39930)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (12100x - 18150x - 5566x + 5808)\|55
+--R Type: Expression(Integer)
+--E 262
+
+)clear all
+
+--S 263 of 502
+t0:=1/((2+3*x)*(3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------
+--R 4 3 2 +--------+
+--R (375x + 925x + 855x + 351x + 54)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 263
+
+--S 264 of 502
+r0:=18*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-2115/121*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(5/11)-5/22*sqrt(1-2*x)/(3+5*x)^2+_
+ 315/242*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--+ \|3 \|- 2x + 1
+--R (108900x + 130680x + 39204)\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +-+ \|5 \|- 2x + 1
+--R (- 105750x - 126900x - 38070)\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--+ +--------+
+--R (1575x + 890)\|7 \|11 \|- 2x + 1
+--R /
+--R 2 +-+ +--+
+--R (6050x + 7260x + 2178)\|7 \|11
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R 2 +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (52875x + 63450x + 19035)\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R 2 +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (54450x + 65340x + 19602)\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--+ +--------+
+--R (1575x + 890)\|7 \|11 \|- 2x + 1
+--R /
+--R 2 +-+ +--+
+--R (6050x + 7260x + 2178)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 265
+
+--S 266 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 2115\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 2178\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R - 4356\|3 \|11 atanh(---------------) + 4230\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 242\|7 \|11
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 267
+
+)clear all
+
+--S 268 of 502
+t0:=1/((2+3*x)^2*(3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (1125x + 3525x + 4415x + 2763x + 864x + 108)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 268
+
+--S 269 of 502
+r0:=1908/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-32025/121*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-505/154*sqrt(1-2*x)/(3+5*x)^2+_
+ 3/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+33465/1694*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+
+--R (34630200x + 64643040x + 40171032x + 8311248)\|3 \|11
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+
+--R (- 33626250x - 62769000x - 39006450x - 8070300)\|5 \|7
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+ +--------+
+--R (501975x + 619170x + 190406)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (127050x + 237160x + 147378x + 30492)\|7 \|11
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +-+
+--R (16813125x + 31384500x + 19503225x + 4035150)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+
+--R (17315100x + 32321520x + 20085516x + 4155624)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +--+ +--------+
+--R (501975x + 619170x + 190406)\|7 \|11 \|- 2x + 1
+--R /
+--R 3 2 +-+ +--+
+--R (127050x + 237160x + 147378x + 30492)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 270
+
+--S 271 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 224175\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 230868\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 461736\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 448350\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 1694\|7 \|11
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 272
+
+)clear all
+
+--S 273 of 502
+t0:=1/((2+3*x)^3*(3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R (1)
+--R 1
+--R ------------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 273
+
+--S 274 of 502
+r0:=134217/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-321825/121*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-35495/1078*_
+ sqrt(1-2*x)/(3+5*x)^2+3/14*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_
+ 429/98*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+1177080/5929*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 7308115650x + 18513892980x + 17571958074x + 7405557192x
+--R +
+--R 1169298504
+--R *
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R \|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2
+--R - 7096241250x - 17977144500x - 17062517850x - 7190857800x
+--R +
+--R - 1135398600
+--R *
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R \|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (105937200x + 201297915x + 127303347x + 26794499)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (2668050x + 6759060x + 6415178x + 2703624x + 426888)\|7 \|11
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (3548120625x + 8988572250x + 8531258925x + 3595428900x + 567699300)
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2
+--R (3654057825x + 9256946490x + 8785979037x + 3702778596x + 584649252)
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (105937200x + 201297915x + 127303347x + 26794499)\|7 \|11 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +--+
+--R (2668050x + 6759060x + 6415178x + 2703624x + 426888)\|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 275
+
+--S 276 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 15769425\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 16240257\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 32480514\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 31538850\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 11858\|7 \|11
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 277
+
+)clear all
+
+--S 278 of 502
+t0:=1/((2+3*x)^4*(3+5*x)^3*sqrt(1-2*x))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 7 6 5 4 3 2
+--R (10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 278
+
+--S 279 of 502
+r0:=7852680/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_
+ 2689875/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-_
+ 2076675/7546*sqrt(1-2*x)/(3+5*x)^2+1/7*sqrt(1-2*x)/((2+3*x)^3*_
+ (3+5*x)^2)+90/49*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_
+ 12555/343*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+137735775/83006*_
+ sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 1282735278000x + 4104752889600x + 5250663071280x + 3356015556960x
+--R +
+--R 1071796587840x + 136825096320
+--R *
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R \|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3
+--R - 1245546618750x - 3985749180000x - 5098437492750x
+--R +
+--R 2
+--R - 3258719005500x - 1040723397000x - 132858306000
+--R *
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R \|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2
+--R 18594329625x + 47728484550x + 45899434890x + 19599448500x
+--R +
+--R 3135381218
+--R *
+--R +-+ +--+ +--------+
+--R \|7 \|11 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 56029050x + 179292960x + 229345578x + 146588596x + 46815384x
+--R +
+--R 5976432
+--R *
+--R +-+ +--+
+--R \|7 \|11
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 622773309375x + 1992874590000x + 2549218746375x + 1629359502750x
+--R +
+--R 520361698500x + 66429153000
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 641367639000x + 2052376444800x + 2625331535640x + 1678007778480x
+--R +
+--R 535898293920x + 68412548160
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2
+--R 18594329625x + 47728484550x + 45899434890x + 19599448500x
+--R +
+--R 3135381218
+--R *
+--R +-+ +--+ +--------+
+--R \|7 \|11 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R 56029050x + 179292960x + 229345578x + 146588596x + 46815384x
+--R +
+--R 5976432
+--R *
+--R +-+ +--+
+--R \|7 \|11
+--R Type: Union(Expression(Integer),...)
+--E 280
+
+--S 281 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 922627125\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 950174280\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 1900348560\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 1845254250\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 83006\|7 \|11
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 282
+
+)clear all
+
+--S 283 of 502
+t0:=(2+3*x)^7*(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R - 10935x - 57591x - 132678x - 174636x - 143640x - 75600x - 24864x
+--R +
+--R - 4672x - 384
+--R /
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 283
+
+--S 284 of 502
+r0:=-7882483/128*(1-2*x)^(3/2)+4084101/128*(1-2*x)^(5/2)-_
+ 787185/64*(1-2*x)^(7/2)+422919/128*(1-2*x)^(9/2)-_
+ 821583/1408*(1-2*x)^(11/2)+101331/1664*(1-2*x)^(13/2)-_
+ 729/256*(1-2*x)^(15/2)+9058973/256/sqrt(1-2*x)+15647317/128*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4 3
+--R - 104247x - 697653x - 2168775x - 4220622x - 5949090x - 6921432x
+--R +
+--R 2
+--R - 8106616x - 16881328x + 16936240
+--R /
+--R +--------+
+--R 143\|- 2x + 1
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4 3
+--R - 104247x - 697653x - 2168775x - 4220622x - 5949090x - 6921432x
+--R +
+--R 2
+--R - 8106616x - 16881328x + 16936240
+--R /
+--R +--------+
+--R 143\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 285
+
+--S 286 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 287
+
+)clear all
+
+--S 288 of 502
+t0:=(2+3*x)^6*(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 3645x - 16767x - 33048x - 36180x - 23760x - 9360x - 2048x - 192
+--R -----------------------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 288
+
+--S 289 of 502
+r0:=-1692705/128*(1-2*x)^(3/2)+731619/128*(1-2*x)^(5/2)-_
+ 225855/128*(1-2*x)^(7/2)+45549/128*(1-2*x)^(9/2)-_
+ 59049/1408*(1-2*x)^(11/2)+3645/1664*(1-2*x)^(13/2)+_
+ 1294139/128/sqrt(1-2*x)+3916031/128*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R - 40095x - 243486x - 687420x - 1230120x - 1663632x - 2109792x
+--R +
+--R - 4512448x + 4539904
+--R /
+--R +--------+
+--R 143\|- 2x + 1
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R - 40095x - 243486x - 687420x - 1230120x - 1663632x - 2109792x
+--R +
+--R - 4512448x + 4539904
+--R /
+--R +--------+
+--R 143\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 290
+
+--S 291 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 292
+
+)clear all
+
+--S 293 of 502
+t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 6 5 4 3 2
+--R - 1215x - 4779x - 7830x - 6840x - 3360x - 880x - 96
+--R (1) --------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 293
+
+--S 294 of 502
+r0:=-173215/64*(1-2*x)^(3/2)+7497/8*(1-2*x)^(5/2)-13905/64*(1-2*x)^(7/2)+_
+ 117/4*(1-2*x)^(9/2)-1215/704*(1-2*x)^(11/2)+_
+ 184877/64/sqrt(1-2*x)+60025/8*sqrt(1-2*x)
+--R
+--R
+--R 6 5 4 3 2
+--R - 1215x - 6651x - 17055x - 28692x - 41012x - 91704x + 92760
+--R (2) ----------------------------------------------------------------
+--R +--------+
+--R 11\|- 2x + 1
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 5 4 3 2
+--R - 1215x - 6651x - 17055x - 28692x - 41012x - 91704x + 92760
+--R (3) ----------------------------------------------------------------
+--R +--------+
+--R 11\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 295
+
+--S 296 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 297
+
+)clear all
+
+--S 298 of 502
+t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 5 4 3 2
+--R - 405x - 1323x - 1728x - 1128x - 368x - 48
+--R (1) ----------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 298
+
+--S 299 of 502
+r0:=-8281/16*(1-2*x)^(3/2)+10773/80*(1-2*x)^(5/2)-4671/224*(1-2*x)^(7/2)+_
+ 45/32*(1-2*x)^(9/2)+26411/32/sqrt(1-2*x)+57281/32*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R - 1575x - 7740x - 18288x - 31448x - 75776x + 77456
+--R (2) ------------------------------------------------------
+--R +--------+
+--R 35\|- 2x + 1
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R - 1575x - 7740x - 18288x - 31448x - 75776x + 77456
+--R (3) ------------------------------------------------------
+--R +--------+
+--R 35\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 300
+
+--S 301 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 302
+
+)clear all
+
+--S 303 of 502
+t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 4 3 2
+--R - 135x - 351x - 342x - 148x - 24
+--R (1) -----------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 303
+
+--S 304 of 502
+r0:=-357/4*(1-2*x)^(3/2)+621/40*(1-2*x)^(5/2)-135/112*(1-2*x)^(7/2)+_
+ 3773/16/sqrt(1-2*x)+3283/8*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2
+--R - 675x - 2997x - 6987x - 19154x + 19994
+--R (2) ------------------------------------------
+--R +--------+
+--R 35\|- 2x + 1
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R - 675x - 2997x - 6987x - 19154x + 19994
+--R (3) ------------------------------------------
+--R +--------+
+--R 35\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 305
+
+--S 306 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 307
+
+)clear all
+
+--S 308 of 502
+t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 3 2
+--R - 45x - 87x - 56x - 12
+--R (1) ------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 502
+r0:=-103/8*(1-2*x)^(3/2)+9/8*(1-2*x)^(5/2)+539/8/sqrt(1-2*x)+707/8*sqrt(1-2*x)
+--R
+--R
+--R 3 2
+--R - 9x - 38x - 132x + 144
+--R (2) -------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R - 9x - 38x - 132x + 144
+--R (3) -------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 310
+
+--S 311 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 312
+
+)clear all
+
+--S 313 of 502
+t0:=(2+3*x)*(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 2
+--R - 15x - 19x - 6
+--R (1) -------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 502
+r0:=-5/4*(1-2*x)^(3/2)+77/4/sqrt(1-2*x)+17*sqrt(1-2*x)
+--R
+--R
+--R 2
+--R - 5x - 29x + 35
+--R (2) ----------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 5x - 29x + 35
+--R (3) ----------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 315
+
+--S 316 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 317
+
+)clear all
+
+--S 318 of 502
+t0:=(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R - 5x - 3
+--R (1) -------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 502
+r0:=11/2/sqrt(1-2*x)+5/2*sqrt(1-2*x)
+--R
+--R
+--R - 5x + 8
+--R (2) -----------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R - 5x + 8
+--R (3) -----------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 320
+
+--S 321 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 322
+
+)clear all
+
+--S 323 of 502
+t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x))
+--R
+--R
+--R - 5x - 3
+--R (1) ------------------------
+--R 2 +--------+
+--R (6x + x - 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 323
+
+--S 324 of 502
+r0:=2/7*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+11/7/sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1 +--+
+--R 2\|- 2x + 1 atanh(---------------) + 11\|21
+--R +-+
+--R \|7
+--R (2) --------------------------------------------
+--R +--+ +--------+
+--R 7\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--+
+--R \|- 2x + 1 log(-------------------------------) + 11\|21
+--R 3x + 2
+--R (3) ---------------------------------------------------------
+--R +--+ +--------+
+--R 7\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 325
+
+--S 326 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R log(-------------------------------) - 2atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------
+--R +--+
+--R 7\|21
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+
+--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21
+--R +
+--R - 42x + 21
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (882x + 147x - 294)\|- 2x + 1 + (- 126x + 189x + 77x - 70)\|21
+--R Type: Expression(Integer)
+--E 327
+
+)clear all
+
+--S 328 of 502
+t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)
+--R
+--R
+--R - 5x - 3
+--R (1) ---------------------------------
+--R 3 2 +--------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 328
+
+--S 329 of 502
+r0:=-64/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+64/147/sqrt(1-2*x)+_
+ 1/21/((2+3*x)*sqrt(1-2*x))
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1 +--+
+--R (- 192x - 128)\|- 2x + 1 atanh(---------------) + (64x + 45)\|21
+--R +-+
+--R \|7
+--R (2) -----------------------------------------------------------------
+--R +--+ +--------+
+--R (147x + 98)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--+
+--R (96x + 64)\|- 2x + 1 log(-----------------------------) + (64x + 45)\|21
+--R 3x + 2
+--R -------------------------------------------------------------------------
+--R +--+ +--------+
+--R (147x + 98)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 330
+
+--S 331 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 32log(-----------------------------) + 64atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 49\|21
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 96x + 160)\|21 + (96x - 160)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 64x + 32)\|3 \|7 \|21 + 1344x - 672
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (6174x + 1029x - 2058)\|- 2x + 1 + (882x - 1323x - 539x + 490)\|21
+--R Type: Expression(Integer)
+--E 332
+
+)clear all
+
+--S 333 of 502
+t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)
+--R
+--R
+--R - 5x - 3
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 333
+
+--S 334 of 502
+r0:=-65/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1/42/((2+3*x)^2*_
+ sqrt(1-2*x))+65/147/((2+3*x)*sqrt(1-2*x))-195/686*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--------+ \|3 \|- 2x + 1
+--R (- 1170x - 1560x - 520)\|3 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +-+
+--R (1170x + 1105x + 233)\|7
+--R /
+--R 2 +-+ +--------+
+--R (6174x + 8232x + 2744)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R 2 +-+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (585x + 780x + 260)\|3 \|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+
+--R (1170x + 1105x + 233)\|7
+--R /
+--R 2 +-+ +--------+
+--R (6174x + 8232x + 2744)\|7 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 335
+
+--S 336 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R 65\|3 log(-------------------------------) + 130\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R --------------------------------------------------------------------------
+--R +-+
+--R 686\|7
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 337
+
+)clear all
+
+--S 338 of 502
+t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^4)
+--R
+--R
+--R - 5x - 3
+--R (1) ----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 338
+
+--S 339 of 502
+r0:=-10/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/63/((2+3*x)^3*_
+ sqrt(1-2*x))+4/9/((2+3*x)^2*sqrt(1-2*x))-5/21*sqrt(1-2*x)/_
+ (2+3*x)^2-5/49*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 +--------+ \|3 \|- 2x + 1
+--R (- 270x - 540x - 360x - 80)\|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+
+--R (90x + 145x + 57x + 1)\|21
+--R /
+--R 3 2 +--+ +--------+
+--R (1323x + 2646x + 1764x + 392)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 3 2 +--------+ 21\|- 2x + 1 + (3x - 5)\|21
+--R (135x + 270x + 180x + 40)\|- 2x + 1 log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+
+--R (90x + 145x + 57x + 1)\|21
+--R /
+--R 3 2 +--+ +--------+
+--R (1323x + 2646x + 1764x + 392)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 340
+
+--S 341 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 5log(-----------------------------) + 10atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------
+--R +--+
+--R 49\|21
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 15x + 25)\|21 + (15x - 25)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 10x + 5)\|3 \|7 \|21 + 210x - 105
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (6174x + 1029x - 2058)\|- 2x + 1 + (882x - 1323x - 539x + 490)\|21
+--R Type: Expression(Integer)
+--E 342
+
+)clear all
+
+--S 343 of 502
+t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^5)
+--R
+--R
+--R - 5x - 3
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 343
+
+--S 344 of 502
+r0:=-655/9604*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/84/((2+3*x)^4*_
+ sqrt(1-2*x))+131/294/((2+3*x)^3*sqrt(1-2*x))-131/588*_
+ sqrt(1-2*x)/(2+3*x)^3-655/8232*sqrt(1-2*x)/(2+3*x)^2-_
+ 655/19208*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (- 106110x - 282960x - 282960x - 125760x - 20960)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+
+--R (35370x + 80565x + 60391x + 10742x - 2566)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (1555848x + 4148928x + 4148928x + 1843968x + 307328)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +--------+
+--R (53055x + 141480x + 141480x + 62880x + 10480)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+
+--R (35370x + 80565x + 60391x + 10742x - 2566)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (1555848x + 4148928x + 4148928x + 1843968x + 307328)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 345
+
+--S 346 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 655log(-----------------------------) + 1310atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 19208\|21
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 1965x + 3275)\|21 + (1965x - 3275)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 1310x + 655)\|3 \|7 \|21 + 27510x - 13755
+--R /
+--R 2 +--------+
+--R (2420208x + 403368x - 806736)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (345744x - 518616x - 211288x + 192080)\|21
+--R Type: Expression(Integer)
+--E 347
+
+)clear all
+
+--S 348 of 502
+t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^6)
+--R
+--R
+--R - 5x - 3
+--R (1) -------------------------------------------------------------------
+--R 7 6 5 4 2 +--------+
+--R (1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 348
+
+--S 349 of 502
+r0:=-123/16807*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1/105/((2+3*x)^5*_
+ sqrt(1-2*x))+328/735/((2+3*x)^4*sqrt(1-2*x))-369/1715*sqrt(1-2*x)/_
+ (2+3*x)^4-123/1715*sqrt(1-2*x)/(2+3*x)^3-123/4802*sqrt(1-2*x)/_
+ (2+3*x)^2-369/33614*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2 +-+
+--R (- 298890x - 996300x - 1328400x - 885600x - 295200x - 39360)\|3
+--R *
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2 +-+
+--R (298890x + 880065x + 964197x + 430992x + 8774x - 32894)\|7
+--R /
+--R 5 4 3 2
+--R 40841010x + 136136700x + 181515600x + 121010400x + 40336800x
+--R +
+--R 5378240
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2 +-+
+--R (149445x + 498150x + 664200x + 442800x + 147600x + 19680)\|3
+--R *
+--R +-+ +--------+ +-+
+--R +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2 +-+
+--R (298890x + 880065x + 964197x + 430992x + 8774x - 32894)\|7
+--R /
+--R 5 4 3 2
+--R 40841010x + 136136700x + 181515600x + 121010400x + 40336800x
+--R +
+--R 5378240
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 350
+
+--S 351 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R 123\|3 log(-------------------------------) + 246\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 33614\|7
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 352
+
+)clear all
+
+--S 353 of 502
+t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^(3/2)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 6075x - 27540x - 53487x - 57690x - 37320x - 14480x - 3120x - 288
+--R ------------------------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 353
+
+--S 354 of 502
+r0:=-8117095/384*(1-2*x)^(3/2)+1179381/128*(1-2*x)^(5/2)-_
+ 367155/128*(1-2*x)^(7/2)+74667/128*(1-2*x)^(9/2)-_
+ 97605/1408*(1-2*x)^(11/2)+6075/1664*(1-2*x)^(13/2)+_
+ 2033647/128/sqrt(1-2*x)+6206585/128*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R - 200475x - 1201635x - 3350637x - 5928885x - 7945164x - 10015804x
+--R +
+--R - 21370088x + 21493640
+--R /
+--R +--------+
+--R 429\|- 2x + 1
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R - 200475x - 1201635x - 3350637x - 5928885x - 7945164x - 10015804x
+--R +
+--R - 21370088x + 21493640
+--R /
+--R +--------+
+--R 429\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 355
+
+--S 356 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 357
+
+)clear all
+
+--S 358 of 502
+t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^(3/2)
+--R
+--R
+--R 6 5 4 3 2
+--R - 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144
+--R (1) ------------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 358
+
+--S 359 of 502
+r0:=-832951/192*(1-2*x)^(3/2)+121359/80*(1-2*x)^(5/2)-_
+ 159111/448*(1-2*x)^(7/2)+1545/32*(1-2*x)^(9/2)-_
+ 2025/704*(1-2*x)^(11/2)+290521/64/sqrt(1-2*x)+381073/32*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 212625x - 1146600x - 2899485x - 4819932x - 6831172x - 15214664x
+--R +
+--R 15380984
+--R /
+--R +--------+
+--R 1155\|- 2x + 1
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 212625x - 1146600x - 2899485x - 4819932x - 6831172x - 15214664x
+--R +
+--R 15380984
+--R /
+--R +--------+
+--R 1155\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 360
+
+--S 361 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 362
+
+)clear all
+
+--S 363 of 502
+t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^(3/2)
+--R
+--R
+--R 5 4 3 2
+--R - 675x - 2160x - 2763x - 1766x - 564x - 72
+--R (1) ----------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 502
+r0:=-39977/48*(1-2*x)^(3/2)+17541/80*(1-2*x)^(5/2)-_
+ 7695/224*(1-2*x)^(7/2)+75/32*(1-2*x)^(9/2)+_
+ 41503/32/sqrt(1-2*x)+91091/32*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R - 7875x - 38025x - 88443x - 150253x - 359726x + 367286
+--R (2) ----------------------------------------------------------
+--R +--------+
+--R 105\|- 2x + 1
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R - 7875x - 38025x - 88443x - 150253x - 359726x + 367286
+--R (3) ----------------------------------------------------------
+--R +--------+
+--R 105\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 365
+
+--S 366 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 367
+
+)clear all
+
+--S 368 of 502
+t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^(3/2)
+--R
+--R
+--R 4 3 2
+--R - 225x - 570x - 541x - 228x - 36
+--R (1) -----------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 502
+r0:=-3467/24*(1-2*x)^(3/2)+51/2*(1-2*x)^(5/2)-225/112*(1-2*x)^(7/2)+_
+ 5929/16/sqrt(1-2*x)+1309/2*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2
+--R - 675x - 2934x - 6721x - 18230x + 18986
+--R (2) ------------------------------------------
+--R +--------+
+--R 21\|- 2x + 1
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R - 675x - 2934x - 6721x - 18230x + 18986
+--R (3) ------------------------------------------
+--R +--------+
+--R 21\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 370
+
+--S 371 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 372
+
+)clear all
+
+--S 373 of 502
+t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^(3/2)
+--R
+--R
+--R 3 2
+--R - 75x - 140x - 87x - 18
+--R (1) -------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 502
+r0:=-505/24*(1-2*x)^(3/2)+15/8*(1-2*x)^(5/2)+847/8/sqrt(1-2*x)+_
+ 1133/8*sqrt(1-2*x)
+--R
+--R
+--R 3 2
+--R - 45x - 185x - 631x + 685
+--R (2) ---------------------------
+--R +--------+
+--R 3\|- 2x + 1
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R - 45x - 185x - 631x + 685
+--R (3) ---------------------------
+--R +--------+
+--R 3\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 375
+
+--S 376 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 377
+
+)clear all
+
+--S 378 of 502
+t0:=(3+5*x)^2/(1-2*x)^(3/2)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) -------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 502
+r0:=-25/12*(1-2*x)^(3/2)+121/4/sqrt(1-2*x)+55/2*sqrt(1-2*x)
+--R
+--R
+--R 2
+--R - 25x - 140x + 167
+--R (2) -------------------
+--R +--------+
+--R 3\|- 2x + 1
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 25x - 140x + 167
+--R (3) -------------------
+--R +--------+
+--R 3\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 380
+
+--S 381 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 382
+
+)clear all
+
+--S 383 of 502
+t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x))
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ------------------------
+--R 2 +--------+
+--R (6x + x - 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 383
+
+--S 384 of 502
+r0:=-2/21*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/sqrt(1-2*x)+_
+ 25/6*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1 +--+
+--R - 2\|- 2x + 1 atanh(---------------) + (- 175x + 269)\|21
+--R +-+
+--R \|7
+--R (2) ----------------------------------------------------------
+--R +--+ +--------+
+--R 21\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--+
+--R \|- 2x + 1 log(-----------------------------) + (- 175x + 269)\|21
+--R 3x + 2
+--R (3) -------------------------------------------------------------------
+--R +--+ +--------+
+--R 21\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 385
+
+--S 386 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 21\|21
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+
+--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (- 2x + 1)\|3 \|7 \|21
+--R +
+--R 42x - 21
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (2646x + 441x - 882)\|- 2x + 1 + (378x - 567x - 231x + 210)\|21
+--R Type: Expression(Integer)
+--E 387
+
+)clear all
+
+--S 388 of 502
+t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^2)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ---------------------------------
+--R 3 2 +--------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 388
+
+--S 389 of 502
+r0:=134/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)*_
+ sqrt(1-2*x))-1091/294*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1 +--+
+--R (402x + 268)\|- 2x + 1 atanh(---------------) + (1091x + 725)\|21
+--R +-+
+--R \|7
+--R (2) ------------------------------------------------------------------
+--R +--+ +--------+
+--R (441x + 294)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21
+--R (201x + 134)\|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +--+
+--R (1091x + 725)\|21
+--R /
+--R +--+ +--------+
+--R (441x + 294)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 390
+
+--S 391 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 67log(-------------------------------) - 134atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 147\|21
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 201x + 335)\|21 + (201x - 335)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (134x - 67)\|3 \|7 \|21 - 2814x + 1407
+--R /
+--R 2 +--------+
+--R (18522x + 3087x - 6174)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 2646x + 3969x + 1617x - 1470)\|21
+--R Type: Expression(Integer)
+--E 392
+
+)clear all
+
+--S 393 of 502
+t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^3)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 393
+
+--S 394 of 502
+r0:=-2045/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^2*_
+ sqrt(1-2*x))-545/147*sqrt(1-2*x)/(2+3*x)^2-2045/2058*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|3 \|- 2x + 1
+--R (- 36810x - 49080x - 16360)\|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+
+--R (12270x + 17305x + 6067)\|21
+--R /
+--R 2 +--+ +--------+
+--R (18522x + 24696x + 8232)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 21\|- 2x + 1 + (3x - 5)\|21
+--R (18405x + 24540x + 8180)\|- 2x + 1 log(-----------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+
+--R (12270x + 17305x + 6067)\|21
+--R /
+--R 2 +--+ +--------+
+--R (18522x + 24696x + 8232)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 395
+
+--S 396 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 2045log(-----------------------------) + 4090atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 2058\|21
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 6135x + 10225)\|21 + (6135x - 10225)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 4090x + 2045)\|3 \|7 \|21 + 85890x - 42945
+--R /
+--R 2 +--------+
+--R (259308x + 43218x - 86436)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (37044x - 55566x - 22638x + 20580)\|21
+--R Type: Expression(Integer)
+--E 397
+
+)clear all
+
+--S 398 of 502
+t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^4)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 502
+r0:=-905/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^3*_
+ sqrt(1-2*x))-467/126*sqrt(1-2*x)/(2+3*x)^3-905/882*_
+ sqrt(1-2*x)/(2+3*x)^2-905/2058*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 +--------+ \|3 \|- 2x + 1
+--R (- 48870x - 97740x - 65160x - 14480)\|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+
+--R (16290x + 26245x + 13747x + 2316)\|21
+--R /
+--R 3 2 +--+ +--------+
+--R (55566x + 111132x + 74088x + 16464)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+
+--R (24435x + 48870x + 32580x + 7240)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+
+--R (16290x + 26245x + 13747x + 2316)\|21
+--R /
+--R 3 2 +--+ +--------+
+--R (55566x + 111132x + 74088x + 16464)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 400
+
+--S 401 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 905log(-----------------------------) + 1810atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 2058\|21
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 2715x + 4525)\|21 + (2715x - 4525)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 1810x + 905)\|3 \|7 \|21 + 38010x - 19005
+--R /
+--R 2 +--------+
+--R (259308x + 43218x - 86436)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (37044x - 55566x - 22638x + 20580)\|21
+--R Type: Expression(Integer)
+--E 402
+
+)clear all
+
+--S 403 of 502
+t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^5)
+--R
+--R
+--R 2
+--R - 25x - 30x - 9
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 403
+
+--S 404 of 502
+r0:=-9145/28812*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^4*_
+ sqrt(1-2*x))-2179/588*sqrt(1-2*x)/(2+3*x)^4-1829/1764*_
+ sqrt(1-2*x)/(2+3*x)^3-9145/24696*sqrt(1-2*x)/(2+3*x)^2-_
+ 9145/57624*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (- 1481490x - 3950640x - 3950640x - 1755840x - 292640)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+
+--R (493830x + 1124835x + 843169x + 218578x + 6486)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +--------+
+--R (740745x + 1975320x + 1975320x + 877920x + 146320)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+
+--R (493830x + 1124835x + 843169x + 218578x + 6486)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 405
+
+--S 406 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 9145log(-----------------------------) + 18290atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 57624\|21
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 27435x + 45725)\|21 + (27435x - 45725)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 18290x + 9145)\|3 \|7 \|21 + 384090x - 192045
+--R /
+--R 2 +--------+
+--R (7260624x + 1210104x - 2420208)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1037232x - 1555848x - 633864x + 576240)\|21
+--R Type: Expression(Integer)
+--E 407
+
+)clear all
+
+--S 408 of 502
+t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^(3/2)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R - 10125x - 45225x - 86535x - 91947x - 58592x - 22392x - 4752x - 432
+--R -------------------------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 408
+
+--S 409 of 502
+r0:=-4324397/128*(1-2*x)^(3/2)+9504551/640*(1-2*x)^(5/2)-_
+ 4177401/896*(1-2*x)^(7/2)+122385/128*(1-2*x)^(9/2)-_
+ 161325/1408*(1-2*x)^(11/2)+10125/1664*(1-2*x)^(13/2)+_
+ 3195731/128/sqrt(1-2*x)+9836211/128*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3
+--R - 3898125x - 23058000x - 63495075x - 111095730x - 147527176x
+--R +
+--R 2
+--R - 184884496x - 393552752x + 395714912
+--R /
+--R +--------+
+--R 5005\|- 2x + 1
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R - 3898125x - 23058000x - 63495075x - 111095730x - 147527176x
+--R +
+--R 2
+--R - 184884496x - 393552752x + 395714912
+--R /
+--R +--------+
+--R 5005\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 410
+
+--S 411 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 412
+
+)clear all
+
+--S 413 of 502
+t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^(3/2)
+--R
+--R
+--R 6 5 4 3 2
+--R - 3375x - 12825x - 20295x - 17119x - 8118x - 2052x - 216
+--R (1) -------------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 413
+
+--S 414 of 502
+r0:=-444983/64*(1-2*x)^(3/2)+98209/40*(1-2*x)^(5/2)-260055/448*(1-2*x)^(7/2)+_
+ 1275/16*(1-2*x)^(9/2)-3375/704*(1-2*x)^(11/2)+456533/64/sqrt(1-2*x)+_
+ 302379/16*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R - 118125x - 627375x - 1564350x - 2569643x - 3611453x - 8012926x
+--R +
+--R 8096086
+--R /
+--R +--------+
+--R 385\|- 2x + 1
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R - 118125x - 627375x - 1564350x - 2569643x - 3611453x - 8012926x
+--R +
+--R 8096086
+--R /
+--R +--------+
+--R 385\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 415
+
+--S 416 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 417
+
+)clear all
+
+--S 418 of 502
+t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^(3/2)
+--R
+--R
+--R 5 4 3 2
+--R - 1125x - 3525x - 4415x - 2763x - 864x - 108
+--R (1) ------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 418
+
+--S 419 of 502
+r0:=-21439/16*(1-2*x)^(3/2)+5711/16*(1-2*x)^(5/2)-12675/224*(1-2*x)^(7/2)+_
+ 125/32*(1-2*x)^(9/2)+65219/32/sqrt(1-2*x)+144837/32*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R - 875x - 4150x - 9501x - 15948x - 37944x + 38700
+--R (2) ----------------------------------------------------
+--R +--------+
+--R 7\|- 2x + 1
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R - 875x - 4150x - 9501x - 15948x - 37944x + 38700
+--R (3) ----------------------------------------------------
+--R +--------+
+--R 7\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 420
+
+--S 421 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 422
+
+)clear all
+
+--S 423 of 502
+t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^(3/2)
+--R
+--R
+--R 4 3 2
+--R - 375x - 925x - 855x - 351x - 54
+--R (1) -----------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 423
+
+--S 424 of 502
+r0:=-935/4*(1-2*x)^(3/2)+335/8*(1-2*x)^(5/2)-375/112*(1-2*x)^(7/2)+_
+ 9317/16/sqrt(1-2*x)+8349/8*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2
+--R - 375x - 1595x - 3590x - 9637x + 10015
+--R (2) -----------------------------------------
+--R +--------+
+--R 7\|- 2x + 1
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R - 375x - 1595x - 3590x - 9637x + 10015
+--R (3) -----------------------------------------
+--R +--------+
+--R 7\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 425
+
+--S 426 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 427
+
+)clear all
+
+--S 428 of 502
+t0:=(3+5*x)^3/(1-2*x)^(3/2)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 502
+r0:=-275/8*(1-2*x)^(3/2)+25/8*(1-2*x)^(5/2)+1331/8/sqrt(1-2*x)+_
+ 1815/8*sqrt(1-2*x)
+--R
+--R
+--R 3 2
+--R - 25x - 100x - 335x + 362
+--R (2) ---------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R - 25x - 100x - 335x + 362
+--R (3) ---------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 430
+
+--S 431 of 502
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 432
+
+)clear all
+
+--S 433 of 502
+t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x))
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------
+--R 2 +--------+
+--R (6x + x - 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 433
+
+--S 434 of 502
+r0:=2/63*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+737/63*(3+5*x)/sqrt(1-2*x)-_
+ 5/9*(3+5*x)^2/sqrt(1-2*x)+3680/63*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1 2 +--+
+--R 2\|- 2x + 1 atanh(---------------) + (- 875x - 4725x + 5576)\|21
+--R +-+
+--R \|7
+--R (2) ------------------------------------------------------------------
+--R +--+ +--------+
+--R 63\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21
+--R \|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+
+--R (- 875x - 4725x + 5576)\|21
+--R /
+--R +--+ +--------+
+--R 63\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 435
+
+--S 436 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R log(-------------------------------) - 2atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------
+--R +--+
+--R 63\|21
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+
+--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21
+--R +
+--R - 42x + 21
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (7938x + 1323x - 2646)\|- 2x + 1 + (- 1134x + 1701x + 693x - 630)\|21
+--R Type: Expression(Integer)
+--E 437
+
+)clear all
+
+--S 438 of 502
+t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^2)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ---------------------------------
+--R 3 2 +--------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 438
+
+--S 439 of 502
+r0:=-68/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+374/21*(3+5*x)/((2+3*x)*_
+ sqrt(1-2*x))-5/3*(3+5*x)^2/((2+3*x)*sqrt(1-2*x))+386/147*_
+ sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R (- 204x - 136)\|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+
+--R (- 6125x + 4968x + 6035)\|21
+--R /
+--R +--+ +--------+
+--R (441x + 294)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21
+--R (102x + 68)\|- 2x + 1 log(-----------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+
+--R (- 6125x + 4968x + 6035)\|21
+--R /
+--R +--+ +--------+
+--R (441x + 294)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 440
+
+--S 441 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 34log(-----------------------------) + 68atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 147\|21
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 102x + 170)\|21 + (102x - 170)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 68x + 34)\|3 \|7 \|21 + 1428x - 714
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (18522x + 3087x - 6174)\|- 2x + 1 + (2646x - 3969x - 1617x + 1470)\|21
+--R Type: Expression(Integer)
+--E 442
+
+)clear all
+
+--S 443 of 502
+t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^3)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 443
+
+--S 444 of 502
+r0:=2245/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+2/7*(3+5*x)^3/_
+ ((2+3*x)^2*sqrt(1-2*x))+650/343*sqrt(1-2*x)+5/98*(3+5*x)^2*_
+ sqrt(1-2*x)/(2+3*x)^2-5/2058*(61+65*x)*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|3 \|- 2x + 1
+--R (40410x + 53880x + 17960)\|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+
+--R (72280x + 95895x + 31811)\|21
+--R /
+--R 2 +--+ +--------+
+--R (18522x + 24696x + 8232)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ - 21\|- 2x + 1 + (3x - 5)\|21
+--R (20205x + 26940x + 8980)\|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+
+--R (72280x + 95895x + 31811)\|21
+--R /
+--R 2 +--+ +--------+
+--R (18522x + 24696x + 8232)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 445
+
+--S 446 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 2245log(-------------------------------) - 4490atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 2058\|21
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 6735x + 11225)\|21 + (6735x - 11225)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (4490x - 2245)\|3 \|7 \|21 - 94290x + 47145
+--R /
+--R 2 +--------+
+--R (259308x + 43218x - 86436)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 37044x + 55566x + 22638x - 20580)\|21
+--R Type: Expression(Integer)
+--E 447
+
+)clear all
+
+--S 448 of 502
+t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^4)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 502
+r0:=-9320/3087*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+2/7*(3+5*x)^3/_
+ ((2+3*x)^3*sqrt(1-2*x))+590/3087*sqrt(1-2*x)/(2+3*x)+_
+ 40/441*(3+5*x)*sqrt(1-2*x)/(2+3*x)^2+1/21*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (- 251640x - 503280x - 335520x - 74560)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+
+--R (83880x + 178015x + 125154x + 29177)\|21
+--R /
+--R 3 2 +--+ +--------+
+--R (83349x + 166698x + 111132x + 24696)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+
+--R (125820x + 251640x + 167760x + 37280)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+
+--R (83880x + 178015x + 125154x + 29177)\|21
+--R /
+--R 3 2 +--+ +--------+
+--R (83349x + 166698x + 111132x + 24696)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 450
+
+--S 451 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 4660log(-----------------------------) + 9320atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 3087\|21
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 13980x + 23300)\|21 + (13980x - 23300)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 9320x + 4660)\|3 \|7 \|21 + 195720x - 97860
+--R /
+--R 2 +--------+
+--R (388962x + 64827x - 129654)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (55566x - 83349x - 33957x + 30870)\|21
+--R Type: Expression(Integer)
+--E 452
+
+)clear all
+
+--S 453 of 502
+t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^5)
+--R
+--R
+--R 3 2
+--R - 125x - 225x - 135x - 27
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 453
+
+--S 454 of 502
+r0:=-39185/28812*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ 2/7*(3+5*x)^3/((2+3*x)^4*sqrt(1-2*x))+375/2744*sqrt(1-2*x)/(2+3*x)^2-_
+ 39185/57624*sqrt(1-2*x)/(2+3*x)+47/588*(3+5*x)*sqrt(1-2*x)/(2+3*x)^3+_
+ 9/196*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (- 6347970x - 16927920x - 16927920x - 7523520x - 1253920)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+
+--R (2115990x + 4819755x + 4093057x + 1534434x + 213998)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +--------+
+--R (3173985x + 8463960x + 8463960x + 3761760x + 626960)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+
+--R (2115990x + 4819755x + 4093057x + 1534434x + 213998)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 455
+
+--S 456 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 39185log(-----------------------------) + 78370atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 57624\|21
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 117555x + 195925)\|21 + (117555x - 195925)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 78370x + 39185)\|3 \|7 \|21 + 1645770x - 822885
+--R /
+--R 2 +--------+
+--R (7260624x + 1210104x - 2420208)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1037232x - 1555848x - 633864x + 576240)\|21
+--R Type: Expression(Integer)
+--E 457
+
+)clear all
+
+--S 458 of 502
+t0:=(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x))
+--R
+--R
+--R 6 5 4 3 2
+--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64
+--R (1) -------------------------------------------------------
+--R 2 +--------+
+--R (10x + x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 458
+
+--S 459 of 502
+r0:=-2/34375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+406/165*(2+3*x)^4/_
+ sqrt(1-2*x)-1/15*(2+3*x)^5/sqrt(1-2*x)+19886122/34375*sqrt(1-2*x)+_
+ 22727/275*(2+3*x)*sqrt(1-2*x)+121752/6875*(2+3*x)^2*sqrt(1-2*x)+_
+ 8117/1925*(2+3*x)^3*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R - 14\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 3898125x - 19824750x - 48323385x - 85159800x - 207964053x
+--R +
+--R 213097384
+--R *
+--R +--+
+--R \|55
+--R /
+--R +--+ +--------+
+--R 240625\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R 7\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R - 3898125x - 19824750x - 48323385x - 85159800x - 207964053x
+--R +
+--R 213097384
+--R *
+--R +--+
+--R \|55
+--R /
+--R +--+ +--------+
+--R 240625\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 460
+
+--S 461 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 34375\|55
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (18906250x + 1890625x - 5671875)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1718750x - 2578125x - 790625x + 825000)\|55
+--R Type: Expression(Integer)
+--E 462
+
+)clear all
+
+--S 463 of 502
+t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x))
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 2 +--------+
+--R (10x + x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 502
+r0:=-2/6875*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+139/55*(2+3*x)^3/_
+ sqrt(1-2*x)-3/35*(2+3*x)^4/sqrt(1-2*x)+1050298/6875*sqrt(1-2*x)+_
+ 6252/1375*(2+3*x)^2*sqrt(1-2*x)+1/6875*(262574+437625*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R - 14\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 334125x - 1545885x - 3732300x - 10459053x + 10972384)\|55
+--R /
+--R +--+ +--------+
+--R 48125\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R 7\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+
+--R (- 334125x - 1545885x - 3732300x - 10459053x + 10972384)\|55
+--R /
+--R +--+ +--------+
+--R 48125\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 465
+
+--S 466 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 6875\|55
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (3781250x + 378125x - 1134375)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (343750x - 515625x - 158125x + 165000)\|55
+--R Type: Expression(Integer)
+--E 467
+
+)clear all
+
+--S 468 of 502
+t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x))
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) ---------------------------------
+--R 2 +--------+
+--R (10x + x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 468
+
+--S 469 of 502
+r0:=-2/1375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+728/275*(2+3*x)^2/_
+ sqrt(1-2*x)-3/25*(2+3*x)^3/sqrt(1-2*x)+50922/1375*sqrt(1-2*x)+_
+ 291/55*(2+3*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R - 2\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (- 4455x - 19800x - 71379x + 78712)\|55
+--R /
+--R +--+ +--------+
+--R 1375\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R \|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (- 4455x - 19800x - 71379x + 78712)\|55
+--R /
+--R +--+ +--------+
+--R 1375\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 470
+
+--S 471 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 1375\|55
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (756250x + 75625x - 226875)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (68750x - 103125x - 31625x + 33000)\|55
+--R Type: Expression(Integer)
+--E 472
+
+)clear all
+
+--S 473 of 502
+t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x))
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) -------------------------
+--R 2 +--------+
+--R (10x + x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 473
+
+--S 474 of 502
+r0:=-2/275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+161/55*(2+3*x)/_
+ sqrt(1-2*x)-1/5*(2+3*x)^2/sqrt(1-2*x)+2412/275*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1 2 +--+
+--R - 2\|- 2x + 1 atanh(---------------) + (- 495x - 3069x + 3802)\|55
+--R +--+
+--R \|11
+--R (2) --------------------------------------------------------------------
+--R +--+ +--------+
+--R 275\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 2 +--+
+--R \|- 2x + 1 log(-----------------------------) + (- 495x - 3069x + 3802)\|55
+--R 5x + 3
+--R -----------------------------------------------------------------------------
+--R +--+ +--------+
+--R 275\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 475
+
+--S 476 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 275\|55
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (151250x + 15125x - 45375)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (13750x - 20625x - 6325x + 6600)\|55
+--R Type: Expression(Integer)
+--E 477
+
+)clear all
+
+--S 478 of 502
+t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x))
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) -------------------------
+--R 2 +--------+
+--R (10x + x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 478
+
+--S 479 of 502
+r0:=-2/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+49/22/sqrt(1-2*x)+_
+ 9/10*sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1 +--+
+--R - 2\|- 2x + 1 atanh(---------------) + (- 99x + 172)\|55
+--R +--+
+--R \|11
+--R (2) ---------------------------------------------------------
+--R +--+ +--------+
+--R 55\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+
+--R \|- 2x + 1 log(-----------------------------) + (- 99x + 172)\|55
+--R 5x + 3
+--R (3) ------------------------------------------------------------------
+--R +--+ +--------+
+--R 55\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 480
+
+--S 481 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 55\|55
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (30250x + 3025x - 9075)\|- 2x + 1 + (2750x - 4125x - 1265x + 1320)\|55
+--R Type: Expression(Integer)
+--E 482
+
+)clear all
+
+--S 483 of 502
+t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x))
+--R
+--R
+--R - 3x - 2
+--R (1) -------------------------
+--R 2 +--------+
+--R (10x + x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 483
+
+--S 484 of 502
+r0:=-2/11*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11/sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1 +--+
+--R - 2\|- 2x + 1 atanh(---------------) + 7\|55
+--R +--+
+--R \|11
+--R (2) ---------------------------------------------
+--R +--+ +--------+
+--R 11\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+
+--R \|- 2x + 1 log(-----------------------------) + 7\|55
+--R 5x + 3
+--R (3) ------------------------------------------------------
+--R +--+ +--------+
+--R 11\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 485
+
+--S 486 of 502
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 11\|55
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (6050x + 605x - 1815)\|- 2x + 1 + (550x - 825x - 253x + 264)\|55
+--R Type: Expression(Integer)
+--E 487
+
+)clear all
+
+--S 488 of 502
+t0:=1/((1-2*x)^(3/2)*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - -------------------------
+--R 2 +--------+
+--R (10x + x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 488
+
+--S 489 of 502
+r0:=-2/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+2/11/sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +-+ +--------+ \|5 \|- 2x + 1 +--+
+--R - 2\|5 \|- 2x + 1 atanh(---------------) + 2\|11
+--R +--+
+--R \|11
+--R (2) -------------------------------------------------
+--R +--+ +--------+
+--R 11\|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +--------+ +--+
+--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--+
+--R \|5 \|- 2x + 1 log(---------------------------------) + 2\|11
+--R 5x + 3
+--R (3) --------------------------------------------------------------
+--R +--+ +--------+
+--R 11\|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 490
+
+--S 491 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+ +-+ +--------+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1
+--R \|5 log(---------------------------------) + 2\|5 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ------------------------------------------------------------------------
+--R +--+
+--R 11\|11
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 492
+
+)clear all
+
+--S 493 of 502
+t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ---------------------------------
+--R 3 2 +--------+
+--R (30x + 23x - 7x - 6)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 502
+r0:=6/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10/11*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))*sqrt(5/11)+4/77/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R 66\|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +-+ +--+
+--R - 70\|5 \|7 \|- 2x + 1 atanh(---------------) + 4\|7 \|11
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+ +--------+
+--R 77\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 35\|5 \|7 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ +--+
+--R 33\|3 \|11 \|- 2x + 1 log(---------------------------------) + 4\|7 \|11
+--R 3x + 2
+--R /
+--R +-+ +--+ +--------+
+--R 77\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 495
+
+--S 496 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 35\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 33\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R - 66\|3 \|11 atanh(---------------) + 70\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 77\|7 \|11
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 497
+
+)clear all
+
+--S 498 of 502
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------
+--R 4 3 2 +--------+
+--R (90x + 129x + 25x - 32x - 12)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 502
+r0:=228/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-50/11*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+4/77/((2+3*x)*_
+ sqrt(1-2*x))+87/539*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R (7524x + 5016)\|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R (- 7350x - 4900)\|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--+
+--R (- 174x + 115)\|7 \|11
+--R /
+--R +-+ +--+ +--------+
+--R (1617x + 1078)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 502
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (3675x + 2450)\|5 \|7 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (3762x + 2508)\|3 \|11 \|- 2x + 1 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--+
+--R (- 174x + 115)\|7 \|11
+--R /
+--R +-+ +--+ +--------+
+--R (1617x + 1078)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 500
+
+--S 501 of 502
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 1225\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 1254\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R - 2508\|3 \|11 atanh(---------------) + 2450\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 539\|7 \|11
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 502
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 502
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3l.input.pdf b/src/axiom-website/CATS/rich3l.input.pdf
new file mode 100644
index 0000000..b47f7e7
Binary files /dev/null and b/src/axiom-website/CATS/rich3l.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3m.input.pamphlet b/src/axiom-website/CATS/rich3m.input.pamphlet
new file mode 100644
index 0000000..ade3647
--- /dev/null
+++ b/src/axiom-website/CATS/rich3m.input.pamphlet
@@ -0,0 +1,8548 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3m.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 55 matching answers.
+\item 37 cases where Axiom supplied 2 results.
+\item 8 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 rich3m.output
+)spool rich3m.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (270x + 567x + 333x - 46x - 100x - 24)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+r0:=8025/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_
+ 250/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 4/77/((2+3*x)^2*sqrt(1-2*x))+75/1078*sqrt(1-2*x)/(2+3*x)^2+_
+ 7575/7546*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R (1588950x + 2118600x + 706200)\|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +-+ +-+ +--------+
+--R (- 1543500x - 2058000x - 686000)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+
+--R (- 45450x - 8625x + 16067)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (67914x + 90552x + 30184)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +-+ +--------+
+--R (771750x + 1029000x + 343000)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--+ +--------+
+--R (794475x + 1059300x + 353100)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +--+
+--R (- 45450x - 8625x + 16067)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (67914x + 90552x + 30184)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 85750\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 88275\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 176550\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 171500\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 7546\|7 \|11
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ----------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (810x + 2241x + 2133x + 528x - 392x - 272x - 48)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+r0:=40140/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_
+ 1250/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 4/77/((2+3*x)^3*sqrt(1-2*x))+3/77*sqrt(1-2*x)/(2+3*x)^3+_
+ 270/539*sqrt(1-2*x)/(2+3*x)^2+19185/3773*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+ +--------+
+--R (11921580x + 23843160x + 15895440x + 3532320)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+ +--------+
+--R (- 11576250x - 23152500x - 15435000x - 3430000)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+
+--R (- 345330x - 299115x + 74556x + 80863)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (101871x + 203742x + 135828x + 30184)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +-+ +--------+
+--R (5788125x + 11576250x + 7717500x + 1715000)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (5960790x + 11921580x + 7947720x + 1766160)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+
+--R (- 345330x - 299115x + 74556x + 80863)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (101871x + 203742x + 135828x + 30184)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 214375\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 220770\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 441540\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 428750\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 3773\|7 \|11
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)^2)
+--R
+--R
+--R 6 5 4 3 2
+--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64
+--R (1) -------------------------------------------------------
+--R 3 2 +--------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+r0:=-402/378125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 139/55*(2+3*x)^4/((3+5*x)*sqrt(1-2*x))-3/35*(2+3*x)^5/((3+5*x)*_
+ sqrt(1-2*x))+36473898/378125*sqrt(1-2*x)+217152/75625*(2+3*x)^2*_
+ sqrt(1-2*x)-4839/21175*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)+_
+ 3/378125*(3039458+5065875*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R (- 14070x - 8442)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 55130625x - 293294925x - 795400155x - 2195407665x + 818846961x
+--R +
+--R 1143572552
+--R *
+--R +--+
+--R \|55
+--R /
+--R +--+ +--------+
+--R (13234375x + 7940625)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (7035x + 4221)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R - 55130625x - 293294925x - 795400155x - 2195407665x + 818846961x
+--R +
+--R 1143572552
+--R *
+--R +--+
+--R \|55
+--R /
+--R +--+ +--------+
+--R (13234375x + 7940625)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 201log(-----------------------------) + 402atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 378125\|55
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 1005x + 1608)\|55 + (1005x - 1608)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 402x + 201)\|5 \|11 \|55 + 22110x - 11055
+--R /
+--R 2 +--------+
+--R (207968750x + 20796875x - 62390625)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (18906250x - 28359375x - 8696875x + 9075000)\|55
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^2)
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 3 2 +--------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+r0:=-336/75625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 728/275*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))-3/25*(2+3*x)^4/((3+5*x)*_
+ sqrt(1-2*x))+1763496/75625*sqrt(1-2*x)+2016/605*(2+3*x)*_
+ sqrt(1-2*x)-3612/15125*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R (- 1680x - 1008)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 735075x - 3789720x - 14309460x + 6264264x + 8186648)\|55
+--R /
+--R +--+ +--------+
+--R (378125x + 226875)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (840x + 504)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+
+--R (- 735075x - 3789720x - 14309460x + 6264264x + 8186648)\|55
+--R /
+--R +--+ +--------+
+--R (378125x + 226875)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 168log(-----------------------------) + 336atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 75625\|55
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 840x + 1344)\|55 + (840x - 1344)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 336x + 168)\|5 \|11 \|55 + 18480x - 9240
+--R /
+--R 2 +--------+
+--R (41593750x + 4159375x - 12478125)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (3781250x - 5671875x - 1739375x + 1815000)\|55
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2)
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+r0:=-54/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 161/55*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))-_
+ 1/5*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))+_
+ 15648/3025*sqrt(1-2*x)+3/3025*(436+815*x)*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R (- 270x - 162)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (- 16335x - 114345x + 68661x + 78832)\|55
+--R /
+--R +--+ +--------+
+--R (15125x + 9075)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (135x + 81)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (- 16335x - 114345x + 68661x + 78832)\|55
+--R /
+--R +--+ +--------+
+--R (15125x + 9075)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 27log(-----------------------------) + 54atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 3025\|55
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 135x + 216)\|55 + (135x - 216)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 54x + 27)\|5 \|11 \|55 + 2970x - 1485
+--R /
+--R 2 +--------+
+--R (1663750x + 166375x - 499125)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (151250x - 226875x - 69575x + 72600)\|55
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+r0:=-204/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 238/55*(2+3*x)/((3+5*x)*sqrt(1-2*x))-3/5*(2+3*x)^2/_
+ ((3+5*x)*sqrt(1-2*x))-1158/3025*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R (- 1020x - 612)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (- 16335x + 19806x + 17762)\|55
+--R /
+--R +--+ +--------+
+--R (15125x + 9075)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (510x + 306)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (- 16335x + 19806x + 17762)\|55
+--R /
+--R +--+ +--------+
+--R (15125x + 9075)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 102log(-----------------------------) + 204atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 3025\|55
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 510x + 816)\|55 + (510x - 816)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 204x + 102)\|5 \|11 \|55 + 11220x - 5610
+--R /
+--R 2 +--------+
+--R (1663750x + 166375x - 499125)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (151250x - 226875x - 69575x + 72600)\|55
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^2)
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+r0:=-138/605*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 49/22/((3+5*x)*sqrt(1-2*x))-1227/1210*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1 +--+
+--R (- 690x - 414)\|- 2x + 1 atanh(---------------) + (1227x + 734)\|55
+--R +--+
+--R \|11
+--R (2) --------------------------------------------------------------------
+--R +--+ +--------+
+--R (3025x + 1815)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (345x + 207)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R +--+
+--R (1227x + 734)\|55
+--R /
+--R +--+ +--------+
+--R (3025x + 1815)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 69log(-----------------------------) + 138atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ----------------------------------------------------------------
+--R +--+
+--R 605\|55
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 345x + 552)\|55 + (345x - 552)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 138x + 69)\|5 \|11 \|55 + 7590x - 3795
+--R /
+--R 2 +--------+
+--R (332750x + 33275x - 99825)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (30250x - 45375x - 13915x + 14520)\|55
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^2)
+--R
+--R
+--R - 3x - 2
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+r0:=-72/121*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 72/605/sqrt(1-2*x)+(-1/55)/((3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1 +--+
+--R (- 360x - 216)\|- 2x + 1 atanh(---------------) + (72x + 41)\|55
+--R +--+
+--R \|11
+--R (2) -----------------------------------------------------------------
+--R +--+ +--------+
+--R (605x + 363)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+
+--R (180x + 108)\|- 2x + 1 log(-----------------------------) + (72x + 41)\|55
+--R 5x + 3
+--R ---------------------------------------------------------------------------
+--R +--+ +--------+
+--R (605x + 363)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 36log(-----------------------------) + 72atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 121\|55
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 180x + 288)\|55 + (180x - 288)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 72x + 36)\|5 \|11 \|55 + 3960x - 1980
+--R /
+--R 2 +--------+
+--R (66550x + 6655x - 19965)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (6050x - 9075x - 2783x + 2904)\|55
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=1/((1-2*x)^(3/2)*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - ----------------------------------
+--R 3 2 +--------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+r0:=-6/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 2/11/((3+5*x)*sqrt(1-2*x))-15/121*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R +-+ +--------+
+--R +-+ +--------+ \|5 \|- 2x + 1 +--+
+--R (- 30x - 18)\|5 \|- 2x + 1 atanh(---------------) + (30x + 7)\|11
+--R +--+
+--R \|11
+--R (2) ------------------------------------------------------------------
+--R +--+ +--------+
+--R (605x + 363)\|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (15x + 9)\|5 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +--+
+--R (30x + 7)\|11
+--R /
+--R +--+ +--------+
+--R (605x + 363)\|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+ +-+ +--------+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1
+--R 3\|5 log(---------------------------------) + 6\|5 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -------------------------------------------------------------------------
+--R +--+
+--R 121\|11
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - --------------------------------------------
+--R 4 3 2 +--------+
+--R (150x + 205x + 34x - 51x - 18)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+r0:=-18/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_
+ 300/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 4/77/((3+5*x)*sqrt(1-2*x))-195/847*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R (- 10890x - 6534)\|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R (10500x + 6300)\|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--+
+--R (390x - 151)\|7 \|11
+--R /
+--R +-+ +--+ +--------+
+--R (4235x + 2541)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ +--+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (5445x + 3267)\|3 \|11 \|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ +--------+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (5250x + 3150)\|5 \|7 \|- 2x + 1 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--+
+--R (390x - 151)\|7 \|11
+--R /
+--R +-+ +--+ +--------+
+--R (4235x + 2541)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 1089\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 1050\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R 2178\|3 \|11 atanh(---------------) - 2100\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 847\|7 \|11
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (450x + 915x + 512x - 85x - 156x - 36)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+r0:=-1314/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_
+ 3150/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 4/77/((2+3*x)*(3+5*x)*sqrt(1-2*x))-11610/5929*sqrt(1-2*x)/(3+5*x)+_
+ 87/539*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 2 +-+ +--+ +--------+
+--R (- 2384910x - 3020886x - 953964)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R (2315250x + 2932650x + 926100)\|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+
+--R (69660x + 9696x - 21955)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (88935x + 112651x + 35574)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +--+ +--------+
+--R (1192455x + 1510443x + 476982)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +-+ +--------+
+--R (1157625x + 1466325x + 463050)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(-----------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--+
+--R (69660x + 9696x - 21955)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (88935x + 112651x + 35574)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 79497\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 77175\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R 158994\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R - 154350\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 5929\|7 \|11
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) - -----------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (1350x + 3645x + 3366x + 769x - 638x - 420x - 72)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+r0:=-70065/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_
+ 24000/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 4/77/((2+3*x)^2*(3+5*x)*sqrt(1-2*x))-_
+ 1229325/83006*sqrt(1-2*x)/(3+5*x)+_
+ 75/1078*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_
+ 5520/3773*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+
+--R (- 763007850x - 1475148510x - 949520880x - 203468760)\|3 \|11
+--R *
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+
+--R (740880000x + 1432368000x + 921984000x + 197568000)\|5 \|7
+--R *
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+
+--R (22127850x + 17711235x - 5050290x - 4664333)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (3735270x + 7221522x + 4648336x + 996072)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +--+
+--R (381503925x + 737574255x + 474760440x + 101734380)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +-+ +--------+
+--R (370440000x + 716184000x + 460992000x + 98784000)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(-----------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+
+--R (22127850x + 17711235x - 5050290x - 4664333)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (3735270x + 7221522x + 4648336x + 996072)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 8477865\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 8232000\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R 16955730\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R - 16464000\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 83006\|7 \|11
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)^3)
+--R
+--R
+--R 6 5 4 3 2
+--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64
+--R (1) -------------------------------------------------------
+--R 4 3 2 +--------+
+--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+r0:=-33873/4159375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 728/275*(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x))-_
+ 3/25*(2+3*x)^5/((3+5*x)^2*sqrt(1-2*x))+_
+ 61055253/4159375*sqrt(1-2*x)+139671/66550*(2+3*x)*sqrt(1-2*x)-_
+ 7219/30250*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-_
+ 125916/831875*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 1693650x - 2032380x - 609714)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 242574750x - 1423105200x - 5682717810x - 762244410x
+--R +
+--R 4150263077x + 1702670584
+--R *
+--R +--+
+--R \|55
+--R /
+--R 2 +--+ +--------+
+--R (207968750x + 249562500x + 74868750)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +--------+
+--R (846825x + 1016190x + 304857)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R - 242574750x - 1423105200x - 5682717810x - 762244410x
+--R +
+--R 4150263077x + 1702670584
+--R *
+--R +--+
+--R \|55
+--R /
+--R 2 +--+ +--------+
+--R (207968750x + 249562500x + 74868750)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 33873log(-----------------------------) + 67746atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 8318750\|55
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 169365x + 270984)\|55 + (169365x - 270984)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 67746x + 33873)\|5 \|11 \|55 + 3726030x - 1863015
+--R /
+--R 2 +--------+
+--R (4575312500x + 457531250x - 1372593750)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (415937500x - 623906250x - 191331250x + 199650000)\|55
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^3)
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+r0:=-4557/166375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 161/55*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))-_
+ 1/5*(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x))+_
+ 538608/166375*sqrt(1-2*x)-1589/6050*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+_
+ 147/332750*(612+1145*x)*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 227850x - 273420x - 82026)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 5390550x - 42046290x + 764310x + 41668993x + 16342856)\|55
+--R /
+--R 2 +--+ +--------+
+--R (8318750x + 9982500x + 2994750)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (113925x + 136710x + 41013)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+
+--R (- 5390550x - 42046290x + 764310x + 41668993x + 16342856)\|55
+--R /
+--R 2 +--+ +--------+
+--R (8318750x + 9982500x + 2994750)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 4557log(-----------------------------) + 9114atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 332750\|55
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 22785x + 36456)\|55 + (22785x - 36456)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 9114x + 4557)\|5 \|11 \|55 + 501270x - 250635
+--R /
+--R 2 +--------+
+--R (183012500x + 18301250x - 54903750)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (16637500x - 24956250x - 7653250x + 7986000)\|55
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^3)
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+r0:=-111/1331*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 238/55*(2+3*x)^2/((3+5*x)^2*sqrt(1-2*x))-3/5*(2+3*x)^3/((3+5*x)^2*_
+ sqrt(1-2*x))-1/6050*(346-195*x)*sqrt(1-2*x)/(3+5*x)^2-_
+ 15759/33275*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 27750x - 33300x - 9990)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (- 215622x + 149298x + 411911x + 146824)\|55
+--R /
+--R 2 +--+ +--------+
+--R (332750x + 399300x + 119790)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (13875x + 16650x + 4995)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (- 215622x + 149298x + 411911x + 146824)\|55
+--R /
+--R 2 +--+ +--------+
+--R (332750x + 399300x + 119790)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 111log(-----------------------------) + 222atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 2662\|55
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 555x + 888)\|55 + (555x - 888)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 222x + 111)\|5 \|11 \|55 + 12210x - 6105
+--R /
+--R 2 +--------+
+--R (1464100x + 146410x - 439230)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (133100x - 199650x - 61226x + 63888)\|55
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^3)
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+r0:=-7143/33275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ 2/11*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))+_
+ 3408/33275*sqrt(1-2*x)-5/242*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+_
+ 3/13310*(24+71*x)*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 357150x - 428580x - 128574)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (430800x + 514727x + 153724)\|55
+--R /
+--R 2 +--+ +--------+
+--R (1663750x + 1996500x + 598950)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (178575x + 214290x + 64287)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (430800x + 514727x + 153724)\|55
+--R /
+--R 2 +--+ +--------+
+--R (1663750x + 1996500x + 598950)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 7143log(-----------------------------) + 14286atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 66550\|55
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 35715x + 57144)\|55 + (35715x - 57144)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 14286x + 7143)\|5 \|11 \|55 + 785730x - 392865
+--R /
+--R 2 +--------+
+--R (36602500x + 3660250x - 10980750)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (3327500x - 4991250x - 1530650x + 1597200)\|55
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^3)
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+r0:=-2589/6655*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+49/22/((3+5*x)^2*_
+ sqrt(1-2*x))-613/605*sqrt(1-2*x)/(3+5*x)^2-2589/13310*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 129450x - 155340x - 46602)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (25890x + 29561x + 8392)\|55
+--R /
+--R 2 +--+ +--------+
+--R (332750x + 399300x + 119790)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (64725x + 77670x + 23301)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (25890x + 29561x + 8392)\|55
+--R /
+--R 2 +--+ +--------+
+--R (332750x + 399300x + 119790)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 2589log(-----------------------------) + 5178atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 13310\|55
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 12945x + 20712)\|55 + (12945x - 20712)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 5178x + 2589)\|5 \|11 \|55 + 284790x - 142395
+--R /
+--R 2 +--------+
+--R (7320500x + 732050x - 2196150)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (665500x - 998250x - 306130x + 319440)\|55
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^3)
+--R
+--R
+--R - 3x - 2
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+r0:=-213/1331*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-1/110)/((3+5*x)^2*_
+ sqrt(1-2*x))+71/605/((3+5*x)*sqrt(1-2*x))-213/2662*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 10650x - 12780x - 3834)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (2130x + 1775x + 274)\|55
+--R /
+--R 2 +--+ +--------+
+--R (66550x + 79860x + 23958)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (5325x + 6390x + 1917)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (2130x + 1775x + 274)\|55
+--R /
+--R 2 +--+ +--------+
+--R (66550x + 79860x + 23958)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 213log(-----------------------------) + 426atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 2662\|55
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 1065x + 1704)\|55 + (1065x - 1704)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 426x + 213)\|5 \|11 \|55 + 23430x - 11715
+--R /
+--R 2 +--------+
+--R (1464100x + 146410x - 439230)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (133100x - 199650x - 61226x + 63888)\|55
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=1/((1-2*x)^(3/2)*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) - --------------------------------------------
+--R 4 3 2 +--------+
+--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+r0:=-15/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+2/11/((3+5*x)^2*_
+ sqrt(1-2*x))-25/242*sqrt(1-2*x)/(3+5*x)^2-75/2662*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--------+ \|5 \|- 2x + 1
+--R (- 750x - 900x - 270)\|5 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (750x + 625x - 16)\|11
+--R /
+--R 2 +--+ +--------+
+--R (66550x + 79860x + 23958)\|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R 2 +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (375x + 450x + 135)\|5 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (750x + 625x - 16)\|11
+--R /
+--R 2 +--+ +--------+
+--R (66550x + 79860x + 23958)\|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+ +-+ +--------+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1
+--R 15\|5 log(---------------------------------) + 30\|5 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ---------------------------------------------------------------------------
+--R +--+
+--R 2662\|11
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (750x + 1475x + 785x - 153x - 243x - 54)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+r0:=54/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-9975/1331*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+4/77/((3+5*x)^2*_
+ sqrt(1-2*x))-215/1694*sqrt(1-2*x)/(3+5*x)^2+10245/18634*_
+ sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 2 +-+ +--+ +--------+
+--R (3593700x + 4312440x + 1293732)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +-+ +-+ +--------+
+--R (- 3491250x - 4189500x - 1256850)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+
+--R (- 102450x - 5515x + 29338)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (465850x + 559020x + 167706)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +-+ +--------+
+--R (1745625x + 2094750x + 628425)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--+ +--------+
+--R (1796850x + 2156220x + 646866)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +--+
+--R (- 102450x - 5515x + 29338)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (465850x + 559020x + 167706)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 69825\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 71874\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 143748\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 139650\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 18634\|7 \|11
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) - --------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (2250x + 5925x + 5305x + 1111x - 1035x - 648x - 108)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+r0:=5832/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_
+ 153825/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 4/77/((2+3*x)*(3+5*x)^2*sqrt(1-2*x))-_
+ 17095/11858*sqrt(1-2*x)/(3+5*x)^2+_
+ 87/539*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+1124835/130438*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+
+--R (1164358800x + 2173469760x + 1350656208x + 279446112)\|3 \|11
+--R *
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+
+--R (- 1130613750x - 2110479000x - 1311511950x - 271347300)\|5 \|7
+--R *
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+
+--R (- 33745050x - 24742935x + 8019782x + 6400750)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (9782850x + 18261320x + 11348106x + 2347884)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +-+
+--R (565306875x + 1055239500x + 655755975x + 135673650)\|5 \|7
+--R *
+--R +-+ +--------+ +--+
+--R +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+
+--R (582179400x + 1086734880x + 675328104x + 139723056)\|3 \|11
+--R *
+--R +-+ +--------+ +-+
+--R +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|- 2x + 1 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+
+--R (- 33745050x - 24742935x + 8019782x + 6400750)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (9782850x + 18261320x + 11348106x + 2347884)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 7537425\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 7762392\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 15524784\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 15074850\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 130438\|7 \|11
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 7 6 5 4 3 2
+--R (6750x + 22275x + 27765x + 13943x - 883x - 4014x - 1620x - 216)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+r0:=414315/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_
+ 1561125/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 4/77/((2+3*x)^2*(3+5*x)^2*sqrt(1-2*x))-_
+ 1205525/83006*sqrt(1-2*x)/(3+5*x)^2+75/1078*sqrt(1-2*x)/_
+ ((2+3*x)^2*(3+5*x)^2)+14505/7546*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_
+ 39968475/456533*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 248153969250x + 628656722100x + 596672432730x + 251462688840x
+--R +
+--R 39704635080
+--R *
+--R +-+ +--------+
+--R +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R \|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2
+--R - 240959643750x - 610431097500x - 579374076750x - 244172439000x
+--R +
+--R - 38553543000
+--R *
+--R +-+ +--------+
+--R +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R \|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2
+--R - 7194325500x - 10073172600x - 1810042755x + 2503057145x
+--R +
+--R 909821467
+--R *
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R 4 3 2 +-+
+--R (205439850x + 520447620x + 493968706x + 208179048x + 32870376)\|7
+--R *
+--R +--+ +--------+
+--R \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 120479821875x + 305215548750x + 289687038375x + 122086219500x
+--R +
+--R 19276771500
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2
+--R 124076984625x + 314328361050x + 298336216365x + 125731344420x
+--R +
+--R 19852317540
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 \|- 2x + 1 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2
+--R - 7194325500x - 10073172600x - 1810042755x + 2503057145x
+--R +
+--R 909821467
+--R *
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R 4 3 2 +-+
+--R (205439850x + 520447620x + 493968706x + 208179048x + 32870376)\|7
+--R *
+--R +--+ +--------+
+--R \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 535465875\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 551453265\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 1102906530\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 1070931750\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 913066\|7 \|11
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 6 5 4 3 2
+--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96
+--R (1) ------------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+r0:=184877/192/(1-2*x)^(3/2)+12495/8*(1-2*x)^(3/2)-19467/64*(1-2*x)^(5/2)+_
+ 1053/28*(1-2*x)^(7/2)-135/64*(1-2*x)^(9/2)+(-60025/8)/sqrt(1-2*x)-_
+ 519645/64*sqrt(1-2*x)
+--R
+--R
+--R 6 5 4 3 2
+--R 2835x + 16767x + 49653x + 114084x + 412812x - 844104x + 280696
+--R (2) -------------------------------------------------------------------
+--R +--------+
+--R (42x - 21)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 5 4 3 2
+--R 2835x + 16767x + 49653x + 114084x + 412812x - 844104x + 280696
+--R (3) -------------------------------------------------------------------
+--R +--------+
+--R (42x - 21)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 5 4 3 2
+--R 405x + 1323x + 1728x + 1128x + 368x + 48
+--R (1) --------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+r0:=26411/96/(1-2*x)^(3/2)+3591/16*(1-2*x)^(3/2)-4671/160*(1-2*x)^(5/2)+_
+ 405/224*(1-2*x)^(7/2)+(-57281/32)/sqrt(1-2*x)-24843/16*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R 6075x + 33858x + 105624x + 435312x - 909264x + 301408
+--R (2) ---------------------------------------------------------
+--R +--------+
+--R (210x - 105)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R 6075x + 33858x + 105624x + 435312x - 909264x + 301408
+--R (3) ---------------------------------------------------------
+--R +--------+
+--R (210x - 105)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 4 3 2
+--R 135x + 351x + 342x + 148x + 24
+--R (1) ---------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+r0:=3773/48/(1-2*x)^(3/2)+207/8*(1-2*x)^(3/2)-27/16*(1-2*x)^(5/2)+_
+ (-3283/8)/sqrt(1-2*x)-1071/4*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2
+--R 81x + 459x + 2403x - 5250x + 1726
+--R (2) ------------------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R 81x + 459x + 2403x - 5250x + 1726
+--R (3) ------------------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 3 2
+--R 45x + 87x + 56x + 12
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+r0:=539/24/(1-2*x)^(3/2)+15/8*(1-2*x)^(3/2)+(-707/8)/sqrt(1-2*x)-_
+ 309/8*sqrt(1-2*x)
+--R
+--R
+--R 3 2
+--R 45x + 396x - 960x + 308
+--R (2) -------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 45x + 396x - 960x + 308
+--R (3) -------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(2+3*x)*(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 2
+--R 15x + 19x + 6
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+r0:=77/12/(1-2*x)^(3/2)+(-17)/sqrt(1-2*x)-15/4*sqrt(1-2*x)
+--R
+--R
+--R 2
+--R 45x - 147x + 43
+--R (2) -------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 45x - 147x + 43
+--R (3) -------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 5x + 3
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+r0:=11/6/(1-2*x)^(3/2)+(-5/2)/sqrt(1-2*x)
+--R
+--R
+--R - 15x + 2
+--R (2) -------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R - 15x + 2
+--R (3) -------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x))
+--R
+--R
+--R 5x + 3
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+r0:=11/21/(1-2*x)^(3/2)+2/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_
+ (-2/49)/sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +-+ +--------+ \|3 \|- 2x + 1 +-+
+--R (12x - 6)\|3 \|- 2x + 1 atanh(---------------) + (- 12x - 71)\|7
+--R +-+
+--R \|7
+--R (2) -----------------------------------------------------------------
+--R +-+ +--------+
+--R (294x - 147)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R +-+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (6x - 3)\|3 \|- 2x + 1 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+
+--R (- 12x - 71)\|7
+--R /
+--R +-+ +--------+
+--R (294x - 147)\|7 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R \|3 log(---------------------------------) - 2\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R ------------------------------------------------------------------------
+--R +-+
+--R 49\|7
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^2)
+--R
+--R
+--R 5x + 3
+--R (1) ----------------------------------------
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+r0:=20/147/(1-2*x)^(3/2)+1/21/((1-2*x)^(3/2)*(2+3*x))-_
+ 60/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+60/343/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--------+ \|3 \|- 2x + 1
+--R (- 1080x - 180x + 360)\|3 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +-+
+--R (1080x - 240x - 689)\|7
+--R /
+--R 2 +-+ +--------+
+--R (6174x + 1029x - 2058)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +-+
+--R 2 +-+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (540x + 90x - 180)\|3 \|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+
+--R (1080x - 240x - 689)\|7
+--R /
+--R 2 +-+ +--------+
+--R (6174x + 1029x - 2058)\|7 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R 30\|3 log(-------------------------------) + 60\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -------------------------------------------------------------------------
+--R +-+
+--R 343\|7
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^3)
+--R
+--R
+--R 5x + 3
+--R (1) -------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+r0:=5/49/(1-2*x)^(3/2)+1/42/((1-2*x)^(3/2)*(2+3*x)^2)+_
+ (-3/14)/((1-2*x)^(3/2)*(2+3*x))-45/343*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(3/7)+45/343/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 +-+ +--------+ \|3 \|- 2x + 1
+--R (- 4860x - 4050x + 1080x + 1080)\|3 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+
+--R (4860x + 2160x - 2277x - 1087)\|7
+--R /
+--R 3 2 +-+ +--------+
+--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +--------+
+--R (2430x + 2025x - 540x - 540)\|3 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+
+--R (4860x + 2160x - 2277x - 1087)\|7
+--R /
+--R 3 2 +-+ +--------+
+--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R 45\|3 log(-------------------------------) + 90\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -------------------------------------------------------------------------
+--R +-+
+--R 686\|7
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^4)
+--R
+--R
+--R 5x + 3
+--R (1) ------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+r0:=1/63/((1-2*x)^(3/2)*(2+3*x)^3)+64/441/((1-2*x)^(3/2)*(2+3*x)^2)-_
+ 160/2401*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+64/147/((2+3*x)^2*_
+ sqrt(1-2*x))-80/343*sqrt(1-2*x)/(2+3*x)^2-240/2401*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +-+ +--------+
+--R (- 25920x - 38880x - 8640x + 9600x + 3840)\|3 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +-+
+--R (25920x + 28800x - 4464x - 11280x - 2237)\|7
+--R /
+--R 4 3 2 +-+ +--------+
+--R (388962x + 583443x + 129654x - 144060x - 57624)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+ +--------+
+--R (12960x + 19440x + 4320x - 4800x - 1920)\|3 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+
+--R (25920x + 28800x - 4464x - 11280x - 2237)\|7
+--R /
+--R 4 3 2 +-+ +--------+
+--R (388962x + 583443x + 129654x - 144060x - 57624)\|7 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R 80\|3 log(-------------------------------) + 160\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R --------------------------------------------------------------------------
+--R +-+
+--R 2401\|7
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^5)
+--R
+--R
+--R (1)
+--R 5x + 3
+--R ------------------------------------------------------------------------
+--R 7 6 5 4 3 2 +--------+
+--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+r0:=1/84/((1-2*x)^(3/2)*(2+3*x)^4)+43/294/((1-2*x)^(3/2)*(2+3*x)^3)-_
+ 1935/67228*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+387/686/((2+3*x)^3*_
+ sqrt(1-2*x))-387/1372*sqrt(1-2*x)/(2+3*x)^3-1935/19208*_
+ sqrt(1-2*x)/(2+3*x)^2-5805/134456*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2 +-+
+--R (- 1880820x - 4075110x - 2507760x + 278640x + 743040x + 185760)\|3
+--R *
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2 +-+
+--R (1880820x + 3343680x + 1069281x - 1034451x - 611202x - 48490)\|7
+--R /
+--R 5 4 3 2
+--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888)
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2 +-+
+--R (940410x + 2037555x + 1253880x - 139320x - 371520x - 92880)\|3
+--R *
+--R +-+ +--------+ +-+
+--R +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2 +-+
+--R (1880820x + 3343680x + 1069281x - 1034451x - 611202x - 48490)\|7
+--R /
+--R 5 4 3 2
+--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888)
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R 1935\|3 log(-------------------------------) + 3870\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 134456\|7
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^(5/2)
+--R
+--R
+--R 7 6 5 4 3 2
+--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288
+--R (1) ----------------------------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+r0:=2033647/384/(1-2*x)^(3/2)+1965635/128*(1-2*x)^(3/2)-_
+ 514017/128*(1-2*x)^(5/2)+672003/896*(1-2*x)^(7/2)-_
+ 10845/128*(1-2*x)^(9/2)+6075/1408*(1-2*x)^(11/2)+_
+ (-6206585/128)/sqrt(1-2*x)-8117095/128*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3 2
+--R 127575x + 806085x + 2456001x + 5121279x + 9702012x + 32450916x
+--R +
+--R - 65622552x + 21852008
+--R /
+--R +--------+
+--R (462x - 231)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3 2
+--R 127575x + 806085x + 2456001x + 5121279x + 9702012x + 32450916x
+--R +
+--R - 65622552x + 21852008
+--R /
+--R +--------+
+--R (462x - 231)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^(5/2)
+--R
+--R
+--R 6 5 4 3 2
+--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144
+--R (1) ----------------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+r0:=290521/192/(1-2*x)^(3/2)+40453/16*(1-2*x)^(3/2)-_
+ 159111/320*(1-2*x)^(5/2)+13905/224*(1-2*x)^(7/2)-_
+ 225/64*(1-2*x)^(9/2)+(-381073/32)/sqrt(1-2*x)-832951/64*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3 2
+--R 23625x + 137700x + 402489x + 915492x + 3294996x - 6731112x + 2238664
+--R -------------------------------------------------------------------------
+--R +--------+
+--R (210x - 105)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 23625x + 137700x + 402489x + 915492x + 3294996x - 6731112x + 2238664
+--R -------------------------------------------------------------------------
+--R +--------+
+--R (210x - 105)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^(5/2)
+--R
+--R
+--R 5 4 3 2
+--R 675x + 2160x + 2763x + 1766x + 564x + 72
+--R (1) --------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+r0:=41503/96/(1-2*x)^(3/2)+5847/16*(1-2*x)^(3/2)-_
+ 1539/32*(1-2*x)^(5/2)+675/224*(1-2*x)^(7/2)+(-91091/32)/sqrt(1-2*x)-_
+ 39977/16*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R 2025x + 11097x + 34137x + 139497x - 290838x + 96442
+--R (2) -------------------------------------------------------
+--R +--------+
+--R (42x - 21)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R 2025x + 11097x + 34137x + 139497x - 290838x + 96442
+--R (3) -------------------------------------------------------
+--R +--------+
+--R (42x - 21)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^(5/2)
+--R
+--R
+--R 4 3 2
+--R 225x + 570x + 541x + 228x + 36
+--R (1) ---------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+r0:=5929/48/(1-2*x)^(3/2)+85/2*(1-2*x)^(3/2)-45/16*(1-2*x)^(5/2)+_
+ (-1309/2)/sqrt(1-2*x)-3467/8*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2
+--R 135x + 750x + 3873x - 8430x + 2774
+--R (2) -------------------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R 135x + 750x + 3873x - 8430x + 2774
+--R (3) -------------------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^(5/2)
+--R
+--R
+--R 3 2
+--R 75x + 140x + 87x + 18
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+r0:=847/24/(1-2*x)^(3/2)+25/8*(1-2*x)^(3/2)+(-1133/8)/sqrt(1-2*x)-_
+ 505/8*sqrt(1-2*x)
+--R
+--R
+--R 3 2
+--R 75x + 645x - 1551x + 499
+--R (2) --------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 75x + 645x - 1551x + 499
+--R (3) --------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(3+5*x)^2/(1-2*x)^(5/2)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+r0:=121/12/(1-2*x)^(3/2)+(-55/2)/sqrt(1-2*x)-25/4*sqrt(1-2*x)
+--R
+--R
+--R 2
+--R 75x - 240x + 71
+--R (2) -------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 75x - 240x + 71
+--R (3) -------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x))
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+r0:=121/42/(1-2*x)^(3/2)-2/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_
+ (-407/98)/sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1 +--+
+--R (- 12x + 6)\|- 2x + 1 atanh(---------------) + (- 1221x + 187)\|21
+--R +-+
+--R \|7
+--R (2) -------------------------------------------------------------------
+--R +--+ +--------+
+--R (294x - 147)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--+
+--R (6x - 3)\|- 2x + 1 log(-----------------------------) + (- 1221x + 187)\|21
+--R 3x + 2
+--R ----------------------------------------------------------------------------
+--R +--+ +--------+
+--R (294x - 147)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 49\|21
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+
+--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (- 2x + 1)\|3 \|7 \|21
+--R +
+--R 42x - 21
+--R /
+--R 2 +--------+ 3 2 +--+
+--R (6174x + 1029x - 2058)\|- 2x + 1 + (882x - 1323x - 539x + 490)\|21
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^2)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) ----------------------------------------
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+r0:=121/42/((1-2*x)^(3/2)*(2+3*x))+130/343*atanh(sqrt(3/7)*sqrt(1-2*x))/_
+ sqrt(21)+(-130/1029)/sqrt(1-2*x)+(-365/294)/((2+3*x)*sqrt(1-2*x))
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|3 \|- 2x + 1
+--R (2340x + 390x - 780)\|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+
+--R (- 780x - 2685x - 1427)\|21
+--R /
+--R 2 +--+ +--------+
+--R (6174x + 1029x - 2058)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ - 21\|- 2x + 1 + (3x - 5)\|21
+--R (1170x + 195x - 390)\|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+
+--R (- 780x - 2685x - 1427)\|21
+--R /
+--R 2 +--+ +--------+
+--R (6174x + 1029x - 2058)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 65log(-------------------------------) - 130atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ------------------------------------------------------------------
+--R +--+
+--R 343\|21
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 195x + 325)\|21 + (195x - 325)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (130x - 65)\|3 \|7 \|21 - 2730x + 1365
+--R /
+--R 2 +--------+
+--R (43218x + 7203x - 14406)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 6174x + 9261x + 3773x - 3430)\|21
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^3)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) -------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+r0:=121/42/((1-2*x)^(3/2)*(2+3*x)^2)-85/343*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(3/7)+(-26/21)/((2+3*x)^2*sqrt(1-2*x))+85/147/((2+3*x)*_
+ sqrt(1-2*x))-255/686*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 +-+ +--------+ \|3 \|- 2x + 1
+--R (- 9180x - 7650x + 2040x + 2040)\|3 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+
+--R (9180x + 4080x - 7731x - 4231)\|7
+--R /
+--R 3 2 +-+ +--------+
+--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +--------+
+--R (4590x + 3825x - 1020x - 1020)\|3 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+
+--R (9180x + 4080x - 7731x - 4231)\|7
+--R /
+--R 3 2 +-+ +--------+
+--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+ +-+ +--------+
+--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1
+--R 85\|3 log(-------------------------------) + 170\|3 atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R --------------------------------------------------------------------------
+--R +-+
+--R 686\|7
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^4)
+--R
+--R
+--R 2
+--R 25x + 30x + 9
+--R (1) ------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+r0:=121/42/((1-2*x)^(3/2)*(2+3*x)^3)-1415/2401*atanh(sqrt(3/7)*sqrt(1-2*x))/_
+ sqrt(21)+(-1091/882)/((2+3*x)^3*sqrt(1-2*x))+566/441/((2+3*x)^2*_
+ sqrt(1-2*x))-1415/2058*sqrt(1-2*x)/(2+3*x)^2-1415/4802*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (- 458460x - 687690x - 152820x + 169800x + 67920)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+
+--R (152820x + 169800x - 26319x - 83655x - 23872)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (777924x + 1166886x + 259308x - 288120x - 115248)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +--------+
+--R (229230x + 343845x + 76410x - 84900x - 33960)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+
+--R (152820x + 169800x - 26319x - 83655x - 23872)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (777924x + 1166886x + 259308x - 288120x - 115248)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 1415log(-----------------------------) + 2830atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 4802\|21
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 4245x + 7075)\|21 + (4245x - 7075)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 2830x + 1415)\|3 \|7 \|21 + 59430x - 29715
+--R /
+--R 2 +--------+
+--R (605052x + 100842x - 201684)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (86436x - 129654x - 52822x + 48020)\|21
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^5)
+--R
+--R
+--R (1)
+--R 2
+--R 25x + 30x + 9
+--R ------------------------------------------------------------------------
+--R 7 6 5 4 3 2 +--------+
+--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+r0:=121/42/((1-2*x)^(3/2)*(2+3*x)^4)-20465/67228*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+(-727/588)/((2+3*x)^4*sqrt(1-2*x))+_
+ 4093/2058/((2+3*x)^3*sqrt(1-2*x))-4093/4116*sqrt(1-2*x)/(2+3*x)^3-_
+ 20465/57624*sqrt(1-2*x)/(2+3*x)^2-20465/134456*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 19891980x - 43099290x - 26522640x + 2946960x + 7858560x
+--R +
+--R 1964640
+--R *
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2 +--+
+--R (6630660x + 11787840x + 3769653x - 3646863x - 2528226x - 401410)\|21
+--R /
+--R 5 4 3 2
+--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R (9945990x + 21549645x + 13261320x - 1473480x - 3929280x - 982320)
+--R *
+--R +--------+ +--+
+--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21
+--R \|- 2x + 1 log(-----------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2 +--+
+--R (6630660x + 11787840x + 3769653x - 3646863x - 2528226x - 401410)\|21
+--R /
+--R 5 4 3 2
+--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 20465log(-----------------------------) + 40930atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 134456\|21
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 61395x + 102325)\|21 + (61395x - 102325)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 40930x + 20465)\|3 \|7 \|21 + 859530x - 429765
+--R /
+--R 2 +--------+
+--R (16941456x + 2823576x - 5647152)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (2420208x - 3630312x - 1479016x + 1344560)\|21
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)^(5/2)
+--R
+--R
+--R (1)
+--R 8 7 6 5 4 3 2
+--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x
+--R +
+--R 10800x + 864
+--R /
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+r0:=22370117/768/(1-2*x)^(3/2)+52725715/384*(1-2*x)^(3/2)-_
+ 2887773/64*(1-2*x)^(5/2)+10121229/896*(1-2*x)^(7/2)-_
+ 246315/128*(1-2*x)^(9/2)+277425/1408*(1-2*x)^(11/2)-_
+ 30375/3328*(1-2*x)^(13/2)+(-39220335/128)/sqrt(1-2*x)-_
+ 60160485/128*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 8 7 6 5 4
+--R 7016625x + 47670525x + 153878760x + 324478899x + 540496701x
+--R +
+--R 3 2
+--R 905206628x + 2892917004x - 5818266408x + 1938557272
+--R /
+--R +--------+
+--R (6006x - 3003)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6 5 4
+--R 7016625x + 47670525x + 153878760x + 324478899x + 540496701x
+--R +
+--R 3 2
+--R 905206628x + 2892917004x - 5818266408x + 1938557272
+--R /
+--R +--------+
+--R (6006x - 3003)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^(5/2)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2
+--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432
+--R -----------------------------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+r0:=3195731/384/(1-2*x)^(3/2)+9504551/384*(1-2*x)^(3/2)-_
+ 4177401/640*(1-2*x)^(5/2)+1101465/896*(1-2*x)^(7/2)-_
+ 17925/128*(1-2*x)^(9/2)+10125/1408*(1-2*x)^(11/2)+_
+ (-9836211/128)/sqrt(1-2*x)-12973191/128*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 7 6 5 4 3
+--R 1063125x + 6630750x + 19961775x + 41201532x + 77493296x
+--R +
+--R 2
+--R 258342648x - 522173856x + 173891632
+--R /
+--R +--------+
+--R (2310x - 1155)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5 4 3
+--R 1063125x + 6630750x + 19961775x + 41201532x + 77493296x
+--R +
+--R 2
+--R 258342648x - 522173856x + 173891632
+--R /
+--R +--------+
+--R (2310x - 1155)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^(5/2)
+--R
+--R
+--R 6 5 4 3 2
+--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216
+--R (1) -----------------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+r0:=456533/192/(1-2*x)^(3/2)+98209/24*(1-2*x)^(3/2)-52011/64*(1-2*x)^(5/2)+_
+ 11475/112*(1-2*x)^(7/2)-375/64*(1-2*x)^(9/2)+(-302379/16)/sqrt(1-2*x)-_
+ 1334949/64*sqrt(1-2*x)
+--R
+--R
+--R 6 5 4 3 2
+--R 7875x + 45225x + 130464x + 293785x + 1051833x - 2146758x + 714074
+--R (2) ----------------------------------------------------------------------
+--R +--------+
+--R (42x - 21)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 5 4 3 2
+--R 7875x + 45225x + 130464x + 293785x + 1051833x - 2146758x + 714074
+--R (3) ----------------------------------------------------------------------
+--R +--------+
+--R (42x - 21)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^(5/2)
+--R
+--R
+--R 5 4 3 2
+--R 1125x + 3525x + 4415x + 2763x + 864x + 108
+--R (1) ----------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+r0:=65219/96/(1-2*x)^(3/2)+28555/48*(1-2*x)^(3/2)-2535/32*(1-2*x)^(5/2)+_
+ 1125/224*(1-2*x)^(7/2)+(-144837/32)/sqrt(1-2*x)-64317/16*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2
+--R 3375x + 18180x + 55145x + 223458x - 465060x + 154264
+--R (2) --------------------------------------------------------
+--R +--------+
+--R (42x - 21)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 3 2
+--R 3375x + 18180x + 55145x + 223458x - 465060x + 154264
+--R (3) --------------------------------------------------------
+--R +--------+
+--R (42x - 21)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^(5/2)
+--R
+--R
+--R 4 3 2
+--R 375x + 925x + 855x + 351x + 54
+--R (1) ---------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+r0:=9317/48/(1-2*x)^(3/2)+1675/24*(1-2*x)^(3/2)-75/16*(1-2*x)^(5/2)+_
+ (-8349/8)/sqrt(1-2*x)-2805/4*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2
+--R 225x + 1225x + 6240x - 13533x + 4457
+--R (2) ---------------------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 2
+--R 225x + 1225x + 6240x - 13533x + 4457
+--R (3) ---------------------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(3+5*x)^3/(1-2*x)^(5/2)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+r0:=1331/24/(1-2*x)^(3/2)+125/24*(1-2*x)^(3/2)+(-1815/8)/sqrt(1-2*x)-_
+ 825/8*sqrt(1-2*x)
+--R
+--R
+--R 3 2
+--R 125x + 1050x - 2505x + 808
+--R (2) ----------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 125x + 1050x - 2505x + 808
+--R (3) ----------------------------
+--R +--------+
+--R (6x - 3)\|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x))
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+r0:=253/21*(3+5*x)/(1-2*x)^(3/2)-5/3*(3+5*x)^2/(1-2*x)^(3/2)+_
+ 2/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+(-2948/49)/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1 2 +--+
+--R (4x - 2)\|- 2x + 1 atanh(---------------) + (6125x - 19193x + 5736)\|21
+--R +-+
+--R \|7
+--R -------------------------------------------------------------------------
+--R +--+ +--------+
+--R (294x - 147)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21
+--R (2x - 1)\|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+
+--R (6125x - 19193x + 5736)\|21
+--R /
+--R +--+ +--------+
+--R (294x - 147)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R log(-------------------------------) - 2atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------
+--R +--+
+--R 147\|21
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+
+--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21
+--R +
+--R - 42x + 21
+--R /
+--R 2 +--------+
+--R (18522x + 3087x - 6174)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 2646x + 3969x + 1617x - 1470)\|21
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^2)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) ----------------------------------------
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x))-200/1029*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)-15/49*(3+5*x)^2/((2+3*x)*sqrt(1-2*x))-_
+ 750/343*sqrt(1-2*x)-50/1029*(3+5*x)*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|3 \|- 2x + 1
+--R (- 1200x - 200x + 400)\|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 2 +--+
+--R (- 42475x - 21050x + 4839)\|21
+--R /
+--R 2 +--+ +--------+
+--R (6174x + 1029x - 2058)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 21\|- 2x + 1 + (3x - 5)\|21
+--R (600x + 100x - 200)\|- 2x + 1 log(-----------------------------)
+--R 3x + 2
+--R +
+--R 2 +--+
+--R (- 42475x - 21050x + 4839)\|21
+--R /
+--R 2 +--+ +--------+
+--R (6174x + 1029x - 2058)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 100log(-----------------------------) + 200atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 1029\|21
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 300x + 500)\|21 + (300x - 500)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 200x + 100)\|3 \|7 \|21 + 4200x - 2100
+--R /
+--R 2 +--------+
+--R (129654x + 21609x - 43218)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (18522x - 27783x - 11319x + 10290)\|21
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^3)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) -------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^2)+905/1029*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+1/7*(3+5*x)^2/((2+3*x)^2*sqrt(1-2*x))-_
+ 5/294*(1+x)*sqrt(1-2*x)/(2+3*x)^2+50/1029*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 3 2 +--------+ \|3 \|- 2x + 1
+--R (32580x + 27150x - 7240x - 7240)\|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +--+
+--R (- 10860x - 33410x - 29593x - 8103)\|21
+--R /
+--R 3 2 +--+ +--------+
+--R (37044x + 30870x - 8232x - 8232)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+
+--R (16290x + 13575x - 3620x - 3620)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R - 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +--+
+--R (- 10860x - 33410x - 29593x - 8103)\|21
+--R /
+--R 3 2 +--+ +--------+
+--R (37044x + 30870x - 8232x - 8232)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 905log(-------------------------------) - 1810atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 2058\|21
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 2715x + 4525)\|21 + (2715x - 4525)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (1810x - 905)\|3 \|7 \|21 - 38010x + 19005
+--R /
+--R 2 +--------+
+--R (259308x + 43218x - 86436)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (- 37044x + 55566x + 22638x - 20580)\|21
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^4)
+--R
+--R
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R (1) ------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^3)-7510/7203*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+29/49*(3+5*x)^2/((2+3*x)^3*sqrt(1-2*x))+_
+ 125/1029*sqrt(1-2*x)/(2+3*x)^2-3755/7203*sqrt(1-2*x)/(2+3*x)+_
+ 4/49*(3+5*x)*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (- 405540x - 608310x - 135180x + 150200x + 60080)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2 +--+
+--R (135180x + 150200x - 83306x - 150295x - 45383)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (388962x + 583443x + 129654x - 144060x - 57624)\|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +--------+
+--R (202770x + 304155x + 67590x - 75100x - 30040)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 21\|- 2x + 1 + (3x - 5)\|21
+--R log(-----------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +--+
+--R (135180x + 150200x - 83306x - 150295x - 45383)\|21
+--R /
+--R 4 3 2 +--+ +--------+
+--R (388962x + 583443x + 129654x - 144060x - 57624)\|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 3755log(-----------------------------) + 7510atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 7203\|21
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 11265x + 18775)\|21 + (11265x - 18775)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 7510x + 3755)\|3 \|7 \|21 + 157710x - 78855
+--R /
+--R 2 +--------+
+--R (907578x + 151263x - 302526)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (129654x - 194481x - 79233x + 72030)\|21
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^5)
+--R
+--R
+--R (1)
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R ------------------------------------------------------------------------
+--R 7 6 5 4 3 2 +--------+
+--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^4)-177635/201684*_
+ atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+51/49*(3+5*x)^2/((2+3*x)^4*_
+ sqrt(1-2*x))+692/3087*sqrt(1-2*x)/(2+3*x)^3-177635/172872*_
+ sqrt(1-2*x)/(2+3*x)^2-177635/403368*sqrt(1-2*x)/(2+3*x)+_
+ 601/4116*(3+5*x)*sqrt(1-2*x)/(2+3*x)^4
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R - 57553740x - 124699770x - 76738320x + 8526480x + 22737280x
+--R +
+--R 5684320
+--R *
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3 2
+--R 19184580x + 34105920x + 10906789x - 12952519x - 10307138x
+--R +
+--R - 2094250
+--R *
+--R +--+
+--R \|21
+--R /
+--R 5 4 3 2
+--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 28776870x + 62349885x + 38369160x - 4263240x - 11368640x
+--R +
+--R - 2842160
+--R *
+--R +--------+ +--+
+--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21
+--R \|- 2x + 1 log(-----------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R 19184580x + 34105920x + 10906789x - 12952519x - 10307138x
+--R +
+--R - 2094250
+--R *
+--R +--+
+--R \|21
+--R /
+--R 5 4 3 2
+--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888)
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 177635log(-----------------------------) + 355270atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R -----------------------------------------------------------------------
+--R +--+
+--R 403368\|21
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 532905x + 888175)\|21 + (532905x - 888175)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 355270x + 177635)\|3 \|7 \|21 + 7460670x - 3730335
+--R /
+--R 2 +--------+
+--R (50824368x + 8470728x - 16941456)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (7260624x - 10890936x - 4437048x + 4033680)\|21
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^6)
+--R
+--R
+--R (1)
+--R 3 2
+--R 125x + 225x + 135x + 27
+--R /
+--R 8 7 6 5 4 3 2
+--R (2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^5)-163474/352947*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))/sqrt(21)+73/49*(3+5*x)^2/((2+3*x)^5*sqrt(1-2*x))+_
+ 3912/12005*sqrt(1-2*x)/(2+3*x)^4-163474/108045*sqrt(1-2*x)/(2+3*x)^3-_
+ 81737/151263*sqrt(1-2*x)/(2+3*x)^2-81737/352947*sqrt(1-2*x)/(2+3*x)+_
+ 1082/5145*(3+5*x)*sqrt(1-2*x)/(2+3*x)^5
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R - 397241820x - 1125518490x - 1103449500x - 294253200x
+--R +
+--R 2
+--R 196168800x + 143857120x + 26155840
+--R *
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 6 5 4 3 2
+--R 132413940x + 323678520x + 232214817x - 22641149x - 99751837x
+--R +
+--R - 42553376x - 5615203
+--R *
+--R +--+
+--R \|21
+--R /
+--R 6 5 4 3 2
+--R 857661210x + 2430040095x + 2382392250x + 635304600x - 423536400x
+--R +
+--R - 310593360x - 56471520
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 198620910x + 562759245x + 551724750x + 147126600x - 98084400x
+--R +
+--R - 71928560x - 13077920
+--R *
+--R +--------+ +--+
+--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21
+--R \|- 2x + 1 log(-----------------------------)
+--R 3x + 2
+--R +
+--R 6 5 4 3 2
+--R 132413940x + 323678520x + 232214817x - 22641149x - 99751837x
+--R +
+--R - 42553376x - 5615203
+--R *
+--R +--+
+--R \|21
+--R /
+--R 6 5 4 3 2
+--R 857661210x + 2430040095x + 2382392250x + 635304600x - 423536400x
+--R +
+--R - 310593360x - 56471520
+--R *
+--R +--+ +--------+
+--R \|21 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1
+--R 81737log(-----------------------------) + 163474atanh(---------------)
+--R 3x + 2 +-+
+--R \|7
+--R (4) ----------------------------------------------------------------------
+--R +--+
+--R 352947\|21
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +-+ +--------+
+--R ((- 245211x + 408685)\|21 + (245211x - 408685)\|3 \|7 )\|- 2x + 1
+--R +
+--R +-+ +-+ +--+
+--R (- 163474x + 81737)\|3 \|7 \|21 + 3432954x - 1716477
+--R /
+--R 2 +--------+
+--R (44471322x + 7411887x - 14823774)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (6353046x - 9529569x - 3882417x + 3529470)\|21
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x))
+--R
+--R
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R (1) -----------------------------------------------------
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+r0:=172/165*(2+3*x)^4/(1-2*x)^(3/2)-3/35*(2+3*x)^5/(1-2*x)^(3/2)-2/75625*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-7561/605*(2+3*x)^3/_
+ sqrt(1-2*x)-55573878/75625*sqrt(1-2*x)-63513/605*(2+3*x)*_
+ sqrt(1-2*x)-340248/15125*(2+3*x)^2*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R (- 84x + 42)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 33078375x + 190531440x + 611141355x + 2562785082x - 5374023537x
+--R +
+--R 1780047848
+--R *
+--R +--+
+--R \|55
+--R /
+--R +--+ +--------+
+--R (3176250x - 1588125)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (42x - 21)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 33078375x + 190531440x + 611141355x + 2562785082x - 5374023537x
+--R +
+--R 1780047848
+--R *
+--R +--+
+--R \|55
+--R /
+--R +--+ +--------+
+--R (3176250x - 1588125)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 75625\|55
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (41593750x + 4159375x - 12478125)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (3781250x - 5671875x - 1739375x + 1815000)\|55
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x))
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+r0:=959/825*(2+3*x)^3/(1-2*x)^(3/2)-3/25*(2+3*x)^4/(1-2*x)^(3/2)-2/15125*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-31612/3025*(2+3*x)^2/_
+ sqrt(1-2*x)-2276102/15125*sqrt(1-2*x)-1/15125*(569026+948375*x)*_
+ sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R (- 12x + 6)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (441045x + 2597265x + 13976226x - 30775791x + 10097264)\|55
+--R /
+--R +--+ +--------+
+--R (90750x - 45375)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (6x - 3)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+
+--R (441045x + 2597265x + 13976226x - 30775791x + 10097264)\|55
+--R /
+--R +--+ +--------+
+--R (90750x - 45375)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 15125\|55
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (8318750x + 831875x - 2495625)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (756250x - 1134375x - 347875x + 363000)\|55
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+r0:=238/165*(2+3*x)^2/(1-2*x)^(3/2)-1/5*(2+3*x)^3/(1-2*x)^(3/2)-_
+ 2/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 7/605*(1426+2377*x)/sqrt(1-2*x)-80818/3025*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R (- 12x + 6)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (49005x + 450846x - 1111431x + 354344)\|55
+--R /
+--R +--+ +--------+
+--R (18150x - 9075)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (6x - 3)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (49005x + 450846x - 1111431x + 354344)\|55
+--R /
+--R +--+ +--------+
+--R (18150x - 9075)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 3025\|55
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (1663750x + 166375x - 499125)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (151250x - 226875x - 69575x + 72600)\|55
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+r0:=469/165*(2+3*x)/(1-2*x)^(3/2)-3/5*(2+3*x)^2/(1-2*x)^(3/2)-_
+ 2/605*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-5152/605)/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1 2 +--+
+--R (- 12x + 6)\|- 2x + 1 atanh(---------------) + (9801x - 33321x + 9494)\|55
+--R +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +--+ +--------+
+--R (3630x - 1815)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (6x - 3)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (9801x - 33321x + 9494)\|55
+--R /
+--R +--+ +--------+
+--R (3630x - 1815)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 605\|55
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (332750x + 33275x - 99825)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (30250x - 45375x - 13915x + 14520)\|55
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+r0:=49/66/(1-2*x)^(3/2)-2/121*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_
+ (-217/242)/sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1 +--+
+--R (- 12x + 6)\|- 2x + 1 atanh(---------------) + (- 651x + 56)\|55
+--R +--+
+--R \|11
+--R (2) -----------------------------------------------------------------
+--R +--+ +--------+
+--R (726x - 363)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+
+--R (6x - 3)\|- 2x + 1 log(-----------------------------) + (- 651x + 56)\|55
+--R 5x + 3
+--R --------------------------------------------------------------------------
+--R +--+ +--------+
+--R (726x - 363)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R log(-----------------------------) + 2atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ------------------------------------------------------------
+--R +--+
+--R 121\|55
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55
+--R /
+--R 2 +--------+
+--R (66550x + 6655x - 19965)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (6050x - 9075x - 2783x + 2904)\|55
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x))
+--R
+--R
+--R 3x + 2
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+r0:=7/33/(1-2*x)^(3/2)-2/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 2/121/sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +-+ +--------+ \|5 \|- 2x + 1 +--+
+--R (- 12x + 6)\|5 \|- 2x + 1 atanh(---------------) + (12x - 83)\|11
+--R +--+
+--R \|11
+--R (2) ------------------------------------------------------------------
+--R +--+ +--------+
+--R (726x - 363)\|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (6x - 3)\|5 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +--+
+--R (12x - 83)\|11
+--R /
+--R +--+ +--------+
+--R (726x - 363)\|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+ +-+ +--------+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1
+--R \|5 log(---------------------------------) + 2\|5 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ------------------------------------------------------------------------
+--R +--+
+--R 121\|11
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=1/((1-2*x)^(5/2)*(3+5*x))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+r0:=2/33/(1-2*x)^(3/2)-10/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 10/121/sqrt(1-2*x)
+--R
+--R
+--R +-+ +--------+
+--R +-+ +--------+ \|5 \|- 2x + 1 +--+
+--R (- 60x + 30)\|5 \|- 2x + 1 atanh(---------------) + (60x - 52)\|11
+--R +--+
+--R \|11
+--R (2) -------------------------------------------------------------------
+--R +--+ +--------+
+--R (726x - 363)\|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (30x - 15)\|5 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +--+
+--R (60x - 52)\|11
+--R /
+--R +--+ +--------+
+--R (726x - 363)\|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+ +-+ +--------+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1
+--R 5\|5 log(---------------------------------) + 10\|5 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R --------------------------------------------------------------------------
+--R +--+
+--R 121\|11
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------
+--R 4 3 2 +--------+
+--R (60x + 16x - 37x - 5x + 6)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+r0:=4/231/(1-2*x)^(3/2)+18/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_
+ 50/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+272/5929/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R (13068x - 6534)\|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R (- 14700x + 7350)\|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--+
+--R (1632x - 1124)\|7 \|11
+--R /
+--R +-+ +--+ +--------+
+--R (35574x - 17787)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (7350x - 3675)\|5 \|7 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R (6534x - 3267)\|3 \|11 \|- 2x + 1 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--+
+--R (1632x - 1124)\|7 \|11
+--R /
+--R +-+ +--+ +--------+
+--R (35574x - 17787)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 1225\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 1089\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R - 2178\|3 \|11 atanh(---------------) + 2450\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 5929\|7 \|11
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+r0:=4/231/((1-2*x)^(3/2)*(2+3*x))+720/343*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(3/7)-250/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 360/5929/((2+3*x)*sqrt(1-2*x))+2055/41503*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R (1568160x + 261360x - 522720)\|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R (- 1543500x - 257250x + 514500)\|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+
+--R (- 24660x + 39780x - 15881)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (747054x + 124509x - 249018)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +-+ +--------+
+--R (771750x + 128625x - 257250)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--+ +--------+
+--R (784080x + 130680x - 261360)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +--+
+--R (- 24660x + 39780x - 15881)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (747054x + 124509x - 249018)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 42875\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 43560\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 87120\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 85750\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 41503\|7 \|11
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2)+3645/343*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(3/7)-1250/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 64/847/((2+3*x)^2*sqrt(1-2*x))+45/11858*sqrt(1-2*x)/(2+3*x)^2+_
+ 36885/83006*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+ +--------+
+--R (47632860x + 39694050x - 10585080x - 10585080)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+ +--------+
+--R (- 46305000x - 38587500x + 10290000x + 10290000)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+
+--R (- 1327860x + 438840x + 594687x - 245383)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (4482324x + 3735270x - 996072x - 996072)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +-+ +--------+
+--R (23152500x + 19293750x - 5145000x - 5145000)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (23816430x + 19847025x - 5292540x - 5292540)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+
+--R (- 1327860x + 438840x + 594687x - 245383)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (4482324x + 3735270x - 996072x - 996072)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 428750\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 441045\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 882090\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 857500\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 83006\|7 \|11
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^4*(3+5*x))
+--R
+--R
+--R (1)
+--R 1
+--R ---------------------------------------------------------------------------
+--R 7 6 5 4 3 2 +--------+
+--R (1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^3)+127710/2401*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(3/7)-6250/121*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(5/11)+536/5929/((2+3*x)^3*sqrt(1-2*x))-93/5929*_
+ sqrt(1-2*x)/(2+3*x)^3+8955/41503*sqrt(1-2*x)/(2+3*x)^2+_
+ 669990/290521*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (2503371420x + 3755057130x + 834457140x - 927174600x - 370869840)
+--R *
+--R +-+ +--------+
+--R +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R \|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2
+--R (- 2431012500x - 3646518750x - 810337500x + 900375000x + 360150000)
+--R *
+--R +-+ +--------+
+--R +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R \|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--+
+--R (- 72358920x - 26376300x + 47036214x + 9083055x - 8496203)\|7 \|11
+--R /
+--R 4 3 2 +-+ +--+
+--R (47064402x + 70596603x + 15688134x - 17431260x - 6972504)\|7 \|11
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (1215506250x + 1823259375x + 405168750x - 450187500x - 180075000)
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2
+--R (1251685710x + 1877528565x + 417228570x - 463587300x - 185434920)
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 \|- 2x + 1 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2 +-+ +--+
+--R (- 72358920x - 26376300x + 47036214x + 9083055x - 8496203)\|7 \|11
+--R /
+--R 4 3 2 +-+ +--+
+--R (47064402x + 70596603x + 15688134x - 17431260x - 6972504)\|7 \|11
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 7503125\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 7726455\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 15452910\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 15006250\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 290521\|7 \|11
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^2)
+--R
+--R
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R (1) -----------------------------------------------------
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+r0:=959/825*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x))-3/25*(2+3*x)^5/_
+ ((1-2*x)^(3/2)*(3+5*x))-406/831875*atanh(sqrt(5/11)*sqrt(1-2*x))/_
+ sqrt(55)-93611/9075*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))-_
+ 77849506/831875*sqrt(1-2*x)+154448/166375*(2+3*x)^2*sqrt(1-2*x)/_
+ (3+5*x)-7/831875*(2780354+4633875*x)*sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 12180x - 1218x + 3654)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 72772425x + 480298005x + 2644064775x - 3837745731x - 1434109759x
+--R +
+--R 1035652776
+--R *
+--R +--+
+--R \|55
+--R /
+--R 2 +--+ +--------+
+--R (24956250x + 2495625x - 7486875)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (6090x + 609x - 1827)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 72772425x + 480298005x + 2644064775x - 3837745731x - 1434109759x
+--R +
+--R 1035652776
+--R *
+--R +--+
+--R \|55
+--R /
+--R 2 +--+ +--------+
+--R (24956250x + 2495625x - 7486875)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 203log(-----------------------------) + 406atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 831875\|55
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 1015x + 1624)\|55 + (1015x - 1624)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 406x + 203)\|5 \|11 \|55 + 22330x - 11165
+--R /
+--R 2 +--------+
+--R (457531250x + 45753125x - 137259375)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (41593750x - 62390625x - 19133125x + 19965000)\|55
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^2)
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+r0:=238/165*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x))-1/5*(2+3*x)^4/_
+ ((1-2*x)^(3/2)*(3+5*x))-68/33275*atanh(sqrt(5/11)*sqrt(1-2*x))/_
+ sqrt(55)-15442/1815*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))-_
+ 532452/33275*sqrt(1-2*x)+1014/1331*(2+3*x)*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 2040x - 204x + 612)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (1617165x + 16171650x - 28677318x - 10671002x + 7204728)\|55
+--R /
+--R 2 +--+ +--------+
+--R (998250x + 99825x - 299475)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (1020x + 102x - 306)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+
+--R (1617165x + 16171650x - 28677318x - 10671002x + 7204728)\|55
+--R /
+--R 2 +--+ +--------+
+--R (998250x + 99825x - 299475)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 34log(-----------------------------) + 68atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------
+--R +--+
+--R 33275\|55
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 170x + 272)\|55 + (170x - 272)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 68x + 34)\|5 \|11 \|55 + 3740x - 1870
+--R /
+--R 2 +--------+
+--R (18301250x + 1830125x - 5490375)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1663750x - 2495625x - 765325x + 798600)\|55
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^2)
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+r0:=469/165*(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x))-3/5*(2+3*x)^3/((1-2*x)^(3/2)*_
+ (3+5*x))-274/33275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_
+ 7/1815*(3944+7323*x)/((3+5*x)*sqrt(1-2*x))-26988/33275*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 8220x - 822x + 2466)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (1617165x - 4634229x - 1790101x + 943584)\|55
+--R /
+--R 2 +--+ +--------+
+--R (998250x + 99825x - 299475)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (4110x + 411x - 1233)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (1617165x - 4634229x - 1790101x + 943584)\|55
+--R /
+--R 2 +--+ +--------+
+--R (998250x + 99825x - 299475)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 137log(-----------------------------) + 274atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 33275\|55
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 685x + 1096)\|55 + (685x - 1096)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 274x + 137)\|5 \|11 \|55 + 15070x - 7535
+--R /
+--R 2 +--------+
+--R (18301250x + 1830125x - 5490375)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1663750x - 2495625x - 765325x + 798600)\|55
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^2)
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+r0:=2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x))-208/6655*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))/sqrt(55)-23/363*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))-_
+ 942/6655*sqrt(1-2*x)+6/1331*(2+3*x)*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 6240x - 624x + 1872)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (- 106563x - 57832x + 3678)\|55
+--R /
+--R 2 +--+ +--------+
+--R (199650x + 19965x - 59895)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (3120x + 312x - 936)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (- 106563x - 57832x + 3678)\|55
+--R /
+--R 2 +--+ +--------+
+--R (199650x + 19965x - 59895)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 104log(-----------------------------) + 208atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -----------------------------------------------------------------
+--R +--+
+--R 6655\|55
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 520x + 832)\|55 + (520x - 832)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 208x + 104)\|5 \|11 \|55 + 11440x - 5720
+--R /
+--R 2 +--------+
+--R (3660250x + 366025x - 1098075)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (332750x - 499125x - 153065x + 159720)\|55
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^2)
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+r0:=49/66/((1-2*x)^(3/2)*(3+5*x))-142/1331*atanh(sqrt(5/11)*sqrt(1-2*x))/_
+ sqrt(55)+142/6655/sqrt(1-2*x)+(-1231/3630)/((3+5*x)*sqrt(1-2*x))
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +--------+ \|5 \|- 2x + 1
+--R (- 4260x - 426x + 1278)\|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (852x - 2623x - 1866)\|55
+--R /
+--R 2 +--+ +--------+
+--R (39930x + 3993x - 11979)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--+
+--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55
+--R (2130x + 213x - 639)\|- 2x + 1 log(-----------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (852x - 2623x - 1866)\|55
+--R /
+--R 2 +--+ +--------+
+--R (39930x + 3993x - 11979)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 71log(-----------------------------) + 142atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ----------------------------------------------------------------
+--R +--+
+--R 1331\|55
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 355x + 568)\|55 + (355x - 568)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 142x + 71)\|5 \|11 \|55 + 7810x - 3905
+--R /
+--R 2 +--------+
+--R (732050x + 73205x - 219615)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (66550x - 99825x - 30613x + 31944)\|55
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^2)
+--R
+--R
+--R 3x + 2
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 500
+r0:=76/1815/(1-2*x)^(3/2)+(-1/55)/((1-2*x)^(3/2)*(3+5*x))-_
+ 76/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+76/1331/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--------+ \|5 \|- 2x + 1
+--R (- 2280x - 228x + 684)\|5 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (2280x - 608x - 1113)\|11
+--R /
+--R 2 +--+ +--------+
+--R (39930x + 3993x - 11979)\|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +--------+
+--R (1140x + 114x - 342)\|5 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (2280x - 608x - 1113)\|11
+--R /
+--R 2 +--+ +--------+
+--R (39930x + 3993x - 11979)\|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 363
+
+--S 364 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+ +-+ +--------+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1
+--R 38\|5 log(---------------------------------) + 76\|5 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ---------------------------------------------------------------------------
+--R +--+
+--R 1331\|11
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=1/((1-2*x)^(5/2)*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+r0:=10/363/(1-2*x)^(3/2)+(-1/11)/((1-2*x)^(3/2)*(3+5*x))-_
+ 50/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+50/1331/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 +-+ +--------+ \|5 \|- 2x + 1
+--R (- 1500x - 150x + 450)\|5 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (1500x - 400x - 417)\|11
+--R /
+--R 2 +--+ +--------+
+--R (39930x + 3993x - 11979)\|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +--+
+--R 2 +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R (750x + 75x - 225)\|5 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 2 +--+
+--R (1500x - 400x - 417)\|11
+--R /
+--R 2 +--+ +--------+
+--R (39930x + 3993x - 11979)\|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 368
+
+--S 369 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+ +-+ +--------+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1
+--R 25\|5 log(---------------------------------) + 50\|5 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R ---------------------------------------------------------------------------
+--R +--+
+--R 1331\|11
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+r0:=4/231/((1-2*x)^(3/2)*(3+5*x))-54/49*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(3/7)+1400/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_
+ 1096/17787/((3+5*x)*sqrt(1-2*x))-8185/65219*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 2 +-+ +--+ +--------+
+--R (- 2156220x - 215622x + 646866)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|3 \|- 2x + 1
+--R atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R 2 +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R (2058000x + 205800x - 617400)\|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--+
+--R (98220x - 74108x + 9111)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (1956570x + 195657x - 586971)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +--+ +--------+
+--R (1078110x + 107811x - 323433)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 2 +-+ +-+ +--------+
+--R (1029000x + 102900x - 308700)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(-----------------------------------)
+--R 5x + 3
+--R +
+--R 2 +-+ +--+
+--R (98220x - 74108x + 9111)\|7 \|11
+--R /
+--R 2 +-+ +--+ +--------+
+--R (1956570x + 195657x - 586971)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 373
+
+--S 374 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 35937\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 34300\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1
+--R 71874\|3 \|11 atanh(---------------) - 68600\|5 \|7 atanh(---------------)
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R +-+ +--+
+--R 65219\|7 \|11
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^2)
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+r0:=4/231/((1-2*x)^(3/2)*(2+3*x)*(3+5*x))-4050/343*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(3/7)+15250/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(5/11)+1360/17787/((2+3*x)*(3+5*x)*sqrt(1-2*x))-_
+ 399500/456533*sqrt(1-2*x)/(3+5*x)+1775/41503*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+
+--R (- 485149500x - 371947950x + 113201550x + 97029900)\|3 \|11
+--R *
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+ +--------+
+--R (470767500x + 360921750x - 109845750x - 94153500)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+
+--R (14382000x - 5028300x - 5548760x + 2209989)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (41087970x + 31500777x - 9587193x - 8217594)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +--+ +--------+
+--R (242574750x + 185973975x - 56600775x - 48514950)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(-------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +-+ +--------+
+--R (235383750x + 180460875x - 54922875x - 47076750)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(-----------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+
+--R (14382000x - 5028300x - 5548760x + 2209989)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (41087970x + 31500777x - 9587193x - 8217594)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 378
+
+--S 379 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 2695275\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 2615375\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R 5390550\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R - 5230750\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 456533\|7 \|11
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^2)
+--R
+--R
+--R (1)
+--R 1
+--R ---------------------------------------------------------------------------
+--R 7 6 5 4 3 2 +--------+
+--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x))-4455/49*atanh(sqrt(3/7)*_
+ sqrt(1-2*x))*sqrt(3/7)+117500/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(5/11)+232/2541/((2+3*x)^2*(3+5*x)*sqrt(1-2*x))-_
+ 860525/130438*sqrt(1-2*x)/(3+5*x)-5/1694*sqrt(1-2*x)/_
+ ((2+3*x)^2*(3+5*x))+3790/5929*sqrt(1-2*x)/((2+3*x)*(3+5*x))
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 3201986700x - 4589514270x - 889440750x + 1138484160x + 426931560)
+--R *
+--R +-+ +--------+
+--R +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R \|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2
+--R (3109050000x + 4456305000x + 863625000x - 1105440000x - 414540000)
+--R *
+--R +-+ +--------+
+--R +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R \|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--+
+--R (92936700x + 27977220x - 58371045x - 9008764x + 9784671)\|7 \|11
+--R /
+--R 4 3 2 +-+ +--+
+--R (35218260x + 50479506x + 9782850x - 12522048x - 4695768)\|7 \|11
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (1600993350x + 2294757135x + 444720375x - 569242080x - 213465780)
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 \|- 2x + 1 log(-------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2
+--R (1554525000x + 2228152500x + 431812500x - 552720000x - 207270000)
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ +--------+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 \|- 2x + 1 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +-+ +--+
+--R (92936700x + 27977220x - 58371045x - 9008764x + 9784671)\|7 \|11
+--R /
+--R 4 3 2 +-+ +--+
+--R (35218260x + 50479506x + 9782850x - 12522048x - 4695768)\|7 \|11
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +-+
+--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 5929605\|3 \|11 log(-------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+ +--+
+--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 5757500\|5 \|7 log(-----------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R 11859210\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R - 11515000\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 130438\|7 \|11
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^3)
+--R
+--R
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+r0:=238/165*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2)-1/5*(2+3*x)^5/_
+ ((1-2*x)^(3/2)*(3+5*x)^2)-6937/1830125*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))/sqrt(55)-15197/1815*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))-_
+ 18063843/1830125*sqrt(1-2*x)+149653/199650*(2+3*x)^2*_
+ sqrt(1-2*x)/(3+5*x)^2+13755/29282*(2+3*x)*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (- 2081100x - 1456770x + 499464x + 374598)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 533664450x + 5763576060x - 6510290070x - 9509366452x + 253794537x
+--R +
+--R 1463964312
+--R *
+--R +--+
+--R \|55
+--R /
+--R 3 2 +--+ +--------+
+--R (549037500x + 384326250x - 131769000x - 98826750)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+
+--R (1040550x + 728385x - 249732x - 187299)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R log(-----------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 533664450x + 5763576060x - 6510290070x - 9509366452x + 253794537x
+--R +
+--R 1463964312
+--R *
+--R +--+
+--R \|55
+--R /
+--R 3 2 +--+ +--------+
+--R (549037500x + 384326250x - 131769000x - 98826750)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 6937log(-----------------------------) + 13874atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 3660250\|55
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 34685x + 55496)\|55 + (34685x - 55496)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 13874x + 6937)\|5 \|11 \|55 + 763070x - 381535
+--R /
+--R 2 +--------+
+--R (2013137500x + 201313750x - 603941250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (183012500x - 274518750x - 84185750x + 87846000)\|55
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^3)
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+r0:=469/165*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2)-3/5*(2+3*x)^4/_
+ ((1-2*x)^(3/2)*(3+5*x)^2)-4693/366025*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))/sqrt(55)-14966/1815*(2+3*x)^2/((3+5*x)^2*_
+ sqrt(1-2*x))+29033/39930*(2+3*x)*sqrt(1-2*x)/(3+5*x)^2+_
+ 164309/366025*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (- 1407900x - 985530x + 337896x + 253422)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (106732890x - 248761830x - 309826828x - 10907307x + 37428168)\|55
+--R /
+--R 3 2 +--+ +--------+
+--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+
+--R (703950x + 492765x - 168948x - 126711)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R log(-----------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2 +--+
+--R (106732890x - 248761830x - 309826828x - 10907307x + 37428168)\|55
+--R /
+--R 3 2 +--+ +--------+
+--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 4693log(-----------------------------) + 9386atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 732050\|55
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 23465x + 37544)\|55 + (23465x - 37544)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 9386x + 4693)\|5 \|11 \|55 + 516230x - 258115
+--R /
+--R 2 +--------+
+--R (402627500x + 40262750x - 120788250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (36602500x - 54903750x - 16837150x + 17569200)\|55
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^3)
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+r0:=2/33*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2)-14423/366025*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-19/363*(2+3*x)^3/_
+ ((3+5*x)^2*sqrt(1-2*x))-29037/366025*sqrt(1-2*x)+_
+ 31/7986*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+141/146410*(2+3*x)*_
+ sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (- 4326900x - 3028830x + 1038456x + 778842)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (- 34712250x - 40823468x - 11479257x + 311208)\|55
+--R /
+--R 3 2 +--+ +--------+
+--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+
+--R (2163450x + 1514415x - 519228x - 389421)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (- 34712250x - 40823468x - 11479257x + 311208)\|55
+--R /
+--R 3 2 +--+ +--------+
+--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 14423log(-----------------------------) + 28846atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) ---------------------------------------------------------------------
+--R +--+
+--R 732050\|55
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 72115x + 115384)\|55 + (72115x - 115384)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 28846x + 14423)\|5 \|11 \|55 + 1586530x - 793265
+--R /
+--R 2 +--------+
+--R (402627500x + 40262750x - 120788250)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (36602500x - 54903750x - 16837150x + 17569200)\|55
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^3)
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+r0:=2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2)-7559/73205*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+47/363*(2+3*x)^2/_
+ ((3+5*x)^2*sqrt(1-2*x))-101/7986*(2+3*x)*sqrt(1-2*x)/(3+5*x)^2-_
+ 683/73205*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (- 2267700x - 1587390x + 544248x + 408186)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (453540x - 639434x - 1242261x - 417036)\|55
+--R /
+--R 3 2 +--+ +--------+
+--R (21961500x + 15373050x - 5270760x - 3953070)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+
+--R (1133850x + 793695x - 272124x - 204093)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (453540x - 639434x - 1242261x - 417036)\|55
+--R /
+--R 3 2 +--+ +--------+
+--R (21961500x + 15373050x - 5270760x - 3953070)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 7559log(-----------------------------) + 15118atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) --------------------------------------------------------------------
+--R +--+
+--R 146410\|55
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 37795x + 60472)\|55 + (37795x - 60472)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 15118x + 7559)\|5 \|11 \|55 + 831490x - 415745
+--R /
+--R 2 +--------+
+--R (80525500x + 8052550x - 24157650)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (7320500x - 10980750x - 3367430x + 3513840)\|55
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^3)
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+r0:=49/66/((1-2*x)^(3/2)*(3+5*x)^2)-2873/14641*atanh(sqrt(5/11)*_
+ sqrt(1-2*x))/sqrt(55)+(-614/1815)/((3+5*x)^2*sqrt(1-2*x))+_
+ 2873/19965/((3+5*x)*sqrt(1-2*x))-2873/29282*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (- 861900x - 603330x + 206856x + 155142)\|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (172380x + 57460x - 107127x - 47568)\|55
+--R /
+--R 3 2 +--+ +--------+
+--R (4392300x + 3074610x - 1054152x - 790614)\|55 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+
+--R (430950x + 301665x - 103428x - 77571)\|- 2x + 1
+--R *
+--R +--------+ +--+
+--R 55\|- 2x + 1 + (5x - 8)\|55
+--R log(-----------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (172380x + 57460x - 107127x - 47568)\|55
+--R /
+--R 3 2 +--+ +--------+
+--R (4392300x + 3074610x - 1054152x - 790614)\|55 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--+ +-+ +--------+
+--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1
+--R 2873log(-----------------------------) + 5746atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R (4) -------------------------------------------------------------------
+--R +--+
+--R 29282\|55
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +-+ +--+ +--------+
+--R ((- 14365x + 22984)\|55 + (14365x - 22984)\|5 \|11 )\|- 2x + 1
+--R +
+--R +-+ +--+ +--+
+--R (- 5746x + 2873)\|5 \|11 \|55 + 316030x - 158015
+--R /
+--R 2 +--------+
+--R (16105100x + 1610510x - 4831530)\|- 2x + 1
+--R +
+--R 3 2 +--+
+--R (1464100x - 2196150x - 673486x + 702768)\|55
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^3)
+--R
+--R
+--R 3x + 2
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+r0:=73/3993/(1-2*x)^(3/2)+(-1/110)/((1-2*x)^(3/2)*(3+5*x)^2)+(-73/1210)/_
+ ((1-2*x)^(3/2)*(3+5*x))-365/14641*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(5/11)+365/14641/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--------+
+--R (- 109500x - 76650x + 26280x + 19710)\|5 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (109500x + 36500x - 47961x - 17466)\|11
+--R /
+--R 3 2 +--+ +--------+
+--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +--------+
+--R (54750x + 38325x - 13140x - 9855)\|5 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (109500x + 36500x - 47961x - 17466)\|11
+--R /
+--R 3 2 +--+ +--------+
+--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+ +-+ +--------+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1
+--R 365\|5 log(---------------------------------) + 730\|5 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -----------------------------------------------------------------------------
+--R +--+
+--R 29282\|11
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=1/((1-2*x)^(5/2)*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+r0:=2/33/((1-2*x)^(3/2)*(3+5*x)^2)-175/14641*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(5/11)+70/363/((3+5*x)^2*sqrt(1-2*x))-875/7986*sqrt(1-2*x)/_
+ (3+5*x)^2-875/29282*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--------+
+--R (- 52500x - 36750x + 12600x + 9450)\|5 \|- 2x + 1
+--R *
+--R +-+ +--------+
+--R \|5 \|- 2x + 1
+--R atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (52500x + 17500x - 22995x - 4764)\|11
+--R /
+--R 3 2 +--+ +--------+
+--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +--------+
+--R (26250x + 18375x - 6300x - 4725)\|5 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +--+
+--R (52500x + 17500x - 22995x - 4764)\|11
+--R /
+--R 3 2 +--+ +--------+
+--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+ +-+ +--------+
+--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1
+--R 175\|5 log(---------------------------------) + 350\|5 atanh(---------------)
+--R 5x + 3 +--+
+--R \|11
+--R -----------------------------------------------------------------------------
+--R +--+
+--R 29282\|11
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^3)
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (1500x + 2200x + 95x - 1091x - 333x + 135x + 54)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+r0:=4/231/((1-2*x)^(3/2)*(3+5*x)^2)+162/49*atanh(sqrt(3/7)*sqrt(1-2*x))*_
+ sqrt(3/7)-47075/14641*atanh(sqrt(5/11)*sqrt(1-2*x))*_
+ sqrt(5/11)+1376/17787/((3+5*x)^2*sqrt(1-2*x))-_
+ 33535/391314*sqrt(1-2*x)/(3+5*x)^2+325835/1434818*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +--+
+--R (711552600x + 498086820x - 170772624x - 128079468)\|3 \|11
+--R *
+--R +-+ +--------+
+--R +--------+ \|3 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 3 2 +-+ +-+
+--R (- 692002500x - 484401750x + 166080600x + 124560450)\|5 \|7
+--R *
+--R +-+ +--------+
+--R +--------+ \|5 \|- 2x + 1
+--R \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--+
+--R (- 19550100x + 9295580x + 6032979x - 2971158)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (215222700x + 150655890x - 51653448x - 38740086)\|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+ +-+ +--------+
+--R (346001250x + 242200875x - 83040300x - 62280225)\|5 \|7 \|- 2x + 1
+--R *
+--R +-+ +--------+ +--+
+--R 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R log(---------------------------------)
+--R 5x + 3
+--R +
+--R 3 2 +-+ +--+ +--------+
+--R (355776300x + 249043410x - 85386312x - 64039734)\|3 \|11 \|- 2x + 1
+--R *
+--R +-+ +--------+ +-+
+--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R log(---------------------------------)
+--R 3x + 2
+--R +
+--R 3 2 +-+ +--+
+--R (- 19550100x + 9295580x + 6032979x - 2971158)\|7 \|11
+--R /
+--R 3 2 +-+ +--+ +--------+
+--R (215222700x + 150655890x - 51653448x - 38740086)\|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 2306675\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 2371842\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 4743684\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 4613350\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 1434818\|7 \|11
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 1
+--R ----------------------------------------------------------------------------
+--R 7 6 5 4 3 2 +--------+
+--R (4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+r0:=4/231/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2)+17820/343*_
+ atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-738625/14641*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+1640/17787/_
+ ((2+3*x)*(3+5*x)^2*sqrt(1-2*x))-1759475/2739198*_
+ sqrt(1-2*x)/(3+5*x)^2+1495/41503*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_
+ 37771225/10043726*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 234812358000x + 320910222600x + 53224134480x - 79836201720x
+--R +
+--R - 28177482960
+--R *
+--R +-+ +--------+
+--R +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R \|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 4 3 2
+--R - 228013537500x - 311618501250x - 51683068500x + 77524602750x
+--R +
+--R 27361624500
+--R *
+--R +-+ +--------+
+--R +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R \|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2
+--R (- 6798820500x - 1580768100x + 4110847595x + 479695050x - 645558882)
+--R *
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R 4 3 2
+--R (4519676700x + 6176891490x + 1024460052x - 1536690078x - 542361204)
+--R *
+--R +-+ +--+ +--------+
+--R \|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 114006768750x + 155809250625x + 25841534250x - 38762301375x
+--R +
+--R - 13680812250
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 4 3 2
+--R 117406179000x + 160455111300x + 26612067240x - 39918100860x
+--R +
+--R - 14088741480
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 \|- 2x + 1 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 4 3 2
+--R (- 6798820500x - 1580768100x + 4110847595x + 479695050x - 645558882)
+--R *
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R 4 3 2
+--R (4519676700x + 6176891490x + 1024460052x - 1536690078x - 542361204)
+--R *
+--R +-+ +--+ +--------+
+--R \|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 253348375\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 260902620\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 521805240\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 506696750\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 10043726\|7 \|11
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x
+--R +
+--R 216
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2)+182655/343*_
+ atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-7570625/14641*_
+ atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+272/2541/((2+3*x)^2*(3+5*x)^2*_
+ sqrt(1-2*x))-17552275/2739198*sqrt(1-2*x)/(3+5*x)^2-_
+ 115/11858*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_
+ 69235/83006*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_
+ 193818700/5021863*sqrt(1-2*x)/(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3
+--R 7220480008500x + 14681642683950x + 8215301698560x
+--R +
+--R 2
+--R - 1363868446050x - 2503099736280x - 577638400680
+--R *
+--R +-+ +--------+
+--R +-+ +--+ +--------+ \|3 \|- 2x + 1
+--R \|3 \|11 \|- 2x + 1 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R 5 4 3
+--R - 7011155812500x - 14256016818750x - 7977137280000x
+--R +
+--R 2
+--R 1324329431250x + 2430534015000x + 560892465000
+--R *
+--R +-+ +--------+
+--R +-+ +-+ +--------+ \|5 \|- 2x + 1
+--R \|5 \|7 \|- 2x + 1 atanh(---------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 209324196000x - 188418548700x + 93885376440x + 99160158305x
+--R +
+--R - 9944654283x - 13236365823
+--R *
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R 5 4 3 2
+--R 13559030100x + 27570027870x + 15427163136x - 2561150130x
+--R +
+--R - 4700463768x - 1084722408
+--R *
+--R +-+ +--+ +--------+
+--R \|7 \|11 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 3505577906250x + 7128008409375x + 3988568640000x - 662164715625x
+--R +
+--R - 1215267007500x - 280446232500
+--R *
+--R +-+ +--------+ +--+
+--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R \|5 \|7 \|- 2x + 1 log(---------------------------------)
+--R 5x + 3
+--R +
+--R 5 4 3 2
+--R 3610240004250x + 7340821341975x + 4107650849280x - 681934223025x
+--R +
+--R - 1251549868140x - 288819200340
+--R *
+--R +-+ +--------+ +-+
+--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R \|3 \|11 \|- 2x + 1 log(---------------------------------)
+--R 3x + 2
+--R +
+--R 5 4 3 2
+--R - 209324196000x - 188418548700x + 93885376440x + 99160158305x
+--R +
+--R - 9944654283x - 13236365823
+--R *
+--R +-+ +--+
+--R \|7 \|11
+--R /
+--R 5 4 3 2
+--R 13559030100x + 27570027870x + 15427163136x - 2561150130x
+--R +
+--R - 4700463768x - 1084722408
+--R *
+--R +-+ +--+ +--------+
+--R \|7 \|11 \|- 2x + 1
+--R Type: Union(Expression(Integer),...)
+--E 433
+
+--S 434 of 500
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +--------+ +--+
+--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11
+--R 2596724375\|5 \|7 log(---------------------------------)
+--R 5x + 3
+--R +
+--R +-+ +--------+ +-+
+--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7
+--R 2674251855\|3 \|11 log(---------------------------------)
+--R 3x + 2
+--R +
+--R +-+ +--------+
+--R +-+ +--+ \|3 \|- 2x + 1
+--R - 5348503710\|3 \|11 atanh(---------------)
+--R +-+
+--R \|7
+--R +
+--R +-+ +--------+
+--R +-+ +-+ \|5 \|- 2x + 1
+--R 5193448750\|5 \|7 atanh(---------------)
+--R +--+
+--R \|11
+--R /
+--R +-+ +--+
+--R 10043726\|7 \|11
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (1) (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+r0:=4122385421/51200000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 32497997/38400000*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 186473/960000*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 3731/80000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 17/3000*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)+1/30*(2+3*x)^4*_
+ (3+5*x)^(3/2)*sqrt(1-2*x)-374762311/51200000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 4122385421asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 691200000x + 2218752000x + 2739830400x + 1468973920x + 45781940x
+--R +
+--R - 518122939
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 51200000\|10
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+--a0:=integrate(t0,x)
+--E 438
+
+--S 439 of 500
+--m0:=a0-r0
+--E 439
+
+--S 440 of 500
+--d0:=D(m0,x)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (1) (27x + 54x + 36x + 8)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+r0:=39142411/1280000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 104377/320000*(3+5*x)^(3/2)*sqrt(1-2*x)-21/2000*(2+3*x)^2*_
+ (3+5*x)^(3/2)*sqrt(1-2*x)+1/25*(2+3*x)^3*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-7/40000*(3+5*x)^(3/2)*(802+1245*x)*sqrt(1-2*x)-_
+ 3558401/1280000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 39142411asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (6912000x + 17366400x + 14946720x + 3002540x - 4282349)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 1280000\|10
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500
+--a0:=integrate(t0,x)
+--E 443
+
+--S 444 of 500
+--m0:=a0-r0
+--E 444
+
+--S 445 of 500
+--d0:=D(m0,x)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (1) (9x + 12x + 4)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+r0:=-37/160*(1-2*x)^(3/2)*(3+5*x)^(3/2)-3/40*(1-2*x)^(3/2)*(2+3*x)*_
+ (3+5*x)^(3/2)+158873/12800*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)-1313/1280*(1-2*x)^(3/2)*sqrt(3+5*x)+14443/12800*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 158873asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (28800x + 51680x + 22500x - 13327)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 12800\|10
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500
+--a0:=integrate(t0,x)
+--E 448
+
+--S 449 of 500
+--m0:=a0-r0
+--E 449
+
+--S 450 of 500
+--d0:=D(m0,x)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +--------+ +------+
+--R (1) (3x + 2)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+r0:=-1/10*(1-2*x)^(3/2)*(3+5*x)^(3/2)+4477/800*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)-37/80*(1-2*x)^(3/2)*sqrt(3+5*x)+407/800*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3 2 +--+ +--------+ +------+
+--R 4477asin(-------------) + (800x + 820x - 203)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R -----------------------------------------------------------------------
+--R +--+
+--R 800\|10
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500
+--a0:=integrate(t0,x)
+--E 453
+
+--S 454 of 500
+--m0:=a0-r0
+--E 454
+
+--S 455 of 500
+--d0:=D(m0,x)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +--------+ +------+
+--R (1) \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+r0:=121/40*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/4*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)+11/40*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R \|2 \|5x + 3 +--+ +--------+ +------+
+--R 121asin(-------------) + (20x + 1)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R (2) -----------------------------------------------------------
+--R +--+
+--R 40\|10
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+--a0:=integrate(t0,x)
+--E 458
+
+--S 459 of 500
+--m0:=a0-r0
+--E 459
+
+--S 460 of 500
+--d0:=D(m0,x)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) --------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+r0:=-2/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_
+ 37/9*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/3*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3
+--R - 2\|7 \|10 atan(-------------) + 37asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R +--+ +--------+ +------+
+--R 3\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 9\|10
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 463
+
+--S 464 of 500
+--m0:=a0-r0
+--E 464
+
+--S 465 of 500
+--d0:=D(m0,x)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) --------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+r0:=37/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 2/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/3*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R \|7 \|5x + 3 +-+ +--+ \|2 \|5x + 3
+--R (111x + 74)atan(-------------) + (- 6x - 4)\|7 \|10 asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R +-+ +--------+ +------+
+--R - 3\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+
+--R (27x + 18)\|7
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 468
+
+--S 469 of 500
+--m0:=a0-r0
+--E 469
+
+--S 470 of 500
+--d0:=D(m0,x)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) ---------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+r0:=121/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/2*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-11/28*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (1089x + 1452x + 484)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+
+--R (37x + 20)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (252x + 336x + 112)\|7
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 2178x - 2904x - 968)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +--------+ +------+ 2
+--R (1036x + 560)\|- 2x + 1 \|5x + 3 + 2205x + 2940x + 980
+--R /
+--R 2
+--R 7056x + 9408x + 3136
+--R Type: Union(Expression(Integer),...)
+--E 473
+
+--S 474 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 484atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +-+
+--R - 242atan(-----------------------------------------------------) + 35\|7
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R /
+--R +-+
+--R 112\|7
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+r0:=4477/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/9*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+37/252*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^2+3547/3528*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (120879x + 241758x + 161172x + 35816)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (3547x + 4902x + 1648)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (10584x + 21168x + 14112x + 3136)\|7
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 120879x - 241758x - 161172x - 35816)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (49658x + 68628x + 23072)\|- 2x + 1 \|5x + 3 - 155736x - 311472x
+--R +
+--R - 207648x - 46144
+--R /
+--R 3 2
+--R 148176x + 296352x + 197568x + 43904
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 8954atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 4477atan(--------------------------------------------------) - 824\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 784\|7
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+r0:=794365/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/12*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+37/504*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^3+6005/14112*sqrt(1-2*x)*sqrt(3+5*x)/_
+ (2+3*x)^2+625115/197568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (64343565x + 171582840x + 171582840x + 76259040x + 12709840)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (1875345x + 3834760x + 2617388x + 594416)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (64343565x + 171582840x + 171582840x + 76259040x + 12709840)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 3 2 +--------+ +------+
+--R (26254830x + 53686640x + 36643432x + 8321824)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 84258468x + 224689248x + 224689248x + 99861888x + 16643648
+--R /
+--R 4 3 2
+--R 24893568x + 66382848x + 66382848x + 29503488x + 4917248
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 1588730atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 794365atan(------------------------------------------------) + 148604\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 43904\|7
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^6
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+r0:=5591773/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+37/840*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^4+403/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 14023/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 1466281/131712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 6794004195x + 22646680650x + 30195574200x + 20130382800x
+--R +
+--R 6710127600x + 894683680
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (197947935x + 536695650x + 546004068x + 247045192x + 41933792)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x
+--R +
+--R 7024640
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 13588008390x + 45293361300x + 60391148400x + 40260765600x
+--R +
+--R 13420255200x + 1789367360
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R \|7 atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 4 3 2
+--R 5542542180x + 15027478200x + 15288113904x + 6917265376x
+--R +
+--R 1174146176
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 15603301917x - 52011006390x - 69348008520x - 46232005680x
+--R +
+--R - 15410668560x - 2054755808
+--R /
+--R 5 4 3 2
+--R 1493614080x + 4978713600x + 6638284800x + 4425523200x + 1475174400x
+--R +
+--R 196689920
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 111835460atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R 55917730atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R +-+
+--R - 9173017\|7
+--R /
+--R +-+
+--R 878080\|7
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^7
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+r0:=588912203/1229312*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/18*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^6+37/1260*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^5+10921/70560*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 126799/141120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 4429459/790272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 463266973/11063808*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R 2146584979935x + 8586339919740x + 14310566532900x
+--R +
+--R 3 2
+--R 12720503584800x + 6360251792400x + 1696067144640x + 188451904960
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 62541041355x + 211260697020x + 285550790544x + 193055073632x
+--R +
+--R 65287037520x + 8835086144
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3
+--R 4480842240x + 17923368960x + 29872281600x + 26553139200x
+--R +
+--R 2
+--R 13276569600x + 3540418560x + 393379840
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R - 8586339919740x - 34345359678960x - 57242266131600x
+--R +
+--R 3 2
+--R - 50882014339200x - 25441007169600x - 6784268578560x - 753807619840
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R \|7 atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 5 4 3
+--R 3502298315880x + 11830599033120x + 15990844270464x
+--R +
+--R 2
+--R 10811084123392x + 3656074101120x + 494764824064
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R 13384741363497x + 53538965453988x + 89231609089980x + 79316985857760x
+--R +
+--R 2
+--R 39658492928880x + 10575598114368x + 1175066457152
+--R /
+--R 6 5 4 3
+--R 250927165440x + 1003708661760x + 1672847769600x + 1486975795200x
+--R +
+--R 2
+--R 743487897600x + 198263439360x + 22029271040
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 23556488120atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R -
+--R 11778244060
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 2622916199\|7
+--R /
+--R +-+
+--R 49172480\|7
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(2+3*x)^4*(3+5*x)^(3/2)*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+
+--R (1) (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+r0:=70224051139/204800000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 580364059/153600000*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 10031801/19200000*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 8223/64000*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 643/20000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 17/4200*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)+_
+ 1/35*(2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 6384004649/204800000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 1474705073919asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 248832000000x + 950400000000x + 1480681728000x + 1161696585600x
+--R +
+--R 2
+--R 402838062880x - 72932734340x - 201521732121
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 4300800000\|10
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500
+--a0:=integrate(t0,x)
+--E 498
+
+--S 499 of 500
+--m0:=a0-r0
+--E 499
+
+--S 500 of 500
+--d0:=D(m0,x)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3m.input.pdf b/src/axiom-website/CATS/rich3m.input.pdf
new file mode 100644
index 0000000..a55bc17
Binary files /dev/null and b/src/axiom-website/CATS/rich3m.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3n.input.pamphlet b/src/axiom-website/CATS/rich3n.input.pamphlet
new file mode 100644
index 0000000..a405749
--- /dev/null
+++ b/src/axiom-website/CATS/rich3n.input.pamphlet
@@ -0,0 +1,6816 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3n.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 35 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 65 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 rich3n.output
+)spool rich3n.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (1) (135x + 351x + 342x + 148x + 24)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+r0:=1269748711/10240000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 10493791/7680000*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 183701/960000*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 7/1000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+_
+ 1/30*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 49/80000*(3+5*x)^(5/2)*(146+225*x)*sqrt(1-2*x)-_
+ 115431701/10240000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 3809246133asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 691200000x + 2163456000x + 2600899200x + 1349400160x + 21761620x
+--R +
+--R - 483864147
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 30720000\|10
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 500
+--m0:=a0-r0
+--E 4
+
+--S 5 of 500
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (1) (45x + 87x + 56x + 12)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+r0:=-9007/9600*(1-2*x)^(3/2)*(3+5*x)^(3/2)-153/800*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)-3/50*(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2)+_
+ 11988317/256000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 99077/25600*(1-2*x)^(3/2)*sqrt(3+5*x)+_
+ 1089847/256000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 35964951asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (6912000x + 16790400x + 13913120x + 2552540x - 4015809)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 768000\|10
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 500
+--m0:=a0-r0
+--E 9
+
+--S 10 of 500
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (1) (15x + 19x + 6)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+r0:=-181/480*(1-2*x)^(3/2)*(3+5*x)^(3/2)-3/40*(1-2*x)^(3/2)*(3+5*x)^(5/2)+_
+ 240911/12800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 1991/1280*(1-2*x)^(3/2)*sqrt(3+5*x)+21901/12800*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 722733asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (144000x + 245600x + 99380x - 63387)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 38400\|10
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 500
+--m0:=a0-r0
+--E 14
+
+--S 15 of 500
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)
+--R
+--R
+--R +--------+ +------+
+--R (1) (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^(3/2)+1331/160*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)-11/16*(1-2*x)^(3/2)*sqrt(3+5*x)+_
+ 121/160*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3 2 +--+ +--------+ +------+
+--R 3993asin(-------------) + (800x + 740x - 207)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R -----------------------------------------------------------------------
+--R +--+
+--R 480\|10
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 500
+--m0:=a0-r0
+--E 19
+
+--S 20 of 500
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+r0:=2/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_
+ 793/216*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1/6*(3+5*x)^(3/2)*sqrt(1-2*x)-41/72*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3
+--R 16\|7 \|10 atan(-------------) + 793asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R +--+ +--------+ +------+
+--R (180x - 15)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 216\|10
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 500
+--m0:=a0-r0
+--E 24
+
+--S 25 of 500
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+r0:=41/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-_
+ 107/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/3*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)+10/9*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R (- 321x - 214)\|2 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +-+ \|2 \|5x + 3
+--R (123x + 82)\|5 \|7 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +--------+ +------+
+--R (45x + 33)\|2 \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+ +-+
+--R (81x + 54)\|2 \|7
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 500
+--m0:=a0-r0
+--E 29
+
+--S 30 of 500
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+r0:=4091/756*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 10/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-_
+ 1/6*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-_
+ 107/252*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (36819x + 49092x + 16364)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 +-+ +--+ \|2 \|5x + 3
+--R (- 2520x - 3360x - 1120)\|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+ +------+
+--R (- 1593x - 1020)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (6804x + 9072x + 3024)\|7
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 500
+--m0:=a0-r0
+--E 34
+
+--S 35 of 500
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+r0:=1331/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 11/84*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+_
+ 1/3*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_
+ 121/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (107811x + 215622x + 143748x + 31944)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (4223x + 4478x + 1152)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (31752x + 63504x + 42336x + 9408)\|7
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (107811x + 215622x + 143748x + 31944)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (59122x + 62692x + 16128)\|- 2x + 1 \|5x + 3 - 129276x - 258552x
+--R +
+--R - 172368x - 38304
+--R /
+--R 3 2
+--R 444528x + 889056x + 592704x + 131712
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2662atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +-+
+--R 1331atan(------------------------------------------------------) - 228\|7
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R /
+--R +-+
+--R 784\|7
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+r0:=153065/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/12*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-_
+ 107/1512*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 4355/42336*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 368045/592704*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (37194795x + 99186120x + 99186120x + 44082720x + 7347120)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (1104135x + 2269240x + 1512052x + 328464)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (5334336x + 14224896x + 14224896x + 6322176x + 1053696)\|7
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 185973975x - 495930600x - 495930600x - 220413600x - 36735600)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 3 2 +--------+ +------+
+--R (77289450x + 158846800x + 105843640x + 22992480)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 325918404x + 869115744x + 869115744x + 386273664x + 64378944
+--R /
+--R 4 3 2
+--R 373403520x + 995742720x + 995742720x + 442552320x + 73758720
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 1530650atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+
+--R - 765325atan(-----------------------------------------------) + 191604\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R /
+--R +-+
+--R 219520\|7
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+r0:=783959/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/15*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-_
+ 107/2520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 641/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 17981/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 1852307/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 2857530555x + 9525101850x + 12700135800x + 8466757200x
+--R +
+--R 2822252400x + 376300320
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (83353815x + 226052850x + 230080132x + 103856008x + 17507808)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 160030080x + 533433600x + 711244800x + 474163200x + 158054400x
+--R +
+--R 21073920
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 14287652775x - 47625509250x - 63500679000x - 42333786000x
+--R +
+--R - 14111262000x - 1881501600
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 4 3 2
+--R 5834767050x + 15823699500x + 16105609240x + 7269920560x
+--R +
+--R 1225546560
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 26058183732x + 86860612440x + 115814149920x + 77209433280x
+--R +
+--R 25736477760x + 3431530368
+--R /
+--R 5 4 3 2
+--R 11202105600x + 37340352000x + 49787136000x + 33191424000x
+--R +
+--R 11063808000x + 1475174400
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 39197950atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R - 19598975atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R 5106444\|7
+--R /
+--R +-+
+--R 2195200\|7
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^7
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+r0:=64645339/1229312*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/18*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-_
+ 107/3780*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+_
+ 4619/211680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 42461/423360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 1460201/2370816*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 152571047/33191424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 706896781965x + 2827587127860x + 4712645213100x + 4189017967200x
+--R +
+--R 2
+--R 2094508983600x + 558535728960x + 62059525440
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 20597091345x + 69576897780x + 94045700016x + 63585046048x
+--R +
+--R 21497808880x + 2906375616
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3
+--R 13442526720x + 53770106880x + 89616844800x + 79659417600x
+--R +
+--R 2
+--R 39829708800x + 10621255680x + 1180139520
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R - 706896781965x - 2827587127860x - 4712645213100x
+--R +
+--R 3 2
+--R - 4189017967200x - 2094508983600x - 558535728960x - 62059525440
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 5 4 3 2
+--R 288359278830x + 974076568920x + 1316639800224x + 890190644672x
+--R +
+--R 300969324320x + 40689258624
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R 926952173028x + 3707808692112x + 6179681153520x + 5493049914240x
+--R +
+--R 2
+--R 2746524957120x + 732406655232x + 81378517248
+--R /
+--R 6 5 4 3
+--R 188195374080x + 752781496320x + 1254635827200x + 1115231846400x
+--R +
+--R 2
+--R 557615923200x + 148697579520x + 16521953280
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 646453390atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 323226695atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R 60549492\|7
+--R /
+--R +-+
+--R 12293120\|7
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x)
+--R
+--R
+--R (1)
+--R 6 5 4 3 2 +--------+
+--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+r0:=1988505613369/1310720000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 16433930689/983040000*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 1493993699/614400000*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 18411711/51200000*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+ 58671/640000*(2+3*x)*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+ 753/32000*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+ 17/5600*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)+_
+ 1/40*(2+3*x)^4*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+ 180773237579/1310720000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 41758617880749asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 7 6 5
+--R 6967296000000x + 30838579200000x + 57746856960000x
+--R +
+--R 4 3 2
+--R 58346097408000x + 32457421737600x + 6882844528480x
+--R +
+--R - 3991703112140x - 5973304472091
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 27525120000\|10
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 500
+--m0:=a0-r0
+--E 59
+
+--S 60 of 500
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+
+--R (1) (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+r0:=4343003753/8192000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 35892593/6144000*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 3262963/3840000*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 8131/64000*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+ 1/200*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)+_
+ 1/35*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+ 3/20000*(3+5*x)^(7/2)*(414+635*x)*sqrt(1-2*x)-_
+ 394818523/8192000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 91203078813asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 16588800000x + 62069760000x + 94673664000x + 72591427200x
+--R +
+--R 2
+--R 24336990560x - 4902803980x - 12531569067
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 172032000\|10
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 500
+--m0:=a0-r0
+--E 64
+
+--S 65 of 500
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (1) (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+r0:=-11759/3072*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1069/1280*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)-13/80*(1-2*x)^(3/2)*(3+5*x)^(7/2)-1/20*(1-2*x)^(3/2)*_
+ (2+3*x)*(3+5*x)^(7/2)+15651229/81920*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)-129349/8192*(1-2*x)^(3/2)*sqrt(3+5*x)+1422839/81920*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 46953687asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R (9216000x + 28108800x + 32887680x + 16507936x + 17884x - 6023169)
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 245760\|10
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 500
+--m0:=a0-r0
+--E 69
+
+--S 70 of 500
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (1) (75x + 140x + 87x + 18)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+r0:=-2761/1920*(1-2*x)^(3/2)*(3+5*x)^(3/2)-251/800*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)-3/50*(1-2*x)^(3/2)*(3+5*x)^(7/2)+_
+ 3674891/51200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 30371/5120*(1-2*x)^(3/2)*sqrt(3+5*x)+334081/51200*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 11024673asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (2304000x + 5404800x + 4310240x + 718340x - 1254087)\|10 \|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R /
+--R +--+
+--R 153600\|10
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 500
+--m0:=a0-r0
+--E 74
+
+--S 75 of 500
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (1) (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+r0:=-55/96*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1/8*(1-2*x)^(3/2)*(3+5*x)^(5/2)+_
+ 14641/512*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 605/256*(1-2*x)^(3/2)*sqrt(3+5*x)+1331/512*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 43923asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (9600x + 15520x + 5836x - 4005)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 1536\|10
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 500
+--m0:=a0-r0
+--E 79
+
+--S 80 of 500
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+r0:=6553/2592*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2/81*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-5/24*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)+1/9*(3+5*x)^(5/2)*sqrt(1-2*x)-925/864*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3
+--R - 64\|2 \|7 atan(-------------) + 6553\|5 asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R 2 +-+ +--------+ +------+
+--R (7200x + 5940x - 1803)\|2 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+
+--R 2592\|2
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 500
+--m0:=a0-r0
+--E 84
+
+--S 85 of 500
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+r0:=155/216*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+59/27*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+5/6*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-1/3*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)-_
+ 95/72*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R (1416x + 944)\|2 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +-+ \|2 \|5x + 3
+--R (465x + 310)\|5 \|7 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +-+ +--------+ +------+
+--R (900x + 405x - 138)\|2 \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+ +-+
+--R (648x + 432)\|2 \|7
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 500
+--m0:=a0-r0
+--E 89
+
+--S 90 of 500
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+r0:=25/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2119/252*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-59/84*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)-1/6*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2+_
+ 215/84*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +-+ \|7 \|5x + 3
+--R (- 19071x - 25428x - 8476)\|2 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 +-+ +-+ \|2 \|5x + 3
+--R (6300x + 8400x + 2800)\|5 \|7 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +-+ +--------+ +------+
+--R (2100x + 3117x + 1140)\|2 \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+ +-+
+--R (2268x + 3024x + 1008)\|2 \|7
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 500
+--m0:=a0-r0
+--E 94
+
+--S 95 of 500
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^4
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+r0:=250433/31752*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 50/81*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-59/252*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^2-1/9*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_
+ 6401/10584*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (6761691x + 13523382x + 9015588x + 2003464)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 3 2 +-+ +--+ \|2 \|5x + 3
+--R (- 529200x - 1058400x - 705600x - 156800)\|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+ +------+
+--R (- 372537x - 477522x - 153168)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (857304x + 1714608x + 1143072x + 254016)\|7
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 500
+--m0:=a0-r0
+--E 99
+
+--S 100 of 500
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^5
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+r0:=73205/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 605/4704*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-11/168*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^3+1/4*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-_
+ 6655/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (17788815x + 47436840x + 47436840x + 21083040x + 3513840)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (814395x + 1285720x + 654436x + 105552)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (5334336x + 14224896x + 14224896x + 6322176x + 1053696)\|7
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (17788815x + 47436840x + 47436840x + 21083040x + 3513840)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 3 2 +--------+ +------+
+--R (11401530x + 18000080x + 9162104x + 1477728)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R - 14961996x - 39898656x - 39898656x - 17732736x - 2955456
+--R /
+--R 4 3 2
+--R 74680704x + 199148544x + 199148544x + 88510464x + 14751744
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 146410atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 73205atan(------------------------------------------------) - 8796\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 43904\|7
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^6
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+r0:=248897/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 59/840*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-1/15*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^5-103/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 947/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+67709/131712*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 907229565x + 3024098550x + 4032131400x + 2688087600x + 896029200x
+--R +
+--R 119470560
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (27422145x + 74915550x + 74550556x + 32206264x + 5112864)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 160030080x + 533433600x + 711244800x + 474163200x + 158054400x
+--R +
+--R 21073920
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 1814459130x + 6048197100x + 8064262800x + 5376175200x
+--R +
+--R 1792058400x + 238941120
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R \|7 atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 4 3 2
+--R (767820060x + 2097635400x + 2087415568x + 901775392x + 143160192)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 1902464739x - 6341549130x - 8455398840x - 5636932560x - 1878977520x
+--R +
+--R - 250530336
+--R /
+--R 5 4 3 2
+--R 4480842240x + 14936140800x + 19914854400x + 13276569600x
+--R +
+--R 4425523200x + 590069760
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 4977940atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R 2488970atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R +-+
+--R - 372813\|7
+--R /
+--R +-+
+--R 878080\|7
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^7
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+r0:=15036307/1229312*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 59/1260*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-1/18*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^6-6533/211680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 47279/1270080*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 1057139/7112448*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 106751933/99574272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 164422017045x + 657688068180x + 1096146780300x + 974352693600x
+--R +
+--R 2
+--R 487176346800x + 129913692480x + 14434854720
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 4803836985x + 16234789140x + 21960917808x + 14818971424x
+--R +
+--R 4978384240x + 665270208
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3
+--R 13442526720x + 53770106880x + 89616844800x + 79659417600x
+--R +
+--R 2
+--R 39829708800x + 10621255680x + 1180139520
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R - 822110085225x - 3288440340900x - 5480733901500x
+--R +
+--R 3 2
+--R - 4871763468000x - 2435881734000x - 649568462400x - 72174273600
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 5 4 3 2
+--R 336268588950x + 1136435239800x + 1537264246560x + 1037327999680x
+--R +
+--R 348486896800x + 46568914560
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R 1485257318748x + 5941029274992x + 9901715458320x + 8801524851840x
+--R +
+--R 2
+--R 4400762425920x + 1173536646912x + 130392960768
+--R /
+--R 6 5 4 3
+--R 940976870400x + 3763907481600x + 6273179136000x + 5576159232000x
+--R +
+--R 2
+--R 2788079616000x + 743487897600x + 82609766400
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 751815350atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R - 375907675atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R 97018572\|7
+--R /
+--R +-+
+--R 61465600\|7
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+r0:=3735929329/120472576*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 59/1764*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-1/21*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^7-6577/370440*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+_
+ 369409/20744640*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 2524471/41489280*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 84539611/232339968*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 8818415317/3252759552*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R 122557161637845x + 571933420976610x + 1143866841953220x
+--R +
+--R 4 3 2
+--R 1270963157725800x + 847308771817200x + 338923508726880x
+--R +
+--R 75316335272640x + 7172984311680
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 6 5 4
+--R 3571458203385x + 14445612678330x + 24351227238888x
+--R +
+--R 3 2
+--R 21898948566336x + 11077661454896x + 2987299350368x + 335335888512
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 7 6 5
+--R 3952102855680x + 18443146659840x + 36886293319680x
+--R +
+--R 4 3 2
+--R 40984770355200x + 27323180236800x + 10929272094720x + 2428727132160x
+--R +
+--R 231307345920
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R - 122557161637845x - 571933420976610x - 1143866841953220x
+--R +
+--R 4 3 2
+--R - 1270963157725800x - 847308771817200x - 338923508726880x
+--R +
+--R - 75316335272640x - 7172984311680
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 6 5 4
+--R 50000414847390x + 202238577496620x + 340917181344432x
+--R +
+--R 3 2
+--R 306585279928704x + 155087260368544x + 41822190905152x + 4694702439168
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 7 6 5
+--R - 160426784913444x - 748658329596072x - 1497316659192144x
+--R +
+--R 4 3 2
+--R - 1663685176880160x - 1109123451253440x - 443649380501376x
+--R +
+--R - 98588751222528x - 9389404878336
+--R /
+--R 7 6 5
+--R 55329439979520x + 258204053237760x + 516408106475520x
+--R +
+--R 4 3 2
+--R 573786784972800x + 382524523315200x + 153009809326080x
+--R +
+--R 34002179850240x + 3238302842880
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 37359293290atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 18679646645atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 3493082172\|7
+--R /
+--R +-+
+--R 1204725760\|7
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R (1) ----------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+r0:=525371/64000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 46613/64000*sqrt(1-2*x)*sqrt(3+5*x)-7/400*(2+3*x)^2*sqrt(1-2*x)*_
+ sqrt(3+5*x)+1/20*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 21/16000*(194+305*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 525371asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (86400x + 162720x + 76140x - 41789)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 64000\|10
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 500
+--m0:=a0-r0
+--E 124
+
+--S 125 of 500
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R (1) --------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+r0:=3047/800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-23/80*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)-1/10*(1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x)+277/800*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3 2 +--+ +--------+ +------+
+--R 3047asin(-------------) + (480x + 540x - 113)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R -----------------------------------------------------------------------
+--R +--+
+--R 800\|10
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 500
+--m0:=a0-r0
+--E 129
+
+--S 130 of 500
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R (1) -------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+r0:=451/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/20*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)+41/200*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R \|2 \|5x + 3 +--+ +--------+ +------+
+--R 451asin(-------------) + (60x + 11)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R (2) ------------------------------------------------------------
+--R +--+
+--R 200\|10
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500
+--a0:=integrate(t0,x)
+--E 133
+
+--S 134 of 500
+--m0:=a0-r0
+--E 134
+
+--S 135 of 500
+--d0:=D(m0,x)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+r0:=11/5*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/5*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R \|2 \|5x + 3 +--+ +--------+ +------+
+--R 11asin(-------------) + \|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R (2) -------------------------------------------------
+--R +--+
+--R 5\|10
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 500
+--m0:=a0-r0
+--E 139
+
+--S 140 of 500
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------------
+--R +------+
+--R (3x + 2)\|5x + 3
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+r0:=-2/3*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+2/3*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)
+--R
+--R
+--R +-+ +------+ +-+ +------+
+--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3
+--R 2\|5 \|7 atan(-------------) - 2\|2 asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R (2) -------------------------------------------------------
+--R +-+
+--R 3\|5
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 500
+--m0:=a0-r0
+--E 144
+
+--S 145 of 500
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|5x + 3
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+r0:=11*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R +-+ +------+
+--R \|7 \|5x + 3 +-+ +--------+ +------+
+--R (33x + 22)atan(-------------) + \|7 \|- 2x + 1 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R (2) --------------------------------------------------------
+--R +-+
+--R (3x + 2)\|7
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R (- 33x - 22)\|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+
+--R 14\|- 2x + 1 \|5x + 3 + 42x + 28
+--R /
+--R 42x + 28
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 22atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 11atan(--------------------------------------------------) + 2\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 2\|7
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) --------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|5x + 3
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+r0:=1177/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1/2*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^2+103/28*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (10593x + 14124x + 4708)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+
+--R (309x + 220)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (252x + 336x + 112)\|7
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 10593x - 14124x - 4708)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+ 2
+--R (4326x + 3080)\|- 2x + 1 \|5x + 3 + 13860x + 18480x + 6160
+--R /
+--R 2
+--R 3528x + 4704x + 1568
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2354atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 1177atan(--------------------------------------------------) + 220\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 56\|7
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^4*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|5x + 3
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+r0:=68959/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+173/84*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^2+18083/1176*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (1861893x + 3723786x + 2482524x + 551672)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (54249x + 74754x + 25856)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (10584x + 21168x + 14112x + 3136)\|7
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 9309465x - 18618930x - 12412620x - 2758360)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 2 +--------+ +------+ 3
+--R (3797430x + 5232780x + 1809920)\|- 2x + 1 \|5x + 3 + 17103744x
+--R +
+--R 2
+--R 34207488x + 22804992x + 5067776
+--R /
+--R 3 2
+--R 740880x + 1481760x + 987840x + 219520
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 689590atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+
+--R - 344795atan(-----------------------------------------------) + 90496\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R /
+--R +-+
+--R 3920\|7
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^5*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|5x + 3
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+r0:=16925425/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/4*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+81/56*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^3+14145/1568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 1479375/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (1370959425x + 3655891800x + 3655891800x + 1624840800x + 270806800)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (39943125x + 81668520x + 55729116x + 12696112)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R - 6854797125x - 18279459000x - 18279459000x - 8124204000x
+--R +
+--R - 1354034000
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 3 2 +--------+
+--R (2796018750x + 5716796400x + 3901038120x + 888727840)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 4 3 2
+--R 12597717132x + 33593912352x + 33593912352x + 14930627712x + 2488437952
+--R /
+--R 4 3 2
+--R 124467840x + 331914240x + 331914240x + 147517440x + 24586240
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 169254250atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R - 84627125atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R 22218196\|7
+--R /
+--R +-+
+--R 219520\|7
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R (1) ----------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+r0:=10409/4000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(2+3*x)^3*_
+ sqrt(1-2*x)/sqrt(3+5*x)-791/4000*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 7/200*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+7/25*(2+3*x)^2*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R 10409\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (7200x + 13140x + 3825x - 893)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R 4000\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 500
+--m0:=a0-r0
+--E 169
+
+--S 170 of 500
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)
+--R
+--R
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R (1) --------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+r0:=317/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*(1-2*x)^(3/2)/_
+ sqrt(3+5*x)-9/100*(1-2*x)^(3/2)*sqrt(3+5*x)+317/2200*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3 2 +--+ +--------+
+--R 317\|5x + 3 asin(-------------) + (180x + 165x + 31)\|10 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ---------------------------------------------------------------------
+--R +--+ +------+
+--R 200\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+--a0:=integrate(t0,x)
+--E 173
+
+--S 174 of 500
+--m0:=a0-r0
+--E 174
+
+--S 175 of 500
+--d0:=D(m0,x)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^(3/2)
+--R
+--R
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R (1) -------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+r0:=29/25*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(1-2*x)^(3/2)/_
+ sqrt(3+5*x)+29/275*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3 +--+ +--------+
+--R 29\|5x + 3 asin(-------------) + (15x + 7)\|10 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------------
+--R +--+ +------+
+--R 25\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500
+--a0:=integrate(t0,x)
+--E 178
+
+--S 179 of 500
+--m0:=a0-r0
+--E 179
+
+--S 180 of 500
+--d0:=D(m0,x)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=sqrt(1-2*x)/(3+5*x)^(3/2)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+r0:=-2/5*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/5*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+
+--R - 2\|2 \|5x + 3 asin(-------------) - 2\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ------------------------------------------------------
+--R +-+ +------+
+--R 5\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+--a0:=integrate(t0,x)
+--E 183
+
+--S 184 of 500
+--m0:=a0-r0
+--E 184
+
+--S 185 of 500
+--d0:=D(m0,x)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -------------------------
+--R 2 +------+
+--R (15x + 19x + 6)\|5x + 3
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+r0:=-2*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-2*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +-+ +------+ \|7 \|5x + 3 +--------+
+--R - 2\|7 \|5x + 3 atan(-------------) - 2\|- 2x + 1
+--R +--------+
+--R \|- 2x + 1
+--R (2) --------------------------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+
+--R (- 60x - 36)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R +--------+ +------+
+--R - 24\|- 2x + 1 \|5x + 3 + 95x + 57
+--R /
+--R 60x + 36
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R 24\|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R - 12\|7 atan(------------------------------------------------------) + 19
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R /
+--R 12
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ---------------------------------
+--R 3 2 +------+
+--R (45x + 87x + 56x + 12)\|5x + 3
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+r0:=-103*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-15*sqrt(1-2*x)/_
+ sqrt(3+5*x)+sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3 +-+ +--------+
+--R (- 309x - 206)\|5x + 3 atan(-------------) + (- 45x - 29)\|7 \|- 2x + 1
+--R +--------+
+--R \|- 2x + 1
+--R ------------------------------------------------------------------------
+--R +-+ +------+
+--R (3x + 2)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 37080x - 46968x - 14832)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R +--------+ +------+ 2
+--R (- 15120x - 9744)\|- 2x + 1 \|5x + 3 + 57855x + 73283x + 23142
+--R /
+--R 2
+--R 5040x + 6384x + 2016
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 4944atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R - 2472atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R +-+
+--R 551\|7
+--R /
+--R +-+
+--R 48\|7
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) --------------------------------------------
+--R 4 3 2 +------+
+--R (135x + 351x + 342x + 148x + 24)\|5x + 3
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+r0:=-17951/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 2615/28*sqrt(1-2*x)/sqrt(3+5*x)+1/2*sqrt(1-2*x)/((2+3*x)^2*_
+ sqrt(3+5*x))+173/28*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +------+ \|7 \|5x + 3
+--R (- 161559x - 215412x - 71804)\|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+
+--R (- 23535x - 30861x - 10100)\|7 \|- 2x + 1
+--R /
+--R 2 +-+ +------+
+--R (252x + 336x + 112)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (9693540x + 18740844x + 12063072x + 2584944)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 2 +--------+ +------+ 3
+--R (- 3953880x - 5184648x - 1696800)\|- 2x + 1 \|5x + 3 - 15112125x
+--R +
+--R 2
+--R - 29216775x - 18806200x - 4029900
+--R /
+--R 3 2
+--R 211680x + 409248x + 263424x + 56448
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 430824atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R 215412atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R - 47975\|7
+--R /
+--R +-+
+--R 672\|7
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +------+
+--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+r0:=-1463447/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 639565/1176*sqrt(1-2*x)/sqrt(3+5*x)+1/3*sqrt(1-2*x)/((2+3*x)^3*_
+ sqrt(3+5*x))+81/28*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_
+ 14101/392*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +------+
+--R (- 39513069x - 79026138x - 52684092x - 11707576)\|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+
+--R (- 5756085x - 11385261x - 7502166x - 1646704)\|7 \|- 2x + 1
+--R /
+--R 3 2 +-+ +------+
+--R (10584x + 21168x + 14112x + 3136)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (592696035x + 1541009691x + 1501496622x + 649770468x + 105368184)
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 3 2 +--------+ +------+
+--R (- 241755570x - 478180962x - 315090972x - 69161568)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 778067640x + 2022975864x + 1971104688x + 852992672x + 138323136
+--R /
+--R 4 3 2
+--R 2222640x + 5778864x + 5630688x + 2436672x + 395136
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 8780682atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R 4390341atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R 823352\|7
+--R /
+--R +-+
+--R 2352\|7
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+r0:=35511/20000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/15*(2+3*x)^4*_
+ sqrt(1-2*x)/(3+5*x)^(3/2)-524/825*(2+3*x)^3*sqrt(1-2*x)/_
+ sqrt(3+5*x)-23779/220000*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 1043/11000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 623/1375*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (5859315x + 3515589)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (3564000x + 8999100x + 6384015x + 995870x - 218953)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (3300000x + 1980000)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 500
+--m0:=a0-r0
+--E 209
+
+--S 210 of 500
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(5/2)
+--R
+--R
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R (1) ----------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+r0:=1071/1000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/15*(2+3*x)^3*_
+ sqrt(1-2*x)/(3+5*x)^(3/2)-392/825*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 11557/11000*sqrt(1-2*x)*sqrt(3+5*x)-21/2750*(34-145*x)*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (176715x + 106029)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (89100x + 147015x + 75470x + 11567)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (165000x + 99000)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 500
+--m0:=a0-r0
+--E 214
+
+--S 215 of 500
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(5/2)
+--R
+--R
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R (1) --------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+r0:=-2/825*(1-2*x)^(3/2)/(3+5*x)^(3/2)+3/5*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)-12/275*(1-2*x)^(3/2)/sqrt(3+5*x)+3/55*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (495x + 297)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (297x + 278x + 59)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (825x + 495)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500
+--a0:=integrate(t0,x)
+--E 218
+
+--S 219 of 500
+--m0:=a0-r0
+--E 219
+
+--S 220 of 500
+--d0:=D(m0,x)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^(5/2)
+--R
+--R
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R (1) -------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+r0:=-2/165*(1-2*x)^(3/2)/(3+5*x)^(3/2)-6/25*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(2/5)-6/25*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3
+--R (- 990x - 594)\|2 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+
+--R (- 970x - 604)\|5 \|- 2x + 1
+--R /
+--R +-+ +------+
+--R (4125x + 2475)\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500
+--a0:=integrate(t0,x)
+--E 223
+
+--S 224 of 500
+--m0:=a0-r0
+--E 224
+
+--S 225 of 500
+--d0:=D(m0,x)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=sqrt(1-2*x)/(3+5*x)^(5/2)
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+r0:=-2/33*(1-2*x)^(3/2)/(3+5*x)^(3/2)
+--R
+--R
+--R +--------+
+--R (4x - 2)\|- 2x + 1
+--R (2) --------------------
+--R +------+
+--R (165x + 99)\|5x + 3
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+ 2
+--R (36x - 18)\|- 2x + 1 \|5x + 3 - 100x - 120x - 36
+--R (3) --------------------------------------------------
+--R 2
+--R 7425x + 8910x + 2673
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 4
+--R (4) - ---
+--R 297
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ----------------------------------
+--R 3 2 +------+
+--R (75x + 140x + 87x + 18)\|5x + 3
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+r0:=6*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_
+ 2/3*sqrt(1-2*x)/(3+5*x)^(3/2)+202/33*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +------+ \|7 \|5x + 3 +--------+
+--R (990x + 594)\|7 \|5x + 3 atan(-------------) + (1010x + 584)\|- 2x + 1
+--R +--------+
+--R \|- 2x + 1
+--R -----------------------------------------------------------------------
+--R +------+
+--R (165x + 99)\|5x + 3
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (22275x + 26730x + 8019)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +--------+ +------+ 2
+--R (9090x + 5256)\|- 2x + 1 \|5x + 3 + 29200x + 35040x + 10512
+--R /
+--R 2
+--R 7425x + 8910x + 2673
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R - 1782\|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 891\|7 atan(------------------------------------------------) + 1168
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R 297
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) --------------------------------------------
+--R 4 3 2 +------+
+--R (225x + 570x + 541x + 228x + 36)\|5x + 3
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+r0:=519*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 25/3*sqrt(1-2*x)/(3+5*x)^(3/2)+sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 2495/33*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +------+ \|7 \|5x + 3
+--R (256905x + 325413x + 102762)\|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+
+--R (37425x + 46580x + 14453)\|7 \|- 2x + 1
+--R /
+--R 2 +-+ +------+
+--R (495x + 627x + 198)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 11560725x - 21580020x - 13410441x - 2774574)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 2 +--------+ +------+ 3
+--R (4715550x + 5869080x + 1821078)\|- 2x + 1 \|5x + 3 + 15175650x
+--R +
+--R 2
+--R 28327880x + 17603754x + 3642156
+--R /
+--R 3 2
+--R 311850x + 582120x + 361746x + 74844
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 308286atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 154143atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R 28906\|7
+--R /
+--R +-+
+--R 594\|7
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+r0:=126513/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 6095/84*sqrt(1-2*x)/(3+5*x)^(3/2)+1/2*sqrt(1-2*x)/((2+3*x)^2*_
+ (3+5*x)^(3/2))+243/28*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 608185/924*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +------+
+--R (187871805x + 363218823x + 233796024x + 50099148)\|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+
+--R (27368325x + 52308690x + 33277877x + 7046540)\|7 \|- 2x + 1
+--R /
+--R 3 2 +-+ +------+
+--R (41580x + 80388x + 51744x + 11088)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 8454231225x + 21417385770x + 20327729301x + 8566954308x
+--R +
+--R 1352676996
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 3 2 +--------+
+--R (3448408950x + 6590894940x + 4193012502x + 887864040)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 4 3 2
+--R - 11098300500x - 28115694600x - 26685246980x - 11246277840x - 1775728080
+--R /
+--R 4 3 2
+--R 26195400x + 66361680x + 62985384x + 26544672x + 4191264
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 75148722atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 37574361atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R - 7046540\|7
+--R /
+--R +-+
+--R 16632\|7
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+r0:=13246251/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 638165/1176*sqrt(1-2*x)/(3+5*x)^(3/2)+1/3*sqrt(1-2*x)/((2+3*x)^3*_
+ (3+5*x)^(3/2))+313/84*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_
+ 25441/392*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 63678595/12936*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 59012048205x + 153431325333x + 149497188786x + 64694689884x
+--R +
+--R 10491030792
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2
+--R 8596610325x + 22161651840x + 21406565457x + 9181937962x
+--R +
+--R 1475586688
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +------+
+--R (1746360x + 4540536x + 4424112x + 1914528x + 310464)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R - 2655542169225x - 8497734941520x - 10870019279361x
+--R +
+--R 2
+--R - 6947685142002x - 2218853012508x - 283257831384
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 4 3 2
+--R 1083172900950x + 2792368131840x + 2697227247582x + 1156924183212x
+--R +
+--R 185923922688
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 3486073550400x + 11155435361280x + 14269661066304x + 9120601318528x
+--R +
+--R 2912808122112x + 371847845376
+--R /
+--R 5 4 3 2
+--R 1100206800x + 3520661760x + 4503513168x + 2878466976x + 919283904x
+--R +
+--R 117355392
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 7868273094atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 3934136547atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R 737793344\|7
+--R /
+--R +-+
+--R 232848\|7
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (1) (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+r0:=1/30*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)+_
+ 452517373/25600000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 3501533/19200000*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 791/120000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 29/1500*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 7/2400000*(3+5*x)^(3/2)*(28458+41105*x)*sqrt(1-2*x)-_
+ 41137943/25600000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 1357552119asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 691200000x - 1251072000x - 308534400x + 623566880x + 374573660x
+--R +
+--R - 81405921
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 76800000\|10
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 500
+--m0:=a0-r0
+--E 254
+
+--S 255 of 500
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (1) (- 18x - 15x + 4x + 4)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+r0:=-567/4000*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/50*(1-2*x)^(5/2)*_
+ (2+3*x)*(3+5*x)^(3/2)+5487713/640000*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)+45353/192000*(1-2*x)^(3/2)*sqrt(3+5*x)-_
+ 4123/9600*(1-2*x)^(5/2)*sqrt(3+5*x)+498883/640000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 16463139asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 6912000x - 7286400x + 3141280x + 4872460x - 382101)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 1920000\|10
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 500
+--m0:=a0-r0
+--E 259
+
+--S 260 of 500
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (1) (- 6x - x + 2)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+r0:=-3/40*(1-2*x)^(5/2)*(3+5*x)^(3/2)+30613/6400*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)+253/1920*(1-2*x)^(3/2)*sqrt(3+5*x)-_
+ 23/96*(1-2*x)^(5/2)*sqrt(3+5*x)+2783/6400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 91839asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (- 28800x - 6880x + 23420x + 1959)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 19200\|10
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 500
+--m0:=a0-r0
+--E 264
+
+--S 265 of 500
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)
+--R
+--R
+--R +--------+ +------+
+--R (1) (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+r0:=1331/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+11/120*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)-1/6*(1-2*x)^(5/2)*sqrt(3+5*x)+121/400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3 2 +--+ +--------+ +------+
+--R 3993asin(-------------) + (- 800x + 580x + 273)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R -------------------------------------------------------------------------
+--R +--+
+--R 1200\|10
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 500
+--m0:=a0-r0
+--E 269
+
+--S 270 of 500
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+r0:=-14/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_
+ 4091/540*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1/6*(1-2*x)^(3/2)*sqrt(3+5*x)+107/180*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3
+--R - 280\|7 \|10 atan(-------------) + 4091asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R +--+ +--------+ +------+
+--R (- 180x + 411)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 540\|10
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 273
+
+--S 274 of 500
+--m0:=a0-r0
+--E 274
+
+--S 275 of 500
+--d0:=D(m0,x)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+r0:=-107/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+41/27*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-1/3*(1-2*x)^(3/2)*sqrt(3+5*x)/_
+ (2+3*x)-4/9*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +-+ \|7 \|5x + 3
+--R (123x + 82)\|5 \|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ \|2 \|5x + 3
+--R (- 321x - 214)\|2 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+ +------+
+--R (- 18x - 33)\|5 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+
+--R (81x + 54)\|5
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 278
+
+--S 279 of 500
+--m0:=a0-r0
+--E 279
+
+--S 280 of 500
+--d0:=D(m0,x)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^3
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+r0:=793/108*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/6*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)/(2+3*x)^2+41/36*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (7137x + 9516x + 3172)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 +-+ +--+ \|2 \|5x + 3
+--R (144x + 192x + 64)\|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+ +------+
+--R (405x + 228)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (972x + 1296x + 432)\|7
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 283
+
+--S 284 of 500
+--m0:=a0-r0
+--E 284
+
+--S 285 of 500
+--d0:=D(m0,x)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) -------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+r0:=1/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3+_
+ 1331/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 11/4*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-121/56*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (107811x + 215622x + 143748x + 31944)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (3103x + 4366x + 1488)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (4536x + 9072x + 6048x + 1344)\|7
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (107811x + 215622x + 143748x + 31944)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (43442x + 61124x + 20832)\|- 2x + 1 \|5x + 3 + 140616x + 281232x
+--R +
+--R 187488x + 41664
+--R /
+--R 3 2
+--R 63504x + 127008x + 84672x + 18816
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2662atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 1331atan(------------------------------------------------) + 248\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 112\|7
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+r0:=240911/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4+41/216*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^3+5413/6048*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 568363/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (58541373x + 156110328x + 156110328x + 69382368x + 11563728)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (1705089x + 3485960x + 2381420x + 541680)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (762048x + 2032128x + 2032128x + 903168x + 150528)\|7
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 58541373x - 156110328x - 156110328x - 69382368x - 11563728)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 3 2 +--------+ +------+
+--R (23871246x + 48803440x + 33339880x + 7583520)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 76783140x + 204755040x + 204755040x + 91002240x + 15167040
+--R /
+--R 4 3 2
+--R 10668672x + 28449792x + 28449792x + 12644352x + 2107392
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 481822atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 240911atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R 45140\|7
+--R /
+--R +-+
+--R 6272\|7
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^6
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+r0:=11988317/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+41/360*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^4+7723/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 270463/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 28291441/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 43697415465x + 145658051550x + 194210735400x + 129473823600x
+--R +
+--R 43157941200x + 5754392160
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2
+--R (1273114845x + 3451770150x + 3511594796x + 1588955864x + 269759904)
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 160030080x + 533433600x + 711244800x + 474163200x + 158054400x
+--R +
+--R 21073920
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 43697415465x - 145658051550x - 194210735400x - 129473823600x
+--R +
+--R - 43157941200x - 5754392160
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 4 3 2
+--R 17823607830x + 48324782100x + 49162327144x + 22245382096x
+--R +
+--R 3776638656
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 57357699588x - 191192331960x - 254923109280x - 169948739520x
+--R +
+--R - 56649579840x - 7553277312
+--R /
+--R 5 4 3 2
+--R 2240421120x + 7468070400x + 9957427200x + 6638284800x + 2212761600x
+--R +
+--R 295034880
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 119883170atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 59941585atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 11239996\|7
+--R /
+--R +-+
+--R 439040\|7
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+
+--R (1) (- 270x - 567x - 333x + 46x + 100x + 24)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+r0:=1/35*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)+_
+ 6219452877/102400000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 17133479/25600000*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 870407/9600000*(3+5*x)^(5/2)*sqrt(1-2*x)+_
+ 51/10000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+29/2100*(2+3*x)^3*_
+ (3+5*x)^(5/2)*sqrt(1-2*x)-1/800000*(3+5*x)^(5/2)*_
+ (35878+51675*x)*sqrt(1-2*x)-565404807/102400000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 43536170139asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R - 27648000000x - 67968000000x - 46732032000x + 12527113600x
+--R +
+--R 2
+--R 28707557280x + 9288436460x - 3952411101
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 716800000\|10
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+--a0:=integrate(t0,x)
+--E 303
+
+--S 304 of 500
+--m0:=a0-r0
+--E 304
+
+--S 305 of 500
+--d0:=D(m0,x)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (1) (- 90x - 129x - 25x + 32x + 12)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+r0:=-3101/6400*(1-2*x)^(5/2)*(3+5*x)^(3/2)-259/2000*(1-2*x)^(5/2)*_
+ (3+5*x)^(5/2)-1/20*(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2)+_
+ 136205223/5120000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 375221/512000*(1-2*x)^(3/2)*sqrt(3+5*x)-34111/25600*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)+12382293/5120000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 136205223asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 76800000x - 132864000x - 27804800x + 66492960x + 37288220x
+--R +
+--R - 8705457
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 5120000\|10
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+--a0:=integrate(t0,x)
+--E 308
+
+--S 309 of 500
+--m0:=a0-r0
+--E 309
+
+--S 310 of 500
+--d0:=D(m0,x)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (1) (- 30x - 23x + 7x + 6)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+r0:=-37/160*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/50*(1-2*x)^(5/2)*(3+5*x)^(5/2)+_
+ 1625151/128000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 4477/12800*(1-2*x)^(3/2)*sqrt(3+5*x)-407/640*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)+147741/128000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 1625151asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 768000x - 745600x + 364320x + 489340x - 46809)\|10 \|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R /
+--R +--+
+--R 128000\|10
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+--a0:=integrate(t0,x)
+--E 313
+
+--S 314 of 500
+--m0:=a0-r0
+--E 314
+
+--S 315 of 500
+--d0:=D(m0,x)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (1) (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+r0:=-1/8*(1-2*x)^(5/2)*(3+5*x)^(3/2)+43923/6400*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)+121/640*(1-2*x)^(3/2)*sqrt(3+5*x)-_
+ 11/32*(1-2*x)^(5/2)*sqrt(3+5*x)+3993/6400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 43923asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (- 16000x - 2400x + 11980x + 603)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 6400\|10
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+--a0:=integrate(t0,x)
+--E 318
+
+--S 319 of 500
+--m0:=a0-r0
+--E 319
+
+--S 320 of 500
+--d0:=D(m0,x)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+r0:=1/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)+14/81*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))*sqrt(7)+19573/6480*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)+37/180*(3+5*x)^(3/2)*sqrt(1-2*x)-1781/2160*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3
+--R 1120\|7 \|10 atan(-------------) + 19573asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R 2 +--+ +--------+ +------+
+--R (- 7200x + 5940x + 813)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 6480\|10
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 323
+
+--S 324 of 500
+--m0:=a0-r0
+--E 324
+
+--S 325 of 500
+--d0:=D(m0,x)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+r0:=-1/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)-37/27*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+1649/108*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)-1/3*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 107/36*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3
+--R (- 444x - 296)\|7 \|10 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R (4947x + 3298)asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+ +------+
+--R (- 180x + 315x + 318)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R (324x + 216)\|10
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 328
+
+--S 329 of 500
+--m0:=a0-r0
+--E 329
+
+--S 330 of 500
+--d0:=D(m0,x)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2+1649/108*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-37/27*asin(sqrt(2/11)*_
+ sqrt(3+5*x))*sqrt(10)+37/12*(3+5*x)^(3/2)*sqrt(1-2*x)/_
+ (2+3*x)-205/36*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (14841x + 19788x + 6596)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 +-+ +--+ \|2 \|5x + 3
+--R (- 1332x - 1776x - 592)\|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+ +------+
+--R (- 360x - 1035x - 516)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (972x + 1296x + 432)\|7
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 333
+
+--S 334 of 500
+--m0:=a0-r0
+--E 334
+
+--S 335 of 500
+--d0:=D(m0,x)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^4
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+r0:=-1/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3+19573/4536*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+20/81*_
+ asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+37/36*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^2-661/1512*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (528471x + 1056942x + 704628x + 156584)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 3 2 +-+ +--+ \|2 \|5x + 3
+--R (30240x + 60480x + 40320x + 8960)\|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+ +------+
+--R (57123x + 65286x + 18528)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (122472x + 244944x + 163296x + 36288)\|7
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 338
+
+--S 339 of 500
+--m0:=a0-r0
+--E 339
+
+--S 340 of 500
+--d0:=D(m0,x)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^5
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+r0:=1/4*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4+_
+ 43923/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_
+ sqrt(7)-121/224*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+_
+ 11/8*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_
+ 3993/3136*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (3557763x + 9487368x + 9487368x + 4216608x + 702768)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (100159x + 213240x + 145940x + 32400)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (254016x + 677376x + 677376x + 301056x + 50176)\|7
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (3557763x + 9487368x + 9487368x + 4216608x + 702768)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 3 2 +--------+ +------+
+--R (1402226x + 2985360x + 2043160x + 453600)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R - 4592700x - 12247200x - 12247200x - 5443200x - 907200
+--R /
+--R 4 3 2
+--R 3556224x + 9483264x + 9483264x + 4214784x + 702464
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 87846atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 43923atan(------------------------------------------------) - 8100\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 6272\|7
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+r0:=-1/15*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^5+_
+ 1625151/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_
+ sqrt(7)+37/120*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-_
+ 5281/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 36149/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 3831323/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 1974558465x + 6581861550x + 8775815400x + 5850543600x
+--R +
+--R 1950181200x + 260024160
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (57469845x + 155783350x + 158785356x + 71866904x + 12157344)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x
+--R +
+--R 7024640
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 1974558465x - 6581861550x - 8775815400x - 5850543600x
+--R +
+--R - 1950181200x - 260024160
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 4 3 2
+--R (804577830x + 2180966900x + 2222994984x + 1006136656x + 170202816)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 2584955268x - 8616517560x - 11488690080x - 7659126720x
+--R +
+--R - 2553042240x - 340405632
+--R /
+--R 5 4 3 2
+--R 746807040x + 2489356800x + 3319142400x + 2212761600x + 737587200x
+--R +
+--R 98344960
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 16251510atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 8125755atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 1519668\|7
+--R /
+--R +-+
+--R 439040\|7
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^7
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+r0:=-1/18*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6+19457889/175616*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+37/180*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^5-7591/30240*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 37333/181440*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 1316353/1016064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 137752591/14224896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 70924005405x + 283696021620x + 472826702700x + 420290402400x
+--R +
+--R 2
+--R 210145201200x + 56038720320x + 6226524480
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 2066288865x + 6979774260x + 9434103472x + 6379024416x
+--R +
+--R 2157325040x + 291805632
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3 2
+--R 640120320x + 2560481280x + 4267468800x + 3793305600x + 1896652800x
+--R +
+--R 505774080x + 56197120
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 70924005405x + 283696021620x + 472826702700x + 420290402400x
+--R +
+--R 2
+--R 210145201200x + 56038720320x + 6226524480
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 5 4 3 2
+--R 28928044110x + 97716839640x + 132077448608x + 89306341824x
+--R +
+--R 30202550560x + 4085278848
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R - 93067758756x - 372271035024x - 620451725040x - 551512644480x
+--R +
+--R 2
+--R - 275756322240x - 73535019264x - 8170557696
+--R /
+--R 6 5 4 3
+--R 8961684480x + 35846737920x + 59744563200x + 53106278400x
+--R +
+--R 2
+--R 26553139200x + 7080837120x + 786759680
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 194578890atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 97289445atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R - 18237852\|7
+--R /
+--R +-+
+--R 1756160\|7
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+r0:=-1/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^7+_
+ 6219452877/17210368*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 37/252*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-_
+ 9901/52920*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+_
+ 341917/2963520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 4014523/5927040*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 140331343/33191424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 14677525921/464679936*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R 68009717209995x + 317378680313310x + 634757360626620x
+--R +
+--R 4 3 2
+--R 705285956251800x + 470190637501200x + 188076255000480x
+--R +
+--R 41794723333440x + 3980449841280
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 6 5 4
+--R 1981465999335x + 8014272743430x + 13509190228248x
+--R +
+--R 3 2
+--R 12147806104256x + 6146173476816x + 1658923773088x + 186609267072
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 7 6 5 4
+--R 188195374080x + 878245079040x + 1756490158080x + 1951655731200x
+--R +
+--R 3 2
+--R 1301103820800x + 520441528320x + 115653672960x + 11014635520
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R - 68009717209995x - 317378680313310x - 634757360626620x
+--R +
+--R 4 3 2
+--R - 705285956251800x - 470190637501200x - 188076255000480x
+--R +
+--R - 41794723333440x - 3980449841280
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 6 5 4
+--R 27740523990690x + 112199818408020x + 189128663195472x
+--R +
+--R 3 2
+--R 170069285459584x + 86046428675424x + 23224932823232x + 2612529739008
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 7 6 5
+--R - 89275039675164x - 416616851817432x - 833233703634864x
+--R +
+--R 4 3 2
+--R - 925815226260960x - 617210150840640x - 246884060336256x
+--R +
+--R - 54863124519168x - 5225059478016
+--R /
+--R 7 6 5 4
+--R 2634735237120x + 12295431106560x + 24590862213120x + 27323180236800x
+--R +
+--R 3 2
+--R 18215453491200x + 7286181396480x + 1619151421440x + 154204897280
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 62194528770atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 31097264385atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 5831539596\|7
+--R /
+--R +-+
+--R 172103680\|7
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)
+--R
+--R
+--R (1)
+--R 6 5 4 3 2 +--------+ +------+
+--R (- 1350x - 3645x - 3366x - 769x + 638x + 420x + 72)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 500
+r0:=1/40*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(7/2)+_
+ 147858829437/655360000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 407324599/163840000*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 37029509/102400000*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 803549/15360000*(3+5*x)^(7/2)*sqrt(1-2*x)+_
+ 193/48000*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)+_
+ 29/2800*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+ 1/1600000*(3+5*x)^(7/2)*(43298+62245*x)*sqrt(1-2*x)-_
+ 13441711767/655360000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 1035011806059asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 7 6 5 4
+--R - 774144000000x - 2394316800000x - 2554199040000x - 592093952000x
+--R +
+--R 3 2
+--R 910419721600x + 749541131680x + 138459209260x - 116041578381
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 4587520000\|10
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+--a0:=integrate(t0,x)
+--E 363
+
+--S 364 of 500
+--m0:=a0-r0
+--E 364
+
+--S 365 of 500
+--d0:=D(m0,x)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+
+--R (1) (- 450x - 915x - 512x + 85x + 156x + 36)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+r0:=-8613/5120*(1-2*x)^(5/2)*(3+5*x)^(3/2)-783/1600*(1-2*x)^(5/2)*_
+ (3+5*x)^(5/2)-47/400*(1-2*x)^(5/2)*(3+5*x)^(7/2)-_
+ 3/70*(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(7/2)+_
+ 378308799/4096000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1042173/409600*(1-2*x)^(3/2)*sqrt(3+5*x)-94743/20480*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)+34391709/4096000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 2648161593asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R - 1843200000x - 4387840000x - 2867456000x + 887043200x
+--R +
+--R 2
+--R 1789716960x + 549624420x - 247243887
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 28672000\|10
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+--a0:=integrate(t0,x)
+--E 368
+
+--S 369 of 500
+--m0:=a0-r0
+--E 369
+
+--S 370 of 500
+--d0:=D(m0,x)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (1) (- 150x - 205x - 34x + 51x + 18)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+r0:=-187/256*(1-2*x)^(5/2)*(3+5*x)^(3/2)-17/80*(1-2*x)^(5/2)*(3+5*x)^(5/2)-_
+ 1/20*(1-2*x)^(5/2)*(3+5*x)^(7/2)+8213601/204800*_
+ asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+22627/20480*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)-2057/1024*(1-2*x)^(5/2)*sqrt(3+5*x)+_
+ 746691/204800*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 8213601asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R (- 5120000x - 8448000x - 1456000x + 4238560x + 2224900x - 555399)
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 204800\|10
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+--a0:=integrate(t0,x)
+--E 373
+
+--S 374 of 500
+--m0:=a0-r0
+--E 374
+
+--S 375 of 500
+--d0:=D(m0,x)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (1) (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+r0:=-11/32*(1-2*x)^(5/2)*(3+5*x)^(3/2)-1/10*(1-2*x)^(5/2)*(3+5*x)^(5/2)+_
+ 483153/25600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1331/2560*(1-2*x)^(3/2)*sqrt(3+5*x)-121/128*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)+43923/25600*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 483153asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 256000x - 227200x + 124640x + 147140x - 16407)\|10 \|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R /
+--R +--+
+--R 25600\|10
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+--a0:=integrate(t0,x)
+--E 378
+
+--S 379 of 500
+--m0:=a0-r0
+--E 379
+
+--S 380 of 500
+--d0:=D(m0,x)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+r0:=1/12*(1-2*x)^(3/2)*(3+5*x)^(5/2)-14/243*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))*sqrt(7)+648919/62208*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)-53/192*(3+5*x)^(3/2)*sqrt(1-2*x)+23/216*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)-15863/20736*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3
+--R - 3584\|7 \|10 atan(-------------) + 648919asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (- 259200x - 15840x + 175068x + 7167)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 62208\|10
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 383
+
+--S 384 of 500
+--m0:=a0-r0
+--E 384
+
+--S 385 of 500
+--d0:=D(m0,x)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+r0:=-1/3*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)-43/3888*asin(sqrt(2/11)*_
+ sqrt(3+5*x))*sqrt(5/2)+181/243*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))*sqrt(7)+25/12*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 8/27*(3+5*x)^(5/2)*sqrt(1-2*x)-3065/1296*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +-+ \|7 \|5x + 3
+--R (8688x + 5792)\|2 \|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ \|2 \|5x + 3
+--R (- 129x - 86)\|5 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (- 21600x + 5580x + 10539x - 2190)\|2 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+
+--R (11664x + 7776)\|2
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 388
+
+--S 389 of 500
+--m0:=a0-r0
+--E 389
+
+--S 390 of 500
+--d0:=D(m0,x)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2+1945/324*_
+ asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-6829/324*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-35/4*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)+181/36*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)+_
+ 185/27*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +-+ \|7 \|5x + 3
+--R (- 61461x - 81948x - 27316)\|2 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 +-+ +-+ \|2 \|5x + 3
+--R (17505x + 23340x + 7780)\|5 \|7 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +-+ +--------+ +------+
+--R (- 2700x + 3285x + 8955x + 3696)\|2 \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+ +-+
+--R (2916x + 3888x + 1296)\|2 \|7
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 393
+
+--S 394 of 500
+--m0:=a0-r0
+--E 394
+
+--S 395 of 500
+--d0:=D(m0,x)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+r0:=-1/9*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3+326717/13608*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-575/243*_
+ asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+331/168*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)+181/108*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2-_
+ 39745/4536*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (8821359x + 17642718x + 11761812x + 2613736)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 3 2 +-+ +--+ \|2 \|5x + 3
+--R (- 869400x - 1738800x - 1159200x - 257600)\|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (- 226800x - 860373x - 825066x - 235248)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (367416x + 734832x + 489888x + 108864)\|7
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 398
+
+--S 399 of 500
+--m0:=a0-r0
+--E 399
+
+--S 400 of 500
+--d0:=D(m0,x)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^5
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+r0:=-1/12*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4+1922677/762048*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+100/243*_
+ asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-871/6048*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^2+181/216*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_
+ 77269/254016*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (155736837x + 415298232x + 415298232x + 184576992x + 30762832)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+ +--+
+--R (25401600x + 67737600x + 67737600x + 30105600x + 5017600)\|7 \|10
+--R *
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (39870441x + 69556680x + 40302540x + 7751280)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (61725888x + 164602368x + 164602368x + 73156608x + 12192768)\|7
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 403
+
+--S 404 of 500
+--m0:=a0-r0
+--E 404
+
+--S 405 of 500
+--d0:=D(m0,x)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^6
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+r0:=1/5*(1-2*x)^(3/2)*(3+5*x)^(7/2)/(2+3*x)^5+483153/43904*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-1331/3136*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^2-121/560*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+_
+ 33/40*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-43923/43904*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x
+--R +
+--R 77304480
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (15899035x + 46076650x + 47906548x + 21437032x + 3507552)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x
+--R +
+--R 7024640
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x
+--R +
+--R 77304480
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 4 3 2
+--R (222586490x + 645073100x + 670691672x + 300118448x + 49105728)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 745793244x - 2485977480x - 3314636640x - 2209757760x - 736585920x
+--R +
+--R - 98211456
+--R /
+--R 5 4 3 2
+--R 746807040x + 2489356800x + 3319142400x + 2212761600x + 737587200x
+--R +
+--R 98344960
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 4831530atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 2415765atan(------------------------------------------------) - 438444\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 439040\|7
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+r0:=-1/18*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^6+4348377/175616*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-2857/10080*_
+ (3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4+181/540*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^5-126463/544320*sqrt(1-2*x)*sqrt(3+5*x)/_
+ (2+3*x)^3+852587/3048192*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 92126789/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 15849834165x + 63399336660x + 105665561100x + 93924943200x
+--R +
+--R 2
+--R 46962471600x + 12523325760x + 1391480640
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 460633945x + 1555340180x + 2108117296x + 1428134688x + 482263920x
+--R +
+--R 64829376
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3 2
+--R 640120320x + 2560481280x + 4267468800x + 3793305600x + 1896652800x
+--R +
+--R 505774080x + 56197120
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R - 15849834165x - 63399336660x - 105665561100x - 93924943200x
+--R +
+--R 2
+--R - 46962471600x - 12523325760x - 1391480640
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 5 4 3 2
+--R 6448875230x + 21774762520x + 29513642144x + 19993885632x
+--R +
+--R 6751694880x + 907611264
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R 20676519108x + 82706076432x + 137843460720x + 122527520640x
+--R +
+--R 2
+--R 61263760320x + 16337002752x + 1815222528
+--R /
+--R 6 5 4 3
+--R 8961684480x + 35846737920x + 59744563200x + 53106278400x
+--R +
+--R 2
+--R 26553139200x + 7080837120x + 786759680
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 43483770atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 21741885atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R 4051836\|7
+--R /
+--R +-+
+--R 1756160\|7
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+r0:=-1/21*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7+1104970911/17210368*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-12421/52920*_
+ (3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5+181/756*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^6-1289227/8890560*sqrt(1-2*x)*sqrt(3+5*x)/_
+ (2+3*x)^4+6249601/53343360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 224018941/298722816*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 23466191827/4182119424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R 12082856911785x + 56386665588330x + 112773331176660x
+--R +
+--R 4 3 2
+--R 125303701307400x + 83535800871600x + 33414320348640x
+--R +
+--R 7425404521920x + 707181383040
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 6 5 4 3
+--R 351992877405x + 1423652835490x + 2399706883464x + 2158260396608x
+--R +
+--R 2
+--R 1092179419888x + 294736348384x + 33120084096
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 7 6 5 4
+--R 188195374080x + 878245079040x + 1756490158080x + 1951655731200x
+--R +
+--R 3 2
+--R 1301103820800x + 520441528320x + 115653672960x + 11014635520
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+--a0:=integrate(t0,x)
+--E 418
+
+--S 419 of 500
+--m0:=a0-r0
+--E 419
+
+--S 420 of 500
+--d0:=D(m0,x)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1
+--R (1) -------------------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+r0:=18648399/3200000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1/25*(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)-_
+ 4802371/9600000*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 511/60000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 29/1000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 7/800000*(21038+30535*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 18648399asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 6912000x - 7862400x + 2952480x + 5372860x - 314441)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 3200000\|10
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+--a0:=integrate(t0,x)
+--E 423
+
+--S 424 of 500
+--m0:=a0-r0
+--E 424
+
+--S 425 of 500
+--d0:=D(m0,x)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2/sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+
+--R (- 18x - 15x + 4x + 4)\|- 2x + 1
+--R (1) -----------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+r0:=109263/32000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 301/3200*(1-2*x)^(3/2)*sqrt(3+5*x)-_
+ 119/800*(1-2*x)^(5/2)*sqrt(3+5*x)-_
+ 3/40*(1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x)+9933/32000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 109263asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (- 28800x - 9440x + 25020x + 3383)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 32000\|10
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+--a0:=integrate(t0,x)
+--E 428
+
+--S 429 of 500
+--m0:=a0-r0
+--E 429
+
+--S 430 of 500
+--d0:=D(m0,x)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)/sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+
+--R (- 6x - x + 2)\|- 2x + 1
+--R (1) --------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+r0:=1089/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 3/40*(1-2*x)^(3/2)*sqrt(3+5*x)-_
+ 1/10*(1-2*x)^(5/2)*sqrt(3+5*x)+99/400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3 2 +--+ +--------+ +------+
+--R 1089asin(-------------) + (- 160x + 100x + 89)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R ------------------------------------------------------------------------
+--R +--+
+--R 400\|10
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 500
+--m0:=a0-r0
+--E 434
+
+--S 435 of 500
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(1-2*x)^(3/2)/sqrt(3+5*x)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+r0:=363/100*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/10*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)+33/100*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R \|2 \|5x + 3 +--+ +--------+ +------+
+--R 363asin(-------------) + (- 20x + 43)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R (2) --------------------------------------------------------------
+--R +--+
+--R 100\|10
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500
+--a0:=integrate(t0,x)
+--E 438
+
+--S 439 of 500
+--m0:=a0-r0
+--E 439
+
+--S 440 of 500
+--d0:=D(m0,x)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------
+--R +------+
+--R (3x + 2)\|5x + 3
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+r0:=-103/45*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+_
+ 14/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_
+ 2/15*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3
+--R 70\|5 \|7 atan(-------------) - 103\|2 asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R +-+ +--------+ +------+
+--R - 6\|5 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+
+--R 45\|5
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 443
+
+--S 444 of 500
+--m0:=a0-r0
+--E 444
+
+--S 445 of 500
+--d0:=D(m0,x)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^2*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|5x + 3
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+r0:=4/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+29/9*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+(1-2*x)^(3/2)*_
+ sqrt(3+5*x)/(2+3*x)+2/3*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3
+--R (87x + 58)\|5 \|7 atan(-------------) + (12x + 8)\|2 asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R +-+ +--------+ +------+
+--R 21\|5 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+
+--R (27x + 18)\|5
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 448
+
+--S 449 of 500
+--m0:=a0-r0
+--E 449
+
+--S 450 of 500
+--d0:=D(m0,x)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^3*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) --------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|5x + 3
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+r0:=363/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/2*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+33/4*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (3267x + 4356x + 1452)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+
+--R (95x + 68)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (36x + 48x + 16)\|7
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 13068x - 17424x - 5808)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +--------+ +------+ 2
+--R (5320x + 3808)\|- 2x + 1 \|5x + 3 + 20349x + 27132x + 9044
+--R /
+--R 2
+--R 2016x + 2688x + 896
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2904atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 1452atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 323\|7
+--R /
+--R +-+
+--R 32\|7
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^4*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|5x + 3
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+r0:=21417/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^3+_
+ 169/36*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 16847/504*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (578259x + 1156518x + 771012x + 171336)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (16847x + 23214x + 8032)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (1512x + 3024x + 2016x + 448)\|7
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (578259x + 1156518x + 771012x + 171336)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (235858x + 324996x + 112448)\|- 2x + 1 \|5x + 3 - 759024x - 1518048x
+--R +
+--R - 1012032x - 224896
+--R /
+--R 3 2
+--R 21168x + 42336x + 28224x + 6272
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 42834atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 21417atan(------------------------------------------------) - 4016\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 112\|7
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^5*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|5x + 3
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+r0:=5274027/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/4*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4+_
+ 239/72*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 39667/2016*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 4148797/28224*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (427196187x + 1139189832x + 1139189832x + 506306592x + 84384432)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (12446391x + 25448120x + 17365300x + 3956240)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (254016x + 677376x + 677376x + 301056x + 50176)\|7
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 854392374x - 2278379664x - 2278379664x - 1012613184x - 168768864)
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R \|7 atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R 3 2 +--------+ +------+
+--R (348498948x + 712547360x + 486228400x + 110774720)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 981394785x + 2617052760x + 2617052760x + 1163134560x + 193855760
+--R /
+--R 4 3 2
+--R 7112448x + 18966528x + 18966528x + 8429568x + 1404928
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 21096108atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R - 10548054atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +-+
+--R 1730855\|7
+--R /
+--R +-+
+--R 12544\|7
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^6*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|5x + 3
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+r0:=333216939/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/5*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+_
+ 103/40*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 23909/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 835409/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 87374783/131712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 404858580885x + 1349528602950x + 1799371470600x + 1199580980400x
+--R +
+--R 399860326800x + 53314710240
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2
+--R 11795595705x + 31981229550x + 32535654204x + 14720806136x
+--R +
+--R 2499608096
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x
+--R +
+--R 7024640
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R - 809717161770x - 2699057205900x - 3598742941200x
+--R +
+--R 2
+--R - 2399161960800x - 799720653600x - 106629420480
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 112\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 2072x + 1120
+--R +
+--R 4 3 2
+--R 330276679740x + 895474427400x + 910998317712x + 412182571808x
+--R +
+--R 69989026688
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 1727307307089x + 5757691023630x + 7676921364840x + 5117947576560x
+--R +
+--R 1705982525520x + 227464336736
+--R /
+--R 5 4 3 2
+--R 1493614080x + 4978713600x + 6638284800x + 4425523200x + 1475174400x
+--R +
+--R 196689920
+--R Type: Union(Expression(Integer),...)
+--E 468
+
+--S 469 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 6664338780atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 112\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R - 3332169390atan(------------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 2072x + 1120
+--R +
+--R +-+
+--R 1015465789\|7
+--R /
+--R +-+
+--R 878080\|7
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(3/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1
+--R (1) -------------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+r0:=390621/160000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 2/5*(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x)-_
+ 23779/160000*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 1043/8000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 623/1000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 9/50*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R 390621\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 432000x - 439200x + 287460x + 317125x + 46783)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R 160000\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+--a0:=integrate(t0,x)
+--E 473
+
+--S 474 of 500
+--m0:=a0-r0
+--E 474
+
+--S 475 of 500
+--d0:=D(m0,x)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+
+--R (- 18x - 15x + 4x + 4)\|- 2x + 1
+--R (1) -----------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+r0:=3927/2000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 2/275*(1-2*x)^(5/2)/sqrt(3+5*x)+_
+ 119/2200*(1-2*x)^(3/2)*sqrt(3+5*x)-_
+ 3/50*(1-2*x)^(5/2)*sqrt(3+5*x)+357/2000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R 3927\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 2400x - 180x + 2575x + 1021)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R 2000\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+--a0:=integrate(t0,x)
+--E 478
+
+--S 479 of 500
+--m0:=a0-r0
+--E 479
+
+--S 480 of 500
+--d0:=D(m0,x)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(3/2)
+--R
+--R
+--R 2 +--------+
+--R (- 6x - x + 2)\|- 2x + 1
+--R (1) --------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+r0:=33/20*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 2/55*(1-2*x)^(5/2)/sqrt(3+5*x)+_
+ 1/22*(1-2*x)^(3/2)*sqrt(3+5*x)+3/20*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3 2 +--+ +--------+
+--R 33\|5x + 3 asin(-------------) + (- 12x + 17x + 11)\|10 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) --------------------------------------------------------------------
+--R +--+ +------+
+--R 20\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500
+--a0:=integrate(t0,x)
+--E 483
+
+--S 484 of 500
+--m0:=a0-r0
+--E 484
+
+--S 485 of 500
+--d0:=D(m0,x)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(1-2*x)^(3/2)/(3+5*x)^(3/2)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+r0:=-33/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-_
+ 2/5*(1-2*x)^(3/2)/sqrt(3+5*x)-6/25*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+
+--R - 33\|2 \|5x + 3 asin(-------------) + (- 10x - 28)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ------------------------------------------------------------------
+--R +-+ +------+
+--R 25\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500
+--a0:=integrate(t0,x)
+--E 488
+
+--S 489 of 500
+--m0:=a0-r0
+--E 489
+
+--S 490 of 500
+--d0:=D(m0,x)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 2 +------+
+--R (15x + 19x + 6)\|5x + 3
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+r0:=4/15*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-_
+ 14/3*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_
+ 2*(1-2*x)^(3/2)/sqrt(3+5*x)-4/5*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +-+ +------+ \|7 \|5x + 3
+--R - 70\|5 \|7 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+
+--R 4\|2 \|5x + 3 asin(-------------) - 66\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R /
+--R +-+ +------+
+--R 15\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 493
+
+--S 494 of 500
+--m0:=a0-r0
+--E 494
+
+--S 495 of 500
+--d0:=D(m0,x)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 3 2 +------+
+--R (45x + 87x + 56x + 12)\|5x + 3
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+r0:=-33*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_
+ (1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))-33*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +------+ \|7 \|5x + 3 +--------+
+--R (- 99x - 66)\|7 \|5x + 3 atan(-------------) + (- 101x - 65)\|- 2x + 1
+--R +--------+
+--R \|- 2x + 1
+--R -----------------------------------------------------------------------
+--R +------+
+--R (3x + 2)\|5x + 3
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 1485x - 1881x - 594)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +--------+ +------+ 2
+--R (- 606x - 390)\|- 2x + 1 \|5x + 3 - 1950x - 2470x - 780
+--R /
+--R 2
+--R 90x + 114x + 36
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R 198\|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R - 99\|7 atan(------------------------------------------------) - 130
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R 6
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3n.input.pdf b/src/axiom-website/CATS/rich3n.input.pdf
new file mode 100644
index 0000000..ec916dd
Binary files /dev/null and b/src/axiom-website/CATS/rich3n.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3o.input.pamphlet b/src/axiom-website/CATS/rich3o.input.pamphlet
new file mode 100644
index 0000000..fada68f
--- /dev/null
+++ b/src/axiom-website/CATS/rich3o.input.pamphlet
@@ -0,0 +1,7197 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3o.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 36 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 64 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 rich3o.output
+)spool rich3o.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 4 3 2 +------+
+--R (135x + 351x + 342x + 148x + 24)\|5x + 3
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+r0:=-5709/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/2*(1-2*x)^(3/2)/((2+3*x)^2*sqrt(3+5*x))-_
+ 2495/12*sqrt(1-2*x)/sqrt(3+5*x)+169/12*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +------+ \|7 \|5x + 3
+--R (- 51381x - 68508x - 22836)\|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+
+--R (- 7485x - 9815x - 3212)\|7 \|- 2x + 1
+--R /
+--R 2 +-+ +------+
+--R (36x + 48x + 16)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (3082860x + 5960196x + 3836448x + 822096)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 2 +--------+ +------+ 3
+--R (- 1257480x - 1648920x - 539616)\|- 2x + 1 \|5x + 3 - 4805955x
+--R +
+--R 2
+--R - 9291513x - 5980744x - 1281588
+--R /
+--R 3 2
+--R 30240x + 58464x + 37632x + 8064
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 137016atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R 68508atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R - 15257\|7
+--R /
+--R +-+
+--R 96\|7
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +------+
+--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+r0:=-463881/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/3*(1-2*x)^(3/2)/((2+3*x)^3*sqrt(3+5*x))-_
+ 608185/504*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 239/36*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_
+ 13409/168*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +------+
+--R (- 12524787x - 25049574x - 16699716x - 3711048)\|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+
+--R (- 1824555x - 3608883x - 2378026x - 521968)\|7 \|- 2x + 1
+--R /
+--R 3 2 +-+ +------+
+--R (1512x + 3024x + 2016x + 448)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 187871805x - 488466693x - 475941906x - 205963164x - 33399432)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 3 2 +--------+ +------+
+--R (- 76631310x - 151573086x - 99877092x - 21922656)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 215801145x + 561082977x + 546696234x + 236581996x + 38364648
+--R /
+--R 4 3 2
+--R 317520x + 825552x + 804384x + 348096x + 56448
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 2783286atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R - 1391643atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R +-+
+--R 228361\|7
+--R /
+--R +-+
+--R 336\|7
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|5x + 3
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+r0:=-145708761/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/4*(1-2*x)^(3/2)/((2+3*x)^4*sqrt(3+5*x))-_
+ 63678595/9408*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 103/24*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+_
+ 8063/224*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_
+ 1403963/3136*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 4 3 2
+--R - 11802409641x - 31473092376x - 31473092376x - 13988041056x
+--R +
+--R - 2331340176
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2
+--R - 1719322065x - 4546951839x - 4508028900x - 1985778980x
+--R +
+--R - 327908240
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +------+
+--R (254016x + 677376x + 677376x + 301056x + 50176)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 177036144615x + 578318072409x + 755354217024x + 493078447224x
+--R +
+--R 160862472144x + 20982061584
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 4 3 2
+--R - 72211526730x - 190971977238x - 189337213800x - 83402717160x
+--R +
+--R - 13772146080
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 325366951140x - 1062865373724x - 1388232324864x - 906207212064x
+--R +
+--R - 295642069184x - 38562009024
+--R /
+--R 5 4 3 2
+--R 53343360x + 174254976x + 227598336x + 148571136x + 48470016x + 6322176
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 874252566atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R 437126283atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R - 114767884\|7
+--R /
+--R +-+
+--R 18816\|7
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1
+--R (1) -------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(3/2)+_
+ 13153/10000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 128/25*(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 1953/10000*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 399/500*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 378/125*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (197295x + 118377)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (- 108000x - 83700x + 118395x + 129910x + 31171)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (150000x + 90000)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 500
+--m0:=a0-r0
+--E 19
+
+--S 20 of 500
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(5/2)
+--R
+--R
+--R 3 2 +--------+
+--R (- 18x - 15x + 4x + 4)\|- 2x + 1
+--R (1) -----------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+r0:=-2/825*(1-2*x)^(5/2)/(3+5*x)^(3/2)+_
+ 343/500*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 388/9075*(1-2*x)^(5/2)/sqrt(3+5*x)+_
+ 343/18150*(1-2*x)^(3/2)*sqrt(3+5*x)+343/5500*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (5145x + 3087)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 2700x + 1845x + 3610x + 901)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (7500x + 4500)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 500
+--m0:=a0-r0
+--E 24
+
+--S 25 of 500
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(5/2)
+--R
+--R
+--R 2 +--------+
+--R (- 6x - x + 2)\|- 2x + 1
+--R (1) --------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+r0:=-2/165*(1-2*x)^(5/2)/(3+5*x)^(3/2)-_
+ 19/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-_
+ 38/165*(1-2*x)^(3/2)/sqrt(3+5*x)-38/275*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3
+--R (- 285x - 171)\|2 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+
+--R (- 90x - 290x - 146)\|5 \|- 2x + 1
+--R /
+--R +-+ +------+
+--R (375x + 225)\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 500
+--m0:=a0-r0
+--E 29
+
+--S 30 of 500
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(1-2*x)^(3/2)/(3+5*x)^(5/2)
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+r0:=-2/15*(1-2*x)^(3/2)/(3+5*x)^(3/2)+_
+ 4/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+4/25*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+
+--R (60x + 36)\|2 \|5x + 3 asin(-------------) + (80x + 26)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------------------------
+--R +-+ +------+
+--R (375x + 225)\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 500
+--m0:=a0-r0
+--E 34
+
+--S 35 of 500
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------------------
+--R 3 2 +------+
+--R (75x + 140x + 87x + 18)\|5x + 3
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+r0:=-2/3*(1-2*x)^(3/2)/(3+5*x)^(3/2)+14*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+14*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +-+ +------+ \|7 \|5x + 3 +--------+
+--R (210x + 126)\|7 \|5x + 3 atan(-------------) + (214x + 124)\|- 2x + 1
+--R +--------+
+--R \|- 2x + 1
+--R (2) ----------------------------------------------------------------------
+--R +------+
+--R (15x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 9450x - 11340x - 3402)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +--------+ +------+ 2
+--R (3852x + 2232)\|- 2x + 1 \|5x + 3 + 14725x + 17670x + 5301
+--R /
+--R 2
+--R 1350x + 1620x + 486
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R - 756\|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 378\|7 atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 589
+--R /
+--R 54
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 4 3 2 +------+
+--R (225x + 570x + 541x + 228x + 36)\|5x + 3
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+r0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(3/2))+_
+ 169*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_
+ 55/3*sqrt(1-2*x)/(3+5*x)^(3/2)+517/3*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +-+ +------+ \|7 \|5x + 3
+--R (7605x + 9633x + 3042)\|7 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +--------+
+--R (7755x + 9652x + 2995)\|- 2x + 1
+--R /
+--R 2 +------+
+--R (45x + 57x + 18)\|5x + 3
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (342225x + 638820x + 396981x + 82134)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (139590x + 173736x + 53910)\|- 2x + 1 \|5x + 3 + 449250x + 838600x
+--R +
+--R 521130x + 107820
+--R /
+--R 3 2
+--R 4050x + 7560x + 4698x + 972
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R - 9126\|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 4563\|7 atan(------------------------------------------------) + 5990
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R 54
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+r0:=1/2*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2))+_
+ 40787/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 655/4*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 239/12*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 17825/12*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 +------+ \|7 \|5x + 3
+--R (5506245x + 10645407x + 6852216x + 1468332)\|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+
+--R (802125x + 1533090x + 975325x + 206524)\|7 \|- 2x + 1
+--R /
+--R 3 2 +-+ +------+
+--R (540x + 1044x + 672x + 144)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (247781025x + 627711930x + 595775709x + 251084772x + 39644964)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 3 2 +--------+ +------+
+--R (101067750x + 193169340x + 122890950x + 26022024)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 325275300x + 824030760x + 782106388x + 329612304x + 52044048
+--R /
+--R 4 3 2
+--R 340200x + 861840x + 817992x + 344736x + 54432
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2202498atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 1101249atan(------------------------------------------------) + 206524\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 216\|7
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+r0:=1/3*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(3/2))+_
+ 4246733/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 204595/168*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 103/12*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_
+ 24469/168*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 618645/56*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (1719926865x + 4471809849x + 4357148058x + 1885549452x + 305764776)
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (250551225x + 645909120x + 623901861x + 267610802x + 43006496)\|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +------+
+--R (22680x + 58968x + 57456x + 24864x + 4032)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 77396708925x - 247669468560x - 316810528533x - 202492722906x
+--R +
+--R - 64669250124x - 8255648952
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R \|7 atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 4 3 2
+--R 31569454350x + 81384549120x + 78611634486x + 33718961052x
+--R +
+--R 5418818496
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 120653380575x + 386090817840x + 493874504487x + 315664992734x
+--R +
+--R 100812602436x + 12869693928
+--R /
+--R 5 4 3 2
+--R 14288400x + 45722880x + 58487184x + 37382688x + 11938752x + 1524096
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 229323582atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 114661791atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 25535107\|7
+--R /
+--R +-+
+--R 3024\|7
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3*sqrt(3+5*x)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+
+--R (1) (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+r0:=17/700*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)+_
+ 1/35*(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2)+_
+ 3735929329/256000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 26653009/192000000*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 35443/1200000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 919/105000*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 1/24000000*(3+5*x)^(3/2)*(1730238+2099155*x)*_
+ sqrt(1-2*x)-339629939/256000000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 78454515909asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 82944000000x + 97459200000x - 52468992000x - 85095638400x
+--R +
+--R 2
+--R 9906627680x + 29819034260x - 679278531
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 5376000000\|10
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 500
+--m0:=a0-r0
+--E 59
+
+--S 60 of 500
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (1) (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+r0:=-193/2000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/20*(1-2*x)^(7/2)*_
+ (2+3*x)*(3+5*x)^(3/2)+105254149/12800000*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)+869869/3840000*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)+79079/960000*(1-2*x)^(5/2)*sqrt(3+5*x)-_
+ 7189/32000*(1-2*x)^(7/2)*sqrt(3+5*x)+9568559/12800000*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 315762447asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 230400000x + 94464000x - 237187200x - 61262560x + 102523580x
+--R +
+--R 9303927
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 38400000\|10
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 500
+--m0:=a0-r0
+--E 64
+
+--S 65 of 500
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (1) (12x - 4x - 5x + 2)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+r0:=-3/50*(1-2*x)^(7/2)*(3+5*x)^(3/2)+1742279/320000*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)+14399/96000*(1-2*x)^(3/2)*sqrt(3+5*x)+_
+ 1309/24000*(1-2*x)^(5/2)*sqrt(3+5*x)-119/800*(1-2*x)^(7/2)*_
+ sqrt(3+5*x)+158389/320000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 5226837asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (2304000x - 931200x - 1849760x + 1108180x + 355917)\|10 \|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R /
+--R +--+
+--R 960000\|10
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 500
+--m0:=a0-r0
+--E 69
+
+--S 70 of 500
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (1) (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+r0:=14641/3200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 121/960*(1-2*x)^(3/2)*sqrt(3+5*x)+11/240*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)-1/8*(1-2*x)^(7/2)*sqrt(3+5*x)+1331/3200*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 43923asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (9600x - 12640x + 3020x + 4443)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 9600\|10
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 500
+--m0:=a0-r0
+--E 74
+
+--S 75 of 500
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+r0:=-98/81*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_
+ 250433/16200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 59/180*(1-2*x)^(3/2)*sqrt(3+5*x)+1/9*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)+6401/5400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3
+--R - 19600\|7 \|10 atan(-------------) + 250433asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R 2 +--+ +--------+ +------+
+--R (7200x - 17820x + 26313)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 16200\|10
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 500
+--m0:=a0-r0
+--E 79
+
+--S 80 of 500
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^2
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+r0:=35/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_
+ 2119/90*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 1/3*(1-2*x)^(3/2)*sqrt(3+5*x)-1/3*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)/(2+3*x)-43/30*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3
+--R (1050x + 700)\|7 \|10 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R (- 6357x - 4238)asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+ +------+
+--R (60x - 237x - 348)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R (270x + 180)\|10
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 500
+--m0:=a0-r0
+--E 84
+
+--S 85 of 500
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+r0:=118/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+_
+ 155/108*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_
+ 1/6*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^2+_
+ 5/4*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)+19/18*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +-+ +-+ \|7 \|5x + 3
+--R (1395x + 1860x + 620)\|5 \|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 +-+ \|2 \|5x + 3
+--R (4248x + 5664x + 1888)\|2 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+ +------+
+--R (144x + 1305x + 708)\|5 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (972x + 1296x + 432)\|5
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 500
+--m0:=a0-r0
+--E 89
+
+--S 90 of 500
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^4
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+r0:=32765/648*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 8/81*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-_
+ 1/9*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3+_
+ 5/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+_
+ 925/216*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (884655x + 1769310x + 1179540x + 262120)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 3 2 +-+ +--+ \|2 \|5x + 3
+--R (- 1728x - 3456x - 2304x - 512)\|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+ +------+
+--R (23067x + 33318x + 11568)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (17496x + 34992x + 23328x + 5184)\|7
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 500
+--m0:=a0-r0
+--E 94
+
+--S 95 of 500
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+r0:=1/4*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+55/24*(1-2*x)^(3/2)*_
+ (3+5*x)^(3/2)/(2+3*x)^3+73205/448*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))/sqrt(7)+605/32*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-_
+ 6655/448*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (17788815x + 47436840x + 47436840x + 21083040x + 3513840)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (518715x + 1059032x + 723428x + 164688)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (108864x + 290304x + 290304x + 129024x + 21504)\|7
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 88944075x - 237184200x - 237184200x - 105415200x - 17569200)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 3 2 +--------+ +------+
+--R (36310050x + 74132240x + 50639960x + 11528160)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 163411668x + 435764448x + 435764448x + 193673088x + 32278848
+--R /
+--R 4 3 2
+--R 7620480x + 20321280x + 20321280x + 9031680x + 1505280
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 732050atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+
+--R - 366025atan(-----------------------------------------------) + 96068\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R /
+--R +-+
+--R 4480\|7
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+r0:=3674891/6272*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/15*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5+1/8*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)/(2+3*x)^4+493/432*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 82937/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 8672663/169344*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 13394977695x + 44649925650x + 59533234200x + 39688822800x
+--R +
+--R 13229607600x + 1763947680
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (390269835x + 1058136330x + 1076423732x + 487066088x + 82697568)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 22861440x + 76204800x + 101606400x + 67737600x + 22579200x
+--R +
+--R 3010560
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 53579910780x - 178599702600x - 238132936800x - 158755291200x
+--R +
+--R - 52918430400x - 7055790720
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R \|7 atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 4 3 2
+--R 21855110760x + 59255634480x + 60279728992x + 27275700928x
+--R +
+--R 4631063808
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 83521959381x + 278406531270x + 371208708360x + 247472472240x
+--R +
+--R 82490824080x + 10998776544
+--R /
+--R 5 4 3 2
+--R 1280240640x + 4267468800x + 5689958400x + 3793305600x + 1264435200x
+--R +
+--R 168591360
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 146995640atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 73497820atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 16367227\|7
+--R /
+--R +-+
+--R 250880\|7
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^7
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+r0:=391280725/175616*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/18*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6+1/12*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)/(2+3*x)^5+647/864*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 151621/36288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 26486645/1016064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 2770202075/14224896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 855730945575x + 3422923782300x + 5704872970500x + 5070998196000x
+--R +
+--R 2
+--R 2535499098000x + 676133092800x + 75125899200
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 24931818675x + 84218501340x + 113834022672x + 76960600672x
+--R +
+--R 26026519504x + 3522190656
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3 2
+--R 384072192x + 1536288768x + 2560481280x + 2275983360x + 1137991680x
+--R +
+--R 303464448x + 33718272
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R - 1711461891150x - 6845847564600x - 11409745941000x
+--R +
+--R 3 2
+--R - 10141996392000x - 5070998196000x - 1352266185600x - 150251798400
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R \|7 atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R 5 4 3 2
+--R 698090922900x + 2358118037520x + 3187352634816x + 2154896818816x
+--R +
+--R 728742546112x + 98621338368
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R 1965877694109x + 7863510776436x + 13105851294060x + 11649645594720x
+--R +
+--R 2
+--R 5824822797360x + 1553286079296x + 172587342144
+--R /
+--R 6 5 4 3
+--R 10754021376x + 43016085504x + 71693475840x + 63727534080x
+--R +
+--R 2
+--R 31863767040x + 8497004544x + 944111616
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 1565122900atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R - 782561450atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +-+
+--R 128413201\|7
+--R /
+--R +-+
+--R 702464\|7
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2)
+--R
+--R
+--R 6 5 4 3 2 +--------+ +------+
+--R (1) (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+r0:=51/2800*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)+1/40*(1-2*x)^(5/2)*_
+ (2+3*x)^3*(3+5*x)^(5/2)+355329559167/8192000000*_
+ asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-978869309/2048000000*_
+ (3+5*x)^(3/2)*sqrt(1-2*x)-135322391/2304000000*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)+16321/800000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+_
+ 2477/504000*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)-1/192000000*_
+ (3+5*x)^(5/2)*(6543814+7759275*x)*sqrt(1-2*x)-_
+ 32302687197/8192000000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 2487306914169asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 7 6 5 4
+--R 3870720000000x + 7105536000000x + 808627200000x - 5264367872000x
+--R +
+--R 3 2
+--R - 2347326614400x + 1304824422880x + 942468770660x - 115416461871
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 57344000000\|10
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 500
+--m0:=a0-r0
+--E 114
+
+--S 115 of 500
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+
+--R (1) (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+r0:=-2287/8000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-263/2800*(1-2*x)^(7/2)*_
+ (3+5*x)^(5/2)-3/70*(1-2*x)^(7/2)*(2+3*x)*(3+5*x)^(5/2)+_
+ 1104970911/51200000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 3043997/5120000*(1-2*x)^(3/2)*sqrt(3+5*x)+_
+ 276727/1280000*(1-2*x)^(5/2)*sqrt(3+5*x)-_
+ 75471/128000*(1-2*x)^(7/2)*sqrt(3+5*x)+_
+ 100451901/51200000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 7734796377asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 9216000000x + 10112000000x - 6123776000x - 8717155200x
+--R +
+--R 2
+--R 1291331040x + 2994263780x - 104420943
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 358400000\|10
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 500
+--m0:=a0-r0
+--E 119
+
+--S 120 of 500
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (1) (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+r0:=-63/400*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/20*(1-2*x)^(7/2)*(3+5*x)^(5/2)+_
+ 30438639/2560000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 83853/256000*(1-2*x)^(3/2)*sqrt(3+5*x)+_
+ 7623/64000*(1-2*x)^(5/2)*sqrt(3+5*x)-_
+ 2079/6400*(1-2*x)^(7/2)*sqrt(3+5*x)+_
+ 2767149/2560000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 30438639asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R (25600000x + 8448000x - 25526400x - 5162720x + 10406460x + 717399)
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 2560000\|10
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 500
+--m0:=a0-r0
+--E 124
+
+--S 125 of 500
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (1) (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+r0:=-1/10*(1-2*x)^(7/2)*(3+5*x)^(3/2)+483153/64000*_
+ asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1331/6400*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)+121/1600*(1-2*x)^(5/2)*sqrt(3+5*x)-33/160*(1-2*x)^(7/2)*_
+ sqrt(3+5*x)+43923/64000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 483153asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+ +------+
+--R (256000x - 124800x - 177440x + 116420x + 29673)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 64000\|10
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 500
+--m0:=a0-r0
+--E 129
+
+--S 130 of 500
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+r0:=181/1080*(1-2*x)^(3/2)*(3+5*x)^(3/2)+1/12*(1-2*x)^(5/2)*(3+5*x)^(3/2)+_
+ 98/243*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_
+ 1922677/777600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 7093/21600*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 390869/259200*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3
+--R 313600\|7 \|10 atan(-------------) + 1922677asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (1296000x - 1821600x + 692820x + 178797)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 777600\|10
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 133
+
+--S 134 of 500
+--m0:=a0-r0
+--E 134
+
+--S 135 of 500
+--d0:=D(m0,x)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^2
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+r0:=-8/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1/3*(1-2*x)^(5/2)*_
+ (3+5*x)^(3/2)/(2+3*x)-805/243*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))*sqrt(7)+326717/9720*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)-247/270*(3+5*x)^(3/2)*sqrt(1-2*x)+24251/3240*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3
+--R (- 96600x - 64400)\|7 \|10 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R (980151x + 653434)asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (21600x - 41220x + 51831x + 65154)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R (29160x + 19440)\|10
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 500
+--m0:=a0-r0
+--E 139
+
+--S 140 of 500
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^3
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+r0:=-1/6*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^2+115/36*(1-2*x)^(3/2)*_
+ (3+5*x)^(3/2)/(2+3*x)+1945/324*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))*sqrt(7)-6829/162*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)+41/18*(3+5*x)^(3/2)*sqrt(1-2*x)-1649/108*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +-+ +--+ \|7 \|5x + 3
+--R (17505x + 23340x + 7780)\|7 \|10 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 \|2 \|5x + 3
+--R (- 122922x - 163896x - 54632)asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (1080x - 3690x - 10413x - 4884)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +--+
+--R (2916x + 3888x + 1296)\|10
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 500
+--m0:=a0-r0
+--E 144
+
+--S 145 of 500
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+r0:=-1/9*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^3+115/108*(1-2*x)^(3/2)*_
+ (3+5*x)^(3/2)/(2+3*x)^2-215/1944*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))/sqrt(7)+362/243*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(10)+365/216*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-_
+ 845/648*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (- 5805x - 11610x - 7740x - 1720)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 3 2 +-+ +--+ \|2 \|5x + 3
+--R (78192x + 156384x + 104256x + 23168)\|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (12960x + 103023x + 108702x + 30912)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (52488x + 104976x + 69984x + 15552)\|7
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 148
+
+--S 149 of 500
+--m0:=a0-r0
+--E 149
+
+--S 150 of 500
+--d0:=D(m0,x)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^5
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+r0:=-1/12*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+115/216*(1-2*x)^(3/2)*_
+ (3+5*x)^(3/2)/(2+3*x)^3+3244595/108864*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))/sqrt(7)-40/243*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(10)+2675/864*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-_
+ 97235/36288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (262812195x + 700832520x + 700832520x + 311481120x + 51913520)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+ +--+
+--R (- 1451520x - 3870720x - 3870720x - 1720320x - 286720)\|7 \|10
+--R *
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (5370975x + 12310776x + 8842644x + 2031504)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (8817984x + 23514624x + 23514624x + 10450944x + 1741824)\|7
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 153
+
+--S 154 of 500
+--m0:=a0-r0
+--E 154
+
+--S 155 of 500
+--d0:=D(m0,x)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^6
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+r0:=1/5*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+11/8*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)/(2+3*x)^4+483153/6272*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))/sqrt(7)-1331/448*(3+5*x)^(3/2)*sqrt(1-2*x)/_
+ (2+3*x)^2+121/16*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_
+ 43923/6272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x
+--R +
+--R 77304480
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (17153435x + 46327530x + 47166452x + 21361768x + 3620448)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2 +-+
+--R (7620480x + 25401600x + 33868800x + 22579200x + 7526400x + 1003520)\|7
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x
+--R +
+--R 77304480
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 4 3 2
+--R (240148090x + 648585420x + 660330328x + 299064752x + 50686272)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 769797756x - 2565992520x - 3421323360x - 2280882240x - 760294080x
+--R +
+--R - 101372544
+--R /
+--R 5 4 3 2
+--R 106686720x + 355622400x + 474163200x + 316108800x + 105369600x
+--R +
+--R 14049280
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 4831530atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 2415765atan(------------------------------------------------) - 452556\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 62720\|7
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^7
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+r0:=-1/18*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^6+23/108*(1-2*x)^(3/2)*_
+ (3+5*x)^(3/2)/(2+3*x)^5+41068005/175616*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1459/864*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^4-241207/108864*sqrt(1-2*x)*sqrt(3+5*x)/_
+ (2+3*x)^3+8346895/3048192*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 872316385/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 29938575645x + 119754302580x + 199590504300x + 177413781600x
+--R +
+--R 2
+--R 88706890800x + 23655170880x + 2628352320
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 872316385x + 2946673460x + 3982356144x + 2692519968x + 910641904x
+--R +
+--R 123208128
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3 2
+--R 128024064x + 512096256x + 853493760x + 758661120x + 379330560x
+--R +
+--R 101154816x + 11239424
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R - 29938575645x - 119754302580x - 199590504300x - 177413781600x
+--R +
+--R 2
+--R - 88706890800x - 23655170880x - 2628352320
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 5 4 3 2
+--R 12212429390x + 41253428440x + 55752986016x + 37695279552x
+--R +
+--R 12748986656x + 1724913792
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R - 39295692324x - 157182769296x - 261971282160x - 232863361920x
+--R +
+--R 2
+--R - 116431680960x - 31048448256x - 3449827584
+--R /
+--R 6 5 4 3
+--R 1792336896x + 7169347584x + 11948912640x + 10621255680x
+--R +
+--R 2
+--R 5310627840x + 1416167424x + 157351936
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 82136010atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 41068005atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 7700508\|7
+--R /
+--R +-+
+--R 351232\|7
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+r0:=-1/21*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^7+115/756*(1-2*x)^(3/2)*_
+ (3+5*x)^(3/2)/(2+3*x)^6+1891543995/2458624*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1921/1512*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^5-443563/254016*sqrt(1-2*x)*sqrt(3+5*x)/_
+ (2+3*x)^4+2199649/1524096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 384136145/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 40175505215/597445632*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R 4136806717065x + 19305098012970x + 38610196025940x
+--R +
+--R 4 3 2
+--R 42900217806600x + 28600145204400x + 11440058081760x
+--R +
+--R 2542235129280x + 242117631360
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 6 5 4 3
+--R 120526515645x + 487483968610x + 821723878536x + 738910550592x
+--R +
+--R 2
+--R 373848853744x + 100906793184x + 11351210112
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 7 6 5 4
+--R 5377010688x + 25092716544x + 50185433088x + 55761592320x
+--R +
+--R 3 2
+--R 37174394880x + 14869757952x + 3304390656x + 314703872
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R 8273613434130x + 38610196025940x + 77220392051880x
+--R +
+--R 4 3 2
+--R 85800435613200x + 57200290408800x + 22880116163520x
+--R +
+--R 5084470258560x + 484235262720
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R \|7 atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 6 5 4
+--R 3374742438060x + 13649551121080x + 23008268599008x
+--R +
+--R 3 2
+--R 20689495416576x + 10467767904832x + 2825390209152x + 317833883136
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 7 6 5
+--R - 9503357259627x - 44349000544926x - 88698001089852x
+--R +
+--R 4 3 2
+--R - 98553334544280x - 65702223029520x - 26280889211808x - 5840197602624x
+--R +
+--R - 556209295488
+--R /
+--R 7 6 5 4
+--R 150556299264x + 702596063232x + 1405192126464x + 1561324584960x
+--R +
+--R 3 2
+--R 1040883056640x + 416353222656x + 92522938368x + 8811708416
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 7566175980atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R 3783087990atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R +-+
+--R - 620769303\|7
+--R /
+--R +-+
+--R 9834496\|7
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(5/2)
+--R
+--R
+--R (1)
+--R 7 6 5 4 3 2 +--------+
+--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+r0:=17/1200*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(7/2)+1/45*(1-2*x)^(5/2)*_
+ (2+3*x)^3*(3+5*x)^(7/2)+932023556783/6553600000*_
+ asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 7702674023/4915200000*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 700243093/3072000000*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 122147797/4147200000*(3+5*x)^(7/2)*sqrt(1-2*x)+_
+ 193049/12960000*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)+_
+ 2197/756000*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+ 1/432000000*(3+5*x)^(7/2)*(7919314+9176285*x)*sqrt(1-2*x)-_
+ 84729414253/6553600000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 19572494692443asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 8 7 6
+--R 41287680000000x + 102445056000000x + 59625676800000x
+--R +
+--R 5 4 3
+--R - 46327577600000x - 60250198784000x - 5712426076800x
+--R +
+--R 2
+--R 16445681555360x + 6397508631020x - 1496712721437
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 137625600000\|10
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500
+--a0:=integrate(t0,x)
+--E 173
+
+--S 174 of 500
+--m0:=a0-r0
+--E 174
+
+--S 175 of 500
+--d0:=D(m0,x)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2)
+--R
+--R
+--R (1)
+--R 6 5 4 3 2 +--------+ +------+
+--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+r0:=-132451/153600*(1-2*x)^(7/2)*(3+5*x)^(3/2)-12041/38400*(1-2*x)^(7/2)*_
+ (3+5*x)^(5/2)-999/11200*(1-2*x)^(7/2)*(3+5*x)^(7/2)-3/80*_
+ (1-2*x)^(7/2)*(2+3*x)*(3+5*x)^(7/2)+21331366001/327680000*_
+ asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+176292281/98304000*_
+ (1-2*x)^(3/2)*sqrt(3+5*x)+16026571/24576000*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)-1456961/819200*(1-2*x)^(7/2)*sqrt(3+5*x)+_
+ 1939215091/327680000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 447958686021asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 7 6 5 4
+--R 774144000000x + 1362124800000x + 97008640000x - 1013681408000x
+--R +
+--R 3 2
+--R - 413675529600x + 252700365920x + 169330465940x - 22414998339
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 6881280000\|10
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500
+--a0:=integrate(t0,x)
+--E 178
+
+--S 179 of 500
+--m0:=a0-r0
+--E 179
+
+--S 180 of 500
+--d0:=D(m0,x)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+
+--R (1) (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+r0:=-407/960*(1-2*x)^(7/2)*(3+5*x)^(3/2)-37/240*(1-2*x)^(7/2)*_
+ (3+5*x)^(5/2)-3/70*(1-2*x)^(7/2)*(3+5*x)^(7/2)+_
+ 65547757/2048000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 541717/614400*(1-2*x)^(3/2)*sqrt(3+5*x)+49247/153600*_
+ (1-2*x)^(5/2)*sqrt(3+5*x)-4477/5120*(1-2*x)^(7/2)*_
+ sqrt(3+5*x)+5958887/2048000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 1376502897asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 1843200000x + 1879040000x - 1272064000x - 1600483200x
+--R +
+--R 2
+--R 287177440x + 540576580x - 24901623
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 43008000\|10
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500
+--a0:=integrate(t0,x)
+--E 183
+
+--S 184 of 500
+--m0:=a0-r0
+--E 184
+
+--S 185 of 500
+--d0:=D(m0,x)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (1) (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+r0:=-11/48*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/12*(1-2*x)^(7/2)*(3+5*x)^(5/2)+_
+ 1771561/102400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 14641/30720*(1-2*x)^(3/2)*sqrt(3+5*x)+_
+ 1331/7680*(1-2*x)^(5/2)*sqrt(3+5*x)-121/256*(1-2*x)^(7/2)*_
+ sqrt(3+5*x)+161051/102400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 5314683asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2 +--+
+--R (5120000x + 1280000x - 4905600x - 748640x + 1895020x + 96003)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 307200\|10
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500
+--a0:=integrate(t0,x)
+--E 188
+
+--S 189 of 500
+--m0:=a0-r0
+--E 189
+
+--S 190 of 500
+--d0:=D(m0,x)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R 3x + 2
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+r0:=37/360*(1-2*x)^(3/2)*(3+5*x)^(5/2)+1/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)-_
+ 98/729*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_
+ 109715471/9331200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 14557/28800*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 4783/32400*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 1994287/3110400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3
+--R - 1254400\|7 \|10 atan(-------------) + 109715471asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R 4 3 2 +--+
+--R (62208000x - 35510400x - 35831520x + 25518780x + 6495351)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 9331200\|10
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 193
+
+--S 194 of 500
+--m0:=a0-r0
+--E 194
+
+--S 195 of 500
+--d0:=D(m0,x)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^2
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R 2
+--R 9x + 12x + 4
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+r0:=-5/18*(1-2*x)^(3/2)*(3+5*x)^(5/2)-1/3*(1-2*x)^(5/2)*(3+5*x)^(5/2)/_
+ (2+3*x)+1295/729*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_
+ 660959/93312*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1453/288*(3+5*x)^(3/2)*sqrt(1-2*x)-247/324*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)-155777/31104*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3
+--R (497280x + 331520)\|7 \|10 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R (- 1982877x - 1321918)asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (777600x - 643680x - 181044x + 218547x - 136974)\|10 \|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R /
+--R +--+
+--R (279936x + 186624)\|10
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 198
+
+--S 199 of 500
+--m0:=a0-r0
+--E 199
+
+--S 200 of 500
+--d0:=D(m0,x)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^3
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+r0:=-1/6*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^2+185/36*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)/(2+3*x)+81733/5832*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(5/2)-21935/2916*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*_
+ sqrt(7)-785/36*(3+5*x)^(3/2)*sqrt(1-2*x)+575/162*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)+34145/1944*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +-+ +-+ \|7 \|5x + 3
+--R (- 394830x - 526440x - 175480)\|2 \|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 +-+ \|2 \|5x + 3
+--R (735597x + 980796x + 326932)\|5 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +--------+ +------+
+--R (64800x - 86940x + 95193x + 361602x + 159612)\|2 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (52488x + 69984x + 23328)\|2
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 203
+
+--S 204 of 500
+--m0:=a0-r0
+--E 204
+
+--S 205 of 500
+--d0:=D(m0,x)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^4
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+r0:=-1/9*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^3+185/108*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)/(2+3*x)^2-21935/1458*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(5/2)+408665/5832*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_
+ sqrt(7)+2075/72*(3+5*x)^(3/2)*sqrt(1-2*x)-10385/648*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)-48625/1944*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 +-+ \|7 \|5x + 3
+--R (11033955x + 22067910x + 14711940x + 3269320)\|2 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 3 2 +-+ +-+ \|2 \|5x + 3
+--R (- 2368980x - 4737960x - 3158640x - 701920)\|5 \|7 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +-+ +--------+
+--R (97200x - 280260x - 1261593x - 1173042x - 323952)\|2 \|7 \|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R /
+--R 3 2 +-+ +-+
+--R (157464x + 314928x + 209952x + 46656)\|2 \|7
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 500
+--m0:=a0-r0
+--E 209
+
+--S 210 of 500
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+r0:=-1/12*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^4+185/216*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)/(2+3*x)^3-3304795/326592*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1850/729*asin(sqrt(2/11)*_
+ sqrt(3+5*x))*sqrt(10)-3485/4032*(3+5*x)^(3/2)*sqrt(1-2*x)/_
+ (2+3*x)+1165/2592*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2+_
+ 249575/108864*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (- 267688395x - 713835720x - 713835720x - 317260320x - 52876720)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (67132800x + 179020800x + 179020800x + 79564800x + 13260800)\|7
+--R *
+--R +-+ +------+
+--R +--+ \|2 \|5x + 3
+--R \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+
+--R (10886400x + 88425945x + 136691784x + 77996556x + 15279216)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (26453952x + 70543872x + 70543872x + 31352832x + 5225472)\|7
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 500
+--m0:=a0-r0
+--E 214
+
+--S 215 of 500
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^6
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+r0:=-1/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+37/72*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)/(2+3*x)^4+109715471/4572288*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-200/729*asin(sqrt(2/11)*_
+ sqrt(3+5*x))*sqrt(10)-32453/36288*(3+5*x)^(3/2)*sqrt(1-2*x)/_
+ (2+3*x)^2+2543/1296*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_
+ 3248687/1524096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 133304297265x + 444347657550x + 592463543400x + 394975695600x
+--R +
+--R 131658565200x + 17554475360
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R - 1524096000x - 5080320000x - 6773760000x - 4515840000x
+--R +
+--R - 1505280000x - 200704000
+--R *
+--R +-+ +------+
+--R +-+ +--+ \|2 \|5x + 3
+--R \|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2
+--R (1471239045x + 5428407510x + 6440871564x + 3132020376x + 542283936)
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 5555329920x + 18517766400x + 24690355200x + 16460236800x
+--R +
+--R 5486745600x + 731566080
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 218
+
+--S 219 of 500
+--m0:=a0-r0
+--E 219
+
+--S 220 of 500
+--d0:=D(m0,x)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^7
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 7 6 5 4 3 2
+--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+r0:=1/6*(1-2*x)^(5/2)*(3+5*x)^(7/2)/(2+3*x)^6+11/12*(1-2*x)^(3/2)*_
+ (3+5*x)^(7/2)/(2+3*x)^5+8857805/175616*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))/sqrt(7)-73205/37632*(3+5*x)^(3/2)*sqrt(1-2*x)/_
+ (2+3*x)^2-1331/1344*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+_
+ 121/32*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-805255/175616*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 19372019535x + 77488078140x + 129146796900x + 114797152800x
+--R +
+--R 2
+--R 57398576400x + 15306287040x + 1700698560
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 568572155x + 1905431420x + 2573967504x + 1743189856x + 589734736x
+--R +
+--R 79536960
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3 2
+--R 384072192x + 1536288768x + 2560481280x + 2275983360x + 1137991680x
+--R +
+--R 303464448x + 33718272
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R - 19372019535x - 77488078140x - 129146796900x - 114797152800x
+--R +
+--R 2
+--R - 57398576400x - 15306287040x - 1700698560
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 5 4 3 2
+--R 7960010170x + 26676039880x + 36035545056x + 24404657984x
+--R +
+--R 8256286304x + 1113517440
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R - 25367319180x - 101469276720x - 169115461200x - 150324854400x
+--R +
+--R 2
+--R - 75162427200x - 20043313920x - 2227034880
+--R /
+--R 6 5 4 3
+--R 5377010688x + 21508042752x + 35846737920x + 31863767040x
+--R +
+--R 2
+--R 15931883520x + 4248502272x + 472055808
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 17715610atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 8857805atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 1657020\|7
+--R /
+--R +-+
+--R 351232\|7
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^8
+--R
+--R
+--R (1)
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+r0:=-1/21*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^7+185/756*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)/(2+3*x)^6+327738785/2458624*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-129911/84672*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^4+7163/4536*(3+5*x)^(5/2)*sqrt(1-2*x)/_
+ (2+3*x)^5-5777249/4572288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 200146505/128024064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 20886641735/1792336896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 7 6 5
+--R 2150294168385x + 10034706119130x + 20069412238260x
+--R +
+--R 4 3 2
+--R 22299346931400x + 14866231287600x + 5946492515040x
+--R +
+--R 1321442781120x + 125851693440
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 6 5 4 3
+--R 62659925205x + 253441751890x + 427105196104x + 384048502848x
+--R +
+--R 2
+--R 194338741616x + 52456780256x + 5897927808
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 7 6 5 4
+--R 16131032064x + 75278149632x + 150556299264x + 167284776960x
+--R +
+--R 3 2
+--R 111523184640x + 44609273856x + 9913171968x + 944111616
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R 8601176673540x + 40138824476520x + 80277648953040x
+--R +
+--R 4 3 2
+--R 89197387725600x + 59464925150400x + 23785970060160x
+--R +
+--R 5285771124480x + 503406773760
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R \|7 atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 6 5 4
+--R 3508955811480x + 14192738105840x + 23917890981824x
+--R +
+--R 3 2
+--R 21506716159488x + 10882969530496x + 2937579694336x + 330283957248
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 7 6 5
+--R - 13402626245631x - 62545589146278x - 125091178292556x
+--R +
+--R 4 3 2
+--R - 138990198102840x - 92660132068560x - 37064052827424x
+--R +
+--R - 8236456183872x - 784424398464
+--R /
+--R 7 6 5 4
+--R 903337795584x + 4215576379392x + 8431152758784x + 9367947509760x
+--R +
+--R 3 2
+--R 6245298339840x + 2498119335936x + 555137630208x + 52870250496
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2621910280atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R 1310955140atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R +-+
+--R - 291824553\|7
+--R /
+--R +-+
+--R 19668992\|7
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^9
+--R
+--R
+--R (1)
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R /
+--R 9 8 7 6 5 4 3
+--R 19683x + 118098x + 314928x + 489888x + 489888x + 326592x + 145152x
+--R +
+--R 2
+--R 41472x + 6912x + 512
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+r0:=-1/24*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^8+185/1008*(1-2*x)^(3/2)*_
+ (3+5*x)^(5/2)/(2+3*x)^7+106656830005/275365888*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-720833/508032*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^5+47365/36288*(3+5*x)^(5/2)*sqrt(1-2*x)/_
+ (2+3*x)^6-75045071/85349376*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 372439373/512096256*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 64983635965/14338695168*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 6796051494355/200741732352*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 8 7 6
+--R 2099326384988415x + 11196407386604880x + 26124950568744720x
+--R +
+--R 5 4 3
+--R 34833267424992960x + 29027722854160800x + 15481452188885760x
+--R +
+--R 2
+--R 5160484062961920x + 982949345326080x + 81912445443840
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 7 6 5
+--R 61164463449195x + 288163475473440x + 581931572602156x
+--R +
+--R 4 3 2
+--R 652979564561296x + 439702534402320x + 177688060285568x
+--R +
+--R 39899303549504x + 3840133416192
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 8 7 6
+--R 5420026773504x + 28906809458688x + 67449222070272x
+--R +
+--R 5 4 3
+--R 89932296093696x + 74943580078080x + 39969909374976x
+--R +
+--R 2
+--R 13323303124992x + 2537772023808x + 211481001984
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 7 6
+--R 2099326384988415x + 11196407386604880x + 26124950568744720x
+--R +
+--R 5 4 3
+--R 34833267424992960x + 29027722854160800x + 15481452188885760x
+--R +
+--R 2
+--R 5160484062961920x + 982949345326080x + 81912445443840
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 7 6 5
+--R 856302488288730x + 4034288656628160x + 8147042016430184x
+--R +
+--R 4 3 2
+--R 9141713903858144x + 6155835481632480x + 2487632843997952x
+--R +
+--R 558590249693056x + 53761867826688
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 8 7 6
+--R - 2755715740710156x - 14697150617120832x - 34293351439948608x
+--R +
+--R 5 4 3
+--R - 45724468586598144x - 38103723822165120x - 20321986038488064x
+--R +
+--R 2
+--R - 6773995346162688x - 1290284827840512x - 107523735653376
+--R /
+--R 8 7 6
+--R 75880374829056x + 404695332421632x + 944289108983808x
+--R +
+--R 5 4 3
+--R 1259052145311744x + 1049210121093120x + 559578731249664x
+--R +
+--R 2
+--R 186526243749888x + 35528808333312x + 2960734027776
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 213313660010atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 106656830005atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R - 20000694876\|7
+--R /
+--R +-+
+--R 550731776\|7
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^4/sqrt(3+5*x)
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R (1) ------------------------------------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+r0:=12679836719/1280000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 149/6300*(1-2*x)^(3/2)*(2+3*x)^4*sqrt(3+5*x)+1/35*(1-2*x)^(5/2)*_
+ (2+3*x)^4*sqrt(3+5*x)-29880867787/34560000000*sqrt(1-2*x)*_
+ sqrt(3+5*x)-280447621/1728000000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 5575081/216000000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 3090401/75600000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 5647/945000*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 266276571099asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 248832000000x + 311731200000x - 147923712000x - 275707382400x
+--R +
+--R 2
+--R 23172376480x + 98827130860x - 920643741
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 26880000000\|10
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500
+--a0:=integrate(t0,x)
+--E 238
+
+--S 239 of 500
+--m0:=a0-r0
+--E 239
+
+--S 240 of 500
+--d0:=D(m0,x)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3/sqrt(3+5*x)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R (1) -------------------------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+r0:=368012183/64000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 17/500*(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)+1/30*(1-2*x)^(5/2)*_
+ (2+3*x)^3*sqrt(3+5*x)-800452163/1728000000*sqrt(1-2*x)*_
+ sqrt(3+5*x)+499583/10800000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 3037/180000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-7/144000000*_
+ (3860014+4790855*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 1104036549asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 691200000x + 338688000x - 729302400x - 233839520x + 334643860x
+--R +
+--R 39899709
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 192000000\|10
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500
+--a0:=integrate(t0,x)
+--E 243
+
+--S 244 of 500
+--m0:=a0-r0
+--E 244
+
+--S 245 of 500
+--d0:=D(m0,x)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2/sqrt(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R (1) ----------------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+r0:=6531217/1600000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+53977/480000*_
+ (1-2*x)^(3/2)*sqrt(3+5*x)+4907/120000*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)-369/4000*(1-2*x)^(7/2)*sqrt(3+5*x)-_
+ 3/50*(1-2*x)^(7/2)*(2+3*x)*sqrt(3+5*x)+593747/1600000*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 19593651asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (6912000x - 2217600x - 6256480x + 3384140x + 1498491)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 4800000\|10
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+--a0:=integrate(t0,x)
+--E 248
+
+--S 249 of 500
+--m0:=a0-r0
+--E 249
+
+--S 250 of 500
+--d0:=D(m0,x)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)/sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R (1) --------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+r0:=65219/16000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+539/4800*_
+ (1-2*x)^(3/2)*sqrt(3+5*x)+49/1200*(1-2*x)^(5/2)*sqrt(3+5*x)-_
+ 3/40*(1-2*x)^(7/2)*sqrt(3+5*x)+5929/16000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 195657asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (28800x - 35360x + 2980x + 21537)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 48000\|10
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 500
+--m0:=a0-r0
+--E 254
+
+--S 255 of 500
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(1-2*x)^(5/2)/sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+r0:=1331/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+11/60*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)+1/15*(1-2*x)^(5/2)*sqrt(3+5*x)+121/200*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3 2 +--+ +--------+ +------+
+--R 3993asin(-------------) + (160x - 380x + 513)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R -----------------------------------------------------------------------
+--R +--+
+--R 600\|10
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 500
+--m0:=a0-r0
+--E 259
+
+--S 260 of 500
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R +------+
+--R (3x + 2)\|5x + 3
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+r0:=98/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_
+ 17687/1350*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/15*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)-239/450*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3
+--R 4900\|7 \|10 atan(-------------) - 17687asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R +--+ +--------+ +------+
+--R (180x - 807)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 1350\|10
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 500
+--m0:=a0-r0
+--E 264
+
+--S 265 of 500
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|5x + 3
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+r0:=346/135*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+175/27*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+2/3*(1-2*x)^(3/2)*sqrt(3+5*x)+_
+ (1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)+74/45*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +-+ \|7 \|5x + 3
+--R (2625x + 1750)\|5 \|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ \|2 \|5x + 3 +-+ +--------+ +------+
+--R (1038x + 692)\|2 asin(-------------) + (36x + 759)\|5 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R (405x + 270)\|5
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 500
+--m0:=a0-r0
+--E 269
+
+--S 270 of 500
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^3*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) --------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|5x + 3
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+r0:=-8/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+3035/108*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+1/2*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)/(2+3*x)^2+95/12*(1-2*x)^(3/2)*sqrt(3+5*x)/_
+ (2+3*x)+91/18*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +-+ +-+ \|7 \|5x + 3
+--R (27315x + 36420x + 12140)\|5 \|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 +-+ \|2 \|5x + 3
+--R (- 288x - 384x - 128)\|2 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+ +------+
+--R (5481x + 3948)\|5 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (972x + 1296x + 432)\|5
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 273
+
+--S 274 of 500
+--m0:=a0-r0
+--E 274
+
+--S 275 of 500
+--d0:=D(m0,x)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^4*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|5x + 3
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+r0:=6655/8*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1/3*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)/(2+3*x)^3+55/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+_
+ 605/8*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (539055x + 1078110x + 718740x + 159720)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (15707x + 21638x + 7488)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (648x + 1296x + 864x + 192)\|7
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 2695275x - 5390550x - 3593700x - 798600)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 2 +--------+ +------+ 3
+--R (1099490x + 1514660x + 524160)\|- 2x + 1 \|5x + 3 + 4953312x
+--R +
+--R 2
+--R 9906624x + 6604416x + 1467648
+--R /
+--R 3 2
+--R 45360x + 90720x + 60480x + 13440
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 66550atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+
+--R - 33275atan(-----------------------------------------------) + 8736\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R /
+--R +-+
+--R 80\|7
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^5*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|5x + 3
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+r0:=1643785/448*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/4*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^4+235/72*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)/(2+3*x)^3+38875/864*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^2+3879245/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (399439755x + 1065172680x + 1065172680x + 473410080x + 78901680)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (11637735x + 23794744x + 16236916x + 3699216)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (108864x + 290304x + 290304x + 129024x + 21504)\|7
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R - 1997198775x - 5325863400x - 5325863400x - 2367050400x
+--R +
+--R - 394508400
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 3 2 +--------+
+--R (814641450x + 1665632080x + 1136584120x + 258945120)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 4 3 2
+--R 3670547076x + 9788125536x + 9788125536x + 4350278016x + 725046336
+--R /
+--R 4 3 2
+--R 7620480x + 20321280x + 20321280x + 9031680x + 1505280
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 16437850atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R - 8218925atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R 2157876\|7
+--R /
+--R +-+
+--R 4480\|7
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^6*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|5x + 3
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+r0:=104040277/6272*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/5*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5+_
+ 61/24*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4+_
+ 14131/432*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 2347559/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 245529161/169344*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 379226809665x + 1264089365550x + 1685452487400x + 1123634991600x
+--R +
+--R 374544997200x + 49939332960
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2
+--R 11048812245x + 29956486710x + 30475811404x + 13788819736x
+--R +
+--R 2341358496
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 22861440x + 76204800x + 101606400x + 67737600x + 22579200x
+--R +
+--R 3010560
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R - 1896134048325x - 6320446827750x - 8427262437000x
+--R +
+--R 2
+--R - 5618174958000x - 1872724986000x - 249696664800
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 4 3 2
+--R 773416857150x + 2096954069700x + 2133306798280x + 965217381520x
+--R +
+--R 163895094720
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 3484819451484x + 11616064838280x + 15488086451040x + 10325390967360x
+--R +
+--R 3441796989120x + 458906265216
+--R /
+--R 5 4 3 2
+--R 1600300800x + 5334336000x + 7112448000x + 4741632000x + 1580544000x
+--R +
+--R 210739200
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 5202013850atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R - 2601006925atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R 682896228\|7
+--R /
+--R +-+
+--R 313600\|7
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^7*sqrt(3+5*x))
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R /
+--R 7 6 5 4 3 2
+--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128)
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+r0:=13391796605/175616*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/6*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6+_
+ 25/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+_
+ 7445/288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 1729615/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 302171615/338688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 31603880465/4741632*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R 29287859175135x + 117151436700540x + 195252394500900x
+--R +
+--R 3 2
+--R 173557684000800x + 86778842000400x + 23141024533440x + 2571224948160
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 853304772555x + 2882422865340x + 3896029345680x + 2634024494432x
+--R +
+--R 890768460368x + 120549503808
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3 2
+--R 384072192x + 1536288768x + 2560481280x + 2275983360x + 1137991680x
+--R +
+--R 303464448x + 33718272
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R - 117151436700540x - 468605746802160x - 781009578003600x
+--R +
+--R 3 2
+--R - 694230736003200x - 347115368001600x - 92564098133760x
+--R +
+--R - 10284899792640
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R \|7 atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 5 4 3
+--R 47785067263080x + 161415680459040x + 218177643358080x
+--R +
+--R 2
+--R 147505371688192x + 49883033780608x + 6750772213248
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4
+--R 182626847511129x + 730507390044516x + 1217512316740860x
+--R +
+--R 3 2
+--R 1082233170436320x + 541116585218160x + 144297756058176x + 16033084006464
+--R /
+--R 6 5 4 3
+--R 21508042752x + 86032171008x + 143386951680x + 127455068160x
+--R +
+--R 2
+--R 63727534080x + 16994009088x + 1888223232
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 107134372840atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R -
+--R 53567186420
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 11929377981\|7
+--R /
+--R +-+
+--R 1404928\|7
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(3/2)
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R (1) ------------------------------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+r0:=1298595837/320000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 2/5*(1-2*x)^(5/2)*(2+3*x)^4/sqrt(3+5*x)-13/75*(1-2*x)^(3/2)*_
+ (2+3*x)^4*sqrt(3+5*x)-320899019/2880000000*sqrt(1-2*x)*_
+ sqrt(3+5*x)-7/240000000*(6000382-1842385*x)*sqrt(1-2*x)*_
+ sqrt(3+5*x)+5421479/18000000*(2+3*x)^2*sqrt(1-2*x)*_
+ sqrt(3+5*x)+1178663/900000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 4439/11250*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R 1298595837\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 3456000000x + 4043520000x - 2530224000x - 3673002400x
+--R +
+--R 2
+--R 938891620x + 1366129125x + 168414751
+--R *
+--R +--+ +--------+
+--R \|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R 320000000\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500
+--a0:=integrate(t0,x)
+--E 298
+
+--S 299 of 500
+--m0:=a0-r0
+--E 299
+
+--S 300 of 500
+--d0:=D(m0,x)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(3/2)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R (1) -------------------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+r0:=24319911/8000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*_
+ (1-2*x)^(5/2)*(2+3*x)^3/sqrt(3+5*x)-22/125*(1-2*x)^(3/2)*_
+ (2+3*x)^3*sqrt(3+5*x)-2987467/24000000*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 386939/1200000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 205079/150000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 1019/2500*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R 24319911\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 34560000x + 12528000x - 39487200x - 4101140x + 20337375x
+--R +
+--R 6089453
+--R *
+--R +--+ +--------+
+--R \|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R 8000000\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500
+--a0:=integrate(t0,x)
+--E 303
+
+--S 304 of 500
+--m0:=a0-r0
+--E 304
+
+--S 305 of 500
+--d0:=D(m0,x)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(3/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R (1) ----------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+r0:=236313/80000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*(1-2*x)^(7/2)/_
+ sqrt(3+5*x)+651/8000*(1-2*x)^(3/2)*sqrt(3+5*x)+_
+ 651/22000*(1-2*x)^(5/2)*sqrt(3+5*x)-9/200*(1-2*x)^(7/2)*_
+ sqrt(3+5*x)+21483/80000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R 236313\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (144000x - 77600x - 112620x + 134625x + 79699)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R 80000\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+--a0:=integrate(t0,x)
+--E 308
+
+--S 309 of 500
+--m0:=a0-r0
+--E 309
+
+--S 310 of 500
+--d0:=D(m0,x)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R (1) --------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+r0:=2541/1000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(1-2*x)^(7/2)/_
+ sqrt(3+5*x)+7/100*(1-2*x)^(3/2)*sqrt(3+5*x)+7/275*(1-2*x)^(5/2)*_
+ sqrt(3+5*x)+231/1000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R 2541\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (800x - 1340x + 1125x + 943)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R 1000\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+--a0:=integrate(t0,x)
+--E 313
+
+--S 314 of 500
+--m0:=a0-r0
+--E 314
+
+--S 315 of 500
+--d0:=D(m0,x)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(1-2*x)^(5/2)/(3+5*x)^(3/2)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+r0:=-363/50*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(1-2*x)^(5/2)/_
+ sqrt(3+5*x)-1/5*(1-2*x)^(3/2)*sqrt(3+5*x)-33/50*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3 2 +--+ +--------+
+--R - 363\|5x + 3 asin(-------------) + (20x - 75x - 149)\|10 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------------------------
+--R +--+ +------+
+--R 50\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+--a0:=integrate(t0,x)
+--E 318
+
+--S 319 of 500
+--m0:=a0-r0
+--E 319
+
+--S 320 of 500
+--d0:=D(m0,x)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 2 +------+
+--R (15x + 19x + 6)\|5x + 3
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+r0:=338/225*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-98/9*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-2*(1-2*x)^(5/2)/sqrt(3+5*x)-_
+ 4/5*(1-2*x)^(3/2)*sqrt(3+5*x)-128/75*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +-+ +------+ \|7 \|5x + 3
+--R - 2450\|5 \|7 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+
+--R 338\|2 \|5x + 3 asin(-------------) + (60x - 2142)\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R /
+--R +-+ +------+
+--R 225\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 323
+
+--S 324 of 500
+--m0:=a0-r0
+--E 324
+
+--S 325 of 500
+--d0:=D(m0,x)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 3 2 +------+
+--R (45x + 87x + 56x + 12)\|5x + 3
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+r0:=-8/45*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-665/9*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-33*(1-2*x)^(3/2)/sqrt(3+5*x)+_
+ (1-2*x)^(5/2)/((2+3*x)*sqrt(3+5*x))-202/15*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +-+ +------+ \|7 \|5x + 3
+--R (- 9975x - 6650)\|5 \|7 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3
+--R (- 24x - 16)\|2 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+
+--R (- 10209x - 6561)\|5 \|- 2x + 1
+--R /
+--R +-+ +------+
+--R (135x + 90)\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 328
+
+--S 329 of 500
+--m0:=a0-r0
+--E 329
+
+--S 330 of 500
+--d0:=D(m0,x)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 4 3 2 +------+
+--R (135x + 351x + 342x + 148x + 24)\|5x + 3
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+r0:=-1815/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+1/2*_
+ (1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x))+55/4*(1-2*x)^(3/2)/((2+3*x)*_
+ sqrt(3+5*x))-1815/4*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +-+ +------+ \|7 \|5x + 3
+--R (- 16335x - 21780x - 7260)\|7 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +--------+
+--R (- 16657x - 21843x - 7148)\|- 2x + 1
+--R /
+--R 2 +------+
+--R (36x + 48x + 16)\|5x + 3
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 980100x - 1894860x - 1219680x - 261360)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 2 +--------+ +------+ 3
+--R (- 399768x - 524232x - 171552)\|- 2x + 1 \|5x + 3 + 1527885x
+--R +
+--R 2
+--R 2953911x + 1901368x + 407436
+--R /
+--R 3 2
+--R 4320x + 8352x + 5376x + 1152
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R 43560\|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R - 21780\|7 atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 33953
+--R /
+--R 96
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +------+
+--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+r0:=-147015/8*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/3*(1-2*x)^(5/2)/((2+3*x)^3*sqrt(3+5*x))+235/36*(1-2*x)^(3/2)/_
+ ((2+3*x)^2*sqrt(3+5*x))-578245/216*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 39155/216*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +------+
+--R (- 3969405x - 7938810x - 5292540x - 1176120)\|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+
+--R (- 578245x - 1143741x - 753654x - 165424)\|7 \|- 2x + 1
+--R /
+--R 3 2 +-+ +------+
+--R (216x + 432x + 288x + 64)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (59541075x + 154806795x + 150837390x + 65274660x + 10585080)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R 3 2 +--------+ +------+
+--R (- 24286290x - 48037122x - 31653468x - 6947808)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R - 68392485x - 177820461x - 173260962x - 74978428x - 12158664
+--R /
+--R 4 3 2
+--R 45360x + 117936x + 114912x + 49728x + 8064
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 882090atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R 441045atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +-+
+--R - 72373\|7
+--R /
+--R +-+
+--R 48\|7
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|5x + 3
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+r0:=-46095555/448*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/4*(1-2*x)^(5/2)/((2+3*x)^4*sqrt(3+5*x))+305/72*(1-2*x)^(3/2)/_
+ ((2+3*x)^3*sqrt(3+5*x))-181304825/12096*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 71215/864*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+3997345/4032*_
+ sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 4 3 2
+--R - 3733739955x - 9956639880x - 9956639880x - 4425173280x
+--R +
+--R - 737528880
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2
+--R (- 543914475x - 1438446565x - 1426133132x - 628209228x - 103735088)
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +------+
+--R (36288x + 96768x + 96768x + 43008x + 7168)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 280030496625x + 914766288975x + 1194796785600x + 779936790600x
+--R +
+--R 254447463600x + 33188799600
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 4 3 2
+--R - 114222039750x - 302073778650x - 299487957720x - 131923937880x
+--R +
+--R - 21784368480
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 514655705340x - 1681208637444x - 2195864342784x - 1433411445984x
+--R +
+--R - 467637776704x - 60996231744
+--R /
+--R 5 4 3 2
+--R 38102400x + 124467840x + 162570240x + 106122240x + 34621440x + 4515840
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 1382866650atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R 691433325atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R - 181536404\|7
+--R /
+--R +-+
+--R 13440\|7
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^(3/2))
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R /
+--R 7 6 5 4 3 2
+--R (3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192)
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+r0:=-3538809681/6272*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/5*(1-2*x)^(5/2)/((2+3*x)^5*sqrt(3+5*x))+25/8*(1-2*x)^(3/2)/_
+ ((2+3*x)^4*sqrt(3+5*x))-4639661185/56448*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 7501/144*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+587477/1344*_
+ sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+102293609/18816*sqrt(1-2*x)/_
+ ((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 5 4 3
+--R - 4299653762415x - 14332179208050x - 19109572277400x
+--R +
+--R 2
+--R - 12739714851600x - 4246571617200x - 566209548960
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3
+--R - 626354259975x - 2074037896035x - 2746600901250x
+--R +
+--R 2
+--R - 1818284414692x - 601741553688x - 79638637088
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R /
+--R 5 4 3 2
+--R (7620480x + 25401600x + 33868800x + 22579200x + 7526400x + 1003520)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R 64494806436225x + 253679571982485x + 415633197033450x
+--R +
+--R 3 2
+--R 363081873270600x + 178356007922400x + 46712287789200x + 5095885940640
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 5 4 3
+--R - 26306878918950x - 87109591633470x - 115357237852500x
+--R +
+--R 2
+--R - 76367945417064x - 25273145254896x - 3344822757696
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4
+--R - 84665826054180x - 333018915813108x - 545624212349160x
+--R +
+--R 3 2
+--R - 476637242971680x - 234137593038720x - 61321750557760x - 6689645515392
+--R /
+--R 6 5 4 3 2
+--R 1600300800x + 6294516480x + 10313049600x + 9009100800x + 4425523200x
+--R +
+--R 1159065600x + 126443520
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 106164290430atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R 53082145215atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 9954829636\|7
+--R /
+--R +-+
+--R 188160\|7
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(5/2)
+--R
+--R
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R (1) ------------------------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(3/2)+_
+ 88296593/40000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 508/75*(1-2*x)^(3/2)*(2+3*x)^4/sqrt(3+5*x)+_
+ 59754401/40000000*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 21/10000000*(191622-763085*x)*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 525259/250000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 109323/12500*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 1676/625*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (1324448895x + 794669337)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 1555200000x + 1626480000x - 1419228000x - 1405199700x
+--R +
+--R 2
+--R 865945995x + 980658710x + 210855251
+--R *
+--R +--+ +--------+
+--R \|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (600000000x + 360000000)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500
+--a0:=integrate(t0,x)
+--E 353
+
+--S 354 of 500
+--m0:=a0-r0
+--E 354
+
+--S 355 of 500
+--d0:=D(m0,x)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(5/2)
+--R
+--R
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R (1) -------------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(3/2)+_
+ 766843/400000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 376/75*(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x)+_
+ 195643/400000*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 34069/20000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 16009/2500*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 247/125*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (11502645x + 6901587)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R (6480000x + 972000x - 7724700x + 3074745x + 7876210x + 2322001)
+--R *
+--R +--+ +--------+
+--R \|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (6000000x + 3600000)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500
+--a0:=integrate(t0,x)
+--E 358
+
+--S 359 of 500
+--m0:=a0-r0
+--E 359
+
+--S 360 of 500
+--d0:=D(m0,x)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R (1) ----------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 500
+r0:=-2/825*(1-2*x)^(7/2)/(3+5*x)^(3/2)+_
+ 3619/5000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 76/1815*(1-2*x)^(7/2)/sqrt(3+5*x)+329/16500*(1-2*x)^(3/2)*_
+ sqrt(3+5*x)+329/45375*(1-2*x)^(5/2)*sqrt(3+5*x)+_
+ 329/5000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (54285x + 32571)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +--------+
+--R (36000x - 35100x + 3585x + 40930x + 10633)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (75000x + 45000)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+--a0:=integrate(t0,x)
+--E 363
+
+--S 364 of 500
+--m0:=a0-r0
+--E 364
+
+--S 365 of 500
+--d0:=D(m0,x)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(5/2)
+--R
+--R
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R (1) --------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+r0:=-2/165*(1-2*x)^(7/2)/(3+5*x)^(3/2)-1001/250*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)-182/825*(1-2*x)^(5/2)/sqrt(3+5*x)-_
+ 91/825*(1-2*x)^(3/2)*sqrt(3+5*x)-91/250*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (- 15015x - 9009)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (900x - 2715x - 7970x - 3707)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (3750x + 2250)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+--a0:=integrate(t0,x)
+--E 368
+
+--S 369 of 500
+--m0:=a0-r0
+--E 369
+
+--S 370 of 500
+--d0:=D(m0,x)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(1-2*x)^(5/2)/(3+5*x)^(5/2)
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+r0:=-2/15*(1-2*x)^(5/2)/(3+5*x)^(3/2)+22/25*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(2/5)+4/15*(1-2*x)^(3/2)/sqrt(3+5*x)+4/25*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3
+--R (330x + 198)\|2 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+
+--R (60x + 380x + 158)\|5 \|- 2x + 1
+--R /
+--R +-+ +------+
+--R (375x + 225)\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+--a0:=integrate(t0,x)
+--E 373
+
+--S 374 of 500
+--m0:=a0-r0
+--E 374
+
+--S 375 of 500
+--d0:=D(m0,x)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(5/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ----------------------------------
+--R 3 2 +------+
+--R (75x + 140x + 87x + 18)\|5x + 3
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+r0:=-2/3*(1-2*x)^(5/2)/(3+5*x)^(3/2)-8/75*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(2/5)+98/3*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_
+ 218/15*(1-2*x)^(3/2)/sqrt(3+5*x)+148/25*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +-+ +------+ \|7 \|5x + 3
+--R (12250x + 7350)\|5 \|7 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3
+--R (- 40x - 24)\|2 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+
+--R (12430x + 7216)\|5 \|- 2x + 1
+--R /
+--R +-+ +------+
+--R (375x + 225)\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 378
+
+--S 379 of 500
+--m0:=a0-r0
+--E 379
+
+--S 380 of 500
+--d0:=D(m0,x)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(5/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) --------------------------------------------
+--R 4 3 2 +------+
+--R (225x + 570x + 541x + 228x + 36)\|5x + 3
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+r0:=-55/3*(1-2*x)^(3/2)/(3+5*x)^(3/2)+(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2))+_
+ 385*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+385*sqrt(1-2*x)/_
+ sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +-+ +------+ \|7 \|5x + 3
+--R (17325x + 21945x + 6930)\|7 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +--------+
+--R (17667x + 21988x + 6823)\|- 2x + 1
+--R /
+--R 2 +------+
+--R (45x + 57x + 18)\|5x + 3
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (779625x + 1455300x + 904365x + 187110)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (318006x + 395784x + 122814)\|- 2x + 1 \|5x + 3 + 1023450x + 1910440x
+--R +
+--R 1187202x + 245628
+--R /
+--R 3 2
+--R 4050x + 7560x + 4698x + 972
+--R Type: Union(Expression(Integer),...)
+--E 383
+
+--S 384 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R - 20790\|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 10395\|7 atan(------------------------------------------------) + 13646
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R 54
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(5/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+r0:=1/2*(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(3/2))+235/12*(1-2*x)^(3/2)/_
+ ((2+3*x)*(3+5*x)^(3/2))+13145/4*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))*sqrt(7)-4279/12*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 40213/12*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +-+ +------+
+--R (1774575x + 3430845x + 2208360x + 473220)\|7 \|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +--------+
+--R (1809585x + 3458634x + 2200321x + 465916)\|- 2x + 1
+--R /
+--R 3 2 +------+
+--R (540x + 1044x + 672x + 144)\|5x + 3
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 79855875x - 202301550x - 192009015x - 80920620x - 12776940)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 3 2 +--------+ +------+
+--R (32572530x + 62255412x + 39605778x + 8386488)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 104831100x + 265572120x + 252060556x + 106228848x + 16772976
+--R /
+--R 4 3 2
+--R 48600x + 123120x + 116856x + 49248x + 7776
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R - 709830\|7 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 354915\|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 465916
+--R /
+--R 216
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(5/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ---------------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+r0:=1/3*(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(3/2))+_
+ 305/36*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2))+_
+ 1361195/8*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 196735/72*sqrt(1-2*x)/(3+5*x)^(3/2)+7975/24*_
+ sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+1784635/72*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (551283975x + 1433338335x + 1396586070x + 604370580x + 98006040)
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (80308575x + 207031680x + 199977747x + 85776638x + 13784768)\|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R /
+--R 4 3 2 +-+ +------+
+--R (3240x + 8424x + 8208x + 3552x + 576)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 24807778875x + 79384892400x + 101546508195x + 64904499990x
+--R +
+--R 20728277460x + 2646163080
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 4 3 2
+--R 10118880450x + 26085991680x + 25197196122x + 10807856388x
+--R +
+--R 1736880768
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 32566514400x + 104212846080x + 133305598944x + 85203651008x
+--R +
+--R 27211132032x + 3473761536
+--R /
+--R 5 4 3 2
+--R 2041200x + 6531840x + 8355312x + 5340384x + 1705536x + 217728
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 73504530atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 36752265atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R 6892384\|7
+--R /
+--R +-+
+--R 432\|7
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R /
+--R 7 6 5 4 3 2
+--R (6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288)
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+r0:=1/4*(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(3/2))+125/24*(1-2*x)^(3/2)/_
+ ((2+3*x)^3*(3+5*x)^(3/2))+519421265/448*atan(sqrt(7)*sqrt(3+5*x)/_
+ sqrt(1-2*x))/sqrt(7)-25024175/1344*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 12595/96*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+2992825/1344*_
+ sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+227000875/1344*_
+ sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 631096836975x + 2061583000785x + 2692679837760x + 1757721560760x
+--R +
+--R 573441076560x + 74796662160
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 91935354375x + 298295199450x + 386933096475x + 250814924064x
+--R +
+--R 81243850516x + 10520317456
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R /
+--R 5 4 3 2 +-+
+--R (544320x + 1778112x + 2322432x + 1516032x + 494592x + 64512)\|7
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R 28399357663875x + 109810849633650x + 176833333720395x
+--R +
+--R 3 2
+--R 151799825853720x + 73263330585720x + 18848758864320x + 2019509878320
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 5 4 3
+--R 11583854651250x + 37585195130700x + 48753570155850x
+--R +
+--R 2
+--R 31602680432064x + 10236725165016x + 1325559999456
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4
+--R - 37281374984700x - 144154649940840x - 232138694904732x
+--R +
+--R 3 2
+--R - 199275853251552x - 96176742182752x - 24743786656512x - 2651119998912
+--R /
+--R 6 5 4 3 2
+--R 342921600x + 1325963520x + 2135258496x + 1832979456x + 884653056x
+--R +
+--R 227598336x + 24385536
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 28048748310atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 14024374155atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R - 2630079364\|7
+--R /
+--R +-+
+--R 24192\|7
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R /
+--R 8 7 6 5 4 3 2
+--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x
+--R +
+--R 7104x + 576
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+r0:=1/5*(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(3/2))+89/24*(1-2*x)^(3/2)/_
+ ((2+3*x)^4*(3+5*x)^(3/2))+46975917593/6272*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-754386765/6272*sqrt(1-2*x)/_
+ (3+5*x)^(3/2)+10945/144*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2))+_
+ 3329689/4032*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_
+ 270667969/18816*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 20529722435/18816*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 6 5 4
+--R 856136098132425x + 3367468652654205x + 5517321521297850x
+--R +
+--R 3 2
+--R 4819729145041800x + 2367586246687200x + 620082112227600x
+--R +
+--R 67645321333920
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 6 5 4
+--R 124718063792625x + 487807977825900x + 794682454662945x
+--R +
+--R 3 2
+--R 690189860794590x + 337048538999244x + 87747789308536x + 9514465420576
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R /
+--R 6 5 4 3 2
+--R 114307200x + 449608320x + 736646400x + 643507200x + 316108800x
+--R +
+--R 82790400x + 9031680
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 6 5
+--R - 77052248831918250x - 349303528038029400x - 678402244160133570x
+--R +
+--R 4 3 2
+--R - 731710985203845900x - 473348136034105200x - 183657047421592800x
+--R +
+--R - 39572512980343200x - 3652847352031680
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R \|7 atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R 6 5 4
+--R 31428952075741500x + 122927610412126800x + 200259978575062140x
+--R +
+--R 3 2
+--R 173927844920236680x + 84936231827809488x + 22112442905751072x
+--R +
+--R 2397645285985152
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 7 6 5
+--R 88506827939686275x + 401230953326577780x + 779253449548971159x
+--R +
+--R 4 3 2
+--R 840487062360576330x + 543716019540591240x + 210959484537721360x
+--R +
+--R 45455358546801840x + 4195879250474016
+--R /
+--R 7 6 5 4
+--R 144027072000x + 652922726400x + 1268078353920x + 1367723750400x
+--R +
+--R 3 2
+--R 884788531200x + 343294156800x + 73969459200x + 6827950080
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 25366995500220atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R -
+--R 12683497750110
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +-+
+--R 2081289310751\|7
+--R /
+--R +-+
+--R 3386880\|7
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(2+3*x)^4*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|5x + 3
+--R (1) ------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+r0:=1067352517/2560000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 96151531/2560000*sqrt(1-2*x)*sqrt(3+5*x)-25529/16000*(2+3*x)^2*_
+ sqrt(1-2*x)*sqrt(3+5*x)-313/800*(2+3*x)^3*sqrt(1-2*x)*_
+ sqrt(3+5*x)-1/10*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 21/640000*(390718+637135*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 1067352517asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 20736000x - 82339200x - 146144160x - 163168620x - 157419203)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 2560000\|10
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500
+--a0:=integrate(t0,x)
+--E 408
+
+--S 409 of 500
+--m0:=a0-r0
+--E 409
+
+--S 410 of 500
+--d0:=D(m0,x)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|5x + 3
+--R (1) --------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+r0:=677017/5120*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 11835/1024*sqrt(1-2*x)*sqrt(3+5*x)-2829/1280*(2+3*x)*_
+ sqrt(1-2*x)*sqrt(3+5*x)-81/160*(2+3*x)^2*sqrt(1-2*x)*_
+ sqrt(3+5*x)-1/8*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 677017asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (- 17280x - 57888x - 88092x - 97295)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 5120\|10
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500
+--a0:=integrate(t0,x)
+--E 413
+
+--S 414 of 500
+--m0:=a0-r0
+--E 414
+
+--S 415 of 500
+--d0:=D(m0,x)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 2 +------+
+--R (9x + 12x + 4)\|5x + 3
+--R (1) ------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+r0:=68959/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 181/400*(3+5*x)^(3/2)*sqrt(1-2*x)-1/10*(2+3*x)*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-6269/1600*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3 2 +--+ +--------+ +------+
+--R 68959asin(-------------) + (- 2400x - 6660x - 9401)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R -----------------------------------------------------------------------------
+--R +--+
+--R 1600\|10
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+--a0:=integrate(t0,x)
+--E 418
+
+--S 419 of 500
+--m0:=a0-r0
+--E 419
+
+--S 420 of 500
+--d0:=D(m0,x)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +------+
+--R (3x + 2)\|5x + 3
+--R (1) -----------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+r0:=1177/80*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/20*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-107/80*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R \|2 \|5x + 3 +--+ +--------+ +------+
+--R 1177asin(-------------) + (- 60x - 143)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------------------
+--R +--+
+--R 80\|10
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+--a0:=integrate(t0,x)
+--E 423
+
+--S 424 of 500
+--m0:=a0-r0
+--E 424
+
+--S 425 of 500
+--d0:=D(m0,x)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) -----------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+r0:=11/2*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/2*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R \|2 \|5x + 3 +--+ +--------+ +------+
+--R 11asin(-------------) - \|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R (2) -------------------------------------------------
+--R +--+
+--R 2\|10
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+--a0:=integrate(t0,x)
+--E 428
+
+--S 429 of 500
+--m0:=a0-r0
+--E 429
+
+--S 430 of 500
+--d0:=D(m0,x)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) -------------------
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+r0:=-2/3*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1/3*_
+ asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)
+--R
+--R
+--R +-+ +------+ +-+ +------+
+--R \|7 \|5x + 3 +-+ +--+ \|2 \|5x + 3
+--R - 2atan(-------------) + \|7 \|10 asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R (2) -----------------------------------------------------
+--R +-+
+--R 3\|7
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 500
+--m0:=a0-r0
+--E 434
+
+--S 435 of 500
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) --------------------------
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+r0:=11/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R +-+ +------+
+--R \|7 \|5x + 3 +-+ +--------+ +------+
+--R (33x + 22)atan(-------------) - \|7 \|- 2x + 1 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R (2) --------------------------------------------------------
+--R +-+
+--R (21x + 14)\|7
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R (- 33x - 22)\|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+
+--R - 14\|- 2x + 1 \|5x + 3 + 42x + 28
+--R /
+--R 294x + 196
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 22atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 11atan(--------------------------------------------------) + 2\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 14\|7
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+r0:=451/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+29/196*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (4059x + 5412x + 1804)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+
+--R (87x + 44)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (1764x + 2352x + 784)\|7
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (4059x + 5412x + 1804)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +--------+ +------+ 2
+--R (1218x + 616)\|- 2x + 1 \|5x + 3 + 2772x + 3696x + 1232
+--R /
+--R 2
+--R 24696x + 32928x + 10976
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 902atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 451atan(------------------------------------------------) + 44\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 392\|7
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+r0:=15235/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 25/588*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 3895/8232*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (411345x + 822690x + 548460x + 121880)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (11685x + 15930x + 5296)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (74088x + 148176x + 98784x + 21952)\|7
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 411345x - 822690x - 548460x - 121880)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (163590x + 223020x + 74144)\|- 2x + 1 \|5x + 3 + 437913x + 875826x
+--R +
+--R 583884x + 129752
+--R /
+--R 3 2
+--R 1037232x + 2074464x + 1382976x + 307328
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 30470atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R - 15235atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +-+
+--R 2317\|7
+--R /
+--R +-+
+--R 5488\|7
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=sqrt(3+5*x)/((2+3*x)^5*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+r0:=375265/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/28*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+1/56*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^3+305/1568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 32735/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (30396465x + 81057240x + 81057240x + 36025440x + 6004240)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (883845x + 1806120x + 1230876x + 278960)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 121585860x - 324228960x - 324228960x - 144101760x - 24016960)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 3 2 +--------+ +------+
+--R (49495320x + 101142720x + 68929056x + 15621760)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 187827255x + 500872680x + 500872680x + 222610080x + 37101680
+--R /
+--R 4 3 2
+--R 99574272x + 265531392x + 265531392x + 118013952x + 19668992
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 3002120atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 1501060atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 331265\|7
+--R /
+--R +-+
+--R 175616\|7
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(2+3*x)^3*(3+5*x)^(3/2)/sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +------+
+--R (135x + 351x + 342x + 148x + 24)\|5x + 3
+--R (1) --------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+r0:=333216939/512000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 875641/128000*(3+5*x)^(3/2)*sqrt(1-2*x)-5029/3200*(2+3*x)*_
+ (3+5*x)^(3/2)*sqrt(1-2*x)-309/800*(2+3*x)^2*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-1/10*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 30292449/512000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 333216939asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 6912000x - 26870400x - 46785120x - 51453140x - 49229901)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 512000\|10
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500
+--a0:=integrate(t0,x)
+--E 458
+
+--S 459 of 500
+--m0:=a0-r0
+--E 459
+
+--S 460 of 500
+--d0:=D(m0,x)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(2+3*x)^2*(3+5*x)^(3/2)/sqrt(1-2*x)
+--R
+--R
+--R 3 2 +------+
+--R (45x + 87x + 56x + 12)\|5x + 3
+--R (1) ---------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+r0:=5274027/25600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 14529/6400*(3+5*x)^(3/2)*sqrt(1-2*x)-251/800*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)-3/40*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 479457/25600*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 5274027asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (- 144000x - 469600x - 698580x - 760653)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 25600\|10
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500
+--a0:=integrate(t0,x)
+--E 463
+
+--S 464 of 500
+--m0:=a0-r0
+--E 464
+
+--S 465 of 500
+--d0:=D(m0,x)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(2+3*x)*(3+5*x)^(3/2)/sqrt(1-2*x)
+--R
+--R
+--R 2 +------+
+--R (15x + 19x + 6)\|5x + 3
+--R (1) -------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+r0:=21417/320*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-59/80*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-1/10*(3+5*x)^(5/2)*sqrt(1-2*x)-1947/320*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3 2 +--+ +--------+ +------+
+--R 21417asin(-------------) + (- 800x - 2140x - 2943)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +--+
+--R 320\|10
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+--a0:=integrate(t0,x)
+--E 468
+
+--S 469 of 500
+--m0:=a0-r0
+--E 469
+
+--S 470 of 500
+--d0:=D(m0,x)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(3+5*x)^(3/2)/sqrt(1-2*x)
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -----------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+r0:=363/16*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/4*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-33/16*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R \|2 \|5x + 3 +--+ +--------+ +------+
+--R 363asin(-------------) + (- 20x - 45)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R (2) --------------------------------------------------------------
+--R +--+
+--R 16\|10
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+--a0:=integrate(t0,x)
+--E 473
+
+--S 474 of 500
+--m0:=a0-r0
+--E 474
+
+--S 475 of 500
+--d0:=D(m0,x)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -------------------
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+r0:=29/18*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_
+ 2/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-5/6*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ \|7 \|5x + 3 +-+ +-+ \|2 \|5x + 3
+--R 4\|2 atan(-------------) + 29\|5 \|7 asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R +-+ +-+ +--------+ +------+
+--R - 15\|2 \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+ +-+
+--R 18\|2 \|7
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 478
+
+--S 479 of 500
+--m0:=a0-r0
+--E 479
+
+--S 480 of 500
+--d0:=D(m0,x)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)^2*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) --------------------------
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+r0:=-103/63*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 5/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/7*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)+5/21*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R (- 309x - 206)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +--+ \|2 \|5x + 3 +-+ +--------+ +------+
+--R (105x + 70)\|7 \|10 asin(-------------) + 3\|7 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R /
+--R +-+
+--R (189x + 126)\|7
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 483
+
+--S 484 of 500
+--m0:=a0-r0
+--E 484
+
+--S 485 of 500
+--d0:=D(m0,x)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)^3*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+r0:=363/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/14*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-33/196*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (3267x + 4356x + 1452)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+
+--R (- 169x - 108)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (1764x + 2352x + 784)\|7
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 3267x - 4356x - 1452)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+ 2
+--R (- 2366x - 1512)\|- 2x + 1 \|5x + 3 - 6804x - 9072x - 3024
+--R /
+--R 2
+--R 24696x + 32928x + 10976
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 726atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 363atan(--------------------------------------------------) - 108\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 392\|7
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)^4*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+r0:=5445/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3-95/1764*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^2+2195/24696*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (147015x + 294030x + 196020x + 43560)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (2195x + 1830x + 288)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (74088x + 148176x + 98784x + 21952)\|7
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 147015x - 294030x - 196020x - 43560)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (30730x + 25620x + 4032)\|- 2x + 1 \|5x + 3 - 27216x - 54432x
+--R +
+--R - 36288x - 8064
+--R /
+--R 3 2
+--R 1037232x + 2074464x + 1382976x + 307328
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 10890atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 5445atan(--------------------------------------------------) - 144\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 5488\|7
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)^5*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+r0:=78045/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/28*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-13/504*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^3+85/14112*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 57595/197568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (6321645x + 16857720x + 16857720x + 7492320x + 1248720)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (172785x + 346760x + 226348x + 48240)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (25286580x + 67430880x + 67430880x + 29969280x + 4994880)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 3 2 +--------+ +------+
+--R (9675960x + 19418560x + 12675488x + 2701440)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R - 32480595x - 86614920x - 86614920x - 38495520x - 6415920
+--R /
+--R 4 3 2
+--R 99574272x + 265531392x + 265531392x + 118013952x + 19668992
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 624360atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R 312180atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R +-+
+--R - 57285\|7
+--R /
+--R +-+
+--R 175616\|7
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3o.input.pdf b/src/axiom-website/CATS/rich3o.input.pdf
new file mode 100644
index 0000000..eb4dbda
Binary files /dev/null and b/src/axiom-website/CATS/rich3o.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3p.input.pamphlet b/src/axiom-website/CATS/rich3p.input.pamphlet
new file mode 100644
index 0000000..a65f92d
--- /dev/null
+++ b/src/axiom-website/CATS/rich3p.input.pamphlet
@@ -0,0 +1,6785 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3p.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 49 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 51 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 rich3p.output
+)spool rich3p.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)^6*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) ------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+r0:=2664057/307328*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 1/35*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-29/1960*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^4-73/11760*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 6107/65856*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+694229/921984*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 3236829255x + 10789430850x + 14385907800x + 9590605200x
+--R +
+--R 3196868400x + 426249120
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (93720915x + 253769850x + 257531412x + 115804328x + 19437408)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 373403520x + 1244678400x + 1659571200x + 1106380800x + 368793600x
+--R +
+--R 49172480
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 6473658510x - 21578861700x - 28771815600x - 19181210400x
+--R +
+--R - 6393736800x - 852498240
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R \|7 atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R 4 3 2
+--R (2624185620x + 7105555800x + 7210879536x + 3242521184x + 544247424)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 7232538033x + 24108460110x + 32144613480x + 21429742320x
+--R +
+--R 7143247440x + 952432992
+--R /
+--R 5 4 3 2
+--R 10455298560x + 34850995200x + 46467993600x + 30978662400x
+--R +
+--R 10326220800x + 1376829440
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 53281140atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R - 26640570atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +-+
+--R 4251933\|7
+--R /
+--R +-+
+--R 6146560\|7
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2 +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3
+--R (1) -------------------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+r0:=2678359321/819200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 22135201/614400*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 382619/76800*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 1569/1280*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 5/16*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 1/12*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 243487211/819200*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 8035077963asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 138240000x - 615168000x - 1229558400x - 1505007200x
+--R +
+--R - 1362715220x - 1202896557
+--R *
+--R +--+ +--------+ +------+
+--R \|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 2457600\|10
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 500
+--m0:=a0-r0
+--E 9
+
+--S 10 of 500
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(2+3*x)^2*(3+5*x)^(5/2)/sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +------+
+--R (225x + 570x + 541x + 228x + 36)\|5x + 3
+--R (1) --------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+r0:=104040277/102400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 859837/76800*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 78167/48000*(3+5*x)^(5/2)*sqrt(1-2*x)-963/4000*(3+5*x)^(7/2)*_
+ sqrt(1-2*x)-3/50*(2+3*x)*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+ 9458207/102400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 312120831asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 6912000x - 26294400x - 44906720x - 48658820x - 46187289)\|10
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 307200\|10
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 500
+--m0:=a0-r0
+--E 14
+
+--S 15 of 500
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(2+3*x)*(3+5*x)^(5/2)/sqrt(1-2*x)
+--R
+--R
+--R 3 2 +------+
+--R (75x + 140x + 87x + 18)\|5x + 3
+--R (1) ----------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+r0:=328757/1024*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 2717/768*(3+5*x)^(3/2)*sqrt(1-2*x)-247/480*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)-3/40*(3+5*x)^(7/2)*sqrt(1-2*x)-29887/1024*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 986271asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (- 28800x - 91360x - 132868x - 142713)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 3072\|10
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 500
+--m0:=a0-r0
+--E 19
+
+--S 20 of 500
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(3+5*x)^(5/2)/sqrt(1-2*x)
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+r0:=1331/64*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-55/48*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-1/6*(3+5*x)^(5/2)*sqrt(1-2*x)-605/64*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ \|2 \|5x + 3
+--R 3993\|5 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +--------+ +------+
+--R (- 800x - 2060x - 2763)\|2 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+
+--R 192\|2
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 500
+--m0:=a0-r0
+--E 24
+
+--S 25 of 500
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -------------------------
+--R +--------+
+--R (3x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+r0:=3035/432*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2/27*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-5/12*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 455/144*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+ +-+ +------+
+--R +-+ \|7 \|5x + 3 +-+ +-+ \|2 \|5x + 3
+--R - 32\|2 atan(-------------) + 3035\|5 \|7 asin(-------------)
+--R +--------+ +--+
+--R \|- 2x + 1 \|11
+--R +
+--R +-+ +-+ +--------+ +------+
+--R (- 900x - 1905)\|2 \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+ +-+
+--R 432\|2 \|7
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 500
+--m0:=a0-r0
+--E 29
+
+--S 30 of 500
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) --------------------------
+--R 2 +--------+
+--R (9x + 12x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+r0:=125/54*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+173/189*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+5/21*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 1/7*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)-185/126*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ \|7 \|5x + 3
+--R (1038x + 692)\|2 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +-+ \|2 \|5x + 3
+--R (2625x + 1750)\|5 \|7 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +--------+ +------+
+--R (- 1575x - 1056)\|2 \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R +-+ +-+
+--R (1134x + 756)\|2 \|7
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 500
+--m0:=a0-r0
+--E 34
+
+--S 35 of 500
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^3*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) ----------------------------------
+--R 3 2 +--------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+r0:=-17687/5292*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 25/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-_
+ 169/588*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-1/14*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^2+1195/1764*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (- 159183x - 212244x - 70748)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R 2 +-+ +--+ \|2 \|5x + 3
+--R (44100x + 58800x + 19600)\|7 \|10 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+ +------+
+--R (2781x + 1812)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (47628x + 63504x + 21168)\|7
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 38
+
+--S 39 of 500
+--m0:=a0-r0
+--E 39
+
+--S 40 of 500
+--d0:=D(m0,x)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^4*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) --------------------------------------------
+--R 4 3 2 +--------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+r0:=6655/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 55/588*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-1/21*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^3-605/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (539055x + 1078110x + 718740x + 159720)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (- 37685x - 48170x - 15408)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (222264x + 444528x + 296352x + 65856)\|7
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (539055x + 1078110x + 718740x + 159720)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 2 +--------+ +------+ 3
+--R (- 527590x - 674380x - 215712)\|- 2x + 1 \|5x + 3 + 1456056x
+--R +
+--R 2
+--R 2912112x + 1941408x + 431424
+--R /
+--R 3 2
+--R 3111696x + 6223392x + 4148928x + 921984
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 13310atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 6655atan(------------------------------------------------) + 2568\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 5488\|7
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^5*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -------------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+r0:=6655/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 23/504*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3-1/28*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^4-295/6048*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 4315/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (1617165x + 4312440x + 4312440x + 1916640x + 319440)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+ +------+
+--R (12945x + 6920x - 6484x - 3600)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (762048x + 2032128x + 2032128x + 903168x + 150528)\|7
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (3234330x + 8624880x + 8624880x + 3833280x + 638880)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 3 2 +--------+ +------+ 4
+--R (362460x + 193760x - 181552x - 100800)\|- 2x + 1 \|5x + 3 + 893025x
+--R +
+--R 3 2
+--R 2381400x + 2381400x + 1058400x + 176400
+--R /
+--R 4 3 2
+--R 21337344x + 56899584x + 56899584x + 25288704x + 4214784
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 26620atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+
+--R 13310atan(---------------------------------------------------) + 525\|7
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R /
+--R +-+
+--R 12544\|7
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^6*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) ------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+r0:=933031/307328*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 157/5880*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-1/35*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^5-1721/105840*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_
+ 12371/592704*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 1948963/8297856*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 3400897995x + 11336326650x + 15115102200x + 10076734800x
+--R +
+--R 3358911600x + 447854880
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (87703335x + 231277650x + 222865988x + 93291272x + 14330592)\|7
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 1120210560x + 3734035200x + 4978713600x + 3319142400x + 1106380800x
+--R +
+--R 147517440
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 13603591980x - 45345306600x - 60460408800x - 40306939200x
+--R +
+--R - 13435646400x - 1791419520
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R \|7 atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 4 3 2
+--R 4911386760x + 12951548400x + 12480495328x + 5224311232x
+--R +
+--R 802513152
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 14473450089x + 48244833630x + 64326444840x + 42884296560x
+--R +
+--R 14294765520x + 1905968736
+--R /
+--R 5 4 3 2
+--R 62731791360x + 209105971200x + 278807961600x + 185871974400x
+--R +
+--R 61957324800x + 8260976640
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 37321240atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 18660620atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 2836263\|7
+--R /
+--R +-+
+--R 12293120\|7
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^7*sqrt(1-2*x))
+--R
+--R
+--R (1)
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R /
+--R 7 6 5 4 3 2
+--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128)
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+r0:=52573169/8605184*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 17/980*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-1/42*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)/(2+3*x)^6-3037/493920*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-_
+ 71369/2963520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 958171/16595712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 122343637/232339968*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 6 5 4 3
+--R 574887603015x + 2299550412060x + 3832584020100x + 3406741351200x
+--R +
+--R 2
+--R 1703370675600x + 454232180160x + 50470242240
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 16516390995x + 55658284380x + 74931979536x + 50261760608x
+--R +
+--R 16771747280x + 2225100096
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 6 5 4 3
+--R 94097687040x + 376390748160x + 627317913600x + 557615923200x
+--R +
+--R 2
+--R 278807961600x + 74348789760x + 8260976640
+--R *
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 574887603015x + 2299550412060x + 3832584020100x + 3406741351200x
+--R +
+--R 2
+--R 1703370675600x + 454232180160x + 50470242240
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 5 4 3 2
+--R 231229473930x + 779215981320x + 1049047713504x + 703664648512x
+--R +
+--R 234804461920x + 31151401344
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R 709667861868x + 2838671447472x + 4731119079120x + 4205439181440x
+--R +
+--R 2
+--R 2102719590720x + 560725224192x + 62302802688
+--R /
+--R 6 5 4 3
+--R 1317367618560x + 5269470474240x + 8782450790400x + 7806622924800x
+--R +
+--R 2
+--R 3903311462400x + 1040883056640x + 115653672960
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 525731690atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 262865845atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R 46356252\|7
+--R /
+--R +-+
+--R 86051840\|7
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(2+3*x)^4/(sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) -------------------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+r0:=10866247/128000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 949753/128000*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 9079/6400*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 259/800*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 3/40*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R 10866247asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+ +------+
+--R (- 259200x - 891360x - 1387620x - 1555473)\|10 \|- 2x + 1 \|5x + 3
+--R /
+--R +--+
+--R 128000\|10
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 500
+--m0:=a0-r0
+--E 64
+
+--S 65 of 500
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) ---------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+r0:=44437/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 799/320*sqrt(1-2*x)*sqrt(3+5*x)-1/10*(2+3*x)^2*sqrt(1-2*x)*_
+ sqrt(3+5*x)-3/400*(114+185*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R \|2 \|5x + 3 2 +--+ +--------+ +------+
+--R 44437asin(-------------) + (- 1440x - 4140x - 6003)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R -----------------------------------------------------------------------------
+--R +--+
+--R 1600\|10
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 500
+--m0:=a0-r0
+--E 69
+
+--S 70 of 500
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) --------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+r0:=3827/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 333/400*sqrt(1-2*x)*sqrt(3+5*x)-3/20*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R \|2 \|5x + 3 +--+ +--------+ +------+
+--R 3827asin(-------------) + (- 180x - 453)\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R (2) -----------------------------------------------------------------
+--R +--+
+--R 400\|10
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 500
+--m0:=a0-r0
+--E 74
+
+--S 75 of 500
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 3x + 2
+--R (1) --------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+r0:=37/10*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/10*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R \|2 \|5x + 3 +--+ +--------+ +------+
+--R 37asin(-------------) - 3\|10 \|- 2x + 1 \|5x + 3
+--R +--+
+--R \|11
+--R (2) --------------------------------------------------
+--R +--+
+--R 10\|10
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 500
+--m0:=a0-r0
+--E 79
+
+--S 80 of 500
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=1/(sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) --------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+r0:=asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)
+--R
+--R
+--R +-+ +------+
+--R +-+ \|2 \|5x + 3
+--R \|2 asin(-------------)
+--R +--+
+--R \|11
+--R (2) -----------------------
+--R +-+
+--R \|5
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 500
+--m0:=a0-r0
+--E 84
+
+--S 85 of 500
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=1/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (3x + 2)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+r0:=2*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)
+--R
+--R
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 2atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R (2) --------------------
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R \|7 atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R (3) - ------------------------------------------------------------------
+--R 7
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R /
+--R +-+
+--R \|7
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=1/((2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------
+--R 2 +--------+ +------+
+--R (9x + 12x + 4)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+r0:=37/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 3/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R +-+ +------+
+--R \|7 \|5x + 3 +-+ +--------+ +------+
+--R (111x + 74)atan(-------------) + 3\|7 \|- 2x + 1 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R (2) ----------------------------------------------------------
+--R +-+
+--R (21x + 14)\|7
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R (- 111x - 74)\|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+
+--R 42\|- 2x + 1 \|5x + 3 - 126x - 84
+--R /
+--R 294x + 196
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 74atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 37atan(--------------------------------------------------) - 6\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 14\|7
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=1/((2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+r0:=3827/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 3/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+333/196*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 \|7 \|5x + 3
+--R (34443x + 45924x + 15308)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+
+--R (999x + 708)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 2 +-+
+--R (1764x + 2352x + 784)\|7
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (34443x + 45924x + 15308)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +--------+ +------+ 2
+--R (13986x + 9912)\|- 2x + 1 \|5x + 3 - 44604x - 59472x - 19824
+--R /
+--R 2
+--R 24696x + 32928x + 10976
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 7654atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 3827atan(------------------------------------------------) - 708\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 392\|7
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=1/((2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+r0:=222185/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 1/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+185/196*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^2+19415/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 \|7 \|5x + 3
+--R (5998995x + 11997990x + 7998660x + 1777480)atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+ +------+
+--R (174735x + 240750x + 83232)\|7 \|- 2x + 1 \|5x + 3
+--R /
+--R 3 2 +-+
+--R (74088x + 148176x + 98784x + 21952)\|7
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 5998995x - 11997990x - 7998660x - 1777480)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 2 +--------+ +------+ 3
+--R (2446290x + 3370500x + 1165248)\|- 2x + 1 \|5x + 3 + 7865424x
+--R +
+--R 2
+--R 15730848x + 10487232x + 2330496
+--R /
+--R 3 2
+--R 1037232x + 2074464x + 1382976x + 307328
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 444370atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 222185atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R 41616\|7
+--R /
+--R +-+
+--R 5488\|7
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(2+3*x)^4/((3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) -------------------------------
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+r0:=143283/8000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 7/550*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-1/10*(2+3*x)^3*_
+ sqrt(1-2*x)/sqrt(3+5*x)-139839/88000*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 63/22000*(194+305*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R 1576113\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 237600x - 849420x - 1477575x - 632101)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R 88000\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 500
+--m0:=a0-r0
+--E 109
+
+--S 110 of 500
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+r0:=2493/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/44*(2+3*x)*_
+ sqrt(1-2*x)/sqrt(3+5*x)-3/20*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-_
+ 2337/4400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R 27423\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (- 5940x - 19305x - 9451)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R 4400\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 500
+--m0:=a0-r0
+--E 114
+
+--S 115 of 500
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(2+3*x)^2/((3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+r0:=123/50*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*sqrt(1-2*x)/_
+ sqrt(3+5*x)-9/50*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3 +--+ +--------+
+--R 1353\|5x + 3 asin(-------------) + (- 495x - 301)\|10 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) -----------------------------------------------------------------
+--R +--+ +------+
+--R 550\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 500
+--m0:=a0-r0
+--E 119
+
+--S 120 of 500
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 3x + 2
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+r0:=3/5*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/55*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+
+--R 33\|2 \|5x + 3 asin(-------------) - 2\|5 \|- 2x + 1
+--R +--+
+--R \|11
+--R (2) -----------------------------------------------------
+--R +-+ +------+
+--R 55\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 500
+--m0:=a0-r0
+--E 124
+
+--S 125 of 500
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=1/((3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+r0:=-2/11*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +--------+
+--R 2\|- 2x + 1
+--R (2) - ------------
+--R +------+
+--R 11\|5x + 3
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+
+--R - 6\|- 2x + 1 \|5x + 3 - 20x - 12
+--R (3) ----------------------------------
+--R 165x + 99
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 4
+--R (4) - --
+--R 33
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=1/((2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (15x + 19x + 6)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+r0:=-6*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 10/11*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3 +-+ +--------+
+--R - 66\|5x + 3 atan(-------------) - 10\|7 \|- 2x + 1
+--R +--------+
+--R \|- 2x + 1
+--R (2) ----------------------------------------------------
+--R +-+ +------+
+--R 11\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R (495x + 297)\|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +--------+ +------+
+--R - 210\|- 2x + 1 \|5x + 3 - 980x - 588
+--R /
+--R 1155x + 693
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 198atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+
+--R 99atan(-----------------------------------------------) - 28\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R /
+--R +-+
+--R 33\|7
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=1/((2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------
+--R 3 2 +--------+ +------+
+--R (45x + 87x + 56x + 12)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+r0:=-321/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 515/77*sqrt(1-2*x)/sqrt(3+5*x)+3/7*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R (- 10593x - 7062)\|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+
+--R (- 1545x - 997)\|7 \|- 2x + 1
+--R /
+--R +-+ +------+
+--R (231x + 154)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (158895x + 201267x + 63558)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+ 2
+--R (- 64890x - 41874)\|- 2x + 1 \|5x + 3 + 209370x + 265202x + 83748
+--R /
+--R 2
+--R 48510x + 61446x + 19404
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 21186atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R 10593atan(--------------------------------------------------) + 1994\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 462\|7
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=1/((2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (135x + 351x + 342x + 148x + 24)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+r0:=-56421/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 90415/2156*sqrt(1-2*x)/sqrt(3+5*x)+3/14*sqrt(1-2*x)/((2+3*x)^2*_
+ sqrt(3+5*x))+543/196*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +------+ \|7 \|5x + 3
+--R (- 5585679x - 7447572x - 2482524)\|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+
+--R (- 813735x - 1067061x - 349252)\|7 \|- 2x + 1
+--R /
+--R 2 +-+ +------+
+--R (19404x + 25872x + 8624)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (335140740x + 647938764x + 417064032x + 89370864)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 2 +--------+ +------+ 3
+--R (- 136707480x - 179266248x - 58674336)\|- 2x + 1 \|5x + 3 - 522568305x
+--R +
+--R 2
+--R - 1010298723x - 650307224x - 139351548
+--R /
+--R 3 2
+--R 16299360x + 31512096x + 20283648x + 4346496
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 14895144atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R 7447572atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R - 1658947\|7
+--R /
+--R +-+
+--R 51744\|7
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=1/((2+3*x)^4*(3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+r0:=-4616025/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 7396875/30184*sqrt(1-2*x)/sqrt(3+5*x)+1/7*sqrt(1-2*x)/_
+ ((2+3*x)^3*sqrt(3+5*x))+255/196*sqrt(1-2*x)/((2+3*x)^2*_
+ sqrt(3+5*x))+44475/2744*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +------+
+--R (- 1370959425x - 2741918850x - 1827945900x - 406210200)\|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+
+--R (- 199715625x - 395028225x - 260298990x - 57135248)\|7 \|- 2x + 1
+--R /
+--R 3 2 +-+ +------+
+--R (814968x + 1629936x + 1086624x + 241472)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R - 20564391375x - 53467417575x - 52096458150x - 22544666100x
+--R +
+--R - 3655891800
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 3 2 +--------+
+--R (- 8388056250x - 16591185450x - 10932557580x - 2399680416)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 4 3 2
+--R 26996404680x + 70190652168x + 68390891856x + 29596058464x + 4799360832
+--R /
+--R 4 3 2
+--R 171143280x + 444972528x + 433562976x + 187623744x + 30425472
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 304657650atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R - 152328825atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R 28567624\|7
+--R /
+--R +-+
+--R 181104\|7
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(2+3*x)^5/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+r0:=462357/40000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+29/1650*(2+3*x)^3*_
+ sqrt(1-2*x)/(3+5*x)^(3/2)-1/10*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+ 511/90750*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-_
+ 4802371/4840000*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 21/1210000*(21038+30535*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (839177955x + 503506773)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2
+--R (- 117612000x - 502791300x - 1030526145x - 795297410x - 199549721)
+--R *
+--R +--+ +--------+
+--R \|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (72600000x + 43560000)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+--a0:=integrate(t0,x)
+--E 153
+
+--S 154 of 500
+--m0:=a0-r0
+--E 154
+
+--S 155 of 500
+--d0:=D(m0,x)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(2+3*x)^4/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+r0:=8127/2000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+91/3300*(2+3*x)^2*_
+ sqrt(1-2*x)/(3+5*x)^(3/2)-3/20*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 119/36300*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-80633/242000*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (14750505x + 8850303)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +--------+
+--R (- 2940300x - 11712195x - 10891910x - 2953931)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (3630000x + 2178000)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+--a0:=integrate(t0,x)
+--E 158
+
+--S 159 of 500
+--m0:=a0-r0
+--E 159
+
+--S 160 of 500
+--d0:=D(m0,x)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(2+3*x)^3/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+r0:=81/50*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+19/330*(2+3*x)*_
+ sqrt(1-2*x)/(3+5*x)^(3/2)-3/10*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 439/18150*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|2 \|5x + 3
+--R (147015x + 88209)\|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +--------+
+--R (- 49005x - 60010x - 18373)\|10 \|- 2x + 1
+--R /
+--R +--+ +------+
+--R (90750x + 54450)\|10 \|5x + 3
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+--a0:=integrate(t0,x)
+--E 163
+
+--S 164 of 500
+--m0:=a0-r0
+--E 164
+
+--S 165 of 500
+--d0:=D(m0,x)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(2+3*x)^2/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+r0:=9/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/825*sqrt(1-2*x)/_
+ (3+5*x)^(3/2)-404/9075*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +------+ \|2 \|5x + 3
+--R (16335x + 9801)\|2 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +--------+
+--R (- 2020x - 1234)\|5 \|- 2x + 1
+--R /
+--R +-+ +------+
+--R (45375x + 27225)\|5 \|5x + 3
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 500
+--m0:=a0-r0
+--E 169
+
+--S 170 of 500
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(2+3*x)/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 3x + 2
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+r0:=-2/165*sqrt(1-2*x)/(3+5*x)^(3/2)-206/1815*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +--------+
+--R (- 206x - 128)\|- 2x + 1
+--R (2) -------------------------
+--R +------+
+--R (1815x + 1089)\|5x + 3
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+ 2
+--R (- 1854x - 1152)\|- 2x + 1 \|5x + 3 - 6400x - 7680x - 2304
+--R (3) ------------------------------------------------------------
+--R 2
+--R 81675x + 98010x + 29403
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 256
+--R (4) - ----
+--R 3267
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=1/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+r0:=-2/33*sqrt(1-2*x)/(3+5*x)^(3/2)-8/363*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +--------+
+--R (- 40x - 46)\|- 2x + 1
+--R (2) -----------------------
+--R +------+
+--R (1815x + 1089)\|5x + 3
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+ 2
+--R (- 360x - 414)\|- 2x + 1 \|5x + 3 - 2300x - 2760x - 828
+--R (3) ---------------------------------------------------------
+--R 2
+--R 81675x + 98010x + 29403
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 92
+--R (4) - ----
+--R 3267
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=1/((2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------
+--R 3 2 +--------+ +------+
+--R (75x + 140x + 87x + 18)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+r0:=18*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 10/33*sqrt(1-2*x)/(3+5*x)^(3/2)+950/363*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3 +-+ +--------+
+--R (32670x + 19602)\|5x + 3 atan(-------------) + (4750x + 2740)\|7 \|- 2x + 1
+--R +--------+
+--R \|- 2x + 1
+--R ----------------------------------------------------------------------------
+--R +-+ +------+
+--R (1815x + 1089)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (735075x + 882090x + 264627)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +--------+ +------+ 2
+--R (299250x + 172620)\|- 2x + 1 \|5x + 3 - 959000x - 1150800x - 345240
+--R /
+--R 2
+--R 571725x + 686070x + 205821
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 58806atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 29403atan(------------------------------------------------) - 5480\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 3267\|7
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=1/((2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+r0:=1593/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 845/231*sqrt(1-2*x)/(3+5*x)^(3/2)+3/7*sqrt(1-2*x)/((2+3*x)*_
+ (3+5*x)^(3/2))+84235/2541*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +------+ \|7 \|5x + 3
+--R (8673885x + 10986921x + 3469554)\|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +--------+
+--R (1263525x + 1572580x + 487909)\|7 \|- 2x + 1
+--R /
+--R 2 +-+ +------+
+--R (38115x + 48279x + 15246)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 390324825x - 728606340x - 452776797x - 93677958)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 2 +--------+ +------+ 3
+--R (159204150x + 198145080x + 61476534)\|- 2x + 1 \|5x + 3 + 512304450x
+--R +
+--R 2
+--R 956301640x + 594273162x + 122953068
+--R /
+--R 3 2
+--R 24012450x + 44823240x + 27854442x + 5762988
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 10408662atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 5204331atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R 975818\|7
+--R /
+--R +-+
+--R 45738\|7
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=1/((2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+r0:=392283/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 207895/6468*sqrt(1-2*x)/(3+5*x)^(3/2)+3/14*sqrt(1-2*x)/_
+ ((2+3*x)^2*(3+5*x)^(3/2))+753/196*sqrt(1-2*x)/((2+3*x)*_
+ (3+5*x)^(3/2))+20743985/71148*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +------+
+--R (6407942805x + 12388689423x + 7974328824x + 1708784748)\|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +--------+
+--R (933479325x + 1784145090x + 1135041037x + 240342364)\|7 \|- 2x + 1
+--R /
+--R 3 2 +-+ +------+
+--R (3201660x + 6189876x + 3984288x + 853776)\|7 \|5x + 3
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R 288357426225x + 730505479770x + 693339411501x + 292202191908x
+--R +
+--R 46137188196
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 3 2
+--R (117618394950x + 224802281340x + 143015170662x + 30283137864)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R - 378539223300x - 958966032360x - 910176532468x - 383586412944x
+--R +
+--R - 60566275728
+--R /
+--R 4 3 2
+--R 2017045800x + 5109849360x + 4849874568x + 2043939744x + 322727328
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2563177122atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 1281588561atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R - 240342364\|7
+--R /
+--R +-+
+--R 1280664\|7
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=1/((2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 6 5 4 3 2 +--------+
+--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+r0:=41307885/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_
+ 21891025/90552*sqrt(1-2*x)/(3+5*x)^(3/2)+1/7*sqrt(1-2*x)/_
+ ((2+3*x)^3*(3+5*x)^(3/2))+325/196*sqrt(1-2*x)/((2+3*x)^2*_
+ (3+5*x)^(3/2))+79335/2744*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 2184369575/996072*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 2024292904425x + 5263161551505x + 5128208691210x + 2219224813740x
+--R +
+--R 359874294120
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2
+--R 294889892625x + 760212086400x + 734310313245x + 314968389410x
+--R +
+--R 50617099616
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R /
+--R 4 3 2 +-+
+--R (134469720x + 349621272x + 340656624x + 147418656x + 23905728)\|7
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R 91093180699125x + 291498178237200x + 372874752995085x
+--R +
+--R 2
+--R 238326751280970x + 76113413206380x + 9716605941240
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R \|7 atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 4 3 2
+--R 37156126470750x + 95786722886400x + 92523099468870x
+--R +
+--R 39686017065660x + 6377754551616
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3
+--R - 104635035612450x - 334832113959840x - 428306079106962x
+--R +
+--R 2
+--R - 273756256135684x - 87428385311736x - 11161070465328
+--R /
+--R 5 4 3 2
+--R 84715923600x + 271090955520x + 346770513936x + 221641957152x
+--R +
+--R 70784860608x + 9036365184
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 269905720590atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R 134952860295atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R +-+
+--R - 22144981082\|7
+--R /
+--R +-+
+--R 17929296\|7
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(2+3*x)^5*sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 5 4 3 2 +------+
+--R (- 243x - 810x - 1080x - 720x - 240x - 32)\|5x + 3
+--R (1) -------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+r0:=-35439958001/5120000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^5*_
+ sqrt(3+5*x)/sqrt(1-2*x)+3192575743/5120000*sqrt(1-2*x)*_
+ sqrt(3+5*x)+847637/32000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 10389/1600*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)+33/20*(2+3*x)^4*_
+ sqrt(1-2*x)*sqrt(3+5*x)+147/1280000*(1853322+3022165*x)*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 35439958001\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 124416000x - 613267200x - 1429191360x - 2297649240x
+--R +
+--R - 3810769458x + 5389783159
+--R *
+--R +--+ +------+
+--R \|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 5120000\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500
+--a0:=integrate(t0,x)
+--E 203
+
+--S 204 of 500
+--m0:=a0-r0
+--E 204
+
+--S 205 of 500
+--d0:=D(m0,x)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 4 3 2 +------+
+--R (- 81x - 216x - 216x - 96x - 16)\|5x + 3
+--R (1) --------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+r0:=-92108287/51200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^4*_
+ sqrt(3+5*x)/sqrt(1-2*x)+8050753/51200*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 15395/512*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+2203/320*(2+3*x)^2*_
+ sqrt(1-2*x)*sqrt(3+5*x)+27/16*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 92108287\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +------+
+--R (- 518400x - 2283840x - 5020200x - 9587886x + 14050073)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 51200\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 500
+--m0:=a0-r0
+--E 209
+
+--S 210 of 500
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 3 2 +------+
+--R (- 27x - 54x - 36x - 8)\|5x + 3
+--R (1) ----------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+r0:=-1463447/3200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^3*_
+ sqrt(3+5*x)/sqrt(1-2*x)+131833/3200*sqrt(1-2*x)*sqrt(3+5*x)+7/4*_
+ (2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+3/160*(750+1223*x)*sqrt(1-2*x)*_
+ sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 1463447\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +------+
+--R (- 14400x - 57960x - 142686x + 224833)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 3200\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 500
+--m0:=a0-r0
+--E 214
+
+--S 215 of 500
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 2 +------+
+--R (- 9x - 12x - 4)\|5x + 3
+--R (1) --------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+r0:=-17951/160*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*(3+5*x)^(3/2)/_
+ sqrt(1-2*x)+9/40*(3+5*x)^(3/2)*sqrt(1-2*x)+17951/1760*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 17951\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +------+
+--R (- 360x - 1518x + 2809)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 160\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500
+--a0:=integrate(t0,x)
+--E 218
+
+--S 219 of 500
+--m0:=a0-r0
+--E 219
+
+--S 220 of 500
+--d0:=D(m0,x)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R +------+
+--R (- 3x - 2)\|5x + 3
+--R (1) -------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+r0:=-103/4*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(3+5*x)^(3/2)/_
+ sqrt(1-2*x)+103/44*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3 +--+ +------+
+--R - 103\|- 2x + 1 asin(-------------) + (- 6x + 17)\|10 \|5x + 3
+--R +--+
+--R \|11
+--R (2) ---------------------------------------------------------------
+--R +--+ +--------+
+--R 4\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500
+--a0:=integrate(t0,x)
+--E 223
+
+--S 224 of 500
+--m0:=a0-r0
+--E 224
+
+--S 225 of 500
+--d0:=D(m0,x)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - -------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+r0:=-asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+
+--R - \|5 \|- 2x + 1 asin(-------------) + \|2 \|5x + 3
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------
+--R +-+ +--------+
+--R \|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500
+--a0:=integrate(t0,x)
+--E 228
+
+--S 229 of 500
+--m0:=a0-r0
+--E 229
+
+--S 230 of 500
+--d0:=D(m0,x)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - ------------------------
+--R 2 +--------+
+--R (6x + x - 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+r0:=-2/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3 +-+ +------+
+--R - 2\|- 2x + 1 atan(-------------) + 2\|7 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R (2) --------------------------------------------------
+--R +-+ +--------+
+--R 7\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R (4x - 2)\|7 atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +--------+ +------+
+--R - 28\|- 2x + 1 \|5x + 3 + 98x - 49
+--R /
+--R 196x - 98
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 4atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +-+
+--R 2atan(-----------------------------------------------------) + 7\|7
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R /
+--R +-+
+--R 14\|7
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - ---------------------------------
+--R 3 2 +--------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+r0:=29/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))-9/49*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3 +-+ +------+
+--R (87x + 58)\|- 2x + 1 atan(-------------) + (18x + 5)\|7 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R (2) -----------------------------------------------------------------
+--R +-+ +--------+
+--R (147x + 98)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 1392x - 232x + 464)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +--------+ +------+ 2
+--R (- 2016x - 560)\|- 2x + 1 \|5x + 3 + 3990x + 665x - 1330
+--R /
+--R 2
+--R 32928x + 5488x - 10976
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 464atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 232atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 95\|7
+--R /
+--R +-+
+--R 784\|7
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - -----------------------------------------
+--R 4 3 2 +--------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+r0:=1585/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))-15/98*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^2+15/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ \|7 \|5x + 3
+--R (14265x + 19020x + 6340)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +------+
+--R (- 90x + 405x + 212)\|7 \|5x + 3
+--R /
+--R 2 +-+ +--------+
+--R (12348x + 16464x + 5488)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 142650x - 118875x + 31700x + 31700)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (6300x - 28350x - 14840)\|- 2x + 1 \|5x + 3 + 186984x + 155820x
+--R +
+--R - 41552x - 41552
+--R /
+--R 3 2
+--R 1728720x + 1440600x - 384160x - 384160
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 15850atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+
+--R - 7925atan(-----------------------------------------------) + 1484\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R /
+--R +-+
+--R 13720\|7
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^4)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - ----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+r0:=7435/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-1/7*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^3-5/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 565/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 +--------+ \|7 \|5x + 3
+--R (200745x + 401490x + 267660x + 59480)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +------+
+--R (- 10170x - 8055x + 3114x + 2512)\|7 \|5x + 3
+--R /
+--R 3 2 +-+ +--------+
+--R (74088x + 148176x + 98784x + 21952)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (802980x + 1204470x + 267660x - 297400x - 118960)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 3 2 +--------+ +------+ 4
+--R (284760x + 225540x - 87192x - 70336)\|- 2x + 1 \|5x + 3 - 1127574x
+--R +
+--R 3 2
+--R - 1691361x - 375858x + 417620x + 167048
+--R /
+--R 4 3 2
+--R 4148928x + 6223392x + 1382976x - 1536640x - 614656
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 29740atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R 14870atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R +-+
+--R - 2983\|7
+--R /
+--R +-+
+--R 10976\|7
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^5)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - ----------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+r0:=1244755/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))-27/196*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^4-13/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 835/10976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+107245/153664*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (100825155x + 268867080x + 268867080x + 119496480x + 19916080)
+--R *
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3
+--R \|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+ +------+
+--R (- 5791230x - 8897265x - 2075184x + 2239092x + 917264)\|7 \|5x + 3
+--R /
+--R 4 3 2 +-+ +--------+
+--R (12446784x + 33191424x + 33191424x + 14751744x + 2458624)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 403300620x + 873818010x + 537734160x - 59748240x - 159328640x
+--R +
+--R - 39832160
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R \|7 atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 4 3 2
+--R (162154440x + 249123420x + 58105152x - 62694576x - 25683392)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 455077602x - 986001471x - 606770136x + 67418904x + 179783744x
+--R +
+--R 44945936
+--R /
+--R 5 4 3 2
+--R 697019904x + 1510209792x + 929359872x - 103262208x - 275365888x
+--R +
+--R - 68841472
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 4979020atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R 2489510atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R +-+
+--R - 401303\|7
+--R /
+--R +-+
+--R 614656\|7
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 5 4 3 2 +------+
+--R (- 405x - 1323x - 1728x - 1128x - 368x - 48)\|5x + 3
+--R (1) ---------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+r0:=-11199264087/1024000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^4*_
+ (3+5*x)^(3/2)/sqrt(1-2*x)+29429853/256000*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)+169017/6400*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 10377/1600*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+33/20*(2+3*x)^3*_
+ (3+5*x)^(3/2)*sqrt(1-2*x)+1018114917/1024000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 11199264087\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 41472000x - 200966400x - 461171520x - 732415080x - 1206337246x
+--R +
+--R 1702927233
+--R *
+--R +--+ +------+
+--R \|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 1024000\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 500
+--m0:=a0-r0
+--E 259
+
+--S 260 of 500
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 4 3 2 +------+
+--R (- 135x - 351x - 342x - 148x - 24)\|5x + 3
+--R (1) ----------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+r0:=-145708761/51200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^3*_
+ (3+5*x)^(3/2)/sqrt(1-2*x)+392979/12800*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)+27/16*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 3/320*(3+5*x)^(3/2)*(1382+2199*x)*sqrt(1-2*x)+_
+ 13246251/51200*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 145708761\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +------+
+--R (- 864000x - 3729600x - 8057880x - 15218818x + 22217679)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 51200\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 500
+--m0:=a0-r0
+--E 264
+
+--S 265 of 500
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 3 2 +------+
+--R (- 45x - 87x - 56x - 12)\|5x + 3
+--R (1) -----------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+r0:=-463881/640*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*(3+5*x)^(5/2)/_
+ sqrt(1-2*x)+14057/1760*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 3/20*(3+5*x)^(5/2)*sqrt(1-2*x)+42171/640*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 463881\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +------+
+--R (- 4800x - 18840x - 45538x + 71199)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 640\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 500
+--m0:=a0-r0
+--E 269
+
+--S 270 of 500
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 2 +------+
+--R (- 15x - 19x - 6)\|5x + 3
+--R (1) ---------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+r0:=-5709/32*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(3+5*x)^(5/2)/_
+ sqrt(1-2*x)+173/88*(3+5*x)^(3/2)*sqrt(1-2*x)+519/32*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3 2 +--+ +------+
+--R - 5709\|- 2x + 1 asin(-------------) + (- 120x - 490x + 891)\|10 \|5x + 3
+--R +--+
+--R \|11
+--R ---------------------------------------------------------------------------
+--R +--+ +--------+
+--R 32\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500
+--a0:=integrate(t0,x)
+--E 273
+
+--S 274 of 500
+--m0:=a0-r0
+--E 274
+
+--S 275 of 500
+--d0:=D(m0,x)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(3+5*x)^(3/2)/(1-2*x)^(3/2)
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) -------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+r0:=-33/4*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+(3+5*x)^(3/2)/_
+ sqrt(1-2*x)+15/4*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+
+--R - 33\|5 \|- 2x + 1 asin(-------------) + (- 10x + 27)\|2 \|5x + 3
+--R +--+
+--R \|11
+--R (2) ------------------------------------------------------------------
+--R +-+ +--------+
+--R 4\|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500
+--a0:=integrate(t0,x)
+--E 278
+
+--S 279 of 500
+--m0:=a0-r0
+--E 279
+
+--S 280 of 500
+--d0:=D(m0,x)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x))
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) ------------------------
+--R 2 +--------+
+--R (6x + x - 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+r0:=-5/3*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_
+ 2/21*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(3/2)/sqrt(1-2*x)+5/7*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|7 \|5x + 3
+--R 2\|2 \|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +-+ +--------+ \|2 \|5x + 3 +-+ +-+ +------+
+--R - 35\|5 \|7 \|- 2x + 1 asin(-------------) + 33\|2 \|7 \|5x + 3
+--R +--+
+--R \|11
+--R /
+--R +-+ +-+ +--------+
+--R 21\|2 \|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 283
+
+--S 284 of 500
+--m0:=a0-r0
+--E 284
+
+--S 285 of 500
+--d0:=D(m0,x)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^2)
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) ---------------------------------
+--R 3 2 +--------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+r0:=-33/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x))+3/49*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3 +-+ +------+
+--R (- 99x - 66)\|- 2x + 1 atan(-------------) + (64x + 45)\|7 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R (2) --------------------------------------------------------------------
+--R +-+ +--------+
+--R (147x + 98)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 198x - 33x + 66)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +--------+ +------+ 2
+--R (- 896x - 630)\|- 2x + 1 \|5x + 3 - 3780x - 630x + 1260
+--R /
+--R 2
+--R 4116x + 686x - 1372
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 66atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R - 33atan(------------------------------------------------) - 90\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 98\|7
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^3)
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+r0:=825/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(3/2)/((2+3*x)^2*sqrt(1-2*x))+_
+ 5/98*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_
+ 425/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ \|7 \|5x + 3
+--R (7425x + 9900x + 3300)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +------+
+--R (2550x + 2245x + 396)\|7 \|5x + 3
+--R /
+--R 2 +-+ +--------+
+--R (12348x + 16464x + 5488)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 59400x - 49500x + 13200x + 13200)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (- 142800x - 125720x - 22176)\|- 2x + 1 \|5x + 3 + 237006x + 197505x
+--R +
+--R - 52668x - 52668
+--R /
+--R 3 2
+--R 1382976x + 1152480x - 307328x - 307328
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 6600atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 3300atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 1881\|7
+--R /
+--R +-+
+--R 10976\|7
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^4)
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) ----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+r0:=2805/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(3/2)/((2+3*x)^3*sqrt(1-2*x))+_
+ 1/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_
+ 145/588*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_
+ 415/8232*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 +--------+ \|7 \|5x + 3
+--R (75735x + 151470x + 100980x + 22440)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +------+
+--R (2490x + 6135x + 3782x + 576)\|7 \|5x + 3
+--R /
+--R 3 2 +-+ +--------+
+--R (74088x + 148176x + 98784x + 21952)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 151470x - 227205x - 50490x + 56100x + 22440)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 3 2 +--------+ +------+ 4
+--R (- 34860x - 85890x - 52948x - 8064)\|- 2x + 1 \|5x + 3 + 108864x
+--R +
+--R 3 2
+--R 163296x + 36288x - 40320x - 16128
+--R /
+--R 4 3 2
+--R 2074464x + 3111696x + 691488x - 768320x - 307328
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 5610atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 2805atan(--------------------------------------------------) + 288\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 5488\|7
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^5)
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+r0:=279015/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(3/2)/((2+3*x)^4*sqrt(1-2*x))+9/196*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^4-89/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_
+ 745/10976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+16985/153664*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (22600215x + 60267240x + 60267240x + 26785440x + 4464240)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+ +------+
+--R (- 917190x - 1188045x + 60048x + 538276x + 163152)\|7 \|5x + 3
+--R /
+--R 4 3 2 +-+ +--------+
+--R (12446784x + 33191424x + 33191424x + 14751744x + 2458624)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 90400860x + 195868530x + 120534480x - 13392720x - 35713920x
+--R +
+--R - 8928480
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R \|7 atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 4 3 2 +--------+
+--R (25681320x + 33265260x - 1681344x - 15071728x - 4568256)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 80943786x - 175378203x - 107925048x + 11991672x + 31977792x + 7994448
+--R /
+--R 5 4 3 2
+--R 697019904x + 1510209792x + 929359872x - 103262208x - 275365888x
+--R +
+--R - 68841472
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 1116060atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+
+--R 558030atan(---------------------------------------------------) - 71379\|7
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R /
+--R +-+
+--R 614656\|7
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(3/2)
+--R
+--R
+--R (1)
+--R 6 5 4 3 2 +------+
+--R (- 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144)\|5x + 3
+--R -----------------------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+r0:=-107121749031/1638400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ (2+3*x)^4*(3+5*x)^(5/2)/sqrt(1-2*x)+295101237/409600*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)+5100983/51200*(3+5*x)^(5/2)*sqrt(1-2*x)+_
+ 62751/2560*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)+999/160*(2+3*x)^2*_
+ (3+5*x)^(5/2)*sqrt(1-2*x)+13/8*(2+3*x)^3*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)+9738340821/1638400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 107121749031\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R - 276480000x - 1479168000x - 3687379200x - 5945485120x
+--R +
+--R 2
+--R - 7755469800x - 11734056318x + 16267424049
+--R *
+--R +--+ +------+
+--R \|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 1638400\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 500
+--a0:=integrate(t0,x)
+--E 308
+
+--S 309 of 500
+--m0:=a0-r0
+--E 309
+
+--S 310 of 500
+--d0:=D(m0,x)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 5 4 3 2 +------+
+--R (- 675x - 2160x - 2763x - 1766x - 564x - 72)\|5x + 3
+--R (1) ---------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+r0:=-3538809681/204800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ (2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x)+9748787/51200*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)+172209/6400*(3+5*x)^(5/2)*sqrt(1-2*x)+33/20*_
+ (2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+3/1600*(3+5*x)^(5/2)*_
+ (6602+10365*x)*sqrt(1-2*x)+321709971/204800*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 3538809681\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R - 13824000x - 65836800x - 148751040x - 233394520x - 381820658x
+--R +
+--R 538018839
+--R *
+--R +--+ +------+
+--R \|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 204800\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 500
+--a0:=integrate(t0,x)
+--E 313
+
+--S 314 of 500
+--m0:=a0-r0
+--E 314
+
+--S 315 of 500
+--d0:=D(m0,x)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 4 3 2 +------+
+--R (- 225x - 570x - 541x - 228x - 36)\|5x + 3
+--R (1) ----------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+r0:=-9219111/2048*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 49/22*(3+5*x)^(7/2)/sqrt(1-2*x)+25397/512*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)+25397/3520*(3+5*x)^(5/2)*sqrt(1-2*x)+_
+ 9/80*(3+5*x)^(7/2)*sqrt(1-2*x)+838101/2048*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 9219111\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +------+
+--R (- 57600x - 243520x - 517096x - 966014x + 1405233)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 2048\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 500
+--a0:=integrate(t0,x)
+--E 318
+
+--S 319 of 500
+--m0:=a0-r0
+--E 319
+
+--S 320 of 500
+--d0:=D(m0,x)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 3 2 +------+
+--R (- 75x - 140x - 87x - 18)\|5x + 3
+--R (1) ------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+r0:=-29403/128*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_
+ 7/11*(3+5*x)^(7/2)/sqrt(1-2*x)+405/32*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)+81/44*(3+5*x)^(5/2)*sqrt(1-2*x)+13365/128*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3
+--R - 29403\|5 \|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +------+
+--R (- 1600x - 6120x - 14526x + 22545)\|2 \|5x + 3
+--R /
+--R +-+ +--------+
+--R 128\|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 500
+--a0:=integrate(t0,x)
+--E 323
+
+--S 324 of 500
+--m0:=a0-r0
+--E 324
+
+--S 325 of 500
+--d0:=D(m0,x)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(3+5*x)^(5/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) ---------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+r0:=-1815/32*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+(3+5*x)^(5/2)/_
+ sqrt(1-2*x)+25/8*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 825/32*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3
+--R - 1815\|5 \|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +------+
+--R (- 200x - 790x + 1413)\|2 \|5x + 3
+--R /
+--R +-+ +--------+
+--R 32\|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 500
+--a0:=integrate(t0,x)
+--E 328
+
+--S 329 of 500
+--m0:=a0-r0
+--E 329
+
+--S 330 of 500
+--d0:=D(m0,x)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x))
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) ---------------------------
+--R 2 +--------+
+--R (6x + x - 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+r0:=-475/36*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-_
+ 2/63*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(5/2)/sqrt(1-2*x)+5/7*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+ 505/84*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|7 \|5x + 3
+--R - 8\|2 \|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +-+ +--------+ \|2 \|5x + 3
+--R - 3325\|5 \|7 \|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +------+
+--R (- 1050x + 2703)\|2 \|7 \|5x + 3
+--R /
+--R +-+ +-+ +--------+
+--R 252\|2 \|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 333
+
+--S 334 of 500
+--m0:=a0-r0
+--E 334
+
+--S 335 of 500
+--d0:=D(m0,x)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^2)
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) ---------------------------------
+--R 3 2 +--------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+r0:=-25/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_
+ 169/441*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(5/2)/((2+3*x)*sqrt(1-2*x))+_
+ 3/49*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)+160/147*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|7 \|5x + 3
+--R (507x + 338)\|2 \|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +-+ +--------+ \|2 \|5x + 3
+--R (- 3675x - 2450)\|5 \|7 \|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +------+
+--R (3273x + 2175)\|2 \|7 \|5x + 3
+--R /
+--R +-+ +-+ +--------+
+--R (1323x + 882)\|2 \|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 338
+
+--S 339 of 500
+--m0:=a0-r0
+--E 339
+
+--S 340 of 500
+--d0:=D(m0,x)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^3)
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) -----------------------------------------
+--R 4 3 2 +--------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+r0:=-1815/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x))+_
+ 5/98*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+_
+ 165/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ \|7 \|5x + 3
+--R (- 16335x - 21780x - 7260)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +------+
+--R (8110x + 11525x + 4068)\|7 \|5x + 3
+--R /
+--R 2 +-+ +--------+
+--R (12348x + 16464x + 5488)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (32670x + 27225x - 7260x - 7260)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (- 113540x - 161350x - 56952)\|- 2x + 1 \|5x + 3 - 512568x - 427140x
+--R +
+--R 113904x + 113904
+--R /
+--R 3 2
+--R 345744x + 288120x - 76832x - 76832
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 3630atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R 1815atan(--------------------------------------------------) - 4068\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 2744\|7
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^4)
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) ----------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+r0:=1815/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(5/2)/((2+3*x)^3*sqrt(1-2*x))+_
+ 1/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3+_
+ 155/1764*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_
+ 12335/24696*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 +--------+ \|7 \|5x + 3
+--R (49005x + 98010x + 65340x + 14520)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +------+
+--R (24670x + 37405x + 17666x + 2448)\|7 \|5x + 3
+--R /
+--R 3 2 +-+ +--------+
+--R (74088x + 148176x + 98784x + 21952)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 490050x - 735075x - 163350x + 181500x + 72600)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 3 2 +--------+ +------+
+--R (- 1726900x - 2618350x - 1236620x - 171360)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 3238704x + 4858056x + 1079568x - 1199520x - 479808
+--R /
+--R 4 3 2
+--R 10372320x + 15558480x + 3457440x - 3841600x - 1536640
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 18150atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+
+--R - 9075atan(-----------------------------------------------) + 8568\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R /
+--R +-+
+--R 27440\|7
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^5)
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+r0:=168795/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(5/2)/((2+3*x)^4*sqrt(1-2*x))+_
+ 9/196*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4+_
+ 277/3528*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_
+ 38365/98784*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_
+ 167155/1382976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (13672395x + 36459720x + 36459720x + 16204320x + 2700720)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+ +------+
+--R (1002930x + 2578615x + 2184144x + 687828x + 53136)\|7 \|5x + 3
+--R /
+--R 4 3 2 +-+ +--------+
+--R (12446784x + 33191424x + 33191424x + 14751744x + 2458624)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 109379160x + 236988180x + 145838880x - 16204320x - 43211520x
+--R +
+--R - 10802880
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R \|7 atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 4 3 2
+--R (- 56164080x - 144402440x - 122312064x - 38518368x - 2975616)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 71554266x - 155034243x - 95405688x + 10600632x + 28268352x + 7067088
+--R /
+--R 5 4 3 2
+--R 1394039808x + 3020419584x + 1858719744x - 206524416x - 550731776x
+--R +
+--R - 137682944
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 1350360atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R 675180atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R +-+
+--R - 63099\|7
+--R /
+--R +-+
+--R 1229312\|7
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^6)
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) -------------------------------------------------------------------
+--R 7 6 5 4 2 +--------+
+--R (1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+r0:=3474273/2151296*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/7*(3+5*x)^(5/2)/((2+3*x)^5*sqrt(1-2*x))+11/245*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)/(2+3*x)^5+1019/13720*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-_
+ 29297/82320*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-55277/460992*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+426781/6453888*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 4221241695x + 14070805650x + 18761074200x + 12507382800x
+--R +
+--R 4169127600x + 555883680
+--R *
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3
+--R \|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R - 115230870x - 180017865x + 19738914x + 164918884x + 95331368x
+--R +
+--R 16456032
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 2613824640x + 8712748800x + 11616998400x + 7744665600x
+--R +
+--R 2581555200x + 344207360
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3
+--R 8442483390x + 23920369605x + 23451342750x + 6253691400x
+--R +
+--R 2
+--R - 4169127600x - 3057360240x - 555883680
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 5 4 3 2
+--R 1613232180x + 2520250110x - 276344796x - 2308864376x
+--R +
+--R - 1334639152x - 230384448
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3
+--R - 6997927608x - 19827461556x - 19438687800x - 5183650080x
+--R +
+--R 2
+--R 3455766720x + 2534228928x + 460768896
+--R /
+--R 6 5 4 3
+--R 73187089920x + 207363421440x + 203297472000x + 54212659200x
+--R +
+--R 2
+--R - 36141772800x - 26503966720x - 4818903040
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 34742730atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 17371365atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R - 2057004\|7
+--R /
+--R +-+
+--R 21512960\|7
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(2+3*x)^5/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 500
+r0:=-291096141/256000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 2191/880*(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x)-3/40*(2+3*x)^4*_
+ sqrt(3+5*x)/sqrt(1-2*x)+288454593/2816000*sqrt(1-2*x)*_
+ sqrt(3+5*x)+76587/17600*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 63/704000*(390718+637135*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 3202057551\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 17107200x - 76887360x - 171939240x - 332129358x + 488641609)\|10
+--R *
+--R +------+
+--R \|5x + 3
+--R /
+--R +--+ +--------+
+--R 2816000\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 500
+--a0:=integrate(t0,x)
+--E 363
+
+--S 364 of 500
+--m0:=a0-r0
+--E 364
+
+--S 365 of 500
+--d0:=D(m0,x)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(2+3*x)^4/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) ---------------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+r0:=-184641/640*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 567/220*(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)-1/10*(2+3*x)^3*_
+ sqrt(3+5*x)/sqrt(1-2*x)+35505/1408*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 8487/1760*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 2031051\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +------+
+--R (- 19008x - 78408x - 196614x + 312365)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 7040\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 500
+--a0:=integrate(t0,x)
+--E 368
+
+--S 369 of 500
+--m0:=a0-r0
+--E 369
+
+--S 370 of 500
+--d0:=D(m0,x)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(2+3*x)^3/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+r0:=-56421/800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1211/440*(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)-3/20*(2+3*x)^2*_
+ sqrt(3+5*x)/sqrt(1-2*x)+54249/8800*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R - 620631\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +------+
+--R (- 11880x - 51678x + 97409)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R 8800\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 500
+--a0:=integrate(t0,x)
+--E 373
+
+--S 374 of 500
+--m0:=a0-r0
+--E 374
+
+--S 375 of 500
+--d0:=D(m0,x)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(2+3*x)^2/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+r0:=-321/20*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 49/22*sqrt(3+5*x)/sqrt(1-2*x)+9/20*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3 +--+ +------+
+--R - 3531\|- 2x + 1 asin(-------------) + (- 198x + 589)\|10 \|5x + 3
+--R +--+
+--R \|11
+--R (2) -------------------------------------------------------------------
+--R +--+ +--------+
+--R 220\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 500
+--a0:=integrate(t0,x)
+--E 378
+
+--S 379 of 500
+--m0:=a0-r0
+--E 379
+
+--S 380 of 500
+--d0:=D(m0,x)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R - 3x - 2
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+r0:=-3*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3 +--+ +------+
+--R - 33\|- 2x + 1 asin(-------------) + 7\|10 \|5x + 3
+--R +--+
+--R \|11
+--R (2) ----------------------------------------------------
+--R +--+ +--------+
+--R 11\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 500
+--a0:=integrate(t0,x)
+--E 383
+
+--S 384 of 500
+--m0:=a0-r0
+--E 384
+
+--S 385 of 500
+--d0:=D(m0,x)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=1/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+r0:=2/11*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +------+
+--R 2\|5x + 3
+--R (2) -------------
+--R +--------+
+--R 11\|- 2x + 1
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+
+--R - 2\|- 2x + 1 \|5x + 3 - 8x + 4
+--R (3) --------------------------------
+--R 22x - 11
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 4
+--R (4) - --
+--R 11
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ---------------------------------
+--R 2 +--------+ +------+
+--R (6x + x - 2)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+r0:=6/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3 +-+ +------+
+--R 66\|- 2x + 1 atan(-------------) + 4\|7 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R (2) -------------------------------------------------
+--R +-+ +--------+
+--R 77\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R (- 66x + 33)\|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+
+--R - 28\|- 2x + 1 \|5x + 3 + 112x - 56
+--R /
+--R 1078x - 539
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 66atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 33atan(--------------------------------------------------) + 8\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 77\|7
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ------------------------------------------
+--R 3 2 +--------+ +------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+r0:=123/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))+87/539*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3 +-+ +------+
+--R (4059x + 2706)\|- 2x + 1 atan(-------------) + (- 174x + 115)\|7 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R --------------------------------------------------------------------------
+--R +-+ +--------+
+--R (1617x + 1078)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (32472x + 5412x - 10824)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R +--------+ +------+ 2
+--R (9744x - 6440)\|- 2x + 1 \|5x + 3 - 33810x - 5635x + 11270
+--R /
+--R 2
+--R 181104x + 30184x - 60368
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 10824atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+
+--R 5412atan(---------------------------------------------------) - 805\|7
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R /
+--R +-+
+--R 4312\|7
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) - --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+r0:=12465/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+_
+ 75/1078*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 11685/15092*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ \|7 \|5x + 3
+--R (1234035x + 1645380x + 548460)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +------+
+--R (- 70110x - 13785x + 25204)\|7 \|5x + 3
+--R /
+--R 2 +-+ +--------+
+--R (135828x + 181104x + 60368)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (4936140x + 4113450x - 1096920x - 1096920)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 2 +--------+ +------+ 3
+--R (1963080x + 385980x - 705712)\|- 2x + 1 \|5x + 3 - 5557482x
+--R +
+--R 2
+--R - 4631235x + 1234996x + 1234996
+--R /
+--R 3 2
+--R 7606368x + 6338640x - 1690304x - 1690304
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 548460atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+
+--R 274230atan(---------------------------------------------------) - 44107\|7
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R /
+--R +-+
+--R 60368\|7
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^4*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+r0:=102345/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))+_
+ 3/77*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 915/2156*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 98205/30184*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (30396465x + 60792930x + 40528620x + 9006360)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +------+
+--R (- 1767690x - 1549935x + 377658x + 421184)\|7 \|5x + 3
+--R /
+--R 3 2 +-+ +--------+
+--R (814968x + 1629936x + 1086624x + 241472)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (60792930x + 91189395x + 20264310x - 22515900x - 9006360)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 3 2 +--------+ +------+
+--R (24747660x + 21699090x - 5287212x - 5896576)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R - 79603776x - 119405664x - 26534592x + 29482880x + 11793152
+--R /
+--R 4 3 2
+--R 22819104x + 34228656x + 7606368x - 8451520x - 3380608
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2251590atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 1125795atan(------------------------------------------------) - 210592\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 60368\|7
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^5*sqrt(3+5*x))
+--R
+--R
+--R (1)
+--R 1
+--R - -------------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+ +------+
+--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+r0:=24922335/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))+_
+ 51/2156*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_
+ 1269/4312*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_
+ 228645/120736*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 23958315/1690304*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 22205800485x + 59215467960x + 59215467960x + 26317985760x
+--R +
+--R 4386330960
+--R *
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3
+--R \|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2
+--R (- 1293749010x - 1998242055x - 482249808x + 491393004x + 205593328)
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (136914624x + 365105664x + 365105664x + 162269184x + 27044864)\|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 88823201940x - 192450270870x - 118430935920x + 13158992880x
+--R +
+--R 35090647680x + 8772661920
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R \|7 atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R 4 3 2
+--R 36224972280x + 55950777540x + 13502994624x - 13759004112x
+--R +
+--R - 5756613184
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 101999989854x + 220999978017x + 135999986472x - 15111109608x
+--R +
+--R - 40296292288x - 10074073072
+--R /
+--R 5 4 3 2
+--R 7667218944x + 16612307712x + 10222958592x - 1135884288x - 3029024768x
+--R +
+--R - 757256192
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 1096582740atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R - 548291370atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +-+
+--R 89947081\|7
+--R /
+--R +-+
+--R 6761216\|7
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+r0:=-2911419/16000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 567/220*(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x))-_
+ 1/10*(2+3*x)^4/(sqrt(1-2*x)*sqrt(3+5*x))-_
+ 2821/12100*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 30791901/1936000*sqrt(1-2*x)*sqrt(3+5*x)+_
+ 294483/96800*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3
+--R - 352281699\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 15681600x - 75663720x - 208989990x + 169670279x + 162727423)\|10
+--R /
+--R +--+ +--------+ +------+
+--R 1936000\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 500
+--a0:=integrate(t0,x)
+--E 418
+
+--S 419 of 500
+--m0:=a0-r0
+--E 419
+
+--S 420 of 500
+--d0:=D(m0,x)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+r0:=-35451/800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1211/440*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))-_
+ 3/20*(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x))+_
+ 1/24200*(31586+54645*x)*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 316941/96800*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3
+--R - 4289571\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (- 392040x - 1992870x + 2323271x + 2026687)\|10
+--R /
+--R +--+ +--------+ +------+
+--R 96800\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 500
+--a0:=integrate(t0,x)
+--E 423
+
+--S 424 of 500
+--m0:=a0-r0
+--E 424
+
+--S 425 of 500
+--d0:=D(m0,x)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+r0:=-999/100*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 721/220*(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_
+ 3/10*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))-_
+ 3547/12100*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3
+--R - 120879\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (- 32670x + 82499x + 61243)\|10
+--R /
+--R +--+ +--------+ +------+
+--R 12100\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 500
+--a0:=integrate(t0,x)
+--E 428
+
+--S 429 of 500
+--m0:=a0-r0
+--E 429
+
+--S 430 of 500
+--d0:=D(m0,x)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+r0:=-9/5*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 49/22/(sqrt(1-2*x)*sqrt(3+5*x))-1229/1210*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3 +--+
+--R - 1089\|- 2x + 1 \|5x + 3 asin(-------------) + (1229x + 733)\|10
+--R +--+
+--R \|11
+--R (2) ------------------------------------------------------------------
+--R +--+ +--------+ +------+
+--R 605\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 500
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 500
+--m0:=a0-r0
+--E 434
+
+--S 435 of 500
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R - 3x - 2
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+r0:=(-2/55)/(sqrt(1-2*x)*sqrt(3+5*x))+74/605*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 74x + 40
+--R (2) -----------------------
+--R +--------+ +------+
+--R 121\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+ 2
+--R (- 222x - 120)\|- 2x + 1 \|5x + 3 - 950x - 95x + 285
+--R (3) ------------------------------------------------------
+--R 2
+--R 3630x + 363x - 1089
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 95
+--R (4) - ---
+--R 363
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=1/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) - ----------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+r0:=2/11/(sqrt(1-2*x)*sqrt(3+5*x))-20/121*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 40x + 2
+--R (2) -----------------------
+--R +--------+ +------+
+--R 121\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+ 2
+--R (- 120x - 6)\|- 2x + 1 \|5x + 3 - 40x - 4x + 12
+--R (3) -------------------------------------------------
+--R 2
+--R 3630x + 363x - 1089
+--R Type: Union(Expression(Integer),...)
+--E 443
+
+--S 444 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 4
+--R (4) - ---
+--R 363
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) - ------------------------------------------
+--R 3 2 +--------+ +------+
+--R (30x + 23x - 7x - 6)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+r0:=-18/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77/(sqrt(1-2*x)*sqrt(3+5*x))-370/847*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ +------+ \|7 \|5x + 3 +-+
+--R - 2178\|- 2x + 1 \|5x + 3 atan(-------------) + (740x - 326)\|7
+--R +--------+
+--R \|- 2x + 1
+--R (2) ----------------------------------------------------------------
+--R +-+ +--------+ +------+
+--R 847\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (32670x + 3267x - 9801)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+ 2
+--R (- 15540x + 6846)\|- 2x + 1 \|5x + 3 + 45640x + 4564x - 13692
+--R /
+--R 2
+--R 177870x + 17787x - 53361
+--R Type: Union(Expression(Integer),...)
+--E 448
+
+--S 449 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 6534atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R 3267atan(--------------------------------------------------) + 652\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 2541\|7
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) - ----------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (90x + 129x + 25x - 32x - 12)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+r0:=-999/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))-_
+ 17735/5929*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 87/539*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|7 \|5x + 3
+--R (- 362637x - 241758)\|- 2x + 1 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+
+--R (106410x + 15821x - 34205)\|7
+--R /
+--R +-+ +--------+ +------+
+--R (17787x + 11858)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (87032880x + 66725208x - 20307672x - 17406576)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 2 +--------+ +------+ 3
+--R (- 35753760x - 5315856x + 11492880)\|- 2x + 1 \|5x + 3 - 136477950x
+--R +
+--R 2
+--R - 104633095x + 31844855x + 27295590
+--R /
+--R 3 2
+--R 59764320x + 45819312x - 13945008x - 11952864
+--R Type: Union(Expression(Integer),...)
+--E 453
+
+--S 454 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 5802192atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R 2901096atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R - 649895\|7
+--R /
+--R +-+
+--R 284592\|7
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) - --------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (270x + 567x + 333x - 46x - 100x - 24)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+r0:=-177255/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77/((2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x))-_
+ 3125575/166012*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 75/1078*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_
+ 18615/15092*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 2 +--------+ +------+
+--R (- 193030695x - 257374260x - 85791420)\|- 2x + 1 \|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+
+--R (56260350x + 45655035x - 12730165x - 12072596)\|7
+--R /
+--R 2 +-+ +--------+ +------+
+--R (1494108x + 1992144x + 664048)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (5790920850x + 8300319885x + 1608589125x - 2058994080x - 772122780)
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 3 2 +--------+
+--R (- 2362934700x - 1917511470x + 534666930x + 507049032)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 4 3 2
+--R - 7605735480x - 10901554188x - 2112704300x + 2704261504x + 1014098064
+--R /
+--R 4 3 2
+--R 627525360x + 899453016x + 174312600x - 223120128x - 83670048
+--R Type: Union(Expression(Integer),...)
+--E 458
+
+--S 459 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 128687130atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R 64343565atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 12072596\|7
+--R /
+--R +-+
+--R 996072\|7
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^(3/2))
+--R
+--R
+--R (1)
+--R 1
+--R - -------------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+ +------+
+--R (810x + 2241x + 2133x + 528x - 392x - 272x - 48)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+r0:=-2079585/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77/((2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x))-_
+ 36657025/332024*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 3/77*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+_
+ 1245/2156*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_
+ 220305/30184*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (- 6794004195x - 13588008390x - 9058672260x - 2013038280)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (1979479350x + 2925598635x + 622325745x - 723664682x - 283149136)\|7
+--R /
+--R 3 2 +-+ +--------+ +------+
+--R (8964648x + 17929296x + 11952864x + 2656192)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 1019100629250x + 2140111321425x + 1256890776075x - 173624551650x
+--R +
+--R - 377444677500x - 90586722600
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 4 3 2
+--R - 415690663500x - 614375713350x - 130688406450x + 151969583220x
+--R +
+--R 59461318560
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 1873031534640x - 3933366222744x - 2310072226056x + 319109076272x
+--R +
+--R 693715383200x + 166491691968
+--R /
+--R 5 4 3 2
+--R 18825760800x + 39534097680x + 23218438320x - 3207351840x
+--R +
+--R - 6972504000x - 1673400960
+--R Type: Union(Expression(Integer),...)
+--E 463
+
+--S 464 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 7548893550atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R 3774446775atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R - 991021976\|7
+--R /
+--R +-+
+--R 9960720\|7
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 5 4 3 2
+--R - 243x - 810x - 1080x - 720x - 240x - 32
+--R (1) --------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+r0:=-111321/4000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1211/440*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 3/20*(2+3*x)^4/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 17983/72600*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 7/3993000*(467578+809265*x)*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 10952053/5324000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3
+--R (- 2222523765x - 1333514259)\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (- 194059800x - 1128781170x + 612106475x + 1785872944x + 632498543)\|10
+--R /
+--R +--+ +--------+ +------+
+--R (79860000x + 47916000)\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 500
+--a0:=integrate(t0,x)
+--E 468
+
+--S 469 of 500
+--m0:=a0-r0
+--E 469
+
+--S 470 of 500
+--d0:=D(m0,x)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 4 3 2
+--R - 81x - 216x - 216x - 96x - 16
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+r0:=-621/100*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 721/220*(2+3*x)^2/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 3/10*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))+_
+ 1/36300*(4706+11385*x)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+ 168781/399300*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3
+--R (- 12398265x - 7438959)\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (- 3234330x + 6746215x + 11581424x + 3821563)\|10
+--R /
+--R +--+ +--------+ +------+
+--R (1996500x + 1197900)\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 500
+--a0:=integrate(t0,x)
+--E 473
+
+--S 474 of 500
+--m0:=a0-r0
+--E 474
+
+--S 475 of 500
+--d0:=D(m0,x)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 3 2
+--R - 27x - 54x - 36x - 8
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+r0:=-27/25*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 2/11*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 8/363*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 4/19965*(158+321*x)*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 3103/33275*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3
+--R (- 539055x - 323433)\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (649265x + 772408x + 229661)\|10
+--R /
+--R +--+ +--------+ +------+
+--R (499125x + 299475)\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 500
+--a0:=integrate(t0,x)
+--E 478
+
+--S 479 of 500
+--m0:=a0-r0
+--E 479
+
+--S 480 of 500
+--d0:=D(m0,x)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 2
+--R - 9x - 12x - 4
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+r0:=49/22/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 3679/3630*sqrt(1-2*x)/(3+5*x)^(3/2)-4091/19965*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 2
+--R 8182x + 8912x + 2392
+--R (2) ------------------------------------
+--R +--------+ +------+
+--R (19965x + 11979)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +--------+ +------+ 3 2
+--R (- 73638x - 80208x - 21528)\|- 2x + 1 \|5x + 3 - 209300x - 146510x
+--R +
+--R 50232x + 37674
+--R /
+--R 3 2
+--R 1796850x + 1257795x - 431244x - 323433
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 4186
+--R (4) - -----
+--R 35937
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R - 3x - 2
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+r0:=7/11/((3+5*x)^(3/2)*sqrt(1-2*x))-107/363*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+ 428/3993*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 2
+--R 4280x + 2782x + 80
+--R (2) ------------------------------------
+--R +--------+ +------+
+--R (19965x + 11979)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +--------+ +------+ 3 2
+--R (- 38520x - 25038x - 720)\|- 2x + 1 \|5x + 3 + 7000x + 4900x - 1680x
+--R +
+--R - 1260
+--R /
+--R 3 2
+--R 1796850x + 1257795x - 431244x - 323433
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 140
+--R (4) -----
+--R 35937
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=1/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+r0:=2/11/((3+5*x)^(3/2)*sqrt(1-2*x))-40/363*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+ 160/3993*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 2
+--R 1600x + 1040x - 194
+--R (2) ------------------------------------
+--R +--------+ +------+
+--R (19965x + 11979)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +--------+ +------+ 3 2
+--R (- 14400x - 9360x + 1746)\|- 2x + 1 \|5x + 3 - 19400x - 13580x
+--R +
+--R 4656x + 3492
+--R /
+--R 3 2
+--R 1796850x + 1257795x - 431244x - 323433
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 388
+--R (4) - -----
+--R 35937
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2))
+--R
+--R
+--R 1
+--R (1) - -----------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (150x + 205x + 34x - 51x - 18)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+r0:=54/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 410/2541*sqrt(1-2*x)/(3+5*x)^(3/2)+31030/27951*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|7 \|5x + 3
+--R (1078110x + 646866)\|- 2x + 1 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+
+--R (- 310300x - 22010x + 90032)\|7
+--R /
+--R +-+ +--------+ +------+
+--R (139755x + 83853)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 48514950x - 33960465x + 11643588x + 8732691)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 2 +--------+ +------+ 3
+--R (19548900x + 1386630x - 5672016)\|- 2x + 1 \|5x + 3 - 63022400x
+--R +
+--R 2
+--R - 44115680x + 15125376x + 11344032
+--R /
+--R 3 2
+--R 88045650x + 61631955x - 21130956x - 15848217
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 1940598atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 970299atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 180064\|7
+--R /
+--R +-+
+--R 251559\|7
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3p.input.pdf b/src/axiom-website/CATS/rich3p.input.pdf
new file mode 100644
index 0000000..1b9a93e
Binary files /dev/null and b/src/axiom-website/CATS/rich3p.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3q.input.pamphlet b/src/axiom-website/CATS/rich3q.input.pamphlet
new file mode 100644
index 0000000..ee96be1
--- /dev/null
+++ b/src/axiom-website/CATS/rich3q.input.pamphlet
@@ -0,0 +1,5581 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3q.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 34 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 25 cases that Axiom failed to integrate.
+\item 41 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3q.output
+)spool rich3q.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2))
+--R
+--R
+--R 1
+--R (1) - --------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (450x + 915x + 512x - 85x - 156x - 36)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+r0:=4887/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77/((2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 28705/17787*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 87/539*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 2841815/195657*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 2 +--------+ +------+
+--R (292706865x + 370762029x + 117082746)\|- 2x + 1 \|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+
+--R (- 85254450x - 63467215x + 20145298x + 16461125)\|7
+--R /
+--R 2 +-+ +--------+ +------+
+--R (2934855x + 3717483x + 1173942)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R - 26343617850x - 36002944395x - 5971220046x + 8956830069x
+--R +
+--R 3161234142
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 3 2 +--------+
+--R (10742060700x + 7996869090x - 2538307548x - 2074101750)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 4 3 2
+--R 48395707500x + 66140800250x + 10969693700x - 16454540550x - 5807484900
+--R /
+--R 4 3 2
+--R 3697917300x + 5053820310x + 838194588x - 1257291882x - 443750076
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 351248238atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R - 175624119atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R 46091150\|7
+--R /
+--R +-+
+--R 3521826\|7
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R - --------------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+ +------+
+--R (1350x + 3645x + 3366x + 769x - 638x - 420x - 72)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+r0:=1215945/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/77/((2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 7090175/498036*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 75/1078*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_
+ 25545/15092*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 707286025/5478396*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2
+--R (218487077325x + 422408349495x + 271895029560x + 58263220620)
+--R *
+--R +-+ +------+
+--R +--------+ +------+ \|7 \|5x + 3
+--R \|- 2x + 1 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2
+--R - 63655742250x - 89836042575x - 16567908760x + 22311149965x
+--R +
+--R 8194676012
+--R *
+--R +-+
+--R \|7
+--R /
+--R 3 2 +-+ +--------+ +------+
+--R (246527820x + 476620452x + 306790176x + 65740752)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3
+--R - 19663836959250x - 39983135150475x - 22373076718080x
+--R +
+--R 2
+--R 3714280314525x + 6816796812540x + 1573106956740
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 4 3 2
+--R 8020623523500x + 11319341364450x + 2087556503760x - 2811204895590x
+--R +
+--R - 1032529177512
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3
+--R - 25813229437800x - 52486899856860x - 29369718827008x
+--R +
+--R 2
+--R 4875832227140x + 8948586205104x + 2065058355024
+--R /
+--R 5 4 3 2
+--R 310625053200x + 631604274840x + 353422282752x - 58673621160x
+--R +
+--R - 107683351776x - 24850004256
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 87394830930atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 43697415465atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R - 8194676012\|7
+--R /
+--R +-+
+--R 98611128\|7
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|5x + 3
+--R (1) ------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+r0:=13246251/6400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/3*(2+3*x)^4*_
+ sqrt(3+5*x)/(1-2*x)^(3/2)-299/66*(2+3*x)^3*sqrt(3+5*x)/_
+ sqrt(1-2*x)-12735719/70400*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 121769/3520*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 697/88*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (874252566x - 437126283)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +------+
+--R (2851200x + 15040080x + 52700868x - 183672928x + 66038637)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (422400x - 211200)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 500
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 500
+--m0:=a0-r0
+--E 14
+
+--S 15 of 500
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|5x + 3
+--R (1) --------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+r0:=126513/320*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_
+ 1/3*(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2)-233/66*(2+3*x)^2*_
+ sqrt(3+5*x)/sqrt(1-2*x)-25073/704*sqrt(1-2*x)*sqrt(3+5*x)-_
+ 3/880*(3566+5815*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (8349858x - 4174929)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +------+
+--R (71280x + 431244x - 1786144x + 625431)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (21120x - 10560)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 500
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 500
+--m0:=a0-r0
+--E 19
+
+--S 20 of 500
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 2 +------+
+--R (9x + 12x + 4)\|5x + 3
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+r0:=49/66*(3+5*x)^(3/2)/(1-2*x)^(3/2)+519/8*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)-21/11*(3+5*x)^(3/2)/sqrt(1-2*x)-519/88*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (34254x - 17127)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +------+
+--R (1188x - 7712x + 2481)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (528x - 264)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 500
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 500
+--m0:=a0-r0
+--E 24
+
+--S 25 of 500
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(2+3*x)*sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R +------+
+--R (3x + 2)\|5x + 3
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+r0:=7/33*(3+5*x)^(3/2)/(1-2*x)^(3/2)+3/2*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(5/2)-3/2*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+
+--R (198x - 99)\|5 \|- 2x + 1 asin(-------------) + (- 268x + 57)\|2 \|5x + 3
+--R +--+
+--R \|11
+--R --------------------------------------------------------------------------
+--R +-+ +--------+
+--R (132x - 66)\|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 500
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 500
+--m0:=a0-r0
+--E 29
+
+--S 30 of 500
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+r0:=2/33*(3+5*x)^(3/2)/(1-2*x)^(3/2)
+--R
+--R
+--R +------+
+--R (- 10x - 6)\|5x + 3
+--R (2) ---------------------
+--R +--------+
+--R (66x - 33)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+ 2
+--R (10x + 6)\|- 2x + 1 \|5x + 3 - 48x + 48x - 12
+--R (3) -----------------------------------------------
+--R 2
+--R 132x - 132x + 33
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 4
+--R (4) - --
+--R 11
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+r0:=-6/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+2/21*sqrt(3+5*x)/_
+ (1-2*x)^(3/2)+128/1617*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3 +-+ +------+
+--R (- 396x + 198)\|- 2x + 1 atan(-------------) + (256x - 282)\|7 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R ------------------------------------------------------------------------
+--R +-+ +--------+
+--R (3234x - 1617)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (396x - 396x + 99)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+ 2
+--R (- 1792x + 1974)\|- 2x + 1 \|5x + 3 + 15792x - 15792x + 3948
+--R /
+--R 2
+--R 45276x - 45276x + 11319
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 66atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R 33atan(--------------------------------------------------) + 188\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 539\|7
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^2)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) ----------------------------------------
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+r0:=75/343*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+2/21*_
+ sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))+260/1617*sqrt(3+5*x)/_
+ ((2+3*x)*sqrt(1-2*x))-425/3773*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ \|7 \|5x + 3
+--R (14850x + 2475x - 4950)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +------+
+--R (5100x - 1460x - 1623)\|7 \|5x + 3
+--R /
+--R 2 +-+ +--------+
+--R (67914x + 11319x - 22638)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 148500x + 49500x + 61875x - 24750)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 2 +--------+ +------+ 3
+--R (- 357000x + 102200x + 113610)\|- 2x + 1 \|5x + 3 + 1908648x
+--R +
+--R 2
+--R - 636216x - 795270x + 318108
+--R /
+--R 3 2
+--R 9507960x - 3169320x - 3961650x + 1584660
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 8250atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+
+--R - 4125atan(-----------------------------------------------) + 7574\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R /
+--R +-+
+--R 37730\|7
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^3)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) -------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+r0:=765/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+2/21*_
+ sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+8/33*sqrt(3+5*x)/_
+ ((2+3*x)^2*sqrt(1-2*x))-145/1078*sqrt(1-2*x)*sqrt(3+5*x)/_
+ (2+3*x)^2-415/15092*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 +--------+ \|7 \|5x + 3
+--R (454410x + 378675x - 100980x - 100980)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +------+
+--R (14940x + 19380x - 8633x - 6708)\|7 \|5x + 3
+--R /
+--R 3 2 +-+ +--------+
+--R (814968x + 679140x - 181104x - 181104)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (908820x + 302940x - 580635x - 100980x + 100980)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 3 2 +--------+ +------+ 4
+--R (- 209160x - 271320x + 120862x + 93912)\|- 2x + 1 \|5x + 3 - 1690416x
+--R +
+--R 3 2
+--R - 563472x + 1079988x + 187824x - 187824
+--R /
+--R 4 3 2
+--R 22819104x + 7606368x - 14578872x - 2535456x + 2535456
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 16830atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 8415atan(------------------------------------------------) - 2236\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 30184\|7
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^4)
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) ------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+r0:=25365/19208*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)+_
+ 524/1617*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-_
+ 89/539*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_
+ 745/15092*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_
+ 16985/211288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (45200430x + 67800645x + 15066810x - 16740900x - 6696360)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+ +------+
+--R (- 1834380x - 235980x + 1465461x + 39530x - 302352)\|7 \|5x + 3
+--R /
+--R 4 3 2 +-+ +--------+
+--R (34228656x + 51342984x + 11409552x - 12677280x - 5070912)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 452004300x - 452004300x + 188335125x + 242743050x - 16740900x
+--R +
+--R - 33481800
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 4 3 2
+--R (128406600x + 16518600x - 102582270x - 2767100x + 21164640)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 800023392x + 800023392x - 333343080x - 429642192x + 29630496x
+--R +
+--R 59260992
+--R /
+--R 5 4 3 2
+--R 4792011840x + 4792011840x - 1996671600x - 2573487840x + 177481920x
+--R +
+--R 354963840
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2790150atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+
+--R - 1395075atan(-----------------------------------------------) + 352744\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R /
+--R +-+
+--R 2112880\|7
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 5 4 3 2 +------+
+--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3
+--R (1) -------------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+r0:=1/3*(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_
+ 1626211523/102400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 123/22*(2+3*x)^3*(3+5*x)^(3/2)/sqrt(1-2*x)-_
+ 47007627/281600*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 269967/7040*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 3315/352*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 1626211523/1126400*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (9757269138x - 4878634569)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 15552000x + 83548800x + 236669040x + 633940524x - 2034703904x
+--R +
+--R 739060191
+--R *
+--R +--+ +------+
+--R \|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (614400x - 307200)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 500
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 500
+--m0:=a0-r0
+--E 59
+
+--S 60 of 500
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 4 3 2 +------+
+--R (135x + 351x + 342x + 148x + 24)\|5x + 3
+--R (1) --------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+r0:=1/3*(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_
+ 4246733/1280*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 101/22*(2+3*x)^2*(3+5*x)^(3/2)/sqrt(1-2*x)-_
+ 125989/3520*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 1/440*(3+5*x)^(3/2)*(6646+10575*x)*sqrt(1-2*x)-_
+ 4246733/14080*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (25480398x - 12740199)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+ +------+
+--R (86400x + 447120x + 1544724x - 5349344x + 1925361)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (7680x - 3840)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 500
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 500
+--m0:=a0-r0
+--E 64
+
+--S 65 of 500
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 3 2 +------+
+--R (45x + 87x + 56x + 12)\|5x + 3
+--R (1) ---------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+r0:=49/66*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_
+ 40787/64*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_
+ 938/363*(3+5*x)^(5/2)/sqrt(1-2*x)-_
+ 40787/5808*(3+5*x)^(3/2)*sqrt(1-2*x)-40787/704*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (244722x - 122361)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +------+
+--R (2160x + 12780x - 52256x + 18351)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (384x - 192)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 500
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 500
+--m0:=a0-r0
+--E 69
+
+--S 70 of 500
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 2 +------+
+--R (15x + 19x + 6)\|5x + 3
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+r0:=7/33*(3+5*x)^(5/2)/(1-2*x)^(3/2)+169/8*asin(sqrt(2/11)*_
+ sqrt(3+5*x))*sqrt(5/2)-169/66*(3+5*x)^(3/2)/sqrt(1-2*x)-_
+ 845/88*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3
+--R (1014x - 507)\|5 \|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +------+
+--R (180x - 1136x + 369)\|2 \|5x + 3
+--R /
+--R +-+ +--------+
+--R (48x - 24)\|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 500
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 500
+--m0:=a0-r0
+--E 74
+
+--S 75 of 500
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(3+5*x)^(3/2)/(1-2*x)^(5/2)
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+r0:=1/3*(3+5*x)^(3/2)/(1-2*x)^(3/2)+5/2*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(5/2)-5/2*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+
+--R (30x - 15)\|5 \|- 2x + 1 asin(-------------) + (- 40x + 9)\|2 \|5x + 3
+--R +--+
+--R \|11
+--R -----------------------------------------------------------------------
+--R +-+ +--------+
+--R (12x - 6)\|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 500
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 500
+--m0:=a0-r0
+--E 79
+
+--S 80 of 500
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+r0:=2/21*(3+5*x)^(3/2)/(1-2*x)^(3/2)+2/49*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-2/49*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3 +-+ +------+
+--R (12x - 6)\|- 2x + 1 atan(-------------) + (- 82x - 36)\|7 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R (2) -------------------------------------------------------------------
+--R +-+ +--------+
+--R (294x - 147)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 12x + 12x - 3)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7
+--R atan(-----------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R +
+--R +--------+ +------+ 2
+--R (574x + 252)\|- 2x + 1 \|5x + 3 + 1764x - 1764x + 441
+--R /
+--R 2
+--R 4116x - 4116x + 1029
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +-+
+--R - atan(-----------------------------------------------------) + 21\|7
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320
+--R /
+--R +-+
+--R 49\|7
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^2)
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) ----------------------------------------
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x))-95/343*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+20/49*sqrt(3+5*x)/((2+3*x)*_
+ sqrt(1-2*x))-55/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ \|7 \|5x + 3
+--R (- 1710x - 285x + 570)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +------+
+--R (660x - 310x - 549)\|7 \|5x + 3
+--R /
+--R 2 +-+ +--------+
+--R (6174x + 1029x - 2058)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 17100x + 5700x + 7125x - 2850)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (333x + 180)\|7
+--R atan(---------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 - 1295x - 700
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (- 46200x + 21700x + 38430)\|- 2x + 1 \|5x + 3 - 645624x + 215208x
+--R +
+--R 269010x - 107604
+--R /
+--R 3 2
+--R 864360x - 288120x - 360150x + 144060
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 950atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (333x + 180)\|7 +-+
+--R - 475atan(---------------------------------------------) - 2562\|7
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 - 1295x - 700
+--R /
+--R +-+
+--R 3430\|7
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^3)
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^2)+5/28*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+6/7*sqrt(3+5*x)/((2+3*x)^2*_
+ sqrt(1-2*x))-5/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-5/28*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 +--------+ \|7 \|5x + 3
+--R (270x + 225x - 60x - 60)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +------+
+--R (180x + 60x - 91x - 36)\|7 \|5x + 3
+--R /
+--R 3 2 +-+ +--------+
+--R (1512x + 1260x - 336x - 336)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (2160x + 720x - 1380x - 240x + 240)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 3 2 +--------+ +------+ 4
+--R (- 10080x - 3360x + 5096x + 2016)\|- 2x + 1 \|5x + 3 - 43092x
+--R +
+--R 3 2
+--R - 14364x + 27531x + 4788x - 4788
+--R /
+--R 4 3 2
+--R 169344x + 56448x - 108192x - 18816x + 18816
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 40atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +-+
+--R 20atan(------------------------------------------------------) - 57\|7
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R /
+--R +-+
+--R 224\|7
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^4)
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) ------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^3)+_
+ 9395/19208*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_
+ sqrt(7)+64/49*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-_
+ 27/49*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-285/1372*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-1395/19208*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (1521990x + 2282985x + 507330x - 563700x - 225480)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+ +------+
+--R (150660x + 193860x - 17127x - 80510x - 19296)\|7 \|5x + 3
+--R /
+--R 4 3 2 +-+ +--------+
+--R (3111696x + 4667544x + 1037232x - 1152480x - 460992)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2 +-+
+--R (3043980x + 3043980x - 1268325x - 1634730x + 112740x + 225480)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 4 3 2 +--------+
+--R (- 2109240x - 2714040x + 239778x + 1127140x + 270144)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 7293888x - 7293888x + 3039120x + 3917088x - 270144x - 540288
+--R /
+--R 5 4 3 2
+--R 87127488x + 87127488x - 36303120x - 46790688x + 3226944x + 6453888
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 18790atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 9395atan(------------------------------------------------) - 3216\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 38416\|7
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 6 5 4 3 2 +------+
+--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+r0:=1/3*(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_
+ 46975917593/409600*asin(sqrt(2/11)*sqrt(3+5*x))/_
+ sqrt(10)-439/66*(2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x)-_
+ 4270537963/3379200*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+ 24606179/140800*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 302699/7040*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 4819/440*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+ 4270537963/409600*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (281855505558x - 140927752779)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 6 5 4 3
+--R 248832000x + 1423526400x + 4002203520x + 8217694800x
+--R +
+--R 2
+--R 18987469764x - 58600061024x + 21368105901
+--R *
+--R +--+ +------+
+--R \|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (2457600x - 1228800)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 500
+--a0:=integrate(t0,x)
+--E 103
+
+--S 104 of 500
+--m0:=a0-r0
+--E 104
+
+--S 105 of 500
+--d0:=D(m0,x)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 5 4 3 2 +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3
+--R (1) -------------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+r0:=1/3*(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2)+103884253/4096*_
+ asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-373/66*(2+3*x)^2*_
+ (3+5*x)^(5/2)/sqrt(1-2*x)-9444023/33792*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-278043/7040*(3+5*x)^(5/2)*sqrt(1-2*x)-1/1760*_
+ (3+5*x)^(5/2)*(31978+50205*x)*sqrt(1-2*x)-9444023/4096*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (623305518x - 311652759)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 1036800x + 5477760x + 15301008x + 40614996x - 129940960x
+--R +
+--R 47216961
+--R *
+--R +--+ +------+
+--R \|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (24576x - 12288)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 500
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 500
+--m0:=a0-r0
+--E 109
+
+--S 110 of 500
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 4 3 2 +------+
+--R (225x + 570x + 541x + 228x + 36)\|5x + 3
+--R (1) --------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+r0:=49/66*(3+5*x)^(7/2)/(1-2*x)^(3/2)+272239/256*asin(sqrt(2/11)*_
+ sqrt(3+5*x))*sqrt(5/2)-1183/363*(3+5*x)^(7/2)/sqrt(1-2*x)-_
+ 123745/2112*(3+5*x)^(3/2)*sqrt(1-2*x)-24749/2904*(3+5*x)^(5/2)*_
+ sqrt(1-2*x)-123745/256*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3
+--R (1633434x - 816717)\|5 \|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +-+ +------+
+--R (28800x + 146160x + 497868x - 1713440x + 617319)\|2 \|5x + 3
+--R /
+--R +-+ +--------+
+--R (1536x - 768)\|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 500
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 500
+--m0:=a0-r0
+--E 114
+
+--S 115 of 500
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 3 2 +------+
+--R (75x + 140x + 87x + 18)\|5x + 3
+--R (1) ----------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+r0:=7/33*(3+5*x)^(7/2)/(1-2*x)^(3/2)+13145/64*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(5/2)-239/66*(3+5*x)^(5/2)/sqrt(1-2*x)-5975/528*(3+5*x)^(3/2)*_
+ sqrt(1-2*x)-5975/64*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3
+--R (78870x - 39435)\|5 \|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +-+ +------+
+--R (3600x + 20820x - 84064x + 29601)\|2 \|5x + 3
+--R /
+--R +-+ +--------+
+--R (384x - 192)\|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 500
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 500
+--m0:=a0-r0
+--E 119
+
+--S 120 of 500
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(3+5*x)^(5/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+r0:=1/3*(3+5*x)^(5/2)/(1-2*x)^(3/2)+275/8*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(5/2)-25/6*(3+5*x)^(3/2)/sqrt(1-2*x)-125/8*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|2 \|5x + 3
+--R (1650x - 825)\|5 \|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +-+ +------+
+--R (300x - 1840x + 603)\|2 \|5x + 3
+--R /
+--R +-+ +--------+
+--R (48x - 24)\|2 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 500
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 500
+--m0:=a0-r0
+--E 124
+
+--S 125 of 500
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) --------------------------------
+--R 3 2 +--------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+r0:=2/21*(3+5*x)^(5/2)/(1-2*x)^(3/2)+25/6*asin(sqrt(2/11)*sqrt(3+5*x))*_
+ sqrt(5/2)-2/147*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_
+ sqrt(7)-76/147*(3+5*x)^(3/2)/sqrt(1-2*x)-185/98*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +-+ +--------+ \|7 \|5x + 3
+--R (- 8x + 4)\|2 \|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +------+
+--R +-+ +-+ +--------+ \|2 \|5x + 3
+--R (2450x - 1225)\|5 \|7 \|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R +-+ +-+ +------+
+--R (- 3212x + 759)\|2 \|7 \|5x + 3
+--R /
+--R +-+ +-+ +--------+
+--R (588x - 294)\|2 \|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 500 (residue poly has multiple non-linear factors)
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 500
+--m0:=a0-r0
+--E 129
+
+--S 130 of 500
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^2)
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) ----------------------------------------
+--R 4 3 2 +--------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x))+55/343*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-10/147*(3+5*x)^(3/2)/((2+3*x)*_
+ sqrt(1-2*x))-5/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ \|7 \|5x + 3
+--R (990x + 165x - 330)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +------+
+--R (- 3090x - 3070x - 657)\|7 \|5x + 3
+--R /
+--R 2 +-+ +--------+
+--R (6174x + 1029x - 2058)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (15840x - 5280x - 6600x + 2640)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 2 +--------+ +------+ 3 2
+--R (346080x + 343840x + 73584)\|- 2x + 1 \|5x + 3 - 1048572x + 349524x
+--R +
+--R 436905x - 174762
+--R /
+--R 3 2
+--R 1382976x - 460992x - 576240x + 230496
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 880atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +-+
+--R 440atan(------------------------------------------------------) - 4161\|7
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R /
+--R +-+
+--R 5488\|7
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^3)
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -------------------------------------------------
+--R 5 4 3 2 +--------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^2)-715/1372*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+8/21*(3+5*x)^(3/2)/((2+3*x)^2*_
+ sqrt(1-2*x))+5/98*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-285/1372*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 3 2 +--------+ \|7 \|5x + 3
+--R (- 38610x - 32175x + 8580x + 8580)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +------+
+--R (10260x + 1620x - 13627x - 6732)\|7 \|5x + 3
+--R /
+--R 3 2 +-+ +--------+
+--R (74088x + 61740x - 16464x - 16464)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 308880x - 102960x + 197340x + 34320x - 34320)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 3 2 +--------+ +------+ 4
+--R (- 574560x - 90720x + 763112x + 376992)\|- 2x + 1 \|5x + 3 - 8058204x
+--R +
+--R 3 2
+--R - 2686068x + 5148297x + 895356x - 895356
+--R /
+--R 4 3 2
+--R 8297856x + 2765952x - 5301408x - 921984x + 921984
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 5720atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R - 2860atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R +-+
+--R - 10659\|7
+--R /
+--R +-+
+--R 10976\|7
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^4)
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) ------------------------------------------------------------
+--R 6 5 4 3 2 +--------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^3)+2585/19208*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+122/147*(3+5*x)^(3/2)/((2+3*x)^3*_
+ sqrt(1-2*x))+17/147*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-2165/4116*_
+ sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-15755/57624*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2 +--------+
+--R (418770x + 628155x + 139590x - 155100x - 62040)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+ +------+
+--R (567180x + 552780x - 169221x - 304730x - 75888)\|7 \|5x + 3
+--R /
+--R 4 3 2 +-+ +--------+
+--R (3111696x + 4667544x + 1037232x - 1152480x - 460992)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2 +-+
+--R (837540x + 837540x - 348975x - 449790x + 31020x + 62040)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 4 3 2 +--------+
+--R (- 7940520x - 7738920x + 2369094x + 4266220x + 1062432)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 5 4 3 2
+--R 28685664x + 28685664x - 11952360x - 15405264x + 1062432x + 2124864
+--R /
+--R 5 4 3 2
+--R 87127488x + 87127488x - 36303120x - 46790688x + 3226944x + 6453888
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 5170atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+
+--R 2585atan(------------------------------------------------) + 12648\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R /
+--R +-+
+--R 38416\|7
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^5)
+--R
+--R
+--R (1)
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R ------------------------------------------------------------------------
+--R 7 6 5 4 3 2 +--------+
+--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^4)+547745/1075648*_
+ atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+188/147*(3+5*x)^(3/2)/_
+ ((2+3*x)^4*sqrt(1-2*x))+247/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-_
+ 2287/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-24335/76832*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^2-139745/1075648*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 5 4 3 2
+--R 266204070x + 576775485x + 354938760x - 39437640x - 105167040x
+--R +
+--R - 26291760
+--R *
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3
+--R \|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R 45277380x + 82071900x + 25673409x - 27318504x - 18627988x
+--R +
+--R - 2906640
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R /
+--R 5 4 3 2
+--R 522764928x + 1132657344x + 697019904x - 77446656x - 206524416x
+--R +
+--R - 51631104
+--R *
+--R +-+ +--------+
+--R \|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4 3 2
+--R 1064816280x + 1774693800x + 266204070x - 867628080x - 341792880x
+--R +
+--R 105167040x + 52583520
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R \|7 atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 5 4 3 2
+--R - 1267766640x - 2298013200x - 718855452x + 764918112x
+--R +
+--R 521583664x + 81385920
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4 3 2
+--R - 2884113540x - 4806855900x - 721028385x + 2350018440x + 925764840x
+--R +
+--R - 284850720x - 142425360
+--R /
+--R 6 5 4 3
+--R 29274835968x + 48791393280x + 7318708992x - 23853570048x
+--R +
+--R 2
+--R - 9396860928x + 2891341824x + 1445670912
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2190980atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R 1095490atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R +-+
+--R - 423885\|7
+--R /
+--R +-+
+--R 4302592\|7
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(2+3*x)^5/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+r0:=8261577/6400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+721/660*(2+3*x)^3*_
+ sqrt(3+5*x)/(1-2*x)^(3/2)-1/10*(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(3/2)-_
+ 167363/14520*(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)-_
+ 90052591/774400*sqrt(1-2*x)*sqrt(3+5*x)-3/193600*_
+ (2561546+4177045*x)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (5997904902x - 2998952451)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (18817920x + 101146320x + 359461476x - 1261070176x + 452899509)\|10
+--R *
+--R +------+
+--R \|5x + 3
+--R /
+--R +--+ +--------+
+--R (4646400x - 2323200)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 500
+--a0:=integrate(t0,x)
+--E 153
+
+--S 154 of 500
+--m0:=a0-r0
+--E 154
+
+--S 155 of 500
+--d0:=D(m0,x)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(2+3*x)^4/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+r0:=392283/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1673/1320*(2+3*x)^2*_
+ sqrt(3+5*x)/(1-2*x)^(3/2)-3/20*(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2)-_
+ 7/29040*(76466+124737*x)*sqrt(3+5*x)/sqrt(1-2*x)-_
+ 4282637/193600*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (284797458x - 142398729)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+ +------+
+--R (2352240x + 14544684x - 61036064x + 21305631)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (1161600x - 580800)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 500
+--a0:=integrate(t0,x)
+--E 158
+
+--S 159 of 500
+--m0:=a0-r0
+--E 159
+
+--S 160 of 500
+--d0:=D(m0,x)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(2+3*x)^3/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+r0:=1593/40*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1183/660*(2+3*x)*_
+ sqrt(3+5*x)/(1-2*x)^(3/2)-3/10*(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(3/2)-_
+ 117929/14520*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3
+--R (1156518x - 578259)\|- 2x + 1 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+ +------+
+--R (39204x - 261664x + 83301)\|10 \|5x + 3
+--R /
+--R +--+ +--------+
+--R (29040x - 14520)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 500
+--a0:=integrate(t0,x)
+--E 163
+
+--S 164 of 500
+--m0:=a0-r0
+--E 164
+
+--S 165 of 500
+--d0:=D(m0,x)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(2+3*x)^2/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+r0:=9/2*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/66*_
+ sqrt(3+5*x)/(1-2*x)^(3/2)-448/363*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|2 \|5x + 3 +--+ +------+
+--R (6534x - 3267)\|- 2x + 1 asin(-------------) + (- 1792x + 357)\|10 \|5x + 3
+--R +--+
+--R \|11
+--R ----------------------------------------------------------------------------
+--R +--+ +--------+
+--R (1452x - 726)\|10 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 500
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 500
+--m0:=a0-r0
+--E 169
+
+--S 170 of 500
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(2+3*x)/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 3x + 2
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+r0:=7/33*sqrt(3+5*x)/(1-2*x)^(3/2)-29/363*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +------+
+--R (- 58x - 48)\|5x + 3
+--R (2) -----------------------
+--R +--------+
+--R (726x - 363)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+ 2
+--R (58x + 48)\|- 2x + 1 \|5x + 3 + 336x - 336x + 84
+--R (3) --------------------------------------------------
+--R 2
+--R 1452x - 1452x + 363
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 28
+--R (4) ---
+--R 121
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=1/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+r0:=2/33*sqrt(3+5*x)/(1-2*x)^(3/2)+20/363*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +------+
+--R (40x - 42)\|5x + 3
+--R (2) -----------------------
+--R +--------+
+--R (726x - 363)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +------+ 2
+--R (- 40x + 42)\|- 2x + 1 \|5x + 3 + 336x - 336x + 84
+--R (3) ----------------------------------------------------
+--R 2
+--R 1452x - 1452x + 363
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 28
+--R (4) ---
+--R 121
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+r0:=18/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+4/231*_
+ sqrt(3+5*x)/(1-2*x)^(3/2)+676/17787*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3 +-+ +------+
+--R (13068x - 6534)\|- 2x + 1 atan(-------------) + (1352x - 984)\|7 \|5x + 3
+--R +--------+
+--R \|- 2x + 1
+--R --------------------------------------------------------------------------
+--R +-+ +--------+
+--R (35574x - 17787)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R (- 13068x + 13068x - 3267)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +--------+ +------+ 2
+--R (- 9464x + 6888)\|- 2x + 1 \|5x + 3 + 55104x - 55104x + 13776
+--R /
+--R 2
+--R 498036x - 498036x + 124509
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 2178atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+
+--R - 1089atan(--------------------------------------------------) + 656\|7
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R /
+--R +-+
+--R 5929\|7
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+r0:=405/343*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+4/231*_
+ sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))+940/17787*sqrt(3+5*x)/_
+ ((2+3*x)*sqrt(1-2*x))+2195/41503*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ \|7 \|5x + 3
+--R (882090x + 147015x - 294030)\|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+ +------+
+--R (- 26340x + 39500x - 15321)\|7 \|5x + 3
+--R /
+--R 2 +-+ +--------+
+--R (747054x + 124509x - 249018)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 14113440x + 4704480x + 5880600x - 2352240)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 2 +--------+ +------+ 3
+--R (2950080x - 4424000x + 1715952)\|- 2x + 1 \|5x + 3 + 24452316x
+--R +
+--R 2
+--R - 8150772x - 10188465x + 4075386
+--R /
+--R 3 2
+--R 167340096x - 55780032x - 69725040x + 27890016
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 784080atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 392040atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 97033\|7
+--R /
+--R +-+
+--R 664048\|7
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+r0:=5805/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+172/2541*_
+ sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+85/11858*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^2+57595/166012*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (37929870x + 31608225x - 8428860x - 8428860)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+ +------+
+--R (- 2073420x + 676860x + 945629x - 391476)\|7 \|5x + 3
+--R /
+--R 3 2 +-+ +--------+
+--R (8964648x + 7470540x - 1992144x - 1992144)\|7 \|- 2x + 1
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2 +-+
+--R (- 303438960x - 101146320x + 193863780x + 33715440x - 33715440)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 3 2 +--------+ +------+
+--R (116111520x - 37904160x - 52955224x + 21922656)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 468596772x + 156198924x - 299381271x - 52066308x + 52066308
+--R /
+--R 4 3 2
+--R 1004040576x + 334680192x - 641470368x - 111560064x + 111560064
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 5619240atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 2809620atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 619837\|7
+--R /
+--R +-+
+--R 1328096\|7
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^4*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+ +------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+r0:=330255/19208*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)+1468/17787*_
+ sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-73/5929*sqrt(1-2*x)*_
+ sqrt(3+5*x)/(2+3*x)^3+30535/166012*sqrt(1-2*x)*sqrt(3+5*x)/_
+ (2+3*x)^2+3471145/2324168*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R (6473658510x + 9710487765x + 2157886170x - 2397651300x - 959060520)
+--R *
+--R +-+ +------+
+--R +--------+ \|7 \|5x + 3
+--R \|- 2x + 1 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (- 374883660x - 140350860x + 244982277x + 48873610x - 44829024)\|7
+--R *
+--R +------+
+--R \|5x + 3
+--R /
+--R 4 3 2 +-+
+--R (376515216x + 564772824x + 125505072x - 139450080x - 55780032)\|7
+--R *
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R - 12947317020x - 12947317020x + 5394715425x + 6953188770x
+--R +
+--R - 479530260x - 959060520
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R \|7 atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 4 3 2
+--R (5248371240x + 1964912040x - 3429751878x - 684230540x + 627606336)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R 20122628148x + 20122628148x - 8384428395x - 10806596598x + 745282524x
+--R +
+--R 1490565048
+--R /
+--R 5 4 3 2
+--R 10542426048x + 10542426048x - 4392677520x - 5661673248x + 390460224x
+--R +
+--R 780920448
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 79921710atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R - 39960855atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 8872411\|7
+--R /
+--R +-+
+--R 4648336\|7
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) ------------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+r0:=243189/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1673/1320*(2+3*x)^3/_
+ ((1-2*x)^(3/2)*sqrt(3+5*x))-3/20*(2+3*x)^4/((1-2*x)^(3/2)*_
+ sqrt(3+5*x))-273749/29040*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))+_
+ 270463/319440*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-28291441/2129600*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3
+--R (1942107354x - 971053677)\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (77623920x + 536898780x - 1790987404x - 525679641x + 435258129)\|10
+--R /
+--R +--+ +--------+ +------+
+--R (12777600x - 6388800)\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 500
+--a0:=integrate(t0,x)
+--E 203
+
+--S 204 of 500
+--m0:=a0-r0
+--E 204
+
+--S 205 of 500
+--d0:=D(m0,x)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+r0:=4887/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1183/660*(2+3*x)^2/_
+ ((1-2*x)^(3/2)*sqrt(3+5*x))-3/10*(2+3*x)^3/((1-2*x)^(3/2)*_
+ sqrt(3+5*x))-7/14520*(31106+53757*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_
+ 212417/798600*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3
+--R (39027582x - 19513791)\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (6468660x - 40488772x - 12657123x + 8379147)\|10
+--R /
+--R +--+ +--------+ +------+
+--R (1597200x - 798600)\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 500
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 500
+--m0:=a0-r0
+--E 209
+
+--S 210 of 500
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+r0:=27/10*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+2/33*(2+3*x)^3/_
+ ((1-2*x)^(3/2)*sqrt(3+5*x))-58/363*(2+3*x)^2/(sqrt(1-2*x)*_
+ sqrt(3+5*x))+50/3993*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-_
+ 3103/13310*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|2 \|5x + 3
+--R (215622x - 107811)\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 2 +--+
+--R (- 298852x - 124263x + 33087)\|10
+--R /
+--R +--+ +--------+ +------+
+--R (79860x - 39930)\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 500
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 500
+--m0:=a0-r0
+--E 214
+
+--S 215 of 500
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+r0:=49/66/((1-2*x)^(3/2)*sqrt(3+5*x))+(-1237/3630)/(sqrt(1-2*x)*_
+ sqrt(3+5*x))-793/19965*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 2
+--R - 1586x - 2880x - 1128
+--R (2) ----------------------------------
+--R +--------+ +------+
+--R (7986x - 3993)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +--------+ +------+ 3 2
+--R (1586x + 2880x + 1128)\|- 2x + 1 \|5x + 3 + 13160x - 5264x - 4606x + 1974
+--R -----------------------------------------------------------------------------
+--R 3 2
+--R 79860x - 31944x - 27951x + 11979
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 658
+--R (4) ----
+--R 3993
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 3x + 2
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+r0:=(-2/55)/((1-2*x)^(3/2)*sqrt(3+5*x))+82/1815*sqrt(3+5*x)/(1-2*x)^(3/2)+_
+ 164/3993*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 2
+--R 1640x - 738x - 888
+--R (2) ----------------------------------
+--R +--------+ +------+
+--R (7986x - 3993)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +--------+ +------+ 3 2
+--R (- 1640x + 738x + 888)\|- 2x + 1 \|5x + 3 + 14060x - 5624x - 4921x + 2109
+--R -----------------------------------------------------------------------------
+--R 3 2
+--R 79860x - 31944x - 27951x + 11979
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 703
+--R (4) ----
+--R 3993
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=1/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+r0:=2/33/((1-2*x)^(3/2)*sqrt(3+5*x))+40/363/(sqrt(1-2*x)*sqrt(3+5*x))-_
+ 400/3993*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 2
+--R 1600x - 720x - 282
+--R (2) ----------------------------------
+--R +--------+ +------+
+--R (7986x - 3993)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +--------+ +------+ 3 2
+--R (- 3200x + 1440x + 564)\|- 2x + 1 \|5x + 3 + 6580x - 2632x - 2303x + 987
+--R ----------------------------------------------------------------------------
+--R 3 2
+--R 159720x - 63888x - 55902x + 23958
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 329
+--R (4) ----
+--R 7986
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+r0:=-54/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/231/((1-2*x)^(3/2)*sqrt(3+5*x))+_
+ 956/17787/(sqrt(1-2*x)*sqrt(3+5*x))-42230/195657*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R +--------+ +------+ \|7 \|5x + 3
+--R (- 431244x + 215622)\|- 2x + 1 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 2 +-+
+--R (168920x - 147888x + 28326)\|7
+--R /
+--R +-+ +--------+ +------+
+--R (391314x - 195657)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +-+
+--R (- 4312440x + 1724976x + 1509354x - 646866)\|7
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R 2 +--------+ +------+ 3
+--R (- 2364880x + 2070432x - 396564)\|- 2x + 1 \|5x + 3 + 4626580x
+--R +
+--R 2
+--R - 1850632x - 1619303x + 693987
+--R /
+--R 3 2
+--R 54783960x - 21913584x - 19174386x + 8217594
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 431244atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7
+--R - 215622atan(---------------------------------------------------)
+--R +--------+ +------+
+--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320
+--R +
+--R +-+
+--R 33047\|7
+--R /
+--R +-+
+--R 391314\|7
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+r0:=-3105/343*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/231/((1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x))+_
+ 1220/17787/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))-_
+ 1840225/1369599*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 1915/41503*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 2 +--------+ +------+
+--R (- 74389590x - 12398265x + 24796530)\|- 2x + 1 \|5x + 3
+--R *
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+
+--R (22082700x - 7613680x - 8760465x + 3499599)\|7
+--R /
+--R 2 +-+ +--------+ +------+
+--R (8217594x + 1369599x - 2739198)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 5951167200x - 1586977920x + 3669886440x + 495930600x - 595116720)
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R \|7 atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R 3 2 +--------+
+--R (- 2473262400x + 852732160x + 981172080x - 391955088)\|- 2x + 1
+--R *
+--R +------+
+--R \|5x + 3
+--R +
+--R 4 3 2
+--R 9308933340x + 2482382224x - 5740508893x - 775744445x + 930893334
+--R /
+--R 4 3 2
+--R 9203705280x + 2454321408x - 5675618256x - 766975440x + 920370528
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 198372240atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7
+--R - 99186120atan(------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320
+--R +
+--R +-+
+--R 22164127\|7
+--R /
+--R +-+
+--R 21913584\|7
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+ +------+
+--R (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+r0:=-79515/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_
+ 4/231/((1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x))+212/2541/((2+3*x)^2*_
+ sqrt(1-2*x)*sqrt(3+5*x))-46307675/5478396*sqrt(1-2*x)/sqrt(3+5*x)+_
+ 5/11858*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_
+ 89945/166012*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (- 5715061110x - 4762550925x + 1270013580x + 1270013580)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (1667076300x + 520073880x - 1053213025x - 169466391x + 178740084)\|7
+--R /
+--R 3 2 +-+ +--------+ +------+
+--R (98611128x + 82175940x - 21913584x - 21913584)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 285753055500x + 266702851800x - 125413841025x - 141289010775x
+--R +
+--R 12700135800x + 19050203700
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R \|7 atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R 4 3 2
+--R - 116695341000x - 36405171600x + 73724911750x + 11862647370x
+--R +
+--R - 12511805880
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 525495846960x - 490462790496x + 230634288388x + 259828502108x
+--R +
+--R - 23355370976x - 35033056464
+--R /
+--R 5 4 3 2
+--R 69027789600x + 64425936960x - 30295529880x - 34130407080x
+--R +
+--R 3067901760x + 4601852640
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R 3175033950atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7
+--R 1587516975atan(-----------------------------------------------)
+--R +--------+ +------+
+--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700
+--R +
+--R +-+
+--R - 417060196\|7
+--R /
+--R +-+
+--R 54783960\|7
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 6 5 4 3 2
+--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64
+--R (1) -----------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+r0:=1673/1320*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2))-3/20*(2+3*x)^5/_
+ ((1-2*x)^(3/2)*(3+5*x)^(3/2))+753543/8000*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)-89943/9680*(2+3*x)^3/((3+5*x)^(3/2)*_
+ sqrt(1-2*x))+1332779/1597200*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 9214471/17569200*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-_
+ 964268137/117128000*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 2 +--------+ +------+
+--R (330978691890x + 33097869189x - 99293607567)\|- 2x + 1 \|5x + 3
+--R *
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 5 4 3 2
+--R 12807946800x + 97980793020x - 252342435560x - 274128335769x
+--R +
+--R 19932058554x + 44437106459
+--R *
+--R +--+
+--R \|10
+--R /
+--R 2 +--+ +--------+ +------+
+--R (3513840000x + 351384000x - 1054152000)\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 500
+--a0:=integrate(t0,x)
+--E 248
+
+--S 249 of 500
+--m0:=a0-r0
+--E 249
+
+--S 250 of 500
+--d0:=D(m0,x)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 5 4 3 2
+--R 243x + 810x + 1080x + 720x + 240x + 32
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+r0:=1183/660*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2))-3/10*(2+3*x)^4/_
+ ((1-2*x)^(3/2)*(3+5*x)^(3/2))+2997/200*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)-38003/4840*(2+3*x)^2/((3+5*x)^(3/2)*_
+ sqrt(1-2*x))+111719/159720*(2+3*x)*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 3831323/8784600*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 2 +--------+ +------+
+--R (1316372310x + 131637231x - 394911693)\|- 2x + 1 \|5x + 3
+--R *
+--R +-+ +------+
+--R \|2 \|5x + 3
+--R asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 4 3 2 +--+
+--R (213465780x - 1247811640x - 1260430251x + 19593966x + 168318961)\|10
+--R /
+--R 2 +--+ +--------+ +------+
+--R (87846000x + 8784600x - 26353800)\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 500
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 500
+--m0:=a0-r0
+--E 254
+
+--S 255 of 500
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 4 3 2
+--R 81x + 216x + 216x + 96x + 16
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+r0:=2/33*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2))+81/50*asin(sqrt(2/11)*_
+ sqrt(3+5*x))/sqrt(10)-18/121*(2+3*x)^3/((3+5*x)^(3/2)*_
+ sqrt(1-2*x))+50/3993*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 1058/219615*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-100159/732050*_
+ sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ +------+ \|2 \|5x + 3
+--R (35577630x + 3557763x - 10673289)\|- 2x + 1 \|5x + 3 asin(-------------)
+--R +--+
+--R \|11
+--R +
+--R 3 2 +--+
+--R (- 49702040x - 51334383x - 7883562x + 3014813)\|10
+--R /
+--R 2 +--+ +--------+ +------+
+--R (21961500x + 2196150x - 6588450)\|10 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 500
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 500
+--m0:=a0-r0
+--E 259
+
+--S 260 of 500
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 3 2
+--R 27x + 54x + 36x + 8
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+r0:=2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2))+49/121/((3+5*x)^(3/2)*_
+ sqrt(1-2*x))-3679/19965*sqrt(1-2*x)/(3+5*x)^(3/2)-8182/_
+ 219615*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 3 2
+--R - 39146x - 124464x - 104088x - 26080
+--R (2) ------------------------------------------------
+--R 2 +--------+ +------+
+--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+ +------+ 4
+--R (352314x + 1120176x + 936792x + 234720)\|- 2x + 1 \|5x + 3 + 5216000x
+--R +
+--R 3 2
+--R 1043200x - 3077440x - 312960x + 469440
+--R /
+--R 4 3 2
+--R 39530700x + 7906140x - 23323113x - 2371842x + 3557763
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 52160
+--R (4) ------
+--R 395307
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 2
+--R 9x + 12x + 4
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+r0:=49/66/((1-2*x)^(3/2)*(3+5*x)^(3/2))+14/121/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 1649/7986*sqrt(1-2*x)/(3+5*x)^(3/2)-3298/43923*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 3 2
+--R 65960x + 9894x - 49200x - 18728
+--R (2) ------------------------------------------------
+--R 2 +--------+ +------+
+--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+ +------+
+--R (- 2968200x - 445230x + 2214000x + 842760)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 26219200x + 5243840x - 15469328x - 1573152x + 2359728
+--R /
+--R 4 3 2
+--R 197653500x + 39530700x - 116615565x - 11859210x + 17788815
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 262192
+--R (4) -------
+--R 1976535
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 3x + 2
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+r0:=(-2/165)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+74/1815/((1-2*x)^(3/2)*_
+ sqrt(3+5*x))+296/3993/(sqrt(1-2*x)*sqrt(3+5*x))-2960/43923*_
+ sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 3 2
+--R 59200x + 8880x - 26418x - 5728
+--R (2) ------------------------------------------------
+--R 2 +--------+ +------+
+--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+ +------+ 4
+--R (- 532800x - 79920x + 237762x + 51552)\|- 2x + 1 \|5x + 3 - 1145600x
+--R +
+--R 3 2
+--R - 229120x + 675904x + 68736x - 103104
+--R /
+--R 4 3 2
+--R 39530700x + 7906140x - 23323113x - 2371842x + 3557763
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 11456
+--R (4) - ------
+--R 395307
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=1/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+r0:=2/33/((1-2*x)^(3/2)*(3+5*x)^(3/2))+20/121/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+ 400/3993*sqrt(1-2*x)/(3+5*x)^(3/2)-1600/43923*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 3 2
+--R 32000x + 4800x - 14280x - 722
+--R (2) ------------------------------------------------
+--R 2 +--------+ +------+
+--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 +--------+ +------+ 4
+--R (- 288000x - 43200x + 128520x + 6498)\|- 2x + 1 \|5x + 3 + 144400x
+--R +
+--R 3 2
+--R 28880x - 85196x - 8664x + 12996
+--R /
+--R 4 3 2
+--R 39530700x + 7906140x - 23323113x - 2371842x + 3557763
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 1444
+--R (4) ------
+--R 395307
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+r0:=4/231/((1-2*x)^(3/2)*(3+5*x)^(3/2))+162/49*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+412/5929/((3+5*x)^(3/2)*_
+ sqrt(1-2*x))-19130/195657*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 1001590/2152227*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R +-+ +------+
+--R 2 +--------+ +------+ \|7 \|5x + 3
+--R (71155260x + 7115526x - 21346578)\|- 2x + 1 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 3 2 +-+
+--R (- 20031800x + 8854440x + 6468522x - 2981164)\|7
+--R /
+--R 2 +-+ +--------+ +------+
+--R (21522270x + 2152227x - 6456681)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 2
+--R (- 3201986700x - 640397340x + 1889172153x + 192119202x - 288178803)
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R \|7 atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R 3 2 +--------+ +------+
+--R (1262003400x - 557829720x - 407516886x + 187813332)\|- 2x + 1 \|5x + 3
+--R +
+--R 4 3 2
+--R 4173629600x + 834725920x - 2462441464x - 250417776x + 375626664
+--R /
+--R 4 3 2
+--R 13559030100x + 2711806020x - 7999827759x - 813541806x + 1220312709
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 64039734atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7
+--R - 32019867atan(--------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540
+--R +
+--R +-+
+--R 5962328\|7
+--R /
+--R +-+
+--R 19370043\|7
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R -----------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+ +------+
+--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+r0:=4/231/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2))+14985/343*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+500/5929/((2+3*x)*(3+5*x)^(3/2)*_
+ sqrt(1-2*x))-985525/1369599*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+ 1635/41503*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 95783075/15065589*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 3 2 +--------+
+--R (19745584650x + 15138281565x - 4607303085x - 3949116930)\|- 2x + 1
+--R *
+--R +-+ +------+
+--R +------+ \|7 \|5x + 3
+--R \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 4 3 2 +-+
+--R (- 5746984500x - 1402439900x + 3498236655x + 429626520x - 555141781)\|7
+--R /
+--R 3 2 +-+ +--------+ +------+
+--R (451967670x + 346508547x - 105459123x - 90393534)\|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 3 2
+--R 1777102618500x + 1540155602700x - 811543529115x - 805619853720x
+--R +
+--R 88855130925x + 106626157110
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R \|7 atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R 4 3 2
+--R 724120047000x + 176707427400x - 440777818530x - 54132941520x
+--R +
+--R 69947864406
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 5 4 3 2
+--R - 2331595480200x - 2020716082840x + 1064761935958x + 1056989951024x
+--R +
+--R - 116579774010x - 139895728812
+--R /
+--R 5 4 3 2
+--R 569479264200x + 493548695640x - 260062197318x - 258163933104x
+--R +
+--R 28473963210x + 34168755852
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 11847350790atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R +-+ +--------+ +------+ +-+
+--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7
+--R 5923675395atan(------------------------------------------------)
+--R +--------+ +------+
+--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540
+--R +
+--R +-+
+--R - 1110283562\|7
+--R /
+--R +-+
+--R 271180602\|7
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 7 6 5 4 3 2
+--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2))+538245/1372*atan(sqrt(7)*_
+ sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+12/121/((2+3*x)^2*(3+5*x)^(3/2)*_
+ sqrt(1-2*x))-34551425/5478396*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+ 75/11858*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_
+ 122295/166012*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_
+ 3443814775/60262356*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R (2)
+--R 4 3 2
+--R 2127720162150x + 3049732232415x + 591033378375x - 756522724320x
+--R +
+--R - 283696021620
+--R *
+--R +-+ +------+
+--R +--------+ +------+ \|7 \|5x + 3
+--R \|- 2x + 1 \|5x + 3 atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R 5 4 3 2
+--R - 619886659500x - 564878517900x + 276089438305x + 297937101390x
+--R +
+--R - 28838387211x - 39900939556
+--R *
+--R +-+
+--R \|7
+--R /
+--R 4 3 2
+--R (5423612040x + 7773843924x + 1506558900x - 1928395392x - 723148272)
+--R *
+--R +-+ +--------+ +------+
+--R \|7 \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 500 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 5 4
+--R - 765979258374000x - 1174501529506800x - 92768599069740x
+--R +
+--R 3 2
+--R 580442060234520x + 193196990723220x - 71491397448240x
+--R +
+--R - 30639170334960
+--R *
+--R +-+ +--------+ +------+ +-+
+--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R \|7 atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R 5 4 3
+--R 312422876388000x + 284698773021600x - 139149076905720x
+--R +
+--R 2
+--R - 150160299100560x + 14534547154344x + 20110073536224
+--R *
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R +
+--R 6 5 4
+--R 1194035616213300x + 1830854611527060x + 144610980185833x
+--R +
+--R 3 2
+--R - 904813655841634x - 301162316533799x + 111443324179908x + 47761424648532
+--R /
+--R 6 5 4 3
+--R 27335004681600x + 41913673845120x + 3310572789216x - 20713859103168x
+--R +
+--R 2
+--R - 6894495625248x + 2551267103616x + 1093400187264
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 500 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +------+
+--R \|7 \|5x + 3
+--R - 1702176129720atan(-------------)
+--R +--------+
+--R \|- 2x + 1
+--R +
+--R -
+--R 851088064860
+--R *
+--R +-+ +--------+ +------+ +-+
+--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7
+--R atan(--------------------------------------------------------)
+--R +--------+ +------+
+--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320
+--R +
+--R +-+
+--R 189529462891\|7
+--R /
+--R +-+
+--R 4338889632\|7
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 500
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+ +------+ +------+
+--R (1) (9x + 12x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+--r0:=167647/101250*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2911577/50625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),_
+-- 33/35)/sqrt(35)-23/1575*(2+3*x)^(3/2)*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)+2/45*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+-- 1244/13125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 175111/236250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 297
+
+--S 298 of 500
+--a0:=integrate(t0,x)
+--E 298
+
+--S 299 of 500
+--m0:=a0-r0
+--E 299
+
+--S 300 of 500
+--d0:=D(m0,x)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)
+--R
+--R
+--R +--------+ +------+ +------+
+--R (1) (3x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+--r0:=796/1125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 55019/2250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 2/35*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-27/875*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-823/2625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 302
+
+--S 303 of 500
+--a0:=integrate(t0,x)
+--E 303
+
+--S 304 of 500
+--m0:=a0-r0
+--E 304
+
+--S 305 of 500
+--d0:=D(m0,x)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--R
+--R
+--R +--------+ +------+ +------+
+--R (1) \|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+--r0:=-1159/675*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 259/675*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/25*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-31/225*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 307
+
+--S 308 of 500
+--a0:=integrate(t0,x)
+--E 308
+
+--S 309 of 500
+--m0:=a0-r0
+--E 309
+
+--S 310 of 500
+--d0:=D(m0,x)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) --------------------
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+--r0:=-37/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 28/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/9*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 312
+
+--S 313 of 500
+--a0:=integrate(t0,x)
+--E 313
+
+--S 314 of 500
+--m0:=a0-r0
+--E 314
+
+--S 315 of 500
+--d0:=D(m0,x)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) --------------------
+--R +------+
+--R (3x + 2)\|3x + 2
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+--r0:=-74/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_
+-- 2/3*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 317
+
+--S 318 of 500
+--a0:=integrate(t0,x)
+--E 318
+
+--S 319 of 500
+--m0:=a0-r0
+--E 319
+
+--S 320 of 500
+--d0:=D(m0,x)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) ------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+--r0:=-74/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 40/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/9*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+74/63*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 322
+
+--S 323 of 500
+--a0:=integrate(t0,x)
+--E 323
+
+--S 324 of 500
+--m0:=a0-r0
+--E 324
+
+--S 325 of 500
+--d0:=D(m0,x)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) --------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+--r0:=148/189*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 4636/189*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 2/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+74/315*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+4636/2205*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 327
+
+--S 328 of 500
+--a0:=integrate(t0,x)
+--E 328
+
+--S 329 of 500
+--m0:=a0-r0
+--E 329
+
+--S 330 of 500
+--d0:=D(m0,x)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(9/2)
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+--r0:=6368/3087*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 220076/3087*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 2/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+74/735*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)+3184/5145*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+220076/36015*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 332
+
+--S 333 of 500
+--a0:=integrate(t0,x)
+--E 333
+
+--S 334 of 500
+--m0:=a0-r0
+--E 334
+
+--S 335 of 500
+--d0:=D(m0,x)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+ +------+ +------+
+--R (1) (45x + 87x + 56x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+--r0:=21713939/3341250*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-1508889271/6682500*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 23/2475*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+2/55*(2+3*x)^(5/2)*_
+-- (3+5*x)^(5/2)*sqrt(1-2*x)-342971/866250*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)-543/9625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 11346991/3898125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 337
+
+--S 338 of 500
+--a0:=integrate(t0,x)
+--E 338
+
+--S 339 of 500
+--m0:=a0-r0
+--E 339
+
+--S 340 of 500
+--d0:=D(m0,x)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)
+--R
+--R
+--R 2 +--------+ +------+ +------+
+--R (1) (15x + 19x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+--r0:=153319/60750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 5327983/60750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/45*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+-- 1208/7875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 3/175*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 160297/141750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 342
+
+--S 343 of 500
+--a0:=integrate(t0,x)
+--E 343
+
+--S 344 of 500
+--m0:=a0-r0
+--E 344
+
+--S 345 of 500
+--d0:=D(m0,x)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)
+--R
+--R
+--R +--------+ +------+ +------+
+--R (1) (5x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+--r0:=2129/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 148831/4050*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-31/525*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 2/35*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-2252/4725*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 347
+
+--S 348 of 500
+--a0:=integrate(t0,x)
+--E 348
+
+--S 349 of 500
+--m0:=a0-r0
+--E 349
+
+--S 350 of 500
+--d0:=D(m0,x)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+--r0:=-974/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 119/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/15*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 41/135*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 352
+
+--S 353 of 500
+--a0:=integrate(t0,x)
+--E 353
+
+--S 354 of 500
+--m0:=a0-r0
+--E 354
+
+--S 355 of 500
+--d0:=D(m0,x)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------
+--R +------+
+--R (3x + 2)\|3x + 2
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+--r0:=362/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 49/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_
+-- 2/3*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+40/27*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 357
+
+--S 358 of 500
+--a0:=integrate(t0,x)
+--E 358
+
+--S 359 of 500
+--m0:=a0-r0
+--E 359
+
+--S 360 of 500
+--d0:=D(m0,x)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 500
+--r0:=494/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 1150/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/9*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_
+-- 214/189*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 362
+
+--S 363 of 500
+--a0:=integrate(t0,x)
+--E 363
+
+--S 364 of 500
+--m0:=a0-r0
+--E 364
+
+--S 365 of 500
+--d0:=D(m0,x)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+--r0:=1252/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 8314/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 2/15*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-214/945*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+8314/6615*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 367
+
+--S 368 of 500
+--a0:=integrate(t0,x)
+--E 368
+
+--S 369 of 500
+--m0:=a0-r0
+--E 369
+
+--S 370 of 500
+--d0:=D(m0,x)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+--r0:=17156/27783*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 475592/27783*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-2/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-_
+-- 214/2205*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+8578/46305*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+475592/324135*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 372
+
+--S 373 of 500
+--a0:=integrate(t0,x)
+--E 373
+
+--S 374 of 500
+--m0:=a0-r0
+--E 374
+
+--S 375 of 500
+--d0:=D(m0,x)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(11/2)
+--R
+--R
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+--r0:=664744/583443*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 22738708/583443*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-2/27*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_
+-- 214/3969*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+8842/138915*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+332372/972405*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+22738708/6806835*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 377
+
+--S 378 of 500
+--a0:=integrate(t0,x)
+--E 378
+
+--S 379 of 500
+--m0:=a0-r0
+--E 379
+
+--S 380 of 500
+--d0:=D(m0,x)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+ +------+
+--R (1) (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+--r0:=472506679/17374500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-16416987253/17374500*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-23/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*_
+-- sqrt(1-2*x)+2/65*(2+3*x)^(5/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+-- 1865989/1126125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 564731/2252250*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 2014/53625*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 493825477/40540500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 382
+
+--S 383 of 500
+--a0:=integrate(t0,x)
+--E 383
+
+--S 384 of 500
+--m0:=a0-r0
+--E 384
+
+--S 385 of 500
+--d0:=D(m0,x)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)
+--R
+--R
+--R 3 2 +--------+ +------+ +------+
+--R (1) (75x + 140x + 87x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+--r0:=222527/22275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 30926081/89100*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/55*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+-- 7031/11550*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 177/1925*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 3/275*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 465127/103950*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 387
+
+--S 388 of 500
+--a0:=integrate(t0,x)
+--E 388
+
+--S 389 of 500
+--m0:=a0-r0
+--E 389
+
+--S 390 of 500
+--d0:=D(m0,x)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)
+--R
+--R
+--R 2 +--------+ +------+ +------+
+--R (1) (25x + 30x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+--r0:=28109/7290*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 488149/3645*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-223/945*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 31/945*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+2/45*(3+5*x)^(7/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-29357/17010*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 392
+
+--S 393 of 500
+--a0:=integrate(t0,x)
+--E 393
+
+--S 394 of 500
+--m0:=a0-r0
+--E 394
+
+--S 395 of 500
+--d0:=D(m0,x)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+--r0:=134/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 9013/162*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-1/7*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 2/21*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 131/189*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 397
+
+--S 398 of 500
+--a0:=integrate(t0,x)
+--E 398
+
+--S 399 of 500
+--m0:=a0-r0
+--E 399
+
+--S 400 of 500
+--d0:=D(m0,x)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R +------+
+--R (3x + 2)\|3x + 2
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+--r0:=-3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/3*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+4/3*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 402
+
+--S 403 of 500
+--a0:=integrate(t0,x)
+--E 403
+
+--S 404 of 500
+--m0:=a0-r0
+--E 404
+
+--S 405 of 500
+--d0:=D(m0,x)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+--r0:=-2209/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 2960/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/9*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_
+-- 118/63*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+2470/567*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 407
+
+--S 408 of 500
+--a0:=integrate(t0,x)
+--E 408
+
+--S 409 of 500
+--m0:=a0-r0
+--E 409
+
+--S 410 of 500
+--d0:=D(m0,x)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+--r0:=-13834/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 31588/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-118/315*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_
+-- 2/15*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-12758/6615*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 412
+
+--S 413 of 500
+--a0:=integrate(t0,x)
+--E 413
+
+--S 414 of 500
+--m0:=a0-r0
+--E 414
+
+--S 415 of 500
+--d0:=D(m0,x)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+--r0:=32176/9261*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 173482/9261*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-118/735*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-_
+-- 2/21*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-4282/15435*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+173482/108045*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 417
+
+--S 418 of 500
+--a0:=integrate(t0,x)
+--E 418
+
+--S 419 of 500
+--m0:=a0-r0
+--E 419
+
+--S 420 of 500
+--d0:=D(m0,x)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+--r0:=1136636/1750329*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-27198452/1750329*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-118/1323*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(7/2)-2/27*(3+5*x)^(5/2)*sqrt(1-2*x)/_
+-- (2+3*x)^(9/2)-12934/138915*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(5/2)+568318/2917215*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+27198452/20420505*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 422
+
+--S 423 of 500
+--a0:=integrate(t0,x)
+--E 423
+
+--S 424 of 500
+--m0:=a0-r0
+--E 424
+
+--S 425 of 500
+--d0:=D(m0,x)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(13/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+--r0:=38834192/44925111*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-1305025844/44925111*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-118/2079*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(9/2)-2/33*(3+5*x)^(5/2)*sqrt(1-2*x)/_
+-- (2+3*x)^(11/2)-13022/305613*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(7/2)+627806/10696455*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(5/2)+19417096/74875185*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+1305025844/524126295*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 427
+
+--S 428 of 500
+--a0:=integrate(t0,x)
+--E 428
+
+--S 429 of 500
+--m0:=a0-r0
+--E 429
+
+--S 430 of 500
+--d0:=D(m0,x)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(a+b*x)^(1/2)/((c+d*x)^(1/2)*(e+f*x)^(1/2))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) --------------------
+--R +-------+ +-------+
+--R \|d x + c \|f x + e
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+--r0:=2*elliptic_e(asin(sqrt(f)*sqrt(c+d*x)/sqrt(-d*e+c*f)),-b*(d*e-c*f)/_
+-- ((b*c-a*d)*f))*sqrt(-d*e+c*f)*sqrt(a+b*x)*sqrt(d*(e+f*x)/_
+-- (d*e-c*f))/(d*sqrt(f)*sqrt(-d*(a+b*x)/(b*c-a*d))*sqrt(e+f*x))
+--E 432
+
+--S 433 of 500
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 500
+--m0:=a0-r0
+--E 434
+
+--S 435 of 500
+--d0:=D(m0,x)
+--E 435
+
+--R
+--R
+--R (2) tpdhere
+--R Type: Variable(tpdhere)
+)clear all
+
+--S 436 of 500
+t0:=(a+b*x)^(1/2)/((c+d*x)^(3/2)*(e+f*x)^(1/2))
+--R
+--R
+--R +-------+
+--R \|b x + a
+--R (1) -----------------------------
+--R +-------+ +-------+
+--R (d x + c)\|d x + c \|f x + e
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+--r0:=-2*sqrt(a+b*x)*sqrt(e+f*x)/((d*e-c*f)*sqrt(c+d*x))+_
+-- 2*elliptic_e(asin(sqrt(d)*sqrt(a+b*x)/sqrt(-b*c+a*d)),_
+-- (b*c-a*d)*f/(d*(b*e-a*f)))*sqrt(-b*c+a*d)*sqrt(b*(c+d*x)/_
+-- (b*c-a*d))*sqrt(e+f*x)/((d*e-c*f)*sqrt(d)*sqrt(c+d*x)*_
+-- sqrt(b*(e+f*x)/(b*e-a*f)))
+--E 437
+
+--S 438 of 500
+--a0:=integrate(t0,x)
+--E 438
+
+--S 439 of 500
+--m0:=a0-r0
+--E 439
+
+--S 440 of 500
+--d0:=D(m0,x)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+--r0:=859/1875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 61151/3750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-23/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 2/35*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-859/4375*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 442
+
+--S 443 of 500
+--a0:=integrate(t0,x)
+--E 443
+
+--S 444 of 500
+--m0:=a0-r0
+--E 444
+
+--S 445 of 500
+--d0:=D(m0,x)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)
+--R
+--R
+--R +--------+ +------+
+--R (3x + 2)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+--r0:=7/125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_
+-- 146/125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+2/25*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 9/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 447
+
+--S 448 of 500
+--a0:=integrate(t0,x)
+--E 448
+
+--S 449 of 500
+--m0:=a0-r0
+--E 449
+
+--S 450 of 500
+--d0:=D(m0,x)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|3x + 2
+--R (1) --------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+--r0:=-31/45*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 14/45*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/15*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 452
+
+--S 453 of 500
+--a0:=integrate(t0,x)
+--E 453
+
+--S 454 of 500
+--m0:=a0-r0
+--E 454
+
+--S 455 of 500
+--d0:=D(m0,x)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ------------------
+--R +------+ +------+
+--R \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+--r0:=2/3*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(7/5)*_
+-- sqrt(-3-5*x)/sqrt(3+5*x)
+--E 457
+
+--S 458 of 500
+--a0:=integrate(t0,x)
+--E 458
+
+--S 459 of 500
+--m0:=a0-r0
+--E 459
+
+--S 460 of 500
+--d0:=D(m0,x)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) --------------------------
+--R +------+ +------+
+--R (3x + 2)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+--r0:=-2*elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(11/3)+_
+-- 2*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 462
+
+--S 463 of 500
+--a0:=integrate(t0,x)
+--E 463
+
+--S 464 of 500
+--m0:=a0-r0
+--E 464
+
+--S 465 of 500
+--d0:=D(m0,x)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ---------------------------------
+--R 2 +------+ +------+
+--R (9x + 12x + 4)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+--r0:=-136/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 20/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 136/21*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 467
+
+--S 468 of 500
+--a0:=integrate(t0,x)
+--E 468
+
+--S 469 of 500
+--m0:=a0-r0
+--E 469
+
+--S 470 of 500
+--d0:=D(m0,x)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------------------------------------
+--R 3 2 +------+ +------+
+--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+--r0:=184/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 6388/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/5*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+92/35*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+6388/245*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 472
+
+--S 473 of 500
+--a0:=integrate(t0,x)
+--E 473
+
+--S 474 of 500
+--m0:=a0-r0
+--E 474
+
+--S 475 of 500
+--d0:=D(m0,x)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2
+--R (1) -------------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+--r0:=226/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*_
+-- sqrt(11/3)-203179/18750*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(2+3*x)^(7/2)*sqrt(1-2*x)/_
+-- sqrt(3+5*x)+183/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 48/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 2486/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 477
+
+--S 478 of 500
+--a0:=integrate(t0,x)
+--E 478
+
+--S 479 of 500
+--m0:=a0-r0
+--E 479
+
+--S 480 of 500
+--d0:=D(m0,x)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+--r0:=-1409/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-91/1875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/5*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 36/125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+13/625*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 482
+
+--S 483 of 500
+--a0:=integrate(t0,x)
+--E 483
+
+--S 484 of 500
+--m0:=a0-r0
+--E 484
+
+--S 485 of 500
+--d0:=D(m0,x)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)
+--R
+--R
+--R +--------+ +------+
+--R (3x + 2)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+--r0:=-19/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-56/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/5*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 8/25*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 487
+
+--S 488 of 500
+--a0:=integrate(t0,x)
+--E 488
+
+--S 489 of 500
+--m0:=a0-r0
+--E 489
+
+--S 490 of 500
+--d0:=D(m0,x)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|3x + 2
+--R (1) --------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+--r0:=4/5*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 14/5*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/5*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 492
+
+--S 493 of 500
+--a0:=integrate(t0,x)
+--E 493
+
+--S 494 of 500
+--m0:=a0-r0
+--E 494
+
+--S 495 of 500
+--d0:=D(m0,x)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) --------------------------
+--R +------+ +------+
+--R (5x + 3)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+--r0:=2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 2*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 497
+
+--S 498 of 500
+--a0:=integrate(t0,x)
+--E 498
+
+--S 499 of 500
+--m0:=a0-r0
+--E 499
+
+--S 500 of 500
+--d0:=D(m0,x)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3q.input.pdf b/src/axiom-website/CATS/rich3q.input.pdf
new file mode 100644
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+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3r.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 0 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 100 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3r.output
+)spool rich3r.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ----------------------------------
+--R 2 +------+ +------+
+--R (15x + 19x + 6)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+--r0:=-4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
+-- 2*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-20*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 2
+
+--S 3 of 500
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 500
+--m0:=a0-r0
+--E 4
+
+--S 5 of 500
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ------------------------------------------
+--R 3 2 +------+ +------+
+--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+--r0:=556/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-80/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
+-- 92/7*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2780/21*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 7
+
+--S 8 of 500
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 500
+--m0:=a0-r0
+--E 9
+
+--S 10 of 500
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 4 3 2 +------+ +------+
+--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+--r0:=-3352/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 116464/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_
+-- 416/105*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
+-- 19268/245*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
+-- 116464/147*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 12
+
+--S 13 of 500
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 500
+--m0:=a0-r0
+--E 14
+
+--S 15 of 500
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+--r0:=12601/103125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-1473539/206250*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-2/15*(2+3*x)^(9/2)*sqrt(1-2*x)/_
+-- (3+5*x)^(3/2)-118/165*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 5153/48125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 958/1925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 12601/240625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 17
+
+--S 18 of 500
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 500
+--m0:=a0-r0
+--E 19
+
+--S 20 of 500
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(5/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2
+--R (1) -------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+--r0:=-47342/103125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-19033/103125*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-2/15*(2+3*x)^(7/2)*sqrt(1-2*x)/_
+-- (3+5*x)^(3/2)-458/825*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 2818/6875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 2719/34375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 22
+
+--S 23 of 500
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 500
+--m0:=a0-r0
+--E 24
+
+--S 25 of 500
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(5/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+--r0:=-169/4125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 3206/4125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/15*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+-- 326/825*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 458/1375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 27
+
+--S 28 of 500
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 500
+--m0:=a0-r0
+--E 29
+
+--S 30 of 500
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(5/2)
+--R
+--R
+--R +--------+ +------+
+--R (3x + 2)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+--r0:=458/825*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 1358/825*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/15*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+-- 194/825*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 32
+
+--S 33 of 500
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 500
+--m0:=a0-r0
+--E 34
+
+--S 35 of 500
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(5/2)
+--R
+--R
+--R +--------+ +------+
+--R \|- 2x + 1 \|3x + 2
+--R (1) -------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+--r0:=62/165*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 28/165*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/15*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-_
+-- 62/165*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 37
+
+--S 38 of 500
+--a0:=integrate(t0,x)
+--E 38
+
+--S 39 of 500
+--m0:=a0-r0
+--E 39
+
+--S 40 of 500
+--d0:=D(m0,x)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=sqrt(1-2*x)/((3+5*x)^(5/2)*sqrt(2+3*x))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ----------------------------------
+--R 2 +------+ +------+
+--R (25x + 30x + 9)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+--r0:=-136/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+28/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 136/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 42
+
+--S 43 of 500
+--a0:=integrate(t0,x)
+--E 43
+
+--S 44 of 500
+--m0:=a0-r0
+--E 44
+
+--S 45 of 500
+--d0:=D(m0,x)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -------------------------------------------
+--R 3 2 +------+ +------+
+--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+--r0:=536/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 532/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
+-- 2*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-40/3*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)+2660/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 47
+
+--S 48 of 500
+--a0:=integrate(t0,x)
+--E 48
+
+--S 49 of 500
+--m0:=a0-r0
+--E 49
+
+--S 50 of 500
+--d0:=D(m0,x)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 4 3 2 +------+ +------+
+--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+--r0:=-36968/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 5320/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+416/21*_
+-- sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-2780/21*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)+184840/231*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 52
+
+--S 53 of 500
+--a0:=integrate(t0,x)
+--E 53
+
+--S 54 of 500
+--m0:=a0-r0
+--E 54
+
+--S 55 of 500
+--d0:=D(m0,x)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R \|- 2x + 1
+--R (1) ----------------------------------------------------------------
+--R 5 4 3 2 +------+ +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+--r0:=296816/231*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-10312712/231*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_
+-- 556/105*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 116044/735*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 155104/147*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 10312712/1617*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 57
+
+--S 58 of 500
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 500
+--m0:=a0-r0
+--E 59
+
+--S 60 of 500
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+ +------+ +------+
+--R (1) (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+--r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+17427983/16706250*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 604915631/16706250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+1103/259875*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+-- 178/7425*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+-- 124891/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 18177329/38981250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 62
+
+--S 63 of 500
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 500
+--m0:=a0-r0
+--E 64
+
+--S 65 of 500
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+ +------+ +------+
+--R (1) (- 6x - x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+--r0:=2/45*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)+83093/151875*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 5684677/303750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+62/1575*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+-- 347/39375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 84134/354375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 67
+
+--S 68 of 500
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 500
+--m0:=a0-r0
+--E 69
+
+--S 70 of 500
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)
+--R
+--R
+--R +--------+ +------+ +------+
+--R (1) (- 2x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+--r0:=4289/10125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 118898/10125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/35*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
+-- 194/2625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 2657/23625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 72
+
+--S 73 of 500
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 500
+--m0:=a0-r0
+--E 74
+
+--S 75 of 500
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+--r0:=-4157/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+4382/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+2/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+214/675*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 77
+
+--S 78 of 500
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 500
+--m0:=a0-r0
+--E 79
+
+--S 80 of 500
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------
+--R +------+
+--R (3x + 2)\|3x + 2
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+--r0:=494/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 1610/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)-16/27*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 82
+
+--S 83 of 500
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 500
+--m0:=a0-r0
+--E 84
+
+--S 85 of 500
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+--r0:=724/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 98/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_
+-- 2/9*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+82/27*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 87
+
+--S 88 of 500
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 500
+--m0:=a0-r0
+--E 89
+
+--S 90 of 500
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+--r0:=68/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 3896/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-2/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 82/135*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+3896/945*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 92
+
+--S 93 of 500
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 500
+--m0:=a0-r0
+--E 94
+
+--S 95 of 500
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+--r0:=17032/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-595324/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-2/21*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
+-- 82/315*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+8516/6615*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+595324/46305*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 97
+
+--S 98 of 500
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 500
+--m0:=a0-r0
+--E 99
+
+--S 100 of 500
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(11/2)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+--r0:=1226552/83349*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-42623864/83349*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-2/27*(1-2*x)^(3/2)*_
+-- sqrt(3+5*x)/(2+3*x)^(9/2)+82/567*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(7/2)+13136/19845*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(5/2)+613276/138915*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+42623864/972405*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 102
+
+--S 103 of 500
+--a0:=integrate(t0,x)
+--E 103
+
+--S 104 of 500
+--m0:=a0-r0
+--E 104
+
+--S 105 of 500
+--d0:=D(m0,x)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+ +------+
+--R (1) (- 90x - 129x - 25x + 32x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+--r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+_
+-- 371279941/108590625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-51601293223/434362500*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+601/160875*(2+3*x)^(3/2)*_
+-- (3+5*x)^(5/2)*sqrt(1-2*x)+178/10725*(2+3*x)^(5/2)*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)-11725073/56306250*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)-18034/625625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 776112041/506756250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 107
+
+--S 108 of 500
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 500
+--m0:=a0-r0
+--E 109
+
+--S 110 of 500
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+ +------+ +------+
+--R (1) (- 30x - 23x + 7x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+--r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+5199979/3341250*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 90397364/1670625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+62/2475*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+-- 40703/433125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 23/9625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 5442127/7796250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 112
+
+--S 113 of 500
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 500
+--m0:=a0-r0
+--E 114
+
+--S 115 of 500
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)
+--R
+--R
+--R 2 +--------+ +------+ +------+
+--R (1) (- 10x - x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+--r0:=70226/91125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 4971289/182250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/45*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_
+-- 839/23625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 194/4725*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 76163/212625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 117
+
+--S 118 of 500
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 500
+--m0:=a0-r0
+--E 119
+
+--S 120 of 500
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+--r0:=-31/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 29933/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
+-- 74/525*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1847/4725*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 122
+
+--S 123 of 500
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 500
+--m0:=a0-r0
+--E 124
+
+--S 125 of 500
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R +------+
+--R (3x + 2)\|3x + 2
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+--r0:=-2209/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+4144/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-_
+-- 8/15*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+494/135*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 127
+
+--S 128 of 500
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 500
+--m0:=a0-r0
+--E 129
+
+--S 130 of 500
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+--r0:=-2/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)-_
+-- 8774/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 592/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(35)+74/9*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-_
+-- 1150/81*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 132
+
+--S 133 of 500
+--a0:=integrate(t0,x)
+--E 133
+
+--S 134 of 500
+--m0:=a0-r0
+--E 134
+
+--S 135 of 500
+--d0:=D(m0,x)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+--r0:=-2/15*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)+_
+-- 1184/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 4418/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+74/45*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+_
+-- 988/945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 137
+
+--S 138 of 500
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 500
+--m0:=a0-r0
+--E 139
+
+--S 140 of 500
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+--r0:=-2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-_
+-- 124/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 119732/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+74/105*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-_
+-- 3632/6615*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 119732/46305*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 142
+
+--S 143 of 500
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 500
+--m0:=a0-r0
+--E 144
+
+--S 145 of 500
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+--r0:=-2/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)+_
+-- 561808/250047*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-19885156/250047*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+74/189*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(7/2)-8252/19845*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(5/2)+280904/416745*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+19885156/2917215*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 147
+
+--S 148 of 500
+--a0:=integrate(t0,x)
+--E 148
+
+--S 149 of 500
+--m0:=a0-r0
+--E 149
+
+--S 150 of 500
+--d0:=D(m0,x)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+--r0:=-2/33*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)+_
+-- 41599832/6417873*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-1446357824/6417873*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+74/297*(3+5*x)^(3/2)*sqrt(1-2*x)/_
+-- (2+3*x)^(9/2)-12872/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
+-- 442076/1528065*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 20799916/10696455*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 1446357824/74875185*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 152
+
+--S 153 of 500
+--a0:=integrate(t0,x)
+--E 153
+
+--S 154 of 500
+--m0:=a0-r0
+--E 154
+
+--S 155 of 500
+--d0:=D(m0,x)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)
+--R
+--R
+--R (1)
+--R 5 4 3 2 +--------+ +------+ +------+
+--R (- 450x - 915x - 512x + 85x + 156x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+--r0:=2/75*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(7/2)+_
+-- 48128081531/3909262500*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-836091184171/1954631250*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 2503/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)+_
+-- 178/14625*(2+3*x)^(5/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+-- 380132617/506756250*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 57509209/506756250*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 199721/12065625*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 50299451003/9121612500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 157
+
+--S 158 of 500
+--a0:=integrate(t0,x)
+--E 158
+
+--S 159 of 500
+--m0:=a0-r0
+--E 159
+
+--S 160 of 500
+--d0:=D(m0,x)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+ +------+
+--R (1) (- 150x - 205x - 34x + 51x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+--r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_
+-- 134992031/26061750*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-9380126059/52123500*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 62/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_
+-- 2133359/6756750*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 160084/3378375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 67/160875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 70536439/30405375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 162
+
+--S 163 of 500
+--a0:=integrate(t0,x)
+--E 163
+
+--S 164 of 500
+--m0:=a0-r0
+--E 164
+
+--S 165 of 500
+--d0:=D(m0,x)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)
+--R
+--R
+--R 3 2 +--------+ +------+ +------+
+--R (1) (- 50x - 35x + 12x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+--r0:=2810993/1202850*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-97540001/1202850*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+2/55*(1-2*x)^(3/2)*(3+5*x)^(7/2)*_
+-- sqrt(2+3*x)-22576/155925*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 2377/155925*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 194/7425*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 2930159/2806650*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 167
+
+--S 168 of 500
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 500
+--m0:=a0-r0
+--E 169
+
+--S 170 of 500
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+--r0:=14101/10935*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 886499/21870*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_
+-- 499/2835*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 46/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 11908/25515*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 172
+
+--S 173 of 500
+--a0:=integrate(t0,x)
+--E 173
+
+--S 174 of 500
+--m0:=a0-r0
+--E 174
+
+--S 175 of 500
+--d0:=D(m0,x)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R +------+
+--R (3x + 2)\|3x + 2
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+--r0:=-835/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2894/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-2/3*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)+_
+-- 202/63*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 32/63*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 1061/567*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 177
+
+--S 178 of 500
+--a0:=integrate(t0,x)
+--E 178
+
+--S 179 of 500
+--m0:=a0-r0
+--E 179
+
+--S 180 of 500
+--d0:=D(m0,x)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+--r0:=-2/9*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)-_
+-- 9587/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+21206/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+362/27*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)-_
+-- 614/27*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+2632/243*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 182
+
+--S 183 of 500
+--a0:=integrate(t0,x)
+--E 183
+
+--S 184 of 500
+--m0:=a0-r0
+--E 184
+
+--S 185 of 500
+--d0:=D(m0,x)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+--r0:=-2/15*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)-_
+-- 47422/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+116854/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+362/135*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+_
+-- 9808/945*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-_
+-- 43214/1701*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 187
+
+--S 188 of 500
+--a0:=integrate(t0,x)
+--E 188
+
+--S 189 of 500
+--m0:=a0-r0
+--E 189
+
+--S 190 of 500
+--d0:=D(m0,x)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ---------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+--r0:=-2/21*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)+_
+-- 290204/11907*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-962678/11907*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+2108/6615*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(3/2)+362/315*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(5/2)+249448/138915*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 192
+
+--S 193 of 500
+--a0:=integrate(t0,x)
+--E 193
+
+--S 194 of 500
+--m0:=a0-r0
+--E 194
+
+--S 195 of 500
+--d0:=D(m0,x)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+--r0:=-2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-_
+-- 600868/750141*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-17830424/750141*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-1864/6615*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(5/2)+362/567*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(7/2)-558524/1250235*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+17830424/8751645*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 197
+
+--S 198 of 500
+--a0:=integrate(t0,x)
+--E 198
+
+--S 199 of 500
+--m0:=a0-r0
+--E 199
+
+--S 200 of 500
+--d0:=D(m0,x)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+--r0:=-2/33*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)+_
+-- 91496584/57760857*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-3316711588/57760857*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-13292/43659*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(7/2)+362/891*(3+5*x)^(5/2)*sqrt(1-2*x)/_
+-- (2+3*x)^(9/2)-1366496/4584195*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(5/2)+45748292/96268095*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+3316711588/673876665*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 202
+
+--S 203 of 500
+--a0:=integrate(t0,x)
+--E 203
+
+--S 204 of 500
+--m0:=a0-r0
+--E 204
+
+--S 205 of 500
+--d0:=D(m0,x)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2)
+--R
+--R
+--R (1)
+--R 3 2 +--------+ +------+
+--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3
+--R /
+--R 7 6 5 4 3 2
+--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128)
+--R *
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+--r0:=-2/39*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_
+-- 7046965448/1752079329*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-245282464136/1752079329*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-20992/81081*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(9/2)+362/1287*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(11/2)-2174468/11918907*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(7/2)+73596464/417161745*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)+3523482724/2920132215*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+245282464136/20440925505*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 207
+
+--S 208 of 500
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 500
+--m0:=a0-r0
+--E 209
+
+--S 210 of 500
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2
+--R (1) --------------------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+--r0:=87476/253125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-6515539/506250*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+2/45*(1-2*x)^(3/2)*(2+3*x)^(5/2)*_
+-- sqrt(3+5*x)+403/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 178/4725*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-87476/590625*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 212
+
+--S 213 of 500
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 500
+--m0:=a0-r0
+--E 214
+
+--S 215 of 500
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 6x - x + 2)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+--r0:=487/5625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 46159/5625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/35*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+_
+-- 62/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-487/13125*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 217
+
+--S 218 of 500
+--a0:=integrate(t0,x)
+--E 218
+
+--S 219 of 500
+--m0:=a0-r0
+--E 219
+
+--S 220 of 500
+--d0:=D(m0,x)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|3x + 2
+--R (1) ------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+--r0:=-2797/3375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-2828/3375*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/25*(1-2*x)^(3/2)*sqrt(2+3*x)*_
+-- sqrt(3+5*x)+194/1125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 222
+
+--S 223 of 500
+--a0:=integrate(t0,x)
+--E 223
+
+--S 224 of 500
+--m0:=a0-r0
+--E 224
+
+--S 225 of 500
+--d0:=D(m0,x)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------
+--R +------+ +------+
+--R \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+--r0:=272/135*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 1442/135*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-4/45*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 227
+
+--S 228 of 500
+--a0:=integrate(t0,x)
+--E 228
+
+--S 229 of 500
+--m0:=a0-r0
+--E 229
+
+--S 230 of 500
+--d0:=D(m0,x)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) --------------------------
+--R +------+ +------+
+--R (3x + 2)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+--r0:=-74/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 56/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+4/3*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 232
+
+--S 233 of 500
+--a0:=integrate(t0,x)
+--E 233
+
+--S 234 of 500
+--m0:=a0-r0
+--E 234
+
+--S 235 of 500
+--d0:=D(m0,x)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 2 +------+ +------+
+--R (9x + 12x + 4)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+--r0:=116/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 124/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(35)+2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 128/9*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 237
+
+--S 238 of 500
+--a0:=integrate(t0,x)
+--E 238
+
+--S 239 of 500
+--m0:=a0-r0
+--E 239
+
+--S 240 of 500
+--d0:=D(m0,x)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -----------------------------------------
+--R 3 2 +------+ +------+
+--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+--r0:=512/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 17804/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/5*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 268/45*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+17804/315*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 242
+
+--S 243 of 500
+--a0:=integrate(t0,x)
+--E 243
+
+--S 244 of 500
+--m0:=a0-r0
+--E 244
+
+--S 245 of 500
+--d0:=D(m0,x)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(9/2)*sqrt(3+5*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ---------------------------------------------------
+--R 4 3 2 +------+ +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+--r0:=36136/441*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 1255552/441*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/7*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
+-- 136/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+18068/735*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+1255552/5145*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 247
+
+--S 248 of 500
+--a0:=integrate(t0,x)
+--E 248
+
+--S 249 of 500
+--m0:=a0-r0
+--E 249
+
+--S 250 of 500
+--d0:=D(m0,x)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+--r0:=12601/84375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-1473539/168750*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(3/2)*(2+3*x)^(7/2)/_
+-- sqrt(3+5*x)+5153/39375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 958/1575*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-8/45*(2+3*x)^(7/2)*_
+-- sqrt(1-2*x)*sqrt(3+5*x)-12601/196875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 252
+
+--S 253 of 500
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 500
+--m0:=a0-r0
+--E 254
+
+--S 255 of 500
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2
+--R (1) --------------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+--r0:=-2719/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 47342/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-2/5*(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)+_
+-- 2818/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 32/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 2719/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 257
+
+--S 258 of 500
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 500
+--m0:=a0-r0
+--E 259
+
+--S 260 of 500
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 6x - x + 2)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+--r0:=-169/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-3206/1875*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-2/5*(1-2*x)^(3/2)*(2+3*x)^(3/2)/_
+-- sqrt(3+5*x)-24/125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 458/625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 262
+
+--S 263 of 500
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 500
+--m0:=a0-r0
+--E 264
+
+--S 265 of 500
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|3x + 2
+--R (1) ------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+--r0:=458/225*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 1358/225*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/5*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-_
+-- 16/75*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 267
+
+--S 268 of 500
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 500
+--m0:=a0-r0
+--E 269
+
+--S 270 of 500
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) --------------------------
+--R +------+ +------+
+--R (5x + 3)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+--r0:=62/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 28/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-4/5*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 272
+
+--S 273 of 500
+--a0:=integrate(t0,x)
+--E 273
+
+--S 274 of 500
+--m0:=a0-r0
+--E 274
+
+--S 275 of 500
+--d0:=D(m0,x)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------------------
+--R 2 +------+ +------+
+--R (15x + 19x + 6)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+--r0:=136/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 28/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2*(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x))-44*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 277
+
+--S 278 of 500
+--a0:=integrate(t0,x)
+--E 278
+
+--S 279 of 500
+--m0:=a0-r0
+--E 279
+
+--S 280 of 500
+--d0:=D(m0,x)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 3 2 +------+ +------+
+--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+--r0:=-536/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 532/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(35)+2/3*(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
+-- 268/9*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2660/9*_
+-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 282
+
+--S 283 of 500
+--a0:=integrate(t0,x)
+--E 283
+
+--S 284 of 500
+--m0:=a0-r0
+--E 284
+
+--S 285 of 500
+--d0:=D(m0,x)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 4 3 2 +------+ +------+
+--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+--r0:=-1064/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 36968/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/5*(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x))+_
+-- 136/15*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+6116/35*_
+-- sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-36968/21*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 287
+
+--S 288 of 500
+--a0:=integrate(t0,x)
+--E 288
+
+--S 289 of 500
+--m0:=a0-r0
+--E 289
+
+--S 290 of 500
+--d0:=D(m0,x)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(9/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------------
+--R 5 4 3 2 +------+ +------+
+--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+--r0:=-296816/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 10312712/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/7*(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+_
+-- 548/105*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+12276/245*_
+-- sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+1706144/1715*_
+-- sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-10312712/1029*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 292
+
+--S 293 of 500
+--a0:=integrate(t0,x)
+--E 293
+
+--S 294 of 500
+--m0:=a0-r0
+--E 294
+
+--S 295 of 500
+--d0:=D(m0,x)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)-_
+-- 4801/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 25643/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-6*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 3872/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 622/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 4801/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 297
+
+--S 298 of 500
+--a0:=integrate(t0,x)
+--E 298
+
+--S 299 of 500
+--m0:=a0-r0
+--E 299
+
+--S 300 of 500
+--d0:=D(m0,x)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2
+--R (1) --------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)+_
+-- 1973/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-15848/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-106/25*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 1558/625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+2264/3125*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 302
+
+--S 303 of 500
+--a0:=integrate(t0,x)
+--E 303
+
+--S 304 of 500
+--m0:=a0-r0
+--E 304
+
+--S 305 of 500
+--d0:=D(m0,x)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (- 6x - x + 2)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)+_
+-- 496/375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-1246/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-62/25*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 178/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 307
+
+--S 308 of 500
+--a0:=integrate(t0,x)
+--E 308
+
+--S 309 of 500
+--m0:=a0-r0
+--E 309
+
+--S 310 of 500
+--d0:=D(m0,x)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(5/2)
+--R
+--R
+--R +--------+ +------+
+--R (- 2x + 1)\|- 2x + 1 \|3x + 2
+--R (1) ------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+--r0:=38/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 112/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/15*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)-_
+-- 18/25*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 312
+
+--S 313 of 500
+--a0:=integrate(t0,x)
+--E 313
+
+--S 314 of 500
+--m0:=a0-r0
+--E 314
+
+--S 315 of 500
+--d0:=D(m0,x)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(1-2*x)^(3/2)/((3+5*x)^(5/2)*sqrt(2+3*x))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------------------
+--R 2 +------+ +------+
+--R (25x + 30x + 9)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+--r0:=-148/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 28/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/3*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)+48/5*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 317
+
+--S 318 of 500
+--a0:=integrate(t0,x)
+--E 318
+
+--S 319 of 500
+--m0:=a0-r0
+--E 319
+
+--S 320 of 500
+--d0:=D(m0,x)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -------------------------------------------
+--R 3 2 +------+ +------+
+--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+--r0:=-556/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 112/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2*(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-88/3*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)+556/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 322
+
+--S 323 of 500
+--a0:=integrate(t0,x)
+--E 323
+
+--S 324 of 500
+--m0:=a0-r0
+--E 324
+
+--S 325 of 500
+--d0:=D(m0,x)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 4 3 2 +------+ +------+
+--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+--r0:=2/3*(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 1096/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 1088/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
+-- 136/3*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-300*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)+5440/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 327
+
+--S 328 of 500
+--a0:=integrate(t0,x)
+--E 328
+
+--S 329 of 500
+--m0:=a0-r0
+--E 329
+
+--S 330 of 500
+--d0:=D(m0,x)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +--------+
+--R (- 2x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------------
+--R 5 4 3 2 +------+ +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+--r0:=2/5*(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_
+-- 8672/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 301304/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+548/45*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 111884/315*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 16616/7*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 301304/21*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 332
+
+--S 333 of 500
+--a0:=integrate(t0,x)
+--E 333
+
+--S 334 of 500
+--m0:=a0-r0
+--E 334
+
+--S 335 of 500
+--d0:=D(m0,x)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+ +------+
+--R (1) (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+--r0:=62/2145*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+_
+-- 2/65*(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+_
+-- 67138787/72393750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-1163388067/36196875*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+32717/1126125*(2+3*x)^(3/2)*_
+-- (3+5*x)^(3/2)*sqrt(1-2*x)+34/2475*(2+3*x)^(5/2)*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)-445024/9384375*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)-69808931/168918750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 337
+
+--S 338 of 500
+--a0:=integrate(t0,x)
+--E 338
+
+--S 339 of 500
+--m0:=a0-r0
+--E 339
+
+--S 340 of 500
+--d0:=D(m0,x)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+ +------+ +------+
+--R (1) (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+--r0:=106/2475*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)+2/55*(1-2*x)^(5/2)*_
+-- (2+3*x)^(3/2)*(3+5*x)^(3/2)+4854274/8353125*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 326256461/16706250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2866/86625*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+_
+-- 38729/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 4738087/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 342
+
+--S 343 of 500
+--a0:=integrate(t0,x)
+--E 343
+
+--S 344 of 500
+--m0:=a0-r0
+--E 344
+
+--S 345 of 500
+--d0:=D(m0,x)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=(1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+ +------+ +------+
+--R (1) (4x - 4x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+--r0:=284159/455625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-6799613/455625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+326/4725*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
+-- 2/45*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
+-- 10214/118125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 110717/1063125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 347
+
+--S 348 of 500
+--a0:=integrate(t0,x)
+--E 348
+
+--S 349 of 500
+--m0:=a0-r0
+--E 349
+
+--S 350 of 500
+--d0:=D(m0,x)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+--r0:=16088/3375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 86741/3375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 118/525*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+2/21*(1-2*x)^(5/2)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)+4282/7875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 352
+
+--S 353 of 500
+--a0:=integrate(t0,x)
+--E 353
+
+--S 354 of 500
+--m0:=a0-r0
+--E 354
+
+--S 355 of 500
+--d0:=D(m0,x)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------
+--R +------+
+--R (3x + 2)\|3x + 2
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+--r0:=31588/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-96838/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/3*(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)-_
+-- 8/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-1076/675*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 357
+
+--S 358 of 500
+--a0:=integrate(t0,x)
+--E 358
+
+--S 359 of 500
+--m0:=a0-r0
+--E 359
+
+--S 360 of 500
+--d0:=D(m0,x)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)
+--E 361
+
+--S 362 of 500
+--r0:=-4418/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+8288/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/9*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 10/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+196/81*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 362
+
+--S 363 of 500
+--Ra0:=integrate(t0,x)
+--R
+--R
+--R (1) t0 x
+--R Type: Polynomial(Fraction(Integer))
+--E 363
+
+--S 364 of 500
+--Rm0:=a0-r0
+--R
+--R
+--R (2) t0 x - r0
+--R Type: Polynomial(Fraction(Integer))
+--E 364
+
+--S 365 of 500
+--Rd0:=D(m0,x)
+--R
+--R
+--R (3) t0
+--R Type: Polynomial(Fraction(Integer))
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+--r0:=-12*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/15*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+2/3*(1-2*x)^(3/2)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+8*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 367
+
+--S 368 of 500
+--a0:=integrate(t0,x)
+--E 368
+
+--S 369 of 500
+--m0:=a0-r0
+--E 369
+
+--S 370 of 500
+--d0:=D(m0,x)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+--r0:=-36052/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 5360/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/21*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+2/7*_
+-- (1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+524/189*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+36052/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 372
+
+--S 373 of 500
+--a0:=integrate(t0,x)
+--E 373
+
+--S 374 of 500
+--m0:=a0-r0
+--E 374
+
+--S 375 of 500
+--d0:=D(m0,x)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(11/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+--r0:=-7810384/35721*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+1124360/35721*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/27*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_
+-- 10/63*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+832/567*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+112436/11907*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+7810384/83349*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 377
+
+--S 378 of 500
+--a0:=integrate(t0,x)
+--E 378
+
+--S 379 of 500
+--m0:=a0-r0
+--E 379
+
+--S 380 of 500
+--d0:=D(m0,x)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(13/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+--r0:=-247408648/305613*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+35604320/305613*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-2/33*(1-2*x)^(5/2)*sqrt(3+5*x)/_
+-- (2+3*x)^(11/2)+10/99*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_
+-- 1900/2079*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
+-- 76492/14553*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 3560432/101871*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 247408648/713097*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 382
+
+--S 383 of 500
+--a0:=integrate(t0,x)
+--E 383
+
+--S 384 of 500
+--m0:=a0-r0
+--E 384
+
+--S 385 of 500
+--d0:=D(m0,x)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+ +------+
+--R (1) (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+--r0:=62/2925*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+2/75*(1-2*x)^(5/2)*_
+-- (2+3*x)^(5/2)*(3+5*x)^(5/2)+25385346787/9773156250*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 1764163292393/19546312500*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+142391/7239375*(2+3*x)^(3/2)*_
+-- (3+5*x)^(5/2)*sqrt(1-2*x)+3698/482625*(2+3*x)^(5/2)*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)-400516993/2533781250*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)-569519/28153125*(3+5*x)^(5/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)-13267820528/11402015625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 387
+
+--S 388 of 500
+--a0:=integrate(t0,x)
+--E 388
+
+--S 389 of 500
+--m0:=a0-r0
+--E 389
+
+--S 390 of 500
+--d0:=D(m0,x)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+ +------+
+--R (1) (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+--r0:=106/3575*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+_
+-- 2/65*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+_
+-- 880870681/651543750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-30660308017/651543750*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+8318/482625*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)-6794792/84459375*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)+25603/1876875*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 923943703/1520268750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 392
+
+--S 393 of 500
+--a0:=integrate(t0,x)
+--E 393
+
+--S 394 of 500
+--m0:=a0-r0
+--E 394
+
+--S 395 of 500
+--d0:=D(m0,x)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)
+--R
+--R
+--R 3 2 +--------+ +------+ +------+
+--R (1) (20x - 8x - 7x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+--r0:=11437073/15035625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-829177897/30071250*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+326/7425*(1-2*x)^(3/2)*_
+-- (3+5*x)^(5/2)*sqrt(2+3*x)+2/55*(1-2*x)^(5/2)*(3+5*x)^(5/2)*_
+-- sqrt(2+3*x)-78797/3898125*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)+30362/779625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 12996374/35083125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 397
+
+--S 398 of 500
+--a0:=integrate(t0,x)
+--E 398
+
+--S 399 of 500
+--m0:=a0-r0
+--E 399
+
+--S 400 of 500
+--d0:=D(m0,x)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+--r0:=-150217/273375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-4457606/273375*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+362/2835*(1-2*x)^(3/2)*(3+5*x)^(3/2)*_
+-- sqrt(2+3*x)+2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
+-- 14318/70875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 429479/637875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 402
+
+--S 403 of 500
+--a0:=integrate(t0,x)
+--E 403
+
+--S 404 of 500
+--m0:=a0-r0
+--E 404
+
+--S 405 of 500
+--d0:=D(m0,x)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------
+--R +------+
+--R (3x + 2)\|3x + 2
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+--r0:=145102/6075*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 481339/6075*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-2/3*(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-_
+-- 32/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)-_
+-- 2108/1575*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 124724/14175*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 407
+
+--S 408 of 500
+--a0:=integrate(t0,x)
+--E 408
+
+--S 409 of 500
+--m0:=a0-r0
+--E 409
+
+--S 410 of 500
+--d0:=D(m0,x)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+--r0:=-2/9*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)+116854/3645*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 331954/3645*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+230/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)+_
+-- 788/135*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-43214/1215*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 412
+
+--S 413 of 500
+--a0:=integrate(t0,x)
+--E 413
+
+--S 414 of 500
+--m0:=a0-r0
+--E 414
+
+--S 415 of 500
+--d0:=D(m0,x)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+--r0:=-2/15*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)+_
+-- 46/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)-_
+-- 19174/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+42412/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-316/27*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+5264/243*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 417
+
+--S 418 of 500
+--a0:=integrate(t0,x)
+--E 418
+
+--S 419 of 500
+--m0:=a0-r0
+--E 419
+
+--S 420 of 500
+--d0:=D(m0,x)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+--r0:=-2/21*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)+_
+-- 46/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)-_
+-- 11576/1701*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-16700/1701*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+608/189*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_
+-- 4244/3969*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 422
+
+--S 423 of 500
+--a0:=integrate(t0,x)
+--E 423
+
+--S 424 of 500
+--m0:=a0-r0
+--E 424
+
+--S 425 of 500
+--d0:=D(m0,x)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+--r0:=-2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)+_
+-- 230/567*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-_
+-- 3545996/107163*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+564040/107163*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+1532/567*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(5/2)-104036/35721*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+3545996/250047*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 427
+
+--S 428 of 500
+--a0:=integrate(t0,x)
+--E 428
+
+--S 429 of 500
+--m0:=a0-r0
+--E 429
+
+--S 430 of 500
+--d0:=D(m0,x)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+--r0:=-2/33*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)+_
+-- 230/891*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)-_
+-- 780320008/8251551*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+112439720/8251551*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+12280/6237*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(7/2)-325796/130977*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)+11243972/2750517*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+780320008/19253619*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 432
+
+--S 433 of 500
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 500
+--m0:=a0-r0
+--E 434
+
+--S 435 of 500
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(15/2)
+--R
+--R
+--R (1)
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R /
+--R 7 6 5 4 3 2
+--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128)
+--R *
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+--r0:=-2/39*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2)+_
+-- 230/1287*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)-_
+-- 75041008472/250297047*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)*sqrt(5/7)+10799362480/250297047*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 1300/891*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_
+-- 3347620/1702701*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
+-- 23210828/11918907*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 1079936248/83432349*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 75041008472/584026443*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 437
+
+--S 438 of 500
+--a0:=integrate(t0,x)
+--E 438
+
+--S 439 of 500
+--m0:=a0-r0
+--E 439
+
+--S 440 of 500
+--d0:=D(m0,x)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)
+--R
+--R
+--R (1)
+--R 5 4 3 2 +--------+ +------+ +------+
+--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+--r0:=106/4875*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_
+-- 2/75*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_
+-- 11371367372/2931946875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-1580201444291/11727787500*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+8038/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*_
+-- sqrt(1-2*x)-359748241/1520268750*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)-26534891/760134375*(3+5*x)^(5/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)+364267/36196875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 23763809947/13682418750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 442
+
+--S 443 of 500
+--a0:=integrate(t0,x)
+--E 443
+
+--S 444 of 500
+--m0:=a0-r0
+--E 444
+
+--S 445 of 500
+--d0:=D(m0,x)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+ +------+
+--R (1) (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+--r0:=469049629/234555750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-8120161139/117277875*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+326/10725*(1-2*x)^(3/2)*(3+5*x)^(7/2)*_
+-- sqrt(2+3*x)+2/65*(1-2*x)^(5/2)*(3+5*x)^(7/2)*sqrt(2+3*x)-_
+-- 3872003/30405375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 121031/30405375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 2314/111375*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 486785077/547296750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 447
+
+--S 448 of 500
+--a0:=integrate(t0,x)
+--E 448
+
+--S 449 of 500
+--m0:=a0-r0
+--E 449
+
+--S 450 of 500
+--d0:=D(m0,x)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+--r0:=2617892/1804275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-146222113/3608550*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+74/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)*_
+-- sqrt(2+3*x)+2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_
+-- 146963/467775*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 9698/93555*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 1654421/4209975*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 452
+
+--S 453 of 500
+--a0:=integrate(t0,x)
+--E 453
+
+--S 454 of 500
+--m0:=a0-r0
+--E 454
+
+--S 455 of 500
+--d0:=D(m0,x)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R +------+
+--R (3x + 2)\|3x + 2
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+--r0:=-291227/32805*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-25111/32805*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-2/3*(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-_
+-- 40/81*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)+_
+-- 64628/8505*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 2108/1701*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 310399/76545*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 457
+
+--S 458 of 500
+--a0:=integrate(t0,x)
+--E 458
+
+--S 459 of 500
+--m0:=a0-r0
+--E 459
+
+--S 460 of 500
+--d0:=D(m0,x)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+--r0:=-2/9*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)+_
+-- 153452/2187*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-452399/2187*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+370/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-_
+-- 31298/567*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 5260/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 135334/5103*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 462
+
+--S 463 of 500
+--a0:=integrate(t0,x)
+--E 463
+
+--S 464 of 500
+--m0:=a0-r0
+--E 464
+
+--S 465 of 500
+--d0:=D(m0,x)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+--r0:=-2/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)+_
+-- 74/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)+_
+-- 136028/2187*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-374366/2187*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-6464/81*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+_
+-- 11036/81*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 48478/729*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 467
+
+--S 468 of 500
+--a0:=integrate(t0,x)
+--E 468
+
+--S 469 of 500
+--m0:=a0-r0
+--E 469
+
+--S 470 of 500
+--d0:=D(m0,x)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) --------------------------------------------------
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+--r0:=-2/21*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)+_
+-- 74/63*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)-904798/15309*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 1534520/15309*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-1844/567*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_
+-- 62596/3969*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+_
+-- 1353340/35721*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 472
+
+--S 473 of 500
+--a0:=integrate(t0,x)
+--E 473
+
+--S 474 of 500
+--m0:=a0-r0
+--E 474
+
+--S 475 of 500
+--d0:=D(m0,x)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+--r0:=-2/27*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)+_
+-- 370/567*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)-_
+-- 100444/321489*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-5824540/321489*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-13316/35721*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(3/2)+2776/1701*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(5/2)-1241596/750141*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 477
+
+--S 478 of 500
+--a0:=integrate(t0,x)
+--E 478
+
+--S 479 of 500
+--m0:=a0-r0
+--E 479
+
+--S 480 of 500
+--d0:=D(m0,x)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 6 5 4 3 2 +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+--r0:=-2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)+_
+-- 370/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-_
+-- 584888452/24754653*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+104715680/24754653*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-55772/43659*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(5/2)+36980/18711*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(7/2)-17089252/8251551*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+584888452/57760857*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 482
+
+--S 483 of 500
+--a0:=integrate(t0,x)
+--E 483
+
+--S 484 of 500
+--m0:=a0-r0
+--E 484
+
+--S 485 of 500
+--d0:=D(m0,x)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2)
+--R
+--R
+--R (1)
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R /
+--R 7 6 5 4 3 2
+--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128)
+--R *
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+--r0:=-2/39*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_
+-- 370/1287*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)-_
+-- 129922578224/2252673423*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)*sqrt(5/7)+18761985160/2252673423*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2622980/1702701*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+_
+-- 60080/34749*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_
+-- 54281308/35756721*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 1876198516/750891141*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 129922578224/5256237987*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 487
+
+--S 488 of 500
+--a0:=integrate(t0,x)
+--E 488
+
+--S 489 of 500
+--m0:=a0-r0
+--E 489
+
+--S 490 of 500
+--d0:=D(m0,x)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(17/2)
+--R
+--R
+--R (1)
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R /
+--R 8 7 6 5 4 3 2
+--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x
+--R +
+--R 3072x + 256
+--R *
+--R +------+
+--R \|3x + 2
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+--r0:=-2/45*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2)+_
+-- 74/351*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_
+-- 363883755904/15768713961*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-12641611554328/15768713961*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 1085156/729729*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+_
+-- 16636/11583*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-_
+-- 112817764/107270163*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
+-- 3914701972/3754455705*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 181941877952/26281189935*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 12641611554328/183968329545*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 492
+
+--S 493 of 500
+--a0:=integrate(t0,x)
+--E 493
+
+--S 494 of 500
+--m0:=a0-r0
+--E 494
+
+--S 495 of 500
+--d0:=D(m0,x)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/sqrt(3+5*x)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2
+--R (1) -------------------------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+--r0:=2865161/8353125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-231061879/16706250*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+62/1485*(1-2*x)^(3/2)*(2+3*x)^(5/2)*_
+-- sqrt(3+5*x)+2/55*(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+_
+-- 181333/3898125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 4258/155925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 2865161/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 497
+
+--S 498 of 500
+--a0:=integrate(t0,x)
+--E 498
+
+--S 499 of 500
+--m0:=a0-r0
+--E 499
+
+--S 500 of 500
+--d0:=D(m0,x)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3r.input.pdf b/src/axiom-website/CATS/rich3r.input.pdf
new file mode 100644
index 0000000..24baa5a
Binary files /dev/null and b/src/axiom-website/CATS/rich3r.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3s.input.pamphlet b/src/axiom-website/CATS/rich3s.input.pamphlet
new file mode 100644
index 0000000..41adf97
--- /dev/null
+++ b/src/axiom-website/CATS/rich3s.input.pamphlet
@@ -0,0 +1,3401 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3s.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 100 integrals in this file.
+\item 100 supplied "optimal results".
+\item 0 matching answers.
+\item 0 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 100 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3s.output
+)spool rich3s.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)/sqrt(3+5*x)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 500
+--r0:=-21547/759375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-8024546/759375*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+106/1575*(1-2*x)^(3/2)*(2+3*x)^(3/2)*_
+-- sqrt(3+5*x)+2/45*(1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+_
+-- 8878/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 21547/1771875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 2
+
+--S 3 of 500
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 500
+--m0:=a0-r0
+--E 4
+
+--S 5 of 500
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 500
+t0:=(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------------
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 500
+--r0:=-101902/50625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-408311/50625*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+326/2625*(1-2*x)^(3/2)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)+2/35*(1-2*x)^(5/2)*sqrt(2+3*x)*_
+-- sqrt(3+5*x)+30922/118125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 7
+
+--S 8 of 500
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 500
+--m0:=a0-r0
+--E 9
+
+--S 10 of 500
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 500
+t0:=(1-2*x)^(5/2)/(sqrt(2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------
+--R +------+ +------+
+--R \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 500
+--r0:=53194/10125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-246694/10125*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-4/75*(1-2*x)^(3/2)*sqrt(2+3*x)*_
+-- sqrt(3+5*x)-1088/3375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 12
+
+--S 13 of 500
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 500
+--m0:=a0-r0
+--E 14
+
+--S 15 of 500
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) --------------------------
+--R +------+ +------+
+--R (3x + 2)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 500
+--r0:=-8314/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 8764/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2*(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)+4/3*(1-2*x)^(3/2)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)+428/135*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 17
+
+--S 18 of 500
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 500
+--m0:=a0-r0
+--E 19
+
+--S 20 of 500
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ---------------------------------
+--R 2 +------+ +------+
+--R (9x + 12x + 4)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 500
+--r0:=-3896/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 476/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/3*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+40/3*(1-2*x)^(3/2)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)+232/27*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 22
+
+--S 23 of 500
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 500
+--m0:=a0-r0
+--E 24
+
+--S 25 of 500
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(7/2)*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -----------------------------------------
+--R 3 2 +------+ +------+
+--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 500
+--r0:=-16564/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 3352/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/5*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+52/9*(1-2*x)^(3/2)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+3412/27*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 27
+
+--S 28 of 500
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 500
+--m0:=a0-r0
+--E 29
+
+--S 30 of 500
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(9/2)*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ---------------------------------------------------
+--R 4 3 2 +------+ +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 500
+--r0:=-703480/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 101240/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+80/21*(1-2*x)^(3/2)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)+10580/189*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+703480/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 32
+
+--S 33 of 500
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 500
+--m0:=a0-r0
+--E 34
+
+--S 35 of 500
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(11/2)*sqrt(3+5*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) --------------------------------------------------------------
+--R 5 4 3 2 +------+ +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 500
+--r0:=-66055016/11907*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+9505840/11907*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/9*(1-2*x)^(5/2)*sqrt(3+5*x)/_
+-- (2+3*x)^(9/2)+20/7*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
+-- 7148/189*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 950584/3969*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 66055016/27783*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 37
+
+--S 38 of 500
+--a0:=integrate(t0,x)
+--E 38
+
+--S 39 of 500
+--m0:=a0-r0
+--E 39
+
+--S 40 of 500
+--d0:=D(m0,x)
+--E 40
+
+)clear all
+
+--S 41 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(13/2)*sqrt(3+5*x))
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R -------------------------------------------------------------------------
+--R 6 5 4 3 2 +------+ +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 500
+--r0:=-23204503328/916839*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+3339309520/916839*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(1-2*x)^(5/2)*sqrt(3+5*x)/_
+-- (2+3*x)^(11/2)+680/297*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_
+-- 180020/6237*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
+-- 7173272/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 333930952/305613*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 23204503328/2139291*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 42
+
+--S 43 of 500
+--a0:=integrate(t0,x)
+--E 43
+
+--S 44 of 500
+--m0:=a0-r0
+--E 44
+
+--S 45 of 500
+--d0:=D(m0,x)
+--E 45
+
+)clear all
+
+--S 46 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 500
+--r0:=703672/13921875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-264260033/27843750*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(5/2)*(2+3*x)^(7/2)/_
+-- sqrt(3+5*x)-48/275*(1-2*x)^(3/2)*(2+3*x)^(7/2)*sqrt(3+5*x)+_
+-- 2020841/6496875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 346636/259875*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 2972/7425*(2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 703672/32484375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 47
+
+--S 48 of 500
+--a0:=integrate(t0,x)
+--E 48
+
+--S 49 of 500
+--m0:=a0-r0
+--E 49
+
+--S 50 of 500
+--d0:=D(m0,x)
+--E 50
+
+)clear all
+
+--S 51 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2
+--R (1) -------------------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 500
+--r0:=-196499/253125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-1509007/253125*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(5/2)*(2+3*x)^(5/2)/_
+-- sqrt(3+5*x)-8/45*(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+_
+-- 167228/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 1972/4725*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 196499/590625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 52
+
+--S 53 of 500
+--a0:=integrate(t0,x)
+--E 53
+
+--S 54 of 500
+--m0:=a0-r0
+--E 54
+
+--S 55 of 500
+--d0:=D(m0,x)
+--E 55
+
+)clear all
+
+--S 56 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 500
+--r0:=-106772/28125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+53279/28125*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(5/2)*(2+3*x)^(3/2)/_
+-- sqrt(3+5*x)-32/175*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)-_
+-- 1972/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 106772/65625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 57
+
+--S 58 of 500
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 500
+--m0:=a0-r0
+--E 59
+
+--S 60 of 500
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 500
+t0:=(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------------
+--R +------+
+--R (5x + 3)\|5x + 3
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 500
+--r0:=81164/16875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 218414/16875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/5*(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x)-_
+-- 24/125*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-_
+-- 3028/5625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 62
+
+--S 63 of 500
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 500
+--m0:=a0-r0
+--E 64
+
+--S 65 of 500
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 500
+t0:=(1-2*x)^(5/2)/((3+5*x)^(3/2)*sqrt(2+3*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) --------------------------
+--R +------+ +------+
+--R (5x + 3)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 500
+--r0:=5594/675*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 5656/675*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2*(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x)-4/5*(1-2*x)^(3/2)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)-388/225*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 67
+
+--S 68 of 500
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 500
+--m0:=a0-r0
+--E 69
+
+--S 70 of 500
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ----------------------------------
+--R 2 +------+ +------+
+--R (15x + 19x + 6)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 500
+--r0:=4636/45*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 1036/45*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2*(1-2*x)^(5/2)/(sqrt(2+3*x)*sqrt(3+5*x))-44*(1-2*x)^(3/2)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)-272/15*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 72
+
+--S 73 of 500
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 500
+--m0:=a0-r0
+--E 74
+
+--S 75 of 500
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ------------------------------------------
+--R 3 2 +------+ +------+
+--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 500
+--r0:=17804/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 3584/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/3*(1-2*x)^(5/2)/((2+3*x)^(3/2)*sqrt(3+5*x))+260/9*(1-2*x)^(3/2)/_
+-- (sqrt(2+3*x)*sqrt(3+5*x))-5764/9*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 77
+
+--S 78 of 500
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 500
+--m0:=a0-r0
+--E 79
+
+--S 80 of 500
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 4 3 2 +------+ +------+
+--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 500
+--r0:=105584/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 21272/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/5*(1-2*x)^(5/2)/((2+3*x)^(5/2)*sqrt(3+5*x))+80/9*(1-2*x)^(3/2)/_
+-- ((2+3*x)^(3/2)*sqrt(3+5*x))+10636/27*sqrt(1-2*x)/(sqrt(2+3*x)*_
+-- sqrt(3+5*x))-105584/27*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 82
+
+--S 83 of 500
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 500
+--m0:=a0-r0
+--E 84
+
+--S 85 of 500
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(9/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------------
+--R 5 4 3 2 +------+ +------+
+--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 500
+--r0:=1959032/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 281920/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*(1-2*x)^(5/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+36/7*(1-2*x)^(3/2)/_
+-- ((2+3*x)^(5/2)*sqrt(3+5*x))+7204/63*sqrt(1-2*x)/((2+3*x)^(3/2)*_
+-- sqrt(3+5*x))+324104/147*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
+-- 9795160/441*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 87
+
+--S 88 of 500
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 500
+--m0:=a0-r0
+--E 89
+
+--S 90 of 500
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(11/2)*(3+5*x)^(3/2))
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R --------------------------------------------------------------------------
+--R 6 5 4 3 2 +------+ +------+
+--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 500
+--r0:=683150096/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-98310640/3969*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/9*(1-2*x)^(5/2)/((2+3*x)^(9/2)*_
+-- sqrt(3+5*x))+680/189*(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+_
+-- 36284/567*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_
+-- 813208/1323*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
+-- 113020952/9261*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
+-- 3415750480/27783*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 92
+
+--S 93 of 500
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 500
+--m0:=a0-r0
+--E 94
+
+--S 95 of 500
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2)
+--R
+--R
+--R 5 4 3 2 +--------+ +------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 500
+--r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)-_
+-- 500501/421875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 1065118/421875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-442/75*(1-2*x)^(3/2)*(2+3*x)^(7/2)/sqrt(3+5*x)+_
+-- 373022/196875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 59662/7875*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 524/225*(2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 500501/984375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 97
+
+--S 98 of 500
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 500
+--m0:=a0-r0
+--E 99
+
+--S 100 of 500
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2)
+--R
+--R
+--R 4 3 2 +--------+ +------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2
+--R (1) -------------------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 500
+--r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)-_
+-- 33778/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 49321/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 62/15*(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)+_
+-- 22866/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 284/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 33778/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 102
+
+--S 103 of 500
+--a0:=integrate(t0,x)
+--E 103
+
+--S 104 of 500
+--m0:=a0-r0
+--E 104
+
+--S 105 of 500
+--d0:=D(m0,x)
+--E 105
+
+)clear all
+
+--S 106 of 500
+t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2)
+--R
+--R
+--R 3 2 +--------+ +------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2
+--R (1) -----------------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 500
+--r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)-_
+-- 6902/3125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*_
+-- sqrt(3/11)+9206/3125*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)*sqrt(7/5)-178/75*(1-2*x)^(3/2)*(2+3*x)^(3/2)/_
+-- sqrt(3+5*x)-572/625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 8874/3125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 107
+
+--S 108 of 500
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 500
+--m0:=a0-r0
+--E 109
+
+--S 110 of 500
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 500
+t0:=(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(5/2)
+--R
+--R
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2
+--R (1) ----------------------------------
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 500
+--r0:=338/1125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 6412/1125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/15*(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2)-46/75*(1-2*x)^(3/2)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)-76/375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 112
+
+--S 113 of 500
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 500
+--m0:=a0-r0
+--E 114
+
+--S 115 of 500
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 500
+t0:=(1-2*x)^(5/2)/((3+5*x)^(5/2)*sqrt(2+3*x))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ----------------------------------
+--R 2 +------+ +------+
+--R (25x + 30x + 9)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 500
+--r0:=28/25*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_
+-- 584/25*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 2/3*(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2)+152/15*(1-2*x)^(3/2)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)+104/25*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 117
+
+--S 118 of 500
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 500
+--m0:=a0-r0
+--E 119
+
+--S 120 of 500
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -------------------------------------------
+--R 3 2 +------+ +------+
+--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 500
+--r0:=-6388/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 1288/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2*(1-2*x)^(5/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-88/3*(1-2*x)^(3/2)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)+2068/5*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 122
+
+--S 123 of 500
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 500
+--m0:=a0-r0
+--E 124
+
+--S 125 of 500
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) -----------------------------------------------------
+--R 4 3 2 +------+ +------+
+--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 500
+--r0:=2/3*(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))-_
+-- 36968/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 7448/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 400/9*(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-5852/9*_
+-- sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+36968/9*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 127
+
+--S 128 of 500
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 500
+--m0:=a0-r0
+--E 129
+
+--S 130 of 500
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R (1) ----------------------------------------------------------------
+--R 5 4 3 2 +------+ +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 500
+--r0:=2/5*(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+12*(1-2*x)^(3/2)/_
+-- ((2+3*x)^(3/2)*(3+5*x)^(3/2))-96808/3*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)*sqrt(7/5)+19504/3*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2420/3*sqrt(1-2*x)/((3+5*x)^(3/2)*_
+-- sqrt(2+3*x))-16016/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 96808/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 132
+
+--S 133 of 500
+--a0:=integrate(t0,x)
+--E 133
+
+--S 134 of 500
+--m0:=a0-r0
+--E 134
+
+--S 135 of 500
+--d0:=D(m0,x)
+--E 135
+
+)clear all
+
+--S 136 of 500
+t0:=(1-2*x)^(5/2)/((2+3*x)^(9/2)*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R /
+--R 6 5 4 3 2 +------+
+--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|3x + 2
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 500
+--r0:=2/7*(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2))+136/21*(1-2*x)^(3/2)/_
+-- ((2+3*x)^(5/2)*(3+5*x)^(3/2))-2234208/7*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)*sqrt(5/7)+321520/7*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+12188/63*sqrt(1-2*x)/((2+3*x)^(3/2)*_
+-- (3+5*x)^(3/2))+2488904/441*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 5544440/147*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+11171040/49*_
+-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 137
+
+--S 138 of 500
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 500
+--m0:=a0-r0
+--E 139
+
+--S 140 of 500
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 500
+t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R 2 +------+ +------+
+--R (9x + 12x + 4)\|3x + 2 \|5x + 3
+--R (1) ---------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 500
+--r0:=1613/250*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 56041/250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 104/175*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-1/7*(2+3*x)^(5/2)*_
+-- sqrt(1-2*x)*sqrt(3+5*x)-4839/1750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 142
+
+--S 143 of 500
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 500
+--m0:=a0-r0
+--E 144
+
+--S 145 of 500
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 500
+t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +------+ +------+
+--R (3x + 2)\|3x + 2 \|5x + 3
+--R (1) --------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 500
+--r0:=-1597/150*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 161/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 1/5*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-23/25*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 147
+
+--S 148 of 500
+--a0:=integrate(t0,x)
+--E 148
+
+--S 149 of 500
+--m0:=a0-r0
+--E 149
+
+--S 150 of 500
+--d0:=D(m0,x)
+--E 150
+
+)clear all
+
+--S 151 of 500
+t0:=sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
+--R
+--R
+--R +------+ +------+
+--R \|3x + 2 \|5x + 3
+--R (1) ------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 500
+--r0:=-34/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 7/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 1/3*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 152
+
+--S 153 of 500
+--a0:=integrate(t0,x)
+--E 153
+
+--S 154 of 500
+--m0:=a0-r0
+--E 154
+
+--S 155 of 500
+--d0:=D(m0,x)
+--E 155
+
+)clear all
+
+--S 156 of 500
+t0:=sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) --------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 500
+--r0:=-elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(11/3)
+--E 157
+
+--S 158 of 500
+--a0:=integrate(t0,x)
+--E 158
+
+--S 159 of 500
+--m0:=a0-r0
+--E 159
+
+--S 160 of 500
+--d0:=D(m0,x)
+--E 160
+
+)clear all
+
+--S 161 of 500
+t0:=sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (3x + 2)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 500
+--r0:=2/3*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(5/7)*_
+-- sqrt(-3-5*x)/sqrt(3+5*x)-2/7*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 162
+
+--S 163 of 500
+--a0:=integrate(t0,x)
+--E 163
+
+--S 164 of 500
+--m0:=a0-r0
+--E 164
+
+--S 165 of 500
+--d0:=D(m0,x)
+--E 165
+
+)clear all
+
+--S 166 of 500
+t0:=sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) -----------------------------------
+--R 2 +--------+ +------+
+--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 500
+--r0:=-62/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 20/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+62/147*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 167
+
+--S 168 of 500
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 500
+--m0:=a0-r0
+--E 169
+
+--S 170 of 500
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 500
+t0:=sqrt(3+5*x)/((2+3*x)^(7/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 500
+--r0:=4/49*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_
+-- 584/49*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 2/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+18/245*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+1752/1715*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 172
+
+--S 173 of 500
+--a0:=integrate(t0,x)
+--E 173
+
+--S 174 of 500
+--m0:=a0-r0
+--E 174
+
+--S 175 of 500
+--d0:=D(m0,x)
+--E 175
+
+)clear all
+
+--S 176 of 500
+t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)
+--R
+--R
+--R 3 2 +------+ +------+
+--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3
+--R (1) ------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 500
+--r0:=317384/10125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 44109377/40500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-137/315*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_
+-- 1/9*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-9547/5250*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-663409/47250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 177
+
+--S 178 of 500
+--a0:=integrate(t0,x)
+--E 178
+
+--S 179 of 500
+--m0:=a0-r0
+--E 179
+
+--S 180 of 500
+--d0:=D(m0,x)
+--E 180
+
+)clear all
+
+--S 181 of 500
+t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)
+--R
+--R
+--R 2 +------+ +------+
+--R (15x + 19x + 6)\|3x + 2 \|5x + 3
+--R (1) ----------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 500
+--r0:=4517/450*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 78472/225*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 1/7*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-102/175*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-4721/1050*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 182
+
+--S 183 of 500
+--a0:=integrate(t0,x)
+--E 183
+
+--S 184 of 500
+--m0:=a0-r0
+--E 184
+
+--S 185 of 500
+--d0:=D(m0,x)
+--E 185
+
+)clear all
+
+--S 186 of 500
+t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)
+--R
+--R
+--R +------+ +------+
+--R (5x + 3)\|3x + 2 \|5x + 3
+--R (1) --------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 500
+--r0:=-4451/270*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 448/135*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 1/5*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-67/45*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 187
+
+--S 188 of 500
+--a0:=integrate(t0,x)
+--E 188
+
+--S 189 of 500
+--m0:=a0-r0
+--E 189
+
+--S 190 of 500
+--d0:=D(m0,x)
+--E 190
+
+)clear all
+
+--S 191 of 500
+t0:=(3+5*x)^(3/2)/(sqrt(1-2*x)*sqrt(2+3*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) --------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 500
+--r0:=29/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 31/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_
+-- 5/9*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 192
+
+--S 193 of 500
+--a0:=integrate(t0,x)
+--E 193
+
+--S 194 of 500
+--m0:=a0-r0
+--E 194
+
+--S 195 of 500
+--d0:=D(m0,x)
+--E 195
+
+)clear all
+
+--S 196 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (3x + 2)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 500
+--r0:=-37/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 20/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/7*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+10/21*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 197
+
+--S 198 of 500
+--a0:=integrate(t0,x)
+--E 198
+
+--S 199 of 500
+--m0:=a0-r0
+--E 199
+
+--S 200 of 500
+--d0:=D(m0,x)
+--E 200
+
+)clear all
+
+--S 201 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -----------------------------------
+--R 2 +--------+ +------+
+--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 500
+--r0:=272/189*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 1030/189*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-202/441*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 202
+
+--S 203 of 500
+--a0:=integrate(t0,x)
+--E 203
+
+--S 204 of 500
+--m0:=a0-r0
+--E 204
+
+--S 205 of 500
+--d0:=D(m0,x)
+--E 205
+
+)clear all
+
+--S 206 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 500
+--r0:=-808/1323*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 5594/1323*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 2/35*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-194/2205*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+5594/15435*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 207
+
+--S 208 of 500
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 500
+--m0:=a0-r0
+--E 209
+
+--S 210 of 500
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 500
+t0:=(3+5*x)^(3/2)/((2+3*x)^(9/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -----------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 500
+--r0:=1948/21609*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 184636/21609*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 2/49*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-62/1715*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)+974/36015*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+184636/252105*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 212
+
+--S 213 of 500
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 500
+--m0:=a0-r0
+--E 214
+
+--S 215 of 500
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 500
+t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/sqrt(1-2*x)
+--R
+--R
+--R 5 4 3 2 +------+ +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3
+--R (1) ----------------------------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 500
+--r0:=8787401429/17374500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-610627101631/34749000*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-14303/12870*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)-41/143*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+-- 1/13*(2+3*x)^(7/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-138809831/4504500*_
+-- (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-221673/50050*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-2295970088/10135125*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 217
+
+--S 218 of 500
+--a0:=integrate(t0,x)
+--E 218
+
+--S 219 of 500
+--m0:=a0-r0
+--E 219
+
+--S 220 of 500
+--d0:=D(m0,x)
+--E 220
+
+)clear all
+
+--S 221 of 500
+t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)
+--R
+--R
+--R 4 3 2 +------+ +------+
+--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3
+--R (1) -----------------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 500
+--r0:=41741369/267300*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-725140729/133650*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)-34/99*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)-1/11*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+-- 329683/34650*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 1053/770*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 43624697/623700*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 222
+
+--S 223 of 500
+--a0:=integrate(t0,x)
+--E 223
+
+--S 224 of 500
+--m0:=a0-r0
+--E 224
+
+--S 225 of 500
+--d0:=D(m0,x)
+--E 225
+
+)clear all
+
+--S 226 of 500
+t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)
+--R
+--R
+--R 3 2 +------+ +------+
+--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3
+--R (1) -------------------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 500
+--r0:=118823/2430*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 8256877/4860*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-1/9*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
+-- 1877/630*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-3/7*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-62092/2835*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 227
+
+--S 228 of 500
+--a0:=integrate(t0,x)
+--E 228
+
+--S 229 of 500
+--m0:=a0-r0
+--E 229
+
+--S 230 of 500
+--d0:=D(m0,x)
+--E 230
+
+)clear all
+
+--S 231 of 500
+t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)
+--R
+--R
+--R 2 +------+ +------+
+--R (25x + 30x + 9)\|3x + 2 \|5x + 3
+--R (1) ----------------------------------
+--R +--------+
+--R \|- 2x + 1
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 500
+--r0:=-17587/162*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 2531/162*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 20/21*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1/7*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-2645/378*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 232
+
+--S 233 of 500
+--a0:=integrate(t0,x)
+--E 233
+
+--S 234 of 500
+--m0:=a0-r0
+--E 234
+
+--S 235 of 500
+--d0:=D(m0,x)
+--E 235
+
+)clear all
+
+--S 236 of 500
+t0:=(3+5*x)^(5/2)/(sqrt(1-2*x)*sqrt(2+3*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -------------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 500
+--r0:=-4141/162*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 419/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 1/3*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-62/27*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 237
+
+--S 238 of 500
+--a0:=integrate(t0,x)
+--E 238
+
+--S 239 of 500
+--m0:=a0-r0
+--E 239
+
+--S 240 of 500
+--d0:=D(m0,x)
+--E 240
+
+)clear all
+
+--S 241 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (3x + 2)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 500
+--r0:=-974/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 85/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/7*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+10/21*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-205/189*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 242
+
+--S 243 of 500
+--a0:=integrate(t0,x)
+--E 243
+
+--S 244 of 500
+--m0:=a0-r0
+--E 244
+
+--S 245 of 500
+--d0:=D(m0,x)
+--E 245
+
+)clear all
+
+--S 246 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -----------------------------------
+--R 2 +--------+ +------+
+--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 500
+--r0:=-4157/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 3130/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/21*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-38/49*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/sqrt(2+3*x)+2060/1323*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 247
+
+--S 248 of 500
+--a0:=integrate(t0,x)
+--E 248
+
+--S 249 of 500
+--m0:=a0-r0
+--E 249
+
+--S 250 of 500
+--d0:=D(m0,x)
+--E 250
+
+)clear all
+
+--S 251 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^(7/2)*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 500
+--r0:=-35242/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 53194/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 334/2205*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-2/35*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(5/2)-34154/46305*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 252
+
+--S 253 of 500
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 500
+--m0:=a0-r0
+--E 254
+
+--S 255 of 500
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^(9/2)*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -----------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 500
+--r0:=-203804/194481*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 816622/194481*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 326/5145*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-2/49*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(7/2)-30922/324135*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+816622/2268945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 257
+
+--S 258 of 500
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 500
+--m0:=a0-r0
+--E 259
+
+--S 260 of 500
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^(11/2)*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 500
+--r0:=-86188/4084101*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 32098184/4084101*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-106/3087*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-_
+-- 2/63*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-8878/324135*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)-43094/6806835*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+32098184/47647845*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 262
+
+--S 263 of 500
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 500
+--m0:=a0-r0
+--E 264
+
+--S 265 of 500
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 500
+t0:=(3+5*x)^(5/2)/((2+3*x)^(13/2)*sqrt(1-2*x))
+--R
+--R
+--R (1)
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R ---------------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+ +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 500
+--r0:=-924247516/314475777*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+114606440/314475777*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-310/14553*(3+5*x)^(3/2)*sqrt(1-2*x)/_
+-- (2+3*x)^(9/2)-2/77*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-_
+-- 21290/2139291*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-_
+-- 362666/14975037*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 11460644/104825259*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 924247516/733776813*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 267
+
+--S 268 of 500
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 500
+--m0:=a0-r0
+--E 269
+
+--S 270 of 500
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 500
+t0:=(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R (1) --------------------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 500
+--r0:=15553/3750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 270248/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 333/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-3/35*(2+3*x)^(5/2)*_
+-- sqrt(1-2*x)*sqrt(3+5*x)-15553/8750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 272
+
+--S 273 of 500
+--a0:=integrate(t0,x)
+--E 273
+
+--S 274 of 500
+--m0:=a0-r0
+--E 274
+
+--S 275 of 500
+--d0:=D(m0,x)
+--E 275
+
+)clear all
+
+--S 276 of 500
+t0:=(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R (1) ------------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 500
+--r0:=-5161/750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 518/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 3/25*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-74/125*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 277
+
+--S 278 of 500
+--a0:=integrate(t0,x)
+--E 278
+
+--S 279 of 500
+--m0:=a0-r0
+--E 279
+
+--S 280 of 500
+--d0:=D(m0,x)
+--E 280
+
+)clear all
+
+--S 281 of 500
+t0:=(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R +------+
+--R (3x + 2)\|3x + 2
+--R (1) --------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 500
+--r0:=-37/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 7/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 1/5*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 282
+
+--S 283 of 500
+--a0:=integrate(t0,x)
+--E 283
+
+--S 284 of 500
+--m0:=a0-r0
+--E 284
+
+--S 285 of 500
+--d0:=D(m0,x)
+--E 285
+
+)clear all
+
+--S 286 of 500
+t0:=sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R +------+
+--R \|3x + 2
+--R (1) --------------------
+--R +--------+ +------+
+--R \|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 500
+--r0:=-elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)
+--E 287
+
+--S 288 of 500
+--a0:=integrate(t0,x)
+--E 288
+
+--S 289 of 500
+--m0:=a0-r0
+--E 289
+
+--S 290 of 500
+--d0:=D(m0,x)
+--E 290
+
+)clear all
+
+--S 291 of 500
+t0:=1/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------
+--R +--------+ +------+ +------+
+--R \|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 500
+--r0:=-2*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)
+--E 292
+
+--S 293 of 500
+--a0:=integrate(t0,x)
+--E 293
+
+--S 294 of 500
+--m0:=a0-r0
+--E 294
+
+--S 295 of 500
+--d0:=D(m0,x)
+--E 295
+
+)clear all
+
+--S 296 of 500
+t0:=1/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R +--------+ +------+ +------+
+--R (3x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 500
+--r0:=-2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 6/7*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 297
+
+--S 298 of 500
+--a0:=integrate(t0,x)
+--E 298
+
+--S 299 of 500
+--m0:=a0-r0
+--E 299
+
+--S 300 of 500
+--d0:=D(m0,x)
+--E 300
+
+)clear all
+
+--S 301 of 500
+t0:=1/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------
+--R 2 +--------+ +------+ +------+
+--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 500
+--r0:=-148/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 20/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+148/49*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 302
+
+--S 303 of 500
+--a0:=integrate(t0,x)
+--E 303
+
+--S 304 of 500
+--m0:=a0-r0
+--E 304
+
+--S 305 of 500
+--d0:=D(m0,x)
+--E 305
+
+)clear all
+
+--S 306 of 500
+t0:=1/((2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------
+--R 3 2 +--------+ +------+ +------+
+--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 500
+--r0:=592/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 20644/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 6/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+296/245*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+20644/1715*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 307
+
+--S 308 of 500
+--a0:=integrate(t0,x)
+--E 308
+
+--S 309 of 500
+--m0:=a0-r0
+--E 309
+
+--S 310 of 500
+--d0:=D(m0,x)
+--E 310
+
+)clear all
+
+--S 311 of 500
+t0:=(2+3*x)^(7/2)/((3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R (1) --------------------------------
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 500
+--r0:=-61151/13750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+6013/6875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/11*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
+-- 69/1375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+6/55*(2+3*x)^(5/2)*_
+-- sqrt(1-2*x)*sqrt(3+5*x)-2577/6875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 312
+
+--S 313 of 500
+--a0:=integrate(t0,x)
+--E 313
+
+--S 314 of 500
+--m0:=a0-r0
+--E 314
+
+--S 315 of 500
+--d0:=D(m0,x)
+--E 315
+
+)clear all
+
+--S 316 of 500
+t0:=(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 500
+--r0:=21/275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_
+-- 438/275*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 2/11*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+6/55*(2+3*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(3+5*x)-27/275*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 317
+
+--S 318 of 500
+--a0:=integrate(t0,x)
+--E 318
+
+--S 319 of 500
+--m0:=a0-r0
+--E 319
+
+--S 320 of 500
+--d0:=D(m0,x)
+--E 320
+
+)clear all
+
+--S 321 of 500
+t0:=(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (3x + 2)\|3x + 2
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 500
+--r0:=-31/55*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 14/55*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/11*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+6/55*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 322
+
+--S 323 of 500
+--a0:=integrate(t0,x)
+--E 323
+
+--S 324 of 500
+--m0:=a0-r0
+--E 324
+
+--S 325 of 500
+--d0:=D(m0,x)
+--E 325
+
+)clear all
+
+--S 326 of 500
+t0:=sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|3x + 2
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (5x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 500
+--r0:=2/11*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(7/5)*_
+-- sqrt(-3-5*x)/sqrt(3+5*x)-2/11*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 327
+
+--S 328 of 500
+--a0:=integrate(t0,x)
+--E 328
+
+--S 329 of 500
+--m0:=a0-r0
+--E 329
+
+--S 330 of 500
+--d0:=D(m0,x)
+--E 330
+
+)clear all
+
+--S 331 of 500
+t0:=1/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R +--------+ +------+ +------+
+--R (5x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 500
+--r0:=2*elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_
+-- 10/11*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 332
+
+--S 333 of 500
+--a0:=integrate(t0,x)
+--E 333
+
+--S 334 of 500
+--m0:=a0-r0
+--E 334
+
+--S 335 of 500
+--d0:=D(m0,x)
+--E 335
+
+)clear all
+
+--S 336 of 500
+t0:=1/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------
+--R 2 +--------+ +------+ +------+
+--R (15x + 19x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 500
+--r0:=136/11*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 20/11*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 6/7*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-680/77*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 337
+
+--S 338 of 500
+--a0:=integrate(t0,x)
+--E 338
+
+--S 339 of 500
+--m0:=a0-r0
+--E 339
+
+--S 340 of 500
+--d0:=D(m0,x)
+--E 340
+
+)clear all
+
+--S 341 of 500
+t0:=1/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 3 2 +--------+ +------+ +------+
+--R (45x + 87x + 56x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 500
+--r0:=6388/77*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 920/77*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+288/49*sqrt(1-2*x)/_
+-- (sqrt(2+3*x)*sqrt(3+5*x))-31940/539*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 342
+
+--S 343 of 500
+--a0:=integrate(t0,x)
+--E 343
+
+--S 344 of 500
+--m0:=a0-r0
+--E 344
+
+--S 345 of 500
+--d0:=D(m0,x)
+--E 345
+
+)clear all
+
+--S 346 of 500
+t0:=1/((2+3*x)^(7/2)*(3+5*x)^(3/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------------
+--R 4 3 2 +--------+ +------+ +------+
+--R (135x + 351x + 342x + 148x + 24)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 500
+--r0:=-12904/539*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_
+-- 1344984/539*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 6/35*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+436/245*sqrt(1-2*x)/_
+-- ((2+3*x)^(3/2)*sqrt(3+5*x))+60684/1715*sqrt(1-2*x)/(sqrt(2+3*x)*_
+-- sqrt(3+5*x))-1344984/3773*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 347
+
+--S 348 of 500
+--a0:=integrate(t0,x)
+--E 348
+
+--S 349 of 500
+--m0:=a0-r0
+--E 349
+
+--S 350 of 500
+--d0:=D(m0,x)
+--E 350
+
+)clear all
+
+--S 351 of 500
+t0:=(2+3*x)^(9/2)/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R (1) ------------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 500
+--r0:=-6515539/2268750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+612332/1134375*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-2/33*(2+3*x)^(9/2)*sqrt(1-2*x)/_
+-- (3+5*x)^(3/2)-602/1815*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 403/75625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+668/3025*_
+-- (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-87476/378125*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 352
+
+--S 353 of 500
+--a0:=integrate(t0,x)
+--E 353
+
+--S 354 of 500
+--m0:=a0-r0
+--E 354
+
+--S 355 of 500
+--d0:=D(m0,x)
+--E 355
+
+)clear all
+
+--S 356 of 500
+t0:=(2+3*x)^(7/2)/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 500
+--r0:=-46159/45375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+3409/45375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-2/33*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+-- 94/363*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+536/3025*_
+-- (2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-487/15125*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 357
+
+--S 358 of 500
+--a0:=integrate(t0,x)
+--E 358
+
+--S 359 of 500
+--m0:=a0-r0
+--E 359
+
+--S 360 of 500
+--d0:=D(m0,x)
+--E 360
+
+)clear all
+
+--S 361 of 500
+t0:=(2+3*x)^(5/2)/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 500
+--r0:=-2797/9075*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 2828/9075*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/33*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-338/1815*(2+3*x)^(3/2)*_
+-- sqrt(1-2*x)/sqrt(3+5*x)+404/3025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 362
+
+--S 363 of 500
+--a0:=integrate(t0,x)
+--E 363
+
+--S 364 of 500
+--m0:=a0-r0
+--E 364
+
+--S 365 of 500
+--d0:=D(m0,x)
+--E 365
+
+)clear all
+
+--S 366 of 500
+t0:=(2+3*x)^(3/2)/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R (3x + 2)\|3x + 2
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 500
+--r0:=272/1815*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 1442/1815*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/33*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-206/1815*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 367
+
+--S 368 of 500
+--a0:=integrate(t0,x)
+--E 368
+
+--S 369 of 500
+--m0:=a0-r0
+--E 369
+
+--S 370 of 500
+--d0:=D(m0,x)
+--E 370
+
+)clear all
+
+--S 371 of 500
+t0:=sqrt(2+3*x)/((3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R +------+
+--R \|3x + 2
+--R (1) ------------------------------------
+--R 2 +--------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 500
+--r0:=74/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 56/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 2/33*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-74/363*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 372
+
+--S 373 of 500
+--a0:=integrate(t0,x)
+--E 373
+
+--S 374 of 500
+--m0:=a0-r0
+--E 374
+
+--S 375 of 500
+--d0:=D(m0,x)
+--E 375
+
+)clear all
+
+--S 376 of 500
+t0:=1/((3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x))
+--R
+--R
+--R 1
+--R (1) ---------------------------------------------
+--R 2 +--------+ +------+ +------+
+--R (25x + 30x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 500
+--r0:=116/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 124/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_
+-- 10/33*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+620/363*_
+-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 377
+
+--S 378 of 500
+--a0:=integrate(t0,x)
+--E 378
+
+--S 379 of 500
+--m0:=a0-r0
+--E 379
+
+--S 380 of 500
+--d0:=D(m0,x)
+--E 380
+
+)clear all
+
+--S 381 of 500
+t0:=1/((2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------
+--R 3 2 +--------+ +------+ +------+
+--R (75x + 140x + 87x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 500
+--r0:=-17804/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 2560/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 6/7*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-1340/231*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)+89020/2541*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 382
+
+--S 383 of 500
+--a0:=integrate(t0,x)
+--E 383
+
+--S 384 of 500
+--m0:=a0-r0
+--E 384
+
+--S 385 of 500
+--d0:=D(m0,x)
+--E 385
+
+)clear all
+
+--S 386 of 500
+t0:=1/((2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------------
+--R 4 3 2 +--------+ +------+ +------+
+--R (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 500
+--r0:=-1255552/2541*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+180680/2541*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+2/7*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 428/49*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 94420/1617*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 6277760/17787*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 387
+
+--S 388 of 500
+--a0:=integrate(t0,x)
+--E 388
+
+--S 389 of 500
+--m0:=a0-r0
+--E 389
+
+--S 390 of 500
+--d0:=D(m0,x)
+--E 390
+
+)clear all
+
+--S 391 of 500
+t0:=1/((2+3*x)^(7/2)*(3+5*x)^(5/2)*sqrt(1-2*x))
+--R
+--R
+--R (1)
+--R 1
+--R ---------------------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+ +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 500
+--r0:=10156288/17787*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 352875016/17787*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+6/35*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_
+-- 576/245*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 120324/1715*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 5307272/11319*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 352875016/124509*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 392
+
+--S 393 of 500
+--a0:=integrate(t0,x)
+--E 393
+
+--S 394 of 500
+--m0:=a0-r0
+--E 394
+
+--S 395 of 500
+--d0:=D(m0,x)
+--E 395
+
+)clear all
+
+--S 396 of 500
+t0:=(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 3 2 +------+ +------+
+--R (- 27x - 54x - 36x - 8)\|3x + 2 \|5x + 3
+--R (1) -------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 500
+--r0:=-2663/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(11/3)+_
+-- 4071079/1500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- (2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)+2517/350*(2+3*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(3+5*x)+12/7*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 29293/875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 397
+
+--S 398 of 500
+--a0:=integrate(t0,x)
+--E 398
+
+--S 399 of 500
+--m0:=a0-r0
+--E 399
+
+--S 400 of 500
+--d0:=D(m0,x)
+--E 400
+
+)clear all
+
+--S 401 of 500
+t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 2 +------+ +------+
+--R (- 9x - 12x - 4)\|3x + 2 \|5x + 3
+--R (1) -----------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 500
+--r0:=7279/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 2933/150*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- (2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)+9/5*(2+3*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(3+5*x)+419/50*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 402
+
+--S 403 of 500
+--a0:=integrate(t0,x)
+--E 403
+
+--S 404 of 500
+--m0:=a0-r0
+--E 404
+
+--S 405 of 500
+--d0:=D(m0,x)
+--E 405
+
+)clear all
+
+--S 406 of 500
+t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R +------+ +------+
+--R (- 3x - 2)\|3x + 2 \|5x + 3
+--R (1) ----------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 500
+--r0:=139/6*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 14/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- (2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)+2*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 407
+
+--S 408 of 500
+--a0:=integrate(t0,x)
+--E 408
+
+--S 409 of 500
+--m0:=a0-r0
+--E 409
+
+--S 410 of 500
+--d0:=D(m0,x)
+--E 410
+
+)clear all
+
+--S 411 of 500
+t0:=sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)
+--R
+--R
+--R +------+ +------+
+--R \|3x + 2 \|5x + 3
+--R (1) - -------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 500
+--r0:=-elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
+-- sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
+--E 412
+
+--S 413 of 500
+--a0:=integrate(t0,x)
+--E 413
+
+--S 414 of 500
+--m0:=a0-r0
+--E 414
+
+--S 415 of 500
+--d0:=D(m0,x)
+--E 415
+
+)clear all
+
+--S 416 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 500
+--r0:=elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 2/7*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
+--E 417
+
+--S 418 of 500
+--a0:=integrate(t0,x)
+--E 418
+
+--S 419 of 500
+--m0:=a0-r0
+--E 419
+
+--S 420 of 500
+--d0:=D(m0,x)
+--E 420
+
+)clear all
+
+--S 421 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - ---------------------------------
+--R 2 +--------+ +------+
+--R (6x + x - 2)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 500
+--r0:=4/7*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 10/7*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))-12/49*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 422
+
+--S 423 of 500
+--a0:=integrate(t0,x)
+--E 423
+
+--S 424 of 500
+--m0:=a0-r0
+--E 424
+
+--S 425 of 500
+--d0:=D(m0,x)
+--E 425
+
+)clear all
+
+--S 426 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - ------------------------------------------
+--R 3 2 +--------+ +------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 500
+--r0:=-38/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 80/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-8/49*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+38/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 427
+
+--S 428 of 500
+--a0:=integrate(t0,x)
+--E 428
+
+--S 429 of 500
+--m0:=a0-r0
+--E 429
+
+--S 430 of 500
+--d0:=D(m0,x)
+--E 430
+
+)clear all
+
+--S 431 of 500
+t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(7/2))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) - --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 500
+--r0:=-52/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 5636/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 2/7*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-36/245*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)-26/1715*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+5636/12005*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 432
+
+--S 433 of 500
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 500
+--m0:=a0-r0
+--E 434
+
+--S 435 of 500
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 500
+t0:=(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 4 3 2 +------+ +------+
+--R (- 135x - 351x - 342x - 148x - 24)\|3x + 2 \|5x + 3
+--R (1) -------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 500
+--r0:=-6478333/13500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 112543103/6750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+(2+3*x)^(7/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+1397/210*_
+-- (2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+5/3*(2+3*x)^(5/2)*_
+-- (3+5*x)^(3/2)*sqrt(1-2*x)+24358/875*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)+6770629/31500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 437
+
+--S 438 of 500
+--a0:=integrate(t0,x)
+--E 438
+
+--S 439 of 500
+--m0:=a0-r0
+--E 439
+
+--S 440 of 500
+--d0:=D(m0,x)
+--E 440
+
+)clear all
+
+--S 441 of 500
+t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 3 2 +------+ +------+
+--R (- 45x - 87x - 56x - 12)\|3x + 2 \|5x + 3
+--R (1) --------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 500
+--r0:=-18551/150*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 1289089/300*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- (2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+12/7*(2+3*x)^(3/2)*_
+-- (3+5*x)^(3/2)*sqrt(1-2*x)+2511/350*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)+9694/175*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 442
+
+--S 443 of 500
+--a0:=integrate(t0,x)
+--E 443
+
+--S 444 of 500
+--m0:=a0-r0
+--E 444
+
+--S 445 of 500
+--d0:=D(m0,x)
+--E 445
+
+)clear all
+
+--S 446 of 500
+t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 2 +------+ +------+
+--R (- 15x - 19x - 6)\|3x + 2 \|5x + 3
+--R (1) ------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 500
+--r0:=4621/30*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 931/30*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- (2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+9/5*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)+139/10*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 447
+
+--S 448 of 500
+--a0:=integrate(t0,x)
+--E 448
+
+--S 449 of 500
+--m0:=a0-r0
+--E 449
+
+--S 450 of 500
+--d0:=D(m0,x)
+--E 450
+
+)clear all
+
+--S 451 of 500
+t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)
+--R
+--R
+--R +------+ +------+
+--R (- 5x - 3)\|3x + 2 \|5x + 3
+--R (1) ----------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 500
+--r0:=-67/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 133/18*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
+-- (3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)+10/3*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 452
+
+--S 453 of 500
+--a0:=integrate(t0,x)
+--E 453
+
+--S 454 of 500
+--m0:=a0-r0
+--E 454
+
+--S 455 of 500
+--d0:=D(m0,x)
+--E 455
+
+)clear all
+
+--S 456 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*sqrt(2+3*x))
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 500
+--r0:=34/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 5/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)+5/7*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 457
+
+--S 458 of 500
+--a0:=integrate(t0,x)
+--E 458
+
+--S 459 of 500
+--m0:=a0-r0
+--E 459
+
+--S 460 of 500
+--d0:=D(m0,x)
+--E 460
+
+)clear all
+
+--S 461 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) ---------------------------------
+--R 2 +--------+ +------+
+--R (6x + x - 2)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 500
+--r0:=31/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 10/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*(3+5*x)^(3/2)/(sqrt(1-2*x)*sqrt(2+3*x))+4/49*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 462
+
+--S 463 of 500
+--a0:=integrate(t0,x)
+--E 463
+
+--S 464 of 500
+--m0:=a0-r0
+--E 464
+
+--S 465 of 500
+--d0:=D(m0,x)
+--E 465
+
+)clear all
+
+--S 466 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) ------------------------------------------
+--R 3 2 +--------+ +------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 500
+--r0:=458/441*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 970/441*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+8/147*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)-458/1029*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 467
+
+--S 468 of 500
+--a0:=integrate(t0,x)
+--E 468
+
+--S 469 of 500
+--m0:=a0-r0
+--E 469
+
+--S 470 of 500
+--d0:=D(m0,x)
+--E 470
+
+)clear all
+
+--S 471 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2))
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 500
+--r0:=-916/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 338/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 2/7*(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+12/245*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)-458/1715*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+338/12005*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 472
+
+--S 473 of 500
+--a0:=integrate(t0,x)
+--E 473
+
+--S 474 of 500
+--m0:=a0-r0
+--E 474
+
+--S 475 of 500
+--d0:=D(m0,x)
+--E 475
+
+)clear all
+
+--S 476 of 500
+t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(9/2))
+--R
+--R
+--R +------+
+--R (- 5x - 3)\|5x + 3
+--R (1) -------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 500
+--r0:=-10876/50421*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 189368/50421*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/7*(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+16/343*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-2818/12005*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)-5438/84035*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+189368/588245*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 477
+
+--S 478 of 500
+--a0:=integrate(t0,x)
+--E 478
+
+--S 479 of 500
+--m0:=a0-r0
+--E 479
+
+--S 480 of 500
+--d0:=D(m0,x)
+--E 480
+
+)clear all
+
+--S 481 of 500
+t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 5 4 3 2 +------+ +------+
+--R (- 675x - 2160x - 2763x - 1766x - 564x - 72)\|3x + 2 \|5x + 3
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 500
+--r0:=-128715331/44550*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+17888580643/178200*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+(2+3*x)^(7/2)*(3+5*x)^(5/2)/_
+-- sqrt(1-2*x)+419/66*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+_
+-- 18/11*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+4066493/23100*_
+-- (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+9741/385*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)+269045681/207900*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 482
+
+--S 483 of 500
+--a0:=integrate(t0,x)
+--E 483
+
+--S 484 of 500
+--m0:=a0-r0
+--E 484
+
+--S 485 of 500
+--d0:=D(m0,x)
+--E 485
+
+)clear all
+
+--S 486 of 500
+t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 4 3 2 +------+ +------+
+--R (- 225x - 570x - 541x - 228x - 36)\|3x + 2 \|5x + 3
+--R (1) -------------------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 500
+--r0:=-1228883/1620*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 42696881/1620*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)+5/3*(2+3*x)^(3/2)*_
+-- (3+5*x)^(5/2)*sqrt(1-2*x)+4853/105*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)+93/14*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 1284329/3780*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 487
+
+--S 488 of 500
+--a0:=integrate(t0,x)
+--E 488
+
+--S 489 of 500
+--m0:=a0-r0
+--E 489
+
+--S 490 of 500
+--d0:=D(m0,x)
+--E 490
+
+)clear all
+
+--S 491 of 500
+t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)
+--R
+--R
+--R 3 2 +------+ +------+
+--R (- 75x - 140x - 87x - 18)\|3x + 2 \|5x + 3
+--R (1) ---------------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 500
+--r0:=-1762/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 244879/36*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- (2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)+167/14*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)+12/7*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
+-- 3683/42*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 492
+
+--S 493 of 500
+--a0:=integrate(t0,x)
+--E 493
+
+--S 494 of 500
+--m0:=a0-r0
+--E 494
+
+--S 495 of 500
+--d0:=D(m0,x)
+--E 495
+
+)clear all
+
+--S 496 of 500
+t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)
+--R
+--R
+--R 2 +------+ +------+
+--R (- 25x - 30x - 9)\|3x + 2 \|5x + 3
+--R (1) ------------------------------------
+--R +--------+
+--R (2x - 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 500
+--r0:=6599/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 2659/54*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- (3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)+3*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)+397/18*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 497
+
+--S 498 of 500
+--a0:=integrate(t0,x)
+--E 498
+
+--S 499 of 500
+--m0:=a0-r0
+--E 499
+
+--S 500 of 500
+--d0:=D(m0,x)
+--E 500
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3s.input.pdf b/src/axiom-website/CATS/rich3s.input.pdf
new file mode 100644
index 0000000..b101f17
Binary files /dev/null and b/src/axiom-website/CATS/rich3s.input.pdf differ
diff --git a/src/axiom-website/CATS/rich3t.input.pamphlet b/src/axiom-website/CATS/rich3t.input.pamphlet
new file mode 100644
index 0000000..8134e56
--- /dev/null
+++ b/src/axiom-website/CATS/rich3t.input.pamphlet
@@ -0,0 +1,5009 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich3t.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b x)^m (c+d)^n (e+f x)^p|
+There are:
+\begin{itemize}
+\item 119 integrals in this file.
+\item 119 supplied "optimal results".
+\item 7 matching answers.
+\item 3 cases where Axiom's result differs from Rubi
+\item 1 case where Axiom supplied 2 results.
+\item 10 cases that Axiom failed to integrate.
+\item 100 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich3t.output
+)spool rich3t.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*sqrt(2+3*x))
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 597
+--r0:=4451/54*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 320/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)+5/7*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)+335/63*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 2
+
+--S 3 of 597
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 597
+--m0:=a0-r0
+--E 4
+
+--S 5 of 597
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) ---------------------------------
+--R 2 +--------+ +------+
+--R (6x + x - 2)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 597
+--r0:=1159/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 185/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*(3+5*x)^(5/2)/(sqrt(1-2*x)*sqrt(2+3*x))+4/49*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/sqrt(2+3*x)+155/147*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 7
+
+--S 8 of 597
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 597
+--m0:=a0-r0
+--E 9
+
+--S 10 of 597
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) ------------------------------------------
+--R 3 2 +--------+ +------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 597
+--r0:=2797/1323*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 2020/1323*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/7*(3+5*x)^(5/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+8/147*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(3/2)+598/3087*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 12
+
+--S 13 of 597
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 597
+--m0:=a0-r0
+--E 14
+
+--S 15 of 597
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2))
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 597
+--r0:=-31202/9261*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 81164/9261*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 2/7*(3+5*x)^(5/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+12/245*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)/(2+3*x)^(5/2)+1514/15435*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)-81164/108045*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 17
+
+--S 18 of 597
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 597
+--m0:=a0-r0
+--E 19
+
+--S 20 of 597
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(9/2))
+--R
+--R
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R (1) -------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 597
+--r0:=-213544/151263*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+106558/151263*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+2/7*(3+5*x)^(5/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+_
+-- 16/343*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+986/12005*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-106772/252105*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)-106558/1764735*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 22
+
+--S 23 of 597
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 597
+--m0:=a0-r0
+--E 24
+
+--S 25 of 597
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(11/2))
+--R
+--R
+--R (1)
+--R 2 +------+
+--R (- 25x - 30x - 9)\|5x + 3
+--R -------------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+ +------+
+--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 597
+--r0:=-6036028/9529569*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-3929980/9529569*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/7*(3+5*x)^(5/2)/((2+3*x)^(9/2)*_
+-- sqrt(1-2*x))+20/441*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+_
+-- 4930/64827*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-167228/453789*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-392998/3176523*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+6036028/22235661*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 27
+
+--S 28 of 597
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 597
+--m0:=a0-r0
+--E 29
+
+--S 30 of 597
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 597
+t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 3 2 +------+
+--R (- 27x - 54x - 36x - 8)\|3x + 2
+--R (1) ----------------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 597
+--r0:=-11291/2750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_
+-- 168123/2750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+2/11*(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)+_
+-- 312/275*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+3/11*(2+3*x)^(5/2)*_
+-- sqrt(1-2*x)*sqrt(3+5*x)+14517/2750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 32
+
+--S 33 of 597
+--a0:=integrate(t0,x)
+--E 33
+
+--S 34 of 597
+--m0:=a0-r0
+--E 34
+
+--S 35 of 597
+--d0:=D(m0,x)
+--E 35
+
+)clear all
+
+--S 36 of 597
+t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 2 +------+
+--R (- 9x - 12x - 4)\|3x + 2
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 597
+--r0:=1597/110*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 161/55*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/11*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)+3/11*(2+3*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(3+5*x)+69/55*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 37
+
+--S 38 of 597
+--a0:=integrate(t0,x)
+--E 38
+
+--S 39 of 597
+--m0:=a0-r0
+--E 39
+
+--S 40 of 597
+--d0:=D(m0,x)
+--E 40
+
+)clear all
+
+--S 41 of 597
+t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R +------+
+--R (- 3x - 2)\|3x + 2
+--R (1) ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 597
+--r0:=34/11*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 7/11*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/11*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)+3/11*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 42
+
+--S 43 of 597
+--a0:=integrate(t0,x)
+--E 43
+
+--S 44 of 597
+--m0:=a0-r0
+--E 44
+
+--S 45 of 597
+--d0:=D(m0,x)
+--E 45
+
+)clear all
+
+--S 46 of 597
+t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R +------+
+--R \|3x + 2
+--R (1) - ----------------------------
+--R +--------+ +------+
+--R (2x - 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 597
+--r0:=elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_
+-- 2/11*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
+--E 47
+
+--S 48 of 597
+--a0:=integrate(t0,x)
+--E 48
+
+--S 49 of 597
+--m0:=a0-r0
+--E 49
+
+--S 50 of 597
+--d0:=D(m0,x)
+--E 50
+
+)clear all
+
+--S 51 of 597
+t0:=1/((1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) - -------------------------------------
+--R +--------+ +------+ +------+
+--R (2x - 1)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 597
+--r0:=2/11*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(5/7)*_
+-- sqrt(-3-5*x)/sqrt(3+5*x)+4/77*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
+--E 52
+
+--S 53 of 597
+--a0:=integrate(t0,x)
+--E 53
+
+--S 54 of 597
+--m0:=a0-r0
+--E 54
+
+--S 55 of 597
+--d0:=D(m0,x)
+--E 55
+
+)clear all
+
+--S 56 of 597
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ------------------------------------------
+--R 2 +--------+ +------+ +------+
+--R (6x + x - 2)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 597
+--r0:=-62/77*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 20/77*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/77*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+186/539*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 57
+
+--S 58 of 597
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 597
+--m0:=a0-r0
+--E 59
+
+--S 60 of 597
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 597
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) - ---------------------------------------------------
+--R 3 2 +--------+ +------+ +------+
+--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 597
+--r0:=60/539*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_
+-- 1752/539*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 4/77*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+54/539*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+5256/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 62
+
+--S 63 of 597
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 597
+--m0:=a0-r0
+--E 64
+
+--S 65 of 597
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 597
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) - -----------------------------------------------------------
+--R 4 3 2 +--------+ +------+ +------+
+--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 597
+--r0:=6872/3773*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 244604/3773*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 4/77*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))+138/2695*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(5/2)+10308/18865*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(3/2)+733812/132055*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 67
+
+--S 68 of 597
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 597
+--m0:=a0-r0
+--E 69
+
+--S 70 of 597
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 597
+t0:=(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 4 3 2 +------+
+--R (- 81x - 216x - 216x - 96x - 16)\|3x + 2
+--R (1) --------------------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 597
+--r0:=2911577/75625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-1173529/151250*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(9/2)/(sqrt(1-2*x)*_
+-- sqrt(3+5*x))-4/121*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 10851/15125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+111/605*_
+-- (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+502941/151250*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 72
+
+--S 73 of 597
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 597
+--m0:=a0-r0
+--E 74
+
+--S 75 of 597
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 597
+t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 3 2 +------+
+--R (- 27x - 54x - 36x - 8)\|3x + 2
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 597
+--r0:=55019/6050*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 5572/3025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/11*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))-4/121*(2+3*x)^(5/2)*_
+-- sqrt(1-2*x)/sqrt(3+5*x)+111/605*(2+3*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(3+5*x)+2388/3025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 77
+
+--S 78 of 597
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 597
+--m0:=a0-r0
+--E 79
+
+--S 80 of 597
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 597
+t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +------+
+--R (- 9x - 12x - 4)\|3x + 2
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 597
+--r0:=1159/605*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 259/605*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/11*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))-4/121*(2+3*x)^(3/2)*_
+-- sqrt(1-2*x)/sqrt(3+5*x)+111/605*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 82
+
+--S 83 of 597
+--a0:=integrate(t0,x)
+--E 83
+
+--S 84 of 597
+--m0:=a0-r0
+--E 84
+
+--S 85 of 597
+--d0:=D(m0,x)
+--E 85
+
+)clear all
+
+--S 86 of 597
+t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +------+
+--R (- 3x - 2)\|3x + 2
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 597
+--r0:=37/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 28/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/11*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))-_
+-- 4/121*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 87
+
+--S 88 of 597
+--a0:=integrate(t0,x)
+--E 88
+
+--S 89 of 597
+--m0:=a0-r0
+--E 89
+
+--S 90 of 597
+--d0:=D(m0,x)
+--E 90
+
+)clear all
+
+--S 91 of 597
+t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +------+
+--R \|3x + 2
+--R (1) - ----------------------------------
+--R 2 +--------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 597
+--r0:=-74/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
+-- 2/11*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-20/121*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 92
+
+--S 93 of 597
+--a0:=integrate(t0,x)
+--E 93
+
+--S 94 of 597
+--m0:=a0-r0
+--E 94
+
+--S 95 of 597
+--d0:=D(m0,x)
+--E 95
+
+)clear all
+
+--S 96 of 597
+t0:=1/((1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x))
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------
+--R 2 +--------+ +------+ +------+
+--R (10x + x - 3)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 597
+--r0:=74/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 40/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/77*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_
+-- 370/847*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 97
+
+--S 98 of 597
+--a0:=integrate(t0,x)
+--E 98
+
+--S 99 of 597
+--m0:=a0-r0
+--E 99
+
+--S 100 of 597
+--d0:=D(m0,x)
+--E 100
+
+)clear all
+
+--S 101 of 597
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) - ---------------------------------------------------
+--R 3 2 +--------+ +------+ +------+
+--R (30x + 23x - 7x - 6)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 597
+--r0:=4636/847*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 740/847*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/77/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+186/539*_
+-- sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-23180/5929*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 102
+
+--S 103 of 597
+--a0:=integrate(t0,x)
+--E 103
+
+--S 104 of 597
+--m0:=a0-r0
+--E 104
+
+--S 105 of 597
+--d0:=D(m0,x)
+--E 105
+
+)clear all
+
+--S 106 of 597
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------------------------
+--R 4 3 2 +--------+ +------+ +------+
+--R (90x + 129x + 25x - 32x - 12)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 597
+--r0:=220076/5929*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 31840/5929*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/77/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+54/539*_
+-- sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+9876/3773*sqrt(1-2*x)/_
+-- (sqrt(2+3*x)*sqrt(3+5*x))-1100380/41503*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 107
+
+--S 108 of 597
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 597
+--m0:=a0-r0
+--E 109
+
+--S 110 of 597
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 597
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2))
+--R
+--R
+--R (1)
+--R 1
+--R - -----------------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+ +------+
+--R (270x + 567x + 333x - 46x - 100x - 24)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 597
+--r0:=-1341176/41503*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+46585232/41503*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+4/77/((2+3*x)^(5/2)*sqrt(1-2*x)*_
+-- sqrt(3+5*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_
+-- 14928/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
+-- 2101332/132055*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
+-- 46585232/290521*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 112
+
+--S 113 of 597
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 597
+--m0:=a0-r0
+--E 114
+
+--S 115 of 597
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 597
+t0:=(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 5 4 3 2 +------+
+--R (- 243x - 810x - 1080x - 720x - 240x - 32)\|3x + 2
+--R (1) -------------------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 597
+--r0:=604915631/24956250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-121995881/24956250*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(11/2)/((3+5*x)^(3/2)*_
+-- sqrt(1-2*x))-8/363*(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+-- 1022/19965*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
+-- 380188/831875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 4553/33275*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
+-- 17427983/8318750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 117
+
+--S 118 of 597
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 597
+--m0:=a0-r0
+--E 119
+
+--S 120 of 597
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 597
+t0:=(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 4 3 2 +------+
+--R (- 81x - 216x - 216x - 96x - 16)\|3x + 2
+--R (1) --------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 597
+--r0:=5684677/998250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-581651/499125*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(9/2)/((3+5*x)^(3/2)*_
+-- sqrt(1-2*x))-8/363*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+-- 178/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+4421/33275*_
+-- (2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+83093/166375*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 122
+
+--S 123 of 597
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 597
+--m0:=a0-r0
+--E 124
+
+--S 125 of 597
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 597
+t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 3 2 +------+
+--R (- 27x - 54x - 36x - 8)\|3x + 2
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 597
+--r0:=118898/99825*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-30023/99825*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(7/2)/((3+5*x)^(3/2)*_
+-- sqrt(1-2*x))-8/363*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
+-- 758/19965*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+4289/33275*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 127
+
+--S 128 of 597
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 597
+--m0:=a0-r0
+--E 129
+
+--S 130 of 597
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 597
+t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 2 +------+
+--R (- 9x - 12x - 4)\|3x + 2
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 597
+--r0:=4157/19965*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 4382/19965*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/11*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-8/363*(2+3*x)^(3/2)*_
+-- sqrt(1-2*x)/(3+5*x)^(3/2)-626/19965*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 132
+
+--S 133 of 597
+--a0:=integrate(t0,x)
+--E 133
+
+--S 134 of 597
+--m0:=a0-r0
+--E 134
+
+--S 135 of 597
+--d0:=D(m0,x)
+--E 135
+
+)clear all
+
+--S 136 of 597
+t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +------+
+--R (- 3x - 2)\|3x + 2
+--R (1) -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 597
+--r0:=494/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
+-- 1610/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/11*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-8/363*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)-494/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 137
+
+--S 138 of 597
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 597
+--m0:=a0-r0
+--E 139
+
+--S 140 of 597
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 597
+t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +------+
+--R \|3x + 2
+--R (1) - -------------------------------------------
+--R 3 2 +--------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 597
+--r0:=-724/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 98/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
+-- 2/11*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-40/363*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)-490/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 142
+
+--S 143 of 597
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 597
+--m0:=a0-r0
+--E 144
+
+--S 145 of 597
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 597
+t0:=1/((1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x))
+--R
+--R
+--R 1
+--R (1) - ----------------------------------------------------
+--R 3 2 +--------+ +------+ +------+
+--R (50x + 35x - 12x - 9)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 597
+--r0:=-3896/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 340/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/77*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-410/2541*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)+19480/27951*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 147
+
+--S 148 of 597
+--a0:=integrate(t0,x)
+--E 148
+
+--S 149 of 597
+--m0:=a0-r0
+--E 149
+
+--S 150 of 597
+--d0:=D(m0,x)
+--E 150
+
+)clear all
+
+--S 151 of 597
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 1
+--R (1) - --------------------------------------------------------------
+--R 4 3 2 +--------+ +------+ +------+
+--R (150x + 205x + 34x - 51x - 18)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 597
+--r0:=-595324/27951*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+85160/27951*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+4/77/((3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x))+186/539*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 45040/17787*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 2976620/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 152
+
+--S 153 of 597
+--a0:=integrate(t0,x)
+--E 153
+
+--S 154 of 597
+--m0:=a0-r0
+--E 154
+
+--S 155 of 597
+--d0:=D(m0,x)
+--E 155
+
+)clear all
+
+--S 156 of 597
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R - -----------------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+ +------+
+--R (450x + 915x + 512x - 85x - 156x - 36)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 597
+--r0:=-42623864/195657*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+6132760/195657*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+4/77/((2+3*x)^(3/2)*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x))+54/539*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 14496/3773*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 3205940/124509*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 213119320/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 157
+
+--S 158 of 597
+--a0:=integrate(t0,x)
+--E 158
+
+--S 159 of 597
+--m0:=a0-r0
+--E 159
+
+--S 160 of 597
+--d0:=D(m0,x)
+--E 160
+
+)clear all
+
+--S 161 of 597
+t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R -
+--R 1
+--R /
+--R 6 5 4 3 2 +--------+
+--R (1350x + 3645x + 3366x + 769x - 638x - 420x - 72)\|- 2x + 1
+--R *
+--R +------+ +------+
+--R \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 597
+--r0:=347423024/1369599*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-12071114168/1369599*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+4/77/((2+3*x)^(5/2)*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_
+-- 19548/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 4115652/132055*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 181551856/871563*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 12071114168/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 162
+
+--S 163 of 597
+--a0:=integrate(t0,x)
+--E 163
+
+--S 164 of 597
+--m0:=a0-r0
+--E 164
+
+--S 165 of 597
+--d0:=D(m0,x)
+--E 165
+
+)clear all
+
+--S 166 of 597
+t0:=(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 4 3 2 +------+ +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2 \|5x + 3
+--R (1) ---------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 597
+--r0:=6478333/16500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 112543103/8250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+1/3*(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-166/33*_
+-- (2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)-139163/3850*(2+3*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(3+5*x)-1327/154*(2+3*x)^(5/2)*sqrt(1-2*x)*_
+-- sqrt(3+5*x)-6478333/38500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 167
+
+--S 168 of 597
+--a0:=integrate(t0,x)
+--E 168
+
+--S 169 of 597
+--m0:=a0-r0
+--E 169
+
+--S 170 of 597
+--d0:=D(m0,x)
+--E 170
+
+)clear all
+
+--S 171 of 597
+t0:=(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 3 2 +------+ +------+
+--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3
+--R (1) -----------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 597
+--r0:=-1289089/3300*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+129857/1650*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+1/3*(2+3*x)^(7/2)*sqrt(3+5*x)/_
+-- (1-2*x)^(3/2)-133/33*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-_
+-- 797/110*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-18551/550*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 172
+
+--S 173 of 597
+--a0:=integrate(t0,x)
+--E 173
+
+--S 174 of 597
+--m0:=a0-r0
+--E 174
+
+--S 175 of 597
+--d0:=D(m0,x)
+--E 175
+
+)clear all
+
+--S 176 of 597
+t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 2 +------+ +------+
+--R (9x + 12x + 4)\|3x + 2 \|5x + 3
+--R (1) ---------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 597
+--r0:=-4621/66*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 931/66*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 1/3*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-100/33*(2+3*x)^(3/2)*_
+-- sqrt(3+5*x)/sqrt(1-2*x)-133/22*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 177
+
+--S 178 of 597
+--a0:=integrate(t0,x)
+--E 178
+
+--S 179 of 597
+--m0:=a0-r0
+--E 179
+
+--S 180 of 597
+--d0:=D(m0,x)
+--E 180
+
+)clear all
+
+--S 181 of 597
+t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R +------+ +------+
+--R (3x + 2)\|3x + 2 \|5x + 3
+--R (1) --------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 597
+--r0:=67/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 133/66*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
+-- 1/3*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-67/33*sqrt(2+3*x)*_
+-- sqrt(3+5*x)/sqrt(1-2*x)
+--E 182
+
+--S 183 of 597
+--a0:=integrate(t0,x)
+--E 183
+
+--S 184 of 597
+--m0:=a0-r0
+--E 184
+
+--S 185 of 597
+--d0:=D(m0,x)
+--E 185
+
+)clear all
+
+--S 186 of 597
+t0:=sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(5/2)
+--R
+--R
+--R +------+ +------+
+--R \|3x + 2 \|5x + 3
+--R (1) -------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 597
+--r0:=-34/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 5/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 1/3*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)-68/231*sqrt(2+3*x)*_
+-- sqrt(3+5*x)/sqrt(1-2*x)
+--E 187
+
+--S 188 of 597
+--a0:=integrate(t0,x)
+--E 188
+
+--S 189 of 597
+--m0:=a0-r0
+--E 189
+
+--S 190 of 597
+--d0:=D(m0,x)
+--E 190
+
+)clear all
+
+--S 191 of 597
+t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*sqrt(2+3*x))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 597
+--r0:=31/231*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 10/231*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/21*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+62/1617*sqrt(2+3*x)*_
+-- sqrt(3+5*x)/sqrt(1-2*x)
+--E 192
+
+--S 193 of 597
+--a0:=integrate(t0,x)
+--E 193
+
+--S 194 of 597
+--m0:=a0-r0
+--E 194
+
+--S 195 of 597
+--d0:=D(m0,x)
+--E 195
+
+)clear all
+
+--S 196 of 597
+t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(3/2))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 597
+--r0:=458/1617*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 970/1617*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+194/1617*sqrt(3+5*x)/_
+-- (sqrt(1-2*x)*sqrt(2+3*x))-458/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 197
+
+--S 198 of 597
+--a0:=integrate(t0,x)
+--E 198
+
+--S 199 of 597
+--m0:=a0-r0
+--E 199
+
+--S 200 of 597
+--d0:=D(m0,x)
+--E 200
+
+)clear all
+
+--S 201 of 597
+t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(5/2))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) -------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 597
+--r0:=-338/11319*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 4580/11319*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+326/1617*sqrt(3+5*x)/_
+-- ((2+3*x)^(3/2)*sqrt(1-2*x))-458/3773*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)+338/26411*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 202
+
+--S 203 of 597
+--a0:=integrate(t0,x)
+--E 203
+
+--S 204 of 597
+--m0:=a0-r0
+--E 204
+
+--S 205 of 597
+--d0:=D(m0,x)
+--E 205
+
+)clear all
+
+--S 206 of 597
+t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(7/2))
+--R
+--R
+--R +------+
+--R \|5x + 3
+--R (1) ----------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 597
+--r0:=-10876/79233*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 189368/79233*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+458/1617*sqrt(3+5*x)/_
+-- ((2+3*x)^(5/2)*sqrt(1-2*x))-2818/18865*sqrt(1-2*x)*sqrt(3+5*x)/_
+-- (2+3*x)^(5/2)-5438/132055*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 189368/924385*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 207
+
+--S 208 of 597
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 597
+--m0:=a0-r0
+--E 209
+
+--S 210 of 597
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 597
+t0:=(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 4 3 2 +------+ +------+
+--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 597
+--r0:=1/3*(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)+188443/300*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-6547351/300*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-56/11*_
+-- (2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-1341/154*(2+3*x)^(3/2)*_
+-- (3+5*x)^(3/2)*sqrt(1-2*x)-140289/3850*(3+5*x)^(3/2)*sqrt(1-2*x)*_
+-- sqrt(2+3*x)-2166399/7700*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 212
+
+--S 213 of 597
+--a0:=integrate(t0,x)
+--E 213
+
+--S 214 of 597
+--m0:=a0-r0
+--E 214
+
+--S 215 of 597
+--d0:=D(m0,x)
+--E 215
+
+)clear all
+
+--S 216 of 597
+t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 3 2 +------+ +------+
+--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3
+--R (1) ------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 597
+--r0:=1/3*(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)-37663/60*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 1897/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 45/11*(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-807/110*(3+5*x)^(3/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-6231/110*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 217
+
+--S 218 of 597
+--a0:=integrate(t0,x)
+--E 218
+
+--S 219 of 597
+--m0:=a0-r0
+--E 219
+
+--S 220 of 597
+--d0:=D(m0,x)
+--E 220
+
+)clear all
+
+--S 221 of 597
+t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 2 +------+ +------+
+--R (15x + 19x + 6)\|3x + 2 \|5x + 3
+--R (1) ----------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 597
+--r0:=1/3*(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_
+-- 137/6*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 68/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_
+-- 34/11*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-225/22*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 222
+
+--S 223 of 597
+--a0:=integrate(t0,x)
+--E 223
+
+--S 224 of 597
+--m0:=a0-r0
+--E 224
+
+--S 225 of 597
+--d0:=D(m0,x)
+--E 225
+
+)clear all
+
+--S 226 of 597
+t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(5/2)
+--R
+--R
+--R +------+ +------+
+--R (5x + 3)\|3x + 2 \|5x + 3
+--R (1) --------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 597
+--r0:=-139/6*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 10/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 1/3*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-23/7*sqrt(2+3*x)*_
+-- sqrt(3+5*x)/sqrt(1-2*x)
+--E 227
+
+--S 228 of 597
+--a0:=integrate(t0,x)
+--E 228
+
+--S 229 of 597
+--m0:=a0-r0
+--E 229
+
+--S 230 of 597
+--d0:=D(m0,x)
+--E 230
+
+)clear all
+
+--S 231 of 597
+t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*sqrt(2+3*x))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 597
+--r0:=-37/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 5/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/21*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-13/49*sqrt(2+3*x)*_
+-- sqrt(3+5*x)/sqrt(1-2*x)
+--E 232
+
+--S 233 of 597
+--a0:=integrate(t0,x)
+--E 233
+
+--S 234 of 597
+--m0:=a0-r0
+--E 234
+
+--S 235 of 597
+--d0:=D(m0,x)
+--E 235
+
+)clear all
+
+--S 236 of 597
+t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 597
+--r0:=19/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 40/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*sqrt(2+3*x))+9/49*sqrt(3+5*x)/_
+-- (sqrt(1-2*x)*sqrt(2+3*x))-19/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 237
+
+--S 238 of 597
+--a0:=integrate(t0,x)
+--E 238
+
+--S 239 of 597
+--m0:=a0-r0
+--E 239
+
+--S 240 of 597
+--d0:=D(m0,x)
+--E 240
+
+)clear all
+
+--S 241 of 597
+t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) -------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 597
+--r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+_
+-- 496/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-890/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+31/49*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-_
+-- 89/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-496/2401*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 242
+
+--S 243 of 597
+--a0:=integrate(t0,x)
+--E 243
+
+--S 244 of 597
+--m0:=a0-r0
+--E 244
+
+--S 245 of 597
+--d0:=D(m0,x)
+--E 245
+
+)clear all
+
+--S 246 of 597
+t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2))
+--R
+--R
+--R +------+
+--R (5x + 3)\|5x + 3
+--R (1) ----------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 597
+--r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))-_
+-- 4528/7203*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 3946/7203*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 53/49*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-_
+-- 779/1715*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-_
+-- 2264/12005*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-_
+-- 3946/84035*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 247
+
+--S 248 of 597
+--a0:=integrate(t0,x)
+--E 248
+
+--S 249 of 597
+--m0:=a0-r0
+--E 249
+
+--S 250 of 597
+--d0:=D(m0,x)
+--E 250
+
+)clear all
+
+--S 251 of 597
+t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 5 4 3 2 +------+ +------+
+--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3
+--R (1) ----------------------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 597
+--r0:=1/3*(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_
+-- 2513419/540*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 174654791/1080*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)-203/33*(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-_
+-- 225/22*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-1310203/4620*_
+-- (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-6277/154*(3+5*x)^(5/2)*_
+-- sqrt(1-2*x)*sqrt(2+3*x)-1313411/630*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 252
+
+--S 253 of 597
+--a0:=integrate(t0,x)
+--E 253
+
+--S 254 of 597
+--m0:=a0-r0
+--E 254
+
+--S 255 of 597
+--d0:=D(m0,x)
+--E 255
+
+)clear all
+
+--S 256 of 597
+t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 4 3 2 +------+ +------+
+--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3
+--R (1) -----------------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 597
+--r0:=1/3*(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_
+-- 4019/4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 69819/2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
+-- 170/33*(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-_
+-- 28283/462*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 1355/154*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 12601/28*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 257
+
+--S 258 of 597
+--a0:=integrate(t0,x)
+--E 258
+
+--S 259 of 597
+--m0:=a0-r0
+--E 259
+
+--S 260 of 597
+--d0:=D(m0,x)
+--E 260
+
+)clear all
+
+--S 261 of 597
+t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2)
+--R
+--R
+--R 3 2 +------+ +------+
+--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3
+--R (1) -------------------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 597
+--r0:=1/3*(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)-_
+-- 12101/12*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 1219/6*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 137/33*(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)-_
+-- 817/66*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
+-- 91*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 262
+
+--S 263 of 597
+--a0:=integrate(t0,x)
+--E 263
+
+--S 264 of 597
+--m0:=a0-r0
+--E 264
+
+--S 265 of 597
+--d0:=D(m0,x)
+--E 265
+
+)clear all
+
+--S 266 of 597
+t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(5/2)
+--R
+--R
+--R 2 +------+ +------+
+--R (25x + 30x + 9)\|3x + 2 \|5x + 3
+--R (1) ----------------------------------
+--R 2 +--------+
+--R (4x - 4x + 1)\|- 2x + 1
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 597
+--r0:=-4621/18*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 665/18*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 1/3*(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-104/21*(3+5*x)^(3/2)*_
+-- sqrt(2+3*x)/sqrt(1-2*x)-695/42*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 267
+
+--S 268 of 597
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 597
+--m0:=a0-r0
+--E 269
+
+--S 270 of 597
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*sqrt(2+3*x))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 597
+--r0:=-1597/42*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 115/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/21*(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-_
+-- 109/147*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-_
+-- 120/49*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 272
+
+--S 273 of 597
+--a0:=integrate(t0,x)
+--E 273
+
+--S 274 of 597
+--m0:=a0-r0
+--E 274
+
+--S 275 of 597
+--d0:=D(m0,x)
+--E 275
+
+)clear all
+
+--S 276 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 597
+--r0:=5/49*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_
+-- 146/49*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*sqrt(2+3*x))-43/147*(3+5*x)^(3/2)/_
+-- (sqrt(1-2*x)*sqrt(2+3*x))-17/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 277
+
+--S 278 of 597
+--a0:=integrate(t0,x)
+--E 278
+
+--S 279 of 597
+--m0:=a0-r0
+--E 279
+
+--S 280 of 597
+--d0:=D(m0,x)
+--E 280
+
+)clear all
+
+--S 281 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) -------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 597
+--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+169/3087*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
+-- 2290/3087*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 23/147*(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+19/1029*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-169/7203*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 282
+
+--S 283 of 597
+--a0:=integrate(t0,x)
+--E 283
+
+--S 284 of 597
+--m0:=a0-r0
+--E 284
+
+--S 285 of 597
+--d0:=D(m0,x)
+--E 285
+
+)clear all
+
+--S 286 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) ----------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 597
+--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))-_
+-- 986/2401*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_
+-- 9206/2401*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 89/147*(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+143/1715*_
+-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-4437/12005*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/(2+3*x)^(3/2)-27618/84035*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 287
+
+--S 288 of 597
+--a0:=integrate(t0,x)
+--E 288
+
+--S 289 of 597
+--m0:=a0-r0
+--E 289
+
+--S 290 of 597
+--d0:=D(m0,x)
+--E 290
+
+)clear all
+
+--S 291 of 597
+t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(9/2))
+--R
+--R
+--R 2 +------+
+--R (25x + 30x + 9)\|5x + 3
+--R (1) ---------------------------------------------------------------------
+--R 6 5 4 3 2 +--------+ +------+
+--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 597
+--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2))+_
+-- 98642/352947*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-337780/352947*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+155/147*(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+_
+-- 355/2401*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-_
+-- 11433/16807*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-_
+-- 33778/117649*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-_
+-- 98642/823543*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 292
+
+--S 293 of 597
+--a0:=integrate(t0,x)
+--E 293
+
+--S 294 of 597
+--m0:=a0-r0
+--E 294
+
+--S 295 of 597
+--d0:=D(m0,x)
+--E 295
+
+)clear all
+
+--S 296 of 597
+t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R (1) ------------------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 597
+--r0:=-44109377/181500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+2221688/45375*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(9/2)*sqrt(3+5*x)/_
+-- (1-2*x)^(3/2)-227/363*(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)-_
+-- 27271/6050*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-130/121*_
+-- (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-317384/15125*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 297
+
+--S 298 of 597
+--a0:=integrate(t0,x)
+--E 298
+
+--S 299 of 597
+--m0:=a0-r0
+--E 299
+
+--S 300 of 597
+--d0:=D(m0,x)
+--E 300
+
+)clear all
+
+--S 301 of 597
+t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 597
+--r0:=-78472/1815*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+31619/3630*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(7/2)*sqrt(3+5*x)/_
+-- (1-2*x)^(3/2)-161/363*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-_
+-- 97/121*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-4517/1210*_
+-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 302
+
+--S 303 of 597
+--a0:=integrate(t0,x)
+--E 303
+
+--S 304 of 597
+--m0:=a0-r0
+--E 304
+
+--S 305 of 597
+--d0:=D(m0,x)
+--E 305
+
+)clear all
+
+--S 306 of 597
+t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 597
+--r0:=-4451/726*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+448/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+2/33*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-_
+-- 95/363*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)-64/121*sqrt(1-2*x)*_
+-- sqrt(2+3*x)*sqrt(3+5*x)
+--E 307
+
+--S 308 of 597
+--a0:=integrate(t0,x)
+--E 308
+
+--S 309 of 597
+--m0:=a0-r0
+--E 309
+
+--S 310 of 597
+--d0:=D(m0,x)
+--E 310
+
+)clear all
+
+--S 311 of 597
+t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R +------+
+--R (3x + 2)\|3x + 2
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 597
+--r0:=29/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 31/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(35)+2/33*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-_
+-- 29/363*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
+--E 312
+
+--S 313 of 597
+--a0:=integrate(t0,x)
+--E 313
+
+--S 314 of 597
+--m0:=a0-r0
+--E 314
+
+--S 315 of 597
+--d0:=D(m0,x)
+--E 315
+
+)clear all
+
+--S 316 of 597
+t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R +------+
+--R \|3x + 2
+--R (1) ----------------------------------
+--R 2 +--------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 597
+--r0:=37/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 20/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/33*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+74/2541*sqrt(2+3*x)*_
+-- sqrt(3+5*x)/sqrt(1-2*x)
+--E 317
+
+--S 318 of 597
+--a0:=integrate(t0,x)
+--E 318
+
+--S 319 of 597
+--m0:=a0-r0
+--E 319
+
+--S 320 of 597
+--d0:=D(m0,x)
+--E 320
+
+)clear all
+
+--S 321 of 597
+t0:=1/((1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------
+--R 2 +--------+ +------+ +------+
+--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 597
+--r0:=272/2541*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 1030/2541*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/231*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+544/17787*_
+-- sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
+--E 322
+
+--S 323 of 597
+--a0:=integrate(t0,x)
+--E 323
+
+--S 324 of 597
+--m0:=a0-r0
+--E 324
+
+--S 325 of 597
+--d0:=D(m0,x)
+--E 325
+
+)clear all
+
+--S 326 of 597
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------
+--R 3 2 +--------+ +------+ +------+
+--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 597
+--r0:=-5594/17787*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 4040/17787*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+808/17787*_
+-- sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+5594/41503*sqrt(1-2*x)*_
+-- sqrt(3+5*x)/sqrt(2+3*x)
+--E 327
+
+--S 328 of 597
+--a0:=integrate(t0,x)
+--E 328
+
+--S 329 of 597
+--m0:=a0-r0
+--E 329
+
+--S 330 of 597
+--d0:=D(m0,x)
+--E 330
+
+)clear all
+
+--S 331 of 597
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------
+--R 4 3 2 +--------+ +------+ +------+
+--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 597
+--r0:=-184636/124509*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+9740/124509*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+_
+-- 1072/17787*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+_
+-- 974/41503*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 184636/290521*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 332
+
+--S 333 of 597
+--a0:=integrate(t0,x)
+--E 333
+
+--S 334 of 597
+--m0:=a0-r0
+--E 334
+
+--S 335 of 597
+--d0:=D(m0,x)
+--E 335
+
+)clear all
+
+--S 336 of 597
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*sqrt(3+5*x))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+ +------+
+--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 597
+--r0:=699808/871563*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 26062156/871563*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
+-- sqrt(35)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+_
+-- 1336/17787*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-_
+-- 806/207515*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
+-- 349904/1452605*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
+-- 26062156/10168235*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
+--E 337
+
+--S 338 of 597
+--a0:=integrate(t0,x)
+--E 338
+
+--S 339 of 597
+--m0:=a0-r0
+--E 339
+
+--S 340 of 597
+--d0:=D(m0,x)
+--E 340
+
+)clear all
+
+--S 341 of 597
+t0:=(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R (1) -----------------------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 597
+--r0:=-1508889271/9982500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+151997573/4991250*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(11/2)/((1-2*x)^(3/2)*_
+-- sqrt(3+5*x))-223/363*(2+3*x)^(9/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_
+-- 215/3993*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
+-- 932783/332750*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 4439/6655*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 21713939/1663750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 342
+
+--S 343 of 597
+--a0:=integrate(t0,x)
+--E 343
+
+--S 344 of 597
+--m0:=a0-r0
+--E 344
+
+--S 345 of 597
+--d0:=D(m0,x)
+--E 345
+
+)clear all
+
+--S 346 of 597
+t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R (1) ------------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 597
+--r0:=-5327983/199650*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+1073233/199650*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*_
+-- sqrt(3+5*x))-157/363*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_
+-- 149/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
+-- 3284/6655*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 153319/66550*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 347
+
+--S 348 of 597
+--a0:=integrate(t0,x)
+--E 348
+
+--S 349 of 597
+--m0:=a0-r0
+--E 349
+
+--S 350 of 597
+--d0:=D(m0,x)
+--E 350
+
+)clear all
+
+--S 351 of 597
+t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 597
+--r0:=-148831/39930*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+14903/19965*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*_
+-- sqrt(3+5*x))-91/363*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_
+-- 83/3993*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
+-- 2129/6655*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 352
+
+--S 353 of 597
+--a0:=integrate(t0,x)
+--E 353
+
+--S 354 of 597
+--m0:=a0-r0
+--E 354
+
+--S 355 of 597
+--d0:=D(m0,x)
+--E 355
+
+)clear all
+
+--S 356 of 597
+t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 597
+--r0:=-974/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
+-- 119/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x))-_
+-- 25/363*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_
+-- 17/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 357
+
+--S 358 of 597
+--a0:=integrate(t0,x)
+--E 358
+
+--S 359 of 597
+--m0:=a0-r0
+--E 359
+
+--S 360 of 597
+--d0:=D(m0,x)
+--E 360
+
+)clear all
+
+--S 361 of 597
+t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +------+
+--R (3x + 2)\|3x + 2
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 597
+--r0:=-362/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 49/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
+-- 2/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x))+_
+-- 41/363*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_
+-- 245/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 362
+
+--S 363 of 597
+--a0:=integrate(t0,x)
+--E 363
+
+--S 364 of 597
+--m0:=a0-r0
+--E 364
+
+--S 365 of 597
+--d0:=D(m0,x)
+--E 365
+
+)clear all
+
+--S 366 of 597
+t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R +------+
+--R \|3x + 2
+--R (1) -----------------------------------------
+--R 3 2 +--------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 597
+--r0:=494/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 1150/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+214/2541*sqrt(2+3*x)/_
+-- (sqrt(1-2*x)*sqrt(3+5*x))-2470/27951*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 367
+
+--S 368 of 597
+--a0:=integrate(t0,x)
+--E 368
+
+--S 369 of 597
+--m0:=a0-r0
+--E 369
+
+--S 370 of 597
+--d0:=D(m0,x)
+--E 370
+
+)clear all
+
+--S 371 of 597
+t0:=1/((1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------
+--R 3 2 +--------+ +------+ +------+
+--R (20x - 8x - 7x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 597
+--r0:=8314/27951*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
+-- 6260/27951*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+_
+-- 824/17787*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_
+-- 41570/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 372
+
+--S 373 of 597
+--a0:=integrate(t0,x)
+--E 373
+
+--S 374 of 597
+--m0:=a0-r0
+--E 374
+
+--S 375 of 597
+--d0:=D(m0,x)
+--E 375
+
+)clear all
+
+--S 376 of 597
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------------
+--R 4 3 2 +--------+ +------+ +------+
+--R (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 597
+--r0:=475592/195657*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-85780/195657*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*sqrt(2+3*x)*_
+-- sqrt(3+5*x))+1088/17787/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+_
+-- 5314/41503*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
+-- 2377960/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 377
+
+--S 378 of 597
+--a0:=integrate(t0,x)
+--E 378
+
+--S 379 of 597
+--m0:=a0-r0
+--E 379
+
+--S 380 of 597
+--d0:=D(m0,x)
+--E 380
+
+)clear all
+
+--S 381 of 597
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+ +------+
+--R (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 597
+--r0:=22738708/1369599*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-3323720/1369599*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*_
+-- sqrt(3+5*x))+1352/17787/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+_
+-- 694/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
+-- 336536/290521*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
+-- 113693540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 382
+
+--S 383 of 597
+--a0:=integrate(t0,x)
+--E 383
+
+--S 384 of 597
+--m0:=a0-r0
+--E 384
+
+--S 385 of 597
+--d0:=D(m0,x)
+--E 385
+
+)clear all
+
+--S 386 of 597
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 6 5 4 3 2 +--------+ +------+
+--R (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 \|3x + 2
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 597
+--r0:=-139423864/9587193*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+4839325048/9587193*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)/sqrt(35)+4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*_
+-- sqrt(3+5*x))+1616/17787/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x))-_
+-- 2206/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_
+-- 499564/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
+-- 72709316/10168235*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
+-- 4839325048/67110351*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 387
+
+--S 388 of 597
+--a0:=integrate(t0,x)
+--E 388
+
+--S 389 of 597
+--m0:=a0-r0
+--E 389
+
+--S 390 of 597
+--d0:=D(m0,x)
+--E 390
+
+)clear all
+
+--S 391 of 597
+t0:=(2+3*x)^(13/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 6 5 4 3 2 +------+
+--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2
+--R (1) ----------------------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 597
+--r0:=2/33*(2+3*x)^(13/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_
+-- 51601293223/549037500*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)*sqrt(7/5)+2598959587/137259375*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
+-- 73/121*(2+3*x)^(11/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+_
+-- 215/3993*(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+-- 6503/219615*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
+-- 31887029/18301250*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 150812/366025*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 371279941/45753125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 392
+
+--S 393 of 597
+--a0:=integrate(t0,x)
+--E 393
+
+--S 394 of 597
+--m0:=a0-r0
+--E 394
+
+--S 395 of 597
+--d0:=D(m0,x)
+--E 395
+
+)clear all
+
+--S 396 of 597
+t0:=(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 5 4 3 2 +------+
+--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2
+--R (1) -----------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 597
+--r0:=2/33*(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_
+-- 90397364/5490375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+36399853/10980750*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-51/121*(2+3*x)^(9/2)/((3+5*x)^(3/2)*_
+-- sqrt(1-2*x))+149/3993*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+-- 865/43923*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
+-- 110519/366025*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
+-- 5199979/3660250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 397
+
+--S 398 of 597
+--a0:=integrate(t0,x)
+--E 398
+
+--S 399 of 597
+--m0:=a0-r0
+--E 399
+
+--S 400 of 597
+--d0:=D(m0,x)
+--E 400
+
+)clear all
+
+--S 401 of 597
+t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 4 3 2 +------+
+--R (81x + 216x + 216x + 96x + 16)\|3x + 2
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 597
+--r0:=2/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_
+-- 4971289/2196150*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)+491582/1098075*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-29/121*(2+3*x)^(7/2)/((3+5*x)^(3/2)*_
+-- sqrt(1-2*x))+83/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_
+-- 2147/219615*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
+-- 70226/366025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
+--E 402
+
+--S 403 of 597
+--a0:=integrate(t0,x)
+--E 403
+
+--S 404 of 597
+--m0:=a0-r0
+--E 404
+
+--S 405 of 597
+--d0:=D(m0,x)
+--E 405
+
+)clear all
+
+--S 406 of 597
+t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 3 2 +------+
+--R (27x + 54x + 36x + 8)\|3x + 2
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 597
+--r0:=2/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_
+-- 29933/219615*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-217/219615*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)-7/121*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+_
+-- 17/3993*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-31/219615*_
+-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 407
+
+--S 408 of 597
+--a0:=integrate(t0,x)
+--E 408
+
+--S 409 of 597
+--m0:=a0-r0
+--E 409
+
+--S 410 of 597
+--d0:=D(m0,x)
+--E 410
+
+)clear all
+
+--S 411 of 597
+t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R 2 +------+
+--R (9x + 12x + 4)\|3x + 2
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 597
+--r0:=2/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 2209/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(7/5)-4144/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+15/121*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+-- 49/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2209/43923*_
+-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 412
+
+--S 413 of 597
+--a0:=integrate(t0,x)
+--E 413
+
+--S 414 of 597
+--m0:=a0-r0
+--E 414
+
+--S 415 of 597
+--d0:=D(m0,x)
+--E 415
+
+)clear all
+
+--S 416 of 597
+t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +------+
+--R (3x + 2)\|3x + 2
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 597
+--r0:=2/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_
+-- 8774/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+592/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(35)+37/121*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+-- 575/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2960/43923*_
+-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 417
+
+--S 418 of 597
+--a0:=integrate(t0,x)
+--E 418
+
+--S 419 of 597
+--m0:=a0-r0
+--E 419
+
+--S 420 of 597
+--d0:=D(m0,x)
+--E 420
+
+)clear all
+
+--S 421 of 597
+t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R +------+
+--R \|3x + 2
+--R (1) --------------------------------------------------
+--R 4 3 2 +--------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 597
+--r0:=4418/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-5920/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+118/847*_
+-- sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-2470/27951*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/(3+5*x)^(3/2)-22090/307461*sqrt(1-2*x)*_
+-- sqrt(2+3*x)/sqrt(3+5*x)
+--E 422
+
+--S 423 of 597
+--a0:=integrate(t0,x)
+--E 423
+
+--S 424 of 597
+--m0:=a0-r0
+--E 424
+
+--S 425 of 597
+--d0:=D(m0,x)
+--E 425
+
+)clear all
+
+--S 426 of 597
+t0:=1/((1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------------
+--R 4 3 2 +--------+ +------+ +------+
+--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 597
+--r0:=-119732/307461*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)-620/307461*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
+-- sqrt(33)+4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 368/5929*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-_
+-- 18470/195657*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 598660/2152227*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 427
+
+--S 428 of 597
+--a0:=integrate(t0,x)
+--E 428
+
+--S 429 of 597
+--m0:=a0-r0
+--E 429
+
+--S 430 of 597
+--d0:=D(m0,x)
+--E 430
+
+)clear all
+
+--S 431 of 597
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R -----------------------------------------------------------------------
+--R 5 4 3 2 +--------+ +------+ +------+
+--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 597
+--r0:=-19885156/2152227*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
+-- sqrt(5/7)+2809040/2152227*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*(3+5*x)^(3/2)*_
+-- sqrt(2+3*x))+456/5929/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x))+_
+-- 5034/41503*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 1523260/1369599*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 99425780/15065589*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 432
+
+--S 433 of 597
+--a0:=integrate(t0,x)
+--E 433
+
+--S 434 of 597
+--m0:=a0-r0
+--E 434
+
+--S 435 of 597
+--d0:=D(m0,x)
+--E 435
+
+)clear all
+
+--S 436 of 597
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 6 5 4 3 2 +--------+ +------+
+--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 \|3x + 2
+--R *
+--R +------+
+--R \|5x + 3
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 597
+--r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2))-_
+-- 1446357824/15065589*elliptic_e(asin(sqrt(5/11)*_
+-- sqrt(1-2*x)),33/35)*sqrt(5/7)+207999160/15065589*_
+-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
+-- 544/5929/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x))+_
+-- 414/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 488436/290521*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 108842540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 7231789120/105459123*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 437
+
+--S 438 of 597
+--a0:=integrate(t0,x)
+--E 438
+
+--S 439 of 597
+--m0:=a0-r0
+--E 439
+
+--S 440 of 597
+--d0:=D(m0,x)
+--E 440
+
+)clear all
+
+--S 441 of 597
+t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 7 6 5 4 3 2
+--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)
+--R *
+--R +--------+ +------+ +------+
+--R \|- 2x + 1 \|3x + 2 \|5x + 3
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 597
+--r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2))+_
+-- 11880958112/105459123*elliptic_f(asin(sqrt(3/7)*_
+-- sqrt(1-2*x)),35/33)/sqrt(33)-412810345784/105459123*_
+-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
+-- 632/5929/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x))-_
+-- 3606/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_
+-- 649224/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
+-- 140700876/10168235*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
+-- 6208896328/67110351*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
+-- 412810345784/738213861*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
+--E 442
+
+--S 443 of 597
+--a0:=integrate(t0,x)
+--E 443
+
+--S 444 of 597
+--m0:=a0-r0
+--E 444
+
+--S 445 of 597
+--d0:=D(m0,x)
+--E 445
+
+)clear all
+
+--S 446 of 597
+t0:=(a+b*x)*(A+B*x)*sqrt(c+d*x)/x
+--R
+--R
+--R 2 +-------+
+--R (B b x + (A b + B a)x + A a)\|d x + c
+--R (1) ---------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 597
+r0:=-2/15*(2*b*B*c-5*A*b*d-2*a*B*d)*(c+d*x)^(3/2)/d^2+_
+ 2/5*B*(a+b*x)*(c+d*x)^(3/2)/d-2*a*A*atanh(sqrt(c+d*x)/sqrt(c))*_
+ sqrt(c)+2*a*A*sqrt(c+d*x)
+--R
+--R
+--R (2)
+--R +-------+
+--R 2 +-+ \|d x + c
+--R - 30A a d \|c atanh(----------)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 2
+--R 6B b d x + ((10A b + 10B a)d + 2B b c d)x + 30A a d
+--R +
+--R 2
+--R (10A b + 10B a)c d - 4B b c
+--R *
+--R +-------+
+--R \|d x + c
+--R /
+--R 2
+--R 15d
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 597
+--a0:=integrate(t0,x)
+--E 448
+
+--S 449 of 597
+--m0:=a0-r0
+--E 449
+
+--S 450 of 597
+--d0:=D(m0,x)
+--E 450
+
+)clear all
+
+--S 451 of 597
+t0:=(A+B*x)*(c+d*x)*sqrt(a+b*x)/x
+--R
+--R
+--R 2 +-------+
+--R (B d x + (A d + B c)x + A c)\|b x + a
+--R (1) ---------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 597
+r0:=2/15*(5*b*B*c+2*A*b*d-2*a*B*d)*(a+b*x)^(3/2)/b^2+_
+ 2/5*d*(a+b*x)^(3/2)*(A+B*x)/b-2*A*c*atanh(sqrt(a+b*x)/sqrt(a))*_
+ sqrt(a)+2*A*c*sqrt(a+b*x)
+--R
+--R
+--R (2)
+--R +-------+
+--R 2 +-+ \|b x + a
+--R - 30A b c\|a atanh(----------)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 2 2
+--R 6B b d x + ((10A b + 2B a b)d + 10B b c)x + (10A a b - 4B a )d
+--R +
+--R 2
+--R (30A b + 10B a b)c
+--R *
+--R +-------+
+--R \|b x + a
+--R /
+--R 2
+--R 15b
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 597
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-+ +-------+
+--R 2 +-+ - 2\|a \|b x + a + b x + 2a
+--R 15A b c\|a log(----------------------------)
+--R x
+--R +
+--R 2 2 2 2 2
+--R 6B b d x + ((10A b + 2B a b)d + 10B b c)x + (10A a b - 4B a )d
+--R +
+--R 2
+--R (30A b + 10B a b)c
+--R *
+--R +-------+
+--R \|b x + a
+--R /
+--R 2
+--R 15b
+--R ,
+--R
+--R +-------+
+--R 2 +---+ \|b x + a
+--R - 30A b c\|- a atan(----------)
+--R +---+
+--R \|- a
+--R +
+--R 2 2 2 2 2
+--R 6B b d x + ((10A b + 2B a b)d + 10B b c)x + (10A a b - 4B a )d
+--R +
+--R 2
+--R (30A b + 10B a b)c
+--R *
+--R +-------+
+--R \|b x + a
+--R /
+--R 2
+--R 15b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 453
+
+--S 454 of 597
+m0a:=a0.1-r0
+--R
+--R
+--R +-+ +-------+ +-------+
+--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a
+--R (4) A c\|a log(----------------------------) + 2A c\|a atanh(----------)
+--R x +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 597
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 455
+
+--S 456 of 597
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R +-+ \|b x + a +---+ \|b x + a
+--R (6) 2A c\|a atanh(----------) - 2A c\|- a atan(----------)
+--R +-+ +---+
+--R \|a \|- a
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 597
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 457
+
+)clear all
+
+--S 458 of 597
+t0:=x^3*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x))
+--R
+--R
+--R 4 3
+--R a x + x
+--R (1) ------------------
+--R +---------+ +---+
+--R \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 458
+
+--S 459 of 597
+r0:=-75/128*asin(1-2*a*x)/a^4-75/64*sqrt(a*x-a^2*x^2)/a^4-_
+ 25/32*x*sqrt(a*x-a^2*x^2)/a^3-5/8*x^2*sqrt(a*x-a^2*x^2)/a^2-_
+ 1/4*x^3*sqrt(a*x-a^2*x^2)/a
+--R
+--R
+--R +------------+
+--R 3 3 2 2 | 2 2
+--R (- 32a x - 80a x - 100a x - 150)\|- a x + a x + 75asin(2a x - 1)
+--R (2) --------------------------------------------------------------------
+--R 4
+--R 128a
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 597
+--a0:=integrate(t0,x)
+--E 460
+
+--S 461 of 597
+--m0:=a0-r0
+--E 461
+
+--S 462 of 597
+--d0:=D(m0,x)
+--E 462
+
+)clear all
+
+--S 463 of 597
+t0:=x^2*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x))
+--R
+--R
+--R 3 2
+--R a x + x
+--R (1) ------------------
+--R +---------+ +---+
+--R \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 597
+r0:=-11/16*asin(1-2*a*x)/a^3-11/8*sqrt(a*x-a^2*x^2)/a^3-_
+ 11/12*x*sqrt(a*x-a^2*x^2)/a^2-1/3*x^2*sqrt(a*x-a^2*x^2)/a
+--R
+--R
+--R +------------+
+--R 2 2 | 2 2
+--R (- 16a x - 44a x - 66)\|- a x + a x + 33asin(2a x - 1)
+--R (2) ---------------------------------------------------------
+--R 3
+--R 48a
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 597
+--a0:=integrate(t0,x)
+--E 465
+
+--S 466 of 597
+--m0:=a0-r0
+--E 466
+
+--S 467 of 597
+--d0:=D(m0,x)
+--E 467
+
+)clear all
+
+--S 468 of 597
+t0:=x*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x))
+--R
+--R
+--R 2
+--R a x + x
+--R (1) ------------------
+--R +---------+ +---+
+--R \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 468
+
+--S 469 of 597
+r0:=-7/8*asin(1-2*a*x)/a^2-5/4*sqrt(a*x)*sqrt(1-a*x)/a^2-_
+ 1/2*(1+a*x)*sqrt(a*x)*sqrt(1-a*x)/a^2
+--R
+--R
+--R +---------+ +---+
+--R (- 4a x - 14)\|- a x + 1 \|a x + 7asin(2a x - 1)
+--R (2) -------------------------------------------------
+--R 2
+--R 8a
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 597
+--a0:=integrate(t0,x)
+--E 470
+
+--S 471 of 597
+--m0:=a0-r0
+--E 471
+
+--S 472 of 597
+--d0:=D(m0,x)
+--E 472
+
+)clear all
+
+--S 473 of 597
+t0:=(1+a*x)/(sqrt(a*x)*sqrt(1-a*x))
+--R
+--R
+--R a x + 1
+--R (1) ------------------
+--R +---------+ +---+
+--R \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 473
+
+--S 474 of 597
+r0:=-3/2*asin(1-2*a*x)/a-sqrt(a*x)*sqrt(1-a*x)/a
+--R
+--R
+--R +---------+ +---+
+--R - 2\|- a x + 1 \|a x + 3asin(2a x - 1)
+--R (2) ---------------------------------------
+--R 2a
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 597
+--a0:=integrate(t0,x)
+--E 475
+
+--S 476 of 597
+--m0:=a0-r0
+--E 476
+
+--S 477 of 597
+--d0:=D(m0,x)
+--E 477
+
+)clear all
+
+--S 478 of 597
+t0:=(1+a*x)/(x*sqrt(a*x)*sqrt(1-a*x))
+--R
+--R
+--R a x + 1
+--R (1) -------------------
+--R +---------+ +---+
+--R x\|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 478
+
+--S 479 of 597
+r0:=-asin(1-2*a*x)-2*sqrt(a*x-a^2*x^2)/(a*x)
+--R
+--R
+--R +------------+
+--R | 2 2
+--R - 2\|- a x + a x + a x asin(2a x - 1)
+--R (2) ---------------------------------------
+--R a x
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 597
+--a0:=integrate(t0,x)
+--E 480
+
+--S 481 of 597
+--m0:=a0-r0
+--E 481
+
+--S 482 of 597
+--d0:=D(m0,x)
+--E 482
+
+)clear all
+
+--S 483 of 597
+t0:=(1+a*x)/(x^2*sqrt(a*x)*sqrt(1-a*x))
+--R
+--R
+--R a x + 1
+--R (1) --------------------
+--R 2 +---------+ +---+
+--R x \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 483
+
+--S 484 of 597
+r0:=-2/3*sqrt(a*x-a^2*x^2)/(a*x^2)-10/3*sqrt(a*x-a^2*x^2)/x
+--R
+--R
+--R +------------+
+--R | 2 2
+--R (- 10a x - 2)\|- a x + a x
+--R (2) ----------------------------
+--R 2
+--R 3a x
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 597
+--a0:=integrate(t0,x)
+--E 485
+
+--S 486 of 597
+--m0:=a0-r0
+--E 486
+
+--S 487 of 597
+--d0:=D(m0,x)
+--E 487
+
+)clear all
+
+--S 488 of 597
+t0:=(1+a*x)/(x^3*sqrt(a*x)*sqrt(1-a*x))
+--R
+--R
+--R a x + 1
+--R (1) --------------------
+--R 3 +---------+ +---+
+--R x \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 488
+
+--S 489 of 597
+r0:=-2/5*sqrt(a*x-a^2*x^2)/(a*x^3)-6/5*sqrt(a*x-a^2*x^2)/x^2-_
+ 12/5*a*sqrt(a*x-a^2*x^2)/x
+--R
+--R
+--R +------------+
+--R 2 2 | 2 2
+--R (- 12a x - 6a x - 2)\|- a x + a x
+--R (2) ------------------------------------
+--R 3
+--R 5a x
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 597
+--a0:=integrate(t0,x)
+--E 490
+
+--S 491 of 597
+--m0:=a0-r0
+--E 491
+
+--S 492 of 597
+--d0:=D(m0,x)
+--E 492
+
+)clear all
+
+--S 493 of 597
+t0:=(1+a*x)/(x^4*sqrt(a*x)*sqrt(1-a*x))
+--R
+--R
+--R a x + 1
+--R (1) --------------------
+--R 4 +---------+ +---+
+--R x \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 597
+r0:=-2/7*sqrt(a*x-a^2*x^2)/(a*x^4)-26/35*sqrt(a*x-a^2*x^2)/x^3-_
+ 104/105*a*sqrt(a*x-a^2*x^2)/x^2-208/105*a^2*sqrt(a*x-a^2*x^2)/x
+--R
+--R
+--R +------------+
+--R 3 3 2 2 | 2 2
+--R (- 208a x - 104a x - 78a x - 30)\|- a x + a x
+--R (2) -------------------------------------------------
+--R 4
+--R 105a x
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 597 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 +---------+ +---+
+--R (- 208a x - 104a x - 78a x - 30)\|- a x + 1 \|a x
+--R +
+--R 3 2 4
+--R (104a + 52a + 39a + 15)x
+--R /
+--R 4
+--R 105a x
+--R Type: Union(Expression(Integer),...)
+--E 495
+
+--S 496 of 597 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 +---------+ +---+
+--R (- 208a x - 104a x - 78a x - 30)\|- a x + 1 \|a x
+--R +
+--R +------------+
+--R 3 3 2 2 | 2 2
+--R (208a x + 104a x + 78a x + 30)\|- a x + a x
+--R +
+--R 3 2 4
+--R (104a + 52a + 39a + 15)x
+--R /
+--R 4
+--R 105a x
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 597
+d0:=D(m0,x)
+--R
+--R
+--R +------------+
+--R +---------+ +---+ | 2 2
+--R (- a x - 1)\|- a x + 1 \|a x + (a x + 1)\|- a x + a x
+--R (5) --------------------------------------------------------
+--R +------------+
+--R 4 | 2 2 +---------+ +---+
+--R x \|- a x + a x \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 497
+
+)clear all
+
+--S 498 of 597
+t0:=(1+a*x)/(x^5*sqrt(a*x)*sqrt(1-a*x))
+--R
+--R
+--R a x + 1
+--R (1) --------------------
+--R 5 +---------+ +---+
+--R x \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 597
+r0:=-2/9*sqrt(a*x-a^2*x^2)/(a*x^5)-34/63*sqrt(a*x-a^2*x^2)/x^4-_
+ 68/105*a*sqrt(a*x-a^2*x^2)/x^3-272/315*a^2*sqrt(a*x-a^2*x^2)/x^2-_
+ 544/315*a^3*sqrt(a*x-a^2*x^2)/x
+--R
+--R
+--R +------------+
+--R 4 4 3 3 2 2 | 2 2
+--R (- 544a x - 272a x - 204a x - 170a x - 70)\|- a x + a x
+--R (2) ------------------------------------------------------------
+--R 5
+--R 315a x
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 597 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 3 3 2 2 +---------+ +---+
+--R (- 1088a x - 544a x - 408a x - 340a x - 140)\|- a x + 1 \|a x
+--R +
+--R 5 4 3 2 5
+--R (816a - 680a - 238a - 153a - 235a - 140)x
+--R /
+--R 5
+--R 630a x
+--R Type: Union(Expression(Integer),...)
+--E 500
+
+--S 501 of 597 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 4 3 3 2 2 +---------+ +---+
+--R (- 1088a x - 544a x - 408a x - 340a x - 140)\|- a x + 1 \|a x
+--R +
+--R +------------+
+--R 4 4 3 3 2 2 | 2 2
+--R (1088a x + 544a x + 408a x + 340a x + 140)\|- a x + a x
+--R +
+--R 5 4 3 2 5
+--R (816a - 680a - 238a - 153a - 235a - 140)x
+--R /
+--R 5
+--R 630a x
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 597
+d0:=D(m0,x)
+--R
+--R
+--R +------------+
+--R +---------+ +---+ | 2 2
+--R (- a x - 1)\|- a x + 1 \|a x + (a x + 1)\|- a x + a x
+--R (5) --------------------------------------------------------
+--R +------------+
+--R 5 | 2 2 +---------+ +---+
+--R x \|- a x + a x \|- a x + 1 \|a x
+--R Type: Expression(Integer)
+--E 502
+
+)clear all
+
+--S 503 of 597
+t0:=x^m*(e+f*x)^n/((a+b*x)*(c+d*x))
+--R
+--R
+--R m n
+--R x (f x + e)
+--R (1) ---------------------------
+--R 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 503
+
+--S 504 of 597
+--r0:=b*x^(1+m)*(e+f*x)^n*_
+-- AppellF1(1+m,1,-n,2+m,-b*x/a,-f*x/e)/(a*(b*c-a*d)*(1+m)*_
+-- ((e+f*x)/e)^n)-d*x^(1+m)*(e+f*x)^n*_
+-- AppellF1(1+m,1,-n,2+m,-d*x/c,-f*x/e)/(c*(b*c-a*d)*(1+m)*_
+-- ((e+f*x)/e)^n)
+--E 504
+
+--S 505 of 597
+--a0:=integrate(t0,x)
+--E 505
+
+--S 506 of 597
+--m0:=a0-r0
+--E 506
+
+--S 507 of 597
+--d0:=D(m0,x)
+--E 507
+
+)clear all
+
+--S 508 of 597
+t0:=x^4*(e+f*x)^n/((a+b*x)*(c+d*x))
+--R
+--R
+--R 4 n
+--R x (f x + e)
+--R (1) ---------------------------
+--R 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 508
+
+--S 509 of 597
+--r0:=e^2*(e+f*x)^(1+n)/(b*d*f^3*(1+n))+(b*c+a*d)*e*(e+f*x)^(1+n)/_
+-- (b^2*d^2*f^2*(1+n))+(b^2*c^2+a*b*c*d+a^2*d^2)*(e+f*x)^(1+n)/_
+-- (b^3*d^3*f*(1+n))-2*e*(e+f*x)^(2+n)/(b*d*f^3*(2+n))-_
+-- (b*c+a*d)*(e+f*x)^(2+n)/(b^2*d^2*f^2*(2+n))+(e+f*x)^(3+n)/_
+-- (b*d*f^3*(3+n))-a^4*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
+-- (b^3*(b*c-a*d)*(b*e-a*f)*(1+n))+c^4*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
+-- (d^3*(b*c-a*d)*(d*e-c*f)*(1+n))
+--E 509
+
+--S 510 of 597
+--a0:=integrate(t0,x)
+--E 510
+
+--S 511 of 597
+--m0:=a0-r0
+--E 511
+
+--S 512 of 597
+--d0:=D(m0,x)
+--E 512
+
+)clear all
+
+--S 513 of 597
+t0:=x^3*(e+f*x)^n/((a+b*x)*(c+d*x))
+--R
+--R
+--R 3 n
+--R x (f x + e)
+--R (1) ---------------------------
+--R 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 513
+
+--S 514 of 597
+--r0:=-e*(e+f*x)^(1+n)/(b*d*f^2*(1+n))-(b*c+a*d)*(e+f*x)^(1+n)/_
+-- (b^2*d^2*f*(1+n))+(e+f*x)^(2+n)/(b*d*f^2*(2+n))+a^3*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
+-- (b^2*(b*c-a*d)*(b*e-a*f)*(1+n))-c^3*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
+-- (d^2*(b*c-a*d)*(d*e-c*f)*(1+n))
+--E 514
+
+--S 515 of 597
+--a0:=integrate(t0,x)
+--E 515
+
+--S 516 of 597
+--m0:=a0-r0
+--E 516
+
+--S 517 of 597
+--d0:=D(m0,x)
+--E 517
+
+)clear all
+
+--S 518 of 597
+t0:=x^2*(e+f*x)^n/((a+b*x)*(c+d*x))
+--R
+--R
+--R 2 n
+--R x (f x + e)
+--R (1) ---------------------------
+--R 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 518
+
+--S 519 of 597
+--r0:=(e+f*x)^(1+n)/(b*d*f*(1+n))-a^2*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
+-- (b*(b*c-a*d)*(b*e-a*f)*(1+n))+c^2*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
+-- (d*(b*c-a*d)*(d*e-c*f)*(1+n))
+--E 519
+
+--S 520 of 597
+--a0:=integrate(t0,x)
+--E 520
+
+--S 521 of 597
+--m0:=a0-r0
+--E 521
+
+--S 522 of 597
+--d0:=D(m0,x)
+--E 522
+
+)clear all
+
+--S 523 of 597
+t0:=x*(e+f*x)^n/((a+b*x)*(c+d*x))
+--R
+--R
+--R n
+--R x (f x + e)
+--R (1) ---------------------------
+--R 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 523
+
+--S 524 of 597
+--r0:=a*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
+-- ((b*c-a*d)*(b*e-a*f)*(1+n))-c*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
+-- ((b*c-a*d)*(d*e-c*f)*(1+n))
+--E 524
+
+--S 525 of 597
+--a0:=integrate(t0,x)
+--E 525
+
+--S 526 of 597
+--m0:=a0-r0
+--E 526
+
+--S 527 of 597
+--d0:=D(m0,x)
+--E 527
+
+)clear all
+
+--S 528 of 597
+t0:=(e+f*x)^n/((a+b*x)*(c+d*x))
+--R
+--R
+--R n
+--R (f x + e)
+--R (1) ---------------------------
+--R 2
+--R b d x + (a d + b c)x + a c
+--R Type: Expression(Integer)
+--E 528
+
+--S 529 of 597
+--r0:=-b*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/_
+-- (b*e-a*f))/((b*c-a*d)*(b*e-a*f)*(1+n))+d*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
+-- ((b*c-a*d)*(d*e-c*f)*(1+n))
+--E 529
+
+--S 530 of 597
+--a0:=integrate(t0,x)
+--E 530
+
+--S 531 of 597
+--m0:=a0-r0
+--E 531
+
+--S 532 of 597
+--d0:=D(m0,x)
+--E 532
+
+)clear all
+
+--S 533 of 597
+t0:=(e+f*x)^n/(x*(a+b*x)*(c+d*x))
+--R
+--R
+--R n
+--R (f x + e)
+--R (1) ------------------------------
+--R 3 2
+--R b d x + (a d + b c)x + a c x
+--R Type: Expression(Integer)
+--E 533
+
+--S 534 of 597
+--r0:=-(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,(e+f*x)/e)/(a*c*e*(1+n))+_
+-- b^2*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
+-- (a*(b*c-a*d)*(b*e-a*f)*(1+n))-d^2*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
+-- (c*(b*c-a*d)*(d*e-c*f)*(1+n))
+--E 534
+
+--S 535 of 597
+--a0:=integrate(t0,x)
+--E 535
+
+--S 536 of 597
+--m0:=a0-r0
+--E 536
+
+--S 537 of 597
+--d0:=D(m0,x)
+--E 537
+
+)clear all
+
+--S 538 of 597
+t0:=(e+f*x)^n/(x^2*(a+b*x)*(c+d*x))
+--R
+--R
+--R n
+--R (f x + e)
+--R (1) -------------------------------
+--R 4 3 2
+--R b d x + (a d + b c)x + a c x
+--R Type: Expression(Integer)
+--E 538
+
+--S 539 of 597
+--r0:=-(e+f*x)^(1+n)/(a*c*e*x)+(b*c+a*d)*(e+f*x)^(1+n)*_
+-- hypergeometric(1,1+n,2+n,(e+f*x)/e)/(a^2*c^2*e*(1+n))-_
+-- f*n*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,(e+f*x)/e)/_
+-- (a*c*e^2*(1+n))-b^3*(e+f*x)^(1+n)*hypergeometric(1,1+n,_
+-- 2+n,b*(e+f*x)/(b*e-a*f))/(a^2*(b*c-a*d)*(b*e-a*f)*(1+n))_
+-- +d^3*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,d*(e+f*x)/_
+-- (d*e-c*f))/(c^2*(b*c-a*d)*(d*e-c*f)*(1+n))
+--E 539
+
+--S 540 of 597
+--a0:=integrate(t0,x)
+--E 540
+
+--S 541 of 597
+--m0:=a0-r0
+--E 541
+
+--S 542 of 597
+--d0:=D(m0,x)
+--E 542
+
+)clear all
+
+--S 543 of 597
+t0:=(a+b*x)*(c+d*x)*(e+f*x)*(g+h*x)
+--R
+--R
+--R (1)
+--R 4 3
+--R b d f h x + (((a d + b c)f + b d e)h + b d f g)x
+--R +
+--R 2
+--R ((a c f + (a d + b c)e)h + ((a d + b c)f + b d e)g)x
+--R +
+--R (a c e h + (a c f + (a d + b c)e)g)x + a c e g
+--R Type: Polynomial(Integer)
+--E 543
+
+--S 544 of 597
+r0:=a*c*e*g*x+1/2*(b*c*e*g+a*(d*e*g+c*f*g+c*e*h))*x^2+_
+ 1/3*(b*(d*e*g+c*f*g+c*e*h)+a*(d*f*g+d*e*h+c*f*h))*x^3+_
+ 1/4*(a*d*f*h+b*(d*f*g+d*e*h+c*f*h))*x^4+1/5*b*d*f*h*x^5
+--R
+--R
+--R (2)
+--R 1 5 1 1 1 1 4
+--R - b d f h x + (((- a d + - b c)f + - b d e)h + - b d f g)x
+--R 5 4 4 4 4
+--R +
+--R 1 1 1 1 1 1 3
+--R ((- a c f + (- a d + - b c)e)h + ((- a d + - b c)f + - b d e)g)x
+--R 3 3 3 3 3 3
+--R +
+--R 1 1 1 1 2
+--R (- a c e h + (- a c f + (- a d + - b c)e)g)x + a c e g x
+--R 2 2 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 544
+
+--S 545 of 597
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 1 1 1 1 4
+--R - b d f h x + (((- a d + - b c)f + - b d e)h + - b d f g)x
+--R 5 4 4 4 4
+--R +
+--R 1 1 1 1 1 1 3
+--R ((- a c f + (- a d + - b c)e)h + ((- a d + - b c)f + - b d e)g)x
+--R 3 3 3 3 3 3
+--R +
+--R 1 1 1 1 2
+--R (- a c e h + (- a c f + (- a d + - b c)e)g)x + a c e g x
+--R 2 2 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 545
+
+--S 546 of 597
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 546
+
+--S 547 of 597
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 547
+
+)clear all
+
+--S 548 of 597
+t0:=(a+b*x)*(c+d*x)*(e+f*x)/(g+h*x)
+--R
+--R
+--R 3 2
+--R b d f x + ((a d + b c)f + b d e)x + (a c f + (a d + b c)e)x + a c e
+--R (1) ---------------------------------------------------------------------
+--R h x + g
+--R Type: Fraction(Polynomial(Integer))
+--E 548
+
+--S 549 of 597
+r0:=(b*(d*g-c*h)*(f*g-e*h)-a*h*(d*f*g-d*e*h-c*f*h))*x/h^3+_
+ 1/2*(a*d*f*h-b*(d*f*g-d*e*h-c*f*h))*x^2/h^2+_
+ 1/3*b*d*f*x^3/h-(b*g-a*h)*(d*g-c*h)*(f*g-e*h)*log(g+h*x)/h^4
+--R
+--R
+--R (2)
+--R 3 2
+--R 6a c e h + (- 6a c f + (- 6a d - 6b c)e)g h
+--R +
+--R 2 3
+--R ((6a d + 6b c)f + 6b d e)g h - 6b d f g
+--R *
+--R log(h x + g)
+--R +
+--R 3 3 3 2 2
+--R 2b d f h x + (((3a d + 3b c)f + 3b d e)h - 3b d f g h )x
+--R +
+--R 3 2
+--R (6a c f + (6a d + 6b c)e)h + ((- 6a d - 6b c)f - 6b d e)g h
+--R +
+--R 2
+--R 6b d f g h
+--R *
+--R x
+--R /
+--R 4
+--R 6h
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 597
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2
+--R 6a c e h + (- 6a c f + (- 6a d - 6b c)e)g h
+--R +
+--R 2 3
+--R ((6a d + 6b c)f + 6b d e)g h - 6b d f g
+--R *
+--R log(h x + g)
+--R +
+--R 3 3 3 2 2
+--R 2b d f h x + (((3a d + 3b c)f + 3b d e)h - 3b d f g h )x
+--R +
+--R 3 2
+--R (6a c f + (6a d + 6b c)e)h + ((- 6a d - 6b c)f - 6b d e)g h
+--R +
+--R 2
+--R 6b d f g h
+--R *
+--R x
+--R /
+--R 4
+--R 6h
+--R Type: Union(Expression(Integer),...)
+--E 550
+
+--S 551 of 597
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 551
+
+--S 552 of 597
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 552
+
+)clear all
+
+--S 553 of 597
+t0:=(a+b*x)*(c+d*x)/((e+f*x)*(g+h*x))
+--R
+--R
+--R 2
+--R b d x + (a d + b c)x + a c
+--R (1) ---------------------------
+--R 2
+--R f h x + (e h + f g)x + e g
+--R Type: Fraction(Polynomial(Integer))
+--E 553
+
+--S 554 of 597
+r0:=b*d*x/(f*h)+(b*e-a*f)*(d*e-c*f)*log(e+f*x)/(f^2*(f*g-e*h))-_
+ (b*g-a*h)*(d*g-c*h)*log(g+h*x)/(h^2*(f*g-e*h))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2
+--R (a c f h + (- a d - b c)f g h + b d f g )log(h x + g)
+--R +
+--R 2 2 2
+--R (- a c f + (a d + b c)e f - b d e )h log(f x + e)
+--R +
+--R 2 2
+--R (b d e f h - b d f g h)x
+--R /
+--R 2 3 3 2
+--R e f h - f g h
+--R Type: Expression(Integer)
+--E 554
+
+--S 555 of 597
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2
+--R (a c f h + (- a d - b c)f g h + b d f g )log(h x + g)
+--R +
+--R 2 2 2
+--R (- a c f + (a d + b c)e f - b d e )h log(f x + e)
+--R +
+--R 2 2
+--R (b d e f h - b d f g h)x
+--R /
+--R 2 3 3 2
+--R e f h - f g h
+--R Type: Union(Expression(Integer),...)
+--E 555
+
+--S 556 of 597
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 597
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 557
+
+)clear all
+
+--S 558 of 597
+t0:=(a+b*x)/((c+d*x)*(e+f*x)*(g+h*x))
+--R
+--R
+--R b x + a
+--R (1) ---------------------------------------------------------------------
+--R 3 2
+--R d f h x + ((c f + d e)h + d f g)x + (c e h + (c f + d e)g)x + c e g
+--R Type: Fraction(Polynomial(Integer))
+--E 558
+
+--S 559 of 597
+r0:=-(b*c-a*d)*log(c+d*x)/((d*e-c*f)*(d*g-c*h))+_
+ (b*e-a*f)*log(e+f*x)/((d*e-c*f)*(f*g-e*h))-_
+ (b*g-a*h)*log(g+h*x)/((d*g-c*h)*(f*g-e*h))
+--R
+--R
+--R (2)
+--R ((a c f - a d e)h + (- b c f + b d e)g)log(h x + g)
+--R +
+--R ((- a c f + b c e)h + (a d f - b d e)g)log(f x + e)
+--R +
+--R ((a d - b c)e h + (- a d + b c)f g)log(d x + c)
+--R /
+--R 2 2 2 2 2 2 2 2 2 2
+--R (c e f - c d e )h + (- c f + d e )g h + (c d f - d e f)g
+--R Type: Expression(Integer)
+--E 559
+
+--S 560 of 597
+--a0:=integrate(t0,x)
+--E 560
+
+--S 561 of 597
+--m0:=a0-r0
+--E 561
+
+--S 562 of 597
+--d0:=D(m0,x)
+--E 562
+
+)clear all
+
+--S 563 of 597
+t0:=1/((a+b*x)*(c+d*x)*(e+f*x)*(g+h*x))
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 4 3
+--R b d f h x + (((a d + b c)f + b d e)h + b d f g)x
+--R +
+--R 2
+--R ((a c f + (a d + b c)e)h + ((a d + b c)f + b d e)g)x
+--R +
+--R (a c e h + (a c f + (a d + b c)e)g)x + a c e g
+--R Type: Fraction(Polynomial(Integer))
+--E 563
+
+--S 564 of 597
+r0:=b^2*log(a+b*x)/((b*c-a*d)*(b*e-a*f)*(b*g-a*h))-_
+ d^2*log(c+d*x)/((b*c-a*d)*(d*e-c*f)*(d*g-c*h))+_
+ f^2*log(e+f*x)/((b*e-a*f)*(d*e-c*f)*(f*g-e*h))-_
+ h^2*log(g+h*x)/((b*g-a*h)*(d*g-c*h)*(f*g-e*h))
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2 2 2 2 2 2
+--R ((a c d - a b c )f + (- a d + b c )e f + (a b d - b c d)e )h
+--R *
+--R log(h x + g)
+--R +
+--R 2 2 2 2 2 2 2 2 2 2 2 2 2
+--R ((- a c d + a b c )f h + (a d - b c )f g h + (- a b d + b c d)f g )
+--R *
+--R log(f x + e)
+--R +
+--R 2 2 2 2 2 2 2 2 2 2 2
+--R (a d e f - a b d e )h + (- a d f + b d e )g h
+--R +
+--R 2 2 2 2 2
+--R (a b d f - b d e f)g
+--R *
+--R log(d x + c)
+--R +
+--R 2 2 2 2 2 2 2 2 2 2 2
+--R (- b c e f + b c d e )h + (b c f - b d e )g h
+--R +
+--R 2 2 2 2 2
+--R (- b c d f + b d e f)g
+--R *
+--R log(b x + a)
+--R /
+--R 3 2 2 3 2 3 2 2 3 2
+--R (a c d - a b c )e f + (- a c d + a b c )e f
+--R +
+--R 2 2 2 2 3
+--R (a b c d - a b c d)e
+--R *
+--R 3
+--R h
+--R +
+--R 3 2 2 3 3 3 3 3 3 2 2 3 3 2 3 2
+--R ((- a c d + a b c )f + (a d - b c )e f + (- a b d + b c d)e )g h
+--R +
+--R 3 2 2 3 3 3 3 3 3 2 2 3 3 2 3 2
+--R ((a c d - a b c )f + (- a d + b c )e f + (a b d - b c d )e )g h
+--R +
+--R 2 2 2 2 3 2 3 3 2 2
+--R (- a b c d + a b c d)f + (a b d - b c d)e f
+--R +
+--R 2 3 3 2 2
+--R (- a b d + b c d )e f
+--R *
+--R 3
+--R g
+--R Type: Expression(Integer)
+--E 564
+
+--S 565 of 597
+--a0:=integrate(t0,x)
+--E 565
+
+--S 566 of 597
+--m0:=a0-r0
+--E 566
+
+--S 567 of 597
+--d0:=D(m0,x)
+--E 567
+
+)clear all
+
+--S 568 of 597
+t0:=(a+b*x)^m*(c+d*x)*(e+f*x)*(g+h*x)
+--R
+--R
+--R (1)
+--R 3 2
+--R (d f h x + ((c f + d e)h + d f g)x + (c e h + (c f + d e)g)x + c e g)
+--R *
+--R m
+--R (b x + a)
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 597
+r0:=(b*c-a*d)*(b*e-a*f)*(b*g-a*h)*(a+b*x)^(1+m)/(b^4*(1+m))+_
+ (3*a^2*d*f*h+b^2*(d*e*g+c*f*g+c*e*h)-_
+ 2*a*b*(d*f*g+d*e*h+c*f*h))*(a+b*x)^(2+m)/(b^4*(2+m))-_
+ (3*a*d*f*h-b*(d*f*g+d*e*h+c*f*h))*(a+b*x)^(3+m)/(b^4*(3+m))+_
+ d*f*h*(a+b*x)^(4+m)/(b^4*(4+m))
+--R
+--R
+--R (2)
+--R 3 2 m + 4
+--R (d f h m + 6d f h m + 11d f h m + 6d f h)(b x + a)
+--R +
+--R 3
+--R (((- 3a d + b c)f + b d e)h + b d f g)m
+--R +
+--R 2
+--R (((- 21a d + 7b c)f + 7b d e)h + 7b d f g)m
+--R +
+--R (((- 42a d + 14b c)f + 14b d e)h + 14b d f g)m
+--R +
+--R ((- 24a d + 8b c)f + 8b d e)h + 8b d f g
+--R *
+--R m + 3
+--R (b x + a)
+--R +
+--R 2 2
+--R ((3a d - 2a b c)f + (- 2a b d + b c)e)h
+--R +
+--R 2 2
+--R ((- 2a b d + b c)f + b d e)g
+--R *
+--R 3
+--R m
+--R +
+--R 2 2
+--R ((24a d - 16a b c)f + (- 16a b d + 8b c)e)h
+--R +
+--R 2 2
+--R ((- 16a b d + 8b c)f + 8b d e)g
+--R *
+--R 2
+--R m
+--R +
+--R 2 2
+--R ((57a d - 38a b c)f + (- 38a b d + 19b c)e)h
+--R +
+--R 2 2
+--R ((- 38a b d + 19b c)f + 19b d e)g
+--R *
+--R m
+--R +
+--R 2 2
+--R ((36a d - 24a b c)f + (- 24a b d + 12b c)e)h
+--R +
+--R 2 2
+--R ((- 24a b d + 12b c)f + 12b d e)g
+--R *
+--R m + 2
+--R (b x + a)
+--R +
+--R 3 2 2 2
+--R ((- a d + a b c)f + (a b d - a b c)e)h
+--R +
+--R 2 2 2 3
+--R ((a b d - a b c)f + (- a b d + b c)e)g
+--R *
+--R 3
+--R m
+--R +
+--R 3 2 2 2
+--R ((- 9a d + 9a b c)f + (9a b d - 9a b c)e)h
+--R +
+--R 2 2 2 3
+--R ((9a b d - 9a b c)f + (- 9a b d + 9b c)e)g
+--R *
+--R 2
+--R m
+--R +
+--R 3 2 2 2
+--R ((- 26a d + 26a b c)f + (26a b d - 26a b c)e)h
+--R +
+--R 2 2 2 3
+--R ((26a b d - 26a b c)f + (- 26a b d + 26b c)e)g
+--R *
+--R m
+--R +
+--R 3 2 2 2
+--R ((- 24a d + 24a b c)f + (24a b d - 24a b c)e)h
+--R +
+--R 2 2 2 3
+--R ((24a b d - 24a b c)f + (- 24a b d + 24b c)e)g
+--R *
+--R m + 1
+--R (b x + a)
+--R /
+--R 4 4 4 3 4 2 4 4
+--R b m + 10b m + 35b m + 50b m + 24b
+--R Type: Expression(Integer)
+--E 569
+
+--S 570 of 597
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 4 2 4 4 4
+--R (b d f h m + 6b d f h m + 11b d f h m + 6b d f h)x
+--R +
+--R 3 4 4 4 3
+--R (((a b d + b c)f + b d e)h + b d f g)m
+--R +
+--R 3 4 4 4 2
+--R (((3a b d + 7b c)f + 7b d e)h + 7b d f g)m
+--R +
+--R 3 4 4 4 4 4
+--R (((2a b d + 14b c)f + 14b d e)h + 14b d f g)m + (8b c f + 8b d e)h
+--R +
+--R 4
+--R 8b d f g
+--R *
+--R 3
+--R x
+--R +
+--R 3 3 4 3 4 4 3
+--R ((a b c f + (a b d + b c)e)h + ((a b d + b c)f + b d e)g)m
+--R +
+--R 2 2 3 3 4
+--R ((- 3a b d + 5a b c)f + (5a b d + 8b c)e)h
+--R +
+--R 3 4 4
+--R ((5a b d + 8b c)f + 8b d e)g
+--R *
+--R 2
+--R m
+--R +
+--R 2 2 3 3 4
+--R ((- 3a b d + 4a b c)f + (4a b d + 19b c)e)h
+--R +
+--R 3 4 4
+--R ((4a b d + 19b c)f + 19b d e)g
+--R *
+--R m
+--R +
+--R 4 4 4
+--R 12b c e h + (12b c f + 12b d e)g
+--R *
+--R 2
+--R x
+--R +
+--R 3 3 3 4 3
+--R (a b c e h + (a b c f + (a b d + b c)e)g)m
+--R +
+--R 2 2 2 2 3
+--R (- 2a b c f + (- 2a b d + 7a b c)e)h
+--R +
+--R 2 2 3 3 4
+--R ((- 2a b d + 7a b c)f + (7a b d + 9b c)e)g
+--R *
+--R 2
+--R m
+--R +
+--R 3 2 2 2 2 3
+--R ((6a b d - 8a b c)f + (- 8a b d + 12a b c)e)h
+--R +
+--R 2 2 3 3 4
+--R ((- 8a b d + 12a b c)f + (12a b d + 26b c)e)g
+--R *
+--R m
+--R +
+--R 4
+--R 24b c e g
+--R *
+--R x
+--R +
+--R 3 3 2 2 2 2 2 2 3 2
+--R a b c e g m + (- a b c e h + (- a b c f + (- a b d + 9a b c)e)g)m
+--R +
+--R 3 3 2 2
+--R (2a b c f + (2a b d - 7a b c)e)h
+--R +
+--R 3 2 2 2 2 3
+--R ((2a b d - 7a b c)f + (- 7a b d + 26a b c)e)g
+--R *
+--R m
+--R +
+--R 4 3 3 2 2
+--R ((- 6a d + 8a b c)f + (8a b d - 12a b c)e)h
+--R +
+--R 3 2 2 2 2 3
+--R ((8a b d - 12a b c)f + (- 12a b d + 24a b c)e)g
+--R *
+--R m log(b x + a)
+--R %e
+--R /
+--R 4 4 4 3 4 2 4 4
+--R b m + 10b m + 35b m + 50b m + 24b
+--R Type: Union(Expression(Integer),...)
+--E 570
+
+--S 571 of 597
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 3 4 2 4 4 4
+--R (b d f h m + 6b d f h m + 11b d f h m + 6b d f h)x
+--R +
+--R 3 4 4 4 3
+--R (((a b d + b c)f + b d e)h + b d f g)m
+--R +
+--R 3 4 4 4 2
+--R (((3a b d + 7b c)f + 7b d e)h + 7b d f g)m
+--R +
+--R 3 4 4 4
+--R (((2a b d + 14b c)f + 14b d e)h + 14b d f g)m
+--R +
+--R 4 4 4
+--R (8b c f + 8b d e)h + 8b d f g
+--R *
+--R 3
+--R x
+--R +
+--R 3 3 4 3 4 4 3
+--R ((a b c f + (a b d + b c)e)h + ((a b d + b c)f + b d e)g)m
+--R +
+--R 2 2 3 3 4
+--R ((- 3a b d + 5a b c)f + (5a b d + 8b c)e)h
+--R +
+--R 3 4 4
+--R ((5a b d + 8b c)f + 8b d e)g
+--R *
+--R 2
+--R m
+--R +
+--R 2 2 3 3 4
+--R ((- 3a b d + 4a b c)f + (4a b d + 19b c)e)h
+--R +
+--R 3 4 4
+--R ((4a b d + 19b c)f + 19b d e)g
+--R *
+--R m
+--R +
+--R 4 4 4
+--R 12b c e h + (12b c f + 12b d e)g
+--R *
+--R 2
+--R x
+--R +
+--R 3 3 3 4 3
+--R (a b c e h + (a b c f + (a b d + b c)e)g)m
+--R +
+--R 2 2 2 2 3
+--R (- 2a b c f + (- 2a b d + 7a b c)e)h
+--R +
+--R 2 2 3 3 4
+--R ((- 2a b d + 7a b c)f + (7a b d + 9b c)e)g
+--R *
+--R 2
+--R m
+--R +
+--R 3 2 2 2 2 3
+--R ((6a b d - 8a b c)f + (- 8a b d + 12a b c)e)h
+--R +
+--R 2 2 3 3 4
+--R ((- 8a b d + 12a b c)f + (12a b d + 26b c)e)g
+--R *
+--R m
+--R +
+--R 4
+--R 24b c e g
+--R *
+--R x
+--R +
+--R 3 3 2 2 2 2 2 2 3 2
+--R a b c e g m + (- a b c e h + (- a b c f + (- a b d + 9a b c)e)g)m
+--R +
+--R 3 3 2 2
+--R (2a b c f + (2a b d - 7a b c)e)h
+--R +
+--R 3 2 2 2 2 3
+--R ((2a b d - 7a b c)f + (- 7a b d + 26a b c)e)g
+--R *
+--R m
+--R +
+--R 4 3 3 2 2
+--R ((- 6a d + 8a b c)f + (8a b d - 12a b c)e)h
+--R +
+--R 3 2 2 2 2 3
+--R ((8a b d - 12a b c)f + (- 12a b d + 24a b c)e)g
+--R *
+--R m log(b x + a)
+--R %e
+--R +
+--R 3 2 m + 4
+--R (- d f h m - 6d f h m - 11d f h m - 6d f h)(b x + a)
+--R +
+--R 3
+--R (((3a d - b c)f - b d e)h - b d f g)m
+--R +
+--R 2
+--R (((21a d - 7b c)f - 7b d e)h - 7b d f g)m
+--R +
+--R (((42a d - 14b c)f - 14b d e)h - 14b d f g)m
+--R +
+--R ((24a d - 8b c)f - 8b d e)h - 8b d f g
+--R *
+--R m + 3
+--R (b x + a)
+--R +
+--R 2 2
+--R ((- 3a d + 2a b c)f + (2a b d - b c)e)h
+--R +
+--R 2 2
+--R ((2a b d - b c)f - b d e)g
+--R *
+--R 3
+--R m
+--R +
+--R 2 2
+--R ((- 24a d + 16a b c)f + (16a b d - 8b c)e)h
+--R +
+--R 2 2
+--R ((16a b d - 8b c)f - 8b d e)g
+--R *
+--R 2
+--R m
+--R +
+--R 2 2
+--R ((- 57a d + 38a b c)f + (38a b d - 19b c)e)h
+--R +
+--R 2 2
+--R ((38a b d - 19b c)f - 19b d e)g
+--R *
+--R m
+--R +
+--R 2 2
+--R ((- 36a d + 24a b c)f + (24a b d - 12b c)e)h
+--R +
+--R 2 2
+--R ((24a b d - 12b c)f - 12b d e)g
+--R *
+--R m + 2
+--R (b x + a)
+--R +
+--R 3 2 2 2
+--R ((a d - a b c)f + (- a b d + a b c)e)h
+--R +
+--R 2 2 2 3
+--R ((- a b d + a b c)f + (a b d - b c)e)g
+--R *
+--R 3
+--R m
+--R +
+--R 3 2 2 2
+--R ((9a d - 9a b c)f + (- 9a b d + 9a b c)e)h
+--R +
+--R 2 2 2 3
+--R ((- 9a b d + 9a b c)f + (9a b d - 9b c)e)g
+--R *
+--R 2
+--R m
+--R +
+--R 3 2 2 2
+--R ((26a d - 26a b c)f + (- 26a b d + 26a b c)e)h
+--R +
+--R 2 2 2 3
+--R ((- 26a b d + 26a b c)f + (26a b d - 26b c)e)g
+--R *
+--R m
+--R +
+--R 3 2 2 2
+--R ((24a d - 24a b c)f + (- 24a b d + 24a b c)e)h
+--R +
+--R 2 2 2 3
+--R ((- 24a b d + 24a b c)f + (24a b d - 24b c)e)g
+--R *
+--R m + 1
+--R (b x + a)
+--R /
+--R 4 4 4 3 4 2 4 4
+--R b m + 10b m + 35b m + 50b m + 24b
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 597
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 3 3 3 3 2
+--R b d f h x + ((b c f + b d e)h + b d f g)x
+--R +
+--R 3 3 3 3
+--R (b c e h + (b c f + b d e)g)x + b c e g
+--R *
+--R m log(b x + a)
+--R %e
+--R +
+--R m + 3
+--R - d f h (b x + a)
+--R +
+--R m + 2
+--R (((3a d - b c)f - b d e)h - b d f g)(b x + a)
+--R +
+--R 2 2 2 2
+--R (((- 3a d + 2a b c)f + (2a b d - b c)e)h + ((2a b d - b c)f - b d e)g)
+--R *
+--R m + 1
+--R (b x + a)
+--R +
+--R 3 2 2 2
+--R ((a d - a b c)f + (- a b d + a b c)e)h
+--R +
+--R 2 2 2 3
+--R ((- a b d + a b c)f + (a b d - b c)e)g
+--R *
+--R m
+--R (b x + a)
+--R /
+--R 3
+--R b
+--R Type: Expression(Integer)
+--E 572
+
+)clear all
+
+--S 573 of 597
+t0:=(a+b*x)^m*(c+d*x)*(e+f*x)/(g+h*x)
+--R
+--R
+--R 2 m
+--R (d f x + (c f + d e)x + c e)(b x + a)
+--R (1) ---------------------------------------
+--R h x + g
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 597
+--r0:=(b*d*e*h*(2+m)+f*(b*c*h-d*(a*h+b*g*(2+m))))*(a+b*x)^(1+m)/_
+-- (b^2*h^2*(1+m)*(2+m))+f*(a+b*x)^(1+m)*(c+d*x)/(b*h*(2+m))+_
+-- (d*g-c*h)*(f*g-e*h)*(a+b*x)^(1+m)*hypergeometric(1,1+m,2+m,_
+-- -h*(a+b*x)/(b*g-a*h))/(h^2*(b*g-a*h)*(1+m))
+--E 574
+
+--S 575 of 597
+--a0:=integrate(t0,x)
+--E 575
+
+--S 576 of 597
+--m0:=a0-r0
+--E 576
+
+--S 577 of 597
+--d0:=D(m0,x)
+--E 577
+
+)clear all
+
+--S 578 of 597
+t0:=(a+b*x)^m*(c+d*x)/((e+f*x)*(g+h*x))
+--R
+--R
+--R m
+--R (d x + c)(b x + a)
+--R (1) ---------------------------
+--R 2
+--R f h x + (e h + f g)x + e g
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 597
+--r0:=-(d*e-c*f)*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*_
+-- (f*g-e*h)*(1+m))+(d*g-c*h)*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-h*(a+b*x)/(b*g-a*h))/((b*g-a*h)*_
+-- (f*g-e*h)*(1+m))
+--E 579
+
+--S 580 of 597
+--a0:=integrate(t0,x)
+--E 580
+
+--S 581 of 597
+--m0:=a0-r0
+--E 581
+
+--S 582 of 597
+--d0:=D(m0,x)
+--E 582
+
+)clear all
+
+--S 583 of 597
+t0:=(a+b*x)^m/((c+d*x)*(e+f*x)*(g+h*x))
+--R
+--R
+--R m
+--R (b x + a)
+--R (1) ---------------------------------------------------------------------
+--R 3 2
+--R d f h x + ((c f + d e)h + d f g)x + (c e h + (c f + d e)g)x + c e g
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 597
+--r0:=d^2*(a+b*x)^(1+m)*hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_
+-- ((b*c-a*d)*(d*e-c*f)*(d*g-c*h)*(1+m))-f^2*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*_
+-- (d*e-c*f)*(f*g-e*h)*(1+m))+h^2*(a+b*x)^(1+m)*_
+-- hypergeometric(1,1+m,2+m,-h*(a+b*x)/(b*g-a*h))/((b*g-a*h)*_
+-- (d*g-c*h)*(f*g-e*h)*(1+m))
+--E 584
+
+--S 585 of 597
+--a0:=integrate(t0,x)
+--E 585
+
+--S 586 of 597
+--m0:=a0-r0
+--E 586
+
+--S 587 of 597
+--d0:=D(m0,x)
+--E 587
+
+)clear all
+
+--S 588 of 597
+t0:=x/((1+x)*(2+x)*(3+x))
+--R
+--R
+--R x
+--R (1) ------------------
+--R 3 2
+--R x + 6x + 11x + 6
+--R Type: Fraction(Polynomial(Integer))
+--E 588
+
+--S 589 of 597
+r0:=-1/2*log(1+x)+2*log(2+x)-3/2*log(3+x)
+--R
+--R
+--R - 3log(x + 3) + 4log(x + 2) - log(x + 1)
+--R (2) ----------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 589
+
+--S 590 of 597
+a0:=integrate(t0,x)
+--R
+--R
+--R - 3log(x + 3) + 4log(x + 2) - log(x + 1)
+--R (3) ----------------------------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 590
+
+--S 591 of 597
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 591
+
+--S 592 of 597
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 592
+
+)clear all
+
+--S 593 of 597
+t0:=(-x^2+x^3)/((-6+x)*(3+5*x)^3)
+--R
+--R
+--R 3 2
+--R x - x
+--R (1) -----------------------------------
+--R 4 3 2
+--R 125x - 525x - 1215x - 783x - 162
+--R Type: Fraction(Polynomial(Integer))
+--E 593
+
+--S 594 of 597
+r0:=(-12/1375)/(3+5*x)^2+201/15125/(3+5*x)+_
+ 20/3993*log(6-x)+1493/499125*log(3+5*x)
+--R
+--R
+--R (2)
+--R 2
+--R (37325x + 44790x + 13437)log(5x + 3)
+--R +
+--R 2
+--R (62500x + 75000x + 22500)log(- x + 6) + 33165x + 15543
+--R /
+--R 2
+--R 12478125x + 14973750x + 4492125
+--R Type: Expression(Integer)
+--E 594
+
+--S 595 of 597
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R (37325x + 44790x + 13437)log(5x + 3)
+--R +
+--R 2
+--R (62500x + 75000x + 22500)log(x - 6) + 33165x + 15543
+--R /
+--R 2
+--R 12478125x + 14973750x + 4492125
+--R Type: Union(Expression(Integer),...)
+--E 595
+
+--S 596 of 597
+m0:=a0-r0
+--R
+--R
+--R 20log(x - 6) - 20log(- x + 6)
+--R (4) -----------------------------
+--R 3993
+--R Type: Expression(Integer)
+--E 596
+
+--S 597 of 597
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 597
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich3t.input.pdf b/src/axiom-website/CATS/rich3t.input.pdf
new file mode 100644
index 0000000..994820e
Binary files /dev/null and b/src/axiom-website/CATS/rich3t.input.pdf differ
diff --git a/src/axiom-website/CATS/rich4a.input.pamphlet b/src/axiom-website/CATS/rich4a.input.pamphlet
new file mode 100644
index 0000000..45696d2
--- /dev/null
+++ b/src/axiom-website/CATS/rich4a.input.pamphlet
@@ -0,0 +1,20344 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich4a.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 255 supplied "optimal results".
+\item 311 matching answers.
+\item 59 cases where Axiom supplied 2 results.
+\item 10 cases that Axiom failed to integrate.
+\item 3 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich4a.output
+)spool rich4a.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1393
+t0:=x^m*(a+b*x^2)
+--R
+--R
+--R 2 m
+--R (1) (b x + a)x
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1393
+r0:=a*x^(1+m)/(1+m)+b*x^(3+m)/(3+m)
+--R
+--R
+--R m + 3 m + 1
+--R (b m + b)x + (a m + 3a)x
+--R (2) ----------------------------------
+--R 2
+--R m + 4m + 3
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 m log(x)
+--R ((b m + b)x + (a m + 3a)x)%e
+--R (3) -------------------------------------
+--R 2
+--R m + 4m + 3
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 m log(x) m + 3
+--R ((b m + b)x + (a m + 3a)x)%e + (- b m - b)x
+--R +
+--R m + 1
+--R (- a m - 3a)x
+--R /
+--R 2
+--R m + 4m + 3
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1393
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1393
+t0:=x^4*(a+b*x^2)
+--R
+--R
+--R 6 4
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 6
+
+--S 7 of 1393
+r0:=1/5*a*x^5+1/7*b*x^7
+--R
+--R
+--R 1 7 1 5
+--R (2) - b x + - a x
+--R 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 7
+
+--S 8 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 7 1 5
+--R (3) - b x + - a x
+--R 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 8
+
+--S 9 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 9
+
+--S 10 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 10
+
+)clear all
+
+--S 11 of 1393
+t0:=x^3*(a+b*x^2)
+--R
+--R
+--R 5 3
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 11
+
+--S 12 of 1393
+r0:=1/4*a*x^4+1/6*b*x^6
+--R
+--R
+--R 1 6 1 4
+--R (2) - b x + - a x
+--R 6 4
+--R Type: Polynomial(Fraction(Integer))
+--E 12
+
+--S 13 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 6 1 4
+--R (3) - b x + - a x
+--R 6 4
+--R Type: Polynomial(Fraction(Integer))
+--E 13
+
+--S 14 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 14
+
+--S 15 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 15
+
+)clear all
+
+--S 16 of 1393
+t0:=x^2*(a+b*x^2)
+--R
+--R
+--R 4 2
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 16
+
+--S 17 of 1393
+r0:=1/3*a*x^3+1/5*b*x^5
+--R
+--R
+--R 1 5 1 3
+--R (2) - b x + - a x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 17
+
+--S 18 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 1 3
+--R (3) - b x + - a x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 18
+
+--S 19 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 19
+
+--S 20 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 20
+
+)clear all
+
+--S 21 of 1393
+t0:=x*(a+b*x^2)
+--R
+--R
+--R 3
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 21
+
+--S 22 of 1393
+r0:=1/2*a*x^2+1/4*b*x^4
+--R
+--R
+--R 1 4 1 2
+--R (2) - b x + - a x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 22
+
+--S 23 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 4 1 2
+--R (3) - b x + - a x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 23
+
+--S 24 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 24
+
+--S 25 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 25
+
+)clear all
+
+--S 26 of 1393
+t0:=a+b*x^2
+--R
+--R
+--R 2
+--R (1) b x + a
+--R Type: Polynomial(Integer)
+--E 26
+
+--S 27 of 1393
+r0:=a*x+1/3*b*x^3
+--R
+--R
+--R 1 3
+--R (2) - b x + a x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 27
+
+--S 28 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3
+--R (3) - b x + a x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 28
+
+--S 29 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 29
+
+--S 30 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 30
+
+)clear all
+
+--S 31 of 1393
+t0:=(a+b*x^2)/x
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 31
+
+--S 32 of 1393
+r0:=1/2*b*x^2+a*log(x)
+--R
+--R
+--R 2
+--R 2a log(x) + b x
+--R (2) ----------------
+--R 2
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 2a log(x) + b x
+--R (3) ----------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 1393
+t0:=(a+b*x^2)/x^2
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 36
+
+--S 37 of 1393
+r0:=-a/x+b*x
+--R
+--R
+--R 2
+--R b x - a
+--R (2) --------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 37
+
+--S 38 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R b x - a
+--R (3) --------
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 1393
+t0:=(a+b*x^2)/x^3
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 41
+
+--S 42 of 1393
+r0:=-1/2*a/x^2+b*log(x)
+--R
+--R
+--R 2
+--R 2b x log(x) - a
+--R (2) ---------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 2b x log(x) - a
+--R (3) ---------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 1393
+t0:=(a+b*x^2)/x^4
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 46
+
+--S 47 of 1393
+r0:=-1/3*a/x^3-b/x
+--R
+--R
+--R 2 1
+--R - b x - - a
+--R 3
+--R (2) ------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 47
+
+--S 48 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 3b x - a
+--R (3) -----------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 1393
+t0:=(a+b*x^2)/x^5
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 1393
+r0:=-1/4*a/x^4-1/2*b/x^2
+--R
+--R
+--R 1 2 1
+--R - - b x - - a
+--R 2 4
+--R (2) --------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 52
+
+--S 53 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 2b x - a
+--R (3) -----------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 1393
+t0:=(a+b*x^2)/x^6
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 56
+
+--S 57 of 1393
+r0:=-1/5*a/x^5-1/3*b/x^3
+--R
+--R
+--R 1 2 1
+--R - - b x - - a
+--R 3 5
+--R (2) --------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 57
+
+--S 58 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 5b x - 3a
+--R (3) ------------
+--R 5
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 1393
+t0:=(a+b*x^2)/x^7
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 61
+
+--S 62 of 1393
+r0:=-1/6*a/x^6-1/4*b/x^4
+--R
+--R
+--R 1 2 1
+--R - - b x - - a
+--R 4 6
+--R (2) --------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 62
+
+--S 63 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 3b x - 2a
+--R (3) ------------
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 1393
+t0:=x^m*(a+b*x^2)^2
+--R
+--R
+--R 2 4 2 2 m
+--R (1) (b x + 2a b x + a )x
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 1393
+r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(3+m)/(3+m)+b^2*x^(5+m)/(5+m)
+--R
+--R
+--R (2)
+--R 2 2 2 2 m + 5 2 m + 3
+--R (b m + 4b m + 3b )x + (2a b m + 12a b m + 10a b)x
+--R +
+--R 2 2 2 2 m + 1
+--R (a m + 8a m + 15a )x
+--R /
+--R 3 2
+--R m + 9m + 23m + 15
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 5 2 3
+--R (b m + 4b m + 3b )x + (2a b m + 12a b m + 10a b)x
+--R +
+--R 2 2 2 2
+--R (a m + 8a m + 15a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 3 2
+--R m + 9m + 23m + 15
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 5 2 3
+--R (b m + 4b m + 3b )x + (2a b m + 12a b m + 10a b)x
+--R +
+--R 2 2 2 2
+--R (a m + 8a m + 15a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 2 2 2 m + 5 2 m + 3
+--R (- b m - 4b m - 3b )x + (- 2a b m - 12a b m - 10a b)x
+--R +
+--R 2 2 2 2 m + 1
+--R (- a m - 8a m - 15a )x
+--R /
+--R 3 2
+--R m + 9m + 23m + 15
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 1393
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 1393
+t0:=x^5*(a+b*x^2)^2
+--R
+--R
+--R 2 9 7 2 5
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 71
+
+--S 72 of 1393
+r0:=1/6*a^2*x^6+1/4*a*b*x^8+1/10*b^2*x^10
+--R
+--R
+--R 1 2 10 1 8 1 2 6
+--R (2) -- b x + - a b x + - a x
+--R 10 4 6
+--R Type: Polynomial(Fraction(Integer))
+--E 72
+
+--S 73 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 10 1 8 1 2 6
+--R (3) -- b x + - a b x + - a x
+--R 10 4 6
+--R Type: Polynomial(Fraction(Integer))
+--E 73
+
+--S 74 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 74
+
+--S 75 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 75
+
+)clear all
+
+--S 76 of 1393
+t0:=x^4*(a+b*x^2)^2
+--R
+--R
+--R 2 8 6 2 4
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 76
+
+--S 77 of 1393
+r0:=1/5*a^2*x^5+2/7*a*b*x^7+1/9*b^2*x^9
+--R
+--R
+--R 1 2 9 2 7 1 2 5
+--R (2) - b x + - a b x + - a x
+--R 9 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 77
+
+--S 78 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 9 2 7 1 2 5
+--R (3) - b x + - a b x + - a x
+--R 9 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 78
+
+--S 79 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 79
+
+--S 80 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 80
+
+)clear all
+
+--S 81 of 1393
+t0:=x^3*(a+b*x^2)^2
+--R
+--R
+--R 2 7 5 2 3
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 81
+
+--S 82 of 1393
+r0:=1/4*a^2*x^4+1/3*a*b*x^6+1/8*b^2*x^8
+--R
+--R
+--R 1 2 8 1 6 1 2 4
+--R (2) - b x + - a b x + - a x
+--R 8 3 4
+--R Type: Polynomial(Fraction(Integer))
+--E 82
+
+--S 83 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 8 1 6 1 2 4
+--R (3) - b x + - a b x + - a x
+--R 8 3 4
+--R Type: Polynomial(Fraction(Integer))
+--E 83
+
+--S 84 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 84
+
+--S 85 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 85
+
+)clear all
+
+--S 86 of 1393
+t0:=x^2*(a+b*x^2)^2
+--R
+--R
+--R 2 6 4 2 2
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 86
+
+--S 87 of 1393
+r0:=1/3*a^2*x^3+2/5*a*b*x^5+1/7*b^2*x^7
+--R
+--R
+--R 1 2 7 2 5 1 2 3
+--R (2) - b x + - a b x + - a x
+--R 7 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 87
+
+--S 88 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 7 2 5 1 2 3
+--R (3) - b x + - a b x + - a x
+--R 7 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 88
+
+--S 89 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 89
+
+--S 90 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 90
+
+)clear all
+
+--S 91 of 1393
+t0:=x*(a+b*x^2)^2
+--R
+--R
+--R 2 5 3 2
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 91
+
+--S 92 of 1393
+r0:=1/6*(a+b*x^2)^3/b
+--R
+--R
+--R 1 3 6 1 2 4 1 2 2 1 3
+--R - b x + - a b x + - a b x + - a
+--R 6 2 2 6
+--R (2) -----------------------------------
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 92
+
+--S 93 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 6 1 4 1 2 2
+--R (3) - b x + - a b x + - a x
+--R 6 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 93
+
+--S 94 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 3
+--R - a
+--R 6
+--R (4) - ----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 94
+
+--S 95 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 95
+
+)clear all
+
+--S 96 of 1393
+t0:=(a+b*x^2)^2
+--R
+--R
+--R 2 4 2 2
+--R (1) b x + 2a b x + a
+--R Type: Polynomial(Integer)
+--E 96
+
+--S 97 of 1393
+r0:=a^2*x+2/3*a*b*x^3+1/5*b^2*x^5
+--R
+--R
+--R 1 2 5 2 3 2
+--R (2) - b x + - a b x + a x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 97
+
+--S 98 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 5 2 3 2
+--R (3) - b x + - a b x + a x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 98
+
+--S 99 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 99
+
+--S 100 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 100
+
+)clear all
+
+--S 101 of 1393
+t0:=(a+b*x^2)^2/x
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 1393
+r0:=a*b*x^2+1/4*b^2*x^4+a^2*log(x)
+--R
+--R
+--R 2 2 4 2
+--R 4a log(x) + b x + 4a b x
+--R (2) --------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 4 2
+--R 4a log(x) + b x + 4a b x
+--R (3) --------------------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 1393
+t0:=(a+b*x^2)^2/x^2
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 106
+
+--S 107 of 1393
+r0:=-a^2/x+2*a*b*x+1/3*b^2*x^3
+--R
+--R
+--R 2 4 2 2
+--R b x + 6a b x - 3a
+--R (2) --------------------
+--R 3x
+--R Type: Fraction(Polynomial(Integer))
+--E 107
+
+--S 108 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R b x + 6a b x - 3a
+--R (3) --------------------
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 1393
+t0:=(a+b*x^2)^2/x^3
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 111
+
+--S 112 of 1393
+r0:=-1/2*a^2/x^2+1/2*b^2*x^2+2*a*b*log(x)
+--R
+--R
+--R 2 2 4 2
+--R 4a b x log(x) + b x - a
+--R (2) -------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 4 2
+--R 4a b x log(x) + b x - a
+--R (3) -------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 1393
+t0:=(a+b*x^2)^2/x^4
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 116
+
+--S 117 of 1393
+r0:=-1/3*a^2/x^3-2*a*b/x+b^2*x
+--R
+--R
+--R 2 4 2 1 2
+--R b x - 2a b x - - a
+--R 3
+--R (2) ---------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 117
+
+--S 118 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R 3b x - 6a b x - a
+--R (3) --------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 1393
+t0:=(a+b*x^2)^2/x^5
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 121
+
+--S 122 of 1393
+r0:=-1/4*a^2/x^4-a*b/x^2+b^2*log(x)
+--R
+--R
+--R 2 4 2 2
+--R 4b x log(x) - 4a b x - a
+--R (2) --------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R 4b x log(x) - 4a b x - a
+--R (3) --------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 1393
+t0:=(a+b*x^2)^2/x^6
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 126
+
+--S 127 of 1393
+r0:=-1/5*a^2/x^5-2/3*a*b/x^3-b^2/x
+--R
+--R
+--R 2 4 2 2 1 2
+--R - b x - - a b x - - a
+--R 3 5
+--R (2) ------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 127
+
+--S 128 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 15b x - 10a b x - 3a
+--R (3) -------------------------
+--R 5
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 1393
+t0:=(a+b*x^2)^2/x^7
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 131
+
+--S 132 of 1393
+r0:=-1/6*(a+b*x^2)^3/(a*x^6)
+--R
+--R
+--R 1 3 6 1 2 4 1 2 2 1 3
+--R - - b x - - a b x - - a b x - - a
+--R 6 2 2 6
+--R (2) -------------------------------------
+--R 6
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 132
+
+--S 133 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 3b x - 3a b x - a
+--R (3) ----------------------
+--R 6
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 1393
+m0:=a0-r0
+--R
+--R
+--R 3
+--R b
+--R (4) --
+--R 6a
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 1393
+t0:=(a+b*x^2)^2/x^8
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 136
+
+--S 137 of 1393
+r0:=-1/7*a^2/x^7-2/5*a*b/x^5-1/3*b^2/x^3
+--R
+--R
+--R 1 2 4 2 2 1 2
+--R - - b x - - a b x - - a
+--R 3 5 7
+--R (2) --------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 137
+
+--S 138 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 35b x - 42a b x - 15a
+--R (3) --------------------------
+--R 7
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 1393
+t0:=(a+b*x^2)^2/x^9
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 141
+
+--S 142 of 1393
+r0:=-1/8*a^2/x^8-1/3*a*b/x^6-1/4*b^2/x^4
+--R
+--R
+--R 1 2 4 1 2 1 2
+--R - - b x - - a b x - - a
+--R 4 3 8
+--R (2) --------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 142
+
+--S 143 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 6b x - 8a b x - 3a
+--R (3) -----------------------
+--R 8
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 1393
+t0:=(a+b*x^2)^2/x^10
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 1393
+r0:=-1/9*a^2/x^9-2/7*a*b/x^7-1/5*b^2/x^5
+--R
+--R
+--R 1 2 4 2 2 1 2
+--R - - b x - - a b x - - a
+--R 5 7 9
+--R (2) --------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 147
+
+--S 148 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 63b x - 90a b x - 35a
+--R (3) --------------------------
+--R 9
+--R 315x
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 1393
+t0:=x^m*(a+b*x^2)^3
+--R
+--R
+--R 3 6 2 4 2 2 3 m
+--R (1) (b x + 3a b x + 3a b x + a )x
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 1393
+r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(3+m)/(3+m)+3*a*b^2*x^(5+m)/(5+m)+_
+ b^3*x^(7+m)/(7+m)
+--R
+--R
+--R (2)
+--R 3 3 3 2 3 3 m + 7
+--R (b m + 9b m + 23b m + 15b )x
+--R +
+--R 2 3 2 2 2 2 m + 5
+--R (3a b m + 33a b m + 93a b m + 63a b )x
+--R +
+--R 2 3 2 2 2 2 m + 3
+--R (3a b m + 39a b m + 141a b m + 105a b)x
+--R +
+--R 3 3 3 2 3 3 m + 1
+--R (a m + 15a m + 71a m + 105a )x
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 3 2 3 3 7
+--R (b m + 9b m + 23b m + 15b )x
+--R +
+--R 2 3 2 2 2 2 5
+--R (3a b m + 33a b m + 93a b m + 63a b )x
+--R +
+--R 2 3 2 2 2 2 3
+--R (3a b m + 39a b m + 141a b m + 105a b)x
+--R +
+--R 3 3 3 2 3 3
+--R (a m + 15a m + 71a m + 105a )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 153
+
+--S 154 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 3 2 3 3 7
+--R (b m + 9b m + 23b m + 15b )x
+--R +
+--R 2 3 2 2 2 2 5
+--R (3a b m + 33a b m + 93a b m + 63a b )x
+--R +
+--R 2 3 2 2 2 2 3
+--R (3a b m + 39a b m + 141a b m + 105a b)x
+--R +
+--R 3 3 3 2 3 3
+--R (a m + 15a m + 71a m + 105a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 3 3 3 2 3 3 m + 7
+--R (- b m - 9b m - 23b m - 15b )x
+--R +
+--R 2 3 2 2 2 2 m + 5
+--R (- 3a b m - 33a b m - 93a b m - 63a b )x
+--R +
+--R 2 3 2 2 2 2 m + 3
+--R (- 3a b m - 39a b m - 141a b m - 105a b)x
+--R +
+--R 3 3 3 2 3 3 m + 1
+--R (- a m - 15a m - 71a m - 105a )x
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 1393
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 1393
+t0:=x^9*(a+b*x^2)^3
+--R
+--R
+--R 3 15 2 13 2 11 3 9
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 156
+
+--S 157 of 1393
+r0:=1/10*a^3*x^10+1/4*a^2*b*x^12+3/14*a*b^2*x^14+1/16*b^3*x^16
+--R
+--R
+--R 1 3 16 3 2 14 1 2 12 1 3 10
+--R (2) -- b x + -- a b x + - a b x + -- a x
+--R 16 14 4 10
+--R Type: Polynomial(Fraction(Integer))
+--E 157
+
+--S 158 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 16 3 2 14 1 2 12 1 3 10
+--R (3) -- b x + -- a b x + - a b x + -- a x
+--R 16 14 4 10
+--R Type: Polynomial(Fraction(Integer))
+--E 158
+
+--S 159 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 159
+
+--S 160 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 160
+
+)clear all
+
+--S 161 of 1393
+t0:=x^7*(a+b*x^2)^3
+--R
+--R
+--R 3 13 2 11 2 9 3 7
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 161
+
+--S 162 of 1393
+r0:=1/8*a^3*x^8+3/10*a^2*b*x^10+1/4*a*b^2*x^12+1/14*b^3*x^14
+--R
+--R
+--R 1 3 14 1 2 12 3 2 10 1 3 8
+--R (2) -- b x + - a b x + -- a b x + - a x
+--R 14 4 10 8
+--R Type: Polynomial(Fraction(Integer))
+--E 162
+
+--S 163 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 14 1 2 12 3 2 10 1 3 8
+--R (3) -- b x + - a b x + -- a b x + - a x
+--R 14 4 10 8
+--R Type: Polynomial(Fraction(Integer))
+--E 163
+
+--S 164 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 164
+
+--S 165 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 165
+
+)clear all
+
+--S 166 of 1393
+t0:=x^5*(a+b*x^2)^3
+--R
+--R
+--R 3 11 2 9 2 7 3 5
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 166
+
+--S 167 of 1393
+r0:=1/6*a^3*x^6+3/8*a^2*b*x^8+3/10*a*b^2*x^10+1/12*b^3*x^12
+--R
+--R
+--R 1 3 12 3 2 10 3 2 8 1 3 6
+--R (2) -- b x + -- a b x + - a b x + - a x
+--R 12 10 8 6
+--R Type: Polynomial(Fraction(Integer))
+--E 167
+
+--S 168 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 12 3 2 10 3 2 8 1 3 6
+--R (3) -- b x + -- a b x + - a b x + - a x
+--R 12 10 8 6
+--R Type: Polynomial(Fraction(Integer))
+--E 168
+
+--S 169 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 169
+
+--S 170 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 170
+
+)clear all
+
+--S 171 of 1393
+t0:=x^3*(a+b*x^2)^3
+--R
+--R
+--R 3 9 2 7 2 5 3 3
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 171
+
+--S 172 of 1393
+r0:=-1/8*a*(a+b*x^2)^4/b^2+1/10*(a+b*x^2)^5/b^2
+--R
+--R
+--R 1 5 10 3 4 8 1 2 3 6 1 3 2 4 1 5
+--R -- b x + - a b x + - a b x + - a b x - -- a
+--R 10 8 2 4 40
+--R (2) -------------------------------------------------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 172
+
+--S 173 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 10 3 2 8 1 2 6 1 3 4
+--R (3) -- b x + - a b x + - a b x + - a x
+--R 10 8 2 4
+--R Type: Polynomial(Fraction(Integer))
+--E 173
+
+--S 174 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 5
+--R -- a
+--R 40
+--R (4) -----
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 174
+
+--S 175 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 175
+
+)clear all
+
+--S 176 of 1393
+t0:=x*(a+b*x^2)^3
+--R
+--R
+--R 3 7 2 5 2 3 3
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 176
+
+--S 177 of 1393
+r0:=1/8*(a+b*x^2)^4/b
+--R
+--R
+--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4
+--R - b x + - a b x + - a b x + - a b x + - a
+--R 8 2 4 2 8
+--R (2) ----------------------------------------------
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 177
+
+--S 178 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 8 1 2 6 3 2 4 1 3 2
+--R (3) - b x + - a b x + - a b x + - a x
+--R 8 2 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 178
+
+--S 179 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 4
+--R - a
+--R 8
+--R (4) - ----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 179
+
+--S 180 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 180
+
+)clear all
+
+--S 181 of 1393
+t0:=(a+b*x^2)^3/x
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 1393
+r0:=3/2*a^2*b*x^2+3/4*a*b^2*x^4+1/6*b^3*x^6+a^3*log(x)
+--R
+--R
+--R 3 3 6 2 4 2 2
+--R 12a log(x) + 2b x + 9a b x + 18a b x
+--R (2) ---------------------------------------
+--R 12
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 6 2 4 2 2
+--R 12a log(x) + 2b x + 9a b x + 18a b x
+--R (3) ---------------------------------------
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 1393
+t0:=(a+b*x^2)^3/x^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
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 186
+
+--S 187 of 1393
+r0:=-1/2*a^3/x^2+3/2*a*b^2*x^2+1/4*b^3*x^4+3*a^2*b*log(x)
+--R
+--R
+--R 2 2 3 6 2 4 3
+--R 12a b x log(x) + b x + 6a b x - 2a
+--R (2) -------------------------------------
+--R 2
+--R 4x
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 3 6 2 4 3
+--R 12a b x log(x) + b x + 6a b x - 2a
+--R (3) -------------------------------------
+--R 2
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 1393
+t0:=(a+b*x^2)^3/x^5
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 1393
+r0:=-1/4*a^3/x^4-3/2*a^2*b/x^2+1/2*b^3*x^2+3*a*b^2*log(x)
+--R
+--R
+--R 2 4 3 6 2 2 3
+--R 12a b x log(x) + 2b x - 6a b x - a
+--R (2) -------------------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 3 6 2 2 3
+--R 12a b x log(x) + 2b x - 6a b x - a
+--R (3) -------------------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 1393
+t0:=(a+b*x^2)^3/x^7
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 196
+
+--S 197 of 1393
+r0:=-1/6*a^3/x^6-3/4*a^2*b/x^4-3/2*a*b^2/x^2+b^3*log(x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 12b x log(x) - 18a b x - 9a b x - 2a
+--R (2) ---------------------------------------
+--R 6
+--R 12x
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 12b x log(x) - 18a b x - 9a b x - 2a
+--R (3) ---------------------------------------
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 1393
+t0:=(a+b*x^2)^3/x^9
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 201
+
+--S 202 of 1393
+r0:=-1/8*(a+b*x^2)^4/(a*x^8)
+--R
+--R
+--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4
+--R - - b x - - a b x - - a b x - - a b x - - a
+--R 8 2 4 2 8
+--R (2) ------------------------------------------------
+--R 8
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 202
+
+--S 203 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 4b x - 6a b x - 4a b x - a
+--R (3) --------------------------------
+--R 8
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 1393
+m0:=a0-r0
+--R
+--R
+--R 4
+--R b
+--R (4) --
+--R 8a
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 1393
+t0:=(a+b*x^2)^3/x^11
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 206
+
+--S 207 of 1393
+r0:=-1/10*a^3/x^10-3/8*a^2*b/x^8-1/2*a*b^2/x^6-1/4*b^3/x^4
+--R
+--R
+--R 1 3 6 1 2 4 3 2 2 1 3
+--R - - b x - - a b x - - a b x - -- a
+--R 4 2 8 10
+--R (2) --------------------------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 207
+
+--S 208 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 10b x - 20a b x - 15a b x - 4a
+--R (3) ------------------------------------
+--R 10
+--R 40x
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 1393
+t0:=(a+b*x^2)^3/x^13
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 211
+
+--S 212 of 1393
+r0:=-1/12*a^3/x^12-3/10*a^2*b/x^10-3/8*a*b^2/x^8-1/6*b^3/x^6
+--R
+--R
+--R 1 3 6 3 2 4 3 2 2 1 3
+--R - - b x - - a b x - -- a b x - -- a
+--R 6 8 10 12
+--R (2) ---------------------------------------
+--R 12
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 212
+
+--S 213 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 20b x - 45a b x - 36a b x - 10a
+--R (3) -------------------------------------
+--R 12
+--R 120x
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 1393
+t0:=(a+b*x^2)^3/x^15
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 216
+
+--S 217 of 1393
+r0:=-1/14*a^3/x^14-1/4*a^2*b/x^12-3/10*a*b^2/x^10-1/8*b^3/x^8
+--R
+--R
+--R 1 3 6 3 2 4 1 2 2 1 3
+--R - - b x - -- a b x - - a b x - -- a
+--R 8 10 4 14
+--R (2) ---------------------------------------
+--R 14
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 217
+
+--S 218 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 35b x - 84a b x - 70a b x - 20a
+--R (3) -------------------------------------
+--R 14
+--R 280x
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 1393
+t0:=x^6*(a+b*x^2)^3
+--R
+--R
+--R 3 12 2 10 2 8 3 6
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 221
+
+--S 222 of 1393
+r0:=1/7*a^3*x^7+1/3*a^2*b*x^9+3/11*a*b^2*x^11+1/13*b^3*x^13
+--R
+--R
+--R 1 3 13 3 2 11 1 2 9 1 3 7
+--R (2) -- b x + -- a b x + - a b x + - a x
+--R 13 11 3 7
+--R Type: Polynomial(Fraction(Integer))
+--E 222
+
+--S 223 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 13 3 2 11 1 2 9 1 3 7
+--R (3) -- b x + -- a b x + - a b x + - a x
+--R 13 11 3 7
+--R Type: Polynomial(Fraction(Integer))
+--E 223
+
+--S 224 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 224
+
+--S 225 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 225
+
+)clear all
+
+--S 226 of 1393
+t0:=x^4*(a+b*x^2)^3
+--R
+--R
+--R 3 10 2 8 2 6 3 4
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 226
+
+--S 227 of 1393
+r0:=1/5*a^3*x^5+3/7*a^2*b*x^7+1/3*a*b^2*x^9+1/11*b^3*x^11
+--R
+--R
+--R 1 3 11 1 2 9 3 2 7 1 3 5
+--R (2) -- b x + - a b x + - a b x + - a x
+--R 11 3 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 227
+
+--S 228 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 11 1 2 9 3 2 7 1 3 5
+--R (3) -- b x + - a b x + - a b x + - a x
+--R 11 3 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 228
+
+--S 229 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 229
+
+--S 230 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 230
+
+)clear all
+
+--S 231 of 1393
+t0:=x^2*(a+b*x^2)^3
+--R
+--R
+--R 3 8 2 6 2 4 3 2
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 231
+
+--S 232 of 1393
+r0:=1/3*a^3*x^3+3/5*a^2*b*x^5+3/7*a*b^2*x^7+1/9*b^3*x^9
+--R
+--R
+--R 1 3 9 3 2 7 3 2 5 1 3 3
+--R (2) - b x + - a b x + - a b x + - a x
+--R 9 7 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 232
+
+--S 233 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 9 3 2 7 3 2 5 1 3 3
+--R (3) - b x + - a b x + - a b x + - a x
+--R 9 7 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 233
+
+--S 234 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 234
+
+--S 235 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 235
+
+)clear all
+
+--S 236 of 1393
+t0:=(a+b*x^2)^3
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R (1) b x + 3a b x + 3a b x + a
+--R Type: Polynomial(Integer)
+--E 236
+
+--S 237 of 1393
+r0:=a^3*x+a^2*b*x^3+3/5*a*b^2*x^5+1/7*b^3*x^7
+--R
+--R
+--R 1 3 7 3 2 5 2 3 3
+--R (2) - b x + - a b x + a b x + a x
+--R 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 237
+
+--S 238 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 7 3 2 5 2 3 3
+--R (3) - b x + - a b x + a b x + a x
+--R 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 238
+
+--S 239 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 239
+
+--S 240 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 240
+
+)clear all
+
+--S 241 of 1393
+t0:=(a+b*x^2)^3/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 x
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 1393
+r0:=-a^3/x+3*a^2*b*x+a*b^2*x^3+1/5*b^3*x^5
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 5a b x + 15a b x - 5a
+--R (2) -------------------------------
+--R 5x
+--R Type: Fraction(Polynomial(Integer))
+--E 242
+
+--S 243 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 5a b x + 15a b x - 5a
+--R (3) -------------------------------
+--R 5x
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 1393
+t0:=(a+b*x^2)^3/x^4
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 1393
+r0:=-1/3*a^3/x^3-3*a^2*b/x+3*a*b^2*x+1/3*b^3*x^3
+--R
+--R
+--R 1 3 6 2 4 2 2 1 3
+--R - b x + 3a b x - 3a b x - - a
+--R 3 3
+--R (2) ---------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 247
+
+--S 248 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 9a b x - 9a b x - a
+--R (3) -----------------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 1393
+t0:=(a+b*x^2)^3/x^6
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 1393
+r0:=-1/5*a^3/x^5-a^2*b/x^3-3*a*b^2/x+b^3*x
+--R
+--R
+--R 3 6 2 4 2 2 1 3
+--R b x - 3a b x - a b x - - a
+--R 5
+--R (2) ------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 252
+
+--S 253 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 5b x - 15a b x - 5a b x - a
+--R (3) -------------------------------
+--R 5
+--R 5x
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 1393
+t0:=(a+b*x^2)^3/x^8
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 1393
+r0:=-1/7*a^3/x^7-3/5*a^2*b/x^5-a*b^2/x^3-b^3/x
+--R
+--R
+--R 3 6 2 4 3 2 2 1 3
+--R - b x - a b x - - a b x - - a
+--R 5 7
+--R (2) ---------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 257
+
+--S 258 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 35b x - 35a b x - 21a b x - 5a
+--R (3) ------------------------------------
+--R 7
+--R 35x
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 1393
+t0:=(a+b*x^2)^3/x^10
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 1393
+r0:=-1/9*a^3/x^9-3/7*a^2*b/x^7-3/5*a*b^2/x^5-1/3*b^3/x^3
+--R
+--R
+--R 1 3 6 3 2 4 3 2 2 1 3
+--R - - b x - - a b x - - a b x - - a
+--R 3 5 7 9
+--R (2) -------------------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 262
+
+--S 263 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 105b x - 189a b x - 135a b x - 35a
+--R (3) ----------------------------------------
+--R 9
+--R 315x
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 1393
+t0:=(a+b*x^2)^3/x^12
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 12
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 266
+
+--S 267 of 1393
+r0:=-1/11*a^3/x^11-1/3*a^2*b/x^9-3/7*a*b^2/x^7-1/5*b^3/x^5
+--R
+--R
+--R 1 3 6 3 2 4 1 2 2 1 3
+--R - - b x - - a b x - - a b x - -- a
+--R 5 7 3 11
+--R (2) --------------------------------------
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 267
+
+--S 268 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 231b x - 495a b x - 385a b x - 105a
+--R (3) -----------------------------------------
+--R 11
+--R 1155x
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 1393
+t0:=x^m*(a+b*x^2)^5
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 m
+--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )x
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 1393
+r0:=a^5*x^(1+m)/(1+m)+5*a^4*b*x^(3+m)/(3+m)+10*a^3*b^2*x^(5+m)/(5+m)+_
+ 10*a^2*b^3*x^(7+m)/(7+m)+5*a*b^4*x^(9+m)/(9+m)+b^5*x^(11+m)/(11+m)
+--R
+--R
+--R (2)
+--R 5 5 5 4 5 3 5 2 5 5 m + 11
+--R (b m + 25b m + 230b m + 950b m + 1689b m + 945b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4 4
+--R (5a b m + 135a b m + 1310a b m + 5610a b m + 10205a b m + 5775a b )
+--R *
+--R m + 9
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R 10a b m + 290a b m + 3020a b m + 13660a b m + 25770a b m
+--R +
+--R 2 3
+--R 14850a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R 10a b m + 310a b m + 3500a b m + 17300a b m + 34890a b m
+--R +
+--R 3 2
+--R 20790a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 165a b m + 2030a b m + 11310a b m + 26765a b m
+--R +
+--R 4
+--R 17325a b
+--R *
+--R m + 3
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5 m + 1
+--R (a m + 35a m + 470a m + 3010a m + 9129a m + 10395a )x
+--R /
+--R 6 5 4 3 2
+--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 5 4 5 3 5 2 5 5 11
+--R (b m + 25b m + 230b m + 950b m + 1689b m + 945b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 135a b m + 1310a b m + 5610a b m + 10205a b m
+--R +
+--R 4
+--R 5775a b
+--R *
+--R 9
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R 10a b m + 290a b m + 3020a b m + 13660a b m + 25770a b m
+--R +
+--R 2 3
+--R 14850a b
+--R *
+--R 7
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R 10a b m + 310a b m + 3500a b m + 17300a b m + 34890a b m
+--R +
+--R 3 2
+--R 20790a b
+--R *
+--R 5
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 165a b m + 2030a b m + 11310a b m + 26765a b m
+--R +
+--R 4
+--R 17325a b
+--R *
+--R 3
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5
+--R (a m + 35a m + 470a m + 3010a m + 9129a m + 10395a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 6 5 4 3 2
+--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 5 5 4 5 3 5 2 5 5 11
+--R (b m + 25b m + 230b m + 950b m + 1689b m + 945b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 135a b m + 1310a b m + 5610a b m + 10205a b m
+--R +
+--R 4
+--R 5775a b
+--R *
+--R 9
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R 10a b m + 290a b m + 3020a b m + 13660a b m + 25770a b m
+--R +
+--R 2 3
+--R 14850a b
+--R *
+--R 7
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R 10a b m + 310a b m + 3500a b m + 17300a b m + 34890a b m
+--R +
+--R 3 2
+--R 20790a b
+--R *
+--R 5
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 165a b m + 2030a b m + 11310a b m + 26765a b m
+--R +
+--R 4
+--R 17325a b
+--R *
+--R 3
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5
+--R (a m + 35a m + 470a m + 3010a m + 9129a m + 10395a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 5 5 5 4 5 3 5 2 5 5 m + 11
+--R (- b m - 25b m - 230b m - 950b m - 1689b m - 945b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R - 5a b m - 135a b m - 1310a b m - 5610a b m - 10205a b m
+--R +
+--R 4
+--R - 5775a b
+--R *
+--R m + 9
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R - 10a b m - 290a b m - 3020a b m - 13660a b m - 25770a b m
+--R +
+--R 2 3
+--R - 14850a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R - 10a b m - 310a b m - 3500a b m - 17300a b m - 34890a b m
+--R +
+--R 3 2
+--R - 20790a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R - 5a b m - 165a b m - 2030a b m - 11310a b m - 26765a b m
+--R +
+--R 4
+--R - 17325a b
+--R *
+--R m + 3
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5 m + 1
+--R (- a m - 35a m - 470a m - 3010a m - 9129a m - 10395a )x
+--R /
+--R 6 5 4 3 2
+--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 1393
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 1393
+t0:=x^11*(a+b*x^2)^5
+--R
+--R
+--R 5 21 4 19 2 3 17 3 2 15 4 13 5 11
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 276
+
+--S 277 of 1393
+r0:=1/12*a^5*x^12+5/14*a^4*b*x^14+5/8*a^3*b^2*x^16+5/9*a^2*b^3*x^18+_
+ 1/4*a*b^4*x^20+1/22*b^5*x^22
+--R
+--R
+--R 1 5 22 1 4 20 5 2 3 18 5 3 2 16 5 4 14 1 5 12
+--R (2) -- b x + - a b x + - a b x + - a b x + -- a b x + -- a x
+--R 22 4 9 8 14 12
+--R Type: Polynomial(Fraction(Integer))
+--E 277
+
+--S 278 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 22 1 4 20 5 2 3 18 5 3 2 16 5 4 14 1 5 12
+--R (3) -- b x + - a b x + - a b x + - a b x + -- a b x + -- a x
+--R 22 4 9 8 14 12
+--R Type: Polynomial(Fraction(Integer))
+--E 278
+
+--S 279 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 279
+
+--S 280 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 280
+
+)clear all
+
+--S 281 of 1393
+t0:=x^9*(a+b*x^2)^5
+--R
+--R
+--R 5 19 4 17 2 3 15 3 2 13 4 11 5 9
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 281
+
+--S 282 of 1393
+r0:=1/10*a^5*x^10+5/12*a^4*b*x^12+5/7*a^3*b^2*x^14+5/8*a^2*b^3*x^16+_
+ 5/18*a*b^4*x^18+1/20*b^5*x^20
+--R
+--R
+--R 1 5 20 5 4 18 5 2 3 16 5 3 2 14 5 4 12 1 5 10
+--R (2) -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a x
+--R 20 18 8 7 12 10
+--R Type: Polynomial(Fraction(Integer))
+--E 282
+
+--S 283 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 20 5 4 18 5 2 3 16 5 3 2 14 5 4 12 1 5 10
+--R (3) -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a x
+--R 20 18 8 7 12 10
+--R Type: Polynomial(Fraction(Integer))
+--E 283
+
+--S 284 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 284
+
+--S 285 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 285
+
+)clear all
+
+--S 286 of 1393
+t0:=x^7*(a+b*x^2)^5
+--R
+--R
+--R 5 17 4 15 2 3 13 3 2 11 4 9 5 7
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 286
+
+--S 287 of 1393
+r0:=1/8*a^5*x^8+1/2*a^4*b*x^10+5/6*a^3*b^2*x^12+5/7*a^2*b^3*x^14+_
+ 5/16*a*b^4*x^16+1/18*b^5*x^18
+--R
+--R
+--R 1 5 18 5 4 16 5 2 3 14 5 3 2 12 1 4 10 1 5 8
+--R (2) -- b x + -- a b x + - a b x + - a b x + - a b x + - a x
+--R 18 16 7 6 2 8
+--R Type: Polynomial(Fraction(Integer))
+--E 287
+
+--S 288 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 18 5 4 16 5 2 3 14 5 3 2 12 1 4 10 1 5 8
+--R (3) -- b x + -- a b x + - a b x + - a b x + - a b x + - a x
+--R 18 16 7 6 2 8
+--R Type: Polynomial(Fraction(Integer))
+--E 288
+
+--S 289 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 289
+
+--S 290 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 290
+
+)clear all
+
+--S 291 of 1393
+t0:=x^5*(a+b*x^2)^5
+--R
+--R
+--R 5 15 4 13 2 3 11 3 2 9 4 7 5 5
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 291
+
+--S 292 of 1393
+r0:=1/12*a^2*(a+b*x^2)^6/b^3-1/7*a*(a+b*x^2)^7/b^3+1/16*(a+b*x^2)^8/b^3
+--R
+--R
+--R (2)
+--R 1 8 16 5 7 14 5 2 6 12 3 5 10 5 4 4 8 1 5 3 6 1 8
+--R -- b x + -- a b x + - a b x + a b x + - a b x + - a b x + --- a
+--R 16 14 6 8 6 336
+--R --------------------------------------------------------------------------
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 292
+
+--S 293 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 16 5 4 14 5 2 3 12 3 2 10 5 4 8 1 5 6
+--R (3) -- b x + -- a b x + - a b x + a b x + - a b x + - a x
+--R 16 14 6 8 6
+--R Type: Polynomial(Fraction(Integer))
+--E 293
+
+--S 294 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 8
+--R --- a
+--R 336
+--R (4) - ------
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 294
+
+--S 295 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 295
+
+)clear all
+
+--S 296 of 1393
+t0:=x^3*(a+b*x^2)^5
+--R
+--R
+--R 5 13 4 11 2 3 9 3 2 7 4 5 5 3
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 296
+
+--S 297 of 1393
+r0:=-1/12*a*(a+b*x^2)^6/b^2+1/14*(a+b*x^2)^7/b^2
+--R
+--R
+--R (2)
+--R 1 7 14 5 6 12 2 5 10 5 3 4 8 5 4 3 6 1 5 2 4 1 7
+--R -- b x + -- a b x + a b x + - a b x + - a b x + - a b x - -- a
+--R 14 12 4 6 4 84
+--R ------------------------------------------------------------------------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 297
+
+--S 298 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 14 5 4 12 2 3 10 5 3 2 8 5 4 6 1 5 4
+--R (3) -- b x + -- a b x + a b x + - a b x + - a b x + - a x
+--R 14 12 4 6 4
+--R Type: Polynomial(Fraction(Integer))
+--E 298
+
+--S 299 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 7
+--R -- a
+--R 84
+--R (4) -----
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 299
+
+--S 300 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 300
+
+)clear all
+
+--S 301 of 1393
+t0:=x*(a+b*x^2)^5
+--R
+--R
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 301
+
+--S 302 of 1393
+r0:=1/12*(a+b*x^2)^6/b
+--R
+--R
+--R (2)
+--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6
+--R -- b x + - a b x + - a b x + - a b x + - a b x + - a b x + -- a
+--R 12 2 4 3 4 2 12
+--R ------------------------------------------------------------------------
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 302
+
+--S 303 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 12 1 4 10 5 2 3 8 5 3 2 6 5 4 4 1 5 2
+--R (3) -- b x + - a b x + - a b x + - a b x + - a b x + - a x
+--R 12 2 4 3 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 303
+
+--S 304 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 6
+--R -- a
+--R 12
+--R (4) - -----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 304
+
+--S 305 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 305
+
+)clear all
+
+--S 306 of 1393
+t0:=(a+b*x^2)^5/x
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 306
+
+--S 307 of 1393
+r0:=5/2*a^4*b*x^2+5/2*a^3*b^2*x^4+5/3*a^2*b^3*x^6+5/8*a*b^4*x^8+_
+ 1/10*b^5*x^10+a^5*log(x)
+--R
+--R
+--R 5 5 10 4 8 2 3 6 3 2 4 4 2
+--R 120a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x
+--R (2) --------------------------------------------------------------------
+--R 120
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5 10 4 8 2 3 6 3 2 4 4 2
+--R 120a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x
+--R (3) --------------------------------------------------------------------
+--R 120
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 1393
+t0:=(a+b*x^2)^5/x^3
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 311
+
+--S 312 of 1393
+r0:=-1/2*a^5/x^2+5*a^3*b^2*x^2+5/2*a^2*b^3*x^4+5/6*a*b^4*x^6+_
+ 1/8*b^5*x^8+5*a^4*b*log(x)
+--R
+--R
+--R 4 2 5 10 4 8 2 3 6 3 2 4 5
+--R 120a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a
+--R (2) -----------------------------------------------------------------
+--R 2
+--R 24x
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2 5 10 4 8 2 3 6 3 2 4 5
+--R 120a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a
+--R (3) -----------------------------------------------------------------
+--R 2
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 1393
+t0:=(a+b*x^2)^5/x^5
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 1393
+r0:=-1/4*a^5/x^4-5/2*a^4*b/x^2+5*a^2*b^3*x^2+5/4*a*b^4*x^4+_
+ 1/6*b^5*x^6+10*a^3*b^2*log(x)
+--R
+--R
+--R 3 2 4 5 10 4 8 2 3 6 4 2 5
+--R 120a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a
+--R (2) ---------------------------------------------------------------
+--R 4
+--R 12x
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 4 5 10 4 8 2 3 6 4 2 5
+--R 120a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a
+--R (3) ---------------------------------------------------------------
+--R 4
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 1393
+t0:=(a+b*x^2)^5/x^7
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 321
+
+--S 322 of 1393
+r0:=-1/6*a^5/x^6-5/4*a^4*b/x^4-5*a^3*b^2/x^2+5/2*a*b^4*x^2+_
+ 1/4*b^5*x^4+10*a^2*b^3*log(x)
+--R
+--R
+--R 2 3 6 5 10 4 8 3 2 4 4 2 5
+--R 120a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a
+--R (2) ---------------------------------------------------------------
+--R 6
+--R 12x
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 6 5 10 4 8 3 2 4 4 2 5
+--R 120a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a
+--R (3) ---------------------------------------------------------------
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 1393
+t0:=(a+b*x^2)^5/x^9
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 326
+
+--S 327 of 1393
+r0:=-1/8*a^5/x^8-5/6*a^4*b/x^6-5/2*a^3*b^2/x^4-5*a^2*b^3/x^2+_
+ 1/2*b^5*x^2+5*a*b^4*log(x)
+--R
+--R
+--R 4 8 5 10 2 3 6 3 2 4 4 2 5
+--R 120a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a
+--R (2) -----------------------------------------------------------------
+--R 8
+--R 24x
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 8 5 10 2 3 6 3 2 4 4 2 5
+--R 120a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a
+--R (3) -----------------------------------------------------------------
+--R 8
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 1393
+t0:=(a+b*x^2)^5/x^11
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 331
+
+--S 332 of 1393
+r0:=-1/10*a^5/x^10-5/8*a^4*b/x^8-5/3*a^3*b^2/x^6-5/2*a^2*b^3/x^4-_
+ 5/2*a*b^4/x^2+b^5*log(x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 120b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a
+--R (2) --------------------------------------------------------------------
+--R 10
+--R 120x
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 120b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a
+--R (3) --------------------------------------------------------------------
+--R 10
+--R 120x
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 1393
+t0:=(a+b*x^2)^5/x^13
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 336
+
+--S 337 of 1393
+r0:=-1/12*(a+b*x^2)^6/(a*x^12)
+--R
+--R
+--R (2)
+--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6
+--R - -- b x - - a b x - - a b x - - a b x - - a b x - - a b x - -- a
+--R 12 2 4 3 4 2 12
+--R --------------------------------------------------------------------------
+--R 12
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 337
+
+--S 338 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a
+--R (3) --------------------------------------------------------
+--R 12
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 1393
+m0:=a0-r0
+--R
+--R
+--R 6
+--R b
+--R (4) ---
+--R 12a
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 1393
+t0:=(a+b*x^2)^5/x^15
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 1393
+r0:=-1/14*(a+b*x^2)^6/(a*x^14)+1/84*b*(a+b*x^2)^6/(a^2*x^12)
+--R
+--R
+--R (2)
+--R 1 7 14 1 2 5 10 5 3 4 8 5 4 3 6 5 2 4 5 6 2 1 7
+--R -- b x - - a b x - - a b x - - a b x - a b x - -- a b x - -- a
+--R 84 4 6 4 12 14
+--R -----------------------------------------------------------------------
+--R 2 14
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 342
+
+--S 343 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 21b x - 70a b x - 105a b x - 84a b x - 35a b x - 6a
+--R (3) ------------------------------------------------------------
+--R 14
+--R 84x
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 1393
+m0:=a0-r0
+--R
+--R
+--R 7
+--R b
+--R (4) - ----
+--R 2
+--R 84a
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 1393
+t0:=(a+b*x^2)^5/x^17
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 17
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 1393
+r0:=-1/16*a^5/x^16-5/14*a^4*b/x^14-5/6*a^3*b^2/x^12-a^2*b^3/x^10-_
+ 5/8*a*b^4/x^8-1/6*b^5/x^6
+--R
+--R
+--R 1 5 10 5 4 8 2 3 6 5 3 2 4 5 4 2 1 5
+--R - - b x - - a b x - a b x - - a b x - -- a b x - -- a
+--R 6 8 6 14 16
+--R (2) ------------------------------------------------------------
+--R 16
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 347
+
+--S 348 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 56b x - 210a b x - 336a b x - 280a b x - 120a b x - 21a
+--R (3) ----------------------------------------------------------------
+--R 16
+--R 336x
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 1393
+t0:=(a+b*x^2)^5/x^19
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 351
+
+--S 352 of 1393
+r0:=-1/18*a^5/x^18-5/16*a^4*b/x^16-5/7*a^3*b^2/x^14-5/6*a^2*b^3/x^12-_
+ 1/2*a*b^4/x^10-1/8*b^5/x^8
+--R
+--R
+--R 1 5 10 1 4 8 5 2 3 6 5 3 2 4 5 4 2 1 5
+--R - - b x - - a b x - - a b x - - a b x - -- a b x - -- a
+--R 8 2 6 7 16 18
+--R (2) --------------------------------------------------------------
+--R 18
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 352
+
+--S 353 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 126b x - 504a b x - 840a b x - 720a b x - 315a b x - 56a
+--R (3) -----------------------------------------------------------------
+--R 18
+--R 1008x
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 1393
+t0:=(a+b*x^2)^5/x^21
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 21
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 356
+
+--S 357 of 1393
+r0:=-1/20*a^5/x^20-5/18*a^4*b/x^18-5/8*a^3*b^2/x^16-5/7*a^2*b^3/x^14-_
+ 5/12*a*b^4/x^12-1/10*b^5/x^10
+--R
+--R
+--R 1 5 10 5 4 8 5 2 3 6 5 3 2 4 5 4 2 1 5
+--R - -- b x - -- a b x - - a b x - - a b x - -- a b x - -- a
+--R 10 12 7 8 18 20
+--R (2) ----------------------------------------------------------------
+--R 20
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 357
+
+--S 358 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 252b x - 1050a b x - 1800a b x - 1575a b x - 700a b x - 126a
+--R (3) ---------------------------------------------------------------------
+--R 20
+--R 2520x
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 1393
+t0:=x^8*(a+b*x^2)^5
+--R
+--R
+--R 5 18 4 16 2 3 14 3 2 12 4 10 5 8
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 361
+
+--S 362 of 1393
+r0:=1/9*a^5*x^9+5/11*a^4*b*x^11+10/13*a^3*b^2*x^13+2/3*a^2*b^3*x^15+_
+ 5/17*a*b^4*x^17+1/19*b^5*x^19
+--R
+--R
+--R 1 5 19 5 4 17 2 2 3 15 10 3 2 13 5 4 11 1 5 9
+--R (2) -- b x + -- a b x + - a b x + -- a b x + -- a b x + - a x
+--R 19 17 3 13 11 9
+--R Type: Polynomial(Fraction(Integer))
+--E 362
+
+--S 363 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 19 5 4 17 2 2 3 15 10 3 2 13 5 4 11 1 5 9
+--R (3) -- b x + -- a b x + - a b x + -- a b x + -- a b x + - a x
+--R 19 17 3 13 11 9
+--R Type: Polynomial(Fraction(Integer))
+--E 363
+
+--S 364 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 364
+
+--S 365 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 365
+
+)clear all
+
+--S 366 of 1393
+t0:=x^6*(a+b*x^2)^5
+--R
+--R
+--R 5 16 4 14 2 3 12 3 2 10 4 8 5 6
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 366
+
+--S 367 of 1393
+r0:=1/7*a^5*x^7+5/9*a^4*b*x^9+10/11*a^3*b^2*x^11+10/13*a^2*b^3*x^13+_
+ 1/3*a*b^4*x^15+1/17*b^5*x^17
+--R
+--R
+--R 1 5 17 1 4 15 10 2 3 13 10 3 2 11 5 4 9 1 5 7
+--R (2) -- b x + - a b x + -- a b x + -- a b x + - a b x + - a x
+--R 17 3 13 11 9 7
+--R Type: Polynomial(Fraction(Integer))
+--E 367
+
+--S 368 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 17 1 4 15 10 2 3 13 10 3 2 11 5 4 9 1 5 7
+--R (3) -- b x + - a b x + -- a b x + -- a b x + - a b x + - a x
+--R 17 3 13 11 9 7
+--R Type: Polynomial(Fraction(Integer))
+--E 368
+
+--S 369 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 369
+
+--S 370 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 370
+
+)clear all
+
+--S 371 of 1393
+t0:=x^4*(a+b*x^2)^5
+--R
+--R
+--R 5 14 4 12 2 3 10 3 2 8 4 6 5 4
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 371
+
+--S 372 of 1393
+r0:=1/5*a^5*x^5+5/7*a^4*b*x^7+10/9*a^3*b^2*x^9+10/11*a^2*b^3*x^11+_
+ 5/13*a*b^4*x^13+1/15*b^5*x^15
+--R
+--R
+--R 1 5 15 5 4 13 10 2 3 11 10 3 2 9 5 4 7 1 5 5
+--R (2) -- b x + -- a b x + -- a b x + -- a b x + - a b x + - a x
+--R 15 13 11 9 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 372
+
+--S 373 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 15 5 4 13 10 2 3 11 10 3 2 9 5 4 7 1 5 5
+--R (3) -- b x + -- a b x + -- a b x + -- a b x + - a b x + - a x
+--R 15 13 11 9 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 373
+
+--S 374 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 374
+
+--S 375 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 375
+
+)clear all
+
+--S 376 of 1393
+t0:=x^2*(a+b*x^2)^5
+--R
+--R
+--R 5 12 4 10 2 3 8 3 2 6 4 4 5 2
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 376
+
+--S 377 of 1393
+r0:=1/3*a^5*x^3+a^4*b*x^5+10/7*a^3*b^2*x^7+10/9*a^2*b^3*x^9+_
+ 5/11*a*b^4*x^11+1/13*b^5*x^13
+--R
+--R
+--R 1 5 13 5 4 11 10 2 3 9 10 3 2 7 4 5 1 5 3
+--R (2) -- b x + -- a b x + -- a b x + -- a b x + a b x + - a x
+--R 13 11 9 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 377
+
+--S 378 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 13 5 4 11 10 2 3 9 10 3 2 7 4 5 1 5 3
+--R (3) -- b x + -- a b x + -- a b x + -- a b x + a b x + - a x
+--R 13 11 9 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 378
+
+--S 379 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 379
+
+--S 380 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 380
+
+)clear all
+
+--S 381 of 1393
+t0:=(a+b*x^2)^5
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R Type: Polynomial(Integer)
+--E 381
+
+--S 382 of 1393
+r0:=a^5*x+5/3*a^4*b*x^3+2*a^3*b^2*x^5+10/7*a^2*b^3*x^7+5/9*a*b^4*x^9+_
+ 1/11*b^5*x^11
+--R
+--R
+--R 1 5 11 5 4 9 10 2 3 7 3 2 5 5 4 3 5
+--R (2) -- b x + - a b x + -- a b x + 2a b x + - a b x + a x
+--R 11 9 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 382
+
+--S 383 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 11 5 4 9 10 2 3 7 3 2 5 5 4 3 5
+--R (3) -- b x + - a b x + -- a b x + 2a b x + - a b x + a x
+--R 11 9 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 383
+
+--S 384 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 384
+
+--S 385 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 385
+
+)clear all
+
+--S 386 of 1393
+t0:=(a+b*x^2)^5/x^2
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 386
+
+--S 387 of 1393
+r0:=-a^5/x+5*a^4*b*x+10/3*a^3*b^2*x^3+2*a^2*b^3*x^5+5/7*a*b^4*x^7+1/9*b^5*x^9
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 7b x + 45a b x + 126a b x + 210a b x + 315a b x - 63a
+--R (2) ------------------------------------------------------------
+--R 63x
+--R Type: Fraction(Polynomial(Integer))
+--E 387
+
+--S 388 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 7b x + 45a b x + 126a b x + 210a b x + 315a b x - 63a
+--R (3) ------------------------------------------------------------
+--R 63x
+--R Type: Union(Expression(Integer),...)
+--E 388
+
+--S 389 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 1393
+t0:=(a+b*x^2)^5/x^4
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 391
+
+--S 392 of 1393
+r0:=-1/3*a^5/x^3-5*a^4*b/x+10*a^3*b^2*x+10/3*a^2*b^3*x^3+a*b^4*x^5+1/7*b^5*x^7
+--R
+--R
+--R 1 5 10 4 8 10 2 3 6 3 2 4 4 2 1 5
+--R - b x + a b x + -- a b x + 10a b x - 5a b x - - a
+--R 7 3 3
+--R (2) --------------------------------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 392
+
+--S 393 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 3b x + 21a b x + 70a b x + 210a b x - 105a b x - 7a
+--R (3) ----------------------------------------------------------
+--R 3
+--R 21x
+--R Type: Union(Expression(Integer),...)
+--E 393
+
+--S 394 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+)clear all
+
+--S 396 of 1393
+t0:=(a+b*x^2)^5/x^6
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 396
+
+--S 397 of 1393
+r0:=-1/5*a^5/x^5-5/3*a^4*b/x^3-10*a^3*b^2/x+10*a^2*b^3*x+_
+ 5/3*a*b^4*x^3+1/5*b^5*x^5
+--R
+--R
+--R 1 5 10 5 4 8 2 3 6 3 2 4 5 4 2 1 5
+--R - b x + - a b x + 10a b x - 10a b x - - a b x - - a
+--R 5 3 3 5
+--R (2) ----------------------------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 397
+
+--S 398 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 3b x + 25a b x + 150a b x - 150a b x - 25a b x - 3a
+--R (3) ----------------------------------------------------------
+--R 5
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 398
+
+--S 399 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 1393
+t0:=(a+b*x^2)^5/x^8
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 401
+
+--S 402 of 1393
+r0:=-1/7*a^5/x^7-a^4*b/x^5-10/3*a^3*b^2/x^3-10*a^2*b^3/x+5*a*b^4*x+1/3*b^5*x^3
+--R
+--R
+--R 1 5 10 4 8 2 3 6 10 3 2 4 4 2 1 5
+--R - b x + 5a b x - 10a b x - -- a b x - a b x - - a
+--R 3 3 7
+--R (2) --------------------------------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 402
+
+--S 403 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 7b x + 105a b x - 210a b x - 70a b x - 21a b x - 3a
+--R (3) ----------------------------------------------------------
+--R 7
+--R 21x
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 1393
+t0:=(a+b*x^2)^5/x^10
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 406
+
+--S 407 of 1393
+r0:=-1/9*a^5/x^9-5/7*a^4*b/x^7-2*a^3*b^2/x^5-10/3*a^2*b^3/x^3-5*a*b^4/x+b^5*x
+--R
+--R
+--R 5 10 4 8 10 2 3 6 3 2 4 5 4 2 1 5
+--R b x - 5a b x - -- a b x - 2a b x - - a b x - - a
+--R 3 7 9
+--R (2) -------------------------------------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 407
+
+--S 408 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 63b x - 315a b x - 210a b x - 126a b x - 45a b x - 7a
+--R (3) ------------------------------------------------------------
+--R 9
+--R 63x
+--R Type: Union(Expression(Integer),...)
+--E 408
+
+--S 409 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+)clear all
+
+--S 411 of 1393
+t0:=(a+b*x^2)^5/x^12
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 12
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 411
+
+--S 412 of 1393
+r0:=-1/11*a^5/x^11-5/9*a^4*b/x^9-10/7*a^3*b^2/x^7-2*a^2*b^3/x^5-_
+ 5/3*a*b^4/x^3-b^5/x
+--R
+--R
+--R 5 10 5 4 8 2 3 6 10 3 2 4 5 4 2 1 5
+--R - b x - - a b x - 2a b x - -- a b x - - a b x - -- a
+--R 3 7 9 11
+--R (2) -----------------------------------------------------------
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 412
+
+--S 413 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 693b x - 1155a b x - 1386a b x - 990a b x - 385a b x - 63a
+--R (3) -------------------------------------------------------------------
+--R 11
+--R 693x
+--R Type: Union(Expression(Integer),...)
+--E 413
+
+--S 414 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 415
+
+)clear all
+
+--S 416 of 1393
+t0:=(a+b*x^2)^5/x^14
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 14
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 416
+
+--S 417 of 1393
+r0:=-1/13*a^5/x^13-5/11*a^4*b/x^11-10/9*a^3*b^2/x^9-10/7*a^2*b^3/x^7-_
+ a*b^4/x^5-1/3*b^5/x^3
+--R
+--R
+--R 1 5 10 4 8 10 2 3 6 10 3 2 4 5 4 2 1 5
+--R - - b x - a b x - -- a b x - -- a b x - -- a b x - -- a
+--R 3 7 9 11 13
+--R (2) --------------------------------------------------------------
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 417
+
+--S 418 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 3003b x - 9009a b x - 12870a b x - 10010a b x - 4095a b x - 693a
+--R -------------------------------------------------------------------------
+--R 13
+--R 9009x
+--R Type: Union(Expression(Integer),...)
+--E 418
+
+--S 419 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 420
+
+)clear all
+
+--S 421 of 1393
+t0:=(a+b*x^2)^5/x^16
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 16
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 421
+
+--S 422 of 1393
+r0:=-1/15*a^5/x^15-5/13*a^4*b/x^13-10/11*a^3*b^2/x^11-10/9*a^2*b^3/x^9-_
+ 5/7*a*b^4/x^7-1/5*b^5/x^5
+--R
+--R
+--R 1 5 10 5 4 8 10 2 3 6 10 3 2 4 5 4 2 1 5
+--R - - b x - - a b x - -- a b x - -- a b x - -- a b x - -- a
+--R 5 7 9 11 13 15
+--R (2) ----------------------------------------------------------------
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 422
+
+--S 423 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 9009b x - 32175a b x - 50050a b x - 40950a b x - 17325a b x - 3003a
+--R ----------------------------------------------------------------------------
+--R 15
+--R 45045x
+--R Type: Union(Expression(Integer),...)
+--E 423
+
+--S 424 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 425
+
+)clear all
+
+--S 426 of 1393
+t0:=(a+b*x^2)^5/x^18
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 18
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 426
+
+--S 427 of 1393
+r0:=-1/17*a^5/x^17-1/3*a^4*b/x^15-10/13*a^3*b^2/x^13-_
+ 10/11*a^2*b^3/x^11-5/9*a*b^4/x^9-1/7*b^5/x^7
+--R
+--R
+--R 1 5 10 5 4 8 10 2 3 6 10 3 2 4 1 4 2 1 5
+--R - - b x - - a b x - -- a b x - -- a b x - - a b x - -- a
+--R 7 9 11 13 3 17
+--R (2) ---------------------------------------------------------------
+--R 17
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 427
+
+--S 428 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 2 3 6 3 2 4 4 2
+--R - 21879b x - 85085a b x - 139230a b x - 117810a b x - 51051a b x
+--R +
+--R 5
+--R - 9009a
+--R /
+--R 17
+--R 153153x
+--R Type: Union(Expression(Integer),...)
+--E 428
+
+--S 429 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 430
+
+)clear all
+
+--S 431 of 1393
+t0:=(a+b*x^2)^5/x^20
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) ----------------------------------------------------
+--R 20
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 431
+
+--S 432 of 1393
+r0:=-1/19*a^5/x^19-5/17*a^4*b/x^17-2/3*a^3*b^2/x^15-10/13*a^2*b^3/x^13-_
+ 5/11*a*b^4/x^11-1/9*b^5/x^9
+--R
+--R
+--R 1 5 10 5 4 8 10 2 3 6 2 3 2 4 5 4 2 1 5
+--R - - b x - -- a b x - -- a b x - - a b x - -- a b x - -- a
+--R 9 11 13 3 17 19
+--R (2) ----------------------------------------------------------------
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 432
+
+--S 433 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 2 3 6 3 2 4 4 2
+--R - 46189b x - 188955a b x - 319770a b x - 277134a b x - 122265a b x
+--R +
+--R 5
+--R - 21879a
+--R /
+--R 19
+--R 415701x
+--R Type: Union(Expression(Integer),...)
+--E 433
+
+--S 434 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 435
+
+)clear all
+
+--S 436 of 1393
+t0:=x^m*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R *
+--R m
+--R x
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 1393
+r0:=a^8*x^(1+m)/(1+m)+8*a^7*b*x^(3+m)/(3+m)+28*a^6*b^2*x^(5+m)/(5+m)+_
+ 56*a^5*b^3*x^(7+m)/(7+m)+70*a^4*b^4*x^(9+m)/(9+m)+_
+ 56*a^3*b^5*x^(11+m)/(11+m)+28*a^2*b^6*x^(13+m)/(13+m)+_
+ 8*a*b^7*x^(15+m)/(15+m)+b^8*x^(17+m)/(17+m)
+--R
+--R
+--R (2)
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R b m + 64b m + 1708b m + 24640b m + 208054b m + 1038016b m
+--R +
+--R 8 2 8 8
+--R 2924172b m + 4098240b m + 2027025b
+--R *
+--R m + 17
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 528a b m + 14448a b m + 212688a b m + 1825152a b m
+--R +
+--R 7 3 7 2 7 7
+--R 9222192a b m + 26230672a b m + 37013232a b m + 18378360a b
+--R *
+--R m + 15
+--R x
+--R +
+--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4
+--R 28a b m + 1904a b m + 53536a b m + 806960a b m + 7063672a b m
+--R +
+--R 2 6 3 2 6 2 2 6 2 6
+--R 36270416a b m + 104457024a b m + 148715280a b m + 74220300a b
+--R *
+--R m + 13
+--R x
+--R +
+--R 3 5 8 3 5 7 3 5 6 3 5 5 3 5 4
+--R 56a b m + 3920a b m + 113456a b m + 1757840a b m + 15772064a b m
+--R +
+--R 3 5 3 3 5 2 3 5 3 5
+--R 82703600a b m + 242205264a b m + 349055280a b m + 175429800a b
+--R *
+--R m + 11
+--R x
+--R +
+--R 4 4 8 4 4 7 4 4 6 4 4 5 4 4 4
+--R 70a b m + 5040a b m + 150360a b m + 2404080a b m + 22248660a b m
+--R +
+--R 4 4 3 4 4 2 4 4 4 4
+--R 120007440a b m + 359864120a b m + 527864400a b m + 268017750a b
+--R *
+--R m + 9
+--R x
+--R +
+--R 5 3 8 5 3 7 5 3 6 5 3 5 5 3 4
+--R 56a b m + 4144a b m + 127568a b m + 2112880a b m + 20318144a b m
+--R +
+--R 5 3 3 5 3 2 5 3 5 3
+--R 113969296a b m + 354159792a b m + 534194640a b m + 275675400a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 6 2 8 6 2 7 6 2 6 6 2 5 6 2 4
+--R 28a b m + 2128a b m + 67648a b m + 1164688a b m + 11730712a b m
+--R +
+--R 6 2 3 6 2 2 6 2 6 2
+--R 69444592a b m + 228749472a b m + 362909232a b m + 192972780a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 624a b m + 20496a b m + 367920a b m + 3911712a b m
+--R +
+--R 7 3 7 2 7 7
+--R 24864336a b m + 89970544a b m + 160561680a b m + 91891800a b
+--R *
+--R m + 3
+--R x
+--R +
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R a m + 80a m + 2716a m + 50960a m + 575974a m + 3998960a m
+--R +
+--R 8 2 8 8
+--R 16571484a m + 37237680a m + 34459425a
+--R *
+--R m + 1
+--R x
+--R /
+--R 9 8 7 6 5 4 3
+--R m + 81m + 2796m + 53676m + 626934m + 4574934m + 20570444m
+--R +
+--R 2
+--R 53809164m + 71697105m + 34459425
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R b m + 64b m + 1708b m + 24640b m + 208054b m + 1038016b m
+--R +
+--R 8 2 8 8
+--R 2924172b m + 4098240b m + 2027025b
+--R *
+--R 17
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 528a b m + 14448a b m + 212688a b m + 1825152a b m
+--R +
+--R 7 3 7 2 7 7
+--R 9222192a b m + 26230672a b m + 37013232a b m + 18378360a b
+--R *
+--R 15
+--R x
+--R +
+--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4
+--R 28a b m + 1904a b m + 53536a b m + 806960a b m + 7063672a b m
+--R +
+--R 2 6 3 2 6 2 2 6 2 6
+--R 36270416a b m + 104457024a b m + 148715280a b m + 74220300a b
+--R *
+--R 13
+--R x
+--R +
+--R 3 5 8 3 5 7 3 5 6 3 5 5
+--R 56a b m + 3920a b m + 113456a b m + 1757840a b m
+--R +
+--R 3 5 4 3 5 3 3 5 2 3 5
+--R 15772064a b m + 82703600a b m + 242205264a b m + 349055280a b m
+--R +
+--R 3 5
+--R 175429800a b
+--R *
+--R 11
+--R x
+--R +
+--R 4 4 8 4 4 7 4 4 6 4 4 5
+--R 70a b m + 5040a b m + 150360a b m + 2404080a b m
+--R +
+--R 4 4 4 4 4 3 4 4 2 4 4
+--R 22248660a b m + 120007440a b m + 359864120a b m + 527864400a b m
+--R +
+--R 4 4
+--R 268017750a b
+--R *
+--R 9
+--R x
+--R +
+--R 5 3 8 5 3 7 5 3 6 5 3 5
+--R 56a b m + 4144a b m + 127568a b m + 2112880a b m
+--R +
+--R 5 3 4 5 3 3 5 3 2 5 3
+--R 20318144a b m + 113969296a b m + 354159792a b m + 534194640a b m
+--R +
+--R 5 3
+--R 275675400a b
+--R *
+--R 7
+--R x
+--R +
+--R 6 2 8 6 2 7 6 2 6 6 2 5
+--R 28a b m + 2128a b m + 67648a b m + 1164688a b m
+--R +
+--R 6 2 4 6 2 3 6 2 2 6 2
+--R 11730712a b m + 69444592a b m + 228749472a b m + 362909232a b m
+--R +
+--R 6 2
+--R 192972780a b
+--R *
+--R 5
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 624a b m + 20496a b m + 367920a b m + 3911712a b m
+--R +
+--R 7 3 7 2 7 7
+--R 24864336a b m + 89970544a b m + 160561680a b m + 91891800a b
+--R *
+--R 3
+--R x
+--R +
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R a m + 80a m + 2716a m + 50960a m + 575974a m + 3998960a m
+--R +
+--R 8 2 8 8
+--R 16571484a m + 37237680a m + 34459425a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 9 8 7 6 5 4 3
+--R m + 81m + 2796m + 53676m + 626934m + 4574934m + 20570444m
+--R +
+--R 2
+--R 53809164m + 71697105m + 34459425
+--R Type: Union(Expression(Integer),...)
+--E 438
+
+--S 439 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R b m + 64b m + 1708b m + 24640b m + 208054b m + 1038016b m
+--R +
+--R 8 2 8 8
+--R 2924172b m + 4098240b m + 2027025b
+--R *
+--R 17
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 528a b m + 14448a b m + 212688a b m + 1825152a b m
+--R +
+--R 7 3 7 2 7 7
+--R 9222192a b m + 26230672a b m + 37013232a b m + 18378360a b
+--R *
+--R 15
+--R x
+--R +
+--R 2 6 8 2 6 7 2 6 6 2 6 5
+--R 28a b m + 1904a b m + 53536a b m + 806960a b m
+--R +
+--R 2 6 4 2 6 3 2 6 2 2 6
+--R 7063672a b m + 36270416a b m + 104457024a b m + 148715280a b m
+--R +
+--R 2 6
+--R 74220300a b
+--R *
+--R 13
+--R x
+--R +
+--R 3 5 8 3 5 7 3 5 6 3 5 5
+--R 56a b m + 3920a b m + 113456a b m + 1757840a b m
+--R +
+--R 3 5 4 3 5 3 3 5 2
+--R 15772064a b m + 82703600a b m + 242205264a b m
+--R +
+--R 3 5 3 5
+--R 349055280a b m + 175429800a b
+--R *
+--R 11
+--R x
+--R +
+--R 4 4 8 4 4 7 4 4 6 4 4 5
+--R 70a b m + 5040a b m + 150360a b m + 2404080a b m
+--R +
+--R 4 4 4 4 4 3 4 4 2
+--R 22248660a b m + 120007440a b m + 359864120a b m
+--R +
+--R 4 4 4 4
+--R 527864400a b m + 268017750a b
+--R *
+--R 9
+--R x
+--R +
+--R 5 3 8 5 3 7 5 3 6 5 3 5
+--R 56a b m + 4144a b m + 127568a b m + 2112880a b m
+--R +
+--R 5 3 4 5 3 3 5 3 2
+--R 20318144a b m + 113969296a b m + 354159792a b m
+--R +
+--R 5 3 5 3
+--R 534194640a b m + 275675400a b
+--R *
+--R 7
+--R x
+--R +
+--R 6 2 8 6 2 7 6 2 6 6 2 5
+--R 28a b m + 2128a b m + 67648a b m + 1164688a b m
+--R +
+--R 6 2 4 6 2 3 6 2 2
+--R 11730712a b m + 69444592a b m + 228749472a b m
+--R +
+--R 6 2 6 2
+--R 362909232a b m + 192972780a b
+--R *
+--R 5
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 624a b m + 20496a b m + 367920a b m + 3911712a b m
+--R +
+--R 7 3 7 2 7 7
+--R 24864336a b m + 89970544a b m + 160561680a b m + 91891800a b
+--R *
+--R 3
+--R x
+--R +
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R a m + 80a m + 2716a m + 50960a m + 575974a m + 3998960a m
+--R +
+--R 8 2 8 8
+--R 16571484a m + 37237680a m + 34459425a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R - b m - 64b m - 1708b m - 24640b m - 208054b m - 1038016b m
+--R +
+--R 8 2 8 8
+--R - 2924172b m - 4098240b m - 2027025b
+--R *
+--R m + 17
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R - 8a b m - 528a b m - 14448a b m - 212688a b m - 1825152a b m
+--R +
+--R 7 3 7 2 7 7
+--R - 9222192a b m - 26230672a b m - 37013232a b m - 18378360a b
+--R *
+--R m + 15
+--R x
+--R +
+--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4
+--R - 28a b m - 1904a b m - 53536a b m - 806960a b m - 7063672a b m
+--R +
+--R 2 6 3 2 6 2 2 6 2 6
+--R - 36270416a b m - 104457024a b m - 148715280a b m - 74220300a b
+--R *
+--R m + 13
+--R x
+--R +
+--R 3 5 8 3 5 7 3 5 6 3 5 5
+--R - 56a b m - 3920a b m - 113456a b m - 1757840a b m
+--R +
+--R 3 5 4 3 5 3 3 5 2 3 5
+--R - 15772064a b m - 82703600a b m - 242205264a b m - 349055280a b m
+--R +
+--R 3 5
+--R - 175429800a b
+--R *
+--R m + 11
+--R x
+--R +
+--R 4 4 8 4 4 7 4 4 6 4 4 5
+--R - 70a b m - 5040a b m - 150360a b m - 2404080a b m
+--R +
+--R 4 4 4 4 4 3 4 4 2 4 4
+--R - 22248660a b m - 120007440a b m - 359864120a b m - 527864400a b m
+--R +
+--R 4 4
+--R - 268017750a b
+--R *
+--R m + 9
+--R x
+--R +
+--R 5 3 8 5 3 7 5 3 6 5 3 5
+--R - 56a b m - 4144a b m - 127568a b m - 2112880a b m
+--R +
+--R 5 3 4 5 3 3 5 3 2 5 3
+--R - 20318144a b m - 113969296a b m - 354159792a b m - 534194640a b m
+--R +
+--R 5 3
+--R - 275675400a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 6 2 8 6 2 7 6 2 6 6 2 5
+--R - 28a b m - 2128a b m - 67648a b m - 1164688a b m
+--R +
+--R 6 2 4 6 2 3 6 2 2 6 2
+--R - 11730712a b m - 69444592a b m - 228749472a b m - 362909232a b m
+--R +
+--R 6 2
+--R - 192972780a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R - 8a b m - 624a b m - 20496a b m - 367920a b m - 3911712a b m
+--R +
+--R 7 3 7 2 7 7
+--R - 24864336a b m - 89970544a b m - 160561680a b m - 91891800a b
+--R *
+--R m + 3
+--R x
+--R +
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R - a m - 80a m - 2716a m - 50960a m - 575974a m - 3998960a m
+--R +
+--R 8 2 8 8
+--R - 16571484a m - 37237680a m - 34459425a
+--R *
+--R m + 1
+--R x
+--R /
+--R 9 8 7 6 5 4 3
+--R m + 81m + 2796m + 53676m + 626934m + 4574934m + 20570444m
+--R +
+--R 2
+--R 53809164m + 71697105m + 34459425
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 1393
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 1393
+t0:=x^13*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 29 7 27 2 6 25 3 5 23 4 4 21 5 3 19
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 17 7 15 8 13
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 441
+
+--S 442 of 1393
+r0:=1/14*a^8*x^14+1/2*a^7*b*x^16+14/9*a^6*b^2*x^18+14/5*a^5*b^3*x^20+_
+ 35/11*a^4*b^4*x^22+7/3*a^3*b^5*x^24+14/13*a^2*b^6*x^26+_
+ 2/7*a*b^7*x^28+1/30*b^8*x^30
+--R
+--R
+--R (2)
+--R 1 8 30 2 7 28 14 2 6 26 7 3 5 24 35 4 4 22 14 5 3 20
+--R -- b x + - a b x + -- a b x + - a b x + -- a b x + -- a b x
+--R 30 7 13 3 11 5
+--R +
+--R 14 6 2 18 1 7 16 1 8 14
+--R -- a b x + - a b x + -- a x
+--R 9 2 14
+--R Type: Polynomial(Fraction(Integer))
+--E 442
+
+--S 443 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 30 2 7 28 14 2 6 26 7 3 5 24 35 4 4 22 14 5 3 20
+--R -- b x + - a b x + -- a b x + - a b x + -- a b x + -- a b x
+--R 30 7 13 3 11 5
+--R +
+--R 14 6 2 18 1 7 16 1 8 14
+--R -- a b x + - a b x + -- a x
+--R 9 2 14
+--R Type: Polynomial(Fraction(Integer))
+--E 443
+
+--S 444 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 444
+
+--S 445 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 445
+
+)clear all
+
+--S 446 of 1393
+t0:=x^11*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 27 7 25 2 6 23 3 5 21 4 4 19 5 3 17
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 15 7 13 8 11
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 446
+
+--S 447 of 1393
+r0:=-1/18*a^5*(a+b*x^2)^9/b^6+1/4*a^4*(a+b*x^2)^10/b^6-_
+ 5/11*a^3*(a+b*x^2)^11/b^6+5/12*a^2*(a+b*x^2)^12/b^6-_
+ 5/26*a*(a+b*x^2)^13/b^6+1/28*(a+b*x^2)^14/b^6
+--R
+--R
+--R (2)
+--R 1 14 28 4 13 26 7 2 12 24 28 3 11 22 7 4 10 20
+--R -- b x + -- a b x + - a b x + -- a b x + - a b x
+--R 28 13 6 11 2
+--R +
+--R 28 5 9 18 7 6 8 16 4 7 7 14 1 8 6 12 1 14
+--R -- a b x + - a b x + - a b x + -- a b x - ----- a
+--R 9 4 7 12 36036
+--R /
+--R 6
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 447
+
+--S 448 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 28 4 7 26 7 2 6 24 28 3 5 22 7 4 4 20 28 5 3 18
+--R -- b x + -- a b x + - a b x + -- a b x + - a b x + -- a b x
+--R 28 13 6 11 2 9
+--R +
+--R 7 6 2 16 4 7 14 1 8 12
+--R - a b x + - a b x + -- a x
+--R 4 7 12
+--R Type: Polynomial(Fraction(Integer))
+--E 448
+
+--S 449 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 14
+--R ----- a
+--R 36036
+--R (4) ---------
+--R 6
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 449
+
+--S 450 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 450
+
+)clear all
+
+--S 451 of 1393
+t0:=x^9*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 25 7 23 2 6 21 3 5 19 4 4 17 5 3 15
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 13 7 11 8 9
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 451
+
+--S 452 of 1393
+r0:=1/18*a^4*(a+b*x^2)^9/b^5-1/5*a^3*(a+b*x^2)^10/b^5+_
+ 3/11*a^2*(a+b*x^2)^11/b^5-1/6*a*(a+b*x^2)^12/b^5+1/26*(a+b*x^2)^13/b^5
+--R
+--R
+--R (2)
+--R 1 13 26 1 12 24 14 2 11 22 14 3 10 20 35 4 9 18
+--R -- b x + - a b x + -- a b x + -- a b x + -- a b x
+--R 26 3 11 5 9
+--R +
+--R 7 5 8 16 6 7 14 2 7 6 12 1 8 5 10 1 13
+--R - a b x + 2a b x + - a b x + -- a b x + ----- a
+--R 2 3 10 12870
+--R /
+--R 5
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 452
+
+--S 453 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 26 1 7 24 14 2 6 22 14 3 5 20 35 4 4 18 7 5 3 16
+--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + - a b x
+--R 26 3 11 5 9 2
+--R +
+--R 6 2 14 2 7 12 1 8 10
+--R 2a b x + - a b x + -- a x
+--R 3 10
+--R Type: Polynomial(Fraction(Integer))
+--E 453
+
+--S 454 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 13
+--R ----- a
+--R 12870
+--R (4) - ---------
+--R 5
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 454
+
+--S 455 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 455
+
+)clear all
+
+--S 456 of 1393
+t0:=x^7*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 23 7 21 2 6 19 3 5 17 4 4 15 5 3 13
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 11 7 9 8 7
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 456
+
+--S 457 of 1393
+r0:=-1/18*a^3*(a+b*x^2)^9/b^4+3/20*a^2*(a+b*x^2)^10/b^4-_
+ 3/22*a*(a+b*x^2)^11/b^4+1/24*(a+b*x^2)^12/b^4
+--R
+--R
+--R (2)
+--R 1 12 24 4 11 22 7 2 10 20 28 3 9 18 35 4 8 16 5 7 14
+--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + 4a b x
+--R 24 11 5 9 8
+--R +
+--R 7 6 6 12 4 7 5 10 1 8 4 8 1 12
+--R - a b x + - a b x + - a b x - ---- a
+--R 3 5 8 3960
+--R /
+--R 4
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 457
+
+--S 458 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 24 4 7 22 7 2 6 20 28 3 5 18 35 4 4 16 5 3 14
+--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + 4a b x
+--R 24 11 5 9 8
+--R +
+--R 7 6 2 12 4 7 10 1 8 8
+--R - a b x + - a b x + - a x
+--R 3 5 8
+--R Type: Polynomial(Fraction(Integer))
+--E 458
+
+--S 459 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 12
+--R ---- a
+--R 3960
+--R (4) --------
+--R 4
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 459
+
+--S 460 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 460
+
+)clear all
+
+--S 461 of 1393
+t0:=x^5*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 21 7 19 2 6 17 3 5 15 4 4 13 5 3 11 6 2 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 7 8 5
+--R 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 461
+
+--S 462 of 1393
+r0:=1/18*a^2*(a+b*x^2)^9/b^3-1/10*a*(a+b*x^2)^10/b^3+1/22*(a+b*x^2)^11/b^3
+--R
+--R
+--R (2)
+--R 1 11 22 2 10 20 14 2 9 18 7 3 8 16 4 7 14 14 5 6 12
+--R -- b x + - a b x + -- a b x + - a b x + 5a b x + -- a b x
+--R 22 5 9 2 3
+--R +
+--R 14 6 5 10 7 4 8 1 8 3 6 1 11
+--R -- a b x + a b x + - a b x + --- a
+--R 5 6 990
+--R /
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 462
+
+--S 463 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 22 2 7 20 14 2 6 18 7 3 5 16 4 4 14 14 5 3 12
+--R -- b x + - a b x + -- a b x + - a b x + 5a b x + -- a b x
+--R 22 5 9 2 3
+--R +
+--R 14 6 2 10 7 8 1 8 6
+--R -- a b x + a b x + - a x
+--R 5 6
+--R Type: Polynomial(Fraction(Integer))
+--E 463
+
+--S 464 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 11
+--R --- a
+--R 990
+--R (4) - -------
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 464
+
+--S 465 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 465
+
+)clear all
+
+--S 466 of 1393
+t0:=x^3*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 19 7 17 2 6 15 3 5 13 4 4 11 5 3 9 6 2 7
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 5 8 3
+--R 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 466
+
+--S 467 of 1393
+r0:=-1/18*a*(a+b*x^2)^9/b^2+1/20*(a+b*x^2)^10/b^2
+--R
+--R
+--R (2)
+--R 1 10 20 4 9 18 7 2 8 16 3 7 14 35 4 6 12 28 5 5 10
+--R -- b x + - a b x + - a b x + 4a b x + -- a b x + -- a b x
+--R 20 9 4 6 5
+--R +
+--R 7 6 4 8 4 7 3 6 1 8 2 4 1 10
+--R - a b x + - a b x + - a b x - --- a
+--R 2 3 4 180
+--R /
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 467
+
+--S 468 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 20 4 7 18 7 2 6 16 3 5 14 35 4 4 12 28 5 3 10
+--R -- b x + - a b x + - a b x + 4a b x + -- a b x + -- a b x
+--R 20 9 4 6 5
+--R +
+--R 7 6 2 8 4 7 6 1 8 4
+--R - a b x + - a b x + - a x
+--R 2 3 4
+--R Type: Polynomial(Fraction(Integer))
+--E 468
+
+--S 469 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 10
+--R --- a
+--R 180
+--R (4) -------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 469
+
+--S 470 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 470
+
+)clear all
+
+--S 471 of 1393
+t0:=x*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 17 7 15 2 6 13 3 5 11 4 4 9 5 3 7 6 2 5
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 3 8
+--R 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 471
+
+--S 472 of 1393
+r0:=1/18*(a+b*x^2)^9/b
+--R
+--R
+--R (2)
+--R 1 9 18 1 8 16 2 7 14 14 3 6 12 4 5 10 5 4 8
+--R -- b x + - a b x + 2a b x + -- a b x + 7a b x + 7a b x
+--R 18 2 3
+--R +
+--R 14 6 3 6 7 2 4 1 8 2 1 9
+--R -- a b x + 2a b x + - a b x + -- a
+--R 3 2 18
+--R /
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 472
+
+--S 473 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 18 1 7 16 2 6 14 14 3 5 12 4 4 10 5 3 8
+--R -- b x + - a b x + 2a b x + -- a b x + 7a b x + 7a b x
+--R 18 2 3
+--R +
+--R 14 6 2 6 7 4 1 8 2
+--R -- a b x + 2a b x + - a x
+--R 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 473
+
+--S 474 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1 9
+--R -- a
+--R 18
+--R (4) - -----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 474
+
+--S 475 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 475
+
+)clear all
+
+--S 476 of 1393
+t0:=(a+b*x^2)^8/x
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 476
+
+--S 477 of 1393
+r0:=4*a^7*b*x^2+7*a^6*b^2*x^4+28/3*a^5*b^3*x^6+35/4*a^4*b^4*x^8+_
+ 28/5*a^3*b^5*x^10+7/3*a^2*b^6*x^12+4/7*a*b^7*x^14+_
+ 1/16*b^8*x^16+a^8*log(x)
+--R
+--R
+--R (2)
+--R 8 8 16 7 14 2 6 12 3 5 10
+--R 1680a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2
+--R 14700a b x + 15680a b x + 11760a b x + 6720a b x
+--R /
+--R 1680
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 8 16 7 14 2 6 12 3 5 10
+--R 1680a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2
+--R 14700a b x + 15680a b x + 11760a b x + 6720a b x
+--R /
+--R 1680
+--R Type: Union(Expression(Integer),...)
+--E 478
+
+--S 479 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 1393
+t0:=(a+b*x^2)^8/x^3
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 481
+
+--S 482 of 1393
+r0:=-1/2*a^8/x^2+14*a^6*b^2*x^2+14*a^5*b^3*x^4+35/3*a^4*b^4*x^6+_
+ 7*a^3*b^5*x^8+14/5*a^2*b^6*x^10+2/3*a*b^7*x^12+_
+ 1/14*b^8*x^14+8*a^7*b*log(x)
+--R
+--R
+--R (2)
+--R 7 2 8 16 7 14 2 6 12 3 5 10
+--R 1680a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 8
+--R 2450a b x + 2940a b x + 2940a b x - 105a
+--R /
+--R 2
+--R 210x
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 2 8 16 7 14 2 6 12 3 5 10
+--R 1680a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 8
+--R 2450a b x + 2940a b x + 2940a b x - 105a
+--R /
+--R 2
+--R 210x
+--R Type: Union(Expression(Integer),...)
+--E 483
+
+--S 484 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 485
+
+)clear all
+
+--S 486 of 1393
+t0:=(a+b*x^2)^8/x^5
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 486
+
+--S 487 of 1393
+r0:=-1/4*a^8/x^4-4*a^7*b/x^2+28*a^5*b^3*x^2+35/2*a^4*b^4*x^4+_
+ 28/3*a^3*b^5*x^6+7/2*a^2*b^6*x^8+4/5*a*b^7*x^10+_
+ 1/12*b^8*x^12+28*a^6*b^2*log(x)
+--R
+--R
+--R (2)
+--R 6 2 4 8 16 7 14 2 6 12 3 5 10
+--R 1680a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x
+--R +
+--R 4 4 8 5 3 6 7 2 8
+--R 1050a b x + 1680a b x - 240a b x - 15a
+--R /
+--R 4
+--R 60x
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 2 4 8 16 7 14 2 6 12 3 5 10
+--R 1680a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x
+--R +
+--R 4 4 8 5 3 6 7 2 8
+--R 1050a b x + 1680a b x - 240a b x - 15a
+--R /
+--R 4
+--R 60x
+--R Type: Union(Expression(Integer),...)
+--E 488
+
+--S 489 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 490
+
+)clear all
+
+--S 491 of 1393
+t0:=(a+b*x^2)^8/x^7
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 491
+
+--S 492 of 1393
+r0:=-1/6*a^8/x^6-2*a^7*b/x^4-14*a^6*b^2/x^2+35*a^4*b^4*x^2+_
+ 14*a^3*b^5*x^4+14/3*a^2*b^6*x^6+a*b^7*x^8+1/10*b^8*x^10+_
+ 56*a^5*b^3*log(x)
+--R
+--R
+--R (2)
+--R 5 3 6 8 16 7 14 2 6 12 3 5 10
+--R 1680a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x
+--R +
+--R 4 4 8 6 2 4 7 2 8
+--R 1050a b x - 420a b x - 60a b x - 5a
+--R /
+--R 6
+--R 30x
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 3 6 8 16 7 14 2 6 12 3 5 10
+--R 1680a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x
+--R +
+--R 4 4 8 6 2 4 7 2 8
+--R 1050a b x - 420a b x - 60a b x - 5a
+--R /
+--R 6
+--R 30x
+--R Type: Union(Expression(Integer),...)
+--E 493
+
+--S 494 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 1393
+t0:=(a+b*x^2)^8/x^9
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 496
+
+--S 497 of 1393
+r0:=-1/8*a^8/x^8-4/3*a^7*b/x^6-7*a^6*b^2/x^4-28*a^5*b^3/x^2+_
+ 28*a^3*b^5*x^2+7*a^2*b^6*x^4+4/3*a*b^7*x^6+1/8*b^8*x^8+70*a^4*b^4*log(x)
+--R
+--R
+--R (2)
+--R 4 4 8 8 16 7 14 2 6 12 3 5 10
+--R 1680a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 672a b x - 168a b x - 32a b x - 3a
+--R /
+--R 8
+--R 24x
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 8 8 16 7 14 2 6 12 3 5 10
+--R 1680a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 672a b x - 168a b x - 32a b x - 3a
+--R /
+--R 8
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 498
+
+--S 499 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+)clear all
+
+--S 501 of 1393
+t0:=(a+b*x^2)^8/x^11
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 501
+
+--S 502 of 1393
+r0:=-1/10*a^8/x^10-a^7*b/x^8-14/3*a^6*b^2/x^6-14*a^5*b^3/x^4-_
+ 35*a^4*b^4/x^2+14*a^2*b^6*x^2+2*a*b^7*x^4+1/6*b^8*x^6+56*a^3*b^5*log(x)
+--R
+--R
+--R (2)
+--R 3 5 10 8 16 7 14 2 6 12 4 4 8
+--R 1680a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 420a b x - 140a b x - 30a b x - 3a
+--R /
+--R 10
+--R 30x
+--R Type: Expression(Integer)
+--E 502
+
+--S 503 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 5 10 8 16 7 14 2 6 12 4 4 8
+--R 1680a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 420a b x - 140a b x - 30a b x - 3a
+--R /
+--R 10
+--R 30x
+--R Type: Union(Expression(Integer),...)
+--E 503
+
+--S 504 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 505
+
+)clear all
+
+--S 506 of 1393
+t0:=(a+b*x^2)^8/x^13
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 506
+
+--S 507 of 1393
+r0:=-1/12*a^8/x^12-4/5*a^7*b/x^10-7/2*a^6*b^2/x^8-28/3*a^5*b^3/x^6-_
+ 35/2*a^4*b^4/x^4-28*a^3*b^5/x^2+4*a*b^7*x^2+1/4*b^8*x^4+28*a^2*b^6*log(x)
+--R
+--R
+--R (2)
+--R 2 6 12 8 16 7 14 3 5 10 4 4 8
+--R 1680a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 560a b x - 210a b x - 48a b x - 5a
+--R /
+--R 12
+--R 60x
+--R Type: Expression(Integer)
+--E 507
+
+--S 508 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 12 8 16 7 14 3 5 10 4 4 8
+--R 1680a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 560a b x - 210a b x - 48a b x - 5a
+--R /
+--R 12
+--R 60x
+--R Type: Union(Expression(Integer),...)
+--E 508
+
+--S 509 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 509
+
+--S 510 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 510
+
+)clear all
+
+--S 511 of 1393
+t0:=(a+b*x^2)^8/x^15
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 511
+
+--S 512 of 1393
+r0:=-1/14*a^8/x^14-2/3*a^7*b/x^12-14/5*a^6*b^2/x^10-7*a^5*b^3/x^8-_
+ 35/3*a^4*b^4/x^6-14*a^3*b^5/x^4-14*a^2*b^6/x^2+1/2*b^8*x^2+8*a*b^7*log(x)
+--R
+--R
+--R (2)
+--R 7 14 8 16 2 6 12 3 5 10 4 4 8
+--R 1680a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 1470a b x - 588a b x - 140a b x - 15a
+--R /
+--R 14
+--R 210x
+--R Type: Expression(Integer)
+--E 512
+
+--S 513 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 14 8 16 2 6 12 3 5 10 4 4 8
+--R 1680a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 1470a b x - 588a b x - 140a b x - 15a
+--R /
+--R 14
+--R 210x
+--R Type: Union(Expression(Integer),...)
+--E 513
+
+--S 514 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 514
+
+--S 515 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 515
+
+)clear all
+
+--S 516 of 1393
+t0:=(a+b*x^2)^8/x^17
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 17
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 516
+
+--S 517 of 1393
+r0:=-1/16*a^8/x^16-4/7*a^7*b/x^14-7/3*a^6*b^2/x^12-28/5*a^5*b^3/x^10-_
+ 35/4*a^4*b^4/x^8-28/3*a^3*b^5/x^6-7*a^2*b^6/x^4-4*a*b^7/x^2+b^8*log(x)
+--R
+--R
+--R (2)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 1680b x log(x) - 6720a b x - 11760a b x - 15680a b x - 14700a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 9408a b x - 3920a b x - 960a b x - 105a
+--R /
+--R 16
+--R 1680x
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 1680b x log(x) - 6720a b x - 11760a b x - 15680a b x - 14700a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 9408a b x - 3920a b x - 960a b x - 105a
+--R /
+--R 16
+--R 1680x
+--R Type: Union(Expression(Integer),...)
+--E 518
+
+--S 519 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 519
+
+--S 520 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 520
+
+)clear all
+
+--S 521 of 1393
+t0:=(a+b*x^2)^8/x^19
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 521
+
+--S 522 of 1393
+r0:=-1/18*(a+b*x^2)^9/(a*x^18)
+--R
+--R
+--R (2)
+--R 1 9 18 1 8 16 2 7 14 14 3 6 12 4 5 10 5 4 8
+--R - -- b x - - a b x - 2a b x - -- a b x - 7a b x - 7a b x
+--R 18 2 3
+--R +
+--R 14 6 3 6 7 2 4 1 8 2 1 9
+--R - -- a b x - 2a b x - - a b x - -- a
+--R 3 2 18
+--R /
+--R 18
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 522
+
+--S 523 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 36a b x - 9a b x - a
+--R /
+--R 18
+--R 18x
+--R Type: Union(Expression(Integer),...)
+--E 523
+
+--S 524 of 1393
+m0:=a0-r0
+--R
+--R
+--R 9
+--R b
+--R (4) ---
+--R 18a
+--R Type: Expression(Integer)
+--E 524
+
+--S 525 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 525
+
+)clear all
+
+--S 526 of 1393
+t0:=(a+b*x^2)^8/x^21
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 21
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 526
+
+--S 527 of 1393
+r0:=-1/20*(a+b*x^2)^9/(a*x^20)+1/180*b*(a+b*x^2)^9/(a^2*x^18)
+--R
+--R
+--R (2)
+--R 1 10 20 1 2 8 16 4 3 7 14 7 4 6 12 28 5 5 10 35 6 4 8
+--R --- b x - - a b x - - a b x - - a b x - -- a b x - -- a b x
+--R 180 4 3 2 5 6
+--R +
+--R 7 3 6 7 8 2 4 4 9 2 1 10
+--R - 4a b x - - a b x - - a b x - -- a
+--R 4 9 20
+--R /
+--R 2 20
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 527
+
+--S 528 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 45b x - 240a b x - 630a b x - 1008a b x - 1050a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 720a b x - 315a b x - 80a b x - 9a
+--R /
+--R 20
+--R 180x
+--R Type: Union(Expression(Integer),...)
+--E 528
+
+--S 529 of 1393
+m0:=a0-r0
+--R
+--R
+--R 10
+--R b
+--R (4) - -----
+--R 2
+--R 180a
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 530
+
+)clear all
+
+--S 531 of 1393
+t0:=(a+b*x^2)^8/x^23
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 23
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 531
+
+--S 532 of 1393
+r0:=-1/22*(a+b*x^2)^9/(a*x^22)+1/110*b*(a+b*x^2)^9/(a^2*x^20)-_
+ 1/990*b^2*(a+b*x^2)^9/(a^3*x^18)
+--R
+--R
+--R (2)
+--R 1 11 22 1 3 8 16 4 7 14 14 5 6 12 14 6 5 10 7 4 8
+--R - --- b x - - a b x - a b x - -- a b x - -- a b x - 5a b x
+--R 990 6 5 3
+--R +
+--R 7 8 3 6 14 9 2 4 2 10 2 1 11
+--R - - a b x - -- a b x - - a b x - -- a
+--R 2 9 5 22
+--R /
+--R 3 22
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 532
+
+--S 533 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 165b x - 990a b x - 2772a b x - 4620a b x - 4950a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 3465a b x - 1540a b x - 396a b x - 45a
+--R /
+--R 22
+--R 990x
+--R Type: Union(Expression(Integer),...)
+--E 533
+
+--S 534 of 1393
+m0:=a0-r0
+--R
+--R
+--R 11
+--R b
+--R (4) -----
+--R 3
+--R 990a
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 535
+
+)clear all
+
+--S 536 of 1393
+t0:=(a+b*x^2)^8/x^25
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 25
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 536
+
+--S 537 of 1393
+r0:=-1/24*(a+b*x^2)^9/(a*x^24)+1/88*b*(a+b*x^2)^9/(a^2*x^22)-_
+ 1/440*b^2*(a+b*x^2)^9/(a^3*x^20)+1/3960*b^3*(a+b*x^2)^9/(a^4*x^18)
+--R
+--R
+--R (2)
+--R 1 12 24 1 4 8 16 4 5 7 14 7 6 6 12 7 5 10 35 8 4 8
+--R ---- b x - - a b x - - a b x - - a b x - 4a b x - -- a b x
+--R 3960 8 5 3 8
+--R +
+--R 28 9 3 6 7 10 2 4 4 11 2 1 12
+--R - -- a b x - - a b x - -- a b x - -- a
+--R 9 5 11 24
+--R /
+--R 4 24
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 537
+
+--S 538 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 495b x - 3168a b x - 9240a b x - 15840a b x - 17325a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 12320a b x - 5544a b x - 1440a b x - 165a
+--R /
+--R 24
+--R 3960x
+--R Type: Union(Expression(Integer),...)
+--E 538
+
+--S 539 of 1393
+m0:=a0-r0
+--R
+--R
+--R 12
+--R b
+--R (4) - ------
+--R 4
+--R 3960a
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 540
+
+)clear all
+
+--S 541 of 1393
+t0:=(a+b*x^2)^8/x^27
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 27
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 541
+
+--S 542 of 1393
+r0:=-1/26*a^8/x^26-1/3*a^7*b/x^24-14/11*a^6*b^2/x^22-14/5*a^5*b^3/x^20-_
+ 35/9*a^4*b^4/x^18-7/2*a^3*b^5/x^16-2*a^2*b^6/x^14-_
+ 2/3*a*b^7/x^12-1/10*b^8/x^10
+--R
+--R
+--R (2)
+--R 1 8 16 2 7 14 2 6 12 7 3 5 10 35 4 4 8 14 5 3 6
+--R - -- b x - - a b x - 2a b x - - a b x - -- a b x - -- a b x
+--R 10 3 2 9 5
+--R +
+--R 14 6 2 4 1 7 2 1 8
+--R - -- a b x - - a b x - -- a
+--R 11 3 26
+--R /
+--R 26
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 542
+
+--S 543 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 1287b x - 8580a b x - 25740a b x - 45045a b x - 50050a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 36036a b x - 16380a b x - 4290a b x - 495a
+--R /
+--R 26
+--R 12870x
+--R Type: Union(Expression(Integer),...)
+--E 543
+
+--S 544 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 544
+
+--S 545 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 545
+
+)clear all
+
+--S 546 of 1393
+t0:=(a+b*x^2)^8/x^29
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 29
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 546
+
+--S 547 of 1393
+r0:=-1/28*a^8/x^28-4/13*a^7*b/x^26-7/6*a^6*b^2/x^24-28/11*a^5*b^3/x^22-_
+ 7/2*a^4*b^4/x^20-28/9*a^3*b^5/x^18-7/4*a^2*b^6/x^16-_
+ 4/7*a*b^7/x^14-1/12*b^8/x^12
+--R
+--R
+--R (2)
+--R 1 8 16 4 7 14 7 2 6 12 28 3 5 10 7 4 4 8 28 5 3 6
+--R - -- b x - - a b x - - a b x - -- a b x - - a b x - -- a b x
+--R 12 7 4 9 2 11
+--R +
+--R 7 6 2 4 4 7 2 1 8
+--R - - a b x - -- a b x - -- a
+--R 6 13 28
+--R /
+--R 28
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 547
+
+--S 548 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 3003b x - 20592a b x - 63063a b x - 112112a b x - 126126a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 91728a b x - 42042a b x - 11088a b x - 1287a
+--R /
+--R 28
+--R 36036x
+--R Type: Union(Expression(Integer),...)
+--E 548
+
+--S 549 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 550
+
+)clear all
+
+--S 551 of 1393
+t0:=(a+b*x^2)^8/x^31
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 31
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 551
+
+--S 552 of 1393
+r0:=-1/30*a^8/x^30-2/7*a^7*b/x^28-14/13*a^6*b^2/x^26-7/3*a^5*b^3/x^24-_
+ 35/11*a^4*b^4/x^22-14/5*a^3*b^5/x^20-14/9*a^2*b^6/x^18-_
+ 1/2*a*b^7/x^16-1/14*b^8/x^14
+--R
+--R
+--R (2)
+--R 1 8 16 1 7 14 14 2 6 12 14 3 5 10 35 4 4 8 7 5 3 6
+--R - -- b x - - a b x - -- a b x - -- a b x - -- a b x - - a b x
+--R 14 2 9 5 11 3
+--R +
+--R 14 6 2 4 2 7 2 1 8
+--R - -- a b x - - a b x - -- a
+--R 13 7 30
+--R /
+--R 30
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 552
+
+--S 553 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 6435b x - 45045a b x - 140140a b x - 252252a b x - 286650a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 210210a b x - 97020a b x - 25740a b x - 3003a
+--R /
+--R 30
+--R 90090x
+--R Type: Union(Expression(Integer),...)
+--E 553
+
+--S 554 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 554
+
+--S 555 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 555
+
+)clear all
+
+--S 556 of 1393
+t0:=(a+b*x^2)^8/x^33
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 33
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 556
+
+--S 557 of 1393
+r0:=-1/32*a^8/x^32-4/15*a^7*b/x^30-a^6*b^2/x^28-28/13*a^5*b^3/x^26-_
+ 35/12*a^4*b^4/x^24-28/11*a^3*b^5/x^22-7/5*a^2*b^6/x^20-_
+ 4/9*a*b^7/x^18-1/16*b^8/x^16
+--R
+--R
+--R (2)
+--R 1 8 16 4 7 14 7 2 6 12 28 3 5 10 35 4 4 8 28 5 3 6
+--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a b x
+--R 16 9 5 11 12 13
+--R +
+--R 6 2 4 4 7 2 1 8
+--R - a b x - -- a b x - -- a
+--R 15 32
+--R /
+--R 32
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 557
+
+--S 558 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10
+--R - 12870b x - 91520a b x - 288288a b x - 524160a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R - 600600a b x - 443520a b x - 205920a b x - 54912a b x - 6435a
+--R /
+--R 32
+--R 205920x
+--R Type: Union(Expression(Integer),...)
+--E 558
+
+--S 559 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 559
+
+--S 560 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 560
+
+)clear all
+
+--S 561 of 1393
+t0:=x^8*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 24 7 22 2 6 20 3 5 18 4 4 16 5 3 14
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 12 7 10 8 8
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 561
+
+--S 562 of 1393
+r0:=1/9*a^8*x^9+8/11*a^7*b*x^11+28/13*a^6*b^2*x^13+56/15*a^5*b^3*x^15+_
+ 70/17*a^4*b^4*x^17+56/19*a^3*b^5*x^19+4/3*a^2*b^6*x^21+_
+ 8/23*a*b^7*x^23+1/25*b^8*x^25
+--R
+--R
+--R (2)
+--R 1 8 25 8 7 23 4 2 6 21 56 3 5 19 70 4 4 17 56 5 3 15
+--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + -- a b x
+--R 25 23 3 19 17 15
+--R +
+--R 28 6 2 13 8 7 11 1 8 9
+--R -- a b x + -- a b x + - a x
+--R 13 11 9
+--R Type: Polynomial(Fraction(Integer))
+--E 562
+
+--S 563 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 25 8 7 23 4 2 6 21 56 3 5 19 70 4 4 17 56 5 3 15
+--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + -- a b x
+--R 25 23 3 19 17 15
+--R +
+--R 28 6 2 13 8 7 11 1 8 9
+--R -- a b x + -- a b x + - a x
+--R 13 11 9
+--R Type: Polynomial(Fraction(Integer))
+--E 563
+
+--S 564 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 564
+
+--S 565 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 565
+
+)clear all
+
+--S 566 of 1393
+t0:=x^6*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 22 7 20 2 6 18 3 5 16 4 4 14 5 3 12
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 10 7 8 8 6
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 566
+
+--S 567 of 1393
+r0:=1/7*a^8*x^7+8/9*a^7*b*x^9+28/11*a^6*b^2*x^11+56/13*a^5*b^3*x^13+_
+ 14/3*a^4*b^4*x^15+56/17*a^3*b^5*x^17+28/19*a^2*b^6*x^19+_
+ 8/21*a*b^7*x^21+1/23*b^8*x^23
+--R
+--R
+--R (2)
+--R 1 8 23 8 7 21 28 2 6 19 56 3 5 17 14 4 4 15 56 5 3 13
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 23 21 19 17 3 13
+--R +
+--R 28 6 2 11 8 7 9 1 8 7
+--R -- a b x + - a b x + - a x
+--R 11 9 7
+--R Type: Polynomial(Fraction(Integer))
+--E 567
+
+--S 568 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 23 8 7 21 28 2 6 19 56 3 5 17 14 4 4 15 56 5 3 13
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 23 21 19 17 3 13
+--R +
+--R 28 6 2 11 8 7 9 1 8 7
+--R -- a b x + - a b x + - a x
+--R 11 9 7
+--R Type: Polynomial(Fraction(Integer))
+--E 568
+
+--S 569 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 569
+
+--S 570 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 570
+
+)clear all
+
+--S 571 of 1393
+t0:=x^4*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 20 7 18 2 6 16 3 5 14 4 4 12 5 3 10 6 2 8
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 6 8 4
+--R 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 571
+
+--S 572 of 1393
+r0:=1/5*a^8*x^5+8/7*a^7*b*x^7+28/9*a^6*b^2*x^9+56/11*a^5*b^3*x^11+_
+ 70/13*a^4*b^4*x^13+56/15*a^3*b^5*x^15+28/17*a^2*b^6*x^17+_
+ 8/19*a*b^7*x^19+1/21*b^8*x^21
+--R
+--R
+--R (2)
+--R 1 8 21 8 7 19 28 2 6 17 56 3 5 15 70 4 4 13 56 5 3 11
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 21 19 17 15 13 11
+--R +
+--R 28 6 2 9 8 7 7 1 8 5
+--R -- a b x + - a b x + - a x
+--R 9 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 572
+
+--S 573 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 21 8 7 19 28 2 6 17 56 3 5 15 70 4 4 13 56 5 3 11
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 21 19 17 15 13 11
+--R +
+--R 28 6 2 9 8 7 7 1 8 5
+--R -- a b x + - a b x + - a x
+--R 9 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 573
+
+--S 574 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 574
+
+--S 575 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 575
+
+)clear all
+
+--S 576 of 1393
+t0:=x^2*(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 18 7 16 2 6 14 3 5 12 4 4 10 5 3 8 6 2 6
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 4 8 2
+--R 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 576
+
+--S 577 of 1393
+r0:=1/3*a^8*x^3+8/5*a^7*b*x^5+4*a^6*b^2*x^7+56/9*a^5*b^3*x^9+_
+ 70/11*a^4*b^4*x^11+56/13*a^3*b^5*x^13+28/15*a^2*b^6*x^15+_
+ 8/17*a*b^7*x^17+1/19*b^8*x^19
+--R
+--R
+--R (2)
+--R 1 8 19 8 7 17 28 2 6 15 56 3 5 13 70 4 4 11 56 5 3 9
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 19 17 15 13 11 9
+--R +
+--R 6 2 7 8 7 5 1 8 3
+--R 4a b x + - a b x + - a x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 577
+
+--S 578 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 19 8 7 17 28 2 6 15 56 3 5 13 70 4 4 11 56 5 3 9
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 19 17 15 13 11 9
+--R +
+--R 6 2 7 8 7 5 1 8 3
+--R 4a b x + - a b x + - a x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 578
+
+--S 579 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 579
+
+--S 580 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 580
+
+)clear all
+
+--S 581 of 1393
+t0:=(a+b*x^2)^8
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R Type: Polynomial(Integer)
+--E 581
+
+--S 582 of 1393
+r0:=a^8*x+8/3*a^7*b*x^3+28/5*a^6*b^2*x^5+8*a^5*b^3*x^7+_
+ 70/9*a^4*b^4*x^9+56/11*a^3*b^5*x^11+28/13*a^2*b^6*x^13+_
+ 8/15*a*b^7*x^15+1/17*b^8*x^17
+--R
+--R
+--R (2)
+--R 1 8 17 8 7 15 28 2 6 13 56 3 5 11 70 4 4 9 5 3 7
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 8a b x
+--R 17 15 13 11 9
+--R +
+--R 28 6 2 5 8 7 3 8
+--R -- a b x + - a b x + a x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 582
+
+--S 583 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 17 8 7 15 28 2 6 13 56 3 5 11 70 4 4 9 5 3 7
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 8a b x
+--R 17 15 13 11 9
+--R +
+--R 28 6 2 5 8 7 3 8
+--R -- a b x + - a b x + a x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 583
+
+--S 584 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 584
+
+--S 585 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 585
+
+)clear all
+
+--S 586 of 1393
+t0:=(a+b*x^2)^8/x^2
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 586
+
+--S 587 of 1393
+r0:=-a^8/x+8*a^7*b*x+28/3*a^6*b^2*x^3+56/5*a^5*b^3*x^5+10*a^4*b^4*x^7+_
+ 56/9*a^3*b^5*x^9+28/11*a^2*b^6*x^11+8/13*a*b^7*x^13+1/15*b^8*x^15
+--R
+--R
+--R (2)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 429b x + 3960a b x + 16380a b x + 40040a b x + 64350a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 72072a b x + 60060a b x + 51480a b x - 6435a
+--R /
+--R 6435x
+--R Type: Fraction(Polynomial(Integer))
+--E 587
+
+--S 588 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 429b x + 3960a b x + 16380a b x + 40040a b x + 64350a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 72072a b x + 60060a b x + 51480a b x - 6435a
+--R /
+--R 6435x
+--R Type: Union(Expression(Integer),...)
+--E 588
+
+--S 589 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 589
+
+--S 590 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 590
+
+)clear all
+
+--S 591 of 1393
+t0:=(a+b*x^2)^8/x^4
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 591
+
+--S 592 of 1393
+r0:=-1/3*a^8/x^3-8*a^7*b/x+28*a^6*b^2*x+56/3*a^5*b^3*x^3+14*a^4*b^4*x^5+_
+ 8*a^3*b^5*x^7+28/9*a^2*b^6*x^9+8/11*a*b^7*x^11+1/13*b^8*x^13
+--R
+--R
+--R (2)
+--R 1 8 16 8 7 14 28 2 6 12 3 5 10 4 4 8 56 5 3 6
+--R -- b x + -- a b x + -- a b x + 8a b x + 14a b x + -- a b x
+--R 13 11 9 3
+--R +
+--R 6 2 4 7 2 1 8
+--R 28a b x - 8a b x - - a
+--R 3
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 592
+
+--S 593 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 99b x + 936a b x + 4004a b x + 10296a b x + 18018a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 24024a b x + 36036a b x - 10296a b x - 429a
+--R /
+--R 3
+--R 1287x
+--R Type: Union(Expression(Integer),...)
+--E 593
+
+--S 594 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 594
+
+--S 595 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 595
+
+)clear all
+
+--S 596 of 1393
+t0:=(a+b*x^2)^8/x^6
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 596
+
+--S 597 of 1393
+r0:=-1/5*a^8/x^5-8/3*a^7*b/x^3-28*a^6*b^2/x+56*a^5*b^3*x+70/3*a^4*b^4*x^3+_
+ 56/5*a^3*b^5*x^5+4*a^2*b^6*x^7+8/9*a*b^7*x^9+1/11*b^8*x^11
+--R
+--R
+--R (2)
+--R 1 8 16 8 7 14 2 6 12 56 3 5 10 70 4 4 8 5 3 6
+--R -- b x + - a b x + 4a b x + -- a b x + -- a b x + 56a b x
+--R 11 9 5 3
+--R +
+--R 6 2 4 8 7 2 1 8
+--R - 28a b x - - a b x - - a
+--R 3 5
+--R /
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 597
+
+--S 598 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 45b x + 440a b x + 1980a b x + 5544a b x + 11550a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 27720a b x - 13860a b x - 1320a b x - 99a
+--R /
+--R 5
+--R 495x
+--R Type: Union(Expression(Integer),...)
+--E 598
+
+--S 599 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 599
+
+--S 600 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 600
+
+)clear all
+
+--S 601 of 1393
+t0:=(a+b*x^2)^8/x^8
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 601
+
+--S 602 of 1393
+r0:=-1/7*a^8/x^7-8/5*a^7*b/x^5-28/3*a^6*b^2/x^3-56*a^5*b^3/x+70*a^4*b^4*x+_
+ 56/3*a^3*b^5*x^3+28/5*a^2*b^6*x^5+8/7*a*b^7*x^7+1/9*b^8*x^9
+--R
+--R
+--R (2)
+--R 1 8 16 8 7 14 28 2 6 12 56 3 5 10 4 4 8 5 3 6
+--R - b x + - a b x + -- a b x + -- a b x + 70a b x - 56a b x
+--R 9 7 5 3
+--R +
+--R 28 6 2 4 8 7 2 1 8
+--R - -- a b x - - a b x - - a
+--R 3 5 7
+--R /
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 602
+
+--S 603 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 35b x + 360a b x + 1764a b x + 5880a b x + 22050a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 17640a b x - 2940a b x - 504a b x - 45a
+--R /
+--R 7
+--R 315x
+--R Type: Union(Expression(Integer),...)
+--E 603
+
+--S 604 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 604
+
+--S 605 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 605
+
+)clear all
+
+--S 606 of 1393
+t0:=(a+b*x^2)^8/x^10
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 606
+
+--S 607 of 1393
+r0:=-1/9*a^8/x^9-8/7*a^7*b/x^7-28/5*a^6*b^2/x^5-56/3*a^5*b^3/x^3-_
+ 70*a^4*b^4/x+56*a^3*b^5*x+28/3*a^2*b^6*x^3+8/5*a*b^7*x^5+1/7*b^8*x^7
+--R
+--R
+--R (2)
+--R 1 8 16 8 7 14 28 2 6 12 3 5 10 4 4 8 56 5 3 6
+--R - b x + - a b x + -- a b x + 56a b x - 70a b x - -- a b x
+--R 7 5 3 3
+--R +
+--R 28 6 2 4 8 7 2 1 8
+--R - -- a b x - - a b x - - a
+--R 5 7 9
+--R /
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 607
+
+--S 608 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 45b x + 504a b x + 2940a b x + 17640a b x - 22050a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 5880a b x - 1764a b x - 360a b x - 35a
+--R /
+--R 9
+--R 315x
+--R Type: Union(Expression(Integer),...)
+--E 608
+
+--S 609 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 609
+
+--S 610 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 610
+
+)clear all
+
+--S 611 of 1393
+t0:=(a+b*x^2)^8/x^12
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 12
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 611
+
+--S 612 of 1393
+r0:=-1/11*a^8/x^11-8/9*a^7*b/x^9-4*a^6*b^2/x^7-56/5*a^5*b^3/x^5-_
+ 70/3*a^4*b^4/x^3-56*a^3*b^5/x+28*a^2*b^6*x+8/3*a*b^7*x^3+1/5*b^8*x^5
+--R
+--R
+--R (2)
+--R 1 8 16 8 7 14 2 6 12 3 5 10 70 4 4 8 56 5 3 6
+--R - b x + - a b x + 28a b x - 56a b x - -- a b x - -- a b x
+--R 5 3 3 5
+--R +
+--R 6 2 4 8 7 2 1 8
+--R - 4a b x - - a b x - -- a
+--R 9 11
+--R /
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 612
+
+--S 613 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 99b x + 1320a b x + 13860a b x - 27720a b x - 11550a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 5544a b x - 1980a b x - 440a b x - 45a
+--R /
+--R 11
+--R 495x
+--R Type: Union(Expression(Integer),...)
+--E 613
+
+--S 614 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 614
+
+--S 615 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 615
+
+)clear all
+
+--S 616 of 1393
+t0:=(a+b*x^2)^8/x^14
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 14
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 616
+
+--S 617 of 1393
+r0:=-1/13*a^8/x^13-8/11*a^7*b/x^11-28/9*a^6*b^2/x^9-8*a^5*b^3/x^7-_
+ 14*a^4*b^4/x^5-56/3*a^3*b^5/x^3-28*a^2*b^6/x+8*a*b^7*x+1/3*b^8*x^3
+--R
+--R
+--R (2)
+--R 1 8 16 7 14 2 6 12 56 3 5 10 4 4 8 5 3 6
+--R - b x + 8a b x - 28a b x - -- a b x - 14a b x - 8a b x
+--R 3 3
+--R +
+--R 28 6 2 4 8 7 2 1 8
+--R - -- a b x - -- a b x - -- a
+--R 9 11 13
+--R /
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 617
+
+--S 618 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 429b x + 10296a b x - 36036a b x - 24024a b x - 18018a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 10296a b x - 4004a b x - 936a b x - 99a
+--R /
+--R 13
+--R 1287x
+--R Type: Union(Expression(Integer),...)
+--E 618
+
+--S 619 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 619
+
+--S 620 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 620
+
+)clear all
+
+--S 621 of 1393
+t0:=(a+b*x^2)^8/x^16
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 16
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 621
+
+--S 622 of 1393
+r0:=-1/15*a^8/x^15-8/13*a^7*b/x^13-28/11*a^6*b^2/x^11-56/9*a^5*b^3/x^9-_
+ 10*a^4*b^4/x^7-56/5*a^3*b^5/x^5-28/3*a^2*b^6/x^3-8*a*b^7/x+b^8*x
+--R
+--R
+--R (2)
+--R 8 16 7 14 28 2 6 12 56 3 5 10 4 4 8 56 5 3 6
+--R b x - 8a b x - -- a b x - -- a b x - 10a b x - -- a b x
+--R 3 5 9
+--R +
+--R 28 6 2 4 8 7 2 1 8
+--R - -- a b x - -- a b x - -- a
+--R 11 13 15
+--R /
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 622
+
+--S 623 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 6435b x - 51480a b x - 60060a b x - 72072a b x - 64350a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 40040a b x - 16380a b x - 3960a b x - 429a
+--R /
+--R 15
+--R 6435x
+--R Type: Union(Expression(Integer),...)
+--E 623
+
+--S 624 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 624
+
+--S 625 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 625
+
+)clear all
+
+--S 626 of 1393
+t0:=(a+b*x^2)^8/x^18
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 18
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 626
+
+--S 627 of 1393
+r0:=-1/17*a^8/x^17-8/15*a^7*b/x^15-28/13*a^6*b^2/x^13-56/11*a^5*b^3/x^11-_
+ 70/9*a^4*b^4/x^9-8*a^3*b^5/x^7-28/5*a^2*b^6/x^5-8/3*a*b^7/x^3-b^8/x
+--R
+--R
+--R (2)
+--R 8 16 8 7 14 28 2 6 12 3 5 10 70 4 4 8 56 5 3 6
+--R - b x - - a b x - -- a b x - 8a b x - -- a b x - -- a b x
+--R 3 5 9 11
+--R +
+--R 28 6 2 4 8 7 2 1 8
+--R - -- a b x - -- a b x - -- a
+--R 13 15 17
+--R /
+--R 17
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 627
+
+--S 628 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10
+--R - 109395b x - 291720a b x - 612612a b x - 875160a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R - 850850a b x - 556920a b x - 235620a b x - 58344a b x - 6435a
+--R /
+--R 17
+--R 109395x
+--R Type: Union(Expression(Integer),...)
+--E 628
+
+--S 629 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 629
+
+--S 630 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 630
+
+)clear all
+
+--S 631 of 1393
+t0:=(a+b*x^2)^8/x^20
+--R
+--R
+--R (1)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 2 8
+--R 8a b x + a
+--R /
+--R 20
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 631
+
+--S 632 of 1393
+r0:=-1/19*a^8/x^19-8/17*a^7*b/x^17-28/15*a^6*b^2/x^15-56/13*a^5*b^3/x^13-_
+ 70/11*a^4*b^4/x^11-56/9*a^3*b^5/x^9-4*a^2*b^6/x^7-_
+ 8/5*a*b^7/x^5-1/3*b^8/x^3
+--R
+--R
+--R (2)
+--R 1 8 16 8 7 14 2 6 12 56 3 5 10 70 4 4 8 56 5 3 6
+--R - - b x - - a b x - 4a b x - -- a b x - -- a b x - -- a b x
+--R 3 5 9 11 13
+--R +
+--R 28 6 2 4 8 7 2 1 8
+--R - -- a b x - -- a b x - -- a
+--R 15 17 19
+--R /
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 632
+
+--S 633 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10
+--R - 692835b x - 3325608a b x - 8314020a b x - 12932920a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R - 13226850a b x - 8953560a b x - 3879876a b x - 978120a b x - 109395a
+--R /
+--R 19
+--R 2078505x
+--R Type: Union(Expression(Integer),...)
+--E 633
+
+--S 634 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 634
+
+--S 635 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 635
+
+)clear all
+
+--S 636 of 1393
+t0:=x^m/(a+b*x^2)
+--R
+--R
+--R m
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 636
+
+--S 637 of 1393
+--r0:=x^(1+m)*hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a*(1+m))
+--E 637
+
+--S 638 of 1393
+--a0:=integrate(t0,x)
+--E 638
+
+--S 639 of 1393
+--m0:=a0-r0
+--E 639
+
+--S 640 of 1393
+--d0:=D(m0,x)
+--E 640
+
+)clear all
+
+--S 641 of 1393
+t0:=x^11/(a+b*x^2)
+--R
+--R
+--R 11
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 641
+
+--S 642 of 1393
+r0:=1/2*a^4*x^2/b^5-1/4*a^3*x^4/b^4+1/6*a^2*x^6/b^3-1/8*a*x^8/b^2+_
+ 1/10*x^10/b-1/2*a^5*log(a+b*x^2)/b^6
+--R
+--R
+--R (2)
+--R 5 2 5 10 4 8 2 3 6 3 2 4 4 2
+--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x
+--R -------------------------------------------------------------------------
+--R 6
+--R 120b
+--R Type: Expression(Integer)
+--E 642
+
+--S 643 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 5 10 4 8 2 3 6 3 2 4 4 2
+--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x
+--R -------------------------------------------------------------------------
+--R 6
+--R 120b
+--R Type: Union(Expression(Integer),...)
+--E 643
+
+--S 644 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 644
+
+--S 645 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 645
+
+)clear all
+
+--S 646 of 1393
+t0:=x^10/(a+b*x^2)
+--R
+--R
+--R 10
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 646
+
+--S 647 of 1393
+r0:=a^4*x/b^5-1/3*a^3*x^3/b^4+1/5*a^2*x^5/b^3-1/7*a*x^7/b^2+_
+ 1/9*x^9/b-a^(9/2)*atan(x*sqrt(b)/sqrt(a))/b^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 +-+ x\|b
+--R - 315a \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (35b x - 45a b x + 63a b x - 105a b x + 315a x)\|b
+--R /
+--R 5 +-+
+--R 315b \|b
+--R Type: Expression(Integer)
+--E 647
+
+--S 648 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 4 | a \| b 4 9 3 7 2 2 5
+--R 315a |- - log(-----------------------) + 70b x - 90a b x + 126a b x
+--R \| b 2
+--R b x + a
+--R +
+--R 3 3 4
+--R - 210a b x + 630a x
+--R /
+--R 5
+--R 630b
+--R ,
+--R +-+
+--R |a
+--R +-+ |-
+--R 4 |a \|b 4 9 3 7 2 2 5 3 3 4
+--R 315a |- atan(----) + 35b x - 45a b x + 63a b x - 105a b x + 315a x
+--R \|b x
+--R -----------------------------------------------------------------------]
+--R 5
+--R 315b
+--R Type: Union(List(Expression(Integer)),...)
+--E 648
+
+--S 649 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R 4 | a +-+ \| b 4 +-+ x\|b
+--R a |- - \|b log(-----------------------) + 2a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) -------------------------------------------------------------
+--R 5 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 649
+
+--S 650 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 650
+
+--S 651 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 4 +-+ x\|b 4 |a +-+ \|b
+--R a \|a atan(-----) + a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------
+--R 5 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 651
+
+--S 652 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 652
+
+)clear all
+
+--S 653 of 1393
+t0:=x^9/(a+b*x^2)
+--R
+--R
+--R 9
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 653
+
+--S 654 of 1393
+r0:=-1/2*a^3*x^2/b^4+1/4*a^2*x^4/b^3-1/6*a*x^6/b^2+1/8*x^8/b+_
+ 1/2*a^4*log(a+b*x^2)/b^5
+--R
+--R
+--R 4 2 4 8 3 6 2 2 4 3 2
+--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x
+--R (2) --------------------------------------------------------
+--R 5
+--R 24b
+--R Type: Expression(Integer)
+--E 654
+
+--S 655 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2 4 8 3 6 2 2 4 3 2
+--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x
+--R (3) --------------------------------------------------------
+--R 5
+--R 24b
+--R Type: Union(Expression(Integer),...)
+--E 655
+
+--S 656 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 656
+
+--S 657 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 657
+
+)clear all
+
+--S 658 of 1393
+t0:=x^8/(a+b*x^2)
+--R
+--R
+--R 8
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 658
+
+--S 659 of 1393
+r0:=-a^3*x/b^4+1/3*a^2*x^3/b^3-1/5*a*x^5/b^2+1/7*x^7/b+_
+ a^(7/2)*atan(x*sqrt(b)/sqrt(a))/b^(9/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|b 3 7 2 5 2 3 3 +-+
+--R 105a \|a atan(-----) + (15b x - 21a b x + 35a b x - 105a x)\|b
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------------------
+--R 4 +-+
+--R 105b \|b
+--R Type: Expression(Integer)
+--E 659
+
+--S 660 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 3 | a \| b 3 7 2 5 2 3
+--R 105a |- - log(---------------------) + 30b x - 42a b x + 70a b x
+--R \| b 2
+--R b x + a
+--R +
+--R 3
+--R - 210a x
+--R /
+--R 4
+--R 210b
+--R ,
+--R +-+
+--R |a
+--R +-+ |-
+--R 3 |a \|b 3 7 2 5 2 3 3
+--R - 105a |- atan(----) + 15b x - 21a b x + 35a b x - 105a x
+--R \|b x
+--R -------------------------------------------------------------]
+--R 4
+--R 105b
+--R Type: Union(List(Expression(Integer)),...)
+--E 660
+
+--S 661 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a +-+
+--R 3 | a +-+ \| b 3 +-+ x\|b
+--R a |- - \|b log(---------------------) - 2a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 662
+
+--S 663 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 3 +-+ x\|b 3 |a +-+ \|b
+--R - a \|a atan(-----) - a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ------------------------------------------
+--R 4 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 664
+
+)clear all
+
+--S 665 of 1393
+t0:=x^7/(a+b*x^2)
+--R
+--R
+--R 7
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 665
+
+--S 666 of 1393
+r0:=1/2*a^2*x^2/b^3-1/4*a*x^4/b^2+1/6*x^6/b-1/2*a^3*log(a+b*x^2)/b^4
+--R
+--R
+--R 3 2 3 6 2 4 2 2
+--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x
+--R (2) ----------------------------------------------
+--R 4
+--R 12b
+--R Type: Expression(Integer)
+--E 666
+
+--S 667 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 3 6 2 4 2 2
+--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x
+--R (3) ----------------------------------------------
+--R 4
+--R 12b
+--R Type: Union(Expression(Integer),...)
+--E 667
+
+--S 668 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 669
+
+)clear all
+
+--S 670 of 1393
+t0:=x^6/(a+b*x^2)
+--R
+--R
+--R 6
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 670
+
+--S 671 of 1393
+r0:=a^2*x/b^3-1/3*a*x^3/b^2+1/5*x^5/b-a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(7/2)
+--R
+--R
+--R +-+
+--R 2 +-+ x\|b 2 5 3 2 +-+
+--R - 15a \|a atan(-----) + (3b x - 5a b x + 15a x)\|b
+--R +-+
+--R \|a
+--R (2) -----------------------------------------------------
+--R 3 +-+
+--R 15b \|b
+--R Type: Expression(Integer)
+--E 671
+
+--S 672 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 | a \| b 2 5 3 2
+--R 15a |- - log(-----------------------) + 6b x - 10a b x + 30a x
+--R \| b 2
+--R b x + a
+--R [-----------------------------------------------------------------,
+--R 3
+--R 30b
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 |a \|b 2 5 3 2
+--R 15a |- atan(----) + 3b x - 5a b x + 15a x
+--R \|b x
+--R --------------------------------------------]
+--R 3
+--R 15b
+--R Type: Union(List(Expression(Integer)),...)
+--E 672
+
+--S 673 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R 2 | a +-+ \| b 2 +-+ x\|b
+--R a |- - \|b log(-----------------------) + 2a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) -------------------------------------------------------------
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 674
+
+--S 675 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R a \|a atan(-----) + a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------
+--R 3 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 675
+
+--S 676 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 676
+
+)clear all
+
+--S 677 of 1393
+t0:=x^5/(a+b*x^2)
+--R
+--R
+--R 5
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 677
+
+--S 678 of 1393
+r0:=-1/2*a*x^2/b^2+1/4*x^4/b+1/2*a^2*log(a+b*x^2)/b^3
+--R
+--R
+--R 2 2 2 4 2
+--R 2a log(b x + a) + b x - 2a b x
+--R (2) ---------------------------------
+--R 3
+--R 4b
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 4 2
+--R 2a log(b x + a) + b x - 2a b x
+--R (3) ---------------------------------
+--R 3
+--R 4b
+--R Type: Union(Expression(Integer),...)
+--E 679
+
+--S 680 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 680
+
+--S 681 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 681
+
+)clear all
+
+--S 682 of 1393
+t0:=x^4/(a+b*x^2)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 682
+
+--S 683 of 1393
+r0:=-a*x/b^2+1/3*x^3/b+a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(5/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b 3 +-+
+--R 3a\|a atan(-----) + (b x - 3a x)\|b
+--R +-+
+--R \|a
+--R (2) -------------------------------------
+--R 2 +-+
+--R 3b \|b
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a \| b 3
+--R 3a |- - log(---------------------) + 2b x - 6a x
+--R \| b 2
+--R b x + a
+--R [-------------------------------------------------,
+--R 2
+--R 6b
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b 3
+--R - 3a |- atan(----) + b x - 3a x
+--R \|b x
+--R --------------------------------]
+--R 2
+--R 3b
+--R Type: Union(List(Expression(Integer)),...)
+--E 684
+
+--S 685 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a +-+
+--R | a +-+ \| b +-+ x\|b
+--R a |- - \|b log(---------------------) - 2a\|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 685
+
+--S 686 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 686
+
+--S 687 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R - a\|a atan(-----) - a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------
+--R 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 687
+
+--S 688 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 688
+
+)clear all
+
+--S 689 of 1393
+t0:=x^3/(a+b*x^2)
+--R
+--R
+--R 3
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 689
+
+--S 690 of 1393
+r0:=1/2*x^2/b-1/2*a*log(a+b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R - a log(b x + a) + b x
+--R (2) ------------------------
+--R 2
+--R 2b
+--R Type: Expression(Integer)
+--E 690
+
+--S 691 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R - a log(b x + a) + b x
+--R (3) ------------------------
+--R 2
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 691
+
+--S 692 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 692
+
+--S 693 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 693
+
+)clear all
+
+--S 694 of 1393
+t0:=x^2/(a+b*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 694
+
+--S 695 of 1393
+r0:=x/b-atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b +-+
+--R - \|a atan(-----) + x\|b
+--R +-+
+--R \|a
+--R (2) -------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 695
+
+--S 696 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+
+--R | a 2 +-+
+--R +---+ - 2b x |- - + b x - a |a
+--R | a \| b +-+ |-
+--R |- - log(-----------------------) + 2x |a \|b
+--R \| b 2 |- atan(----) + x
+--R b x + a \|b x
+--R (3) [---------------------------------------,------------------]
+--R 2b b
+--R Type: Union(List(Expression(Integer)),...)
+--E 696
+
+--S 697 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R | a +-+ \| b +-+ x\|b
+--R |- - \|b log(-----------------------) + 2\|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 697
+
+--S 698 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R \|a atan(-----) + |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ------------------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 699
+
+--S 700 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 700
+
+)clear all
+
+--S 701 of 1393
+t0:=x/(a+b*x^2)
+--R
+--R
+--R x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 701
+
+--S 702 of 1393
+r0:=1/2*log(a+b*x^2)/b
+--R
+--R
+--R 2
+--R log(b x + a)
+--R (2) -------------
+--R 2b
+--R Type: Expression(Integer)
+--E 702
+
+--S 703 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R log(b x + a)
+--R (3) -------------
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 703
+
+--S 704 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 704
+
+--S 705 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 705
+
+)clear all
+
+--S 706 of 1393
+t0:=1/(a+b*x^2)
+--R
+--R
+--R 1
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 706
+
+--S 707 of 1393
+r0:=atan(x*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b))
+--R
+--R
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R (2) -----------
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x +---+
+--R log(---------------------------) x\|a b
+--R 2 atan(-------)
+--R b x + a a
+--R (3) [--------------------------------,-------------]
+--R +-----+ +---+
+--R 2\|- a b \|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 708
+
+--S 709 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R \|a \|b log(---------------------------) - 2\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 2\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 709
+
+--S 710 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 710
+
+--S 711 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R \|a \|b atan(-------) - \|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------
+--R +-+ +-+ +---+
+--R \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 712
+
+)clear all
+
+--S 713 of 1393
+t0:=1/(x*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) ----------
+--R 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 713
+
+--S 714 of 1393
+r0:=log(x)/a-1/2*log(a+b*x^2)/a
+--R
+--R
+--R 2
+--R - log(b x + a) + 2log(x)
+--R (2) -------------------------
+--R 2a
+--R Type: Expression(Integer)
+--E 714
+
+--S 715 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - log(b x + a) + 2log(x)
+--R (3) -------------------------
+--R 2a
+--R Type: Union(Expression(Integer),...)
+--E 715
+
+--S 716 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 717
+
+)clear all
+
+--S 718 of 1393
+t0:=1/(x^2*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 4 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 718
+
+--S 719 of 1393
+r0:=(-1)/(a*x)-atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b +-+
+--R - x\|b atan(-----) - \|a
+--R +-+
+--R \|a
+--R (2) -------------------------
+--R +-+
+--R a x\|a
+--R Type: Expression(Integer)
+--E 719
+
+--S 720 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+
+--R | b 2 +-+
+--R +---+ - 2a x |- - + b x - a |b
+--R | b \| a +-+ a |-
+--R x |- - log(-----------------------) - 2 |b \|a
+--R \| a 2 x |- atan(-----) - 1
+--R b x + a \|a b x
+--R (3) [---------------------------------------,--------------------]
+--R 2a x a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 720
+
+--S 721 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R |- - \|a log(-----------------------) + 2\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 721
+
+--S 722 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 722
+
+--S 723 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R \|b atan(-----) + \|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -------------------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 724
+
+)clear all
+
+--S 725 of 1393
+t0:=1/(x^3*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 5 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 725
+
+--S 726 of 1393
+r0:=(-1/2)/(a*x^2)-b*log(x)/a^2+1/2*b*log(a+b*x^2)/a^2
+--R
+--R
+--R 2 2 2
+--R b x log(b x + a) - 2b x log(x) - a
+--R (2) -----------------------------------
+--R 2 2
+--R 2a x
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R b x log(b x + a) - 2b x log(x) - a
+--R (3) -----------------------------------
+--R 2 2
+--R 2a x
+--R Type: Union(Expression(Integer),...)
+--E 727
+
+--S 728 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 729
+
+)clear all
+
+--S 730 of 1393
+t0:=1/(x^4*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 6 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 730
+
+--S 731 of 1393
+r0:=(-1/3)/(a*x^3)+b/(a^2*x)+b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(5/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|b 2 +-+
+--R 3b x \|b atan(-----) + (3b x - a)\|a
+--R +-+
+--R \|a
+--R (2) --------------------------------------
+--R 2 3 +-+
+--R 3a x \|a
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 | b \| a 2
+--R 3b x |- - log(---------------------) + 6b x - 2a
+--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 - 3b x |- atan(-----) + 3b x - a
+--R \|a b x
+--R ----------------------------------]
+--R 2 3
+--R 3a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 732
+
+--S 733 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R b |- - \|a log(---------------------) - 2b\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 734
+
+--S 735 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R - b\|b atan(-----) - b\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -----------------------------------------
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 735
+
+--S 736 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 736
+
+)clear all
+
+--S 737 of 1393
+t0:=1/(x^5*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 7 5
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 737
+
+--S 738 of 1393
+r0:=(-1/4)/(a*x^4)+1/2*b/(a^2*x^2)+b^2*log(x)/a^3-1/2*b^2*log(a+b*x^2)/a^3
+--R
+--R
+--R 2 4 2 2 4 2 2
+--R - 2b x log(b x + a) + 4b x log(x) + 2a b x - a
+--R (2) -------------------------------------------------
+--R 3 4
+--R 4a x
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2 4 2 2
+--R - 2b x log(b x + a) + 4b x log(x) + 2a b x - a
+--R (3) -------------------------------------------------
+--R 3 4
+--R 4a x
+--R Type: Union(Expression(Integer),...)
+--E 739
+
+--S 740 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 740
+
+--S 741 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 741
+
+)clear all
+
+--S 742 of 1393
+t0:=1/(x^6*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 8 6
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 742
+
+--S 743 of 1393
+r0:=(-1/5)/(a*x^5)+1/3*b/(a^2*x^3)-b^2/(a^3*x)-_
+ b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(7/2)
+--R
+--R
+--R +-+
+--R 2 5 +-+ x\|b 2 4 2 2 +-+
+--R - 15b x \|b atan(-----) + (- 15b x + 5a b x - 3a )\|a
+--R +-+
+--R \|a
+--R (2) --------------------------------------------------------
+--R 3 5 +-+
+--R 15a x \|a
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 5 | b \| a 2 4 2 2
+--R 15b x |- - log(-----------------------) - 30b x + 10a b x - 6a
+--R \| a 2
+--R b x + a
+--R [------------------------------------------------------------------,
+--R 3 5
+--R 30a x
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 5 |b \|a 2 4 2 2
+--R 15b x |- atan(-----) - 15b x + 5a b x - 3a
+--R \|a b x
+--R ----------------------------------------------]
+--R 3 5
+--R 15a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 744
+
+--S 745 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R 2 | b +-+ \| a 2 +-+ x\|b
+--R b |- - \|a log(-----------------------) + 2b \|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) -------------------------------------------------------------
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 745
+
+--S 746 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 746
+
+--S 747 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 2 +-+ x\|b 2 +-+ |b \|a
+--R b \|b atan(-----) + b \|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -----------------------------------------
+--R 3 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 747
+
+--S 748 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 748
+
+)clear all
+
+--S 749 of 1393
+t0:=1/(x^7*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 9 7
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 749
+
+--S 750 of 1393
+r0:=(-1/6)/(a*x^6)+1/4*b/(a^2*x^4)-1/2*b^2/(a^3*x^2)-b^3*log(x)/a^4+_
+ 1/2*b^3*log(a+b*x^2)/a^4
+--R
+--R
+--R 3 6 2 3 6 2 4 2 2 3
+--R 6b x log(b x + a) - 12b x log(x) - 6a b x + 3a b x - 2a
+--R (2) -----------------------------------------------------------
+--R 4 6
+--R 12a x
+--R Type: Expression(Integer)
+--E 750
+
+--S 751 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 3 6 2 4 2 2 3
+--R 6b x log(b x + a) - 12b x log(x) - 6a b x + 3a b x - 2a
+--R (3) -----------------------------------------------------------
+--R 4 6
+--R 12a x
+--R Type: Union(Expression(Integer),...)
+--E 751
+
+--S 752 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 752
+
+--S 753 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 753
+
+)clear all
+
+--S 754 of 1393
+t0:=1/(x^8*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 10 8
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 754
+
+--S 755 of 1393
+r0:=(-1/7)/(a*x^7)+1/5*b/(a^2*x^5)-1/3*b^2/(a^3*x^3)+_
+ b^3/(a^4*x)+b^(7/2)*atan(x*sqrt(b)/sqrt(a))/a^(9/2)
+--R
+--R
+--R +-+
+--R 3 7 +-+ x\|b 3 6 2 4 2 2 3 +-+
+--R 105b x \|b atan(-----) + (105b x - 35a b x + 21a b x - 15a )\|a
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------------
+--R 4 7 +-+
+--R 105a x \|a
+--R Type: Expression(Integer)
+--E 755
+
+--S 756 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 7 | b \| a 3 6 2 4 2 2
+--R 105b x |- - log(---------------------) + 210b x - 70a b x + 42a b x
+--R \| a 2
+--R b x + a
+--R +
+--R 3
+--R - 30a
+--R /
+--R 4 7
+--R 210a x
+--R ,
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 7 |b \|a 3 6 2 4 2 2 3
+--R - 105b x |- atan(-----) + 105b x - 35a b x + 21a b x - 15a
+--R \|a b x
+--R ---------------------------------------------------------------]
+--R 4 7
+--R 105a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 756
+
+--S 757 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a +-+
+--R 3 | b +-+ \| a 3 +-+ x\|b
+--R b |- - \|a log(---------------------) - 2b \|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R 4 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 757
+
+--S 758 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 758
+
+--S 759 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 3 +-+ x\|b 3 +-+ |b \|a
+--R - b \|b atan(-----) - b \|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -------------------------------------------
+--R 4 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 759
+
+--S 760 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 760
+
+)clear all
+
+--S 761 of 1393
+t0:=1/(x^9*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 11 9
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 761
+
+--S 762 of 1393
+r0:=(-1/8)/(a*x^8)+1/6*b/(a^2*x^6)-1/4*b^2/(a^3*x^4)+1/2*b^3/(a^4*x^2)+_
+ b^4*log(x)/a^5-1/2*b^4*log(a+b*x^2)/a^5
+--R
+--R
+--R (2)
+--R 4 8 2 4 8 3 6 2 2 4 3 2 4
+--R - 12b x log(b x + a) + 24b x log(x) + 12a b x - 6a b x + 4a b x - 3a
+--R -------------------------------------------------------------------------
+--R 5 8
+--R 24a x
+--R Type: Expression(Integer)
+--E 762
+
+--S 763 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 8 2 4 8 3 6 2 2 4 3 2 4
+--R - 12b x log(b x + a) + 24b x log(x) + 12a b x - 6a b x + 4a b x - 3a
+--R -------------------------------------------------------------------------
+--R 5 8
+--R 24a x
+--R Type: Union(Expression(Integer),...)
+--E 763
+
+--S 764 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 764
+
+--S 765 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 765
+
+)clear all
+
+--S 766 of 1393
+t0:=x^m/(a+b*x^2)^2
+--R
+--R
+--R m
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 766
+
+--S 767 of 1393
+--r0:=1/2*x^(1+m)/(a*(a+b*x^2))+1/2*(1-m)*x^(1+m)*_
+-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a^2*(1+m))
+--E 767
+
+--S 768 of 1393
+--a0:=integrate(t0,x)
+--E 768
+
+--S 769 of 1393
+--m0:=a0-r0
+--E 769
+
+--S 770 of 1393
+--d0:=D(m0,x)
+--E 770
+
+)clear all
+
+--S 771 of 1393
+t0:=x^13/(a+b*x^2)^2
+--R
+--R
+--R 13
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 771
+
+--S 772 of 1393
+r0:=5/2*a^4*x^2/b^6-a^3*x^4/b^5+1/2*a^2*x^6/b^4-1/4*a*x^8/b^3+_
+ 1/10*x^10/b^2-1/2*a^6/(b^7*(a+b*x^2))-3*a^5*log(a+b*x^2)/b^7
+--R
+--R
+--R (2)
+--R 5 2 6 2 6 12 5 10 2 4 8 3 3 6
+--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x
+--R +
+--R 4 2 4 5 2 6
+--R 30a b x + 50a b x - 10a
+--R /
+--R 8 2 7
+--R 20b x + 20a b
+--R Type: Expression(Integer)
+--E 772
+
+--S 773 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 6 2 6 12 5 10 2 4 8 3 3 6
+--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x
+--R +
+--R 4 2 4 5 2 6
+--R 30a b x + 50a b x - 10a
+--R /
+--R 8 2 7
+--R 20b x + 20a b
+--R Type: Union(Expression(Integer),...)
+--E 773
+
+--S 774 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 774
+
+--S 775 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 775
+
+)clear all
+
+--S 776 of 1393
+t0:=x^12/(a+b*x^2)^2
+--R
+--R
+--R 12
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 776
+
+--S 777 of 1393
+r0:=11/2*a^4*x/b^6-11/6*a^3*x^3/b^5+11/10*a^2*x^5/b^4-11/14*a*x^7/b^3+_
+ 11/18*x^9/b^2-1/2*x^11/(b*(a+b*x^2))-_
+ 11/2*a^(9/2)*atan(x*sqrt(b)/sqrt(a))/b^(13/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 2 5 +-+ x\|b
+--R (- 3465a b x - 3465a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+
+--R (70b x - 110a b x + 198a b x - 462a b x + 2310a b x + 3465a x)\|b
+--R /
+--R 7 2 6 +-+
+--R (630b x + 630a b )\|b
+--R Type: Expression(Integer)
+--E 777
+
+--S 778 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 4 2 5 | a \| b 5 11
+--R (3465a b x + 3465a ) |- - log(-----------------------) + 140b x
+--R \| b 2
+--R b x + a
+--R +
+--R 4 9 2 3 7 3 2 5 4 3 5
+--R - 220a b x + 396a b x - 924a b x + 4620a b x + 6930a x
+--R /
+--R 7 2 6
+--R 1260b x + 1260a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 4 2 5 |a \|b 5 11 4 9 2 3 7
+--R (3465a b x + 3465a ) |- atan(----) + 70b x - 110a b x + 198a b x
+--R \|b x
+--R +
+--R 3 2 5 4 3 5
+--R - 462a b x + 2310a b x + 3465a x
+--R /
+--R 7 2 6
+--R 630b x + 630a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 778
+
+--S 779 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R 4 | a +-+ \| b 4 +-+ x\|b
+--R 11a |- - \|b log(-----------------------) + 22a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ----------------------------------------------------------------
+--R 6 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 779
+
+--S 780 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 780
+
+--S 781 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 4 +-+ x\|b 4 |a +-+ \|b
+--R 11a \|a atan(-----) + 11a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------
+--R 6 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 781
+
+--S 782 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 782
+
+)clear all
+
+--S 783 of 1393
+t0:=x^11/(a+b*x^2)^2
+--R
+--R
+--R 11
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 783
+
+--S 784 of 1393
+r0:=-2*a^3*x^2/b^5+3/4*a^2*x^4/b^4-1/3*a*x^6/b^3+1/8*x^8/b^2+_
+ 1/2*a^5/(b^6*(a+b*x^2))+5/2*a^4*log(a+b*x^2)/b^6
+--R
+--R
+--R (2)
+--R 4 2 5 2 5 10 4 8 2 3 6 3 2 4
+--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x
+--R +
+--R 4 2 5
+--R - 48a b x + 12a
+--R /
+--R 7 2 6
+--R 24b x + 24a b
+--R Type: Expression(Integer)
+--E 784
+
+--S 785 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 5 2 5 10 4 8 2 3 6 3 2 4
+--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x
+--R +
+--R 4 2 5
+--R - 48a b x + 12a
+--R /
+--R 7 2 6
+--R 24b x + 24a b
+--R Type: Union(Expression(Integer),...)
+--E 785
+
+--S 786 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 786
+
+--S 787 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 787
+
+)clear all
+
+--S 788 of 1393
+t0:=x^10/(a+b*x^2)^2
+--R
+--R
+--R 10
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 788
+
+--S 789 of 1393
+r0:=-9/2*a^3*x/b^5+3/2*a^2*x^3/b^4-9/10*a*x^5/b^3+9/14*x^7/b^2-_
+ 1/2*x^9/(b*(a+b*x^2))+9/2*a^(7/2)*atan(x*sqrt(b)/sqrt(a))/b^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 4 +-+ x\|b
+--R (315a b x + 315a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (10b x - 18a b x + 42a b x - 210a b x - 315a x)\|b
+--R /
+--R 6 2 5 +-+
+--R (70b x + 70a b )\|b
+--R Type: Expression(Integer)
+--E 789
+
+--S 790 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 3 2 4 | a \| b 4 9 3 7
+--R (315a b x + 315a ) |- - log(---------------------) + 20b x - 36a b x
+--R \| b 2
+--R b x + a
+--R +
+--R 2 2 5 3 3 4
+--R 84a b x - 420a b x - 630a x
+--R /
+--R 6 2 5
+--R 140b x + 140a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 3 2 4 |a \|b 4 9 3 7 2 2 5
+--R (- 315a b x - 315a ) |- atan(----) + 10b x - 18a b x + 42a b x
+--R \|b x
+--R +
+--R 3 3 4
+--R - 210a b x - 315a x
+--R /
+--R 6 2 5
+--R 70b x + 70a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 790
+
+--S 791 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a +-+
+--R 3 | a +-+ \| b 3 +-+ x\|b
+--R 9a |- - \|b log(---------------------) - 18a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) -------------------------------------------------------------
+--R 5 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 791
+
+--S 792 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 792
+
+--S 793 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 3 +-+ x\|b 3 |a +-+ \|b
+--R - 9a \|a atan(-----) - 9a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------
+--R 5 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 793
+
+--S 794 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 794
+
+)clear all
+
+--S 795 of 1393
+t0:=x^9/(a+b*x^2)^2
+--R
+--R
+--R 9
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 795
+
+--S 796 of 1393
+r0:=3/2*a^2*x^2/b^4-1/2*a*x^4/b^3+1/6*x^6/b^2-1/2*a^4/(b^5*(a+b*x^2))-_
+ 2*a^3*log(a+b*x^2)/b^5
+--R
+--R
+--R (2)
+--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4
+--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a
+--R ---------------------------------------------------------------------------
+--R 6 2 5
+--R 6b x + 6a b
+--R Type: Expression(Integer)
+--E 796
+
+--S 797 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4
+--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a
+--R ---------------------------------------------------------------------------
+--R 6 2 5
+--R 6b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 797
+
+--S 798 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 798
+
+--S 799 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 799
+
+)clear all
+
+--S 800 of 1393
+t0:=x^8/(a+b*x^2)^2
+--R
+--R
+--R 8
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 800
+
+--S 801 of 1393
+r0:=7/2*a^2*x/b^4-7/6*a*x^3/b^3+7/10*x^5/b^2-1/2*x^7/(b*(a+b*x^2))-_
+ 7/2*a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 3 +-+ x\|b
+--R (- 105a b x - 105a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (6b x - 14a b x + 70a b x + 105a x)\|b
+--R /
+--R 5 2 4 +-+
+--R (30b x + 30a b )\|b
+--R Type: Expression(Integer)
+--E 801
+
+--S 802 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 2 3 | a \| b 3 7
+--R (105a b x + 105a ) |- - log(-----------------------) + 12b x
+--R \| b 2
+--R b x + a
+--R +
+--R 2 5 2 3 3
+--R - 28a b x + 140a b x + 210a x
+--R /
+--R 5 2 4
+--R 60b x + 60a b
+--R ,
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 3 |a \|b 3 7 2 5 2 3 3
+--R (105a b x + 105a ) |- atan(----) + 6b x - 14a b x + 70a b x + 105a x
+--R \|b x
+--R ------------------------------------------------------------------------]
+--R 5 2 4
+--R 30b x + 30a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 802
+
+--S 803 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R 2 | a +-+ \| b 2 +-+ x\|b
+--R 7a |- - \|b log(-----------------------) + 14a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------
+--R 4 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 803
+
+--S 804 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 804
+
+--S 805 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R 7a \|a atan(-----) + 7a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ------------------------------------------
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 805
+
+--S 806 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 806
+
+)clear all
+
+--S 807 of 1393
+t0:=x^7/(a+b*x^2)^2
+--R
+--R
+--R 7
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 807
+
+--S 808 of 1393
+r0:=-a*x^2/b^3+1/4*x^4/b^2+1/2*a^3/(b^4*(a+b*x^2))+3/2*a^2*log(a+b*x^2)/b^4
+--R
+--R
+--R 2 2 3 2 3 6 2 4 2 2 3
+--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a
+--R (2) -------------------------------------------------------------
+--R 5 2 4
+--R 4b x + 4a b
+--R Type: Expression(Integer)
+--E 808
+
+--S 809 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 3 2 3 6 2 4 2 2 3
+--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a
+--R (3) -------------------------------------------------------------
+--R 5 2 4
+--R 4b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 809
+
+--S 810 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 810
+
+--S 811 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 811
+
+)clear all
+
+--S 812 of 1393
+t0:=x^6/(a+b*x^2)^2
+--R
+--R
+--R 6
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 812
+
+--S 813 of 1393
+r0:=-5/2*a*x/b^3+5/6*x^3/b^2-1/2*x^5/(b*(a+b*x^2))+_
+ 5/2*a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(7/2)
+--R
+--R
+--R +-+
+--R 2 2 +-+ x\|b 2 5 3 2 +-+
+--R (15a b x + 15a )\|a atan(-----) + (2b x - 10a b x - 15a x)\|b
+--R +-+
+--R \|a
+--R (2) -----------------------------------------------------------------
+--R 4 2 3 +-+
+--R (6b x + 6a b )\|b
+--R Type: Expression(Integer)
+--E 813
+
+--S 814 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 2 | a \| b 2 5 3 2
+--R (15a b x + 15a ) |- - log(---------------------) + 4b x - 20a b x - 30a x
+--R \| b 2
+--R b x + a
+--R [----------------------------------------------------------------------------
+--R 4 2 3
+--R 12b x + 12a b
+--R ,
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 |a \|b 2 5 3 2
+--R (- 15a b x - 15a ) |- atan(----) + 2b x - 10a b x - 15a x
+--R \|b x
+--R ------------------------------------------------------------]
+--R 4 2 3
+--R 6b x + 6a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 814
+
+--S 815 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a +-+
+--R | a +-+ \| b +-+ x\|b
+--R 5a |- - \|b log(---------------------) - 10a\|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R 3 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 815
+
+--S 816 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 816
+
+--S 817 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R - 5a\|a atan(-----) - 5a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ------------------------------------------
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 817
+
+--S 818 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 818
+
+)clear all
+
+--S 819 of 1393
+t0:=x^5/(a+b*x^2)^2
+--R
+--R
+--R 5
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 819
+
+--S 820 of 1393
+r0:=1/2*x^2/b^2-1/2*a^2/(b^3*(a+b*x^2))-a*log(a+b*x^2)/b^3
+--R
+--R
+--R 2 2 2 2 4 2 2
+--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a
+--R (2) ---------------------------------------------------
+--R 4 2 3
+--R 2b x + 2a b
+--R Type: Expression(Integer)
+--E 820
+
+--S 821 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2 4 2 2
+--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a
+--R (3) ---------------------------------------------------
+--R 4 2 3
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 821
+
+--S 822 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 823
+
+)clear all
+
+--S 824 of 1393
+t0:=x^4/(a+b*x^2)^2
+--R
+--R
+--R 4
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 824
+
+--S 825 of 1393
+r0:=3/2*x/b^2-1/2*x^3/(b*(a+b*x^2))-3/2*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(5/2)
+--R
+--R
+--R +-+
+--R 2 +-+ x\|b 3 +-+
+--R (- 3b x - 3a)\|a atan(-----) + (2b x + 3a x)\|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------------------
+--R 3 2 2 +-+
+--R (2b x + 2a b )\|b
+--R Type: Expression(Integer)
+--E 825
+
+--S 826 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 | a \| b 3
+--R (3b x + 3a) |- - log(-----------------------) + 4b x + 6a x
+--R \| b 2
+--R b x + a
+--R [-------------------------------------------------------------,
+--R 3 2 2
+--R 4b x + 4a b
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 |a \|b 3
+--R (3b x + 3a) |- atan(----) + 2b x + 3a x
+--R \|b x
+--R -----------------------------------------]
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 826
+
+--S 827 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R | a +-+ \| b +-+ x\|b
+--R 3 |- - \|b log(----------------------- + 6\|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ----------------------------------------------------------
+--R 2 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 827
+
+--S 828 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 828
+
+--S 829 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R 3\|a atan(-----) + 3 |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 829
+
+--S 830 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 830
+
+)clear all
+
+--S 831 of 1393
+t0:=x^3/(a+b*x^2)^2
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 831
+
+--S 832 of 1393
+r0:=1/2*a/(b^2*(a+b*x^2))+1/2*log(a+b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R (b x + a)log(b x + a) + a
+--R (2) ---------------------------
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Expression(Integer)
+--E 832
+
+--S 833 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R (b x + a)log(b x + a) + a
+--R (3) ---------------------------
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 833
+
+--S 834 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 835
+
+)clear all
+
+--S 836 of 1393
+t0:=x^2/(a+b*x^2)^2
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 836
+
+--S 837 of 1393
+r0:=-1/2*x/(b*(a+b*x^2))+1/2*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R 2 x\|b +-+ +-+
+--R (b x + a)atan(-----) - x\|a \|b
+--R +-+
+--R \|a
+--R (2) ---------------------------------
+--R 2 2 +-+ +-+
+--R (2b x + 2a b)\|a \|b
+--R Type: Expression(Integer)
+--E 837
+
+--S 838 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R 2 (b x - a)\|- a b + 2a b x +-----+
+--R (b x + a)log(---------------------------) - 2x\|- a b
+--R 2
+--R b x + a
+--R [-------------------------------------------------------,
+--R 2 2 +-----+
+--R (4b x + 4a b)\|- a b
+--R +---+
+--R 2 x\|a b +---+
+--R (b x + a)atan(-------) - x\|a b
+--R a
+--R ---------------------------------]
+--R 2 2 +---+
+--R (2b x + 2a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 838
+
+--S 839 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R \|a \|b log(---------------------------) - 2\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 4b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 839
+
+--S 840 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 840
+
+--S 841 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R \|a \|b atan(-------) - \|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------
+--R +-+ +-+ +---+
+--R 2b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 842
+
+)clear all
+
+--S 843 of 1393
+t0:=x/(a+b*x^2)^2
+--R
+--R
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 843
+
+--S 844 of 1393
+r0:=(-1/2)/(b*(a+b*x^2))
+--R
+--R
+--R 1
+--R -
+--R 2
+--R (2) - ----------
+--R 2 2
+--R b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 844
+
+--S 845 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ------------
+--R 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 845
+
+--S 846 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 847
+
+)clear all
+
+--S 848 of 1393
+t0:=1/(a+b*x^2)^2
+--R
+--R
+--R 1
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 848
+
+--S 849 of 1393
+r0:=1/2*x/(a*(a+b*x^2))+1/2*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R 2 x\|b +-+ +-+
+--R (b x + a)atan(-----) + x\|a \|b
+--R +-+
+--R \|a
+--R (2) ---------------------------------
+--R 2 2 +-+ +-+
+--R (2a b x + 2a )\|a \|b
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R 2 (b x - a)\|- a b + 2a b x +-----+
+--R (b x + a)log(---------------------------) + 2x\|- a b
+--R 2
+--R b x + a
+--R [-------------------------------------------------------,
+--R 2 2 +-----+
+--R (4a b x + 4a )\|- a b
+--R +---+
+--R 2 x\|a b +---+
+--R (b x + a)atan(-------) + x\|a b
+--R a
+--R ---------------------------------]
+--R 2 2 +---+
+--R (2a b x + 2a )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 850
+
+--S 851 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R \|a \|b log(---------------------------) - 2\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 4a\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 851
+
+--S 852 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 852
+
+--S 853 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R \|a \|b atan(-------) - \|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------
+--R +-+ +-+ +---+
+--R 2a\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 853
+
+--S 854 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 854
+
+)clear all
+
+--S 855 of 1393
+t0:=1/(x*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) --------------------
+--R 2 5 3 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 855
+
+--S 856 of 1393
+r0:=1/2/(a*(a+b*x^2))+log(x)/a^2-1/2*log(a+b*x^2)/a^2
+--R
+--R
+--R 2 2 2
+--R (- b x - a)log(b x + a) + (2b x + 2a)log(x) + a
+--R (2) --------------------------------------------------
+--R 2 2 3
+--R 2a b x + 2a
+--R Type: Expression(Integer)
+--E 856
+
+--S 857 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R (- b x - a)log(b x + a) + (2b x + 2a)log(x) + a
+--R (3) --------------------------------------------------
+--R 2 2 3
+--R 2a b x + 2a
+--R Type: Union(Expression(Integer),...)
+--E 857
+
+--S 858 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 858
+
+--S 859 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 859
+
+)clear all
+
+--S 860 of 1393
+t0:=1/(x^2*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 860
+
+--S 861 of 1393
+r0:=(-3/2)/(a^2*x)+1/2/(a*x*(a+b*x^2))-_
+ 3/2*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|b 2 +-+
+--R (- 3b x - 3a x)\|b atan(-----) + (- 3b x - 2a)\|a
+--R +-+
+--R \|a
+--R (2) ----------------------------------------------------
+--R 2 3 3 +-+
+--R (2a b x + 2a x)\|a
+--R Type: Expression(Integer)
+--E 861
+
+--S 862 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 3 | b \| a 2
+--R (3b x + 3a x) |- - log(-----------------------) - 6b x - 4a
+--R \| a 2
+--R b x + a
+--R [-------------------------------------------------------------,
+--R 2 3 3
+--R 4a b x + 4a x
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 |b \|a 2
+--R (3b x + 3a x) |- atan(-----) - 3b x - 2a
+--R \|a b x
+--R ------------------------------------------]
+--R 2 3 3
+--R 2a b x + 2a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 862
+
+--S 863 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R 3 |- - \|a log(----------------------- + 6\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) ----------------------------------------------------------
+--R 2 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 863
+
+--S 864 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 864
+
+--S 865 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R 3\|b atan(-----) + 3\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) ---------------------------------------
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 865
+
+--S 866 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 866
+
+)clear all
+
+--S 867 of 1393
+t0:=1/(x^3*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 867
+
+--S 868 of 1393
+r0:=(-1)/(a^2*x^2)+1/2/(a*x^2*(a+b*x^2))-2*b*log(x)/a^3+b*log(a+b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 2 4 2 2 2
+--R (2b x + 2a b x )log(b x + a) + (- 4b x - 4a b x )log(x) - 2a b x - a
+--R -------------------------------------------------------------------------
+--R 3 4 4 2
+--R 2a b x + 2a x
+--R Type: Expression(Integer)
+--E 868
+
+--S 869 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2 4 2 2 2
+--R (2b x + 2a b x )log(b x + a) + (- 4b x - 4a b x )log(x) - 2a b x - a
+--R -------------------------------------------------------------------------
+--R 3 4 4 2
+--R 2a b x + 2a x
+--R Type: Union(Expression(Integer),...)
+--E 869
+
+--S 870 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 870
+
+--S 871 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 871
+
+)clear all
+
+--S 872 of 1393
+t0:=1/(x^4*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 8 6 2 4
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 872
+
+--S 873 of 1393
+r0:=(-5/6)/(a^2*x^3)+5/2*b/(a^3*x)+1/2/(a*x^3*(a+b*x^2))+_
+ 5/2*b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(7/2)
+--R
+--R
+--R +-+
+--R 2 5 3 +-+ x\|b 2 4 2 2 +-+
+--R (15b x + 15a b x )\|b atan(-----) + (15b x + 10a b x - 2a )\|a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------------------
+--R 3 5 4 3 +-+
+--R (6a b x + 6a x )\|a
+--R Type: Expression(Integer)
+--E 873
+
+--S 874 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 5 3 | b \| a 2 4 2
+--R (15b x + 15a b x ) |- - log(---------------------) + 30b x + 20a b x
+--R \| a 2
+--R b x + a
+--R +
+--R 2
+--R - 4a
+--R /
+--R 3 5 4 3
+--R 12a b x + 12a x
+--R ,
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 5 3 |b \|a 2 4 2 2
+--R (- 15b x - 15a b x ) |- atan(-----) + 15b x + 10a b x - 2a
+--R \|a b x
+--R --------------------------------------------------------------]
+--R 3 5 4 3
+--R 6a b x + 6a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 874
+
+--S 875 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R 5b |- - \|a log(---------------------) - 10b\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R 3 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 875
+
+--S 876 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 876
+
+--S 877 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R - 5b\|b atan(-----) - 5b\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -------------------------------------------
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 877
+
+--S 878 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 878
+
+)clear all
+
+--S 879 of 1393
+t0:=1/(x^5*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 9 7 2 5
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 879
+
+--S 880 of 1393
+r0:=(-3/4)/(a^2*x^4)+3/2*b/(a^3*x^2)+1/2/(a*x^4*(a+b*x^2))+_
+ 3*b^2*log(x)/a^4-3/2*b^2*log(a+b*x^2)/a^4
+--R
+--R
+--R (2)
+--R 3 6 2 4 2 3 6 2 4 2 4
+--R (- 6b x - 6a b x )log(b x + a) + (12b x + 12a b x )log(x) + 6a b x
+--R +
+--R 2 2 3
+--R 3a b x - a
+--R /
+--R 4 6 5 4
+--R 4a b x + 4a x
+--R Type: Expression(Integer)
+--E 880
+
+--S 881 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 6 2 4 2 3 6 2 4 2 4
+--R (- 6b x - 6a b x )log(b x + a) + (12b x + 12a b x )log(x) + 6a b x
+--R +
+--R 2 2 3
+--R 3a b x - a
+--R /
+--R 4 6 5 4
+--R 4a b x + 4a x
+--R Type: Union(Expression(Integer),...)
+--E 881
+
+--S 882 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 882
+
+--S 883 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 883
+
+)clear all
+
+--S 884 of 1393
+t0:=1/(x^6*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 2 10 8 2 6
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 884
+
+--S 885 of 1393
+r0:=(-7/10)/(a^2*x^5)+7/6*b/(a^3*x^3)-7/2*b^2/(a^4*x)+_
+ 1/2/(a*x^5*(a+b*x^2))-7/2*b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 7 2 5 +-+ x\|b
+--R (- 105b x - 105a b x )\|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 105b x - 70a b x + 14a b x - 6a )\|a
+--R /
+--R 4 7 5 5 +-+
+--R (30a b x + 30a x )\|a
+--R Type: Expression(Integer)
+--E 885
+
+--S 886 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 3 7 2 5 | b \| a 3 6
+--R (105b x + 105a b x ) |- - log(-----------------------) - 210b x
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 2 2 3
+--R - 140a b x + 28a b x - 12a
+--R /
+--R 4 7 5 5
+--R 60a b x + 60a x
+--R ,
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 7 2 5 |b \|a 3 6 2 4 2 2 3
+--R (105b x + 105a b x ) |- atan(-----) - 105b x - 70a b x + 14a b x - 6a
+--R \|a b x
+--R --------------------------------------------------------------------------]
+--R 4 7 5 5
+--R 30a b x + 30a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 886
+
+--S 887 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R 2 | b +-+ \| a 2 +-+ x\|b
+--R 7b |- - \|a log(-----------------------) + 14b \|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------
+--R 4 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 887
+
+--S 888 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 888
+
+--S 889 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 2 +-+ x\|b 2 +-+ |b \|a
+--R 7b \|b atan(-----) + 7b \|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -------------------------------------------
+--R 4 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 890
+
+)clear all
+
+--S 891 of 1393
+t0:=1/(x^7*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 2 11 9 2 7
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 891
+
+--S 892 of 1393
+r0:=(-2/3)/(a^2*x^6)+b/(a^3*x^4)-2*b^2/(a^4*x^2)+1/2/(a*x^6*(a+b*x^2))-_
+ 4*b^3*log(x)/a^5+2*b^3*log(a+b*x^2)/a^5
+--R
+--R
+--R (2)
+--R 4 8 3 6 2 4 8 3 6 3 6
+--R (12b x + 12a b x )log(b x + a) + (- 24b x - 24a b x )log(x) - 12a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 6a b x + 2a b x - a
+--R /
+--R 5 8 6 6
+--R 6a b x + 6a x
+--R Type: Expression(Integer)
+--E 892
+
+--S 893 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 8 3 6 2 4 8 3 6 3 6
+--R (12b x + 12a b x )log(b x + a) + (- 24b x - 24a b x )log(x) - 12a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 6a b x + 2a b x - a
+--R /
+--R 5 8 6 6
+--R 6a b x + 6a x
+--R Type: Union(Expression(Integer),...)
+--E 893
+
+--S 894 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 894
+
+--S 895 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 895
+
+)clear all
+
+--S 896 of 1393
+t0:=1/(x^8*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 2 12 10 2 8
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 896
+
+--S 897 of 1393
+r0:=(-9/14)/(a^2*x^7)+9/10*b/(a^3*x^5)-3/2*b^2/(a^4*x^3)+9/2*b^3/(a^5*x)+_
+ 1/2/(a*x^7*(a+b*x^2))+9/2*b^(7/2)*atan(x*sqrt(b)/sqrt(a))/a^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 9 3 7 +-+ x\|b
+--R (315b x + 315a b x )\|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315b x + 210a b x - 42a b x + 18a b x - 10a )\|a
+--R /
+--R 5 9 6 7 +-+
+--R (70a b x + 70a x )\|a
+--R Type: Expression(Integer)
+--E 897
+
+--S 898 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 4 9 3 7 | b \| a 4 8
+--R (315b x + 315a b x ) |- - log(---------------------) + 630b x
+--R \| a 2
+--R b x + a
+--R +
+--R 3 6 2 2 4 3 2 4
+--R 420a b x - 84a b x + 36a b x - 20a
+--R /
+--R 5 9 6 7
+--R 140a b x + 140a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 4 9 3 7 |b \|a 4 8 3 6 2 2 4
+--R (- 315b x - 315a b x ) |- atan(-----) + 315b x + 210a b x - 42a b x
+--R \|a b x
+--R +
+--R 3 2 4
+--R 18a b x - 10a
+--R /
+--R 5 9 6 7
+--R 70a b x + 70a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 898
+
+--S 899 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a +-+
+--R 3 | b +-+ \| a 3 +-+ x\|b
+--R 9b |- - \|a log(---------------------) - 18b \|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) -------------------------------------------------------------
+--R 5 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 899
+
+--S 900 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 900
+
+--S 901 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 3 +-+ x\|b 3 +-+ |b \|a
+--R - 9b \|b atan(-----) - 9b \|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) ---------------------------------------------
+--R 5 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 901
+
+--S 902 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 902
+
+)clear all
+
+--S 903 of 1393
+t0:=1/(x^9*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 2 13 11 2 9
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 903
+
+--S 904 of 1393
+r0:=(-5/8)/(a^2*x^8)+5/6*b/(a^3*x^6)-5/4*b^2/(a^4*x^4)+5/2*b^3/(a^5*x^2)+_
+ 1/2/(a*x^8*(a+b*x^2))+5*b^4*log(x)/a^6-5/2*b^4*log(a+b*x^2)/a^6
+--R
+--R
+--R (2)
+--R 5 10 4 8 2 5 10 4 8
+--R (- 60b x - 60a b x )log(b x + a) + (120b x + 120a b x )log(x)
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R 60a b x + 30a b x - 10a b x + 5a b x - 3a
+--R /
+--R 6 10 7 8
+--R 24a b x + 24a x
+--R Type: Expression(Integer)
+--E 904
+
+--S 905 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 2 5 10 4 8
+--R (- 60b x - 60a b x )log(b x + a) + (120b x + 120a b x )log(x)
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R 60a b x + 30a b x - 10a b x + 5a b x - 3a
+--R /
+--R 6 10 7 8
+--R 24a b x + 24a x
+--R Type: Union(Expression(Integer),...)
+--E 905
+
+--S 906 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 907
+
+)clear all
+
+--S 908 of 1393
+t0:=x^m/(a+b*x^2)^3
+--R
+--R
+--R m
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Expression(Integer)
+--E 908
+
+--S 909 of 1393
+--r0:=1/4*x^(1+m)/(a*(a+b*x^2)^2)+1/8*(3-m)*x^(1+m)/(a^2*(a+b*x^2))+_
+-- 1/8*(1-m)*(3-m)*x^(1+m)*hypergeometric(1,1/2*(1+m),_
+-- 1/2*(3+m),-b*x^2/a)/(a^3*(1+m))
+--E 909
+
+--S 910 of 1393
+--a0:=integrate(t0,x)
+--E 910
+
+--S 911 of 1393
+--m0:=a0-r0
+--E 911
+
+--S 912 of 1393
+--d0:=D(m0,x)
+--E 912
+
+)clear all
+
+--S 913 of 1393
+t0:=x^15/(a+b*x^2)^3
+--R
+--R
+--R 15
+--R x
+--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 913
+
+--S 914 of 1393
+r0:=15/2*a^4*x^2/b^7-5/2*a^3*x^4/b^6+a^2*x^6/b^5-3/8*a*x^8/b^4+_
+ 1/10*x^10/b^3+1/4*a^7/(b^8*(a+b*x^2)^2)-7/2*a^6/(b^8*(a+b*x^2))-_
+ 21/2*a^5*log(a+b*x^2)/b^8
+--R
+--R
+--R (2)
+--R 5 2 4 6 2 7 2 7 14 6 12
+--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x
+--R +
+--R 2 5 10 3 4 8 4 3 6 5 2 4 6 2 7
+--R 14a b x - 35a b x + 140a b x + 500a b x + 160a b x - 130a
+--R /
+--R 10 4 9 2 2 8
+--R 40b x + 80a b x + 40a b
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 4 6 2 7 2 7 14 6 12
+--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x
+--R +
+--R 2 5 10 3 4 8 4 3 6 5 2 4 6 2 7
+--R 14a b x - 35a b x + 140a b x + 500a b x + 160a b x - 130a
+--R /
+--R 10 4 9 2 2 8
+--R 40b x + 80a b x + 40a b
+--R Type: Union(Expression(Integer),...)
+--E 915
+
+--S 916 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 916
+
+--S 917 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 917
+
+)clear all
+
+--S 918 of 1393
+t0:=x^14/(a+b*x^2)^3
+--R
+--R
+--R 14
+--R x
+--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 918
+
+--S 919 of 1393
+r0:=143/8*a^4*x/b^7-143/24*a^3*x^3/b^6+143/40*a^2*x^5/b^5-_
+ 143/56*a*x^7/b^4+143/72*x^9/b^3-1/4*x^13/(b*(a+b*x^2)^2)-_
+ 13/8*x^11/(b^2*(a+b*x^2))-143/8*a^(9/2)*atan(x*sqrt(b)/sqrt(a))/b^(15/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 2 4 5 2 6 +-+ x\|b
+--R (- 45045a b x - 90090a b x - 45045a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 6 13 5 11 2 4 9 3 3 7 4 2 5
+--R 280b x - 520a b x + 1144a b x - 3432a b x + 24024a b x
+--R +
+--R 5 3 6
+--R 75075a b x + 45045a x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 9 4 8 2 2 7 +-+
+--R (2520b x + 5040a b x + 2520a b )\|b
+--R Type: Expression(Integer)
+--E 919
+
+--S 920 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 4 2 4 5 2 6 | a \| b
+--R (45045a b x + 90090a b x + 45045a ) |- - log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 6 13 5 11 2 4 9 3 3 7 4 2 5
+--R 560b x - 1040a b x + 2288a b x - 6864a b x + 48048a b x
+--R +
+--R 5 3 6
+--R 150150a b x + 90090a x
+--R /
+--R 9 4 8 2 2 7
+--R 5040b x + 10080a b x + 5040a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 4 2 4 5 2 6 |a \|b 6 13
+--R (45045a b x + 90090a b x + 45045a ) |- atan(----) + 280b x
+--R \|b x
+--R +
+--R 5 11 2 4 9 3 3 7 4 2 5 5 3
+--R - 520a b x + 1144a b x - 3432a b x + 24024a b x + 75075a b x
+--R +
+--R 6
+--R 45045a x
+--R /
+--R 9 4 8 2 2 7
+--R 2520b x + 5040a b x + 2520a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 920
+
+--S 921 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R 4 | a +-+ \| b 4 +-+ x\|b
+--R 143a |- - \|b log(-----------------------) + 286a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ------------------------------------------------------------------
+--R 7 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 921
+
+--S 922 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 922
+
+--S 923 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 4 +-+ x\|b 4 |a +-+ \|b
+--R 143a \|a atan(-----) + 143a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------------
+--R 7 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 923
+
+--S 924 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 924
+
+)clear all
+
+--S 925 of 1393
+t0:=x^13/(a+b*x^2)^3
+--R
+--R
+--R 13
+--R x
+--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 925
+
+--S 926 of 1393
+r0:=-5*a^3*x^2/b^6+3/2*a^2*x^4/b^5-1/2*a*x^6/b^4+1/8*x^8/b^3-_
+ 1/4*a^6/(b^7*(a+b*x^2)^2)+3*a^5/(b^7*(a+b*x^2))+15/2*a^4*log(a+b*x^2)/b^7
+--R
+--R
+--R (2)
+--R 4 2 4 5 2 6 2 6 12 5 10 2 4 8
+--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x
+--R +
+--R 3 3 6 4 2 4 5 2 6
+--R - 20a b x - 68a b x - 16a b x + 22a
+--R /
+--R 9 4 8 2 2 7
+--R 8b x + 16a b x + 8a b
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 4 5 2 6 2 6 12 5 10 2 4 8
+--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x
+--R +
+--R 3 3 6 4 2 4 5 2 6
+--R - 20a b x - 68a b x - 16a b x + 22a
+--R /
+--R 9 4 8 2 2 7
+--R 8b x + 16a b x + 8a b
+--R Type: Union(Expression(Integer),...)
+--E 927
+
+--S 928 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 928
+
+--S 929 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 929
+
+)clear all
+
+--S 930 of 1393
+t0:=x^12/(a+b*x^2)^3
+--R
+--R
+--R 12
+--R x
+--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 930
+
+--S 931 of 1393
+r0:=-99/8*a^3*x/b^6+33/8*a^2*x^3/b^5-99/40*a*x^5/b^4+99/56*x^7/b^3-_
+ 1/4*x^11/(b*(a+b*x^2)^2)-11/8*x^9/(b^2*(a+b*x^2))+_
+ 99/8*a^(7/2)*atan(x*sqrt(b)/sqrt(a))/b^(13/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 4 4 2 5 +-+ x\|b
+--R (3465a b x + 6930a b x + 3465a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+
+--R (40b x - 88a b x + 264a b x - 1848a b x - 5775a b x - 3465a x)\|b
+--R /
+--R 8 4 7 2 2 6 +-+
+--R (280b x + 560a b x + 280a b )\|b
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 3 2 4 4 2 5 | a \| b
+--R (3465a b x + 6930a b x + 3465a ) |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5
+--R 80b x - 176a b x + 528a b x - 3696a b x - 11550a b x - 6930a x
+--R /
+--R 8 4 7 2 2 6
+--R 560b x + 1120a b x + 560a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 3 2 4 4 2 5 |a \|b 5 11 4 9
+--R (- 3465a b x - 6930a b x - 3465a ) |- atan(----) + 40b x - 88a b x
+--R \|b x
+--R +
+--R 2 3 7 3 2 5 4 3 5
+--R 264a b x - 1848a b x - 5775a b x - 3465a x
+--R /
+--R 8 4 7 2 2 6
+--R 280b x + 560a b x + 280a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 932
+
+--S 933 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a +-+
+--R 3 | a +-+ \| b 3 +-+ x\|b
+--R 99a |- - \|b log(---------------------) - 198a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------
+--R 6 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 933
+
+--S 934 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 3 +-+ x\|b 3 |a +-+ \|b
+--R - 99a \|a atan(-----) - 99a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------------
+--R 6 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 935
+
+--S 936 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 936
+
+)clear all
+
+--S 937 of 1393
+t0:=x^11/(a+b*x^2)^3
+--R
+--R
+--R 11
+--R x
+--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 937
+
+--S 938 of 1393
+r0:=3*a^2*x^2/b^5-3/4*a*x^4/b^4+1/6*x^6/b^3+1/4*a^5/(b^6*(a+b*x^2)^2)-_
+ 5/2*a^4/(b^6*(a+b*x^2))-5*a^3*log(a+b*x^2)/b^6
+--R
+--R
+--R (2)
+--R 3 2 4 4 2 5 2 5 10 4 8
+--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x
+--R +
+--R 2 3 6 3 2 4 4 2 5
+--R 20a b x + 63a b x + 6a b x - 27a
+--R /
+--R 8 4 7 2 2 6
+--R 12b x + 24a b x + 12a b
+--R Type: Expression(Integer)
+--E 938
+
+--S 939 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 4 2 5 2 5 10 4 8
+--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x
+--R +
+--R 2 3 6 3 2 4 4 2 5
+--R 20a b x + 63a b x + 6a b x - 27a
+--R /
+--R 8 4 7 2 2 6
+--R 12b x + 24a b x + 12a b
+--R Type: Union(Expression(Integer),...)
+--E 939
+
+--S 940 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 940
+
+--S 941 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 941
+
+)clear all
+
+--S 942 of 1393
+t0:=x^10/(a+b*x^2)^3
+--R
+--R
+--R 10
+--R x
+--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 942
+
+--S 943 of 1393
+r0:=63/8*a^2*x/b^5-21/8*a*x^3/b^4+63/40*x^5/b^3-1/4*x^9/(b*(a+b*x^2)^2)-_
+ 9/8*x^7/(b^2*(a+b*x^2))-63/8*a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 4 3 2 4 +-+ x\|b
+--R (- 315a b x - 630a b x - 315a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (8b x - 24a b x + 168a b x + 525a b x + 315a x)\|b
+--R /
+--R 7 4 6 2 2 5 +-+
+--R (40b x + 80a b x + 40a b )\|b
+--R Type: Expression(Integer)
+--E 943
+
+--S 944 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 2 4 3 2 4 | a \| b
+--R (315a b x + 630a b x + 315a ) |- - log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 4 9 3 7 2 2 5 3 3 4
+--R 16b x - 48a b x + 336a b x + 1050a b x + 630a x
+--R /
+--R 7 4 6 2 2 5
+--R 80b x + 160a b x + 80a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 4 3 2 4 |a \|b 4 9 3 7
+--R (315a b x + 630a b x + 315a ) |- atan(----) + 8b x - 24a b x
+--R \|b x
+--R +
+--R 2 2 5 3 3 4
+--R 168a b x + 525a b x + 315a x
+--R /
+--R 7 4 6 2 2 5
+--R 40b x + 80a b x + 40a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 944
+
+--S 945 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R 2 | a +-+ \| b 2 +-+ x\|b
+--R 63a |- - \|b log(-----------------------) + 126a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------------
+--R 5 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 945
+
+--S 946 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R 63a \|a atan(-----) + 63a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------
+--R 5 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 947
+
+--S 948 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 948
+
+)clear all
+
+--S 949 of 1393
+t0:=x^9/(a+b*x^2)^3
+--R
+--R
+--R 9
+--R x
+--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 949
+
+--S 950 of 1393
+r0:=-3/2*a*x^2/b^4+1/4*x^4/b^3-1/4*a^4/(b^5*(a+b*x^2)^2)+_
+ 2*a^3/(b^5*(a+b*x^2))+3*a^2*log(a+b*x^2)/b^5
+--R
+--R
+--R (2)
+--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4
+--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x
+--R +
+--R 3 2 4
+--R 2a b x + 7a
+--R /
+--R 7 4 6 2 2 5
+--R 4b x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 950
+
+--S 951 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4
+--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x
+--R +
+--R 3 2 4
+--R 2a b x + 7a
+--R /
+--R 7 4 6 2 2 5
+--R 4b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 951
+
+--S 952 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 952
+
+--S 953 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 953
+
+)clear all
+
+--S 954 of 1393
+t0:=x^8/(a+b*x^2)^3
+--R
+--R
+--R 8
+--R x
+--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 954
+
+--S 955 of 1393
+r0:=-35/8*a*x/b^4+35/24*x^3/b^3-1/4*x^7/(b*(a+b*x^2)^2)-_
+ 7/8*x^5/(b^2*(a+b*x^2))+35/8*a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 4 2 2 3 +-+ x\|b
+--R (105a b x + 210a b x + 105a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (8b x - 56a b x - 175a b x - 105a x)\|b
+--R /
+--R 6 4 5 2 2 4 +-+
+--R (24b x + 48a b x + 24a b )\|b
+--R Type: Expression(Integer)
+--E 955
+
+--S 956 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 4 2 2 3 | a \| b
+--R (105a b x + 210a b x + 105a ) |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 3 7 2 5 2 3 3
+--R 16b x - 112a b x - 350a b x - 210a x
+--R /
+--R 6 4 5 2 2 4
+--R 48b x + 96a b x + 48a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 4 2 2 3 |a \|b 3 7 2 5
+--R (- 105a b x - 210a b x - 105a ) |- atan(----) + 8b x - 56a b x
+--R \|b x
+--R +
+--R 2 3 3
+--R - 175a b x - 105a x
+--R /
+--R 6 4 5 2 2 4
+--R 24b x + 48a b x + 24a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 956
+
+--S 957 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a +-+
+--R | a +-+ \| b +-+ x\|b
+--R 35a |- - \|b log(---------------------) - 70a\|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ------------------------------------------------------------
+--R 4 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 957
+
+--S 958 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 958
+
+--S 959 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R - 35a\|a atan(-----) - 35a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------
+--R 4 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 960
+
+)clear all
+
+--S 961 of 1393
+t0:=x^7/(a+b*x^2)^3
+--R
+--R
+--R 7
+--R x
+--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 961
+
+--S 962 of 1393
+r0:=1/2*x^2/b^3+1/4*a^3/(b^4*(a+b*x^2)^2)-3/2*a^2/(b^4*(a+b*x^2))-_
+ 3/2*a*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 2 4 2 2 3 2 3 6 2 4 2 2 3
+--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a
+--R ---------------------------------------------------------------------------
+--R 6 4 5 2 2 4
+--R 4b x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 3 2 3 6 2 4 2 2 3
+--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a
+--R ---------------------------------------------------------------------------
+--R 6 4 5 2 2 4
+--R 4b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 963
+
+--S 964 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 964
+
+--S 965 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 965
+
+)clear all
+
+--S 966 of 1393
+t0:=x^6/(a+b*x^2)^3
+--R
+--R
+--R 6
+--R x
+--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 966
+
+--S 967 of 1393
+r0:=15/8*x/b^3-1/4*x^5/(b*(a+b*x^2)^2)-5/8*x^3/(b^2*(a+b*x^2))-_
+ 15/8*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 4 2 2 +-+ x\|b 2 5 3 2 +-+
+--R (- 15b x - 30a b x - 15a )\|a atan(-----) + (8b x + 25a b x + 15a x)\|b
+--R +-+
+--R \|a
+--R ----------------------------------------------------------------------------
+--R 5 4 4 2 2 3 +-+
+--R (8b x + 16a b x + 8a b )\|b
+--R Type: Expression(Integer)
+--E 967
+
+--S 968 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 4 2 2 | a \| b 2 5
+--R (15b x + 30a b x + 15a ) |- - log(-----------------------) + 16b x
+--R \| b 2
+--R b x + a
+--R +
+--R 3 2
+--R 50a b x + 30a x
+--R /
+--R 5 4 4 2 2 3
+--R 16b x + 32a b x + 16a b
+--R ,
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 4 2 2 |a \|b 2 5 3 2
+--R (15b x + 30a b x + 15a ) |- atan(----) + 8b x + 25a b x + 15a x
+--R \|b x
+--R -------------------------------------------------------------------]
+--R 5 4 4 2 2 3
+--R 8b x + 16a b x + 8a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 968
+
+--S 969 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R | a +-+ \| b +-+ x\|b
+--R 15 |- - \|b log(----------------------- + 30\|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ------------------------------------------------------------
+--R 3 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 969
+
+--S 970 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 970
+
+--S 971 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R 15\|a atan(-----) + 15 |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------
+--R 3 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 972
+
+)clear all
+
+--S 973 of 1393
+t0:=x^5/(a+b*x^2)^3
+--R
+--R
+--R 5
+--R x
+--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 973
+
+--S 974 of 1393
+r0:=-1/4*a^2/(b^3*(a+b*x^2)^2)+a/(b^3*(a+b*x^2))+1/2*log(a+b*x^2)/b^3
+--R
+--R
+--R 2 4 2 2 2 2 2
+--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a
+--R (2) ----------------------------------------------------
+--R 5 4 4 2 2 3
+--R 4b x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2 2 2 2
+--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a
+--R (3) ----------------------------------------------------
+--R 5 4 4 2 2 3
+--R 4b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 975
+
+--S 976 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 977
+
+)clear all
+
+--S 978 of 1393
+t0:=x^4/(a+b*x^2)^3
+--R
+--R
+--R 4
+--R x
+--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 978
+
+--S 979 of 1393
+r0:=-1/4*x^3/(b*(a+b*x^2)^2)-3/8*x/(b^2*(a+b*x^2))+_
+ 3/8*atan(x*sqrt(b)/sqrt(a))/(b^(5/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R 2 4 2 2 x\|b 3 +-+ +-+
+--R (3b x + 6a b x + 3a )atan(-----) + (- 5b x - 3a x)\|a \|b
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------
+--R 4 4 3 2 2 2 +-+ +-+
+--R (8b x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 979
+
+--S 980 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 4 2 2 (b x - a)\|- a b + 2a b x
+--R (3b x + 6a b x + 3a )log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 +-----+
+--R (- 10b x - 6a x)\|- a b
+--R /
+--R 4 4 3 2 2 2 +-----+
+--R (16b x + 32a b x + 16a b )\|- a b
+--R ,
+--R +---+
+--R 2 4 2 2 x\|a b 3 +---+
+--R (3b x + 6a b x + 3a )atan(-------) + (- 5b x - 3a x)\|a b
+--R a
+--R -------------------------------------------------------------]
+--R 4 4 3 2 2 2 +---+
+--R (8b x + 16a b x + 8a b )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 980
+
+--S 981 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ----------------------------------------------------------------
+--R 2 +-----+ +-+ +-+
+--R 16b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 982
+
+--S 983 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 3\|a \|b atan(-------) - 3\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 983
+
+--S 984 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 984
+
+)clear all
+
+--S 985 of 1393
+t0:=x^3/(a+b*x^2)^3
+--R
+--R
+--R 3
+--R x
+--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 985
+
+--S 986 of 1393
+r0:=1/4*x^4/(a*(a+b*x^2)^2)
+--R
+--R
+--R 1 4
+--R - x
+--R 4
+--R (2) ---------------------
+--R 2 4 2 2 3
+--R a b x + 2a b x + a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 986
+
+--S 987 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 2b x - a
+--R (3) -----------------------
+--R 4 4 3 2 2 2
+--R 4b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 987
+
+--S 988 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - -----
+--R 2
+--R 4a b
+--R Type: Expression(Integer)
+--E 988
+
+--S 989 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 989
+
+)clear all
+
+--S 990 of 1393
+t0:=x^2/(a+b*x^2)^3
+--R
+--R
+--R 2
+--R x
+--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 990
+
+--S 991 of 1393
+r0:=-1/4*x/(b*(a+b*x^2)^2)+1/8*x/(a*b*(a+b*x^2))+_
+ 1/8*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2))
+--R
+--R
+--R +-+
+--R 2 4 2 2 x\|b 3 +-+ +-+
+--R (b x + 2a b x + a )atan(-----) + (b x - a x)\|a \|b
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------
+--R 3 4 2 2 2 3 +-+ +-+
+--R (8a b x + 16a b x + 8a b)\|a \|b
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 4 2 2 (b x - a)\|- a b + 2a b x
+--R (b x + 2a b x + a )log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 +-----+
+--R (2b x - 2a x)\|- a b
+--R /
+--R 3 4 2 2 2 3 +-----+
+--R (16a b x + 32a b x + 16a b)\|- a b
+--R ,
+--R +---+
+--R 2 4 2 2 x\|a b 3 +---+
+--R (b x + 2a b x + a )atan(-------) + (b x - a x)\|a b
+--R a
+--R -------------------------------------------------------]
+--R 3 4 2 2 2 3 +---+
+--R (8a b x + 16a b x + 8a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 992
+
+--S 993 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R \|a \|b log(---------------------------) - 2\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 16a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 993
+
+--S 994 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 994
+
+--S 995 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R \|a \|b atan(-------) - \|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------
+--R +-+ +-+ +---+
+--R 8a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 995
+
+--S 996 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 996
+
+)clear all
+
+--S 997 of 1393
+t0:=x/(a+b*x^2)^3
+--R
+--R
+--R x
+--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 997
+
+--S 998 of 1393
+r0:=(-1/4)/(b*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R -
+--R 4
+--R (2) - --------------------
+--R 3 4 2 2 2
+--R b x + 2a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 998
+
+--S 999 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ----------------------
+--R 3 4 2 2 2
+--R 4b x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 999
+
+--S 1000 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1000
+
+--S 1001 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1001
+
+)clear all
+
+--S 1002 of 1393
+t0:=1/(a+b*x^2)^3
+--R
+--R
+--R 1
+--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 1002
+
+--S 1003 of 1393
+r0:=1/4*x/(a*(a+b*x^2)^2)+3/8*x/(a^2*(a+b*x^2))+_
+ 3/8*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R 2 4 2 2 x\|b 3 +-+ +-+
+--R (3b x + 6a b x + 3a )atan(-----) + (3b x + 5a x)\|a \|b
+--R +-+
+--R \|a
+--R (2) -----------------------------------------------------------
+--R 2 2 4 3 2 4 +-+ +-+
+--R (8a b x + 16a b x + 8a )\|a \|b
+--R Type: Expression(Integer)
+--E 1003
+
+--S 1004 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 4 2 2 (b x - a)\|- a b + 2a b x
+--R (3b x + 6a b x + 3a )log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 +-----+
+--R (6b x + 10a x)\|- a b
+--R /
+--R 2 2 4 3 2 4 +-----+
+--R (16a b x + 32a b x + 16a )\|- a b
+--R ,
+--R +---+
+--R 2 4 2 2 x\|a b 3 +---+
+--R (3b x + 6a b x + 3a )atan(-------) + (3b x + 5a x)\|a b
+--R a
+--R -----------------------------------------------------------]
+--R 2 2 4 3 2 4 +---+
+--R (8a b x + 16a b x + 8a )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1004
+
+--S 1005 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ----------------------------------------------------------------
+--R 2 +-----+ +-+ +-+
+--R 16a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1005
+
+--S 1006 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1006
+
+--S 1007 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 3\|a \|b atan(-------) - 3\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1007
+
+--S 1008 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1008
+
+)clear all
+
+--S 1009 of 1393
+t0:=1/(x*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) ------------------------------
+--R 3 7 2 5 2 3 3
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1009
+
+--S 1010 of 1393
+r0:=1/4/(a*(a+b*x^2)^2)+1/2/(a^2*(a+b*x^2))+log(x)/a^3-1/2*log(a+b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 2 2 4 2 2
+--R (- 2b x - 4a b x - 2a )log(b x + a) + (4b x + 8a b x + 4a )log(x)
+--R +
+--R 2 2
+--R 2a b x + 3a
+--R /
+--R 3 2 4 4 2 5
+--R 4a b x + 8a b x + 4a
+--R Type: Expression(Integer)
+--E 1010
+
+--S 1011 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2 2 4 2 2
+--R (- 2b x - 4a b x - 2a )log(b x + a) + (4b x + 8a b x + 4a )log(x)
+--R +
+--R 2 2
+--R 2a b x + 3a
+--R /
+--R 3 2 4 4 2 5
+--R 4a b x + 8a b x + 4a
+--R Type: Union(Expression(Integer),...)
+--E 1011
+
+--S 1012 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1012
+
+--S 1013 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1013
+
+)clear all
+
+--S 1014 of 1393
+t0:=1/(x^2*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 8 2 6 2 4 3 2
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1014
+
+--S 1015 of 1393
+r0:=(-15/8)/(a^3*x)+1/4/(a*x*(a+b*x^2)^2)+5/8/(a^2*x*(a+b*x^2))-_
+ 15/8*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 5 3 2 +-+ x\|b
+--R (- 15b x - 30a b x - 15a x)\|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 +-+
+--R (- 15b x - 25a b x - 8a )\|a
+--R /
+--R 3 2 5 4 3 5 +-+
+--R (8a b x + 16a b x + 8a x)\|a
+--R Type: Expression(Integer)
+--E 1015
+
+--S 1016 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 5 3 2 | b \| a 2 4
+--R (15b x + 30a b x + 15a x) |- - log(-----------------------) - 30b x
+--R \| a 2
+--R b x + a
+--R +
+--R 2 2
+--R - 50a b x - 16a
+--R /
+--R 3 2 5 4 3 5
+--R 16a b x + 32a b x + 16a x
+--R ,
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 5 3 2 |b \|a 2 4 2 2
+--R (15b x + 30a b x + 15a x) |- atan(-----) - 15b x - 25a b x - 8a
+--R \|a b x
+--R --------------------------------------------------------------------]
+--R 3 2 5 4 3 5
+--R 8a b x + 16a b x + 8a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1016
+
+--S 1017 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R 15 |- - \|a log(----------------------- + 30\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) ------------------------------------------------------------
+--R 3 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 1017
+
+--S 1018 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1018
+
+--S 1019 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R 15\|b atan(-----) + 15\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -----------------------------------------
+--R 3 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1019
+
+--S 1020 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1020
+
+)clear all
+
+--S 1021 of 1393
+t0:=1/(x^3*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 9 2 7 2 5 3 3
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1021
+
+--S 1022 of 1393
+r0:=(-3/2)/(a^3*x^2)+1/4/(a*x^2*(a+b*x^2)^2)+3/4/(a^2*x^2*(a+b*x^2))-_
+ 3*b*log(x)/a^4+3/2*b*log(a+b*x^2)/a^4
+--R
+--R
+--R (2)
+--R 3 6 2 4 2 2 2
+--R (6b x + 12a b x + 6a b x )log(b x + a)
+--R +
+--R 3 6 2 4 2 2 2 4 2 2 3
+--R (- 12b x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2a
+--R /
+--R 4 2 6 5 4 6 2
+--R 4a b x + 8a b x + 4a x
+--R Type: Expression(Integer)
+--E 1022
+
+--S 1023 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 6 2 4 2 2 2
+--R (6b x + 12a b x + 6a b x )log(b x + a)
+--R +
+--R 3 6 2 4 2 2 2 4 2 2 3
+--R (- 12b x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2a
+--R /
+--R 4 2 6 5 4 6 2
+--R 4a b x + 8a b x + 4a x
+--R Type: Union(Expression(Integer),...)
+--E 1023
+
+--S 1024 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1024
+
+--S 1025 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1025
+
+)clear all
+
+--S 1026 of 1393
+t0:=1/(x^4*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 3 10 2 8 2 6 3 4
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1026
+
+--S 1027 of 1393
+r0:=(-35/24)/(a^3*x^3)+35/8*b/(a^4*x)+1/4/(a*x^3*(a+b*x^2)^2)+_
+ 7/8/(a^2*x^3*(a+b*x^2))+35/8*b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 7 2 5 2 3 +-+ x\|b
+--R (105b x + 210a b x + 105a b x )\|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (105b x + 175a b x + 56a b x - 8a )\|a
+--R /
+--R 4 2 7 5 5 6 3 +-+
+--R (24a b x + 48a b x + 24a x )\|a
+--R Type: Expression(Integer)
+--E 1027
+
+--S 1028 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 7 2 5 2 3 | b \| a
+--R (105b x + 210a b x + 105a b x ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 6 2 4 2 2 3
+--R 210b x + 350a b x + 112a b x - 16a
+--R /
+--R 4 2 7 5 5 6 3
+--R 48a b x + 96a b x + 48a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 7 2 5 2 3 |b \|a 3 6
+--R (- 105b x - 210a b x - 105a b x ) |- atan(-----) + 105b x
+--R \|a b x
+--R +
+--R 2 4 2 2 3
+--R 175a b x + 56a b x - 8a
+--R /
+--R 4 2 7 5 5 6 3
+--R 24a b x + 48a b x + 24a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1028
+
+--S 1029 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R 35b |- - \|a log(---------------------) - 70b\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) ------------------------------------------------------------
+--R 4 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 1029
+
+--S 1030 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1030
+
+--S 1031 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R - 35b\|b atan(-----) - 35b\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) ---------------------------------------------
+--R 4 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1031
+
+--S 1032 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1032
+
+)clear all
+
+--S 1033 of 1393
+t0:=1/(x^5*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 3 11 2 9 2 7 3 5
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1033
+
+--S 1034 of 1393
+r0:=(-3/2)/(a^3*x^4)+3*b/(a^4*x^2)+1/4/(a*x^4*(a+b*x^2)^2)+_
+ 1/(a^2*x^4*(a+b*x^2))+6*b^2*log(x)/a^5-3*b^2*log(a+b*x^2)/a^5
+--R
+--R
+--R (2)
+--R 4 8 3 6 2 2 4 2
+--R (- 12b x - 24a b x - 12a b x )log(b x + a)
+--R +
+--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4
+--R (24b x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - a
+--R /
+--R 5 2 8 6 6 7 4
+--R 4a b x + 8a b x + 4a x
+--R Type: Expression(Integer)
+--E 1034
+
+--S 1035 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 8 3 6 2 2 4 2
+--R (- 12b x - 24a b x - 12a b x )log(b x + a)
+--R +
+--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4
+--R (24b x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - a
+--R /
+--R 5 2 8 6 6 7 4
+--R 4a b x + 8a b x + 4a x
+--R Type: Union(Expression(Integer),...)
+--E 1035
+
+--S 1036 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1036
+
+--S 1037 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1037
+
+)clear all
+
+--S 1038 of 1393
+t0:=1/(x^6*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 3 12 2 10 2 8 3 6
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1038
+
+--S 1039 of 1393
+r0:=(-63/40)/(a^3*x^5)+21/8*b/(a^4*x^3)-63/8*b^2/(a^5*x)+_
+ 1/4/(a*x^5*(a+b*x^2)^2)+9/8/(a^2*x^5*(a+b*x^2))-_
+ 63/8*b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 9 3 7 2 2 5 +-+ x\|b
+--R (- 315b x - 630a b x - 315a b x )\|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- 315b x - 525a b x - 168a b x + 24a b x - 8a )\|a
+--R /
+--R 5 2 9 6 7 7 5 +-+
+--R (40a b x + 80a b x + 40a x )\|a
+--R Type: Expression(Integer)
+--E 1039
+
+--S 1040 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 4 9 3 7 2 2 5 | b \| a
+--R (315b x + 630a b x + 315a b x ) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4
+--R - 630b x - 1050a b x - 336a b x + 48a b x - 16a
+--R /
+--R 5 2 9 6 7 7 5
+--R 80a b x + 160a b x + 80a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 4 9 3 7 2 2 5 |b \|a 4 8 3 6
+--R (315b x + 630a b x + 315a b x ) |- atan(-----) - 315b x - 525a b x
+--R \|a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 168a b x + 24a b x - 8a
+--R /
+--R 5 2 9 6 7 7 5
+--R 40a b x + 80a b x + 40a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1040
+
+--S 1041 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R 2 | b +-+ \| a 2 +-+ x\|b
+--R 63b |- - \|a log(-----------------------) + 126b \|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------------
+--R 5 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 1041
+
+--S 1042 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1042
+
+--S 1043 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 2 +-+ x\|b 2 +-+ |b \|a
+--R 63b \|b atan(-----) + 63b \|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) ---------------------------------------------
+--R 5 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1043
+
+--S 1044 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1044
+
+)clear all
+
+--S 1045 of 1393
+t0:=1/(x^7*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 3 13 2 11 2 9 3 7
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1045
+
+--S 1046 of 1393
+r0:=(-5/3)/(a^3*x^6)+5/2*b/(a^4*x^4)-5*b^2/(a^5*x^2)+_
+ 1/4/(a*x^6*(a+b*x^2)^2)+5/4/(a^2*x^6*(a+b*x^2))-_
+ 10*b^3*log(x)/a^6+5*b^3*log(a+b*x^2)/a^6
+--R
+--R
+--R (2)
+--R 5 10 4 8 2 3 6 2
+--R (60b x + 120a b x + 60a b x )log(b x + a)
+--R +
+--R 5 10 4 8 2 3 6 4 8 2 3 6
+--R (- 120b x - 240a b x - 120a b x )log(x) - 60a b x - 90a b x
+--R +
+--R 3 2 4 4 2 5
+--R - 20a b x + 5a b x - 2a
+--R /
+--R 6 2 10 7 8 8 6
+--R 12a b x + 24a b x + 12a x
+--R Type: Expression(Integer)
+--E 1046
+
+--S 1047 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 2 3 6 2
+--R (60b x + 120a b x + 60a b x )log(b x + a)
+--R +
+--R 5 10 4 8 2 3 6 4 8 2 3 6
+--R (- 120b x - 240a b x - 120a b x )log(x) - 60a b x - 90a b x
+--R +
+--R 3 2 4 4 2 5
+--R - 20a b x + 5a b x - 2a
+--R /
+--R 6 2 10 7 8 8 6
+--R 12a b x + 24a b x + 12a x
+--R Type: Union(Expression(Integer),...)
+--E 1047
+
+--S 1048 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1048
+
+--S 1049 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1049
+
+)clear all
+
+--S 1050 of 1393
+t0:=1/(x^8*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R 3 14 2 12 2 10 3 8
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1050
+
+--S 1051 of 1393
+r0:=(-99/56)/(a^3*x^7)+99/40*b/(a^4*x^5)-33/8*b^2/(a^5*x^3)+_
+ 99/8*b^3/(a^6*x)+1/4/(a*x^7*(a+b*x^2)^2)+11/8/(a^2*x^7*(a+b*x^2))+_
+ 99/8*b^(7/2)*atan(x*sqrt(b)/sqrt(a))/a^(13/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 5 11 4 9 2 3 7 +-+ x\|b
+--R (3465b x + 6930a b x + 3465a b x )\|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+
+--R (3465b x + 5775a b x + 1848a b x - 264a b x + 88a b x - 40a )\|a
+--R /
+--R 6 2 11 7 9 8 7 +-+
+--R (280a b x + 560a b x + 280a x )\|a
+--R Type: Expression(Integer)
+--E 1051
+
+--S 1052 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 5 11 4 9 2 3 7 | b \| a
+--R (3465b x + 6930a b x + 3465a b x ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 6930b x + 11550a b x + 3696a b x - 528a b x + 176a b x - 80a
+--R /
+--R 6 2 11 7 9 8 7
+--R 560a b x + 1120a b x + 560a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 5 11 4 9 2 3 7 |b \|a 5 10
+--R (- 3465b x - 6930a b x - 3465a b x ) |- atan(-----) + 3465b x
+--R \|a b x
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R 5775a b x + 1848a b x - 264a b x + 88a b x - 40a
+--R /
+--R 6 2 11 7 9 8 7
+--R 280a b x + 560a b x + 280a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1052
+
+--S 1053 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a +-+
+--R 3 | b +-+ \| a 3 +-+ x\|b
+--R 99b |- - \|a log(---------------------) - 198b \|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------
+--R 6 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 1053
+
+--S 1054 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1054
+
+--S 1055 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 3 +-+ x\|b 3 +-+ |b \|a
+--R - 99b \|b atan(-----) - 99b \|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -----------------------------------------------
+--R 6 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1055
+
+--S 1056 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1056
+
+)clear all
+
+--S 1057 of 1393
+t0:=1/(x^9*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R 3 15 2 13 2 11 3 9
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1057
+
+--S 1058 of 1393
+r0:=(-15/8)/(a^3*x^8)+5/2*b/(a^4*x^6)-15/4*b^2/(a^5*x^4)+_
+ 15/2*b^3/(a^6*x^2)+1/4/(a*x^8*(a+b*x^2)^2)+3/2/(a^2*x^8*(a+b*x^2))+_
+ 15*b^4*log(x)/a^7-15/2*b^4*log(a+b*x^2)/a^7
+--R
+--R
+--R (2)
+--R 6 12 5 10 2 4 8 2
+--R (- 60b x - 120a b x - 60a b x )log(b x + a)
+--R +
+--R 6 12 5 10 2 4 8 5 10 2 4 8
+--R (120b x + 240a b x + 120a b x )log(x) + 60a b x + 90a b x
+--R +
+--R 3 3 6 4 2 4 5 2 6
+--R 20a b x - 5a b x + 2a b x - a
+--R /
+--R 7 2 12 8 10 9 8
+--R 8a b x + 16a b x + 8a x
+--R Type: Expression(Integer)
+--E 1058
+
+--S 1059 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 12 5 10 2 4 8 2
+--R (- 60b x - 120a b x - 60a b x )log(b x + a)
+--R +
+--R 6 12 5 10 2 4 8 5 10 2 4 8
+--R (120b x + 240a b x + 120a b x )log(x) + 60a b x + 90a b x
+--R +
+--R 3 3 6 4 2 4 5 2 6
+--R 20a b x - 5a b x + 2a b x - a
+--R /
+--R 7 2 12 8 10 9 8
+--R 8a b x + 16a b x + 8a x
+--R Type: Union(Expression(Integer),...)
+--E 1059
+
+--S 1060 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1060
+
+--S 1061 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1061
+
+)clear all
+
+--S 1062 of 1393
+t0:=x^25/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 25
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1062
+
+--S 1063 of 1393
+r0:=55/2*a^2*x^2/b^12-5/2*a*x^4/b^11+1/6*x^6/b^10-_
+ 1/18*a^12/(b^13*(a+b*x^2)^9)+3/4*a^11/(b^13*(a+b*x^2)^8)-_
+ 33/7*a^10/(b^13*(a+b*x^2)^7)+55/3*a^9/(b^13*(a+b*x^2)^6)-_
+ 99/2*a^8/(b^13*(a+b*x^2)^5)+99*a^7/(b^13*(a+b*x^2)^4)-_
+ 154*a^6/(b^13*(a+b*x^2)^3)+198*a^5/(b^13*(a+b*x^2)^2)-_
+ 495/2*a^4/(b^13*(a+b*x^2))-110*a^3*log(a+b*x^2)/b^13
+--R
+--R
+--R (2)
+--R 3 9 18 4 8 16 5 7 14 6 6 12
+--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x
+--R +
+--R 7 5 10 8 4 8 9 3 6 10 2 4
+--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x
+--R +
+--R 11 2 12
+--R - 249480a b x - 27720a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 12 24 11 22 2 10 20 3 9 18 4 8 16
+--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x
+--R +
+--R 5 7 14 6 6 12 7 5 10 8 4 8
+--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x
+--R +
+--R 9 3 6 10 2 4 11 2 12
+--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a
+--R /
+--R 22 18 21 16 2 20 14 3 19 12 4 18 10
+--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x
+--R +
+--R 5 17 8 6 16 6 7 15 4 8 14 2 9 13
+--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b
+--R Type: Expression(Integer)
+--E 1063
+
+--S 1064 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 9 18 4 8 16 5 7 14 6 6 12
+--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x
+--R +
+--R 7 5 10 8 4 8 9 3 6 10 2 4
+--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x
+--R +
+--R 11 2 12
+--R - 249480a b x - 27720a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 12 24 11 22 2 10 20 3 9 18 4 8 16
+--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x
+--R +
+--R 5 7 14 6 6 12 7 5 10 8 4 8
+--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x
+--R +
+--R 9 3 6 10 2 4 11 2 12
+--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a
+--R /
+--R 22 18 21 16 2 20 14 3 19 12 4 18 10
+--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x
+--R +
+--R 5 17 8 6 16 6 7 15 4 8 14 2 9 13
+--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b
+--R Type: Union(Expression(Integer),...)
+--E 1064
+
+--S 1065 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1065
+
+--S 1066 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1066
+
+)clear all
+
+--S 1067 of 1393
+t0:=x^23/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 23
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1067
+
+--S 1068 of 1393
+r0:=-5*a*x^2/b^11+1/4*x^4/b^10+1/18*a^11/(b^12*(a+b*x^2)^9)-_
+ 11/16*a^10/(b^12*(a+b*x^2)^8)+55/14*a^9/(b^12*(a+b*x^2)^7)-_
+ 55/4*a^8/(b^12*(a+b*x^2)^6)+33*a^7/(b^12*(a+b*x^2)^5)-_
+ 231/4*a^6/(b^12*(a+b*x^2)^4)+77*a^5/(b^12*(a+b*x^2)^3)-_
+ 165/2*a^4/(b^12*(a+b*x^2)^2)+165/2*a^3/(b^12*(a+b*x^2))+_
+ 55/2*a^2*log(a+b*x^2)/b^12
+--R
+--R
+--R (2)
+--R 2 9 18 3 8 16 4 7 14 5 6 12
+--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x
+--R +
+--R 6 5 10 7 4 8 8 3 6 9 2 4
+--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x
+--R +
+--R 10 2 11
+--R 249480a b x + 27720a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 11 22 10 20 2 9 18 3 8 16 4 7 14
+--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8 8 3 6
+--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x
+--R +
+--R 9 2 4 10 2 11
+--R 1281096a b x + 351459a b x + 42131a
+--R /
+--R 21 18 20 16 2 19 14 3 18 12
+--R 1008b x + 9072a b x + 36288a b x + 84672a b x
+--R +
+--R 4 17 10 5 16 8 6 15 6 7 14 4
+--R 127008a b x + 127008a b x + 84672a b x + 36288a b x
+--R +
+--R 8 13 2 9 12
+--R 9072a b x + 1008a b
+--R Type: Expression(Integer)
+--E 1068
+
+--S 1069 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 9 18 3 8 16 4 7 14 5 6 12
+--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x
+--R +
+--R 6 5 10 7 4 8 8 3 6 9 2 4
+--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x
+--R +
+--R 10 2 11
+--R 249480a b x + 27720a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 11 22 10 20 2 9 18 3 8 16 4 7 14
+--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8 8 3 6
+--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x
+--R +
+--R 9 2 4 10 2 11
+--R 1281096a b x + 351459a b x + 42131a
+--R /
+--R 21 18 20 16 2 19 14 3 18 12
+--R 1008b x + 9072a b x + 36288a b x + 84672a b x
+--R +
+--R 4 17 10 5 16 8 6 15 6 7 14 4
+--R 127008a b x + 127008a b x + 84672a b x + 36288a b x
+--R +
+--R 8 13 2 9 12
+--R 9072a b x + 1008a b
+--R Type: Union(Expression(Integer),...)
+--E 1069
+
+--S 1070 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1070
+
+--S 1071 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1071
+
+)clear all
+
+--S 1072 of 1393
+t0:=x^21/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 21
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1072
+
+--S 1073 of 1393
+r0:=1/2*x^2/b^10-1/18*a^10/(b^11*(a+b*x^2)^9)+5/8*a^9/(b^11*(a+b*x^2)^8)-_
+ 45/14*a^8/(b^11*(a+b*x^2)^7)+10*a^7/(b^11*(a+b*x^2)^6)-_
+ 21*a^6/(b^11*(a+b*x^2)^5)+63/2*a^5/(b^11*(a+b*x^2)^4)-_
+ 35*a^4/(b^11*(a+b*x^2)^3)+30*a^3/(b^11*(a+b*x^2)^2)-_
+ 45/2*a^2/(b^11*(a+b*x^2))-5*a*log(a+b*x^2)/b^11
+--R
+--R
+--R (2)
+--R 9 18 2 8 16 3 7 14 4 6 12
+--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x
+--R +
+--R 9 2 10
+--R - 22680a b x - 2520a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12
+--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x
+--R +
+--R 9 2 10
+--R - 41229a b x - 4861a
+--R /
+--R 20 18 19 16 2 18 14 3 17 12 4 16 10
+--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x
+--R +
+--R 5 15 8 6 14 6 7 13 4 8 12 2 9 11
+--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b
+--R Type: Expression(Integer)
+--E 1073
+
+--S 1074 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 18 2 8 16 3 7 14 4 6 12
+--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x
+--R +
+--R 9 2 10
+--R - 22680a b x - 2520a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12
+--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x
+--R +
+--R 9 2 10
+--R - 41229a b x - 4861a
+--R /
+--R 20 18 19 16 2 18 14 3 17 12 4 16 10
+--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x
+--R +
+--R 5 15 8 6 14 6 7 13 4 8 12 2 9 11
+--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b
+--R Type: Union(Expression(Integer),...)
+--E 1074
+
+--S 1075 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1075
+
+--S 1076 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1076
+
+)clear all
+
+--S 1077 of 1393
+t0:=x^19/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 19
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1077
+
+--S 1078 of 1393
+r0:=1/18*a^9/(b^10*(a+b*x^2)^9)-9/16*a^8/(b^10*(a+b*x^2)^8)+_
+ 18/7*a^7/(b^10*(a+b*x^2)^7)-7*a^6/(b^10*(a+b*x^2)^6)+_
+ 63/5*a^5/(b^10*(a+b*x^2)^5)-63/4*a^4/(b^10*(a+b*x^2)^4)+_
+ 14*a^3/(b^10*(a+b*x^2)^3)-9*a^2/(b^10*(a+b*x^2)^2)+_
+ 9/2*a/(b^10*(a+b*x^2))+1/2*log(a+b*x^2)/b^10
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 2520b x + 22680a b x + 90720a b x + 211680a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 317520a b x + 317520a b x + 211680a b x + 90720a b x
+--R +
+--R 8 2 9
+--R 22680a b x + 2520a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R 22680a b x + 136080a b x + 388080a b x + 661500a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 725004a b x + 518616a b x + 235224a b x + 61641a b x + 7129a
+--R /
+--R 19 18 18 16 2 17 14 3 16 12
+--R 5040b x + 45360a b x + 181440a b x + 423360a b x
+--R +
+--R 4 15 10 5 14 8 6 13 6 7 12 4
+--R 635040a b x + 635040a b x + 423360a b x + 181440a b x
+--R +
+--R 8 11 2 9 10
+--R 45360a b x + 5040a b
+--R Type: Expression(Integer)
+--E 1078
+
+--S 1079 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 2520b x + 22680a b x + 90720a b x + 211680a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 317520a b x + 317520a b x + 211680a b x + 90720a b x
+--R +
+--R 8 2 9
+--R 22680a b x + 2520a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R 22680a b x + 136080a b x + 388080a b x + 661500a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 725004a b x + 518616a b x + 235224a b x + 61641a b x + 7129a
+--R /
+--R 19 18 18 16 2 17 14 3 16 12
+--R 5040b x + 45360a b x + 181440a b x + 423360a b x
+--R +
+--R 4 15 10 5 14 8 6 13 6 7 12 4
+--R 635040a b x + 635040a b x + 423360a b x + 181440a b x
+--R +
+--R 8 11 2 9 10
+--R 45360a b x + 5040a b
+--R Type: Union(Expression(Integer),...)
+--E 1079
+
+--S 1080 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1080
+
+--S 1081 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1081
+
+)clear all
+
+--S 1082 of 1393
+t0:=x^17/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 17
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1082
+
+--S 1083 of 1393
+r0:=1/18*x^18/(a*(a+b*x^2)^9)
+--R
+--R
+--R (2)
+--R 1 18
+--R -- x
+--R 18
+--R /
+--R 9 18 2 8 16 3 7 14 4 6 12 5 5 10 6 4 8
+--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x
+--R +
+--R 7 3 6 8 2 4 9 2 10
+--R 84a b x + 36a b x + 9a b x + a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1083
+
+--S 1084 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 36a b x - 9a b x - a
+--R /
+--R 18 18 17 16 2 16 14 3 15 12 4 14 10
+--R 18b x + 162a b x + 648a b x + 1512a b x + 2268a b x
+--R +
+--R 5 13 8 6 12 6 7 11 4 8 10 2 9 9
+--R 2268a b x + 1512a b x + 648a b x + 162a b x + 18a b
+--R Type: Union(Expression(Integer),...)
+--E 1084
+
+--S 1085 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - ------
+--R 9
+--R 18a b
+--R Type: Expression(Integer)
+--E 1085
+
+--S 1086 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1086
+
+)clear all
+
+--S 1087 of 1393
+t0:=x^15/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 15
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1087
+
+--S 1088 of 1393
+r0:=1/18*x^16/(a*(a+b*x^2)^9)+1/144*x^16/(a^2*(a+b*x^2)^8)
+--R
+--R
+--R (2)
+--R 1 18 1 16
+--R --- b x + -- a x
+--R 144 16
+--R /
+--R 2 9 18 3 8 16 4 7 14 5 6 12 6 5 10 7 4 8
+--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x
+--R +
+--R 8 3 6 9 2 4 10 2 11
+--R 84a b x + 36a b x + 9a b x + a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1088
+
+--S 1089 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R - 36b x - 84a b x - 126a b x - 126a b x - 84a b x - 36a b x
+--R +
+--R 6 2 7
+--R - 9a b x - a
+--R /
+--R 17 18 16 16 2 15 14 3 14 12 4 13 10
+--R 144b x + 1296a b x + 5184a b x + 12096a b x + 18144a b x
+--R +
+--R 5 12 8 6 11 6 7 10 4 8 9 2 9 8
+--R 18144a b x + 12096a b x + 5184a b x + 1296a b x + 144a b
+--R Type: Union(Expression(Integer),...)
+--E 1089
+
+--S 1090 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - -------
+--R 2 8
+--R 144a b
+--R Type: Expression(Integer)
+--E 1090
+
+--S 1091 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1091
+
+)clear all
+
+--S 1092 of 1393
+t0:=x^13/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 13
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1092
+
+--S 1093 of 1393
+r0:=1/18*x^14/(a*(a+b*x^2)^9)+1/72*x^14/(a^2*(a+b*x^2)^8)+_
+ 1/504*x^14/(a^3*(a+b*x^2)^7)
+--R
+--R
+--R (2)
+--R 1 2 18 1 16 1 2 14
+--R --- b x + -- a b x + -- a x
+--R 504 56 14
+--R /
+--R 3 9 18 4 8 16 5 7 14 6 6 12 7 5 10 8 4 8
+--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x
+--R +
+--R 9 3 6 10 2 4 11 2 12
+--R 84a b x + 36a b x + 9a b x + a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1093
+
+--S 1094 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6
+--R - 84b x - 126a b x - 126a b x - 84a b x - 36a b x - 9a b x - a
+--R /
+--R 16 18 15 16 2 14 14 3 13 12 4 12 10
+--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x
+--R +
+--R 5 11 8 6 10 6 7 9 4 8 8 2 9 7
+--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b
+--R Type: Union(Expression(Integer),...)
+--E 1094
+
+--S 1095 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - -------
+--R 3 7
+--R 504a b
+--R Type: Expression(Integer)
+--E 1095
+
+--S 1096 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1096
+
+)clear all
+
+--S 1097 of 1393
+t0:=x^11/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 11
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1097
+
+--S 1098 of 1393
+r0:=1/18*x^12/(a*(a+b*x^2)^9)+1/48*x^12/(a^2*(a+b*x^2)^8)+_
+ 1/168*x^12/(a^3*(a+b*x^2)^7)+1/1008*x^12/(a^4*(a+b*x^2)^6)
+--R
+--R
+--R (2)
+--R 1 3 18 1 2 16 1 2 14 1 3 12
+--R ---- b x + --- a b x + -- a b x + -- a x
+--R 1008 112 28 12
+--R /
+--R 4 9 18 5 8 16 6 7 14 7 6 12 8 5 10 9 4 8
+--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x
+--R +
+--R 10 3 6 11 2 4 12 2 13
+--R 84a b x + 36a b x + 9a b x + a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1098
+
+--S 1099 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 126b x - 126a b x - 84a b x - 36a b x - 9a b x - a
+--R /
+--R 15 18 14 16 2 13 14 3 12 12
+--R 1008b x + 9072a b x + 36288a b x + 84672a b x
+--R +
+--R 4 11 10 5 10 8 6 9 6 7 8 4 8 7 2
+--R 127008a b x + 127008a b x + 84672a b x + 36288a b x + 9072a b x
+--R +
+--R 9 6
+--R 1008a b
+--R Type: Union(Expression(Integer),...)
+--E 1099
+
+--S 1100 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - --------
+--R 4 6
+--R 1008a b
+--R Type: Expression(Integer)
+--E 1100
+
+--S 1101 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1101
+
+)clear all
+
+--S 1102 of 1393
+t0:=x^9/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 9
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1102
+
+--S 1103 of 1393
+r0:=-1/18*a^4/(b^5*(a+b*x^2)^9)+1/4*a^3/(b^5*(a+b*x^2)^8)-_
+ 3/7*a^2/(b^5*(a+b*x^2)^7)+1/3*a/(b^5*(a+b*x^2)^6)+_
+ (-1/10)/(b^5*(a+b*x^2)^5)
+--R
+--R
+--R (2)
+--R 1 4 8 1 3 6 1 2 2 4 1 3 2 1 4
+--R - -- b x - -- a b x - -- a b x - --- a b x - ---- a
+--R 10 15 35 140 1260
+--R /
+--R 14 18 13 16 2 12 14 3 11 12 4 10 10 5 9 8
+--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x
+--R +
+--R 6 8 6 7 7 4 8 6 2 9 5
+--R 84a b x + 36a b x + 9a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1103
+
+--S 1104 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 8 3 6 2 2 4 3 2 4
+--R - 126b x - 84a b x - 36a b x - 9a b x - a
+--R /
+--R 14 18 13 16 2 12 14 3 11 12
+--R 1260b x + 11340a b x + 45360a b x + 105840a b x
+--R +
+--R 4 10 10 5 9 8 6 8 6 7 7 4 8 6 2
+--R 158760a b x + 158760a b x + 105840a b x + 45360a b x + 11340a b x
+--R +
+--R 9 5
+--R 1260a b
+--R Type: Union(Expression(Integer),...)
+--E 1104
+
+--S 1105 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1105
+
+--S 1106 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1106
+
+)clear all
+
+--S 1107 of 1393
+t0:=x^7/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 7
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1107
+
+--S 1108 of 1393
+r0:=1/18*a^3/(b^4*(a+b*x^2)^9)-3/16*a^2/(b^4*(a+b*x^2)^8)+_
+ 3/14*a/(b^4*(a+b*x^2)^7)+(-1/12)/(b^4*(a+b*x^2)^6)
+--R
+--R
+--R (2)
+--R 1 3 6 1 2 4 1 2 2 1 3
+--R - -- b x - -- a b x - --- a b x - ---- a
+--R 12 28 112 1008
+--R /
+--R 13 18 12 16 2 11 14 3 10 12 4 9 10 5 8 8
+--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x
+--R +
+--R 6 7 6 7 6 4 8 5 2 9 4
+--R 84a b x + 36a b x + 9a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1108
+
+--S 1109 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 6 2 4 2 2 3
+--R - 84b x - 36a b x - 9a b x - a
+--R /
+--R 13 18 12 16 2 11 14 3 10 12 4 9 10
+--R 1008b x + 9072a b x + 36288a b x + 84672a b x + 127008a b x
+--R +
+--R 5 8 8 6 7 6 7 6 4 8 5 2 9 4
+--R 127008a b x + 84672a b x + 36288a b x + 9072a b x + 1008a b
+--R Type: Union(Expression(Integer),...)
+--E 1109
+
+--S 1110 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1110
+
+--S 1111 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1111
+
+)clear all
+
+--S 1112 of 1393
+t0:=x^5/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 5
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1112
+
+--S 1113 of 1393
+r0:=-1/18*a^2/(b^3*(a+b*x^2)^9)+1/8*a/(b^3*(a+b*x^2)^8)+_
+ (-1/14)/(b^3*(a+b*x^2)^7)
+--R
+--R
+--R (2)
+--R 1 2 4 1 2 1 2
+--R - -- b x - -- a b x - --- a
+--R 14 56 504
+--R /
+--R 12 18 11 16 2 10 14 3 9 12 4 8 10 5 7 8
+--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x
+--R +
+--R 6 6 6 7 5 4 8 4 2 9 3
+--R 84a b x + 36a b x + 9a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1113
+
+--S 1114 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2
+--R - 36b x - 9a b x - a
+--R /
+--R 12 18 11 16 2 10 14 3 9 12 4 8 10
+--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x
+--R +
+--R 5 7 8 6 6 6 7 5 4 8 4 2 9 3
+--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b
+--R Type: Union(Expression(Integer),...)
+--E 1114
+
+--S 1115 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1115
+
+--S 1116 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1116
+
+)clear all
+
+--S 1117 of 1393
+t0:=x^3/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 3
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1117
+
+--S 1118 of 1393
+r0:=1/18*a/(b^2*(a+b*x^2)^9)+(-1/16)/(b^2*(a+b*x^2)^8)
+--R
+--R
+--R (2)
+--R 1 2 1
+--R - -- b x - --- a
+--R 16 144
+--R /
+--R 11 18 10 16 2 9 14 3 8 12 4 7 10 5 6 8
+--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x
+--R +
+--R 6 5 6 7 4 4 8 3 2 9 2
+--R 84a b x + 36a b x + 9a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1118
+
+--S 1119 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2
+--R - 9b x - a
+--R /
+--R 11 18 10 16 2 9 14 3 8 12 4 7 10
+--R 144b x + 1296a b x + 5184a b x + 12096a b x + 18144a b x
+--R +
+--R 5 6 8 6 5 6 7 4 4 8 3 2 9 2
+--R 18144a b x + 12096a b x + 5184a b x + 1296a b x + 144a b
+--R Type: Union(Expression(Integer),...)
+--E 1119
+
+--S 1120 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1120
+
+--S 1121 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1121
+
+)clear all
+
+--S 1122 of 1393
+t0:=x/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1122
+
+--S 1123 of 1393
+r0:=(-1/18)/(b*(a+b*x^2)^9)
+--R
+--R
+--R (2)
+--R -
+--R 1
+--R --
+--R 18
+--R /
+--R 10 18 9 16 2 8 14 3 7 12 4 6 10 5 5 8
+--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x
+--R +
+--R 6 4 6 7 3 4 8 2 2 9
+--R 84a b x + 36a b x + 9a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1123
+
+--S 1124 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 1
+--R /
+--R 10 18 9 16 2 8 14 3 7 12 4 6 10
+--R 18b x + 162a b x + 648a b x + 1512a b x + 2268a b x
+--R +
+--R 5 5 8 6 4 6 7 3 4 8 2 2 9
+--R 2268a b x + 1512a b x + 648a b x + 162a b x + 18a b
+--R Type: Union(Expression(Integer),...)
+--E 1124
+
+--S 1125 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1125
+
+--S 1126 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1126
+
+)clear all
+
+--S 1127 of 1393
+t0:=1/(x*(a+b*x^2)^10)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 10 21 9 19 2 8 17 3 7 15 4 6 13 5 5 11
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 9 7 3 7 8 2 5 9 3 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1127
+
+--S 1128 of 1393
+r0:=1/18/(a*(a+b*x^2)^9)+1/16/(a^2*(a+b*x^2)^8)+1/14/(a^3*(a+b*x^2)^7)+_
+ 1/12/(a^4*(a+b*x^2)^6)+1/10/(a^5*(a+b*x^2)^5)+_
+ 1/8/(a^6*(a+b*x^2)^4)+1/6/(a^7*(a+b*x^2)^3)+_
+ 1/4/(a^8*(a+b*x^2)^2)+1/2/(a^9*(a+b*x^2))+log(x)/a^10-_
+ 1/2*log(a+b*x^2)/a^10
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R - 2520b x - 22680a b x - 90720a b x - 211680a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x
+--R +
+--R 8 2 9
+--R - 22680a b x - 2520a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 9 18 8 16 2 7 14 3 6 12
+--R 5040b x + 45360a b x + 181440a b x + 423360a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 635040a b x + 635040a b x + 423360a b x + 181440a b x
+--R +
+--R 8 2 9
+--R 45360a b x + 5040a
+--R *
+--R log(x)
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10 5 4 8
+--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R 210756a b x + 120564a b x + 41481a b x + 7129a
+--R /
+--R 10 9 18 11 8 16 12 7 14 13 6 12
+--R 5040a b x + 45360a b x + 181440a b x + 423360a b x
+--R +
+--R 14 5 10 15 4 8 16 3 6 17 2 4
+--R 635040a b x + 635040a b x + 423360a b x + 181440a b x
+--R +
+--R 18 2 19
+--R 45360a b x + 5040a
+--R Type: Expression(Integer)
+--E 1128
+
+--S 1129 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 18 8 16 2 7 14 3 6 12
+--R - 2520b x - 22680a b x - 90720a b x - 211680a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x
+--R +
+--R 8 2 9
+--R - 22680a b x - 2520a
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 9 18 8 16 2 7 14 3 6 12
+--R 5040b x + 45360a b x + 181440a b x + 423360a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 635040a b x + 635040a b x + 423360a b x + 181440a b x
+--R +
+--R 8 2 9
+--R 45360a b x + 5040a
+--R *
+--R log(x)
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10 5 4 8
+--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R 210756a b x + 120564a b x + 41481a b x + 7129a
+--R /
+--R 10 9 18 11 8 16 12 7 14 13 6 12
+--R 5040a b x + 45360a b x + 181440a b x + 423360a b x
+--R +
+--R 14 5 10 15 4 8 16 3 6 17 2 4
+--R 635040a b x + 635040a b x + 423360a b x + 181440a b x
+--R +
+--R 18 2 19
+--R 45360a b x + 5040a
+--R Type: Union(Expression(Integer),...)
+--E 1129
+
+--S 1130 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1130
+
+--S 1131 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1131
+
+)clear all
+
+--S 1132 of 1393
+t0:=1/(x^3*(a+b*x^2)^10)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 10 23 9 21 2 8 19 3 7 17 4 6 15 5 5 13
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 11 7 3 9 8 2 7 9 5 10 3
+--R 210a b x + 120a b x + 45a b x + 10a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1132
+
+--S 1133 of 1393
+r0:=(-5)/(a^10*x^2)+1/18/(a*x^2*(a+b*x^2)^9)+5/72/(a^2*x^2*(a+b*x^2)^8)+_
+ 5/56/(a^3*x^2*(a+b*x^2)^7)+5/42/(a^4*x^2*(a+b*x^2)^6)+_
+ 1/6/(a^5*x^2*(a+b*x^2)^5)+1/4/(a^6*x^2*(a+b*x^2)^4)+_
+ 5/12/(a^7*x^2*(a+b*x^2)^3)+5/6/(a^8*x^2*(a+b*x^2)^2)+_
+ 5/2/(a^9*x^2*(a+b*x^2))-10*b*log(x)/a^11+5*b*log(a+b*x^2)/a^11
+--R
+--R
+--R (2)
+--R 10 20 9 18 2 8 16 3 7 14
+--R 2520b x + 22680a b x + 90720a b x + 211680a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8 7 3 6
+--R 317520a b x + 317520a b x + 211680a b x + 90720a b x
+--R +
+--R 8 2 4 9 2
+--R 22680a b x + 2520a b x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 10 20 9 18 2 8 16 3 7 14
+--R - 5040b x - 45360a b x - 181440a b x - 423360a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8 7 3 6
+--R - 635040a b x - 635040a b x - 423360a b x - 181440a b x
+--R +
+--R 8 2 4 9 2
+--R - 45360a b x - 5040a b x
+--R *
+--R log(x)
+--R +
+--R 9 18 2 8 16 3 7 14 4 6 12
+--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2
+--R - 236754a b x - 210756a b x - 120564a b x - 41481a b x - 7129a b x
+--R +
+--R 10
+--R - 252a
+--R /
+--R 11 9 20 12 8 18 13 7 16 14 6 14
+--R 504a b x + 4536a b x + 18144a b x + 42336a b x
+--R +
+--R 15 5 12 16 4 10 17 3 8 18 2 6 19 4
+--R 63504a b x + 63504a b x + 42336a b x + 18144a b x + 4536a b x
+--R +
+--R 20 2
+--R 504a x
+--R Type: Expression(Integer)
+--E 1133
+
+--S 1134 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 20 9 18 2 8 16 3 7 14
+--R 2520b x + 22680a b x + 90720a b x + 211680a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8 7 3 6
+--R 317520a b x + 317520a b x + 211680a b x + 90720a b x
+--R +
+--R 8 2 4 9 2
+--R 22680a b x + 2520a b x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 10 20 9 18 2 8 16 3 7 14
+--R - 5040b x - 45360a b x - 181440a b x - 423360a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8 7 3 6
+--R - 635040a b x - 635040a b x - 423360a b x - 181440a b x
+--R +
+--R 8 2 4 9 2
+--R - 45360a b x - 5040a b x
+--R *
+--R log(x)
+--R +
+--R 9 18 2 8 16 3 7 14 4 6 12
+--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2
+--R - 236754a b x - 210756a b x - 120564a b x - 41481a b x - 7129a b x
+--R +
+--R 10
+--R - 252a
+--R /
+--R 11 9 20 12 8 18 13 7 16 14 6 14
+--R 504a b x + 4536a b x + 18144a b x + 42336a b x
+--R +
+--R 15 5 12 16 4 10 17 3 8 18 2 6 19 4
+--R 63504a b x + 63504a b x + 42336a b x + 18144a b x + 4536a b x
+--R +
+--R 20 2
+--R 504a x
+--R Type: Union(Expression(Integer),...)
+--E 1134
+
+--S 1135 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1135
+
+--S 1136 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1136
+
+)clear all
+
+--S 1137 of 1393
+t0:=1/(x^5*(a+b*x^2)^10)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 10 25 9 23 2 8 21 3 7 19 4 6 17 5 5 15
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 13 7 3 11 8 2 9 9 7 10 5
+--R 210a b x + 120a b x + 45a b x + 10a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1137
+
+--S 1138 of 1393
+r0:=(-55/4)/(a^10*x^4)+55/2*b/(a^11*x^2)+1/18/(a*x^4*(a+b*x^2)^9)+_
+ 11/144/(a^2*x^4*(a+b*x^2)^8)+55/504/(a^3*x^4*(a+b*x^2)^7)+_
+ 55/336/(a^4*x^4*(a+b*x^2)^6)+11/42/(a^5*x^4*(a+b*x^2)^5)+_
+ 11/24/(a^6*x^4*(a+b*x^2)^4)+11/12/(a^7*x^4*(a+b*x^2)^3)+_
+ 55/24/(a^8*x^4*(a+b*x^2)^2)+55/6/(a^9*x^4*(a+b*x^2))+_
+ 55*b^2*log(x)/a^12-55/2*b^2*log(a+b*x^2)/a^12
+--R
+--R
+--R (2)
+--R 11 22 10 20 2 9 18 3 8 16
+--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x
+--R +
+--R 4 7 14 5 6 12 6 5 10 7 4 8
+--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x
+--R +
+--R 8 3 6 9 2 4
+--R - 249480a b x - 27720a b x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 11 22 10 20 2 9 18 3 8 16
+--R 55440b x + 498960a b x + 1995840a b x + 4656960a b x
+--R +
+--R 4 7 14 5 6 12 6 5 10 7 4 8
+--R 6985440a b x + 6985440a b x + 4656960a b x + 1995840a b x
+--R +
+--R 8 3 6 9 2 4
+--R 498960a b x + 55440a b x
+--R *
+--R log(x)
+--R +
+--R 10 20 2 9 18 3 8 16 4 7 14
+--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8 8 3 6
+--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x
+--R +
+--R 9 2 4 10 2 11
+--R 78419a b x + 2772a b x - 252a
+--R /
+--R 12 9 22 13 8 20 14 7 18 15 6 16
+--R 1008a b x + 9072a b x + 36288a b x + 84672a b x
+--R +
+--R 16 5 14 17 4 12 18 3 10 19 2 8
+--R 127008a b x + 127008a b x + 84672a b x + 36288a b x
+--R +
+--R 20 6 21 4
+--R 9072a b x + 1008a x
+--R Type: Expression(Integer)
+--E 1138
+
+--S 1139 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 11 22 10 20 2 9 18 3 8 16
+--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x
+--R +
+--R 4 7 14 5 6 12 6 5 10 7 4 8
+--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x
+--R +
+--R 8 3 6 9 2 4
+--R - 249480a b x - 27720a b x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 11 22 10 20 2 9 18 3 8 16
+--R 55440b x + 498960a b x + 1995840a b x + 4656960a b x
+--R +
+--R 4 7 14 5 6 12 6 5 10 7 4 8
+--R 6985440a b x + 6985440a b x + 4656960a b x + 1995840a b x
+--R +
+--R 8 3 6 9 2 4
+--R 498960a b x + 55440a b x
+--R *
+--R log(x)
+--R +
+--R 10 20 2 9 18 3 8 16 4 7 14
+--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8 8 3 6
+--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x
+--R +
+--R 9 2 4 10 2 11
+--R 78419a b x + 2772a b x - 252a
+--R /
+--R 12 9 22 13 8 20 14 7 18 15 6 16
+--R 1008a b x + 9072a b x + 36288a b x + 84672a b x
+--R +
+--R 16 5 14 17 4 12 18 3 10 19 2 8
+--R 127008a b x + 127008a b x + 84672a b x + 36288a b x
+--R +
+--R 20 6 21 4
+--R 9072a b x + 1008a x
+--R Type: Union(Expression(Integer),...)
+--E 1139
+
+--S 1140 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1140
+
+--S 1141 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1141
+
+)clear all
+
+--S 1142 of 1393
+t0:=1/(x^7*(a+b*x^2)^10)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 10 27 9 25 2 8 23 3 7 21 4 6 19 5 5 17
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 15 7 3 13 8 2 11 9 9 10 7
+--R 210a b x + 120a b x + 45a b x + 10a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1142
+
+--S 1143 of 1393
+r0:=(-110/3)/(a^10*x^6)+55*b/(a^11*x^4)-110*b^2/(a^12*x^2)+_
+ 1/18/(a*x^6*(a+b*x^2)^9)+1/12/(a^2*x^6*(a+b*x^2)^8)+_
+ 11/84/(a^3*x^6*(a+b*x^2)^7)+55/252/(a^4*x^6*(a+b*x^2)^6)+_
+ 11/28/(a^5*x^6*(a+b*x^2)^5)+11/14/(a^6*x^6*(a+b*x^2)^4)+_
+ 11/6/(a^7*x^6*(a+b*x^2)^3)+11/2/(a^8*x^6*(a+b*x^2)^2)+_
+ 55/2/(a^9*x^6*(a+b*x^2))-220*b^3*log(x)/a^13+110*b^3*log(a+b*x^2)/a^13
+--R
+--R
+--R (2)
+--R 12 24 11 22 2 10 20 3 9 18
+--R 27720b x + 249480a b x + 997920a b x + 2328480a b x
+--R +
+--R 4 8 16 5 7 14 6 6 12 7 5 10
+--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x
+--R +
+--R 8 4 8 9 3 6
+--R 249480a b x + 27720a b x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 12 24 11 22 2 10 20 3 9 18
+--R - 55440b x - 498960a b x - 1995840a b x - 4656960a b x
+--R +
+--R 4 8 16 5 7 14 6 6 12 7 5 10
+--R - 6985440a b x - 6985440a b x - 4656960a b x - 1995840a b x
+--R +
+--R 8 4 8 9 3 6
+--R - 498960a b x - 55440a b x
+--R *
+--R log(x)
+--R +
+--R 11 22 2 10 20 3 9 18 4 8 16
+--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x
+--R +
+--R 5 7 14 6 6 12 7 5 10 8 4 8
+--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x
+--R +
+--R 9 3 6 10 2 4 11 2 12
+--R - 78419a b x - 2772a b x + 252a b x - 42a
+--R /
+--R 13 9 24 14 8 22 15 7 20 16 6 18 17 5 16
+--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x
+--R +
+--R 18 4 14 19 3 12 20 2 10 21 8 22 6
+--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x
+--R Type: Expression(Integer)
+--E 1143
+
+--S 1144 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 24 11 22 2 10 20 3 9 18
+--R 27720b x + 249480a b x + 997920a b x + 2328480a b x
+--R +
+--R 4 8 16 5 7 14 6 6 12 7 5 10
+--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x
+--R +
+--R 8 4 8 9 3 6
+--R 249480a b x + 27720a b x
+--R *
+--R 2
+--R log(b x + a)
+--R +
+--R 12 24 11 22 2 10 20 3 9 18
+--R - 55440b x - 498960a b x - 1995840a b x - 4656960a b x
+--R +
+--R 4 8 16 5 7 14 6 6 12 7 5 10
+--R - 6985440a b x - 6985440a b x - 4656960a b x - 1995840a b x
+--R +
+--R 8 4 8 9 3 6
+--R - 498960a b x - 55440a b x
+--R *
+--R log(x)
+--R +
+--R 11 22 2 10 20 3 9 18 4 8 16
+--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x
+--R +
+--R 5 7 14 6 6 12 7 5 10 8 4 8
+--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x
+--R +
+--R 9 3 6 10 2 4 11 2 12
+--R - 78419a b x - 2772a b x + 252a b x - 42a
+--R /
+--R 13 9 24 14 8 22 15 7 20 16 6 18 17 5 16
+--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x
+--R +
+--R 18 4 14 19 3 12 20 2 10 21 8 22 6
+--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x
+--R Type: Union(Expression(Integer),...)
+--E 1144
+
+--S 1145 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1145
+
+--S 1146 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1146
+
+)clear all
+
+--S 1147 of 1393
+t0:=x^24/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 24
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1147
+
+--S 1148 of 1393
+r0:=7436429/65536*a^2*x/b^12-7436429/196608*a*x^3/b^11+_
+ 7436429/327680*x^5/b^10-1/18*x^23/(b*(a+b*x^2)^9)-_
+ 23/288*x^21/(b^2*(a+b*x^2)^8)-23/192*x^19/(b^3*(a+b*x^2)^7)-_
+ 437/2304*x^17/(b^4*(a+b*x^2)^6)-7429/23040*x^15/(b^5*(a+b*x^2)^5)-_
+ 7429/12288*x^13/(b^6*(a+b*x^2)^4)-96577/73728*x^11/(b^7*(a+b*x^2)^3)-_
+ 1062347/294912*x^9/(b^8*(a+b*x^2)^2)-_
+ 1062347/65536*x^7/(b^9*(a+b*x^2))-_
+ 7436429/65536*a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(25/2)
+--R
+--R
+--R (2)
+--R 2 9 18 3 8 16 4 7 14
+--R - 334639305a b x - 3011753745a b x - 12047014980a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8
+--R - 28109701620a b x - 42164552430a b x - 42164552430a b x
+--R +
+--R 8 3 6 9 2 4 10 2
+--R - 28109701620a b x - 12047014980a b x - 3011753745a b x
+--R +
+--R 11
+--R - 334639305a
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 11 23 10 21 2 9 19 3 8 17
+--R 589824b x - 4521984a b x + 94961664a b x + 1469632311a b x
+--R +
+--R 4 7 15 5 6 13 6 5 11
+--R 7323998514a b x + 19562592546a b x + 32314857354a b x
+--R +
+--R 7 4 9 8 3 7 9 2 5
+--R 34810986496a b x + 24648575094a b x + 11110024926a b x
+--R +
+--R 10 3 11
+--R 2900207310a b x + 334639305a x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 21 18 20 16 2 19 14
+--R 2949120b x + 26542080a b x + 106168320a b x
+--R +
+--R 3 18 12 4 17 10 5 16 8
+--R 247726080a b x + 371589120a b x + 371589120a b x
+--R +
+--R 6 15 6 7 14 4 8 13 2 9 12
+--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a b
+--R *
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1148
+
+--S 1149 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 9 18 3 8 16 4 7 14
+--R 334639305a b x + 3011753745a b x + 12047014980a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8
+--R 28109701620a b x + 42164552430a b x + 42164552430a b x
+--R +
+--R 8 3 6 9 2 4 10 2
+--R 28109701620a b x + 12047014980a b x + 3011753745a b x
+--R +
+--R 11
+--R 334639305a
+--R *
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 11 23 10 21 2 9 19 3 8 17
+--R 1179648b x - 9043968a b x + 189923328a b x + 2939264622a b x
+--R +
+--R 4 7 15 5 6 13 6 5 11
+--R 14647997028a b x + 39125185092a b x + 64629714708a b x
+--R +
+--R 7 4 9 8 3 7 9 2 5
+--R 69621972992a b x + 49297150188a b x + 22220049852a b x
+--R +
+--R 10 3 11
+--R 5800414620a b x + 669278610a x
+--R /
+--R 21 18 20 16 2 19 14
+--R 5898240b x + 53084160a b x + 212336640a b x
+--R +
+--R 3 18 12 4 17 10 5 16 8
+--R 495452160a b x + 743178240a b x + 743178240a b x
+--R +
+--R 6 15 6 7 14 4 8 13 2 9 12
+--R 495452160a b x + 212336640a b x + 53084160a b x + 5898240a b
+--R ,
+--R
+--R 2 9 18 3 8 16 4 7 14
+--R 334639305a b x + 3011753745a b x + 12047014980a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8
+--R 28109701620a b x + 42164552430a b x + 42164552430a b x
+--R +
+--R 8 3 6 9 2 4 10 2
+--R 28109701620a b x + 12047014980a b x + 3011753745a b x
+--R +
+--R 11
+--R 334639305a
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 11 23 10 21 2 9 19 3 8 17
+--R 589824b x - 4521984a b x + 94961664a b x + 1469632311a b x
+--R +
+--R 4 7 15 5 6 13 6 5 11
+--R 7323998514a b x + 19562592546a b x + 32314857354a b x
+--R +
+--R 7 4 9 8 3 7 9 2 5
+--R 34810986496a b x + 24648575094a b x + 11110024926a b x
+--R +
+--R 10 3 11
+--R 2900207310a b x + 334639305a x
+--R /
+--R 21 18 20 16 2 19 14
+--R 2949120b x + 26542080a b x + 106168320a b x
+--R +
+--R 3 18 12 4 17 10 5 16 8
+--R 247726080a b x + 371589120a b x + 371589120a b x
+--R +
+--R 6 15 6 7 14 4 8 13 2 9 12
+--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1149
+
+--S 1150 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R 2 | a +-+ \| b 2 +-+ x\|b
+--R 7436429a |- - \|b log(-----------------------) + 14872858a \|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R ---------------------------------------------------------------------------
+--R 12 +-+
+--R 131072b \|b
+--R Type: Expression(Integer)
+--E 1150
+
+--S 1151 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1151
+
+--S 1152 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R 7436429a \|a atan(-----) + 7436429a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ------------------------------------------------------
+--R 12 +-+
+--R 65536b \|b
+--R Type: Expression(Integer)
+--E 1152
+
+--S 1153 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1153
+
+)clear all
+
+--S 1154 of 1393
+t0:=x^22/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 22
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1154
+
+--S 1155 of 1393
+r0:=-1616615/65536*a*x/b^11+1616615/196608*x^3/b^10-_
+ 1/18*x^21/(b*(a+b*x^2)^9)-7/96*x^19/(b^2*(a+b*x^2)^8)-_
+ 19/192*x^17/(b^3*(a+b*x^2)^7)-323/2304*x^15/(b^4*(a+b*x^2)^6)-_
+ 323/1536*x^13/(b^5*(a+b*x^2)^5)-4199/12288*x^11/(b^6*(a+b*x^2)^4)-_
+ 46189/73728*x^9/(b^7*(a+b*x^2)^3)-46189/32768*x^7/(b^8*(a+b*x^2)^2)-_
+ 323323/65536*x^5/(b^9*(a+b*x^2))+_
+ 1616615/65536*a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(23/2)
+--R
+--R
+--R (2)
+--R 9 18 2 8 16 3 7 14
+--R 14549535a b x + 130945815a b x + 523783260a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8
+--R 1222160940a b x + 1833241410a b x + 1833241410a b x
+--R +
+--R 7 3 6 8 2 4 9 2 10
+--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 10 21 9 19 2 8 17 3 7 15
+--R 196608b x - 4128768a b x - 63897057a b x - 318434718a b x
+--R +
+--R 4 6 13 5 5 11 6 4 9
+--R - 850547502a b x - 1404993798a b x - 1513521152a b x
+--R +
+--R 7 3 7 8 2 5 9 3 10
+--R - 1071677178a b x - 483044562a b x - 126095970a b x - 14549535a x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 20 18 19 16 2 18 14 3 17 12
+--R 589824b x + 5308416a b x + 21233664a b x + 49545216a b x
+--R +
+--R 4 16 10 5 15 8 6 14 6 7 13 4
+--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x
+--R +
+--R 8 12 2 9 11
+--R 5308416a b x + 589824a b
+--R *
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1155
+
+--S 1156 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 2 8 16 3 7 14
+--R 14549535a b x + 130945815a b x + 523783260a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8
+--R 1222160940a b x + 1833241410a b x + 1833241410a b x
+--R +
+--R 7 3 6 8 2 4 9 2 10
+--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a
+--R *
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 10 21 9 19 2 8 17 3 7 15
+--R 393216b x - 8257536a b x - 127794114a b x - 636869436a b x
+--R +
+--R 4 6 13 5 5 11 6 4 9
+--R - 1701095004a b x - 2809987596a b x - 3027042304a b x
+--R +
+--R 7 3 7 8 2 5 9 3 10
+--R - 2143354356a b x - 966089124a b x - 252191940a b x - 29099070a x
+--R /
+--R 20 18 19 16 2 18 14 3 17 12
+--R 1179648b x + 10616832a b x + 42467328a b x + 99090432a b x
+--R +
+--R 4 16 10 5 15 8 6 14 6
+--R 148635648a b x + 148635648a b x + 99090432a b x
+--R +
+--R 7 13 4 8 12 2 9 11
+--R 42467328a b x + 10616832a b x + 1179648a b
+--R ,
+--R
+--R 9 18 2 8 16 3 7 14
+--R - 14549535a b x - 130945815a b x - 523783260a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8
+--R - 1222160940a b x - 1833241410a b x - 1833241410a b x
+--R +
+--R 7 3 6 8 2 4 9 2 10
+--R - 1222160940a b x - 523783260a b x - 130945815a b x - 14549535a
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 10 21 9 19 2 8 17 3 7 15
+--R 196608b x - 4128768a b x - 63897057a b x - 318434718a b x
+--R +
+--R 4 6 13 5 5 11 6 4 9
+--R - 850547502a b x - 1404993798a b x - 1513521152a b x
+--R +
+--R 7 3 7 8 2 5 9 3 10
+--R - 1071677178a b x - 483044562a b x - 126095970a b x - 14549535a x
+--R /
+--R 20 18 19 16 2 18 14 3 17 12
+--R 589824b x + 5308416a b x + 21233664a b x + 49545216a b x
+--R +
+--R 4 16 10 5 15 8 6 14 6 7 13 4
+--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x
+--R +
+--R 8 12 2 9 11
+--R 5308416a b x + 589824a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1156
+
+--S 1157 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a +-+
+--R | a +-+ \| b +-+ x\|b
+--R 1616615a |- - \|b log(---------------------) - 3233230a\|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) ----------------------------------------------------------------------
+--R 11 +-+
+--R 131072b \|b
+--R Type: Expression(Integer)
+--E 1157
+
+--S 1158 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1158
+
+--S 1159 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R - 1616615a\|a atan(-----) - 1616615a |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ------------------------------------------------------
+--R 11 +-+
+--R 65536b \|b
+--R Type: Expression(Integer)
+--E 1159
+
+--S 1160 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1160
+
+)clear all
+
+--S 1161 of 1393
+t0:=x^20/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 20
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1161
+
+--S 1162 of 1393
+r0:=230945/65536*x/b^10-1/18*x^19/(b*(a+b*x^2)^9)-_
+ 19/288*x^17/(b^2*(a+b*x^2)^8)-323/4032*x^15/(b^3*(a+b*x^2)^7)-_
+ 1615/16128*x^13/(b^4*(a+b*x^2)^6)-4199/32256*x^11/(b^5*(a+b*x^2)^5)-_
+ 46189/258048*x^9/(b^6*(a+b*x^2)^4)-_
+ 46189/172032*x^7/(b^7*(a+b*x^2)^3)-46189/98304*x^5/(b^8*(a+b*x^2)^2)-_
+ 230945/196608*x^3/(b^9*(a+b*x^2))-_
+ 230945/65536*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(21/2)
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14
+--R - 14549535b x - 130945815a b x - 523783260a b x
+--R +
+--R 3 6 12 4 5 10 5 4 8
+--R - 1222160940a b x - 1833241410a b x - 1833241410a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R - 1222160940a b x - 523783260a b x - 130945815a b x - 14549535a
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 9 19 8 17 2 7 15 3 6 13
+--R 4128768b x + 63897057a b x + 318434718a b x + 850547502a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7
+--R 1404993798a b x + 1513521152a b x + 1071677178a b x
+--R +
+--R 7 2 5 8 3 9
+--R 483044562a b x + 126095970a b x + 14549535a x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 19 18 18 16 2 17 14
+--R 4128768b x + 37158912a b x + 148635648a b x
+--R +
+--R 3 16 12 4 15 10 5 14 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 6 13 6 7 12 4 8 11 2 9 10
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1162
+
+--S 1163 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14
+--R 14549535b x + 130945815a b x + 523783260a b x
+--R +
+--R 3 6 12 4 5 10 5 4 8
+--R 1222160940a b x + 1833241410a b x + 1833241410a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a
+--R *
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a \| b
+--R |- - log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R 9 19 8 17 2 7 15 3 6 13
+--R 8257536b x + 127794114a b x + 636869436a b x + 1701095004a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7
+--R 2809987596a b x + 3027042304a b x + 2143354356a b x
+--R +
+--R 7 2 5 8 3 9
+--R 966089124a b x + 252191940a b x + 29099070a x
+--R /
+--R 19 18 18 16 2 17 14
+--R 8257536b x + 74317824a b x + 297271296a b x
+--R +
+--R 3 16 12 4 15 10 5 14 8
+--R 693633024a b x + 1040449536a b x + 1040449536a b x
+--R +
+--R 6 13 6 7 12 4 8 11 2 9 10
+--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14
+--R 14549535b x + 130945815a b x + 523783260a b x
+--R +
+--R 3 6 12 4 5 10 5 4 8
+--R 1222160940a b x + 1833241410a b x + 1833241410a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a
+--R *
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b
+--R |- atan(----)
+--R \|b x
+--R +
+--R 9 19 8 17 2 7 15 3 6 13
+--R 4128768b x + 63897057a b x + 318434718a b x + 850547502a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7
+--R 1404993798a b x + 1513521152a b x + 1071677178a b x
+--R +
+--R 7 2 5 8 3 9
+--R 483044562a b x + 126095970a b x + 14549535a x
+--R /
+--R 19 18 18 16 2 17 14
+--R 4128768b x + 37158912a b x + 148635648a b x
+--R +
+--R 3 16 12 4 15 10 5 14 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 6 13 6 7 12 4 8 11 2 9 10
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1163
+
+--S 1164 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a +-+
+--R | a +-+ \| b +-+ x\|b
+--R 230945 |- - \|b log(----------------------- + 461890\|a atan(-----)
+--R \| b 2 +-+
+--R b x + a \|a
+--R (4) --------------------------------------------------------------------
+--R 10 +-+
+--R 131072b \|b
+--R Type: Expression(Integer)
+--E 1164
+
+--S 1165 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1165
+
+--S 1166 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R 230945\|a atan(-----) + 230945 |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ------------------------------------------------
+--R 10 +-+
+--R 65536b \|b
+--R Type: Expression(Integer)
+--E 1166
+
+--S 1167 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1167
+
+)clear all
+
+--S 1168 of 1393
+t0:=x^18/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 18
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1168
+
+--S 1169 of 1393
+r0:=-1/18*x^17/(b*(a+b*x^2)^9)-17/288*x^15/(b^2*(a+b*x^2)^8)-_
+ 85/1344*x^13/(b^3*(a+b*x^2)^7)-1105/16128*x^11/(b^4*(a+b*x^2)^6)-_
+ 2431/32256*x^9/(b^5*(a+b*x^2)^5)-2431/28672*x^7/(b^6*(a+b*x^2)^4)-_
+ 2431/24576*x^5/(b^7*(a+b*x^2)^3)-12155/98304*x^3/(b^8*(a+b*x^2)^2)-_
+ 12155/65536*x/(b^9*(a+b*x^2))+_
+ 12155/65536*atan(x*sqrt(b)/sqrt(a))/(b^(19/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x
+--R +
+--R 8 2 9
+--R 6891885a b x + 765765a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R - 3363003b x - 16759722a b x - 44765658a b x - 73947042a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 79659008a b x - 56404062a b x - 25423398a b x - 6636630a b x
+--R +
+--R 8
+--R - 765765a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 18 18 17 16 2 16 14
+--R 4128768b x + 37158912a b x + 148635648a b x
+--R +
+--R 3 15 12 4 14 10 5 13 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 6 12 6 7 11 4 8 10 2 9 9
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1169
+
+--S 1170 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12
+--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x
+--R +
+--R 8 2 9
+--R 6891885a b x + 765765a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13
+--R - 6726006b x - 33519444a b x - 89531316a b x
+--R +
+--R 3 5 11 4 4 9 5 3 7
+--R - 147894084a b x - 159318016a b x - 112808124a b x
+--R +
+--R 6 2 5 7 3 8
+--R - 50846796a b x - 13273260a b x - 1531530a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 18 18 17 16 2 16 14
+--R 8257536b x + 74317824a b x + 297271296a b x
+--R +
+--R 3 15 12 4 14 10 5 13 8
+--R 693633024a b x + 1040449536a b x + 1040449536a b x
+--R +
+--R 6 12 6 7 11 4 8 10 2 9 9
+--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12
+--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x
+--R +
+--R 8 2 9
+--R 6891885a b x + 765765a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13
+--R - 3363003b x - 16759722a b x - 44765658a b x
+--R +
+--R 3 5 11 4 4 9 5 3 7
+--R - 73947042a b x - 79659008a b x - 56404062a b x
+--R +
+--R 6 2 5 7 3 8
+--R - 25423398a b x - 6636630a b x - 765765a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 18 18 17 16 2 16 14
+--R 4128768b x + 37158912a b x + 148635648a b x
+--R +
+--R 3 15 12 4 14 10 5 13 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 6 12 6 7 11 4 8 10 2 9 9
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1170
+
+--S 1171 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 12155\|a \|b log(---------------------------) - 24310\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R ------------------------------------------------------------------------
+--R 9 +-----+ +-+ +-+
+--R 131072b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1171
+
+--S 1172 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1172
+
+--S 1173 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 12155\|a \|b atan(-------) - 12155\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) ---------------------------------------------------
+--R 9 +-+ +-+ +---+
+--R 65536b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1173
+
+--S 1174 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1174
+
+)clear all
+
+--S 1175 of 1393
+t0:=x^16/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 16
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1175
+
+--S 1176 of 1393
+r0:=-1/18*x^15/(b*(a+b*x^2)^9)-5/96*x^13/(b^2*(a+b*x^2)^8)-_
+ 65/1344*x^11/(b^3*(a+b*x^2)^7)-715/16128*x^9/(b^4*(a+b*x^2)^6)-_
+ 143/3584*x^7/(b^5*(a+b*x^2)^5)-143/4096*x^5/(b^6*(a+b*x^2)^4)-_
+ 715/24576*x^3/(b^7*(a+b*x^2)^3)-715/32768*x/(b^8*(a+b*x^2)^2)+_
+ 715/65536*x/(a*b^8*(a+b*x^2))+_
+ 715/65536*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(17/2))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 45045b x - 985866a b x - 2633274a b x - 4349826a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x
+--R +
+--R 8
+--R - 45045a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 17 18 2 16 16 3 15 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 4 14 12 5 13 10 6 12 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 7 11 6 8 10 4 9 9 2 10 8
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1176
+
+--S 1177 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 90090b x - 1971732a b x - 5266548a b x - 8699652a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 9371648a b x - 6635772a b x - 2990988a b x - 780780a b x
+--R +
+--R 8
+--R - 90090a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 17 18 2 16 16 3 15 14
+--R 8257536a b x + 74317824a b x + 297271296a b x
+--R +
+--R 4 14 12 5 13 10 6 12 8
+--R 693633024a b x + 1040449536a b x + 1040449536a b x
+--R +
+--R 7 11 6 8 10 4 9 9 2 10 8
+--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 45045b x - 985866a b x - 2633274a b x - 4349826a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x
+--R +
+--R 8
+--R - 45045a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 17 18 2 16 16 3 15 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 4 14 12 5 13 10 6 12 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 7 11 6 8 10 4 9 9 2 10 8
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1177
+
+--S 1178 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 715\|a \|b log(---------------------------) - 1430\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------------
+--R 8 +-----+ +-+ +-+
+--R 131072a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1178
+
+--S 1179 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1179
+
+--S 1180 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 715\|a \|b atan(-------) - 715\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------
+--R 8 +-+ +-+ +---+
+--R 65536a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1180
+
+--S 1181 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1181
+
+)clear all
+
+--S 1182 of 1393
+t0:=x^14/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 14
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1182
+
+--S 1183 of 1393
+r0:=-1/18*x^13/(b*(a+b*x^2)^9)-13/288*x^11/(b^2*(a+b*x^2)^8)-_
+ 143/4032*x^9/(b^3*(a+b*x^2)^7)-143/5376*x^7/(b^4*(a+b*x^2)^6)-_
+ 143/7680*x^5/(b^5*(a+b*x^2)^5)-143/12288*x^3/(b^6*(a+b*x^2)^4)-_
+ 143/24576*x/(b^7*(a+b*x^2)^3)+143/98304*x/(a*b^7*(a+b*x^2)^2)+_
+ 143/65536*x/(a^2*b^7*(a+b*x^2))+_
+ 143/65536*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(15/2))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 45045b x + 390390a b x - 2633274a b x - 4349826a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x
+--R +
+--R 8
+--R - 45045a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 2 16 18 3 15 16 4 14 14
+--R 20643840a b x + 185794560a b x + 743178240a b x
+--R +
+--R 5 13 12 6 12 10 7 11 8
+--R 1734082560a b x + 2601123840a b x + 2601123840a b x
+--R +
+--R 8 10 6 9 9 4 10 8 2 11 7
+--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1183
+
+--S 1184 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 90090b x + 780780a b x - 5266548a b x - 8699652a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 9371648a b x - 6635772a b x - 2990988a b x - 780780a b x
+--R +
+--R 8
+--R - 90090a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 2 16 18 3 15 16 4 14 14
+--R 41287680a b x + 371589120a b x + 1486356480a b x
+--R +
+--R 5 13 12 6 12 10 7 11 8
+--R 3468165120a b x + 5202247680a b x + 5202247680a b x
+--R +
+--R 8 10 6 9 9 4 10 8 2 11 7
+--R 3468165120a b x + 1486356480a b x + 371589120a b x + 41287680a b
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 45045b x + 390390a b x - 2633274a b x - 4349826a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x
+--R +
+--R 8
+--R - 45045a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 2 16 18 3 15 16 4 14 14
+--R 20643840a b x + 185794560a b x + 743178240a b x
+--R +
+--R 5 13 12 6 12 10 7 11 8
+--R 1734082560a b x + 2601123840a b x + 2601123840a b x
+--R +
+--R 8 10 6 9 9 4 10 8 2 11 7
+--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1184
+
+--S 1185 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 143\|a \|b log(---------------------------) - 286\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) --------------------------------------------------------------------
+--R 2 7 +-----+ +-+ +-+
+--R 131072a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1185
+
+--S 1186 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1186
+
+--S 1187 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 143\|a \|b atan(-------) - 143\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------
+--R 2 7 +-+ +-+ +---+
+--R 65536a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1187
+
+--S 1188 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1188
+
+)clear all
+
+--S 1189 of 1393
+t0:=x^12/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 12
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1189
+
+--S 1190 of 1393
+r0:=-1/18*x^11/(b*(a+b*x^2)^9)-11/288*x^9/(b^2*(a+b*x^2)^8)-_
+ 11/448*x^7/(b^3*(a+b*x^2)^7)-11/768*x^5/(b^4*(a+b*x^2)^6)-_
+ 11/1536*x^3/(b^5*(a+b*x^2)^5)-11/4096*x/(b^6*(a+b*x^2)^4)+_
+ 11/24576*x/(a*b^6*(a+b*x^2)^3)+55/98304*x/(a^2*b^6*(a+b*x^2)^2)+_
+ 55/65536*x/(a^3*b^6*(a+b*x^2))+_
+ 55/65536*atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(13/2))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 3465b x + 31185a b x + 124740a b x + 291060a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 436590a b x + 436590a b x + 291060a b x + 124740a b x
+--R +
+--R 8 2 9
+--R 31185a b x + 3465a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 3465b x + 30030a b x + 115038a b x - 334602a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3 8
+--R - 360448a b x - 255222a b x - 115038a b x - 30030a b x - 3465a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 3 15 18 4 14 16 5 13 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 6 12 12 7 11 10 8 10 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 9 9 6 10 8 4 11 7 2 12 6
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1190
+
+--S 1191 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12
+--R 3465b x + 31185a b x + 124740a b x + 291060a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 436590a b x + 436590a b x + 291060a b x + 124740a b x
+--R +
+--R 8 2 9
+--R 31185a b x + 3465a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 6930b x + 60060a b x + 230076a b x - 669204a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3 8
+--R - 720896a b x - 510444a b x - 230076a b x - 60060a b x - 6930a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 3 15 18 4 14 16 5 13 14
+--R 8257536a b x + 74317824a b x + 297271296a b x
+--R +
+--R 6 12 12 7 11 10 8 10 8
+--R 693633024a b x + 1040449536a b x + 1040449536a b x
+--R +
+--R 9 9 6 10 8 4 11 7 2 12 6
+--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12
+--R 3465b x + 31185a b x + 124740a b x + 291060a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 436590a b x + 436590a b x + 291060a b x + 124740a b x
+--R +
+--R 8 2 9
+--R 31185a b x + 3465a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 3465b x + 30030a b x + 115038a b x - 334602a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3 8
+--R - 360448a b x - 255222a b x - 115038a b x - 30030a b x - 3465a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 3 15 18 4 14 16 5 13 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 6 12 12 7 11 10 8 10 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 9 9 6 10 8 4 11 7 2 12 6
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1191
+
+--S 1192 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 55\|a \|b log(---------------------------) - 110\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) -------------------------------------------------------------------
+--R 3 6 +-----+ +-+ +-+
+--R 131072a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1192
+
+--S 1193 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1193
+
+--S 1194 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 55\|a \|b atan(-------) - 55\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) ---------------------------------------------
+--R 3 6 +-+ +-+ +---+
+--R 65536a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1194
+
+--S 1195 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1195
+
+)clear all
+
+--S 1196 of 1393
+t0:=x^10/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 10
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1196
+
+--S 1197 of 1393
+r0:=-1/18*x^9/(b*(a+b*x^2)^9)-1/32*x^7/(b^2*(a+b*x^2)^8)-_
+ 1/64*x^5/(b^3*(a+b*x^2)^7)-5/768*x^3/(b^4*(a+b*x^2)^6)-_
+ 1/512*x/(b^5*(a+b*x^2)^5)+1/4096*x/(a*b^5*(a+b*x^2)^4)+_
+ 7/24576*x/(a^2*b^5*(a+b*x^2)^3)+35/98304*x/(a^3*b^5*(a+b*x^2)^2)+_
+ 35/65536*x/(a^4*b^5*(a+b*x^2))+_
+ 35/65536*atan(x*sqrt(b)/sqrt(a))/(a^(9/2)*b^(11/2))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11 4 4 9
+--R 315b x + 2730a b x + 10458a b x + 23202a b x - 32768a b x
+--R +
+--R 5 3 7 6 2 5 7 3 8
+--R - 23202a b x - 10458a b x - 2730a b x - 315a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 4 14 18 5 13 16 6 12 14 7 11 12
+--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x
+--R +
+--R 8 10 10 9 9 8 10 8 6 11 7 4
+--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x
+--R +
+--R 12 6 2 13 5
+--R 5308416a b x + 589824a b
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1197
+
+--S 1198 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11 4 4 9
+--R 630b x + 5460a b x + 20916a b x + 46404a b x - 65536a b x
+--R +
+--R 5 3 7 6 2 5 7 3 8
+--R - 46404a b x - 20916a b x - 5460a b x - 630a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 4 14 18 5 13 16 6 12 14
+--R 1179648a b x + 10616832a b x + 42467328a b x
+--R +
+--R 7 11 12 8 10 10 9 9 8
+--R 99090432a b x + 148635648a b x + 148635648a b x
+--R +
+--R 10 8 6 11 7 4 12 6 2 13 5
+--R 99090432a b x + 42467328a b x + 10616832a b x + 1179648a b
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11 4 4 9
+--R 315b x + 2730a b x + 10458a b x + 23202a b x - 32768a b x
+--R +
+--R 5 3 7 6 2 5 7 3 8
+--R - 23202a b x - 10458a b x - 2730a b x - 315a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 4 14 18 5 13 16 6 12 14
+--R 589824a b x + 5308416a b x + 21233664a b x
+--R +
+--R 7 11 12 8 10 10 9 9 8
+--R 49545216a b x + 74317824a b x + 74317824a b x
+--R +
+--R 10 8 6 11 7 4 12 6 2 13 5
+--R 49545216a b x + 21233664a b x + 5308416a b x + 589824a b
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1198
+
+--S 1199 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 35\|a \|b log(---------------------------) - 70\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ------------------------------------------------------------------
+--R 4 5 +-----+ +-+ +-+
+--R 131072a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1199
+
+--S 1200 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1200
+
+--S 1201 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 35\|a \|b atan(-------) - 35\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) ---------------------------------------------
+--R 4 5 +-+ +-+ +---+
+--R 65536a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1201
+
+--S 1202 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1202
+
+)clear all
+
+--S 1203 of 1393
+t0:=x^8/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 8
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1203
+
+--S 1204 of 1393
+r0:=-1/18*x^7/(b*(a+b*x^2)^9)-7/288*x^5/(b^2*(a+b*x^2)^8)-_
+ 5/576*x^3/(b^3*(a+b*x^2)^7)-5/2304*x/(b^4*(a+b*x^2)^6)+_
+ 1/4608*x/(a*b^4*(a+b*x^2)^5)+1/4096*x/(a^2*b^4*(a+b*x^2)^4)+_
+ 7/24576*x/(a^3*b^4*(a+b*x^2)^3)+35/98304*x/(a^4*b^4*(a+b*x^2)^2)+_
+ 35/65536*x/(a^5*b^4*(a+b*x^2))+_
+ 35/65536*atan(x*sqrt(b)/sqrt(a))/(a^(11/2)*b^(9/2))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11 4 4 9
+--R 315b x + 2730a b x + 10458a b x + 23202a b x + 32768a b x
+--R +
+--R 5 3 7 6 2 5 7 3 8
+--R - 23202a b x - 10458a b x - 2730a b x - 315a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 5 13 18 6 12 16 7 11 14 8 10 12
+--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x
+--R +
+--R 9 9 10 10 8 8 11 7 6 12 6 4
+--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x
+--R +
+--R 13 5 2 14 4
+--R 5308416a b x + 589824a b
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1204
+
+--S 1205 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11 4 4 9
+--R 630b x + 5460a b x + 20916a b x + 46404a b x + 65536a b x
+--R +
+--R 5 3 7 6 2 5 7 3 8
+--R - 46404a b x - 20916a b x - 5460a b x - 630a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 5 13 18 6 12 16 7 11 14
+--R 1179648a b x + 10616832a b x + 42467328a b x
+--R +
+--R 8 10 12 9 9 10 10 8 8
+--R 99090432a b x + 148635648a b x + 148635648a b x
+--R +
+--R 11 7 6 12 6 4 13 5 2 14 4
+--R 99090432a b x + 42467328a b x + 10616832a b x + 1179648a b
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11 4 4 9
+--R 315b x + 2730a b x + 10458a b x + 23202a b x + 32768a b x
+--R +
+--R 5 3 7 6 2 5 7 3 8
+--R - 23202a b x - 10458a b x - 2730a b x - 315a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 5 13 18 6 12 16 7 11 14
+--R 589824a b x + 5308416a b x + 21233664a b x
+--R +
+--R 8 10 12 9 9 10 10 8 8
+--R 49545216a b x + 74317824a b x + 74317824a b x
+--R +
+--R 11 7 6 12 6 4 13 5 2 14 4
+--R 49545216a b x + 21233664a b x + 5308416a b x + 589824a b
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1205
+
+--S 1206 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 35\|a \|b log(---------------------------) - 70\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ------------------------------------------------------------------
+--R 5 4 +-----+ +-+ +-+
+--R 131072a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1206
+
+--S 1207 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1207
+
+--S 1208 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 35\|a \|b atan(-------) - 35\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) ---------------------------------------------
+--R 5 4 +-+ +-+ +---+
+--R 65536a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1208
+
+--S 1209 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1209
+
+)clear all
+
+--S 1210 of 1393
+t0:=x^6/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 6
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1210
+
+--S 1211 of 1393
+r0:=-1/18*x^5/(b*(a+b*x^2)^9)-5/288*x^3/(b^2*(a+b*x^2)^8)-_
+ 5/1344*x/(b^3*(a+b*x^2)^7)+5/16128*x/(a*b^3*(a+b*x^2)^6)+_
+ 11/32256*x/(a^2*b^3*(a+b*x^2)^5)+11/28672*x/(a^3*b^3*(a+b*x^2)^4)+_
+ 11/24576*x/(a^4*b^3*(a+b*x^2)^3)+55/98304*x/(a^5*b^3*(a+b*x^2)^2)+_
+ 55/65536*x/(a^6*b^3*(a+b*x^2))+_
+ 55/65536*atan(x*sqrt(b)/sqrt(a))/(a^(13/2)*b^(7/2))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 3465b x + 31185a b x + 124740a b x + 291060a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 436590a b x + 436590a b x + 291060a b x + 124740a b x
+--R +
+--R 8 2 9
+--R 31185a b x + 3465a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 3465b x + 30030a b x + 115038a b x + 255222a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3 8
+--R 360448a b x + 334602a b x - 115038a b x - 30030a b x - 3465a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 6 12 18 7 11 16 8 10 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 9 9 12 10 8 10 11 7 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 12 6 6 13 5 4 14 4 2 15 3
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1211
+
+--S 1212 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12
+--R 3465b x + 31185a b x + 124740a b x + 291060a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 436590a b x + 436590a b x + 291060a b x + 124740a b x
+--R +
+--R 8 2 9
+--R 31185a b x + 3465a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 6930b x + 60060a b x + 230076a b x + 510444a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3 8
+--R 720896a b x + 669204a b x - 230076a b x - 60060a b x - 6930a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 6 12 18 7 11 16 8 10 14
+--R 8257536a b x + 74317824a b x + 297271296a b x
+--R +
+--R 9 9 12 10 8 10 11 7 8
+--R 693633024a b x + 1040449536a b x + 1040449536a b x
+--R +
+--R 12 6 6 13 5 4 14 4 2 15 3
+--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12
+--R 3465b x + 31185a b x + 124740a b x + 291060a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 436590a b x + 436590a b x + 291060a b x + 124740a b x
+--R +
+--R 8 2 9
+--R 31185a b x + 3465a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 3465b x + 30030a b x + 115038a b x + 255222a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3 8
+--R 360448a b x + 334602a b x - 115038a b x - 30030a b x - 3465a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 6 12 18 7 11 16 8 10 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 9 9 12 10 8 10 11 7 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 12 6 6 13 5 4 14 4 2 15 3
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1212
+
+--S 1213 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 55\|a \|b log(---------------------------) - 110\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) -------------------------------------------------------------------
+--R 6 3 +-----+ +-+ +-+
+--R 131072a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1213
+
+--S 1214 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1214
+
+--S 1215 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 55\|a \|b atan(-------) - 55\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) ---------------------------------------------
+--R 6 3 +-+ +-+ +---+
+--R 65536a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1215
+
+--S 1216 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1216
+
+)clear all
+
+--S 1217 of 1393
+t0:=x^4/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 4
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1217
+
+--S 1218 of 1393
+r0:=-1/18*x^3/(b*(a+b*x^2)^9)-1/96*x/(b^2*(a+b*x^2)^8)+_
+ 1/1344*x/(a*b^2*(a+b*x^2)^7)+13/16128*x/(a^2*b^2*(a+b*x^2)^6)+_
+ 143/161280*x/(a^3*b^2*(a+b*x^2)^5)+143/143360*x/(a^4*b^2*(a+b*x^2)^4)+_
+ 143/122880*x/(a^5*b^2*(a+b*x^2)^3)+143/98304*x/(a^6*b^2*(a+b*x^2)^2)+_
+ 143/65536*x/(a^7*b^2*(a+b*x^2))+_
+ 143/65536*atan(x*sqrt(b)/sqrt(a))/(a^(15/2)*b^(5/2))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3 8
+--R 4685824a b x + 4349826a b x + 2633274a b x - 390390a b x - 45045a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 7 11 18 8 10 16 9 9 14
+--R 20643840a b x + 185794560a b x + 743178240a b x
+--R +
+--R 10 8 12 11 7 10 12 6 8
+--R 1734082560a b x + 2601123840a b x + 2601123840a b x
+--R +
+--R 13 5 6 14 4 4 15 3 2 16 2
+--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1218
+
+--S 1219 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 90090b x + 780780a b x + 2990988a b x + 6635772a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 9371648a b x + 8699652a b x + 5266548a b x - 780780a b x
+--R +
+--R 8
+--R - 90090a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 7 11 18 8 10 16 9 9 14
+--R 41287680a b x + 371589120a b x + 1486356480a b x
+--R +
+--R 10 8 12 11 7 10 12 6 8
+--R 3468165120a b x + 5202247680a b x + 5202247680a b x
+--R +
+--R 13 5 6 14 4 4 15 3 2
+--R 3468165120a b x + 1486356480a b x + 371589120a b x
+--R +
+--R 16 2
+--R 41287680a b
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 4685824a b x + 4349826a b x + 2633274a b x - 390390a b x
+--R +
+--R 8
+--R - 45045a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 7 11 18 8 10 16 9 9 14
+--R 20643840a b x + 185794560a b x + 743178240a b x
+--R +
+--R 10 8 12 11 7 10 12 6 8
+--R 1734082560a b x + 2601123840a b x + 2601123840a b x
+--R +
+--R 13 5 6 14 4 4 15 3 2 16 2
+--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1219
+
+--S 1220 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 143\|a \|b log(---------------------------) - 286\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) --------------------------------------------------------------------
+--R 7 2 +-----+ +-+ +-+
+--R 131072a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1220
+
+--S 1221 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1221
+
+--S 1222 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 143\|a \|b atan(-------) - 143\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------
+--R 7 2 +-+ +-+ +---+
+--R 65536a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1222
+
+--S 1223 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1223
+
+)clear all
+
+--S 1224 of 1393
+t0:=x^2/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 2
+--R x
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1224
+
+--S 1225 of 1393
+r0:=-1/18*x/(b*(a+b*x^2)^9)+1/288*x/(a*b*(a+b*x^2)^8)+_
+ 5/1344*x/(a^2*b*(a+b*x^2)^7)+65/16128*x/(a^3*b*(a+b*x^2)^6)+_
+ 143/32256*x/(a^4*b*(a+b*x^2)^5)+143/28672*x/(a^5*b*(a+b*x^2)^4)+_
+ 143/24576*x/(a^6*b*(a+b*x^2)^3)+715/98304*x/(a^7*b*(a+b*x^2)^2)+_
+ 715/65536*x/(a^8*b*(a+b*x^2))+_
+ 715/65536*atan(x*sqrt(b)/sqrt(a))/(a^(17/2)*b^(3/2))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3 8
+--R 4685824a b x + 4349826a b x + 2633274a b x + 985866a b x - 45045a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 8 10 18 9 9 16 10 8 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 11 7 12 12 6 10 13 5 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 14 4 6 15 3 4 16 2 2 17
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1225
+
+--S 1226 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 90090b x + 780780a b x + 2990988a b x + 6635772a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 9371648a b x + 8699652a b x + 5266548a b x + 1971732a b x
+--R +
+--R 8
+--R - 90090a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 8 10 18 9 9 16 10 8 14
+--R 8257536a b x + 74317824a b x + 297271296a b x
+--R +
+--R 11 7 12 12 6 10 13 5 8
+--R 693633024a b x + 1040449536a b x + 1040449536a b x
+--R +
+--R 14 4 6 15 3 4 16 2 2 17
+--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12
+--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x
+--R +
+--R 8 2 9
+--R 405405a b x + 45045a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 4685824a b x + 4349826a b x + 2633274a b x + 985866a b x
+--R +
+--R 8
+--R - 45045a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 8 10 18 9 9 16 10 8 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 11 7 12 12 6 10 13 5 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 14 4 6 15 3 4 16 2 2 17
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1226
+
+--S 1227 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 715\|a \|b log(---------------------------) - 1430\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R (4) ---------------------------------------------------------------------
+--R 8 +-----+ +-+ +-+
+--R 131072a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1227
+
+--S 1228 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1228
+
+--S 1229 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 715\|a \|b atan(-------) - 715\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------
+--R 8 +-+ +-+ +---+
+--R 65536a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1229
+
+--S 1230 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1230
+
+)clear all
+
+--S 1231 of 1393
+t0:=1/(a+b*x^2)^10
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 210a b x + 120a b x + 45a b x + 10a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1231
+
+--S 1232 of 1393
+r0:=1/18*x/(a*(a+b*x^2)^9)+17/288*x/(a^2*(a+b*x^2)^8)+_
+ 85/1344*x/(a^3*(a+b*x^2)^7)+1105/16128*x/(a^4*(a+b*x^2)^6)+_
+ 2431/32256*x/(a^5*(a+b*x^2)^5)+2431/28672*x/(a^6*(a+b*x^2)^4)+_
+ 2431/24576*x/(a^7*(a+b*x^2)^3)+12155/98304*x/(a^8*(a+b*x^2)^2)+_
+ 12155/65536*x/(a^9*(a+b*x^2))+_
+ 12155/65536*atan(x*sqrt(b)/sqrt(a))/(a^(19/2)*sqrt(b))
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12
+--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x
+--R +
+--R 8 2 9
+--R 6891885a b x + 765765a
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 765765b x + 6636630a b x + 25423398a b x + 56404062a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 79659008a b x + 73947042a b x + 44765658a b x + 16759722a b x
+--R +
+--R 8
+--R 3363003a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 9 9 18 10 8 16 11 7 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 12 6 12 13 5 10 14 4 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 15 3 6 16 2 4 17 2 18
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1232
+
+--S 1233 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 18 8 16 2 7 14 3 6 12
+--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x
+--R +
+--R 8 2 9
+--R 6891885a b x + 765765a
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 1531530b x + 13273260a b x + 50846796a b x + 112808124a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 159318016a b x + 147894084a b x + 89531316a b x + 33519444a b x
+--R +
+--R 8
+--R 6726006a x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 9 9 18 10 8 16 11 7 14
+--R 8257536a b x + 74317824a b x + 297271296a b x
+--R +
+--R 12 6 12 13 5 10 14 4 8
+--R 693633024a b x + 1040449536a b x + 1040449536a b x
+--R +
+--R 15 3 6 16 2 4 17 2 18
+--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a
+--R *
+--R +-----+
+--R \|- a b
+--R ,
+--R
+--R 9 18 8 16 2 7 14 3 6 12
+--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x
+--R +
+--R 8 2 9
+--R 6891885a b x + 765765a
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 765765b x + 6636630a b x + 25423398a b x + 56404062a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 79659008a b x + 73947042a b x + 44765658a b x + 16759722a b x
+--R +
+--R 8
+--R 3363003a x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 9 9 18 10 8 16 11 7 14
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 12 6 12 13 5 10 14 4 8
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 15 3 6 16 2 4 17 2 18
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a
+--R *
+--R +---+
+--R \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1233
+
+--S 1234 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+ +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b
+--R 12155\|a \|b log(---------------------------) - 24310\|- a b atan(-----)
+--R 2 +-+
+--R b x + a \|a
+--R ------------------------------------------------------------------------
+--R 9 +-----+ +-+ +-+
+--R 131072a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1234
+
+--S 1235 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1235
+
+--S 1236 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R 12155\|a \|b atan(-------) - 12155\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) ---------------------------------------------------
+--R 9 +-+ +-+ +---+
+--R 65536a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1236
+
+--S 1237 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1237
+
+)clear all
+
+--S 1238 of 1393
+t0:=1/(x^2*(a+b*x^2)^10)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 10 22 9 20 2 8 18 3 7 16 4 6 14 5 5 12
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 10 7 3 8 8 2 6 9 4 10 2
+--R 210a b x + 120a b x + 45a b x + 10a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1238
+
+--S 1239 of 1393
+r0:=(-230945/65536)/(a^10*x)+1/18/(a*x*(a+b*x^2)^9)+_
+ 19/288/(a^2*x*(a+b*x^2)^8)+323/4032/(a^3*x*(a+b*x^2)^7)+_
+ 1615/16128/(a^4*x*(a+b*x^2)^6)+4199/32256/(a^5*x*(a+b*x^2)^5)+_
+ 46189/258048/(a^6*x*(a+b*x^2)^4)+46189/172032/(a^7*x*(a+b*x^2)^3)+_
+ 46189/98304/(a^8*x*(a+b*x^2)^2)+230945/196608/(a^9*x*(a+b*x^2))-_
+ 230945/65536*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(21/2)
+--R
+--R
+--R (2)
+--R 9 19 8 17 2 7 15
+--R - 14549535b x - 130945815a b x - 523783260a b x
+--R +
+--R 3 6 13 4 5 11 5 4 9
+--R - 1222160940a b x - 1833241410a b x - 1833241410a b x
+--R +
+--R 6 3 7 7 2 5 8 3 9
+--R - 1222160940a b x - 523783260a b x - 130945815a b x - 14549535a x
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 9 18 8 16 2 7 14
+--R - 14549535b x - 126095970a b x - 483044562a b x
+--R +
+--R 3 6 12 4 5 10 5 4 8
+--R - 1071677178a b x - 1513521152a b x - 1404993798a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R - 850547502a b x - 318434718a b x - 63897057a b x - 4128768a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 10 9 19 11 8 17 12 7 15
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 13 6 13 14 5 11 15 4 9
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 16 3 7 17 2 5 18 3 19
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a x
+--R *
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 1239
+
+--S 1240 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 9 19 8 17 2 7 15
+--R 14549535b x + 130945815a b x + 523783260a b x
+--R +
+--R 3 6 13 4 5 11 5 4 9
+--R 1222160940a b x + 1833241410a b x + 1833241410a b x
+--R +
+--R 6 3 7 7 2 5 8 3 9
+--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a x
+--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 9 18 8 16 2 7 14
+--R - 29099070b x - 252191940a b x - 966089124a b x
+--R +
+--R 3 6 12 4 5 10 5 4 8
+--R - 2143354356a b x - 3027042304a b x - 2809987596a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R - 1701095004a b x - 636869436a b x - 127794114a b x - 8257536a
+--R /
+--R 10 9 19 11 8 17 12 7 15
+--R 8257536a b x + 74317824a b x + 297271296a b x
+--R +
+--R 13 6 13 14 5 11 15 4 9
+--R 693633024a b x + 1040449536a b x + 1040449536a b x
+--R +
+--R 16 3 7 17 2 5 18 3 19
+--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a x
+--R ,
+--R
+--R 9 19 8 17 2 7 15
+--R 14549535b x + 130945815a b x + 523783260a b x
+--R +
+--R 3 6 13 4 5 11 5 4 9
+--R 1222160940a b x + 1833241410a b x + 1833241410a b x
+--R +
+--R 6 3 7 7 2 5 8 3 9
+--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 9 18 8 16 2 7 14
+--R - 14549535b x - 126095970a b x - 483044562a b x
+--R +
+--R 3 6 12 4 5 10 5 4 8
+--R - 1071677178a b x - 1513521152a b x - 1404993798a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R - 850547502a b x - 318434718a b x - 63897057a b x - 4128768a
+--R /
+--R 10 9 19 11 8 17 12 7 15
+--R 4128768a b x + 37158912a b x + 148635648a b x
+--R +
+--R 13 6 13 14 5 11 15 4 9
+--R 346816512a b x + 520224768a b x + 520224768a b x
+--R +
+--R 16 3 7 17 2 5 18 3 19
+--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1240
+
+--S 1241 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R 230945 |- - \|a log(----------------------- + 461890\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) --------------------------------------------------------------------
+--R 10 +-+
+--R 131072a \|a
+--R Type: Expression(Integer)
+--E 1241
+
+--S 1242 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1242
+
+--S 1243 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R 230945\|b atan(-----) + 230945\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -------------------------------------------------
+--R 10 +-+
+--R 65536a \|a
+--R Type: Expression(Integer)
+--E 1243
+
+--S 1244 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1244
+
+)clear all
+
+--S 1245 of 1393
+t0:=1/(x^4*(a+b*x^2)^10)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 10 24 9 22 2 8 20 3 7 18 4 6 16 5 5 14
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 12 7 3 10 8 2 8 9 6 10 4
+--R 210a b x + 120a b x + 45a b x + 10a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1245
+
+--S 1246 of 1393
+r0:=(-1616615/196608)/(a^10*x^3)+1616615/65536*b/(a^11*x)+_
+ 1/18/(a*x^3*(a+b*x^2)^9)+7/96/(a^2*x^3*(a+b*x^2)^8)+_
+ 19/192/(a^3*x^3*(a+b*x^2)^7)+323/2304/(a^4*x^3*(a+b*x^2)^6)+_
+ 323/1536/(a^5*x^3*(a+b*x^2)^5)+4199/12288/(a^6*x^3*(a+b*x^2)^4)+_
+ 46189/73728/(a^7*x^3*(a+b*x^2)^3)+46189/32768/(a^8*x^3*(a+b*x^2)^2)+_
+ 323323/65536/(a^9*x^3*(a+b*x^2))+_
+ 1616615/65536*b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(23/2)
+--R
+--R
+--R (2)
+--R 10 21 9 19 2 8 17
+--R 14549535b x + 130945815a b x + 523783260a b x
+--R +
+--R 3 7 15 4 6 13 5 5 11
+--R 1222160940a b x + 1833241410a b x + 1833241410a b x
+--R +
+--R 6 4 9 7 3 7 8 2 5 9 3
+--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a b x
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 10 20 9 18 2 8 16
+--R 14549535b x + 126095970a b x + 483044562a b x
+--R +
+--R 3 7 14 4 6 12 5 5 10
+--R 1071677178a b x + 1513521152a b x + 1404993798a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2
+--R 850547502a b x + 318434718a b x + 63897057a b x + 4128768a b x
+--R +
+--R 10
+--R - 196608a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 11 9 21 12 8 19 13 7 17 14 6 15
+--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x
+--R +
+--R 15 5 13 16 4 11 17 3 9 18 2 7
+--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x
+--R +
+--R 19 5 20 3
+--R 5308416a b x + 589824a x
+--R *
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 1246
+
+--S 1247 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 10 21 9 19 2 8 17
+--R 14549535b x + 130945815a b x + 523783260a b x
+--R +
+--R 3 7 15 4 6 13 5 5 11
+--R 1222160940a b x + 1833241410a b x + 1833241410a b x
+--R +
+--R 6 4 9 7 3 7 8 2 5 9 3
+--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a b x
+--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 10 20 9 18 2 8 16
+--R 29099070b x + 252191940a b x + 966089124a b x
+--R +
+--R 3 7 14 4 6 12 5 5 10
+--R 2143354356a b x + 3027042304a b x + 2809987596a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2
+--R 1701095004a b x + 636869436a b x + 127794114a b x + 8257536a b x
+--R +
+--R 10
+--R - 393216a
+--R /
+--R 11 9 21 12 8 19 13 7 17
+--R 1179648a b x + 10616832a b x + 42467328a b x
+--R +
+--R 14 6 15 15 5 13 16 4 11
+--R 99090432a b x + 148635648a b x + 148635648a b x
+--R +
+--R 17 3 9 18 2 7 19 5 20 3
+--R 99090432a b x + 42467328a b x + 10616832a b x + 1179648a x
+--R ,
+--R
+--R 10 21 9 19 2 8 17
+--R - 14549535b x - 130945815a b x - 523783260a b x
+--R +
+--R 3 7 15 4 6 13 5 5 11
+--R - 1222160940a b x - 1833241410a b x - 1833241410a b x
+--R +
+--R 6 4 9 7 3 7 8 2 5
+--R - 1222160940a b x - 523783260a b x - 130945815a b x
+--R +
+--R 9 3
+--R - 14549535a b x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 10 20 9 18 2 8 16
+--R 14549535b x + 126095970a b x + 483044562a b x
+--R +
+--R 3 7 14 4 6 12 5 5 10
+--R 1071677178a b x + 1513521152a b x + 1404993798a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2
+--R 850547502a b x + 318434718a b x + 63897057a b x + 4128768a b x
+--R +
+--R 10
+--R - 196608a
+--R /
+--R 11 9 21 12 8 19 13 7 17 14 6 15
+--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x
+--R +
+--R 15 5 13 16 4 11 17 3 9 18 2 7
+--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x
+--R +
+--R 19 5 20 3
+--R 5308416a b x + 589824a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1247
+
+--S 1248 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a +-+
+--R | b +-+ \| a +-+ x\|b
+--R 1616615b |- - \|a log(---------------------) - 3233230b\|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R (4) ----------------------------------------------------------------------
+--R 11 +-+
+--R 131072a \|a
+--R Type: Expression(Integer)
+--E 1248
+
+--S 1249 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1249
+
+--S 1250 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R - 1616615b\|b atan(-----) - 1616615b\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -------------------------------------------------------
+--R 11 +-+
+--R 65536a \|a
+--R Type: Expression(Integer)
+--E 1250
+
+--S 1251 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1251
+
+)clear all
+
+--S 1252 of 1393
+t0:=1/(x^6*(a+b*x^2)^10)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 10 26 9 24 2 8 22 3 7 20 4 6 18 5 5 16
+--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x
+--R +
+--R 6 4 14 7 3 12 8 2 10 9 8 10 6
+--R 210a b x + 120a b x + 45a b x + 10a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1252
+
+--S 1253 of 1393
+r0:=(-7436429/327680)/(a^10*x^5)+7436429/196608*b/(a^11*x^3)-_
+ 7436429/65536*b^2/(a^12*x)+1/18/(a*x^5*(a+b*x^2)^9)+_
+ 23/288/(a^2*x^5*(a+b*x^2)^8)+23/192/(a^3*x^5*(a+b*x^2)^7)+_
+ 437/2304/(a^4*x^5*(a+b*x^2)^6)+7429/23040/(a^5*x^5*(a+b*x^2)^5)+_
+ 7429/12288/(a^6*x^5*(a+b*x^2)^4)+96577/73728/(a^7*x^5*(a+b*x^2)^3)+_
+ 1062347/294912/(a^8*x^5*(a+b*x^2)^2)+_
+ 1062347/65536/(a^9*x^5*(a+b*x^2))-_
+ 7436429/65536*b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(25/2)
+--R
+--R
+--R (2)
+--R 11 23 10 21 2 9 19
+--R - 334639305b x - 3011753745a b x - 12047014980a b x
+--R +
+--R 3 8 17 4 7 15 5 6 13
+--R - 28109701620a b x - 42164552430a b x - 42164552430a b x
+--R +
+--R 6 5 11 7 4 9 8 3 7
+--R - 28109701620a b x - 12047014980a b x - 3011753745a b x
+--R +
+--R 9 2 5
+--R - 334639305a b x
+--R *
+--R +-+
+--R +-+ x\|b
+--R \|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 11 22 10 20 2 9 18
+--R - 334639305b x - 2900207310a b x - 11110024926a b x
+--R +
+--R 3 8 16 4 7 14 5 6 12
+--R - 24648575094a b x - 34810986496a b x - 32314857354a b x
+--R +
+--R 6 5 10 7 4 8 8 3 6
+--R - 19562592546a b x - 7323998514a b x - 1469632311a b x
+--R +
+--R 9 2 4 10 2 11
+--R - 94961664a b x + 4521984a b x - 589824a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 12 9 23 13 8 21 14 7 19
+--R 2949120a b x + 26542080a b x + 106168320a b x
+--R +
+--R 15 6 17 16 5 15 17 4 13
+--R 247726080a b x + 371589120a b x + 371589120a b x
+--R +
+--R 18 3 11 19 2 9 20 7 21 5
+--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a x
+--R *
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 1253
+
+--S 1254 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 11 23 10 21 2 9 19
+--R 334639305b x + 3011753745a b x + 12047014980a b x
+--R +
+--R 3 8 17 4 7 15 5 6 13
+--R 28109701620a b x + 42164552430a b x + 42164552430a b x
+--R +
+--R 6 5 11 7 4 9 8 3 7
+--R 28109701620a b x + 12047014980a b x + 3011753745a b x
+--R +
+--R 9 2 5
+--R 334639305a b x
+--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 11 22 10 20 2 9 18
+--R - 669278610b x - 5800414620a b x - 22220049852a b x
+--R +
+--R 3 8 16 4 7 14 5 6 12
+--R - 49297150188a b x - 69621972992a b x - 64629714708a b x
+--R +
+--R 6 5 10 7 4 8 8 3 6
+--R - 39125185092a b x - 14647997028a b x - 2939264622a b x
+--R +
+--R 9 2 4 10 2 11
+--R - 189923328a b x + 9043968a b x - 1179648a
+--R /
+--R 12 9 23 13 8 21 14 7 19
+--R 5898240a b x + 53084160a b x + 212336640a b x
+--R +
+--R 15 6 17 16 5 15 17 4 13
+--R 495452160a b x + 743178240a b x + 743178240a b x
+--R +
+--R 18 3 11 19 2 9 20 7 21 5
+--R 495452160a b x + 212336640a b x + 53084160a b x + 5898240a x
+--R ,
+--R
+--R 11 23 10 21 2 9 19
+--R 334639305b x + 3011753745a b x + 12047014980a b x
+--R +
+--R 3 8 17 4 7 15 5 6 13
+--R 28109701620a b x + 42164552430a b x + 42164552430a b x
+--R +
+--R 6 5 11 7 4 9 8 3 7
+--R 28109701620a b x + 12047014980a b x + 3011753745a b x
+--R +
+--R 9 2 5
+--R 334639305a b x
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 11 22 10 20 2 9 18
+--R - 334639305b x - 2900207310a b x - 11110024926a b x
+--R +
+--R 3 8 16 4 7 14 5 6 12
+--R - 24648575094a b x - 34810986496a b x - 32314857354a b x
+--R +
+--R 6 5 10 7 4 8 8 3 6
+--R - 19562592546a b x - 7323998514a b x - 1469632311a b x
+--R +
+--R 9 2 4 10 2 11
+--R - 94961664a b x + 4521984a b x - 589824a
+--R /
+--R 12 9 23 13 8 21 14 7 19
+--R 2949120a b x + 26542080a b x + 106168320a b x
+--R +
+--R 15 6 17 16 5 15 17 4 13
+--R 247726080a b x + 371589120a b x + 371589120a b x
+--R +
+--R 18 3 11 19 2 9 20 7 21 5
+--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1254
+
+--S 1255 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R 2 | b +-+ \| a 2 +-+ x\|b
+--R 7436429b |- - \|a log(-----------------------) + 14872858b \|b atan(-----)
+--R \| a 2 +-+
+--R b x + a \|a
+--R ---------------------------------------------------------------------------
+--R 12 +-+
+--R 131072a \|a
+--R Type: Expression(Integer)
+--E 1255
+
+--S 1256 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1256
+
+--S 1257 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 2 +-+ x\|b 2 +-+ |b \|a
+--R 7436429b \|b atan(-----) + 7436429b \|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -------------------------------------------------------
+--R 12 +-+
+--R 65536a \|a
+--R Type: Expression(Integer)
+--E 1257
+
+--S 1258 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1258
+
+)clear all
+
+--S 1259 of 1393
+t0:=x^3/(a-b*x^2)
+--R
+--R
+--R 3
+--R x
+--R (1) - --------
+--R 2
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 1259
+
+--S 1260 of 1393
+r0:=-1/2*x^2/b-1/2*a*log(a-b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R - a log(- b x + a) - b x
+--R (2) --------------------------
+--R 2
+--R 2b
+--R Type: Expression(Integer)
+--E 1260
+
+--S 1261 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R - a log(b x - a) - b x
+--R (3) ------------------------
+--R 2
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 1261
+
+--S 1262 of 1393
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - a log(b x - a) + a log(- b x + a)
+--R (4) -------------------------------------
+--R 2
+--R 2b
+--R Type: Expression(Integer)
+--E 1262
+
+--S 1263 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1263
+
+)clear all
+
+--S 1264 of 1393
+t0:=x^2/(a-b*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) - --------
+--R 2
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 1264
+
+--S 1265 of 1393
+r0:=-x/b+atanh(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b +-+
+--R \|a atanh(-----) - x\|b
+--R +-+
+--R \|a
+--R (2) ------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 1265
+
+--S 1266 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R |a 2 +---+
+--R +-+ 2b x |- + b x + a | a
+--R |a \|b +---+ |- -
+--R |- log(-------------------) - 2x | a \| b
+--R \|b 2 - |- - atan(------) - x
+--R b x - a \| b x
+--R (3) [---------------------------------,------------------------]
+--R 2b b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1266
+
+--S 1267 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +-+
+--R |a 2
+--R +-+ 2b x |- + b x + a +-+
+--R |a +-+ \|b +-+ x\|b
+--R |- \|b log(-------------------) - 2\|a atanh(-----)
+--R \|b 2 +-+
+--R b x - a \|a
+--R (4) ----------------------------------------------------
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 1267
+
+--S 1268 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1268
+
+--S 1269 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+
+--R | a
+--R +-+ +---+ |- -
+--R +-+ x\|b | a +-+ \| b
+--R - \|a atanh(-----) - |- - \|b atan(------)
+--R +-+ \| b x
+--R \|a
+--R (6) -------------------------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 1269
+
+--S 1270 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1270
+
+)clear all
+
+--S 1271 of 1393
+t0:=x/(a-b*x^2)
+--R
+--R
+--R x
+--R (1) - --------
+--R 2
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 1271
+
+--S 1272 of 1393
+r0:=-1/2*log(a-b*x^2)/b
+--R
+--R
+--R 2
+--R log(- b x + a)
+--R (2) - ---------------
+--R 2b
+--R Type: Expression(Integer)
+--E 1272
+
+--S 1273 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R log(b x - a)
+--R (3) - -------------
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 1273
+
+--S 1274 of 1393
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(b x - a) + log(- b x + a)
+--R (4) ---------------------------------
+--R 2b
+--R Type: Expression(Integer)
+--E 1274
+
+--S 1275 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1275
+
+)clear all
+
+--S 1276 of 1393
+t0:=1/(a-b*x^2)
+--R
+--R
+--R 1
+--R (1) - --------
+--R 2
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 1276
+
+--S 1277 of 1393
+r0:=atanh(x*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b))
+--R
+--R
+--R +-+
+--R x\|b
+--R atanh(-----)
+--R +-+
+--R \|a
+--R (2) ------------
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1277
+
+--S 1278 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +---+
+--R (b x + a)\|a b + 2a b x +-----+
+--R log(-------------------------) x\|- a b
+--R 2 atan(---------)
+--R b x - a a
+--R (3) [------------------------------,---------------]
+--R +---+ +-----+
+--R 2\|a b \|- a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1278
+
+--S 1279 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +---+ +-+
+--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b
+--R \|a \|b log(-------------------------) - 2\|a b atanh(-----)
+--R 2 +-+
+--R b x - a \|a
+--R (4) ------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 2\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1279
+
+--S 1280 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1280
+
+--S 1281 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-----+
+--R +-----+ x\|b +-+ +-+ x\|- a b
+--R - \|- a b atanh(-----) + \|a \|b atan(---------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------
+--R +-----+ +-+ +-+
+--R \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1281
+
+--S 1282 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1282
+
+)clear all
+
+--S 1283 of 1393
+t0:=1/(x*(a-b*x^2))
+--R
+--R
+--R 1
+--R (1) - ----------
+--R 3
+--R b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1283
+
+--S 1284 of 1393
+r0:=log(x)/a-1/2*log(a-b*x^2)/a
+--R
+--R
+--R 2
+--R 2log(x) - log(- b x + a)
+--R (2) -------------------------
+--R 2a
+--R Type: Expression(Integer)
+--E 1284
+
+--S 1285 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - log(b x - a) + 2log(x)
+--R (3) -------------------------
+--R 2a
+--R Type: Union(Expression(Integer),...)
+--E 1285
+
+--S 1286 of 1393
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(b x - a) + log(- b x + a)
+--R (4) ---------------------------------
+--R 2a
+--R Type: Expression(Integer)
+--E 1286
+
+--S 1287 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1287
+
+)clear all
+
+--S 1288 of 1393
+t0:=1/(x^2*(a-b*x^2))
+--R
+--R
+--R 1
+--R (1) - -----------
+--R 4 2
+--R b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1288
+
+--S 1289 of 1393
+r0:=(-1)/(a*x)+atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b +-+
+--R x\|b atanh(-----) - \|a
+--R +-+
+--R \|a
+--R (2) ------------------------
+--R +-+
+--R a x\|a
+--R Type: Expression(Integer)
+--E 1289
+
+--S 1290 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R |b 2 +---+
+--R +-+ 2a x |- + b x + a | b
+--R |b \|a +---+ a |- -
+--R x |- log(-------------------) - 2 | b \| a
+--R \|a 2 - x |- - atan(-------) - 1
+--R b x - a \| a b x
+--R (3) [---------------------------------,--------------------------]
+--R 2a x a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1290
+
+--S 1291 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +-+
+--R |b 2
+--R +-+ 2a x |- + b x + a +-+
+--R +-+ |b \|a +-+ x\|b
+--R \|a |- log(-------------------) - 2\|b atanh(-----)
+--R \|a 2 +-+
+--R b x - a \|a
+--R (4) ----------------------------------------------------
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 1291
+
+--S 1292 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1292
+
+--S 1293 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+
+--R | b
+--R +-+ +---+ a |- -
+--R +-+ x\|b | b +-+ \| a
+--R - \|b atanh(-----) - |- - \|a atan(-------)
+--R +-+ \| a b x
+--R \|a
+--R (6) --------------------------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 1293
+
+--S 1294 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1294
+
+)clear all
+
+--S 1295 of 1393
+t0:=1/(x^3*(a-b*x^2))
+--R
+--R
+--R 1
+--R (1) - -----------
+--R 5 3
+--R b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1295
+
+--S 1296 of 1393
+r0:=(-1/2)/(a*x^2)+b*log(x)/a^2-1/2*b*log(a-b*x^2)/a^2
+--R
+--R
+--R 2 2 2
+--R 2b x log(x) - b x log(- b x + a) - a
+--R (2) -------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Expression(Integer)
+--E 1296
+
+--S 1297 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R - b x log(b x - a) + 2b x log(x) - a
+--R (3) -------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Union(Expression(Integer),...)
+--E 1297
+
+--S 1298 of 1393
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - b log(b x - a) + b log(- b x + a)
+--R (4) -------------------------------------
+--R 2
+--R 2a
+--R Type: Expression(Integer)
+--E 1298
+
+--S 1299 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1299
+
+)clear all
+
+--S 1300 of 1393
+t0:=x^3/(a-b*x^2)^2
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x - 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1300
+
+--S 1301 of 1393
+r0:=1/2*a/(b^2*(a-b*x^2))+1/2*log(a-b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R (b x - a)log(- b x + a) - a
+--R (2) -----------------------------
+--R 3 2 2
+--R 2b x - 2a b
+--R Type: Expression(Integer)
+--E 1301
+
+--S 1302 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R (b x - a)log(b x - a) - a
+--R (3) ---------------------------
+--R 3 2 2
+--R 2b x - 2a b
+--R Type: Union(Expression(Integer),...)
+--E 1302
+
+--S 1303 of 1393
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R log(b x - a) - log(- b x + a)
+--R (4) -------------------------------
+--R 2
+--R 2b
+--R Type: Expression(Integer)
+--E 1303
+
+--S 1304 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1304
+
+)clear all
+
+--S 1305 of 1393
+t0:=x^2/(a-b*x^2)^2
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x - 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1305
+
+--S 1306 of 1393
+r0:=1/2*x/(b*(a-b*x^2))-1/2*atanh(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R 2 x\|b +-+ +-+
+--R (- b x + a)atanh(-----) - x\|a \|b
+--R +-+
+--R \|a
+--R (2) ------------------------------------
+--R 2 2 +-+ +-+
+--R (2b x - 2a b)\|a \|b
+--R Type: Expression(Integer)
+--E 1306
+
+--S 1307 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +---+
+--R 2 (b x + a)\|a b - 2a b x +---+
+--R (b x - a)log(-------------------------) - 2x\|a b
+--R 2
+--R b x - a
+--R [---------------------------------------------------,
+--R 2 2 +---+
+--R (4b x - 4a b)\|a b
+--R +-----+
+--R 2 x\|- a b +-----+
+--R (- b x + a)atan(---------) - x\|- a b
+--R a
+--R ---------------------------------------]
+--R 2 2 +-----+
+--R (2b x - 2a b)\|- a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1307
+
+--S 1308 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +---+ +-+
+--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b
+--R \|a \|b log(-------------------------) + 2\|a b atanh(-----)
+--R 2 +-+
+--R b x - a \|a
+--R (4) ------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 4b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1308
+
+--S 1309 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1309
+
+--S 1310 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-----+
+--R +-----+ x\|b +-+ +-+ x\|- a b
+--R \|- a b atanh(-----) - \|a \|b atan(---------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------
+--R +-----+ +-+ +-+
+--R 2b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1310
+
+--S 1311 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1311
+
+)clear all
+
+--S 1312 of 1393
+t0:=x/(a-b*x^2)^2
+--R
+--R
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x - 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1312
+
+--S 1313 of 1393
+r0:=1/2/(b*(a-b*x^2))
+--R
+--R
+--R 1
+--R -
+--R 2
+--R (2) - ----------
+--R 2 2
+--R b x - a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1313
+
+--S 1314 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ------------
+--R 2 2
+--R 2b x - 2a b
+--R Type: Union(Expression(Integer),...)
+--E 1314
+
+--S 1315 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1315
+
+--S 1316 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1316
+
+)clear all
+
+--S 1317 of 1393
+t0:=1/(a-b*x^2)^2
+--R
+--R
+--R 1
+--R (1) -------------------
+--R 2 4 2 2
+--R b x - 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1317
+
+--S 1318 of 1393
+r0:=1/2*x/(a*(a-b*x^2))+1/2*atanh(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R 2 x\|b +-+ +-+
+--R (b x - a)atanh(-----) - x\|a \|b
+--R +-+
+--R \|a
+--R (2) ----------------------------------
+--R 2 2 +-+ +-+
+--R (2a b x - 2a )\|a \|b
+--R Type: Expression(Integer)
+--E 1318
+
+--S 1319 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +---+
+--R 2 (b x + a)\|a b + 2a b x +---+
+--R (b x - a)log(-------------------------) - 2x\|a b
+--R 2
+--R b x - a
+--R [---------------------------------------------------,
+--R 2 2 +---+
+--R (4a b x - 4a )\|a b
+--R +-----+
+--R 2 x\|- a b +-----+
+--R (b x - a)atan(---------) - x\|- a b
+--R a
+--R -------------------------------------]
+--R 2 2 +-----+
+--R (2a b x - 2a )\|- a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1319
+
+--S 1320 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +---+ +-+
+--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b
+--R \|a \|b log(-------------------------) - 2\|a b atanh(-----)
+--R 2 +-+
+--R b x - a \|a
+--R (4) ------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 4a\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1320
+
+--S 1321 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1321
+
+--S 1322 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-----+
+--R +-----+ x\|b +-+ +-+ x\|- a b
+--R - \|- a b atanh(-----) + \|a \|b atan(---------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------
+--R +-----+ +-+ +-+
+--R 2a\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1322
+
+--S 1323 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1323
+
+)clear all
+
+--S 1324 of 1393
+t0:=1/(x*(a-b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) --------------------
+--R 2 5 3 2
+--R b x - 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1324
+
+--S 1325 of 1393
+r0:=1/2/(a*(a-b*x^2))+log(x)/a^2-1/2*log(a-b*x^2)/a^2
+--R
+--R
+--R 2 2 2
+--R (2b x - 2a)log(x) + (- b x + a)log(- b x + a) - a
+--R (2) ----------------------------------------------------
+--R 2 2 3
+--R 2a b x - 2a
+--R Type: Expression(Integer)
+--E 1325
+
+--S 1326 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R (- b x + a)log(b x - a) + (2b x - 2a)log(x) - a
+--R (3) --------------------------------------------------
+--R 2 2 3
+--R 2a b x - 2a
+--R Type: Union(Expression(Integer),...)
+--E 1326
+
+--S 1327 of 1393
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(b x - a) + log(- b x + a)
+--R (4) ---------------------------------
+--R 2
+--R 2a
+--R Type: Expression(Integer)
+--E 1327
+
+--S 1328 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1328
+
+)clear all
+
+--S 1329 of 1393
+t0:=1/(x^2*(a-b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R b x - 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1329
+
+--S 1330 of 1393
+r0:=(-3/2)/(a^2*x)+1/2/(a*x*(a-b*x^2))+_
+ 3/2*atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|b 2 +-+
+--R (3b x - 3a x)\|b atanh(-----) + (- 3b x + 2a)\|a
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------
+--R 2 3 3 +-+
+--R (2a b x - 2a x)\|a
+--R Type: Expression(Integer)
+--E 1330
+
+--S 1331 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+
+--R |b 2
+--R +-+ 2a x |- + b x + a
+--R 3 |b \|a 2
+--R (3b x - 3a x) |- log(-------------------) - 6b x + 4a
+--R \|a 2
+--R b x - a
+--R [-------------------------------------------------------,
+--R 2 3 3
+--R 4a b x - 4a x
+--R +---+
+--R | b
+--R +---+ a |- -
+--R 3 | b \| a 2
+--R (- 3b x + 3a x) |- - atan(-------) - 3b x + 2a
+--R \| a b x
+--R ------------------------------------------------]
+--R 2 3 3
+--R 2a b x - 2a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1331
+
+--S 1332 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +-+
+--R |b 2
+--R +-+ 2a x |- + b x + a +-+
+--R +-+ |b \|a +-+ x\|b
+--R 3\|a |- log(-------------------) - 6\|b atanh(-----)
+--R \|a 2 +-+
+--R b x - a \|a
+--R (4) -----------------------------------------------------
+--R 2 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 1332
+
+--S 1333 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1333
+
+--S 1334 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+
+--R | b
+--R +-+ +---+ a |- -
+--R +-+ x\|b | b +-+ \| a
+--R - 3\|b atanh(-----) - 3 |- - \|a atan(-------)
+--R +-+ \| a b x
+--R \|a
+--R (6) ----------------------------------------------
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 1334
+
+--S 1335 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1335
+
+)clear all
+
+--S 1336 of 1393
+t0:=1/(x^3*(a-b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R b x - 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1336
+
+--S 1337 of 1393
+r0:=(-1)/(a^2*x^2)+1/2/(a*x^2*(a-b*x^2))+2*b*log(x)/a^3-b*log(a-b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 4 2 2 2 2
+--R (4b x - 4a b x )log(x) + (- 2b x + 2a b x )log(- b x + a) - 2a b x + a
+--R ---------------------------------------------------------------------------
+--R 3 4 4 2
+--R 2a b x - 2a x
+--R Type: Expression(Integer)
+--E 1337
+
+--S 1338 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2 4 2 2 2
+--R (- 2b x + 2a b x )log(b x - a) + (4b x - 4a b x )log(x) - 2a b x + a
+--R -------------------------------------------------------------------------
+--R 3 4 4 2
+--R 2a b x - 2a x
+--R Type: Union(Expression(Integer),...)
+--E 1338
+
+--S 1339 of 1393
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - b log(b x - a) + b log(- b x + a)
+--R (4) -------------------------------------
+--R 3
+--R a
+--R Type: Expression(Integer)
+--E 1339
+
+--S 1340 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1340
+
+)clear all
+
+--S 1341 of 1393
+t0:=x^3/(a-b*x^2)^3
+--R
+--R
+--R 3
+--R x
+--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 1341
+
+--S 1342 of 1393
+r0:=1/4*x^4/(a*(a-b*x^2)^2)
+--R
+--R
+--R 1 4
+--R - x
+--R 4
+--R (2) ---------------------
+--R 2 4 2 2 3
+--R a b x - 2a b x + a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1342
+
+--S 1343 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 2b x - a
+--R (3) -----------------------
+--R 4 4 3 2 2 2
+--R 4b x - 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 1343
+
+--S 1344 of 1393
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - -----
+--R 2
+--R 4a b
+--R Type: Expression(Integer)
+--E 1344
+
+--S 1345 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1345
+
+)clear all
+
+--S 1346 of 1393
+t0:=x^2/(a-b*x^2)^3
+--R
+--R
+--R 2
+--R x
+--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 1346
+
+--S 1347 of 1393
+r0:=1/4*x/(b*(a-b*x^2)^2)-1/8*x/(a*b*(a-b*x^2))-_
+ 1/8*atanh(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2))
+--R
+--R
+--R +-+
+--R 2 4 2 2 x\|b 3 +-+ +-+
+--R (- b x + 2a b x - a )atanh(-----) + (b x + a x)\|a \|b
+--R +-+
+--R \|a
+--R (2) ----------------------------------------------------------
+--R 3 4 2 2 2 3 +-+ +-+
+--R (8a b x - 16a b x + 8a b)\|a \|b
+--R Type: Expression(Integer)
+--E 1347
+
+--S 1348 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +---+
+--R 2 4 2 2 (b x + a)\|a b - 2a b x 3 +---+
+--R (b x - 2a b x + a )log(-------------------------) + (2b x + 2a x)\|a b
+--R 2
+--R b x - a
+--R [--------------------------------------------------------------------------,
+--R 3 4 2 2 2 3 +---+
+--R (16a b x - 32a b x + 16a b)\|a b
+--R +-----+
+--R 2 4 2 2 x\|- a b 3 +-----+
+--R (- b x + 2a b x - a )atan(---------) + (b x + a x)\|- a b
+--R a
+--R -------------------------------------------------------------]
+--R 3 4 2 2 2 3 +-----+
+--R (8a b x - 16a b x + 8a b)\|- a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1348
+
+--S 1349 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +---+ +-+
+--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b
+--R \|a \|b log(-------------------------) + 2\|a b atanh(-----)
+--R 2 +-+
+--R b x - a \|a
+--R (4) ------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 16a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1349
+
+--S 1350 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1350
+
+--S 1351 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-----+
+--R +-----+ x\|b +-+ +-+ x\|- a b
+--R \|- a b atanh(-----) - \|a \|b atan(---------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------
+--R +-----+ +-+ +-+
+--R 8a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1351
+
+--S 1352 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1352
+
+)clear all
+
+--S 1353 of 1393
+t0:=x/(a-b*x^2)^3
+--R
+--R
+--R x
+--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 1353
+
+--S 1354 of 1393
+r0:=1/4/(b*(a-b*x^2)^2)
+--R
+--R
+--R 1
+--R -
+--R 4
+--R (2) --------------------
+--R 3 4 2 2 2
+--R b x - 2a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1354
+
+--S 1355 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) ----------------------
+--R 3 4 2 2 2
+--R 4b x - 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 1355
+
+--S 1356 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1356
+
+--S 1357 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1357
+
+)clear all
+
+--S 1358 of 1393
+t0:=1/(a-b*x^2)^3
+--R
+--R
+--R 1
+--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 1358
+
+--S 1359 of 1393
+r0:=1/4*x/(a*(a-b*x^2)^2)+3/8*x/(a^2*(a-b*x^2))+_
+ 3/8*atanh(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R 2 4 2 2 x\|b 3 +-+ +-+
+--R (3b x - 6a b x + 3a )atanh(-----) + (- 3b x + 5a x)\|a \|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------------------------------
+--R 2 2 4 3 2 4 +-+ +-+
+--R (8a b x - 16a b x + 8a )\|a \|b
+--R Type: Expression(Integer)
+--E 1359
+
+--S 1360 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +---+
+--R 2 4 2 2 (b x + a)\|a b + 2a b x
+--R (3b x - 6a b x + 3a )log(-------------------------)
+--R 2
+--R b x - a
+--R +
+--R 3 +---+
+--R (- 6b x + 10a x)\|a b
+--R /
+--R 2 2 4 3 2 4 +---+
+--R (16a b x - 32a b x + 16a )\|a b
+--R ,
+--R +-----+
+--R 2 4 2 2 x\|- a b 3 +-----+
+--R (3b x - 6a b x + 3a )atan(---------) + (- 3b x + 5a x)\|- a b
+--R a
+--R -----------------------------------------------------------------]
+--R 2 2 4 3 2 4 +-----+
+--R (8a b x - 16a b x + 8a )\|- a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1360
+
+--S 1361 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +---+ +-+
+--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b
+--R 3\|a \|b log(-------------------------) - 6\|a b atanh(-----)
+--R 2 +-+
+--R b x - a \|a
+--R (4) -------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 16a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1361
+
+--S 1362 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1362
+
+--S 1363 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-----+
+--R +-----+ x\|b +-+ +-+ x\|- a b
+--R - 3\|- a b atanh(-----) + 3\|a \|b atan(---------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------
+--R 2 +-----+ +-+ +-+
+--R 8a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1363
+
+--S 1364 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1364
+
+)clear all
+
+--S 1365 of 1393
+t0:=1/(x*(a-b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) - ------------------------------
+--R 3 7 2 5 2 3 3
+--R b x - 3a b x + 3a b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1365
+
+--S 1366 of 1393
+r0:=1/4/(a*(a-b*x^2)^2)+1/2/(a^2*(a-b*x^2))+log(x)/a^3-1/2*log(a-b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 2 4 2 2 2
+--R (4b x - 8a b x + 4a )log(x) + (- 2b x + 4a b x - 2a )log(- b x + a)
+--R +
+--R 2 2
+--R - 2a b x + 3a
+--R /
+--R 3 2 4 4 2 5
+--R 4a b x - 8a b x + 4a
+--R Type: Expression(Integer)
+--E 1366
+
+--S 1367 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2 2 4 2 2
+--R (- 2b x + 4a b x - 2a )log(b x - a) + (4b x - 8a b x + 4a )log(x)
+--R +
+--R 2 2
+--R - 2a b x + 3a
+--R /
+--R 3 2 4 4 2 5
+--R 4a b x - 8a b x + 4a
+--R Type: Union(Expression(Integer),...)
+--E 1367
+
+--S 1368 of 1393
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(b x - a) + log(- b x + a)
+--R (4) ---------------------------------
+--R 3
+--R 2a
+--R Type: Expression(Integer)
+--E 1368
+
+--S 1369 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1369
+
+)clear all
+
+--S 1370 of 1393
+t0:=1/(x^2*(a-b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) - -------------------------------
+--R 3 8 2 6 2 4 3 2
+--R b x - 3a b x + 3a b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1370
+
+--S 1371 of 1393
+r0:=(-15/8)/(a^3*x)+1/4/(a*x*(a-b*x^2)^2)+5/8/(a^2*x*(a-b*x^2))+_
+ 15/8*atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 5 3 2 +-+ x\|b 2 4 2 2 +-+
+--R (15b x - 30a b x + 15a x)\|b atanh(-----) + (- 15b x + 25a b x - 8a )\|a
+--R +-+
+--R \|a
+--R -----------------------------------------------------------------------------
+--R 3 2 5 4 3 5 +-+
+--R (8a b x - 16a b x + 8a x)\|a
+--R Type: Expression(Integer)
+--E 1371
+
+--S 1372 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-+
+--R |b 2
+--R +-+ 2a x |- + b x + a
+--R 2 5 3 2 |b \|a 2 4
+--R (15b x - 30a b x + 15a x) |- log(-------------------) - 30b x
+--R \|a 2
+--R b x - a
+--R +
+--R 2 2
+--R 50a b x - 16a
+--R /
+--R 3 2 5 4 3 5
+--R 16a b x - 32a b x + 16a x
+--R ,
+--R +---+
+--R | b
+--R +---+ a |- -
+--R 2 5 3 2 | b \| a 2 4 2 2
+--R (- 15b x + 30a b x - 15a x) |- - atan(-------) - 15b x + 25a b x - 8a
+--R \| a b x
+--R --------------------------------------------------------------------------]
+--R 3 2 5 4 3 5
+--R 8a b x - 16a b x + 8a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1372
+
+--S 1373 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R +-+
+--R |b 2
+--R +-+ 2a x |- + b x + a +-+
+--R +-+ |b \|a +-+ x\|b
+--R 15\|a |- log(-------------------) - 30\|b atanh(-----)
+--R \|a 2 +-+
+--R b x - a \|a
+--R (4) -------------------------------------------------------
+--R 3 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 1373
+
+--S 1374 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1374
+
+--S 1375 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +---+
+--R | b
+--R +-+ +---+ a |- -
+--R +-+ x\|b | b +-+ \| a
+--R - 15\|b atanh(-----) - 15 |- - \|a atan(-------)
+--R +-+ \| a b x
+--R \|a
+--R (6) ------------------------------------------------
+--R 3 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1375
+
+--S 1376 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1376
+
+)clear all
+
+--S 1377 of 1393
+t0:=1/(x^3*(a-b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) - -------------------------------
+--R 3 9 2 7 2 5 3 3
+--R b x - 3a b x + 3a b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1377
+
+--S 1378 of 1393
+r0:=(-3/2)/(a^3*x^2)+1/4/(a*x^2*(a-b*x^2)^2)+_
+ 3/4/(a^2*x^2*(a-b*x^2))+3*b*log(x)/a^4-3/2*b*log(a-b*x^2)/a^4
+--R
+--R
+--R (2)
+--R 3 6 2 4 2 2
+--R (12b x - 24a b x + 12a b x )log(x)
+--R +
+--R 3 6 2 4 2 2 2 2 4 2 2 3
+--R (- 6b x + 12a b x - 6a b x )log(- b x + a) - 6a b x + 9a b x - 2a
+--R /
+--R 4 2 6 5 4 6 2
+--R 4a b x - 8a b x + 4a x
+--R Type: Expression(Integer)
+--E 1378
+
+--S 1379 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 6 2 4 2 2 2
+--R (- 6b x + 12a b x - 6a b x )log(b x - a)
+--R +
+--R 3 6 2 4 2 2 2 4 2 2 3
+--R (12b x - 24a b x + 12a b x )log(x) - 6a b x + 9a b x - 2a
+--R /
+--R 4 2 6 5 4 6 2
+--R 4a b x - 8a b x + 4a x
+--R Type: Union(Expression(Integer),...)
+--E 1379
+
+--S 1380 of 1393
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - 3b log(b x - a) + 3b log(- b x + a)
+--R (4) ---------------------------------------
+--R 4
+--R 2a
+--R Type: Expression(Integer)
+--E 1380
+
+--S 1381 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1381
+
+)clear all
+
+--S 1382 of 1393
+t0:=x^3/(a-b*x^2)^5
+--R
+--R
+--R 3
+--R x
+--R (1) - ----------------------------------------------------
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 1382
+
+--S 1383 of 1393
+r0:=1/8*a/(b^2*(a-b*x^2)^4)+(-1/6)/(b^2*(a-b*x^2)^3)
+--R
+--R
+--R 1 2 1
+--R - b x - -- a
+--R 6 24
+--R (2) -----------------------------------------
+--R 6 8 5 6 2 4 4 3 3 2 4 2
+--R b x - 4a b x + 6a b x - 4a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1383
+
+--S 1384 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 4b x - a
+--R (3) -------------------------------------------------
+--R 6 8 5 6 2 4 4 3 3 2 4 2
+--R 24b x - 96a b x + 144a b x - 96a b x + 24a b
+--R Type: Union(Expression(Integer),...)
+--E 1384
+
+--S 1385 of 1393
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1385
+
+--S 1386 of 1393
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1386
+
+)clear all
+
+--S 1387 of 1393
+t0:=x^2/(a-b*x^2)^5
+--R
+--R
+--R 2
+--R x
+--R (1) - ----------------------------------------------------
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 1387
+
+--S 1388 of 1393
+r0:=1/8*x/(b*(a-b*x^2)^4)-1/48*x/(a*b*(a-b*x^2)^3)-_
+ 5/192*x/(a^2*b*(a-b*x^2)^2)-5/128*x/(a^3*b*(a-b*x^2))-_
+ 5/128*atanh(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(3/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 4 8 3 6 2 2 4 3 2 4 x\|b
+--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atanh(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (15b x - 55a b x + 73a b x + 15a x)\|a \|b
+--R /
+--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-+ +-+
+--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|a \|b
+--R Type: Expression(Integer)
+--E 1388
+
+--S 1389 of 1393
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 8 3 6 2 2 4 3 2 4
+--R (15b x - 60a b x + 90a b x - 60a b x + 15a )
+--R *
+--R 2 +---+
+--R (b x + a)\|a b - 2a b x
+--R log(-------------------------)
+--R 2
+--R b x - a
+--R +
+--R 3 7 2 5 2 3 3 +---+
+--R (30b x - 110a b x + 146a b x + 30a x)\|a b
+--R /
+--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +---+
+--R (768a b x - 3072a b x + 4608a b x - 3072a b x + 768a b)\|a b
+--R ,
+--R
+--R +-----+
+--R 4 8 3 6 2 2 4 3 2 4 x\|- a b
+--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atan(---------)
+--R a
+--R +
+--R 3 7 2 5 2 3 3 +-----+
+--R (15b x - 55a b x + 73a b x + 15a x)\|- a b
+--R /
+--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-----+
+--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|- a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1389
+
+--S 1390 of 1393
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +---+ +-+
+--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b
+--R 5\|a \|b log(-------------------------) + 10\|a b atanh(-----)
+--R 2 +-+
+--R b x - a \|a
+--R (4) --------------------------------------------------------------
+--R 3 +-+ +-+ +---+
+--R 256a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1390
+
+--S 1391 of 1393
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1391
+
+--S 1392 of 1393
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-----+
+--R +-----+ x\|b +-+ +-+ x\|- a b
+--R 5\|- a b atanh(-----) - 5\|a \|b atan(---------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------
+--R 3 +-----+ +-+ +-+
+--R 128a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1392
+
+--S 1393 of 1393
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1393
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich4a.input.pdf b/src/axiom-website/CATS/rich4a.input.pdf
new file mode 100644
index 0000000..b71ccd1
Binary files /dev/null and b/src/axiom-website/CATS/rich4a.input.pdf differ
diff --git a/src/axiom-website/CATS/rich4b.input.pamphlet b/src/axiom-website/CATS/rich4b.input.pamphlet
new file mode 100644
index 0000000..bb0584e
--- /dev/null
+++ b/src/axiom-website/CATS/rich4b.input.pamphlet
@@ -0,0 +1,25024 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich4b.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 255 supplied "optimal results".
+\item 287 matching answers.
+\item 6 cases where Axiom answer differs from Rubi
+\item 47 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 9 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich4b.output
+)spool rich4b.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1369
+t0:=x/(a-b*x^2)^5
+--R
+--R
+--R x
+--R (1) - ----------------------------------------------------
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 1
+
+--S 2 of 1369
+r0:=1/8/(b*(a-b*x^2)^4)
+--R
+--R
+--R 1
+--R -
+--R 8
+--R (2) ----------------------------------------
+--R 5 8 4 6 2 3 4 3 2 2 4
+--R b x - 4a b x + 6a b x - 4a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 2
+
+--S 3 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) ---------------------------------------------
+--R 5 8 4 6 2 3 4 3 2 2 4
+--R 8b x - 32a b x + 48a b x - 32a b x + 8a b
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1369
+t0:=1/(a-b*x^2)^5
+--R
+--R
+--R 1
+--R (1) - ----------------------------------------------------
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 6
+
+--S 7 of 1369
+r0:=1/8*x/(a*(a-b*x^2)^4)+7/48*x/(a^2*(a-b*x^2)^3)+_
+ 35/192*x/(a^3*(a-b*x^2)^2)+35/128*x/(a^4*(a-b*x^2))+_
+ 35/128*atanh(x*sqrt(b)/sqrt(a))/(a^(9/2)*sqrt(b))
+--R
+--R
+--R (2)
+--R +-+
+--R 4 8 3 6 2 2 4 3 2 4 x\|b
+--R (105b x - 420a b x + 630a b x - 420a b x + 105a )atanh(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (- 105b x + 385a b x - 511a b x + 279a x)\|a \|b
+--R /
+--R 4 4 8 5 3 6 6 2 4 7 2 8 +-+ +-+
+--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a )\|a \|b
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 8 3 6 2 2 4 3 2 4
+--R (105b x - 420a b x + 630a b x - 420a b x + 105a )
+--R *
+--R 2 +---+
+--R (b x + a)\|a b + 2a b x
+--R log(-------------------------)
+--R 2
+--R b x - a
+--R +
+--R 3 7 2 5 2 3 3 +---+
+--R (- 210b x + 770a b x - 1022a b x + 558a x)\|a b
+--R /
+--R 4 4 8 5 3 6 6 2 4 7 2 8 +---+
+--R (768a b x - 3072a b x + 4608a b x - 3072a b x + 768a )\|a b
+--R ,
+--R
+--R +-----+
+--R 4 8 3 6 2 2 4 3 2 4 x\|- a b
+--R (105b x - 420a b x + 630a b x - 420a b x + 105a )atan(---------)
+--R a
+--R +
+--R 3 7 2 5 2 3 3 +-----+
+--R (- 105b x + 385a b x - 511a b x + 279a x)\|- a b
+--R /
+--R 4 4 8 5 3 6 6 2 4 7 2 8 +-----+
+--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a )\|- a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 8
+
+--S 9 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +---+ +-+
+--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b
+--R 35\|a \|b log(-------------------------) - 70\|a b atanh(-----)
+--R 2 +-+
+--R b x - a \|a
+--R (4) ---------------------------------------------------------------
+--R 4 +-+ +-+ +---+
+--R 256a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+--S 11 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-----+
+--R +-----+ x\|b +-+ +-+ x\|- a b
+--R - 35\|- a b atanh(-----) + 35\|a \|b atan(---------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------
+--R 4 +-----+ +-+ +-+
+--R 128a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 12
+
+)clear all
+
+--S 13 of 1369
+t0:=1/(x*(a-b*x^2)^5)
+--R
+--R
+--R 1
+--R (1) - -----------------------------------------------------
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5
+--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 13
+
+--S 14 of 1369
+r0:=1/8/(a*(a-b*x^2)^4)+1/6/(a^2*(a-b*x^2)^3)+1/4/(a^3*(a-b*x^2)^2)+_
+ 1/2/(a^4*(a-b*x^2))+log(x)/a^5-1/2*log(a-b*x^2)/a^5
+--R
+--R
+--R (2)
+--R 4 8 3 6 2 2 4 3 2 4
+--R (24b x - 96a b x + 144a b x - 96a b x + 24a )log(x)
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 2
+--R (- 12b x + 48a b x - 72a b x + 48a b x - 12a )log(- b x + a)
+--R +
+--R 3 6 2 2 4 3 2 4
+--R - 12a b x + 42a b x - 52a b x + 25a
+--R /
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 24a b x - 96a b x + 144a b x - 96a b x + 24a
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 8 3 6 2 2 4 3 2 4 2
+--R (- 12b x + 48a b x - 72a b x + 48a b x - 12a )log(b x - a)
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 3 6
+--R (24b x - 96a b x + 144a b x - 96a b x + 24a )log(x) - 12a b x
+--R +
+--R 2 2 4 3 2 4
+--R 42a b x - 52a b x + 25a
+--R /
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 24a b x - 96a b x + 144a b x - 96a b x + 24a
+--R Type: Union(Expression(Integer),...)
+--E 15
+
+--S 16 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(b x - a) + log(- b x + a)
+--R (4) ---------------------------------
+--R 5
+--R 2a
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 17
+
+)clear all
+
+--S 18 of 1369
+t0:=1/(x^2*(a-b*x^2)^5)
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------------------
+--R 5 12 4 10 2 3 8 3 2 6 4 4 5 2
+--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 18
+
+--S 19 of 1369
+r0:=(-315/128)/(a^5*x)+1/8/(a*x*(a-b*x^2)^4)+3/16/(a^2*x*(a-b*x^2)^3)+_
+ 21/64/(a^3*x*(a-b*x^2)^2)+105/128/(a^4*x*(a-b*x^2))+_
+ 315/128*atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 9 3 7 2 2 5 3 3 4 +-+ x\|b
+--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x)\|b atanh(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- 315b x + 1155a b x - 1533a b x + 837a b x - 128a )\|a
+--R /
+--R 5 4 9 6 3 7 7 2 5 8 3 9 +-+
+--R (128a b x - 512a b x + 768a b x - 512a b x + 128a x)\|a
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-+
+--R 4 9 3 7 2 2 5 3 3 4 |b
+--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x) |-
+--R \|a
+--R *
+--R +-+
+--R |b 2
+--R 2a x |- + b x + a
+--R \|a
+--R log(-------------------)
+--R 2
+--R b x - a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4
+--R - 630b x + 2310a b x - 3066a b x + 1674a b x - 256a
+--R /
+--R 5 4 9 6 3 7 7 2 5 8 3 9
+--R 256a b x - 1024a b x + 1536a b x - 1024a b x + 256a x
+--R ,
+--R
+--R +---+
+--R 4 9 3 7 2 2 5 3 3 4 | b
+--R (- 315b x + 1260a b x - 1890a b x + 1260a b x - 315a x) |- -
+--R \| a
+--R *
+--R +---+
+--R | b
+--R a |- -
+--R \| a
+--R atan(-------)
+--R b x
+--R +
+--R 4 8 3 6 2 2 4 3 2 4
+--R - 315b x + 1155a b x - 1533a b x + 837a b x - 128a
+--R /
+--R 5 4 9 6 3 7 7 2 5 8 3 9
+--R 128a b x - 512a b x + 768a b x - 512a b x + 128a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 20
+
+--S 21 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-+
+--R |b 2
+--R +-+ 2a x |- + b x + a +-+
+--R +-+ |b \|a +-+ x\|b
+--R 315\|a |- log(-------------------) - 630\|b atanh(-----)
+--R \|a 2 +-+
+--R b x - a \|a
+--R (4) ---------------------------------------------------------
+--R 5 +-+
+--R 256a \|a
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +---+
+--R | b
+--R +-+ +---+ a |- -
+--R +-+ x\|b | b +-+ \| a
+--R - 315\|b atanh(-----) - 315 |- - \|a atan(-------)
+--R +-+ \| a b x
+--R \|a
+--R (6) --------------------------------------------------
+--R 5 +-+
+--R 128a \|a
+--R Type: Expression(Integer)
+--E 23
+
+--S 24 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 24
+
+)clear all
+
+--S 25 of 1369
+t0:=1/(x^3*(a-b*x^2)^5)
+--R
+--R
+--R 1
+--R (1) - -------------------------------------------------------
+--R 5 13 4 11 2 3 9 3 2 7 4 5 5 3
+--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 25
+
+--S 26 of 1369
+r0:=(-5/2)/(a^5*x^2)+1/8/(a*x^2*(a-b*x^2)^4)+5/24/(a^2*x^2*(a-b*x^2)^3)+_
+ 5/12/(a^3*x^2*(a-b*x^2)^2)+5/4/(a^4*x^2*(a-b*x^2))+_
+ 5*b*log(x)/a^6-5/2*b*log(a-b*x^2)/a^6
+--R
+--R
+--R (2)
+--R 5 10 4 8 2 3 6 3 2 4 4 2
+--R (120b x - 480a b x + 720a b x - 480a b x + 120a b x )log(x)
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 2
+--R (- 60b x + 240a b x - 360a b x + 240a b x - 60a b x )log(- b x + a)
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 60a b x + 210a b x - 260a b x + 125a b x - 12a
+--R /
+--R 6 4 10 7 3 8 8 2 6 9 4 10 2
+--R 24a b x - 96a b x + 144a b x - 96a b x + 24a x
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 2 3 6 3 2 4 4 2 2
+--R (- 60b x + 240a b x - 360a b x + 240a b x - 60a b x )log(b x - a)
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2
+--R (120b x - 480a b x + 720a b x - 480a b x + 120a b x )log(x)
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 60a b x + 210a b x - 260a b x + 125a b x - 12a
+--R /
+--R 6 4 10 7 3 8 8 2 6 9 4 10 2
+--R 24a b x - 96a b x + 144a b x - 96a b x + 24a x
+--R Type: Union(Expression(Integer),...)
+--E 27
+
+--S 28 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - 5b log(b x - a) + 5b log(- b x + a)
+--R (4) ---------------------------------------
+--R 6
+--R 2a
+--R Type: Expression(Integer)
+--E 28
+
+--S 29 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 29
+
+)clear all
+
+--S 30 of 1369
+t0:=1/(x*(1+b*x^2))
+--R
+--R
+--R 1
+--R (1) --------
+--R 3
+--R b x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 30
+
+--S 31 of 1369
+r0:=-atanh(1+2*b*x^2)
+--R
+--R
+--R 2
+--R (2) - atanh(2b x + 1)
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - log(b x + 1) + 2log(x)
+--R (3) -------------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 32
+
+--S 33 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(b x + 1) + 2log(x) + 2atanh(2b x + 1)
+--R (4) ---------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 33
+
+--S 34 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 34
+
+)clear all
+
+--S 35 of 1369
+t0:=1/(x*(-1+b*x^2))
+--R
+--R
+--R 1
+--R (1) --------
+--R 3
+--R b x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 35
+
+--S 36 of 1369
+r0:=atanh(1-2*b*x^2)
+--R
+--R
+--R 2
+--R (2) - atanh(2b x - 1)
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R log(b x - 1) - 2log(x)
+--R (3) -----------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 37
+
+--S 38 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R log(b x - 1) - 2log(x) + 2atanh(2b x - 1)
+--R (4) -------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 38
+
+--S 39 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 39
+
+)clear all
+
+--S 40 of 1369
+t0:=1/(x^3*(1+b*x^2))
+--R
+--R
+--R 1
+--R (1) ---------
+--R 5 3
+--R b x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 40
+
+--S 41 of 1369
+r0:=(-1/2)/x^2+b*atanh(1+2*b*x^2)
+--R
+--R
+--R 2 2
+--R 2b x atanh(2b x + 1) - 1
+--R (2) -------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R b x log(b x + 1) - 2b x log(x) - 1
+--R (3) -----------------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 42
+
+--S 43 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R b log(b x + 1) - 2b log(x) - 2b atanh(2b x + 1)
+--R (4) -------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 43
+
+--S 44 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 44
+
+)clear all
+
+--S 45 of 1369
+t0:=1/(x^3*(-1+b*x^2))
+--R
+--R
+--R 1
+--R (1) ---------
+--R 5 3
+--R b x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 45
+
+--S 46 of 1369
+r0:=1/2/x^2+b*atanh(1-2*b*x^2)
+--R
+--R
+--R 2 2
+--R - 2b x atanh(2b x - 1) + 1
+--R (2) ---------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R b x log(b x - 1) - 2b x log(x) + 1
+--R (3) -----------------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 47
+
+--S 48 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R b log(b x - 1) - 2b log(x) + 2b atanh(2b x - 1)
+--R (4) -------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 48
+
+--S 49 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 49
+
+)clear all
+
+--S 50 of 1369
+t0:=1/(-1+a+a*x^2)
+--R
+--R
+--R 1
+--R (1) ------------
+--R 2
+--R a x + a - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 50
+
+--S 51 of 1369
+r0:=-atanh(x*sqrt(a)/sqrt(1-a))/sqrt((1-a)*a)
+--R
+--R
+--R +-+
+--R x\|a
+--R atanh(----------)
+--R +-------+
+--R \|- a + 1
+--R (2) - -----------------
+--R +--------+
+--R | 2
+--R \|- a + a
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 | 2 2 +------+
+--R (a x - a + 1)\|- a + a + (2a - 2a)x | 2
+--R log(---------------------------------------) x\|a - a
+--R 2 atan(----------)
+--R a x + a - 1 a - 1
+--R (3) [--------------------------------------------,----------------]
+--R +--------+ +------+
+--R | 2 | 2
+--R 2\|- a + a \|a - a
+--R Type: Union(List(Expression(Integer)),...)
+--E 52
+
+--S 53 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+
+--R 2 | 2 2 +-+
+--R (a x - a + 1)\|- a + a + (2a - 2a)x x\|a
+--R log(---------------------------------------) + 2atanh(----------)
+--R 2 +-------+
+--R a x + a - 1 \|- a + 1
+--R (4) -----------------------------------------------------------------
+--R +--------+
+--R | 2
+--R 2\|- a + a
+--R Type: Expression(Integer)
+--E 53
+
+--S 54 of 1369
+d0a:=normalize(D(m0a,x))
+--R
+--R
+--R (5)
+--R +--------+ +--------+
+--R | 2 2 +-------+ +-+ 2 | 2
+--R (2x\|- a + a - a x + a - 1)\|- a + 1 \|a + (a x - a + 1)\|- a + a
+--R +
+--R 2
+--R (2a - 2a)x
+--R /
+--R +--------+
+--R 2 4 2 | 2 3 2 3 3 2
+--R (a x - a + 2a - 1)\|- a + a + (2a - 2a )x + (2a - 4a + 2a)x
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +------+
+--R +------+ +-+ +--------+ | 2
+--R | 2 x\|a | 2 x\|a - a
+--R \|a - a atanh(----------) + \|- a + a atan(----------)
+--R +-------+ a - 1
+--R \|- a + 1
+--R (6) --------------------------------------------------------
+--R +--------+ +------+
+--R | 2 | 2
+--R \|- a + a \|a - a
+--R Type: Expression(Integer)
+--E 55
+
+--S 56 of 1369
+d0b:=normalize(D(m0b,x))
+--R
+--R
+--R +--------+
+--R | 2 +-------+ +-+ 2
+--R \|- a + a \|- a + 1 \|a + a - a
+--R (7) ----------------------------------
+--R 3 2 2 3 2
+--R (a - a )x + a - 2a + a
+--R Type: Expression(Integer)
+--E 56
+
+)clear all
+
+--S 57 of 1369
+t0:=1/(-c-d+(c-d)*x^2)
+--R
+--R
+--R 1
+--R (1) - -----------------
+--R 2
+--R (d - c)x + d + c
+--R Type: Fraction(Polynomial(Integer))
+--E 57
+
+--S 58 of 1369
+r0:=-atanh(x*sqrt(c-d)/sqrt(c+d))/(sqrt(c-d)*sqrt(c+d))
+--R
+--R
+--R +-------+
+--R x\|- d + c
+--R atanh(-----------)
+--R +-----+
+--R \|d + c
+--R (2) - ------------------
+--R +-------+ +-----+
+--R \|- d + c \|d + c
+--R Type: Expression(Integer)
+--E 58
+
+--S 59 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 2 | 2 2 2 2 +-------+
+--R ((d - c)x - d - c)\|- d + c + (- 2d + 2c )x | 2 2
+--R log(------------------------------------------------) x\|d - c
+--R 2 atan(-----------)
+--R (d - c)x + d + c d + c
+--R [-----------------------------------------------------,- -----------------]
+--R +---------+ +-------+
+--R | 2 2 | 2 2
+--R 2\|- d + c \|d - c
+--R Type: Union(List(Expression(Integer)),...)
+--E 59
+
+--S 60 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 | 2 2 2 2
+--R +-------+ +-----+ ((d - c)x - d - c)\|- d + c + (- 2d + 2c )x
+--R \|- d + c \|d + c log(------------------------------------------------)
+--R 2
+--R (d - c)x + d + c
+--R +
+--R +---------+ +-------+
+--R | 2 2 x\|- d + c
+--R 2\|- d + c atanh(-----------)
+--R +-----+
+--R \|d + c
+--R /
+--R +---------+
+--R | 2 2 +-------+ +-----+
+--R 2\|- d + c \|- d + c \|d + c
+--R Type: Expression(Integer)
+--E 60
+
+--S 61 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+
+--R +-------+ +-------+ | 2 2
+--R | 2 2 x\|- d + c +-------+ +-----+ x\|d - c
+--R \|d - c atanh(-----------) - \|- d + c \|d + c atan(-----------)
+--R +-----+ d + c
+--R \|d + c
+--R (6) ------------------------------------------------------------------
+--R +-------+
+--R +-------+ +-----+ | 2 2
+--R \|- d + c \|d + c \|d - c
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 63
+
+)clear all
+
+--S 64 of 1369
+t0:=1/(x*(1+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ----------------
+--R 2 5 3
+--R b x + 2b x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 64
+
+--S 65 of 1369
+r0:=1/2/(1+b*x^2)-atanh(1+2*b*x^2)
+--R
+--R
+--R 2 2
+--R (- 2b x - 2)atanh(2b x + 1) + 1
+--R (2) ---------------------------------
+--R 2
+--R 2b x + 2
+--R Type: Expression(Integer)
+--E 65
+
+--S 66 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R (- b x - 1)log(b x + 1) + (2b x + 2)log(x) + 1
+--R (3) -------------------------------------------------
+--R 2
+--R 2b x + 2
+--R Type: Union(Expression(Integer),...)
+--E 66
+
+--S 67 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(b x + 1) + 2log(x) + 2atanh(2b x + 1)
+--R (4) ---------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 68
+
+)clear all
+
+--S 69 of 1369
+t0:=1/(x*(-1+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ----------------
+--R 2 5 3
+--R b x - 2b x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 69
+
+--S 70 of 1369
+r0:=1/2/(1-b*x^2)-atanh(1-2*b*x^2)
+--R
+--R
+--R 2 2
+--R (2b x - 2)atanh(2b x - 1) - 1
+--R (2) -------------------------------
+--R 2
+--R 2b x - 2
+--R Type: Expression(Integer)
+--E 70
+
+--S 71 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R (- b x + 1)log(b x - 1) + (2b x - 2)log(x) - 1
+--R (3) -------------------------------------------------
+--R 2
+--R 2b x - 2
+--R Type: Union(Expression(Integer),...)
+--E 71
+
+--S 72 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(b x - 1) + 2log(x) - 2atanh(2b x - 1)
+--R (4) ---------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 73
+
+)clear all
+
+--S 74 of 1369
+t0:=x^m/(1+a*x^2/b)^2
+--R
+--R
+--R 2 m
+--R b x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 1369
+--r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_
+-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m)
+--E 75
+
+--S 76 of 1369
+--a0:=integrate(t0,x)
+--E 76
+
+--S 77 of 1369
+--m0:=a0-r0
+--E 77
+
+--S 78 of 1369
+--d0:=D(m0,x)
+--E 78
+
+)clear all
+
+--S 79 of 1369
+t0:=x^m*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R m | 2
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 1369
+--r0:=x^(1+m)*sqrt(a+b*x^2)/(2+m)+a*x^(1+m)*_
+-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+-- sqrt((a+b*x^2)/a)/((2+3*m+m^2)*sqrt(a+b*x^2))
+--E 80
+
+--S 81 of 1369
+--a0:=integrate(t0,x)
+--E 81
+
+--S 82 of 1369
+--m0:=a0-r0
+--E 82
+
+--S 83 of 1369
+--d0:=D(m0,x)
+--E 83
+
+)clear all
+
+--S 84 of 1369
+t0:=x^7*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 7 | 2
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 1369
+r0:=-1/3*a^3*(a+b*x^2)^(3/2)/b^4+3/5*a^2*(a+b*x^2)^(5/2)/b^4-_
+ 3/7*a*(a+b*x^2)^(7/2)/b^4+1/9*(a+b*x^2)^(9/2)/b^4
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (35b x + 5a b x - 6a b x + 8a b x - 16a )\|b x + a
+--R (2) --------------------------------------------------------
+--R 4
+--R 315b
+--R Type: Expression(Integer)
+--E 85
+
+--S 86 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 16 2 3 14 3 2 12 4 10 5 8
+--R (- 315a b x - 4245a b x - 15666a b x - 21672a b x - 10080a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 18 4 16 2 3 14 3 2 12 4 10
+--R 35b x + 1440a b x + 9999a b x + 25242a b x + 26712a b x
+--R +
+--R 5 8
+--R 10080a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a
+--R Type: Union(Expression(Integer),...)
+--E 86
+
+--S 87 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 5 4 8 6 3 6 7 2 4 8 2 9 | 2
+--R (- 16a b x - 640a b x - 3840a b x - 7168a b x - 4096a )\|b x + a
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+
+--R (144a b x + 1920a b x + 6912a b x + 9216a b x + 4096a )\|a
+--R /
+--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a b
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 88
+
+)clear all
+
+--S 89 of 1369
+t0:=x^5*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 5 | 2
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 1369
+r0:=1/3*a^2*(a+b*x^2)^(3/2)/b^3-2/5*a*(a+b*x^2)^(5/2)/b^3+_
+ 1/7*(a+b*x^2)^(7/2)/b^3
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (15b x + 3a b x - 4a b x + 8a )\|b x + a
+--R (2) ---------------------------------------------
+--R 3
+--R 105b
+--R Type: Expression(Integer)
+--E 90
+
+--S 91 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 12 2 2 10 3 8 4 6 | 2
+--R (- 105a b x - 861a b x - 1820a b x - 1120a x )\|b x + a
+--R +
+--R 4 14 3 12 2 2 10 3 8 4 6 +-+
+--R (15b x + 378a b x + 1631a b x + 2380a b x + 1120a x )\|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (105b x + 2520a b x + 8400a b x + 6720a )\|a \|b x + a - 735a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 5880a b x - 11760a b x - 6720a
+--R Type: Union(Expression(Integer),...)
+--E 91
+
+--S 92 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 | 2
+--R (8a b x + 192a b x + 640a b x + 512a )\|b x + a
+--R +
+--R 4 3 6 5 2 4 6 2 7 +-+
+--R (- 56a b x - 448a b x - 896a b x - 512a )\|a
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +-+ | 2 6 6
+--R (105b x + 2520a b x + 8400a b x + 6720a b )\|a \|b x + a - 735a b x
+--R +
+--R 2 5 4 3 4 2 4 3
+--R - 5880a b x - 11760a b x - 6720a b
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 93
+
+)clear all
+
+--S 94 of 1369
+t0:=x^3*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 3 | 2
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 1369
+r0:=-1/3*a*(a+b*x^2)^(3/2)/b^2+1/5*(a+b*x^2)^(5/2)/b^2
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (3b x + a b x - 2a )\|b x + a
+--R (2) ---------------------------------
+--R 2
+--R 15b
+--R Type: Expression(Integer)
+--E 95
+
+--S 96 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 8 2 6 3 4 | 2
+--R (- 15a b x - 65a b x - 60a x )\|b x + a
+--R +
+--R 3 10 2 8 2 6 3 4 +-+
+--R (3b x + 40a b x + 95a b x + 60a x )\|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a
+--R Type: Union(Expression(Integer),...)
+--E 96
+
+--S 97 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 2 4 4 2 5 | 2 3 2 4 4 2 5 +-+
+--R (- 2a b x - 24a b x - 32a )\|b x + a + (10a b x + 40a b x + 32a )\|a
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ | 2 4 4 2 3 2
+--R (15b x + 180a b x + 240a b )\|a \|b x + a - 75a b x - 300a b x
+--R +
+--R 3 2
+--R - 240a b
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 98
+
+)clear all
+
+--S 99 of 1369
+t0:=x*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R (1) x\|b x + a
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 1369
+r0:=1/3*(a+b*x^2)^(3/2)/b
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (2) ---------------------
+--R 3b
+--R Type: Expression(Integer)
+--E 100
+
+--S 101 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 4 2 2 | 2 2 6 4 2 2 +-+
+--R (- 3a b x - 6a x )\|b x + a + (b x + 6a b x + 6a x )\|a
+--R (3) -------------------------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 101
+
+--S 102 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R 2 2 3 | 2 2 2 3 +-+
+--R (a b x + 4a )\|b x + a + (- 3a b x - 4a )\|a
+--R (4) -------------------------------------------------
+--R +--------+
+--R 2 2 +-+ | 2 2 2 2
+--R (3b x + 12a b)\|a \|b x + a - 9a b x - 12a b
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 103
+
+)clear all
+
+--S 104 of 1369
+t0:=sqrt(a+b*x^2)/x
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R x
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 1369
+r0:=-atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R +-+ \|b x + a | 2
+--R (2) - \|a atanh(-----------) + \|b x + a
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 105
+
+--S 106 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 +-+ \|b x + a - \|a 2 +-+
+--R (a\|b x + a - a\|a )log(------------------) + b x \|a
+--R x
+--R (3) --------------------------------------------------------
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R Type: Union(Expression(Integer),...)
+--E 106
+
+--S 107 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 +-+ \|b x + a - \|a
+--R (a\|b x + a - a\|a )log(------------------)
+--R x
+--R +
+--R +--------+
+--R +--------+ | 2 +--------+
+--R | 2 +-+ \|b x + a | 2 +-+
+--R (a\|b x + a - a\|a )atanh(-----------) + a\|b x + a - a\|a
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 108
+
+)clear all
+
+--S 109 of 1369
+t0:=sqrt(a+b*x^2)/x^3
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 1369
+r0:=-1/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-1/2*sqrt(a+b*x^2)/x^2
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 \|b x + a +-+ | 2
+--R - b x atanh(-----------) - \|a \|b x + a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------
+--R 2 +-+
+--R 2x \|a
+--R Type: Expression(Integer)
+--E 110
+
+--S 111 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 | 2 2 4 2 +-+ \|b x + a - \|a
+--R (2a b x \|b x + a + (- b x - 2a b x )\|a )log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a b x + 2a )\|b x + a + (- 2a b x - 2a )\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R 4a x \|a \|b x + a - 2a b x - 4a x
+--R Type: Union(Expression(Integer),...)
+--E 111
+
+--S 112 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a - \|a \|b x + a
+--R b log(------------------) + b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) ------------------------------------------------
+--R +-+
+--R 2\|a
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 113
+
+)clear all
+
+--S 114 of 1369
+t0:=sqrt(a+b*x^2)/x^5
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 1369
+r0:=1/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-1/4*sqrt(a+b*x^2)/x^4-_
+ 1/8*b*sqrt(a+b*x^2)/(a*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 4 \|b x + a 2 +-+ | 2
+--R b x atanh(-----------) + (- b x - 2a)\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) -----------------------------------------------------
+--R 4 +-+
+--R 8a x \|a
+--R Type: Expression(Integer)
+--E 115
+
+--S 116 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 6 2 2 4 | 2 4 8 3 6 2 2 4 +-+
+--R ((- 4a b x - 8a b x )\|b x + a + (b x + 8a b x + 8a b x )\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 6 2 2 4 3 2 4 | 2
+--R (a b x + 10a b x + 24a b x + 16a )\|b x + a
+--R +
+--R 3 6 2 2 4 3 2 4 +-+
+--R (- 4a b x - 20a b x - 32a b x - 16a )\|a
+--R /
+--R +--------+
+--R 2 6 3 4 +-+ | 2 2 2 8 3 6 4 4
+--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x
+--R Type: Union(Expression(Integer),...)
+--E 116
+
+--S 117 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 2 \|b x + a - \|a 2 \|b x + a
+--R - b log(------------------) - b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------------
+--R +-+
+--R 8a\|a
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 118
+
+)clear all
+
+--S 119 of 1369
+t0:=sqrt(a+b*x^2)/x^7
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 1369
+r0:=-1/16*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-1/6*sqrt(a+b*x^2)/x^6-_
+ 1/24*b*sqrt(a+b*x^2)/(a*x^4)+1/16*b^2*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 3 6 \|b x + a 2 4 2 2 +-+ | 2
+--R - 3b x atanh(-----------) + (3b x - 2a b x - 8a )\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------------------
+--R 2 6 +-+
+--R 48a x \|a
+--R Type: Expression(Integer)
+--E 120
+
+--S 121 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 5 10 2 4 8 3 3 6 | 2
+--R (18a b x + 96a b x + 96a b x )\|b x + a
+--R +
+--R 6 12 5 10 2 4 8 3 3 6 +-+
+--R (- 3b x - 54a b x - 144a b x - 96a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6
+--R (- 3a b x - 52a b x - 100a b x + 144a b x + 448a b x + 256a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +-+
+--R (18a b x + 102a b x + 68a b x - 336a b x - 576a b x - 256a )\|a
+--R /
+--R +--------+
+--R 3 2 10 4 8 5 6 +-+ | 2 3 3 12
+--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x
+--R +
+--R 4 2 10 5 8 6 6
+--R - 864a b x - 2304a b x - 1536a x
+--R Type: Union(Expression(Integer),...)
+--E 121
+
+--S 122 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 3 \|b x + a - \|a 3 \|b x + a
+--R b log(------------------) + b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) ------------------------------------------------
+--R 2 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 123
+
+)clear all
+
+--S 124 of 1369
+t0:=x^4*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 4 | 2
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 1369
+r0:=1/16*a^3*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_
+ 1/16*a^2*x*sqrt(a+b*x^2)/b^2+1/24*a*x^3*sqrt(a+b*x^2)/b+_
+ 1/6*x^5*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R 3 x\|b 2 5 3 2 +-+ | 2
+--R 3a atanh(-----------) + (8b x + 2a b x - 3a x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ---------------------------------------------------------------
+--R 2 +-+
+--R 48b \|b
+--R Type: Expression(Integer)
+--E 125
+
+--S 126 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4
+--R (18a b x + 96a b x + 96a )\|a \|b x + a - 3a b x - 54a b x
+--R +
+--R 5 2 6
+--R - 144a b x - 96a
+--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 9 2 3 7 3 2 5 4 3 5 +-+
+--R (- 8b x - 146a b x - 417a b x - 298a b x + 80a b x + 96a x)\|b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+ +-+
+--R (48b x + 316a b x + 570a b x + 270a b x - 128a b x - 96a x)\|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 +--------+
+--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4
+--R (36a b x + 192a b x + 192a )\|a \|b x + a - 6a b x - 108a b x
+--R +
+--R 5 2 6
+--R - 288a b x - 192a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5
+--R (- 8b x - 146a b x - 417a b x - 298a b x + 80a b x + 96a x)
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5
+--R (48b x + 316a b x + 570a b x + 270a b x - 128a b x - 96a 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 126
+
+--S 127 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 3 (\|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 3 x\|b
+--R - a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 128
+
+--S 129 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 3 +---+ x\|b 3 +-+ \|- b \|b x + a - \|- b \|a
+--R - a \|- b atanh(-----------) + 2a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R --------------------------------------------------------------------------
+--R 2 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 1369
+t0:=x^2*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 1369
+r0:=-1/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_
+ 1/8*a*x*sqrt(a+b*x^2)/b+1/4*x^3*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R 2 x\|b 3 +-+ | 2
+--R - a atanh(-----------) + (2b x + a x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------------------------------------------------
+--R +-+
+--R 8b\|b
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((4a b x + 8a )\|a \|b x + a - a b x - 8a b x - 8a )
+--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 - 17a b x - 24a b x - 8a x)\|b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8b x + 28a b x + 28a b x + 8a x)\|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 3 +-+ | 2 2 2 4 3 2 4
+--R ((- 8a b x - 16a )\|a \|b x + a + 2a b x + 16a b x + 16a )
+--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 - 17a b x - 24a b x - 8a x)\|- b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (8b x + 28a b x + 28a b x + 8a x)\|- 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 133
+
+--S 134 of 1369
+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 a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 8b\|b
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+--S 136 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 2 +---+ x\|b 2 +-+ \|- 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 8b\|- b \|b
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 137
+
+)clear all
+
+--S 138 of 1369
+t0:=sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R (1) \|b x + a
+--R Type: Expression(Integer)
+--E 138
+
+--S 139 of 1369
+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 139
+
+--S 140 of 1369
+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 140
+
+--S 141 of 1369
+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 141
+
+--S 142 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 1369
+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 143
+
+--S 144 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 144
+
+)clear all
+
+--S 145 of 1369
+t0:=sqrt(a+b*x^2)/x^2
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 145
+
+--S 146 of 1369
+r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)-sqrt(a+b*x^2)/x
+--R
+--R
+--R +-+ +--------+
+--R +-+ x\|b | 2
+--R x\|b atanh(-----------) - \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R (x\|b \|b x + a - x\|a \|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
+--R \|a \|b x + a - b x - a
+--R /
+--R +--------+
+--R | 2 +-+
+--R x\|b x + a - x\|a
+--R ,
+--R
+--R +--------+
+--R +--------+ | 2 +-+
+--R +---+ | 2 +---+ +-+ \|b x + a - \|a
+--R (2x\|- b \|b x + a - 2x\|- b \|a )atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R +-+ | 2 2
+--R \|a \|b x + a - b x - a
+--R /
+--R +--------+
+--R | 2 +-+
+--R x\|b x + a - x\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 147
+
+--S 148 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--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 +-+ x\|b
+--R - \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 148
+
+--S 149 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R +-+ x\|b +---+ \|b x + a - \|a
+--R (6) - \|b atanh(-----------) + 2\|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 150
+
+--S 151 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 151
+
+)clear all
+
+--S 152 of 1369
+t0:=sqrt(a+b*x^2)/x^4
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 1369
+r0:=-1/3*(a+b*x^2)^(3/2)/(a*x^3)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (- b x - a)\|b x + a
+--R (2) -----------------------
+--R 3
+--R 3a x
+--R Type: Expression(Integer)
+--E 153
+
+--S 154 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3
+--R (3b x + 7a b x + 4a )\|a \|b x + a - b x - 6a b x - 9a b x - 4a
+--R -----------------------------------------------------------------------
+--R +--------+
+--R 5 2 3 | 2 5 2 3 +-+
+--R (3a b x + 12a x )\|b x + a + (- 9a b x - 12a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 154
+
+--S 155 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 155
+
+--S 156 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 156
+
+)clear all
+
+--S 157 of 1369
+t0:=sqrt(a+b*x^2)/x^6
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 1369
+r0:=-1/5*(a+b*x^2)^(3/2)/(a*x^5)+2/15*b*(a+b*x^2)^(3/2)/(a^2*x^3)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (2b x - a b x - 3a )\|b x + a
+--R (2) ---------------------------------
+--R 2 5
+--R 15a x
+--R Type: Expression(Integer)
+--E 158
+
+--S 159 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10
+--R (- 10b x - 35a b x + 3a b x + 76a b x + 48a )\|a \|b x + a + 2b x
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R 25a b x + 40a b x - 35a b x - 100a b x - 48a
+--R /
+--R +--------+
+--R 2 2 9 3 7 4 5 | 2
+--R (15a b x + 180a b x + 240a x )\|b x + a
+--R +
+--R 2 2 9 3 7 4 5 +-+
+--R (- 75a b x - 300a b x - 240a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 159
+
+--S 160 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 160
+
+--S 161 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 161
+
+)clear all
+
+--S 162 of 1369
+t0:=sqrt(a+b*x^2)/x^8
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 1369
+r0:=-1/7*(a+b*x^2)^(3/2)/(a*x^7)+4/35*b*(a+b*x^2)^(3/2)/(a^2*x^5)-_
+ 8/105*b^2*(a+b*x^2)^(3/2)/(a^3*x^3)
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (- 8b x + 4a b x - 3a b x - 15a )\|b x + a
+--R (2) -----------------------------------------------
+--R 3 7
+--R 105a x
+--R Type: Expression(Integer)
+--E 163
+
+--S 164 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2
+--R 56b x + 420a b x + 693a b x + 337a b x + 920a b x + 1872a b x
+--R +
+--R 6
+--R 960a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R - 8b x - 196a b x - 735a b x - 826a b x - 623a b x - 1736a b x
+--R +
+--R 6 2 7
+--R - 2352a b x - 960a
+--R /
+--R +--------+
+--R 3 3 13 4 2 11 5 9 6 7 | 2
+--R (105a b x + 2520a b x + 8400a b x + 6720a x )\|b x + a
+--R +
+--R 3 3 13 4 2 11 5 9 6 7 +-+
+--R (- 735a b x - 5880a b x - 11760a b x - 6720a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 164
+
+--S 165 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 165
+
+--S 166 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 166
+
+)clear all
+
+--S 167 of 1369
+t0:=sqrt(a+b*x^2)/x^10
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 1369
+r0:=-1/9*(a+b*x^2)^(3/2)/(a*x^9)+2/21*b*(a+b*x^2)^(3/2)/(a^2*x^7)-_
+ 8/105*b^2*(a+b*x^2)^(3/2)/(a^3*x^5)+16/315*b^3*(a+b*x^2)^(3/2)/(a^4*x^3)
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (16b x - 8a b x + 6a b x - 5a b x - 35a )\|b x + a
+--R (2) --------------------------------------------------------
+--R 4 9
+--R 315a x
+--R Type: Expression(Integer)
+--E 168
+
+--S 169 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 144b x - 1848a b x - 6006a b x - 6435a b x - 1165a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 4952a b x + 16464a b x + 21440a b x + 8960a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 16b x + 648a b x + 4158a b x + 9009a b x + 7200a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 243a b x - 11064a b x - 26064a b x - 25920a b x - 8960a
+--R /
+--R 4 4 17 5 3 15 6 2 13 7 11 8 9
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 4 17 5 3 15 6 2 13 7 11
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 8 9
+--R - 80640a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 169
+
+--S 170 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 170
+
+--S 171 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 171
+
+)clear all
+
+--S 172 of 1369
+t0:=x^m*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 m | 2
+--R (1) (b x + a)x \|b x + a
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 1369
+--r0:=x^(1+m)*(a+b*x^2)^(3/2)/(4+m)+3*a*x^(1+m)*sqrt(a+b*x^2)/(8+6*m+m^2)+_
+-- 3*a^2*x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+-- sqrt((a+b*x^2)/a)/((8+14*m+7*m^2+m^3)*sqrt(a+b*x^2))
+--E 173
+
+--S 174 of 1369
+--a0:=integrate(t0,x)
+--E 174
+
+--S 175 of 1369
+--m0:=a0-r0
+--E 175
+
+--S 176 of 1369
+--d0:=D(m0,x)
+--E 176
+
+)clear all
+
+--S 177 of 1369
+t0:=x^7*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 9 7 | 2
+--R (1) (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 1369
+r0:=-1/5*a^3*(a+b*x^2)^(5/2)/b^4+3/7*a^2*(a+b*x^2)^(7/2)/b^4-_
+ 1/3*a*(a+b*x^2)^(9/2)/b^4+1/11*(a+b*x^2)^(11/2)/b^4
+--R
+--R
+--R +--------+
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2
+--R (105b x + 140a b x + 5a b x - 6a b x + 8a b x - 16a )\|b x + a
+--R (2) ----------------------------------------------------------------------
+--R 4
+--R 1155b
+--R Type: Expression(Integer)
+--E 178
+
+--S 179 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 20 2 5 18 3 4 16 4 3 14
+--R - 1155a b x - 24640a b x - 160215a b x - 469194a b x
+--R +
+--R 5 2 12 6 10 7 8
+--R - 694848a b x - 510048a b x - 147840a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 22 6 20 2 5 18 3 4 16 4 3 14
+--R 105b x + 6545a b x + 73645a b x + 334059a b x + 762102a b x
+--R +
+--R 5 2 12 6 10 7 8
+--R 931392a b x + 583968a b x + 147840a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 10 4 8 2 3 6 3 2 4
+--R 1155b x + 69300a b x + 646800a b x + 2069760a b x
+--R +
+--R 4 2 5
+--R 2661120a b x + 1182720a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4
+--R - 12705a b x - 254100a b x - 1422960a b x - 3252480a b x
+--R +
+--R 5 2 6
+--R - 3252480a b x - 1182720a
+--R Type: Union(Expression(Integer),...)
+--E 179
+
+--S 180 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2
+--R - 16a b x - 960a b x - 8960a b x - 28672a b x - 36864a b x
+--R +
+--R 11
+--R - 16384a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2
+--R 176a b x + 3520a b x + 19712a b x + 45056a b x + 45056a b x
+--R +
+--R 11
+--R 16384a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 9 10 8 8 2 7 6 3 6 4
+--R 1155b x + 69300a b x + 646800a b x + 2069760a b x
+--R +
+--R 4 5 2 5 4
+--R 2661120a b x + 1182720a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 10 2 8 8 3 7 6 4 6 4
+--R - 12705a b x - 254100a b x - 1422960a b x - 3252480a b x
+--R +
+--R 5 5 2 6 4
+--R - 3252480a b x - 1182720a b
+--R Type: Expression(Integer)
+--E 180
+
+--S 181 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 181
+
+)clear all
+
+--S 182 of 1369
+t0:=x^5*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 7 5 | 2
+--R (1) (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 1369
+r0:=1/5*a^2*(a+b*x^2)^(5/2)/b^3-2/7*a*(a+b*x^2)^(7/2)/b^3+_
+ 1/9*(a+b*x^2)^(9/2)/b^3
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (35b x + 50a b x + 3a b x - 4a b x + 8a )\|b x + a
+--R (2) --------------------------------------------------------
+--R 3
+--R 315b
+--R Type: Expression(Integer)
+--E 183
+
+--S 184 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 16 2 4 14 3 3 12 4 2 10
+--R - 315a b x - 4650a b x - 21147a b x - 42084a b x
+--R +
+--R 5 8 6 6
+--R - 38640a b x - 13440a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 18 5 16 2 4 14 3 3 12 4 2 10
+--R 35b x + 1485a b x + 11853a b x + 38199a b x + 59724a b x
+--R +
+--R 5 8 6 6
+--R 45360a b x + 13440a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a
+--R Type: Union(Expression(Integer),...)
+--E 184
+
+--S 185 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 5 4 8 6 3 6 7 2 4 8 2 9 | 2
+--R (8a b x + 320a b x + 1920a b x + 3584a b x + 2048a )\|b x + a
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+
+--R (- 72a b x - 960a b x - 3456a b x - 4608a b x - 2048a )\|a
+--R /
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 8 2 6 6 3 5 4 4 4 2 5 3
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a b
+--R Type: Expression(Integer)
+--E 185
+
+--S 186 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 186
+
+)clear all
+
+--S 187 of 1369
+t0:=x^3*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 5 3 | 2
+--R (1) (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 1369
+r0:=-1/5*a*(a+b*x^2)^(5/2)/b^2+1/7*(a+b*x^2)^(7/2)/b^2
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (5b x + 8a b x + a b x - 2a )\|b x + a
+--R (2) -------------------------------------------
+--R 2
+--R 35b
+--R Type: Expression(Integer)
+--E 188
+
+--S 189 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 12 2 3 10 3 2 8 4 6 5 4 | 2
+--R (- 35a b x - 336a b x - 1015a b x - 1260a b x - 560a x )\|b x + a
+--R +
+--R 5 14 4 12 2 3 10 3 2 8 4 6 5 4 +-+
+--R (5b x + 133a b x + 721a b x + 1575a b x + 1540a b x + 560a x )\|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (35b x + 840a b x + 2800a b x + 2240a )\|a \|b x + a - 245a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 1960a b x - 3920a b x - 2240a
+--R Type: Union(Expression(Integer),...)
+--E 189
+
+--S 190 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 | 2
+--R (- 2a b x - 48a b x - 160a b x - 128a )\|b x + a
+--R +
+--R 4 3 6 5 2 4 6 2 7 +-+
+--R (14a b x + 112a b x + 224a b x + 128a )\|a
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +-+ | 2 5 6
+--R (35b x + 840a b x + 2800a b x + 2240a b )\|a \|b x + a - 245a b x
+--R +
+--R 2 4 4 3 3 2 4 2
+--R - 1960a b x - 3920a b x - 2240a b
+--R Type: Expression(Integer)
+--E 190
+
+--S 191 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 191
+
+)clear all
+
+--S 192 of 1369
+t0:=x*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 3 | 2
+--R (1) (b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 1369
+r0:=1/5*(a+b*x^2)^(5/2)/b
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (2) --------------------------------
+--R 5b
+--R Type: Expression(Integer)
+--E 193
+
+--S 194 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 8 2 2 6 3 4 4 2 | 2
+--R (- 5a b x - 30a b x - 60a b x - 40a x )\|b x + a
+--R +
+--R 4 10 3 8 2 2 6 3 4 4 2 +-+
+--R (b x + 15a b x + 55a b x + 80a b x + 40a x )\|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (5b x + 60a b x + 80a )\|a \|b x + a - 25a b x - 100a b x - 80a
+--R Type: Union(Expression(Integer),...)
+--E 194
+
+--S 195 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 2 4 4 2 5 | 2 3 2 4 4 2 5 +-+
+--R (a b x + 12a b x + 16a )\|b x + a + (- 5a b x - 20a b x - 16a )\|a
+--R -------------------------------------------------------------------------
+--R +--------+
+--R 3 4 2 2 2 +-+ | 2 3 4 2 2 2 3
+--R (5b x + 60a b x + 80a b)\|a \|b x + a - 25a b x - 100a b x - 80a b
+--R Type: Expression(Integer)
+--E 195
+
+--S 196 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 196
+
+)clear all
+
+--S 197 of 1369
+t0:=(a+b*x^2)^(3/2)/x
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R x
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 1369
+r0:=1/3*(a+b*x^2)^(3/2)-a^(3/2)*atanh(sqrt(a+b*x^2)/sqrt(a))+a*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R +-+ \|b x + a 2 | 2
+--R - 3a\|a atanh(-----------) + (b x + 4a)\|b x + a
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 198
+
+--S 199 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 3 | 2 2 2 3 +-+
+--R ((3a b x + 12a )\|b x + a + (- 9a b x - 12a )\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+
+--R (- 3a b x - 12a b x )\|b x + a + (b x + 9a b x + 12a b x )\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 199
+
+--S 200 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 3 | 2 2 2 3 +-+
+--R ((3a b x + 12a )\|b x + a + (- 9a b x - 12a )\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R +--------+ | 2
+--R 2 2 3 | 2 2 2 3 +-+ \|b x + a
+--R ((3a b x + 12a )\|b x + a + (- 9a b x - 12a )\|a )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 3 | 2 2 2 3 +-+
+--R (4a b x + 16a )\|b x + a + (- 12a b x - 16a )\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a
+--R Type: Expression(Integer)
+--E 200
+
+--S 201 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 201
+
+)clear all
+
+--S 202 of 1369
+t0:=(a+b*x^2)^(3/2)/x^3
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 1369
+r0:=-1/2*(a+b*x^2)^(3/2)/x^2-3/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))*_
+ sqrt(a)+3/2*b*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 +-+ \|b x + a 2 | 2
+--R - 3b x \|a atanh(-----------) + (2b x - a)\|b x + a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 203
+
+--S 204 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 | 2 2 4 2 2 +-+
+--R ((3a b x + 12a b x )\|b x + a + (- 9a b x - 12a b x )\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 2 3 | 2
+--R (- 4a b x + 3a b x + 4a )\|b x + a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (2b x + 3a b x - 5a b x - 4a )\|a
+--R /
+--R +--------+
+--R 4 2 +-+ | 2 4 2 2
+--R (2b x + 8a x )\|a \|b x + a - 6a b x - 8a x
+--R Type: Union(Expression(Integer),...)
+--E 204
+
+--S 205 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 2 | 2 2 2 2 +-+
+--R ((3a b x + 12a b)\|b x + a + (- 9a b x - 12a b)\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 2 | 2 2 2 2 +-+
+--R ((3a b x + 12a b)\|b x + a + (- 9a b x - 12a b)\|a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 2 | 2 2 2 2 +-+
+--R (2a b x + 8a b)\|b x + a + (- 6a b x - 8a b)\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (2b x + 8a)\|a \|b x + a - 6a b x - 8a
+--R Type: Expression(Integer)
+--E 205
+
+--S 206 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 206
+
+)clear all
+
+--S 207 of 1369
+t0:=(a+b*x^2)^(3/2)/x^5
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 1369
+r0:=-1/4*(a+b*x^2)^(3/2)/x^4-3/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-_
+ 3/8*b*sqrt(a+b*x^2)/x^2
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 4 \|b x + a 2 +-+ | 2
+--R - 3b x atanh(-----------) + (- 5b x - 2a)\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------------
+--R 4 +-+
+--R 8x \|a
+--R Type: Expression(Integer)
+--E 208
+
+--S 209 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 6 2 2 4 | 2
+--R (12a b x + 24a b x )\|b x + a
+--R +
+--R 4 8 3 6 2 2 4 +-+
+--R (- 3b x - 24a b x - 24a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 6 2 2 4 3 2 4 | 2
+--R (5a b x + 42a b x + 56a b x + 16a )\|b x + a
+--R +
+--R 3 6 2 2 4 3 2 4 +-+
+--R (- 20a b x - 68a b x - 64a b x - 16a )\|a
+--R /
+--R +--------+
+--R 6 2 4 +-+ | 2 2 8 2 6 3 4
+--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x
+--R Type: Union(Expression(Integer),...)
+--E 209
+
+--S 210 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 2 \|b x + a - \|a 2 \|b x + a
+--R 3b log(------------------) + 3b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------------
+--R +-+
+--R 8\|a
+--R Type: Expression(Integer)
+--E 210
+
+--S 211 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 211
+
+)clear all
+
+--S 212 of 1369
+t0:=(a+b*x^2)^(3/2)/x^7
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 1369
+r0:=-1/6*(a+b*x^2)^(3/2)/x^6+1/16*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_
+ 1/8*b*sqrt(a+b*x^2)/x^4-1/16*b^2*sqrt(a+b*x^2)/(a*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 3 6 \|b x + a 2 4 2 2 +-+ | 2
+--R 3b x atanh(-----------) + (- 3b x - 14a b x - 8a )\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------------
+--R 6 +-+
+--R 48a x \|a
+--R Type: Expression(Integer)
+--E 213
+
+--S 214 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 5 10 2 4 8 3 3 6 | 2
+--R (- 18a b x - 96a b x - 96a b x )\|b x + a
+--R +
+--R 6 12 5 10 2 4 8 3 3 6 +-+
+--R (3b x + 54a b x + 144a b x + 96a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6
+--R (3a b x + 68a b x + 404a b x + 912a b x + 832a b x + 256a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +-+
+--R (- 18a b x - 198a b x - 772a b x - 1296a b x - 960a b x - 256a )\|a
+--R /
+--R +--------+
+--R 2 2 10 3 8 4 6 +-+ | 2 2 3 12
+--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x
+--R +
+--R 3 2 10 4 8 5 6
+--R - 864a b x - 2304a b x - 1536a x
+--R Type: Union(Expression(Integer),...)
+--E 214
+
+--S 215 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 3 \|b x + a - \|a 3 \|b x + a
+--R - b log(------------------) - b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------------
+--R +-+
+--R 16a\|a
+--R Type: Expression(Integer)
+--E 215
+
+--S 216 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 216
+
+)clear all
+
+--S 217 of 1369
+t0:=(a+b*x^2)^(3/2)/x^9
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 1369
+r0:=-1/8*(a+b*x^2)^(3/2)/x^8-3/128*b^4*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_
+ 1/16*b*sqrt(a+b*x^2)/x^6-1/64*b^2*sqrt(a+b*x^2)/(a*x^4)+_
+ 3/128*b^3*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 4 8 \|b x + a
+--R - 3b x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2
+--R (3b x - 2a b x - 24a b x - 16a )\|a \|b x + a
+--R /
+--R 2 8 +-+
+--R 128a x \|a
+--R Type: Expression(Integer)
+--E 218
+
+--S 219 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 7 14 2 6 12 3 5 10 4 4 8 | 2
+--R (24a b x + 240a b x + 576a b x + 384a b x )\|b x + a
+--R +
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +-+
+--R (- 3b x - 96a b x - 480a b x - 768a b x - 384a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R - 3a b x - 94a b x - 392a b x + 336a b x + 4480a b x
+--R +
+--R 6 2 4 7 2 8
+--R 8960a b x + 7168a b x + 2048a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R 24a b x + 248a b x + 448a b x - 1824a b x - 8192a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 12288a b x - 8192a b x - 2048a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 3 14 4 2 12 5 10 6 8 +-+ | 2
+--R (1024a b x + 10240a b x + 24576a b x + 16384a x )\|a \|b x + a
+--R +
+--R 3 4 16 4 3 14 5 2 12 6 10 7 8
+--R - 128a b x - 4096a b x - 20480a b x - 32768a b x - 16384a x
+--R Type: Union(Expression(Integer),...)
+--E 219
+
+--S 220 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 4 \|b x + a - \|a 4 \|b x + a
+--R 3b log(------------------) + 3b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------------
+--R 2 +-+
+--R 128a \|a
+--R Type: Expression(Integer)
+--E 220
+
+--S 221 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 221
+
+)clear all
+
+--S 222 of 1369
+t0:=x^4*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 6 4 | 2
+--R (1) (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 1369
+r0:=1/8*x^5*(a+b*x^2)^(3/2)+3/128*a^4*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_
+ 3/128*a^3*x*sqrt(a+b*x^2)/b^2+1/64*a^2*x^3*sqrt(a+b*x^2)/b+_
+ 1/16*a*x^5*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 4 x\|b 3 7 2 5 2 3 3 +-+ | 2
+--R 3a atanh(-----------) + (16b x + 24a b x + 2a b x - 3a x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R ---------------------------------------------------------------------------
+--R 2 +-+
+--R 128b \|b
+--R Type: Expression(Integer)
+--E 223
+
+--S 224 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2 4 4 8
+--R (24a b x + 240a b x + 576a b x + 384a )\|a \|b x + a - 3a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 96a b x - 480a b x - 768a b x - 384a
+--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 15 6 13 2 5 11 3 4 9 4 3 7
+--R - 16b x - 536a b x - 3330a b x - 7997a b x - 8416a b x
+--R +
+--R 5 2 5 6 3 7
+--R - 3104a b x + 512a b x + 384a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 15 6 13 2 5 11 3 4 9 4 3 7
+--R 128b x + 1600a b x + 6480a b x + 11800a b x + 10008a b x
+--R +
+--R 5 2 5 6 3 7
+--R 2896a b x - 704a b x - 384a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +-+ +-+ | 2
+--R (1024b x + 10240a b x + 24576a b x + 16384a b )\|a \|b \|b x + a
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+
+--R (- 128b x - 4096a b x - 20480a b x - 32768a b x - 16384a b )\|b
+--R ,
+--R
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2
+--R (48a b x + 480a b x + 1152a b x + 768a )\|a \|b x + a
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R - 6a b x - 192a b x - 960a b x - 1536a b x - 768a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 7 15 6 13 2 5 11 3 4 9 4 3 7
+--R - 16b x - 536a b x - 3330a b x - 7997a b x - 8416a b x
+--R +
+--R 5 2 5 6 3 7
+--R - 3104a b x + 512a b x + 384a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 15 6 13 2 5 11 3 4 9 4 3 7
+--R 128b x + 1600a b x + 6480a b x + 11800a b x + 10008a b x
+--R +
+--R 5 2 5 6 3 7
+--R 2896a b x - 704a b x - 384a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +---+ +-+ | 2
+--R (1024b x + 10240a b x + 24576a b x + 16384a b )\|- b \|a \|b x + a
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +---+
+--R (- 128b x - 4096a b x - 20480a b x - 32768a b x - 16384a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 224
+
+--S 225 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 4 (\|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 4 x\|b
+--R - 3a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 128b \|b
+--R Type: Expression(Integer)
+--E 225
+
+--S 226 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 4 +---+ x\|b 4 +-+ \|- b \|b x + a - \|- b \|a
+--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ---------------------------------------------------------------------------
+--R 2 +---+ +-+
+--R 128b \|- b \|b
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 228
+
+)clear all
+
+--S 229 of 1369
+t0:=x^2*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (1) (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 1369
+r0:=1/6*x^3*(a+b*x^2)^(3/2)-1/16*a^3*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_
+ 1/16*a^2*x*sqrt(a+b*x^2)/b+1/8*a*x^3*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R 3 x\|b 2 5 3 2 +-+ | 2
+--R - 3a atanh(-----------) + (8b x + 14a b x + 3a x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ------------------------------------------------------------------
+--R +-+
+--R 48b\|b
+--R Type: Expression(Integer)
+--E 230
+
+--S 231 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4
+--R (18a b x + 96a b x + 96a )\|a \|b x + a - 3a b x - 54a b x
+--R +
+--R 5 2 6
+--R - 144a b x - 96a
+--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 9 2 3 7 3 2 5 4 3 5
+--R (- 8b x - 158a b x - 639a b x - 982a b x - 592a b x - 96a x)
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5
+--R (48b x + 388a b x + 1062a b x + 1266a b x + 640a b x + 96a 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 +--------+
+--R 3 2 4 4 2 5 +-+ | 2 3 3 6
+--R (- 36a b x - 192a b x - 192a )\|a \|b x + a + 6a b x
+--R +
+--R 4 2 4 5 2 6
+--R 108a b x + 288a b x + 192a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5
+--R (- 8b x - 158a b x - 639a b x - 982a b x - 592a b x - 96a x)
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3 5
+--R (48b x + 388a b x + 1062a b x + 1266a b x + 640a b x + 96a 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 231
+
+--S 232 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 3 (\|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 3 x\|b
+--R a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 16b\|b
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 233
+
+--S 234 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 3 +---+ x\|b 3 +-+ \|- 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 16b\|- b \|b
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 1369
+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 236
+
+--S 237 of 1369
+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 237
+
+--S 238 of 1369
+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 238
+
+--S 239 of 1369
+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 239
+
+--S 240 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+--S 241 of 1369
+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 241
+
+--S 242 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 242
+
+)clear all
+
+--S 243 of 1369
+t0:=(a+b*x^2)^(3/2)/x^2
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 243
+
+--S 244 of 1369
+r0:=-(a+b*x^2)^(3/2)/x+3/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+_
+ 3/2*b*x*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R +-+ x\|b 2 | 2
+--R 3a x\|b atanh(-----------) + (b x - 2a)\|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ---------------------------------------------------
+--R 2x
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 2 +-+ | 2 3 2 +-+ +-+
+--R ((3a b x + 12a x)\|b \|b x + a + (- 9a b x - 12a x)\|a \|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 4 2 2 +-+ | 2 3 6 2 4 2 2 3
+--R (- 3b x + 2a b x + 8a )\|a \|b x + a + b x + 3a b x - 6a b x - 8a
+--R /
+--R +--------+
+--R 3 | 2 3 +-+
+--R (2b x + 8a x)\|b x + a + (- 6b x - 8a x)\|a
+--R ,
+--R
+--R +--------+
+--R 3 2 +---+ | 2 3 2 +---+ +-+
+--R ((6a b x + 24a x)\|- b \|b x + a + (- 18a b x - 24a x)\|- b \|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3
+--R (- 3b x + 2a b x + 8a )\|a \|b x + a + b x + 3a b x - 6a b x - 8a
+--R /
+--R +--------+
+--R 3 | 2 3 +-+
+--R (2b x + 8a x)\|b x + a + (- 6b x - 8a x)\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 245
+
+--S 246 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 3a\|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ x\|b
+--R - 3a\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R +-+ x\|b +---+ \|b x + a - \|a
+--R - 3a\|b atanh(-----------) + 6a\|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R (6) -------------------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 248
+
+--S 249 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 249
+
+)clear all
+
+--S 250 of 1369
+t0:=(a+b*x^2)^(3/2)/x^4
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 250
+
+--S 251 of 1369
+r0:=-1/3*(a+b*x^2)^(3/2)/x^3+b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))-_
+ b*sqrt(a+b*x^2)/x
+--R
+--R
+--R +-+ +--------+
+--R 3 +-+ x\|b 2 | 2
+--R 3b x \|b atanh(-----------) + (- 4b x - a)\|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ------------------------------------------------------
+--R 3
+--R 3x
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+
+--R ((3b x + 12a b x )\|b \|b x + a + (- 9b x - 12a b x )\|a \|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 4 2 2 +-+ | 2 3 6 2 4 2 2
+--R (12b x + 19a b x + 4a )\|a \|b x + a - 4b x - 21a b x - 21a b x
+--R +
+--R 3
+--R - 4a
+--R /
+--R +--------+
+--R 5 3 | 2 5 3 +-+
+--R (3b x + 12a x )\|b x + a + (- 9b x - 12a x )\|a
+--R ,
+--R
+--R +--------+
+--R 2 5 3 +---+ | 2
+--R (6b x + 24a b x )\|- b \|b x + a
+--R +
+--R 2 5 3 +---+ +-+
+--R (- 18b x - 24a b x )\|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2
+--R (12b x + 19a b x + 4a )\|a \|b x + a - 4b x - 21a b x - 21a b x
+--R +
+--R 3
+--R - 4a
+--R /
+--R +--------+
+--R 5 3 | 2 5 3 +-+
+--R (3b x + 12a x )\|b x + a + (- 9b x - 12a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 252
+
+--S 253 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R b\|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ x\|b
+--R - b\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 253
+
+--S 254 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R +-+ x\|b +---+ \|b x + a - \|a
+--R (6) - b\|b atanh(-----------) + 2b\|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 255
+
+--S 256 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 256
+
+)clear all
+
+--S 257 of 1369
+t0:=(a+b*x^2)^(3/2)/x^6
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 1369
+r0:=-1/5*(a+b*x^2)^(5/2)/(a*x^5)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (- b x - 2a b x - a )\|b x + a
+--R (2) ----------------------------------
+--R 5
+--R 5a x
+--R Type: Expression(Integer)
+--E 258
+
+--S 259 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10
+--R (5b x + 30a b x + 61a b x + 52a b x + 16a )\|a \|b x + a - b x
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 15a b x - 55a b x - 85a b x - 60a b x - 16a
+--R /
+--R +--------+
+--R 2 9 2 7 3 5 | 2
+--R (5a b x + 60a b x + 80a x )\|b x + a
+--R +
+--R 2 9 2 7 3 5 +-+
+--R (- 25a b x - 100a b x - 80a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 259
+
+--S 260 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 260
+
+--S 261 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 261
+
+)clear all
+
+--S 262 of 1369
+t0:=(a+b*x^2)^(3/2)/x^8
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 1369
+r0:=-1/7*(a+b*x^2)^(5/2)/(a*x^7)+2/35*b*(a+b*x^2)^(5/2)/(a^2*x^5)
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (2b x - a b x - 8a b x - 5a )\|b x + a
+--R (2) -------------------------------------------
+--R 2 7
+--R 35a x
+--R Type: Expression(Integer)
+--E 263
+
+--S 264 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4
+--R - 14b x - 105a b x - 112a b x + 467a b x + 1240a b x
+--R +
+--R 5 2 6
+--R 1072a b x + 320a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R 2b x + 49a b x + 175a b x - 21a b x - 973a b x - 1736a b x
+--R +
+--R 6 2 7
+--R - 1232a b x - 320a
+--R /
+--R +--------+
+--R 2 3 13 3 2 11 4 9 5 7 | 2
+--R (35a b x + 840a b x + 2800a b x + 2240a x )\|b x + a
+--R +
+--R 2 3 13 3 2 11 4 9 5 7 +-+
+--R (- 245a b x - 1960a b x - 3920a b x - 2240a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 264
+
+--S 265 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 265
+
+--S 266 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 266
+
+)clear all
+
+--S 267 of 1369
+t0:=(a+b*x^2)^(3/2)/x^10
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 1369
+r0:=-1/9*(a+b*x^2)^(5/2)/(a*x^9)+4/63*b*(a+b*x^2)^(5/2)/(a^2*x^7)-_
+ 8/315*b^2*(a+b*x^2)^(5/2)/(a^3*x^5)
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (- 8b x + 4a b x - 3a b x - 50a b x - 35a )\|b x + a
+--R (2) ----------------------------------------------------------
+--R 3 9
+--R 315a x
+--R Type: Expression(Integer)
+--E 268
+
+--S 269 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 72b x + 924a b x + 3003a b x + 3690a b x + 7355a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 26504a b x + 44688a b x + 32960a b x + 8960a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R - 8b x - 324a b x - 2079a b x - 4557a b x - 5805a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 16731a b x - 45288a b x - 60048a b x - 37440a b x - 8960a
+--R /
+--R 3 4 17 4 3 15 5 2 13 6 11 7 9
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 17 4 3 15 5 2 13 6 11
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 7 9
+--R - 80640a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 269
+
+--S 270 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 270
+
+--S 271 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 271
+
+)clear all
+
+--S 272 of 1369
+t0:=(a+b*x^2)^(3/2)/x^12
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 12
+--R x
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 1369
+r0:=-1/11*(a+b*x^2)^(5/2)/(a*x^11)+2/33*b*(a+b*x^2)^(5/2)/(a^2*x^9)-_
+ 8/231*b^2*(a+b*x^2)^(5/2)/(a^3*x^7)+16/1155*b^3*(a+b*x^2)^(5/2)/(a^4*x^5)
+--R
+--R
+--R +--------+
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2
+--R (16b x - 8a b x + 6a b x - 5a b x - 140a b x - 105a )\|b x + a
+--R (2) ----------------------------------------------------------------------
+--R 4 11
+--R 1155a x
+--R Type: Expression(Integer)
+--E 273
+
+--S 274 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 20 9 18 2 8 16 3 7 14
+--R - 176b x - 3432a b x - 18018a b x - 36465a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8 7 3 6
+--R - 27280a b x + 27363a b x + 200956a b x + 531536a b x
+--R +
+--R 8 2 4 9 2 10
+--R 695040a b x + 439040a b x + 107520a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 11 22 10 20 2 9 18 3 8 16 4 7 14
+--R 16b x + 968a b x + 9438a b x + 33033a b x + 49995a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8 8 3 6 9 2 4
+--R 22847a b x - 90629a b x - 403084a b x - 830896a b x - 901120a b x
+--R +
+--R 10 2 11
+--R - 492800a b x - 107520a
+--R /
+--R 4 5 21 5 4 19 6 3 17 7 2 15
+--R 1155a b x + 69300a b x + 646800a b x + 2069760a b x
+--R +
+--R 8 13 9 11
+--R 2661120a b x + 1182720a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 5 21 5 4 19 6 3 17 7 2 15
+--R - 12705a b x - 254100a b x - 1422960a b x - 3252480a b x
+--R +
+--R 8 13 9 11
+--R - 3252480a b x - 1182720a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 274
+
+--S 275 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 275
+
+--S 276 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 276
+
+)clear all
+
+--S 277 of 1369
+t0:=x^m*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 m | 2
+--R (1) (b x + 2a b x + a )x \|b x + a
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 1369
+--r0:=5*a*x^(1+m)*(a+b*x^2)^(3/2)/((4+m)*(6+m))+x^(1+m)*(a+b*x^2)^(5/2)/_
+-- (6+m)+15*a^2*x^(1+m)*sqrt(a+b*x^2)/((6+m)*(8+6*m+m^2))+15*_
+-- a^3*x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+-- sqrt((a+b*x^2)/a)/((6+m)*(8+14*m+7*m^2+m^3)*sqrt(a+b*x^2))
+--E 278
+
+--S 279 of 1369
+--a0:=integrate(t0,x)
+--E 279
+
+--S 280 of 1369
+--m0:=a0-r0
+--E 280
+
+--S 281 of 1369
+--d0:=D(m0,x)
+--E 281
+
+)clear all
+
+--S 282 of 1369
+t0:=x^7*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 11 9 2 7 | 2
+--R (1) (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 1369
+r0:=-1/7*a^3*(a+b*x^2)^(7/2)/b^4+1/3*a^2*(a+b*x^2)^(9/2)/b^4-_
+ 3/11*a*(a+b*x^2)^(11/2)/b^4+1/13*(a+b*x^2)^(13/2)/b^4
+--R
+--R
+--R (2)
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6
+--R (231b x + 567a b x + 371a b x + 5a b x - 6a b x + 8a b x - 16a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4
+--R 3003b
+--R Type: Expression(Integer)
+--E 283
+
+--S 284 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 2 7 22 3 6 20 4 5 18
+--R - 3003a b x - 91455a b x - 883883a b x - 4092517a b x
+--R +
+--R 5 4 16 6 3 14 7 2 12
+--R - 10586862a b x - 16226496a b x - 14702688a b x
+--R +
+--R 8 10 9 8
+--R - 7303296a b x - 1537536a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 26 8 24 2 7 22 3 6 20
+--R 231b x + 20202a b x + 326690a b x + 2214784a b x
+--R +
+--R 4 5 18 5 4 16 6 3 14 7 2 12
+--R 8033311a b x + 17258670a b x + 22761024a b x + 18162144a b x
+--R +
+--R 8 10 9 8
+--R 8072064a b x + 1537536a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 12 5 10 2 4 8 3 3 6
+--R 3003b x + 252252a b x + 3363360a b x + 16144128a b x
+--R +
+--R 4 2 4 5 2 6
+--R 34594560a b x + 33825792a b x + 12300288a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 12 2 5 10 3 4 8 4 3 6
+--R - 39039a b x - 1093092a b x - 8744736a b x - 29981952a b x
+--R +
+--R 5 2 4 6 2 7
+--R - 49969920a b x - 39975936a b x - 12300288a
+--R Type: Union(Expression(Integer),...)
+--E 284
+
+--S 285 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 7 6 12 8 5 10 9 4 8 10 3 6
+--R - 16a b x - 1344a b x - 17920a b x - 86016a b x
+--R +
+--R 11 2 4 12 2 13
+--R - 184320a b x - 180224a b x - 65536a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 6 12 8 5 10 9 4 8 10 3 6
+--R 208a b x + 5824a b x + 46592a b x + 159744a b x
+--R +
+--R 11 2 4 12 2 13
+--R 266240a b x + 212992a b x + 65536a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 10 12 9 10 2 8 8 3 7 6
+--R 3003b x + 252252a b x + 3363360a b x + 16144128a b x
+--R +
+--R 4 6 4 5 5 2 6 4
+--R 34594560a b x + 33825792a b x + 12300288a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 10 12 2 9 10 3 8 8 4 7 6
+--R - 39039a b x - 1093092a b x - 8744736a b x - 29981952a b x
+--R +
+--R 5 6 4 6 5 2 7 4
+--R - 49969920a b x - 39975936a b x - 12300288a b
+--R Type: Expression(Integer)
+--E 285
+
+--S 286 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 286
+
+)clear all
+
+--S 287 of 1369
+t0:=x^5*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (1) (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 1369
+r0:=1/7*a^2*(a+b*x^2)^(7/2)/b^3-2/9*a*(a+b*x^2)^(9/2)/b^3+_
+ 1/11*(a+b*x^2)^(11/2)/b^3
+--R
+--R
+--R +--------+
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2
+--R (63b x + 161a b x + 113a b x + 3a b x - 4a b x + 8a )\|b x + a
+--R (2) ----------------------------------------------------------------------
+--R 3
+--R 693b
+--R Type: Expression(Integer)
+--E 288
+
+--S 289 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 20 2 6 18 3 5 16 4 4 14
+--R - 693a b x - 15631a b x - 114279a b x - 400653a b x
+--R +
+--R 5 3 12 6 2 10 7 8 8 6
+--R - 770616a b x - 838992a b x - 487872a b x - 118272a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 22 7 20 2 6 18 3 5 16 4 4 14
+--R 63b x + 4004a b x + 48994a b x + 254892a b x + 706959a b x
+--R +
+--R 5 3 12 6 2 10 7 8 8 6
+--R 1136520a b x + 1068144a b x + 547008a b x + 118272a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 10 4 8 2 3 6 3 2 4 4 2
+--R 693b x + 41580a b x + 388080a b x + 1241856a b x + 1596672a b x
+--R +
+--R 5
+--R 709632a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4
+--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x
+--R +
+--R 5 2 6
+--R - 1951488a b x - 709632a
+--R Type: Union(Expression(Integer),...)
+--E 289
+
+--S 290 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2
+--R 8a b x + 480a b x + 4480a b x + 14336a b x + 18432a b x
+--R +
+--R 11
+--R 8192a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2
+--R - 88a b x - 1760a b x - 9856a b x - 22528a b x - 22528a b x
+--R +
+--R 11
+--R - 8192a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 8 10 7 8 2 6 6 3 5 4 4 4 2
+--R 693b x + 41580a b x + 388080a b x + 1241856a b x + 1596672a b x
+--R +
+--R 5 3
+--R 709632a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 10 2 7 8 3 6 6 4 5 4
+--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x
+--R +
+--R 5 4 2 6 3
+--R - 1951488a b x - 709632a b
+--R Type: Expression(Integer)
+--E 290
+
+--S 291 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 291
+
+)clear all
+
+--S 292 of 1369
+t0:=x^3*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (1) (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 1369
+r0:=-1/7*a*(a+b*x^2)^(7/2)/b^2+1/9*(a+b*x^2)^(9/2)/b^2
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (7b x + 19a b x + 15a b x + a b x - 2a )\|b x + a
+--R (2) -------------------------------------------------------
+--R 2
+--R 63b
+--R Type: Expression(Integer)
+--E 293
+
+--S 294 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 16 2 5 14 3 4 12 4 3 10 5 2 8
+--R - 63a b x - 1011a b x - 5439a b x - 14049a b x - 19320a b x
+--R +
+--R 6 6 7 4
+--R - 13776a b x - 4032a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 18 6 16 2 5 14 3 4 12 4 3 10
+--R 7b x + 306a b x + 2754a b x + 10752a b x + 22239a b x
+--R +
+--R 5 2 8 6 6 7 4
+--R 25704a b x + 15792a b x + 4032a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (63b x + 2520a b x + 15120a b x + 28224a b x + 16128a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a
+--R Type: Union(Expression(Integer),...)
+--E 294
+
+--S 295 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 5 4 8 6 3 6 7 2 4 8 2 9 | 2
+--R (- 2a b x - 80a b x - 480a b x - 896a b x - 512a )\|b x + a
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+
+--R (18a b x + 240a b x + 864a b x + 1152a b x + 512a )\|a
+--R /
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+
+--R (63b x + 2520a b x + 15120a b x + 28224a b x + 16128a b )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 8 2 5 6 3 4 4 4 3 2 5 2
+--R - 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a b
+--R Type: Expression(Integer)
+--E 295
+
+--S 296 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 296
+
+)clear all
+
+--S 297 of 1369
+t0:=x*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 5 3 2 | 2
+--R (1) (b x + 2a b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 1369
+r0:=1/7*(a+b*x^2)^(7/2)/b
+--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 (2) ------------------------------------------
+--R 7b
+--R Type: Expression(Integer)
+--E 298
+
+--S 299 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 2 4 10 3 3 8 4 2 6 5 4 6 2
+--R (- 7a b x - 77a b x - 301a b x - 574a b x - 560a b x - 224a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 14 5 12 2 4 10 3 3 8 4 2 6 5 4
+--R b x + 28a b x + 182a b x + 532a b x + 826a b x + 672a b x
+--R +
+--R 6 2
+--R 224a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (7b x + 168a b x + 560a b x + 448a )\|a \|b x + a - 49a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 392a b x - 784a b x - 448a
+--R Type: Union(Expression(Integer),...)
+--E 299
+
+--S 300 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 | 2
+--R (a b x + 24a b x + 80a b x + 64a )\|b x + a
+--R +
+--R 4 3 6 5 2 4 6 2 7 +-+
+--R (- 7a b x - 56a b x - 112a b x - 64a )\|a
+--R /
+--R +--------+
+--R 4 6 3 4 2 2 2 3 +-+ | 2 4 6
+--R (7b x + 168a b x + 560a b x + 448a b)\|a \|b x + a - 49a b x
+--R +
+--R 2 3 4 3 2 2 4
+--R - 392a b x - 784a b x - 448a b
+--R Type: Expression(Integer)
+--E 300
+
+--S 301 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 301
+
+)clear all
+
+--S 302 of 1369
+t0:=(a+b*x^2)^(5/2)/x
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 1369
+r0:=1/3*a*(a+b*x^2)^(3/2)+1/5*(a+b*x^2)^(5/2)-_
+ a^(5/2)*atanh(sqrt(a+b*x^2)/sqrt(a))+a^2*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 +-+ \|b x + a 2 4 2 2 | 2
+--R - 15a \|a atanh(-----------) + (3b x + 11a b x + 23a )\|b x + a
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------------
+--R 15
+--R Type: Expression(Integer)
+--E 303
+
+--S 304 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 2 4 4 2 5 | 2
+--R (15a b x + 180a b x + 240a )\|b x + a
+--R +
+--R 3 2 4 4 2 5 +-+
+--R (- 75a b x - 300a b x - 240a )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 8 2 3 6 3 2 4 4 2 | 2
+--R (- 15a b x - 115a b x - 360a b x - 360a b x )\|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 +-+
+--R (3b x + 50a b x + 250a b x + 540a b x + 360a b x )\|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a
+--R Type: Union(Expression(Integer),...)
+--E 304
+
+--S 305 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 2 4 4 2 5 | 2
+--R (15a b x + 180a b x + 240a )\|b x + a
+--R +
+--R 3 2 4 4 2 5 +-+
+--R (- 75a b x - 300a b x - 240a )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 2 4 4 2 5 | 2
+--R (15a b x + 180a b x + 240a )\|b x + a
+--R +
+--R 3 2 4 4 2 5 +-+
+--R (- 75a b x - 300a b x - 240a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 3 2 4 4 2 5 | 2
+--R (23a b x + 276a b x + 368a )\|b x + a
+--R +
+--R 3 2 4 4 2 5 +-+
+--R (- 115a b x - 460a b x - 368a )\|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a
+--R Type: Expression(Integer)
+--E 305
+
+--S 306 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 306
+
+)clear all
+
+--S 307 of 1369
+t0:=(a+b*x^2)^(5/2)/x^3
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 1369
+r0:=5/6*b*(a+b*x^2)^(3/2)-1/2*(a+b*x^2)^(5/2)/x^2-_
+ 5/2*a^(3/2)*b*atanh(sqrt(a+b*x^2)/sqrt(a))+5/2*a*b*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 +-+ \|b x + a 2 4 2 2 | 2
+--R - 15a b x \|a atanh(-----------) + (2b x + 14a b x - 3a )\|b x + a
+--R +-+
+--R \|a
+--R (2) ----------------------------------------------------------------------
+--R 2
+--R 6x
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 3 6 3 2 4 4 2 | 2
+--R (15a b x + 180a b x + 240a b x )\|b x + a
+--R +
+--R 2 3 6 3 2 4 4 2 +-+
+--R (- 75a b x - 300a b x - 240a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 8 2 3 6 3 2 4 4 2 5 | 2
+--R (- 10a b x - 96a b x - 129a b x + 60a b x + 48a )\|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+
+--R (2b x + 40a b x + 165a b x + 105a b x - 84a b x - 48a )\|a
+--R /
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2
+--R (6b x + 72a b x + 96a x )\|a \|b x + a - 30a b x - 120a b x - 96a x
+--R Type: Union(Expression(Integer),...)
+--E 309
+
+--S 310 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 3 4 3 2 2 4 | 2
+--R (15a b x + 180a b x + 240a b)\|b x + a
+--R +
+--R 2 3 4 3 2 2 4 +-+
+--R (- 75a b x - 300a b x - 240a b)\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 3 4 3 2 2 4 | 2
+--R (15a b x + 180a b x + 240a b)\|b x + a
+--R +
+--R 2 3 4 3 2 2 4 +-+
+--R (- 75a b x - 300a b x - 240a b)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 3 4 3 2 2 4 | 2
+--R (14a b x + 168a b x + 224a b)\|b x + a
+--R +
+--R 2 3 4 3 2 2 4 +-+
+--R (- 70a b x - 280a b x - 224a b)\|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (6b x + 72a b x + 96a )\|a \|b x + a - 30a b x - 120a b x - 96a
+--R Type: Expression(Integer)
+--E 310
+
+--S 311 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 311
+
+)clear all
+
+--S 312 of 1369
+t0:=(a+b*x^2)^(5/2)/x^5
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 1369
+r0:=-5/8*b*(a+b*x^2)^(3/2)/x^2-1/4*(a+b*x^2)^(5/2)/x^4-_
+ 15/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+15/8*b^2*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 4 +-+ \|b x + a 2 4 2 2 | 2
+--R - 15b x \|a atanh(-----------) + (8b x - 9a b x - 2a )\|b x + a
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------------
+--R 4
+--R 8x
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 8 2 3 6 3 2 4 | 2
+--R (15a b x + 180a b x + 240a b x )\|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 +-+
+--R (- 75a b x - 300a b x - 240a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 8 2 3 6 3 2 4 4 2 5 | 2
+--R (- 32a b x - 19a b x + 190a b x + 184a b x + 32a )\|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+
+--R (8b x + 55a b x - 55a b x - 278a b x - 200a b x - 32a )\|a
+--R /
+--R +--------+
+--R 2 8 6 2 4 +-+ | 2 2 8 2 6
+--R (8b x + 96a b x + 128a x )\|a \|b x + a - 40a b x - 160a b x
+--R +
+--R 3 4
+--R - 128a x
+--R Type: Union(Expression(Integer),...)
+--E 314
+
+--S 315 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 4 4 2 3 2 3 2 | 2
+--R (15a b x + 180a b x + 240a b )\|b x + a
+--R +
+--R 4 4 2 3 2 3 2 +-+
+--R (- 75a b x - 300a b x - 240a b )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 4 2 3 2 3 2 | 2
+--R (15a b x + 180a b x + 240a b )\|b x + a
+--R +
+--R 4 4 2 3 2 3 2 +-+
+--R (- 75a b x - 300a b x - 240a b )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 4 2 3 2 3 2 | 2
+--R (8a b x + 96a b x + 128a b )\|b x + a
+--R +
+--R 4 4 2 3 2 3 2 +-+
+--R (- 40a b x - 160a b x - 128a b )\|a
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (8b x + 96a b x + 128a )\|a \|b x + a - 40a b x - 160a b x - 128a
+--R Type: Expression(Integer)
+--E 315
+
+--S 316 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 316
+
+)clear all
+
+--S 317 of 1369
+t0:=(a+b*x^2)^(5/2)/x^7
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 1369
+r0:=-5/24*b*(a+b*x^2)^(3/2)/x^4-1/6*(a+b*x^2)^(5/2)/x^6-_
+ 5/16*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-5/16*b^2*sqrt(a+b*x^2)/x^2
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2 +--------+
+--R 3 6 \|b x + a 2 4 2 2 +-+ | 2
+--R - 15b x atanh(-----------) + (- 33b x - 26a b x - 8a )\|a \|b x + a
+--R +-+
+--R \|a
+--R -----------------------------------------------------------------------
+--R 6 +-+
+--R 48x \|a
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 5 10 2 4 8 3 3 6 | 2
+--R (90a b x + 480a b x + 480a b x )\|b x + a
+--R +
+--R 6 12 5 10 2 4 8 3 3 6 +-+
+--R (- 15b x - 270a b x - 720a b x - 480a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6
+--R (33a b x + 620a b x + 2060a b x + 2448a b x + 1216a b x + 256a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4 5 2
+--R - 198a b x - 1410a b x - 3148a b x - 3024a b x - 1344a b x
+--R +
+--R 6
+--R - 256a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 10 2 8 3 6 +-+ | 2 3 12
+--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x
+--R +
+--R 2 2 10 3 8 4 6
+--R - 864a b x - 2304a b x - 1536a x
+--R Type: Union(Expression(Integer),...)
+--E 319
+
+--S 320 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 3 \|b x + a - \|a 3 \|b x + a
+--R 5b log(------------------) + 5b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------------
+--R +-+
+--R 16\|a
+--R Type: Expression(Integer)
+--E 320
+
+--S 321 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 321
+
+)clear all
+
+--S 322 of 1369
+t0:=(a+b*x^2)^(5/2)/x^9
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 1369
+r0:=-5/48*b*(a+b*x^2)^(3/2)/x^6-1/8*(a+b*x^2)^(5/2)/x^8+_
+ 5/128*b^4*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_
+ 5/64*b^2*sqrt(a+b*x^2)/x^4-5/128*b^3*sqrt(a+b*x^2)/(a*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 4 8 \|b x + a
+--R 15b x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2
+--R (- 15b x - 118a b x - 136a b x - 48a )\|a \|b x + a
+--R /
+--R 8 +-+
+--R 384a x \|a
+--R Type: Expression(Integer)
+--E 323
+
+--S 324 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 7 14 2 6 12 3 5 10 4 4 8 | 2
+--R (- 120a b x - 1200a b x - 2880a b x - 1920a b x )\|b x + a
+--R +
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +-+
+--R (15b x + 480a b x + 2400a b x + 3840a b x + 1920a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R 15a b x + 598a b x + 6312a b x + 27120a b x + 55424a b x
+--R +
+--R 6 2 4 7 2 8
+--R 57600a b x + 29696a b x + 6144a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R - 120a b x - 2264a b x - 15552a b x - 49248a b x - 80896a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 71680a b x - 32768a b x - 6144a
+--R *
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R 2 3 14 3 2 12 4 10 5 8 +-+ | 2
+--R (3072a b x + 30720a b x + 73728a b x + 49152a x )\|a \|b x + a
+--R +
+--R 2 4 16 3 3 14 4 2 12 5 10 6 8
+--R - 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152a x
+--R Type: Union(Expression(Integer),...)
+--E 324
+
+--S 325 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 4 \|b x + a - \|a 4 \|b x + a
+--R - 5b log(------------------) - 5b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) ----------------------------------------------------
+--R +-+
+--R 128a\|a
+--R Type: Expression(Integer)
+--E 325
+
+--S 326 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 326
+
+)clear all
+
+--S 327 of 1369
+t0:=(a+b*x^2)^(5/2)/x^11
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 1369
+r0:=-1/16*b*(a+b*x^2)^(3/2)/x^8-1/10*(a+b*x^2)^(5/2)/x^10-_
+ 3/256*b^5*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_
+ 1/32*b^2*sqrt(a+b*x^2)/x^6-1/128*b^3*sqrt(a+b*x^2)/(a*x^4)+_
+ 3/256*b^4*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 5 10 \|b x + a
+--R - 15b x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (15b x - 10a b x - 248a b x - 336a b x - 128a )\|a \|b x + a
+--R /
+--R 2 10 +-+
+--R 1280a x \|a
+--R Type: Expression(Integer)
+--E 328
+
+--S 329 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 18 2 8 16 3 7 14 4 6 12
+--R 150a b x + 2400a b x + 10080a b x + 15360a b x
+--R +
+--R 5 5 10
+--R 7680a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 10 20 9 18 2 8 16 3 7 14
+--R - 15b x - 750a b x - 6000a b x - 16800a b x
+--R +
+--R 4 6 12 5 5 10
+--R - 19200a b x - 7680a b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R - 15a b x - 740a b x - 5252a b x - 64a b x + 108128a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R 423680a b x + 750080a b x + 700416a b x + 335872a b x + 65536a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R 150a b x + 2450a b x + 8300a b x - 28400a b x - 258656a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R - 729600a b x - 1062400a b x - 860160a b x - 368640a b x - 65536a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 3 4 18 4 3 16 5 2 14 6 12
+--R 12800a b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 7 10
+--R 655360a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 5 20 4 4 18 5 3 16 6 2 14
+--R - 1280a b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 7 12 8 10
+--R - 1638400a b x - 655360a x
+--R Type: Union(Expression(Integer),...)
+--E 329
+
+--S 330 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 5 \|b x + a - \|a 5 \|b x + a
+--R 3b log(------------------) + 3b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------------
+--R 2 +-+
+--R 256a \|a
+--R Type: Expression(Integer)
+--E 330
+
+--S 331 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 331
+
+)clear all
+
+--S 332 of 1369
+t0:=x^4*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 8 6 2 4 | 2
+--R (1) (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1369
+r0:=1/16*a*x^5*(a+b*x^2)^(3/2)+1/10*x^5*(a+b*x^2)^(5/2)+_
+ 3/256*a^5*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_
+ 3/256*a^4*x*sqrt(a+b*x^2)/b^2+1/128*a^3*x^3*sqrt(a+b*x^2)/b+_
+ 1/32*a^2*x^5*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 5 x\|b
+--R 15a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2
+--R (128b x + 336a b x + 248a b x + 10a b x - 15a x)\|b \|b x + a
+--R /
+--R 2 +-+
+--R 1280b \|b
+--R Type: Expression(Integer)
+--E 333
+
+--S 334 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+
+--R (150a b x + 2400a b x + 10080a b x + 15360a b x + 7680a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2
+--R - 15a b x - 750a b x - 6000a b x - 16800a b x - 19200a b x
+--R +
+--R 10
+--R - 7680a
+--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 19 8 17 2 7 15 3 6 13
+--R - 128b x - 6736a b x - 68248a b x - 290170a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7 7 2 5
+--R - 639845a b x - 776626a b x - 494672a b x - 122976a b x
+--R +
+--R 8 3 9
+--R 14080a b x + 7680a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 9 19 8 17 2 7 15 3 6 13
+--R 1280b x + 25120a b x + 166096a b x + 538900a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7 7 2 5
+--R 974350a b x + 1008010a b x + 557440a b x + 116896a b x
+--R +
+--R 8 3 9
+--R - 17920a b x - 7680a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 6 8 5 6 2 4 4 3 3 2
+--R 12800b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 4 2
+--R 655360a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 7 10 6 8 2 5 6 3 4 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 3 2 5 2
+--R - 1638400a b x - 655360a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R (300a b x + 4800a b x + 20160a b x + 30720a b x + 15360a )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2
+--R - 30a b x - 1500a b x - 12000a b x - 33600a b x - 38400a b x
+--R +
+--R 10
+--R - 15360a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 9 19 8 17 2 7 15 3 6 13
+--R - 128b x - 6736a b x - 68248a b x - 290170a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7 7 2 5
+--R - 639845a b x - 776626a b x - 494672a b x - 122976a b x
+--R +
+--R 8 3 9
+--R 14080a b x + 7680a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 9 19 8 17 2 7 15 3 6 13
+--R 1280b x + 25120a b x + 166096a b x + 538900a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7 7 2 5
+--R 974350a b x + 1008010a b x + 557440a b x + 116896a b x
+--R +
+--R 8 3 9
+--R - 17920a b x - 7680a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 6 8 5 6 2 4 4 3 3 2
+--R 12800b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 4 2
+--R 655360a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 7 10 6 8 2 5 6 3 4 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 3 2 5 2
+--R - 1638400a b x - 655360a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 334
+
+--S 335 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 5 (\|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 5 x\|b
+--R - 3a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 256b \|b
+--R Type: Expression(Integer)
+--E 335
+
+--S 336 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 5 +---+ x\|b 5 +-+ \|- b \|b x + a - \|- b \|a
+--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ---------------------------------------------------------------------------
+--R 2 +---+ +-+
+--R 256b \|- b \|b
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 338
+
+)clear all
+
+--S 339 of 1369
+t0:=x^2*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 6 4 2 2 | 2
+--R (1) (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1369
+r0:=5/48*a*x^3*(a+b*x^2)^(3/2)+1/8*x^3*(a+b*x^2)^(5/2)-_
+ 5/128*a^4*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_
+ 5/128*a^3*x*sqrt(a+b*x^2)/b+5/64*a^2*x^3*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 x\|b
+--R - 15a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +-+ | 2
+--R (48b x + 136a b x + 118a b x + 15a x)\|b \|b x + a
+--R /
+--R +-+
+--R 384b\|b
+--R Type: Expression(Integer)
+--E 340
+
+--S 341 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2
+--R (120a b x + 1200a b x + 2880a b x + 1920a )\|a \|b x + a
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R - 15a b x - 480a b x - 2400a b x - 3840a b x - 1920a
+--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 15 6 13 2 5 11 3 4 9 4 3 7
+--R - 48b x - 1672a b x - 12150a b x - 37839a b x - 60320a b x
+--R +
+--R 5 2 5 6 3 7
+--R - 50016a b x - 18944a b x - 1920a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 15 6 13 2 5 11 3 4 9 4 3 7
+--R 384b x + 5312a b x + 25968a b x + 62856a b x + 83080a b x
+--R +
+--R 5 2 5 6 3 7
+--R 59248a b x + 19904a b x + 1920a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 4 6 3 4 2 2 2 3 +-+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b)\|a \|b \|b x + a
+--R +
+--R 5 8 4 6 2 3 4 3 2 2 4 +-+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b)\|b
+--R ,
+--R
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2
+--R (- 240a b x - 2400a b x - 5760a b x - 3840a )\|a \|b x + a
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R 30a b x + 960a b x + 4800a b x + 7680a b x + 3840a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 7 15 6 13 2 5 11 3 4 9 4 3 7
+--R - 48b x - 1672a b x - 12150a b x - 37839a b x - 60320a b x
+--R +
+--R 5 2 5 6 3 7
+--R - 50016a b x - 18944a b x - 1920a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 15 6 13 2 5 11 3 4 9 4 3 7
+--R 384b x + 5312a b x + 25968a b x + 62856a b x + 83080a b x
+--R +
+--R 5 2 5 6 3 7
+--R 59248a b x + 19904a b x + 1920a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 4 6 3 4 2 2 2 3 +---+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b)\|- b \|a \|b x + a
+--R +
+--R 5 8 4 6 2 3 4 3 2 2 4 +---+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 341
+
+--S 342 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 4 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R 5a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 4 x\|b
+--R 5a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 128b\|b
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 343
+
+--S 344 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 4 +---+ x\|b 4 +-+ \|- b \|b x + a - \|- b \|a
+--R 5a \|- b atanh(-----------) - 10a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R --------------------------------------------------------------------------
+--R +---+ +-+
+--R 128b\|- b \|b
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 1369
+t0:=(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (1) (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 1369
+r0:=5/24*a*x*(a+b*x^2)^(3/2)+1/6*x*(a+b*x^2)^(5/2)+_
+ 5/16*a^3*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+5/16*a^2*x*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R 3 x\|b 2 5 3 2 +-+ | 2
+--R 15a atanh(-----------) + (8b x + 26a b x + 33a x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ------------------------------------------------------------------
+--R +-+
+--R 48\|b
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 3 3 6
+--R (90a b x + 480a b x + 480a )\|a \|b x + a - 15a b x
+--R +
+--R 4 2 4 5 2 6
+--R - 270a b x - 720a b x - 480a
+--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 9 2 3 7 3 2 5 4 3
+--R - 8b x - 170a b x - 885a b x - 2098a b x - 2416a b x
+--R +
+--R 5
+--R - 1056a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3
+--R 48b x + 460a b x + 1698a b x + 3174a b x + 2944a b x
+--R +
+--R 5
+--R 1056a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 2 4 2 2 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a )\|a \|b \|b x + a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a )\|b
+--R ,
+--R
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 3 3 6
+--R (180a b x + 960a b x + 960a )\|a \|b x + a - 30a b x
+--R +
+--R 4 2 4 5 2 6
+--R - 540a b x - 1440a b x - 960a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3
+--R - 8b x - 170a b x - 885a b x - 2098a b x - 2416a b x
+--R +
+--R 5
+--R - 1056a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3
+--R 48b x + 460a b x + 1698a b x + 3174a b x + 2944a b x
+--R +
+--R 5
+--R 1056a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 2 4 2 2 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a )\|- b \|a \|b x + a
+--R +
+--R 3 6 2 4 2 2 3 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 348
+
+--S 349 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 3 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R 5a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 x\|b
+--R - 5a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 16\|b
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+--S 351 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 3 +---+ x\|b 3 +-+ \|- b \|b x + a - \|- b \|a
+--R - 5a \|- b atanh(-----------) + 10a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ----------------------------------------------------------------------------
+--R +---+ +-+
+--R 16\|- b \|b
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 352
+
+)clear all
+
+--S 353 of 1369
+t0:=(a+b*x^2)^(5/2)/x^2
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 353
+
+--S 354 of 1369
+r0:=5/4*b*x*(a+b*x^2)^(3/2)-(a+b*x^2)^(5/2)/x+_
+ 15/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+15/8*a*b*x*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R 2 +-+ x\|b 2 4 2 2 | 2
+--R 15a x\|b atanh(-----------) + (2b x + 9a b x - 8a )\|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ----------------------------------------------------------------
+--R 8x
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 5 3 3 4 +-+ | 2
+--R (15a b x + 180a b x + 240a x)\|b \|b x + a
+--R +
+--R 2 2 5 3 3 4 +-+ +-+
+--R (- 75a b x - 300a b x - 240a x)\|a \|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 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 10b x - 85a b x - 172a b x + 16a b x + 128a )\|a \|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 2b x + 35a b x + 165a b x + 180a b x - 80a b x - 128a
+--R /
+--R +--------+
+--R 2 5 3 2 | 2
+--R (8b x + 96a b x + 128a x)\|b x + a
+--R +
+--R 2 5 3 2 +-+
+--R (- 40b x - 160a b x - 128a x)\|a
+--R ,
+--R
+--R +--------+
+--R 2 2 5 3 3 4 +---+ | 2
+--R (30a b x + 360a b x + 480a x)\|- b \|b x + a
+--R +
+--R 2 2 5 3 3 4 +---+ +-+
+--R (- 150a b x - 600a b x - 480a x)\|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 10b x - 85a b x - 172a b x + 16a b x + 128a )\|a \|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 2b x + 35a b x + 165a b x + 180a b x - 80a b x - 128a
+--R /
+--R +--------+
+--R 2 5 3 2 | 2
+--R (8b x + 96a b x + 128a x)\|b x + a
+--R +
+--R 2 5 3 2 +-+
+--R (- 40b x - 160a b x - 128a x)\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 355
+
+--S 356 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 15a \|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R - 15a \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 8
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R 2 +-+ x\|b 2 +---+ \|b x + a - \|a
+--R - 15a \|b atanh(-----------) + 30a \|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R (6) -----------------------------------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 358
+
+--S 359 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 359
+
+)clear all
+
+--S 360 of 1369
+t0:=(a+b*x^2)^(5/2)/x^4
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 360
+
+--S 361 of 1369
+r0:=-5/3*b*(a+b*x^2)^(3/2)/x-1/3*(a+b*x^2)^(5/2)/x^3+_
+ 5/2*a*b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+5/2*b^2*x*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R 3 +-+ x\|b 2 4 2 2 | 2
+--R 15a b x \|b atanh(-----------) + (3b x - 14a b x - 2a )\|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) --------------------------------------------------------------------
+--R 3
+--R 6x
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 7 2 2 5 3 3 +-+ | 2
+--R (15a b x + 180a b x + 240a b x )\|b \|b x + a
+--R +
+--R 3 7 2 2 5 3 3 +-+ +-+
+--R (- 75a b x - 300a b x - 240a b x )\|a \|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 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 15b x + 10a b x + 242a b x + 264a b x + 32a )\|a \|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 3b x + 25a b x - 100a b x - 370a b x - 280a b x - 32a
+--R /
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (6b x + 72a b x + 96a x )\|b x + a
+--R +
+--R 2 7 5 2 3 +-+
+--R (- 30b x - 120a b x - 96a x )\|a
+--R ,
+--R
+--R +--------+
+--R 3 7 2 2 5 3 3 +---+ | 2
+--R (30a b x + 360a b x + 480a b x )\|- b \|b x + a
+--R +
+--R 3 7 2 2 5 3 3 +---+ +-+
+--R (- 150a b x - 600a b x - 480a b x )\|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 15b x + 10a b x + 242a b x + 264a b x + 32a )\|a \|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 3b x + 25a b x - 100a b x - 370a b x - 280a b x - 32a
+--R /
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (6b x + 72a b x + 96a x )\|b x + a
+--R +
+--R 2 7 5 2 3 +-+
+--R (- 30b x - 120a b x - 96a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 362
+
+--S 363 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 5a b\|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ x\|b
+--R - 5a b\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R +-+ x\|b +---+ \|b x + a - \|a
+--R - 5a b\|b atanh(-----------) + 10a b\|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R (6) ------------------------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 365
+
+--S 366 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 366
+
+)clear all
+
+--S 367 of 1369
+t0:=(a+b*x^2)^(5/2)/x^6
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 1369
+r0:=-1/3*b*(a+b*x^2)^(3/2)/x^3-1/5*(a+b*x^2)^(5/2)/x^5+_
+ b^(5/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))-b^2*sqrt(a+b*x^2)/x
+--R
+--R
+--R +-+ +--------+
+--R 2 5 +-+ x\|b 2 4 2 2 | 2
+--R 15b x \|b atanh(-----------) + (- 23b x - 11a b x - 3a )\|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ---------------------------------------------------------------------
+--R 5
+--R 15x
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 4 9 3 7 2 2 5 +-+ | 2
+--R (15b x + 180a b x + 240a b x )\|b \|b x + a
+--R +
+--R 4 9 3 7 2 2 5 +-+ +-+
+--R (- 75b x - 300a b x - 240a b x )\|a \|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 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (115b x + 515a b x + 603a b x + 236a b x + 48a )\|a \|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 23b x - 310a b x - 790a b x - 715a b x - 260a b x - 48a
+--R /
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (15b x + 180a b x + 240a x )\|b x + a
+--R +
+--R 2 9 7 2 5 +-+
+--R (- 75b x - 300a b x - 240a x )\|a
+--R ,
+--R
+--R +--------+
+--R 4 9 3 7 2 2 5 +---+ | 2
+--R (30b x + 360a b x + 480a b x )\|- b \|b x + a
+--R +
+--R 4 9 3 7 2 2 5 +---+ +-+
+--R (- 150b x - 600a b x - 480a b x )\|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (115b x + 515a b x + 603a b x + 236a b x + 48a )\|a \|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R - 23b x - 310a b x - 790a b x - 715a b x - 260a b x - 48a
+--R /
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (15b x + 180a b x + 240a x )\|b x + a
+--R +
+--R 2 9 7 2 5 +-+
+--R (- 75b x - 300a b x - 240a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 369
+
+--S 370 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R b \|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R - b \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 370
+
+--S 371 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R 2 +-+ x\|b 2 +---+ \|b x + a - \|a
+--R (6) - b \|b atanh(-----------) + 2b \|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 373
+
+)clear all
+
+--S 374 of 1369
+t0:=(a+b*x^2)^(5/2)/x^8
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 1369
+r0:=-1/7*(a+b*x^2)^(7/2)/(a*x^7)
+--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 (2) --------------------------------------------
+--R 7
+--R 7a x
+--R Type: Expression(Integer)
+--E 375
+
+--S 376 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2
+--R 7b x + 77a b x + 301a b x + 575a b x + 584a b x + 304a b x
+--R +
+--R 6
+--R 64a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R - b x - 28a b x - 182a b x - 532a b x - 833a b x - 728a b x
+--R +
+--R 6 2 7
+--R - 336a b x - 64a
+--R /
+--R +--------+
+--R 3 13 2 2 11 3 9 4 7 | 2
+--R (7a b x + 168a b x + 560a b x + 448a x )\|b x + a
+--R +
+--R 3 13 2 2 11 3 9 4 7 +-+
+--R (- 49a b x - 392a b x - 784a b x - 448a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 376
+
+--S 377 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 378
+
+)clear all
+
+--S 379 of 1369
+t0:=(a+b*x^2)^(5/2)/x^10
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 1369
+r0:=-1/9*(a+b*x^2)^(7/2)/(a*x^9)+2/63*b*(a+b*x^2)^(7/2)/(a^2*x^7)
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (2b x - a b x - 15a b x - 19a b x - 7a )\|b x + a
+--R (2) -------------------------------------------------------
+--R 2 9
+--R 63a x
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 18b x - 231a b x - 609a b x + 1251a b x + 8887a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 17944a b x + 17808a b x + 8896a b x + 1792a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10 5 4 8
+--R 2b x + 81a b x + 504a b x + 462a b x - 4266a b x - 16119a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R - 25848a b x - 22032a b x - 9792a b x - 1792a
+--R /
+--R 2 4 17 3 3 15 4 2 13 5 11 6 9
+--R (63a b x + 2520a b x + 15120a b x + 28224a b x + 16128a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 4 17 3 3 15 4 2 13 5 11 6 9 +-+
+--R (- 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 381
+
+--S 382 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 383
+
+)clear all
+
+--S 384 of 1369
+t0:=(a+b*x^2)^(5/2)/x^12
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 12
+--R x
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 1369
+r0:=-1/11*(a+b*x^2)^(7/2)/(a*x^11)+4/99*b*(a+b*x^2)^(7/2)/(a^2*x^9)-_
+ 8/693*b^2*(a+b*x^2)^(7/2)/(a^3*x^7)
+--R
+--R
+--R (2)
+--R +--------+
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2
+--R (- 8b x + 4a b x - 3a b x - 113a b x - 161a b x - 63a )\|b x + a
+--R ------------------------------------------------------------------------
+--R 3 11
+--R 693a x
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12
+--R 88b x + 1716a b x + 9009a b x + 19503a b x + 41591a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R 180705a b x + 534772a b x + 852272a b x + 746496a b x
+--R +
+--R 9 2 10
+--R 342272a b x + 64512a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 11 22 10 20 2 9 18 3 8 16 4 7 14
+--R - 8b x - 484a b x - 4719a b x - 16632a b x - 32274a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8 8 3 6
+--R - 97240a b x - 376607a b x - 886468a b x - 1186768a b x
+--R +
+--R 9 2 4 10 2 11
+--R - 909568a b x - 374528a b x - 64512a
+--R /
+--R 3 5 21 4 4 19 5 3 17 6 2 15
+--R 693a b x + 41580a b x + 388080a b x + 1241856a b x
+--R +
+--R 7 13 8 11
+--R 1596672a b x + 709632a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 5 21 4 4 19 5 3 17 6 2 15
+--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x
+--R +
+--R 7 13 8 11
+--R - 1951488a b x - 709632a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 386
+
+--S 387 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 388
+
+)clear all
+
+--S 389 of 1369
+t0:=(a+b*x^2)^(5/2)/x^14
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 14
+--R x
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 1369
+r0:=-1/13*(a+b*x^2)^(7/2)/(a*x^13)+6/143*b*(a+b*x^2)^(7/2)/(a^2*x^11)-_
+ 8/429*b^2*(a+b*x^2)^(7/2)/(a^3*x^9)+16/3003*b^3*(a+b*x^2)^(7/2)/(a^4*x^7)
+--R
+--R
+--R (2)
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6
+--R (16b x - 8a b x + 6a b x - 5a b x - 371a b x - 567a b x - 231a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4 13
+--R 3003a x
+--R Type: Expression(Integer)
+--E 390
+
+--S 391 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 24 11 22 2 10 20 3 9 18
+--R - 208b x - 5720a b x - 43758a b x - 138567a b x
+--R +
+--R 4 8 16 5 7 14 6 6 12 7 5 10
+--R - 197197a b x + 17199a b x + 1280783a b x + 5475348a b x
+--R +
+--R 8 4 8 9 3 6 10 2 4 11 2
+--R 12549024a b x + 16700416a b x + 12911360a b x + 5397504a b x
+--R +
+--R 12
+--R 946176a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 13 26 12 24 2 11 22 3 10 20 4 9 18
+--R 16b x + 1352a b x + 18590a b x + 94809a b x + 224796a b x
+--R +
+--R 5 8 16 6 7 14 7 6 12 8 5 10
+--R 230230a b x - 362726a b x - 3117439a b x - 10284300a b x
+--R +
+--R 9 4 8 10 3 6 11 2 4 12 2
+--R - 19585696a b x - 22540544a b x - 15491840a b x - 5870592a b x
+--R +
+--R 13
+--R - 946176a
+--R /
+--R 4 6 25 5 5 23 6 4 21 7 3 19
+--R 3003a b x + 252252a b x + 3363360a b x + 16144128a b x
+--R +
+--R 8 2 17 9 15 10 13
+--R 34594560a b x + 33825792a b x + 12300288a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 6 25 5 5 23 6 4 21 7 3 19
+--R - 39039a b x - 1093092a b x - 8744736a b x - 29981952a b x
+--R +
+--R 8 2 17 9 15 10 13
+--R - 49969920a b x - 39975936a b x - 12300288a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 391
+
+--S 392 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 393
+
+)clear all
+
+--S 394 of 1369
+t0:=(a+b*x^2)^(5/2)/x^16
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 16
+--R x
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 1369
+r0:=-1/15*(a+b*x^2)^(7/2)/(a*x^15)+8/195*b*(a+b*x^2)^(7/2)/(a^2*x^13)-_
+ 16/715*b^2*(a+b*x^2)^(7/2)/(a^3*x^11)+_
+ 64/6435*b^3*(a+b*x^2)^(7/2)/(a^4*x^9)-_
+ 128/45045*b^4*(a+b*x^2)^(7/2)/(a^5*x^7)
+--R
+--R
+--R (2)
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R - 128b x + 64a b x - 48a b x + 40a b x - 35a b x - 4473a b x
+--R +
+--R 6 2 7
+--R - 7161a b x - 3003a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 5 15
+--R 45045a x
+--R Type: Expression(Integer)
+--E 395
+
+--S 396 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 14 28 13 26 2 12 24 3 11 22
+--R 1920b x + 70720a b x + 739024a b x + 3325608a b x
+--R +
+--R 4 10 20 5 9 18 6 8 16 7 7 14
+--R 7436429a b x + 8518055a b x + 7017255a b x + 31888581a b x
+--R +
+--R 8 6 12 9 5 10 10 4 8
+--R 174491952a b x + 540852576a b x + 1004347520a b x
+--R +
+--R 11 3 6 12 2 4 13 2 14
+--R 1146763520a b x + 790013952a b x + 301830144a b x + 49201152a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 15 30 14 28 2 13 26 3 12 24
+--R - 128b x - 14400a b x - 265200a b x - 1847560a b x
+--R +
+--R 4 11 22 5 10 20 6 9 18 7 8 16
+--R - 6235515a b x - 11159148a b x - 11079250a b x - 15095700a b x
+--R +
+--R 8 7 14 9 6 12 10 5 10
+--R - 85709115a b x - 367431760a b x - 938611872a b x
+--R +
+--R 11 4 8 12 3 6 13 2 4
+--R - 1495920000a b x - 1507116800a b x - 934778880a b x
+--R +
+--R 14 2 15
+--R - 326430720a b x - 49201152a
+--R /
+--R 5 7 29 6 6 27 7 5 25 8 4 23
+--R 45045a b x + 5045040a b x + 90810720a b x + 605404800a b x
+--R +
+--R 9 3 21 10 2 19 11 17
+--R 1902700800a b x + 3044321280a b x + 2398556160a b x
+--R +
+--R 12 15
+--R 738017280a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 7 29 6 6 27 7 5 25
+--R - 675675a b x - 25225200a b x - 272432160a b x
+--R +
+--R 8 4 23 9 3 21 10 2 19
+--R - 1297296000a b x - 3171168000a b x - 4151347200a b x
+--R +
+--R 11 17 12 15
+--R - 2767564800a b x - 738017280a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 396
+
+--S 397 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 398
+
+)clear all
+
+--S 399 of 1369
+t0:=(a+b*x^2)^(5/2)/x^18
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 18
+--R x
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 1369
+r0:=-1/17*(a+b*x^2)^(7/2)/(a*x^17)+2/51*b*(a+b*x^2)^(7/2)/(a^2*x^15)-_
+ 16/663*b^2*(a+b*x^2)^(7/2)/(a^3*x^13)+_
+ 32/2431*b^3*(a+b*x^2)^(7/2)/(a^4*x^11)-_
+ 128/21879*b^4*(a+b*x^2)^(7/2)/(a^5*x^9)+_
+ 256/153153*b^5*(a+b*x^2)^(7/2)/(a^6*x^7)
+--R
+--R
+--R (2)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R 256b x - 128a b x + 96a b x - 80a b x + 70a b x - 63a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 12705a b x - 21021a b x - 9009a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 6 17
+--R 153153a x
+--R Type: Expression(Integer)
+--E 400
+
+--S 401 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 16 32 15 30 2 14 28 3 13 26
+--R - 4352b x - 206720a b x - 2821728a b x - 16997552a b x
+--R +
+--R 4 12 24 5 11 22 6 10 20
+--R - 53117350a b x - 91265265a b x - 84612927a b x
+--R +
+--R 7 9 18 8 8 16 9 7 14
+--R - 26796675a b x + 158507217a b x + 1163856848a b x
+--R +
+--R 10 6 12 11 5 10 12 4 8
+--R 4663848992a b x + 11445343104a b x + 17876348672a b x
+--R +
+--R 13 3 6 14 2 4 15 2
+--R 17866512384a b x + 11078774784a b x + 3886891008a b x
+--R +
+--R 16
+--R 590413824a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 17 34 16 32 2 15 30 3 14 28
+--R 256b x + 36992a b x + 878560a b x + 7994896a b x
+--R +
+--R 4 13 26 5 12 24 6 11 22
+--R 36119798a b x + 90299495a b x + 129279696a b x
+--R +
+--R 7 10 20 8 9 18 9 8 16
+--R 101136162a b x - 7854510a b x - 490730449a b x
+--R +
+--R 10 7 14 11 6 12 12 5 10
+--R - 2717211728a b x - 8930043424a b x - 18706939264a b x
+--R +
+--R 13 4 8 14 3 6 15 2 4
+--R - 25644625664a b x - 22956939264a b x - 12948418560a b x
+--R +
+--R 16 2 17
+--R - 4182097920a b x - 590413824a
+--R /
+--R 6 8 33 7 7 31 8 6 29
+--R 153153a b x + 22054032a b x + 514594080a b x
+--R +
+--R 9 5 27 10 4 25 11 3 23
+--R 4528427904a b x + 19407548160a b x + 44853000192a b x
+--R +
+--R 12 2 21 13 19 14 17
+--R 57085636608a b x + 37638881280a b x + 10037035008a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 8 33 7 7 31 8 6 29
+--R - 2603601a b x - 124972848a b x - 1749619872a b x
+--R +
+--R 9 5 27 10 4 25 11 3 23
+--R - 10997610624a b x - 36658702080a b x - 69318273024a b x
+--R +
+--R 12 2 21 13 19 14 17
+--R - 74650447872a b x - 42657398784a b x - 10037035008a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 401
+
+--S 402 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 403
+
+)clear all
+
+--S 404 of 1369
+t0:=x^m*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 m | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a )x \|b x + a
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 1369
+--r0:=315*a^3*x^(1+m)*(a+b*x^2)^(3/2)/((4+m)*(6+m)*(8+m)*(10+m))+_
+-- 63*a^2*x^(1+m)*(a+b*x^2)^(5/2)/((6+m)*(8+m)*(10+m))+_
+-- 9*a*x^(1+m)*(a+b*x^2)^(7/2)/(80+18*m+m^2)+x^(1+m)*_
+-- (a+b*x^2)^(9/2)/(10+m)+945*a^4*x^(1+m)*sqrt(a+b*x^2)/_
+-- ((6+m)*(8+m)*(10+m)*(8+6*m+m^2))+945*a^5*x^(1+m)*_
+-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+-- sqrt((a+b*x^2)/a)/((6+m)*(8+m)*(10+m)*(8+14*m+7*m^2+m^3)*sqrt(a+b*x^2))
+--E 405
+
+--S 406 of 1369
+--a0:=integrate(t0,x)
+--E 406
+
+--S 407 of 1369
+--m0:=a0-r0
+--E 407
+
+--S 408 of 1369
+--d0:=D(m0,x)
+--E 408
+
+)clear all
+
+--S 409 of 1369
+t0:=x^15*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 23 3 21 2 2 19 3 17 4 15 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 1369
+r0:=-1/11*a^7*(a+b*x^2)^(11/2)/b^8+7/13*a^6*(a+b*x^2)^(13/2)/b^8-_
+ 7/5*a^5*(a+b*x^2)^(15/2)/b^8+35/17*a^4*(a+b*x^2)^(17/2)/b^8-_
+ 35/19*a^3*(a+b*x^2)^(19/2)/b^8+a^2*(a+b*x^2)^(21/2)/b^8-_
+ 7/23*a*(a+b*x^2)^(23/2)/b^8+1/25*(a+b*x^2)^(25/2)/b^8
+--R
+--R
+--R (2)
+--R 12 24 11 22 2 10 20 3 9 18
+--R 1062347b x + 4665089a b x + 7759752a b x + 5810090a b x
+--R +
+--R 4 8 16 5 7 14 6 6 12 7 5 10 8 4 8
+--R 1659515a b x + 429a b x - 462a b x + 504a b x - 560a b x
+--R +
+--R 9 3 6 10 2 4 11 2 12
+--R 640a b x - 768a b x + 1024a b x - 2048a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 8
+--R 26558675b
+--R Type: Expression(Integer)
+--E 410
+
+--S 411 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 16 48 2 15 46 3 14 44
+--R - 26558675a b x - 2878729425a b x - 97395972960a b x
+--R +
+--R 4 13 42 5 12 40
+--R - 1609225902570a b x - 15696010222035a b x
+--R +
+--R 6 11 38 7 10 36
+--R - 100124312670525a b x - 444286575778650a b x
+--R +
+--R 8 9 34 9 8 32
+--R - 1425766406694360a b x - 3390169039300720a b x
+--R +
+--R 10 7 30 11 6 28
+--R - 6054288088284160a b x - 8157338113996800a b x
+--R +
+--R 12 5 26 13 4 24
+--R - 8256379402444800a b x - 6184960931901440a b x
+--R +
+--R 14 3 22 15 2 20
+--R - 3328737290977280a b x - 1218036417495040a b x
+--R +
+--R 16 18 17 16
+--R - 271525694668800a b x - 27848789196800a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 17 50 16 48 2 15 46
+--R 1062347b x + 337179700a b x + 18813934425a b x
+--R +
+--R 3 14 44 4 13 42 5 12 40
+--R 435911726250a b x + 5537985721125a b x + 44226266816160a b x
+--R +
+--R 6 11 38 7 10 36
+--R 240242576724975a b x + 932460385321650a b x
+--R +
+--R 8 9 34 9 8 32
+--R 2668614201361000a b x + 5742120965670000a b x
+--R +
+--R 10 7 30 11 6 28
+--R 9385626998420480a b x + 11679727644825600a b x
+--R +
+--R 12 5 26 13 4 24
+--R 10999050000998400a b x + 7712957537792000a b x
+--R +
+--R 14 3 22 15 2 20
+--R 3905555337216000a b x + 1350318166179840a b x
+--R +
+--R 16 18 17 16
+--R 285450089267200a b x + 27848789196800a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 12 24 11 22 2 10 20
+--R 26558675b x + 8286306600a b x + 425363738800a b x
+--R +
+--R 3 9 18 4 8 16 5 7 14
+--R 8507274776000a b x + 87503397696000a b x + 528909426073600a b x
+--R +
+--R 6 6 12 7 5 10
+--R 2019472354099200a b x + 5059776887193600a b x
+--R +
+--R 8 4 8 9 3 6
+--R 8432961478656000a b x + 9259722407936000a b x
+--R +
+--R 10 2 4 11 2 12
+--R 6433070304460800a b x + 2562088606105600a b x + 445580627148800a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 12 24 2 11 22 3 10 20
+--R - 663966875a b x - 69052555000a b x - 2126818694000a b x
+--R +
+--R 4 9 18 5 8 16
+--R - 30383124200000a b x - 243064993600000a b x
+--R +
+--R 6 7 14 7 6 12
+--R - 1202066877440000a b x - 3883600680960000a b x
+--R +
+--R 8 5 10 9 4 8
+--R - 8432961478656000a b x - 12401413939200000a b x
+--R +
+--R 10 3 6 11 2 4
+--R - 12183845273600000a b x - 7658417029120000a b x
+--R +
+--R 12 2 13
+--R - 2784878919680000a b x - 445580627148800a
+--R Type: Union(Expression(Integer),...)
+--E 411
+
+--S 412 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 13 12 24 14 11 22 15 10 20
+--R - 2048a b x - 638976a b x - 32800768a b x
+--R +
+--R 16 9 18 17 8 16 18 7 14
+--R - 656015360a b x - 6747586560a b x - 40785412096a b x
+--R +
+--R 19 6 12 20 5 10 21 4 8
+--R - 155726118912a b x - 390170935296a b x - 650284892160a b x
+--R +
+--R 22 3 6 23 2 4 24 2
+--R - 714038312960a b x - 496068722688a b x - 197568495616a b x
+--R +
+--R 25
+--R - 34359738368a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 13 12 24 14 11 22 15 10 20
+--R 51200a b x + 5324800a b x + 164003840a b x
+--R +
+--R 16 9 18 17 8 16 18 7 14
+--R 2342912000a b x + 18743296000a b x + 92694118400a b x
+--R +
+--R 19 6 12 20 5 10 21 4 8
+--R 299473305600a b x + 650284892160a b x + 956301312000a b x
+--R +
+--R 22 3 6 23 2 4 24 2
+--R 939524096000a b x + 590558003200a b x + 214748364800a b x
+--R +
+--R 25
+--R 34359738368a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 20 24 19 22 2 18 20
+--R 26558675b x + 8286306600a b x + 425363738800a b x
+--R +
+--R 3 17 18 4 16 16
+--R 8507274776000a b x + 87503397696000a b x
+--R +
+--R 5 15 14 6 14 12
+--R 528909426073600a b x + 2019472354099200a b x
+--R +
+--R 7 13 10 8 12 8
+--R 5059776887193600a b x + 8432961478656000a b x
+--R +
+--R 9 11 6 10 10 4
+--R 9259722407936000a b x + 6433070304460800a b x
+--R +
+--R 11 9 2 12 8
+--R 2562088606105600a b x + 445580627148800a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 20 24 2 19 22 3 18 20
+--R - 663966875a b x - 69052555000a b x - 2126818694000a b x
+--R +
+--R 4 17 18 5 16 16
+--R - 30383124200000a b x - 243064993600000a b x
+--R +
+--R 6 15 14 7 14 12
+--R - 1202066877440000a b x - 3883600680960000a b x
+--R +
+--R 8 13 10 9 12 8
+--R - 8432961478656000a b x - 12401413939200000a b x
+--R +
+--R 10 11 6 11 10 4
+--R - 12183845273600000a b x - 7658417029120000a b x
+--R +
+--R 12 9 2 13 8
+--R - 2784878919680000a b x - 445580627148800a b
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 413
+
+)clear all
+
+--S 414 of 1369
+t0:=x^13*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 21 3 19 2 2 17 3 15 4 13 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 1369
+r0:=1/11*a^6*(a+b*x^2)^(11/2)/b^7-6/13*a^5*(a+b*x^2)^(13/2)/b^7+_
+ a^4*(a+b*x^2)^(15/2)/b^7-20/17*a^3*(a+b*x^2)^(17/2)/b^7+_
+ 15/19*a^2*(a+b*x^2)^(19/2)/b^7-2/7*a*(a+b*x^2)^(21/2)/b^7+_
+ 1/23*(a+b*x^2)^(23/2)/b^7
+--R
+--R
+--R (2)
+--R 11 22 10 20 2 9 18 3 8 16
+--R 323323b x + 1431859a b x + 2406690a b x + 1826110a b x
+--R +
+--R 4 7 14 5 6 12 6 5 10 7 4 8 8 3 6
+--R 530959a b x + 231a b x - 252a b x + 280a b x - 320a b x
+--R +
+--R 9 2 4 10 2 11
+--R 384a b x - 512a b x + 1024a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 7
+--R 7436429b
+--R Type: Expression(Integer)
+--E 415
+
+--S 416 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 44 2 14 42 3 13 40
+--R - 7436429a b x - 687338509a b x - 19967986038a b x
+--R +
+--R 4 12 38 5 11 36
+--R - 284437883730a b x - 2395723653609a b x
+--R +
+--R 6 10 34 7 9 32
+--R - 13188629174457a b x - 50362304666532a b x
+--R +
+--R 8 8 30 9 7 28
+--R - 138351752027384a b x - 279320372632960a b x
+--R +
+--R 10 6 26 11 5 24
+--R - 418520250502144a b x - 465098909929472a b x
+--R +
+--R 12 4 22 13 3 20
+--R - 378714457991168a b x - 219779163242496a b x
+--R +
+--R 14 2 18 15 16 16 14
+--R - 86157191577600a b x - 20468860059648a b x - 2227903135744a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 16 46 15 44 2 14 42
+--R 323323b x + 87112454a b x + 4166021717a b x
+--R +
+--R 3 13 40 4 12 38 5 11 36
+--R 83236985832a b x + 914994133053a b x + 6329511736350a b x
+--R +
+--R 6 10 34 7 9 32
+--R 29751877154187a b x + 99605609581396a b x
+--R +
+--R 8 8 30 9 7 28
+--R 244515399050696a b x + 447499652195968a b x
+--R +
+--R 10 6 26 11 5 24
+--R 614615086597120a b x + 631629922373632a b x
+--R +
+--R 12 4 22 13 3 20
+--R 479026666952704a b x + 260438395469824a b x
+--R +
+--R 14 2 18 15 16 16 14
+--R 96113133715456a b x + 21582811627520a b x + 2227903135744a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 11 22 10 20 2 9 18
+--R 7436429b x + 1963217256a b x + 85072747760a b x
+--R +
+--R 3 8 16 4 7 14 5 6 12
+--R 1429222162368a b x + 12250475677440a b x + 60980145594368a b x
+--R +
+--R 6 5 10 7 4 8
+--R 188484086382592a b x + 372825665372160a b x
+--R +
+--R 8 3 6 9 2 4
+--R 472245842804736a b x + 370388896317440a b x
+--R +
+--R 10 2 11
+--R 163750880477184a b x + 31190643900416a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 11 22 2 10 20 3 9 18
+--R - 171037867a b x - 15051332296a b x - 391334639696a b x
+--R +
+--R 4 8 16 5 7 14 6 6 12
+--R - 4696015676352a b x - 31306771175680a b x - 127503940788224a b x
+--R +
+--R 7 5 10 8 4 8 9 3 6
+--R - 333471845138432a b x - 571666020237312a b x - 638920846147584a b x
+--R +
+--R 10 2 4 11 2 12
+--R - 448365506068480a b x - 179346202427392a b x - 31190643900416a
+--R Type: Union(Expression(Integer),...)
+--E 416
+
+--S 417 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 12 11 22 13 10 20 14 9 18
+--R 1024a b x + 270336a b x + 11714560a b x
+--R +
+--R 15 8 16 16 7 14 17 6 12
+--R 196804608a b x + 1686896640a b x + 8396996608a b x
+--R +
+--R 18 5 10 19 4 8 20 3 6
+--R 25954353152a b x + 51338280960a b x + 65028489216a b x
+--R +
+--R 21 2 4 22 2 23
+--R 51002736640a b x + 22548578304a b x + 4294967296a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 12 11 22 13 10 20 14 9 18
+--R - 23552a b x - 2072576a b x - 53886976a b x
+--R +
+--R 15 8 16 16 7 14 17 6 12
+--R - 646643712a b x - 4310958080a b x - 17557356544a b x
+--R +
+--R 18 5 10 19 4 8 20 3 6
+--R - 45919240192a b x - 78718697472a b x - 87979720704a b x
+--R +
+--R 21 2 4 22 2 23
+--R - 61740154880a b x - 24696061952a b x - 4294967296a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 18 22 17 20 2 16 18
+--R 7436429b x + 1963217256a b x + 85072747760a b x
+--R +
+--R 3 15 16 4 14 14
+--R 1429222162368a b x + 12250475677440a b x
+--R +
+--R 5 13 12 6 12 10
+--R 60980145594368a b x + 188484086382592a b x
+--R +
+--R 7 11 8 8 10 6
+--R 372825665372160a b x + 472245842804736a b x
+--R +
+--R 9 9 4 10 8 2 11 7
+--R 370388896317440a b x + 163750880477184a b x + 31190643900416a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 18 22 2 17 20 3 16 18
+--R - 171037867a b x - 15051332296a b x - 391334639696a b x
+--R +
+--R 4 15 16 5 14 14
+--R - 4696015676352a b x - 31306771175680a b x
+--R +
+--R 6 13 12 7 12 10
+--R - 127503940788224a b x - 333471845138432a b x
+--R +
+--R 8 11 8 9 10 6
+--R - 571666020237312a b x - 638920846147584a b x
+--R +
+--R 10 9 4 11 8 2 12 7
+--R - 448365506068480a b x - 179346202427392a b x - 31190643900416a b
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 418
+
+)clear all
+
+--S 419 of 1369
+t0:=x^11*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 19 3 17 2 2 15 3 13 4 11 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 1369
+r0:=-1/11*a^5*(a+b*x^2)^(11/2)/b^6+5/13*a^4*(a+b*x^2)^(13/2)/b^6-_
+ 2/3*a^3*(a+b*x^2)^(15/2)/b^6+10/17*a^2*(a+b*x^2)^(17/2)/b^6-_
+ 5/19*a*(a+b*x^2)^(19/2)/b^6+1/21*(a+b*x^2)^(21/2)/b^6
+--R
+--R
+--R (2)
+--R 10 20 9 18 2 8 16 3 7 14
+--R 46189b x + 206635a b x + 351780a b x + 271414a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8 7 3 6 8 2 4 9 2
+--R 80773a b x + 63a b x - 70a b x + 80a b x - 96a b x + 128a b x
+--R +
+--R 10
+--R - 256a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 6
+--R 969969b
+--R Type: Expression(Integer)
+--E 420
+
+--S 421 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 14 40 2 13 38 3 12 36
+--R - 969969a b x - 75470395a b x - 1862036176a b x
+--R +
+--R 4 11 34 5 10 32 6 9 30
+--R - 22638929742a b x - 163055189121a b x - 766871351007a b x
+--R +
+--R 7 8 28 8 7 26 9 6 24
+--R - 2492419193070a b x - 5787415877768a b x - 9769603014080a b x
+--R +
+--R 10 5 22 11 4 20
+--R - 12043338268416a b x - 10749571143168a b x
+--R +
+--R 12 3 18 13 2 16
+--R - 6775372032000a b x - 2863960399872a b x
+--R +
+--R 14 14 15 12
+--R - 729517195264a b x - 84757184512a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 15 42 14 40 2 13 38
+--R 46189b x + 10414404a b x + 421996575a b x
+--R +
+--R 3 12 36 4 11 34 5 10 32
+--R 7198501310a b x + 67834869795a b x + 402738128856a b x
+--R +
+--R 6 9 30 7 8 28 8 7 26
+--R 1622318410937a b x + 4634906061510a b x + 9638701659384a b x
+--R +
+--R 9 6 24 10 5 22
+--R 14777372605632a b x + 16724020674816a b x
+--R +
+--R 11 4 20 12 3 18
+--R 13821546106368a b x + 8121459906560a b x
+--R +
+--R 13 2 16 14 14 15 12
+--R 3218124349440a b x + 771895787520a b x + 84757184512a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 10 20 9 18 2 8 16
+--R 969969b x + 213393180a b x + 7682154480a b x
+--R +
+--R 3 7 14 4 6 12 5 5 10
+--R 106525875456a b x + 745681128192a b x + 2982724512768a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4
+--R 7230847303680a b x + 10806541025280a b x + 9725886922752a b x
+--R +
+--R 9 2 10
+--R 4831159517184a b x + 1017086214144a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 10 20 2 9 18 3 8 16
+--R - 20369349a b x - 1493752260a b x - 32265048816a b x
+--R +
+--R 4 7 14 5 6 12 6 5 10
+--R - 319577626368a b x - 1739922632448a b x - 5694292251648a b x
+--R +
+--R 7 4 8 8 3 6 9 2 4
+--R - 11680599490560a b x - 15129157435392a b x - 12014330904576a b x
+--R +
+--R 10 2 11
+--R - 5339702624256a b x - 1017086214144a
+--R Type: Union(Expression(Integer),...)
+--E 421
+
+--S 422 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 11 10 20 12 9 18 13 8 16 14 7 14
+--R - 256a b x - 56320a b x - 2027520a b x - 28114944a b x
+--R +
+--R 15 6 12 16 5 10 17 4 8
+--R - 196804608a b x - 787218432a b x - 1908408320a b x
+--R +
+--R 18 3 6 19 2 4 20 2
+--R - 2852126720a b x - 2566914048a b x - 1275068416a b x
+--R +
+--R 21
+--R - 268435456a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 11 10 20 12 9 18 13 8 16 14 7 14
+--R 5376a b x + 394240a b x + 8515584a b x + 84344832a b x
+--R +
+--R 15 6 12 16 5 10 17 4 8
+--R 459210752a b x + 1502871552a b x + 3082813440a b x
+--R +
+--R 18 3 6 19 2 4 20 2
+--R 3992977408a b x + 3170893824a b x + 1409286144a b x
+--R +
+--R 21
+--R 268435456a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 16 20 15 18 2 14 16
+--R 969969b x + 213393180a b x + 7682154480a b x
+--R +
+--R 3 13 14 4 12 12 5 11 10
+--R 106525875456a b x + 745681128192a b x + 2982724512768a b x
+--R +
+--R 6 10 8 7 9 6 8 8 4
+--R 7230847303680a b x + 10806541025280a b x + 9725886922752a b x
+--R +
+--R 9 7 2 10 6
+--R 4831159517184a b x + 1017086214144a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 16 20 2 15 18 3 14 16
+--R - 20369349a b x - 1493752260a b x - 32265048816a b x
+--R +
+--R 4 13 14 5 12 12 6 11 10
+--R - 319577626368a b x - 1739922632448a b x - 5694292251648a b x
+--R +
+--R 7 10 8 8 9 6 9 8 4
+--R - 11680599490560a b x - 15129157435392a b x - 12014330904576a b x
+--R +
+--R 10 7 2 11 6
+--R - 5339702624256a b x - 1017086214144a b
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 423
+
+)clear all
+
+--S 424 of 1369
+t0:=x^9*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 17 3 15 2 2 13 3 11 4 9 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 1369
+r0:=1/11*a^4*(a+b*x^2)^(11/2)/b^5-4/13*a^3*(a+b*x^2)^(13/2)/b^5+_
+ 2/5*a^2*(a+b*x^2)^(15/2)/b^5-4/17*a*(a+b*x^2)^(17/2)/b^5+_
+ 1/19*(a+b*x^2)^(19/2)/b^5
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 12155b x + 55055a b x + 95238a b x + 75086a b x + 23063a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 35a b x - 40a b x + 48a b x - 64a b x + 128a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 5
+--R 230945b
+--R Type: Expression(Integer)
+--E 425
+
+--S 426 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 13 36 2 12 34 3 11 32
+--R - 230945a b x - 14902745a b x - 308450142a b x
+--R +
+--R 4 10 30 5 9 28 6 8 26
+--R - 3165644834a b x - 19288314189a b x - 76633654085a b x
+--R +
+--R 7 7 24 8 6 22 9 5 20
+--R - 209340893060a b x - 404778695568a b x - 560641342976a b x
+--R +
+--R 10 4 18 11 3 16 12 2 14
+--R - 554291648768a b x - 382873553920a b x - 175946833920a b x
+--R +
+--R 13 12 14 10
+--R - 48432676864a b x - 6054084608a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 14 38 13 36 2 12 34 3 11 32
+--R 12155b x + 2255110a b x + 76426493a b x + 1100889944a b x
+--R +
+--R 4 10 30 5 9 28 6 8 26
+--R 8803566229a b x + 44407707326a b x + 151656893155a b x
+--R +
+--R 7 7 24 8 6 22 9 5 20
+--R 365252651972a b x + 634069759856a b x + 799198290176a b x
+--R +
+--R 10 4 18 11 3 16 12 2 14
+--R 726525626112a b x + 465171266560a b x + 199406411776a b x
+--R +
+--R 13 12 14 10
+--R 51459719168a b x + 6054084608a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 9 18 8 16 2 7 14
+--R 230945b x + 41570100a b x + 1219389600a b x
+--R +
+--R 3 6 12 4 5 10 5 4 8
+--R 13657163520a b x + 76089911040a b x + 236724167680a b x
+--R +
+--R 6 3 6 7 2 4 8 2
+--R 430407577600a b x + 454056345600a b x + 257298595840a b x
+--R +
+--R 9
+--R 60540846080a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 2 8 16 3 7 14
+--R - 4387955a b x - 263277300a b x - 4633680480a b x
+--R +
+--R 4 6 12 5 5 10 6 4 8
+--R - 37069443840a b x - 160634256640a b x - 408887198720a b x
+--R +
+--R 7 3 6 8 2 4 9 2
+--R - 629057228800a b x - 575138037760a b x - 287569018880a b x
+--R +
+--R 10
+--R - 60540846080a
+--R Type: Union(Expression(Integer),...)
+--E 426
+
+--S 427 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 10 9 18 11 8 16 12 7 14 13 6 12
+--R 128a b x + 23040a b x + 675840a b x + 7569408a b x
+--R +
+--R 14 5 10 15 4 8 16 3 6
+--R 42172416a b x + 131203072a b x + 238551040a b x
+--R +
+--R 17 2 4 18 2 19
+--R 251658240a b x + 142606336a b x + 33554432a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 10 9 18 11 8 16 12 7 14 13 6 12
+--R - 2432a b x - 145920a b x - 2568192a b x - 20545536a b x
+--R +
+--R 14 5 10 15 4 8 16 3 6
+--R - 89030656a b x - 226623488a b x - 348651520a b x
+--R +
+--R 17 2 4 18 2 19
+--R - 318767104a b x - 159383552a b x - 33554432a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 14 18 13 16 2 12 14
+--R 230945b x + 41570100a b x + 1219389600a b x
+--R +
+--R 3 11 12 4 10 10 5 9 8
+--R 13657163520a b x + 76089911040a b x + 236724167680a b x
+--R +
+--R 6 8 6 7 7 4 8 6 2
+--R 430407577600a b x + 454056345600a b x + 257298595840a b x
+--R +
+--R 9 5
+--R 60540846080a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 14 18 2 13 16 3 12 14
+--R - 4387955a b x - 263277300a b x - 4633680480a b x
+--R +
+--R 4 11 12 5 10 10 6 9 8
+--R - 37069443840a b x - 160634256640a b x - 408887198720a b x
+--R +
+--R 7 8 6 8 7 4 9 6 2
+--R - 629057228800a b x - 575138037760a b x - 287569018880a b x
+--R +
+--R 10 5
+--R - 60540846080a b
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 428
+
+)clear all
+
+--S 429 of 1369
+t0:=x^7*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 15 3 13 2 2 11 3 9 4 7 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 1369
+r0:=-1/11*a^3*(a+b*x^2)^(11/2)/b^4+3/13*a^2*(a+b*x^2)^(13/2)/b^4-_
+ 1/5*a*(a+b*x^2)^(15/2)/b^4+1/17*(a+b*x^2)^(17/2)/b^4
+--R
+--R
+--R (2)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R 715b x + 3289a b x + 5808a b x + 4714a b x + 1515a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 5a b x - 6a b x + 8a b x - 16a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4
+--R 12155b
+--R Type: Expression(Integer)
+--E 430
+
+--S 431 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 32 2 11 30 3 10 28 4 9 26
+--R - 12155a b x - 639353a b x - 10950720a b x - 93735722a b x
+--R +
+--R 5 8 24 6 7 22 7 6 20
+--R - 477541883a b x - 1583019685a b x - 3583153002a b x
+--R +
+--R 8 5 18 9 4 16 10 3 14
+--R - 5668216840a b x - 6290416704a b x - 4817502976a b x
+--R +
+--R 11 2 12 12 10 13 8
+--R - 2433333760a b x - 731867136a b x - 99573760a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 13 34 12 32 2 11 30 3 10 28
+--R 715b x + 106964a b x + 2988073a b x + 35915050a b x
+--R +
+--R 4 9 26 5 8 24 6 7 22
+--R 241082389a b x + 1022017152a b x + 2924168351a b x
+--R +
+--R 7 6 20 8 5 18 9 4 16
+--R 5854971122a b x + 8337454840a b x + 8436853568a b x
+--R +
+--R 10 3 14 11 2 12 12 10
+--R 5948909824a b x + 2786820608a b x + 781654016a b x
+--R +
+--R 13 8
+--R 99573760a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 8 16 7 14 2 6 12 3 5 10
+--R 12155b x + 1750320a b x + 40840800a b x + 359399040a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4
+--R 1540281600a b x + 3559761920a b x + 4530606080a b x
+--R +
+--R 7 2 8
+--R 2987212800a b x + 796590080a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R - 206635a b x - 9918480a b x - 138858720a b x - 872826240a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4
+--R - 2909420800a b x - 5501450240a b x - 5924638720a b x
+--R +
+--R 8 2 9
+--R - 3385507840a b x - 796590080a
+--R Type: Union(Expression(Integer),...)
+--E 431
+
+--S 432 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 9 8 16 10 7 14 11 6 12 12 5 10
+--R - 16a b x - 2304a b x - 53760a b x - 473088a b x
+--R +
+--R 13 4 8 14 3 6 15 2 4 16 2
+--R - 2027520a b x - 4685824a b x - 5963776a b x - 3932160a b x
+--R +
+--R 17
+--R - 1048576a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 8 16 10 7 14 11 6 12 12 5 10
+--R 272a b x + 13056a b x + 182784a b x + 1148928a b x
+--R +
+--R 13 4 8 14 3 6 15 2 4 16 2
+--R 3829760a b x + 7241728a b x + 7798784a b x + 4456448a b x
+--R +
+--R 17
+--R 1048576a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 12 16 11 14 2 10 12 3 9 10
+--R 12155b x + 1750320a b x + 40840800a b x + 359399040a b x
+--R +
+--R 4 8 8 5 7 6 6 6 4
+--R 1540281600a b x + 3559761920a b x + 4530606080a b x
+--R +
+--R 7 5 2 8 4
+--R 2987212800a b x + 796590080a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 12 16 2 11 14 3 10 12 4 9 10
+--R - 206635a b x - 9918480a b x - 138858720a b x - 872826240a b x
+--R +
+--R 5 8 8 6 7 6 7 6 4
+--R - 2909420800a b x - 5501450240a b x - 5924638720a b x
+--R +
+--R 8 5 2 9 4
+--R - 3385507840a b x - 796590080a b
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 433
+
+)clear all
+
+--S 434 of 1369
+t0:=x^5*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 13 3 11 2 2 9 3 7 4 5 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 1369
+r0:=1/11*a^2*(a+b*x^2)^(11/2)/b^3-2/13*a*(a+b*x^2)^(13/2)/b^3+_
+ 1/15*(a+b*x^2)^(15/2)/b^3
+--R
+--R
+--R (2)
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R 143b x + 671a b x + 1218a b x + 1030a b x + 355a b x + 3a b x
+--R +
+--R 6 2 7
+--R - 4a b x + 8a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3
+--R 2145b
+--R Type: Expression(Integer)
+--E 435
+
+--S 436 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 11 28 2 10 26 3 9 24 4 8 22
+--R - 2145a b x - 90145a b x - 1258894a b x - 8874138a b x
+--R +
+--R 5 7 20 6 6 18 7 5 16
+--R - 37340589a b x - 101923965a b x - 188185140a b x
+--R +
+--R 8 4 14 9 3 12 10 2 10
+--R - 238572048a b x - 205810176a b x - 116083968a b x
+--R +
+--R 11 8 12 6
+--R - 38804480a b x - 5857280a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 12 30 11 28 2 10 26 3 9 24
+--R 143b x + 16830a b x + 381345a b x + 3776760a b x
+--R +
+--R 4 8 22 5 7 20 6 6 18
+--R 21041865a b x + 74123478a b x + 175464575a b x
+--R +
+--R 7 5 16 8 4 14 9 3 12
+--R 287644500a b x + 329163120a b x + 259367680a b x
+--R +
+--R 10 2 10 11 8 12 6
+--R 134754048a b x + 41733120a b x + 5857280a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 7 14 6 12 2 5 10 3 4 8
+--R 2145b x + 240240a b x + 4324320a b x + 28828800a b x
+--R +
+--R 4 3 6 5 2 4 6 2 7
+--R 90604800a b x + 144967680a b x + 114216960a b x + 35143680a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 14 2 6 12 3 5 10 4 4 8
+--R - 32175a b x - 1201200a b x - 12972960a b x - 61776000a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 151008000a b x - 197683200a b x - 131788800a b x - 35143680a
+--R Type: Union(Expression(Integer),...)
+--E 436
+
+--S 437 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8 7 14 9 6 12 10 5 10 11 4 8 12 3 6
+--R 8a b x + 896a b x + 16128a b x + 107520a b x + 337920a b x
+--R +
+--R 13 2 4 14 2 15
+--R 540672a b x + 425984a b x + 131072a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 7 14 9 6 12 10 5 10 11 4 8
+--R - 120a b x - 4480a b x - 48384a b x - 230400a b x
+--R +
+--R 12 3 6 13 2 4 14 2 15
+--R - 563200a b x - 737280a b x - 491520a b x - 131072a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 10 14 9 12 2 8 10 3 7 8
+--R 2145b x + 240240a b x + 4324320a b x + 28828800a b x
+--R +
+--R 4 6 6 5 5 4 6 4 2 7 3
+--R 90604800a b x + 144967680a b x + 114216960a b x + 35143680a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 10 14 2 9 12 3 8 10 4 7 8
+--R - 32175a b x - 1201200a b x - 12972960a b x - 61776000a b x
+--R +
+--R 5 6 6 6 5 4 7 4 2 8 3
+--R - 151008000a b x - 197683200a b x - 131788800a b x - 35143680a b
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 438
+
+)clear all
+
+--S 439 of 1369
+t0:=x^3*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 11 3 9 2 2 7 3 5 4 3 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 1369
+r0:=-1/11*a*(a+b*x^2)^(11/2)/b^2+1/13*(a+b*x^2)^(13/2)/b^2
+--R
+--R
+--R (2)
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6
+--R (11b x + 53a b x + 100a b x + 90a b x + 35a b x + a b x - 2a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2
+--R 143b
+--R Type: Expression(Integer)
+--E 440
+
+--S 441 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 24 2 9 22 3 8 20 4 7 18
+--R - 143a b x - 4693a b x - 52624a b x - 301730a b x
+--R +
+--R 5 6 16 6 5 14 7 4 12 8 3 10
+--R - 1036607a b x - 2301585a b x - 3415412a b x - 3397680a b x
+--R +
+--R 9 2 8 10 6 11 4
+--R - 2196480a b x - 841984a b x - 146432a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 11 26 10 24 2 9 22 3 8 20 4 7 18
+--R 11b x + 988a b x + 17849a b x + 143858a b x + 658229a b x
+--R +
+--R 5 6 16 6 5 14 7 4 12 8 3 10
+--R 1907048a b x + 3692975a b x + 4886596a b x + 4399824a b x
+--R +
+--R 9 2 8 10 6 11 4
+--R 2599168a b x + 915200a b x + 146432a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4
+--R 143b x + 12012a b x + 160160a b x + 768768a b x + 1647360a b x
+--R +
+--R 5 2 6
+--R 1610752a b x + 585728a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 12 2 5 10 3 4 8 4 3 6
+--R - 1859a b x - 52052a b x - 416416a b x - 1427712a b x
+--R +
+--R 5 2 4 6 2 7
+--R - 2379520a b x - 1903616a b x - 585728a
+--R Type: Union(Expression(Integer),...)
+--E 441
+
+--S 442 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 7 6 12 8 5 10 9 4 8 10 3 6 11 2 4
+--R - 2a b x - 168a b x - 2240a b x - 10752a b x - 23040a b x
+--R +
+--R 12 2 13
+--R - 22528a b x - 8192a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 6 12 8 5 10 9 4 8 10 3 6 11 2 4
+--R 26a b x + 728a b x + 5824a b x + 19968a b x + 33280a b x
+--R +
+--R 12 2 13
+--R 26624a b x + 8192a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 8 12 7 10 2 6 8 3 5 6 4 4 4
+--R 143b x + 12012a b x + 160160a b x + 768768a b x + 1647360a b x
+--R +
+--R 5 3 2 6 2
+--R 1610752a b x + 585728a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 12 2 7 10 3 6 8 4 5 6
+--R - 1859a b x - 52052a b x - 416416a b x - 1427712a b x
+--R +
+--R 5 4 4 6 3 2 7 2
+--R - 2379520a b x - 1903616a b x - 585728a b
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 443
+
+)clear all
+
+--S 444 of 1369
+t0:=x*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 9 3 7 2 2 5 3 3 4 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 1369
+r0:=1/11*(a+b*x^2)^(11/2)/b
+--R
+--R
+--R +--------+
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2
+--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + a
+--R (2) -----------------------------------------------------------------
+--R 11b
+--R Type: Expression(Integer)
+--E 445
+
+--S 446 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 20 2 8 18 3 7 16 4 6 14 5 5 12
+--R - 11a b x - 275a b x - 2442a b x - 11286a b x - 31471a b x
+--R +
+--R 6 4 10 7 3 8 8 2 6 9 4 10 2
+--R - 56694a b x - 67760a b x - 53152a b x - 25344a b x - 5632a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 10 22 9 20 2 8 18 3 7 16 4 6 14
+--R b x + 66a b x + 935a b x + 6072a b x + 22671a b x
+--R +
+--R 5 5 12 6 4 10 7 3 8 8 2 6 9 4
+--R 53834a b x + 85294a b x + 91520a b x + 65120a b x + 28160a b x
+--R +
+--R 10 2
+--R 5632a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 10 4 8 2 3 6 3 2 4 4 2
+--R 11b x + 660a b x + 6160a b x + 19712a b x + 25344a b x
+--R +
+--R 5
+--R 11264a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 10 2 4 8 3 3 6 4 2 4 5 2
+--R - 121a b x - 2420a b x - 13552a b x - 30976a b x - 30976a b x
+--R +
+--R 6
+--R - 11264a
+--R Type: Union(Expression(Integer),...)
+--E 446
+
+--S 447 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 11
+--R (a b x + 60a b x + 560a b x + 1792a b x + 2304a b x + 1024a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2
+--R - 11a b x - 220a b x - 1232a b x - 2816a b x - 2816a b x
+--R +
+--R 11
+--R - 1024a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 10 5 8 2 4 6 3 3 4 4 2 2
+--R 11b x + 660a b x + 6160a b x + 19712a b x + 25344a b x
+--R +
+--R 5
+--R 11264a b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 10 2 5 8 3 4 6 4 3 4 5 2 2
+--R - 121a b x - 2420a b x - 13552a b x - 30976a b x - 30976a b x
+--R +
+--R 6
+--R - 11264a b
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 448
+
+)clear all
+
+--S 449 of 1369
+t0:=(a+b*x^2)^(9/2)/x
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 1369
+r0:=1/3*a^3*(a+b*x^2)^(3/2)+1/5*a^2*(a+b*x^2)^(5/2)+1/7*a*(a+b*x^2)^(7/2)+_
+ 1/9*(a+b*x^2)^(9/2)-a^(9/2)*atanh(sqrt(a+b*x^2)/sqrt(a))+_
+ a^4*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 4 +-+ \|b x + a
+--R - 315a \|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (35b x + 185a b x + 408a b x + 506a b x + 563a )\|b x + a
+--R /
+--R 315
+--R Type: Expression(Integer)
+--E 450
+
+--S 451 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 9
+--R - 80640a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R - 315a b x - 5865a b x - 40992a b x - 153594a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R - 357000a b x - 546000a b x - 504000a b x - 201600a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 35b x + 1620a b x + 17793a b x + 93114a b x + 287469a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R 579600a b x + 772800a b x + 604800a b x + 201600a b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a
+--R Type: Union(Expression(Integer),...)
+--E 451
+
+--S 452 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 9
+--R - 80640a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 9
+--R - 80640a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R (563a b x + 22520a b x + 135120a b x + 252224a b x + 144128a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+
+--R (- 5067a b x - 67560a b x - 243216a b x - 324288a b x - 144128a )\|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 453
+
+)clear all
+
+--S 454 of 1369
+t0:=(a+b*x^2)^(9/2)/x^3
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 1369
+r0:=3/2*a^2*b*(a+b*x^2)^(3/2)+9/10*a*b*(a+b*x^2)^(5/2)+_
+ 9/14*b*(a+b*x^2)^(7/2)-1/2*(a+b*x^2)^(9/2)/x^2-_
+ 9/2*a^(7/2)*b*atanh(sqrt(a+b*x^2)/sqrt(a))+9/2*a^3*b*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 3 2 +-+ \|b x + a
+--R - 315a b x \|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (10b x + 58a b x + 156a b x + 388a b x - 35a )\|b x + a
+--R /
+--R 2
+--R 70x
+--R Type: Expression(Integer)
+--E 455
+
+--S 456 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 315a b x + 12600a b x + 75600a b x + 141120a b x
+--R +
+--R 8 2
+--R 80640a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 8 2
+--R - 80640a b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R - 90a b x - 1722a b x - 12684a b x - 52640a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 134085a b x - 175000a b x - 74480a b x + 20160a b x + 8960a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 10b x + 468a b x + 5334a b x + 29904a b x + 103005a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 211365a b x + 214200a b x + 65520a b x - 24640a b x - 8960a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 10 3 8 2 2 6 3 4 4 2 +-+
+--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a x )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 10 2 3 8 3 2 6 4 4 5 2
+--R - 630a b x - 8400a b x - 30240a b x - 40320a b x - 17920a x
+--R Type: Union(Expression(Integer),...)
+--E 456
+
+--S 457 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 5 8 5 4 6 6 3 4 7 2 2 8
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b)
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 5 8 5 4 6 6 3 4 7 2 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 8
+--R - 80640a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 4 5 8 5 4 6 6 3 4 7 2 2 8
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b)
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 5 8 5 4 6 6 3 4 7 2 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 8
+--R - 80640a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 5 8 5 4 6 6 3 4 7 2 2 8
+--R (388a b x + 15520a b x + 93120a b x + 173824a b x + 99328a b)
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 5 8 5 4 6 6 3 4 7 2 2 8 +-+
+--R (- 3492a b x - 46560a b x - 167616a b x - 223488a b x - 99328a b)\|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 630a b x - 8400a b x - 30240a b x - 40320a b x - 17920a
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 458
+
+)clear all
+
+--S 459 of 1369
+t0:=(a+b*x^2)^(9/2)/x^5
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 1369
+r0:=21/8*a*b^2*(a+b*x^2)^(3/2)+63/40*b^2*(a+b*x^2)^(5/2)-_
+ 9/8*b*(a+b*x^2)^(7/2)/x^2-1/4*(a+b*x^2)^(9/2)/x^4-_
+ 63/8*a^(5/2)*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))+63/8*a^2*b^2*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 2 2 4 +-+ \|b x + a
+--R - 315a b x \|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (8b x + 56a b x + 288a b x - 85a b x - 10a )\|b x + a
+--R /
+--R 4
+--R 40x
+--R Type: Expression(Integer)
+--E 460
+
+--S 461 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 6 12 4 5 10 5 4 8 6 3 6
+--R 315a b x + 12600a b x + 75600a b x + 141120a b x
+--R +
+--R 7 2 4
+--R 80640a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 6 12 4 5 10 5 4 8 6 3 6
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 7 2 4
+--R - 80640a b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10 5 4 8
+--R - 72a b x - 1464a b x - 12480a b x - 51075a b x - 79310a b x
+--R +
+--R 6 3 6 7 2 4 8 2 9
+--R - 13280a b x + 53280a b x + 27520a b x + 2560a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 8b x + 384a b x + 4824a b x + 30315a b x + 86745a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 90990a b x - 10080a b x - 66720a b x - 28800a b x - 2560a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 12 3 10 2 2 8 3 6 4 4 +-+
+--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a x )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 12 2 3 10 3 2 8 4 6 5 4
+--R - 360a b x - 4800a b x - 17280a b x - 23040a b x - 10240a x
+--R Type: Union(Expression(Integer),...)
+--E 461
+
+--S 462 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 6 8 4 5 6 5 4 4 6 3 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 7 2
+--R - 80640a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 6 8 4 5 6 5 4 4 6 3 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 7 2
+--R - 80640a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2
+--R (288a b x + 11520a b x + 69120a b x + 129024a b x + 73728a b )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2 +-+
+--R (- 2592a b x - 34560a b x - 124416a b x - 165888a b x - 73728a b )\|a
+--R /
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a )\|a \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 360a b x - 4800a b x - 17280a b x - 23040a b x - 10240a
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 463
+
+)clear all
+
+--S 464 of 1369
+t0:=(a+b*x^2)^(9/2)/x^7
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 1369
+r0:=35/16*b^3*(a+b*x^2)^(3/2)-21/16*b^2*(a+b*x^2)^(5/2)/x^2-_
+ 3/8*b*(a+b*x^2)^(7/2)/x^4-1/6*(a+b*x^2)^(9/2)/x^6-_
+ 105/16*a^(3/2)*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))+_
+ 105/16*a*b^3*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 3 6 +-+ \|b x + a
+--R - 315a b x \|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (16b x + 208a b x - 165a b x - 50a b x - 8a )\|b x + a
+--R /
+--R 6
+--R 48x
+--R Type: Expression(Integer)
+--E 465
+
+--S 466 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 7 14 3 6 12 4 5 10 5 4 8
+--R 315a b x + 12600a b x + 75600a b x + 141120a b x
+--R +
+--R 6 3 6
+--R 80640a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 7 14 3 6 12 4 5 10 5 4 8
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 6 3 6
+--R - 80640a b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R - 144a b x - 3584a b x - 22067a b x - 28902a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 46632a b x + 117600a b x + 74496a b x + 17408a b x + 2048a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 16b x + 864a b x + 10971a b x + 37473a b x + 16254a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 97128a b x - 152800a b x - 82944a b x - 18432a b x - 2048a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 14 3 12 2 2 10 3 8 4 6 +-+
+--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a x )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 14 2 3 12 3 2 10 4 8 5 6
+--R - 432a b x - 5760a b x - 20736a b x - 27648a b x - 12288a x
+--R Type: Union(Expression(Integer),...)
+--E 466
+
+--S 467 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 7 8 3 6 6 4 5 4 5 4 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 6 3
+--R - 80640a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 7 8 3 6 6 4 5 4 5 4 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 6 3
+--R - 80640a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3
+--R (208a b x + 8320a b x + 49920a b x + 93184a b x + 53248a b )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3 +-+
+--R (- 1872a b x - 24960a b x - 89856a b x - 119808a b x - 53248a b )\|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 432a b x - 5760a b x - 20736a b x - 27648a b x - 12288a
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 468
+
+)clear all
+
+--S 469 of 1369
+t0:=(a+b*x^2)^(9/2)/x^9
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 1369
+r0:=-105/128*b^3*(a+b*x^2)^(3/2)/x^2-21/64*b^2*(a+b*x^2)^(5/2)/x^4-_
+ 3/16*b*(a+b*x^2)^(7/2)/x^6-1/8*(a+b*x^2)^(9/2)/x^8-_
+ 315/128*b^4*atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+_
+ 315/128*b^4*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 4 8 +-+ \|b x + a
+--R - 315b x \|a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (128b x - 325a b x - 210a b x - 88a b x - 16a )\|b x + a
+--R /
+--R 8
+--R 128x
+--R Type: Expression(Integer)
+--E 470
+
+--S 471 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R 315a b x + 12600a b x + 75600a b x + 141120a b x
+--R +
+--R 5 4 8
+--R 80640a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 5 4 8
+--R - 80640a b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R - 1024a b x - 7315a b x + 16314a b x + 150008a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 288624a b x + 244096a b x + 111360a b x + 31744a b x + 4096a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 128b x + 3771a b x + 6945a b x - 66930a b x - 269640a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 398576a b x - 296064a b x - 126720a b x - 33792a b x - 4096a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 16 3 14 2 2 12 3 10 4 8 +-+
+--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a x )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 16 2 3 14 3 2 12 4 10 5 8
+--R - 1152a b x - 15360a b x - 55296a b x - 73728a b x - 32768a x
+--R Type: Union(Expression(Integer),...)
+--E 471
+
+--S 472 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 5 4
+--R - 80640a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 5 4
+--R - 80640a b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4
+--R (128a b x + 5120a b x + 30720a b x + 57344a b x + 32768a b )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +-+
+--R (- 1152a b x - 15360a b x - 55296a b x - 73728a b x - 32768a b )\|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 1152a b x - 15360a b x - 55296a b x - 73728a b x - 32768a
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 473
+
+)clear all
+
+--S 474 of 1369
+t0:=(a+b*x^2)^(9/2)/x^11
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 1369
+r0:=-21/128*b^3*(a+b*x^2)^(3/2)/x^4-21/160*b^2*(a+b*x^2)^(5/2)/x^6-_
+ 9/80*b*(a+b*x^2)^(7/2)/x^8-1/10*(a+b*x^2)^(9/2)/x^10-_
+ 63/256*b^5*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-_
+ 63/256*b^4*sqrt(a+b*x^2)/x^2
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 5 10 \|b x + a
+--R - 315b x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 965b x - 1490a b x - 1368a b x - 656a b x - 128a )\|a \|b x + a
+--R /
+--R 10 +-+
+--R 1280x \|a
+--R Type: Expression(Integer)
+--E 475
+
+--S 476 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 18 2 8 16 3 7 14 4 6 12
+--R 3150a b x + 50400a b x + 211680a b x + 322560a b x
+--R +
+--R 5 5 10
+--R 161280a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 10 20 9 18 2 8 16 3 7 14
+--R - 315b x - 15750a b x - 126000a b x - 352800a b x
+--R +
+--R 4 6 12 5 5 10
+--R - 403200a b x - 161280a b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 9 18 2 8 16 3 7 14 4 6 12
+--R 965a b x + 49740a b x + 461868a b x + 1745856a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R 3484128a b x + 4202240a b x + 3299840a b x + 1683456a b x
+--R +
+--R 9 2 10
+--R 499712a b x + 65536a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 18 2 8 16 3 7 14 4 6 12
+--R - 9650a b x - 178950a b x - 1069860a b x - 3115440a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R - 5260256a b x - 5670400a b x - 4083200a b x - 1925120a b x
+--R +
+--R 9 2 10
+--R - 532480a b x - 65536a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 18 2 3 16 3 2 14 4 12
+--R 12800a b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 5 10
+--R 655360a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 20 2 4 18 3 3 16 4 2 14
+--R - 1280a b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 5 12 6 10
+--R - 1638400a b x - 655360a x
+--R Type: Union(Expression(Integer),...)
+--E 476
+
+--S 477 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 5 \|b x + a - \|a 5 \|b x + a
+--R 63b log(------------------) + 63b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) ----------------------------------------------------
+--R +-+
+--R 256\|a
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 478
+
+)clear all
+
+--S 479 of 1369
+t0:=(a+b*x^2)^(9/2)/x^13
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 13
+--R x
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 1369
+r0:=-7/128*b^3*(a+b*x^2)^(3/2)/x^6-21/320*b^2*(a+b*x^2)^(5/2)/x^8-_
+ 3/40*b*(a+b*x^2)^(7/2)/x^10-1/12*(a+b*x^2)^(9/2)/x^12+_
+ 21/1024*b^6*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_
+ 21/512*b^4*sqrt(a+b*x^2)/x^4-21/1024*b^5*sqrt(a+b*x^2)/(a*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 6 12 \|b x + a
+--R 315b x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2
+--R - 315b x - 4910a b x - 11432a b x - 12144a b x - 6272a b x
+--R +
+--R 5
+--R - 1280a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R /
+--R 12 +-+
+--R 15360a x \|a
+--R Type: Expression(Integer)
+--E 480
+
+--S 481 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 11 22 2 10 20 3 9 18 4 8 16
+--R - 3780a b x - 88200a b x - 564480a b x - 1451520a b x
+--R +
+--R 5 7 14 6 6 12
+--R - 1612800a b x - 645120a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 12 24 11 22 2 10 20 3 9 18
+--R 315b x + 22680a b x + 264600a b x + 1128960a b x
+--R +
+--R 4 8 16 5 7 14 6 6 12
+--R 2177280a b x + 1935360a b x + 645120a b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 11 22 2 10 20 3 9 18 4 8 16
+--R 315a b x + 27590a b x + 629552a b x + 6088608a b x
+--R +
+--R 5 7 14 6 6 12 7 5 10
+--R 30258240a b x + 87499392a b x + 158714880a b x
+--R +
+--R 8 4 8 9 3 6 10 2 4 11 2
+--R 187787264a b x + 145965056a b x + 72253440a b x + 20709376a b x
+--R +
+--R 12
+--R 2621440a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 11 22 2 10 20 3 9 18 4 8 16
+--R - 3780a b x - 150900a b x - 2223584a b x - 15673392a b x
+--R +
+--R 5 7 14 6 6 12 7 5 10
+--R - 61796736a b x - 150196352a b x - 238141440a b x
+--R +
+--R 8 4 8 9 3 6 10 2 4
+--R - 252930048a b x - 179666944a b x - 82280448a b x
+--R +
+--R 11 2 12
+--R - 22020096a b x - 2621440a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 2 5 22 3 4 20 4 3 18 5 2 16
+--R 184320a b x + 4300800a b x + 27525120a b x + 70778880a b x
+--R +
+--R 6 14 7 12
+--R 78643200a b x + 31457280a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 6 24 3 5 22 4 4 20 5 3 18
+--R - 15360a b x - 1105920a b x - 12902400a b x - 55050240a b x
+--R +
+--R 6 2 16 7 14 8 12
+--R - 106168320a b x - 94371840a b x - 31457280a x
+--R Type: Union(Expression(Integer),...)
+--E 481
+
+--S 482 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 6 \|b x + a - \|a 6 \|b x + a
+--R - 21b log(------------------) - 21b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) ------------------------------------------------------
+--R +-+
+--R 1024a\|a
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 483
+
+)clear all
+
+--S 484 of 1369
+t0:=(a+b*x^2)^(9/2)/x^15
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 15
+--R x
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 1369
+r0:=-3/128*b^3*(a+b*x^2)^(3/2)/x^8-3/80*b^2*(a+b*x^2)^(5/2)/x^10-_
+ 3/56*b*(a+b*x^2)^(7/2)/x^12-1/14*(a+b*x^2)^(9/2)/x^14-_
+ 9/2048*b^7*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_
+ 3/256*b^4*sqrt(a+b*x^2)/x^6-3/1024*b^5*sqrt(a+b*x^2)/(a*x^4)+_
+ 9/2048*b^6*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R 7 14 \|b x + a
+--R - 315b x atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4
+--R 315b x - 210a b x - 14168a b x - 39056a b x - 44928a b x
+--R +
+--R 5 2 6
+--R - 24320a b x - 5120a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R /
+--R 2 14 +-+
+--R 71680a x \|a
+--R Type: Expression(Integer)
+--E 485
+
+--S 486 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 13 26 2 12 24 3 11 22 4 10 20
+--R 4410a b x + 141120a b x + 1270080a b x + 4838400a b x
+--R +
+--R 5 9 18 6 8 16 7 7 14
+--R 8870400a b x + 7741440a b x + 2580480a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 14 28 13 26 2 12 24 3 11 22
+--R - 315b x - 30870a b x - 493920a b x - 2963520a b x
+--R +
+--R 4 10 20 5 9 18 6 8 16
+--R - 8467200a b x - 12418560a b x - 9031680a b x
+--R +
+--R 7 7 14
+--R - 2580480a b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 13 26 2 12 24 3 11 22 4 10 20
+--R - 315a b x - 30660a b x - 459172a b x - 1206720a b x
+--R +
+--R 5 9 18 6 8 16 7 7 14
+--R 19596320a b x + 192185856a b x + 820357632a b x
+--R +
+--R 8 6 12 9 5 10 10 4 8
+--R 2073143296a b x + 3392184320a b x + 3709009920a b x
+--R +
+--R 11 3 6 12 2 4 13 2 14
+--R 2704539648a b x + 1267204096a b x + 346030080a b x + 41943040a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 13 26 2 12 24 3 11 22 4 10 20
+--R 4410a b x + 142590a b x + 1115828a b x - 1924720a b x
+--R +
+--R 5 9 18 6 8 16 7 7 14
+--R - 72509024a b x - 463341312a b x - 1587302912a b x
+--R +
+--R 8 6 12 9 5 10 10 4 8
+--R - 3433744384a b x - 4975452160a b x - 4922867712a b x
+--R +
+--R 11 3 6 12 2 4 13 2
+--R - 3297509376a b x - 1434976256a b x - 367001600a b x
+--R +
+--R 14
+--R - 41943040a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 3 6 26 4 5 24 5 4 22
+--R 1003520a b x + 32112640a b x + 289013760a b x
+--R +
+--R 6 3 20 7 2 18 8 16
+--R 1101004800a b x + 2018508800a b x + 1761607680a b x
+--R +
+--R 9 14
+--R 587202560a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 7 28 4 6 26 5 5 24 6 4 22
+--R - 71680a b x - 7024640a b x - 112394240a b x - 674365440a b x
+--R +
+--R 7 3 20 8 2 18 9 16
+--R - 1926758400a b x - 2825912320a b x - 2055208960a b x
+--R +
+--R 10 14
+--R - 587202560a x
+--R Type: Union(Expression(Integer),...)
+--E 486
+
+--S 487 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 7 \|b x + a - \|a 7 \|b x + a
+--R 9b log(------------------) + 9b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------------
+--R 2 +-+
+--R 2048a \|a
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 488
+
+)clear all
+
+--S 489 of 1369
+t0:=x^6*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 14 3 12 2 2 10 3 8 4 6 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 1369
+r0:=3/256*a^3*x^7*(a+b*x^2)^(3/2)+3/128*a^2*x^7*(a+b*x^2)^(5/2)+_
+ 9/224*a*x^7*(a+b*x^2)^(7/2)+1/16*x^7*(a+b*x^2)^(9/2)-_
+ 45/32768*a^8*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)+_
+ 45/32768*a^7*x*sqrt(a+b*x^2)/b^3-15/16384*a^6*x^3*_
+ sqrt(a+b*x^2)/b^2+3/4096*a^5*x^5*sqrt(a+b*x^2)/b+_
+ 9/2048*a^4*x^7*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 8 x\|b
+--R - 315a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 15 6 13 2 5 11 3 4 9 4 3 7
+--R 14336b x + 66560a b x + 119040a b x + 98432a b x + 32624a b x
+--R +
+--R 5 2 5 6 3 7
+--R 168a b x - 210a b x + 315a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 229376b \|b
+--R Type: Expression(Integer)
+--E 490
+
+--S 491 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 8 7 14 9 6 12 10 5 10 11 4 8
+--R 5040a b x + 211680a b x + 2540160a b x + 13305600a b x
+--R +
+--R 12 3 6 13 2 4 14 2 15
+--R 35481600a b x + 50319360a b x + 36126720a b x + 10321920a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 8 16 9 7 14 10 6 12 11 5 10
+--R - 315a b x - 40320a b x - 846720a b x - 6773760a b x
+--R +
+--R 12 4 8 13 3 6 14 2 4
+--R - 26611200a b x - 56770560a b x - 67092480a b x
+--R +
+--R 15 2 16
+--R - 41287680a b x - 10321920a
+--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 15 31 14 29 2 13 27
+--R - 14336b x - 1901568a b x - 47173888a b x
+--R +
+--R 3 12 25 4 11 23 5 10 21
+--R - 502530176a b x - 2975022960a b x - 11035277480a b x
+--R +
+--R 6 9 19 7 8 17 8 7 15
+--R - 27310058286a b x - 46527167547a b x - 55047454848a b x
+--R +
+--R 9 6 13 10 5 11 11 4 9
+--R - 44639228800a b x - 23770343424a b x - 7526059520a b x
+--R +
+--R 12 3 7 13 2 5 14 3
+--R - 1103085568a b x - 45072384a b x - 34406400a b x
+--R +
+--R 15
+--R - 10321920a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 15 31 14 29 2 13 27
+--R 229376b x + 10928128a b x + 172937216a b x
+--R +
+--R 3 12 25 4 11 23 5 10 21
+--R 1386100736a b x + 6676770560a b x + 21084247936a b x
+--R +
+--R 6 9 19 7 8 17 8 7 15
+--R 45737690208a b x + 69692308560a b x + 74823758928a b x
+--R +
+--R 9 6 13 10 5 11 11 4 9
+--R 55651554400a b x + 27397242752a b x + 8073715456a b x
+--R +
+--R 12 3 7 13 2 5 14 3 15
+--R 1121966080a b x + 60985344a b x + 39567360a b x + 10321920a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 10 14 9 12 2 8 10
+--R 3670016b x + 154140672a b x + 1849688064a b x
+--R +
+--R 3 7 8 4 6 6 5 5 4
+--R 9688842240a b x + 25836912640a b x + 36641439744a b x
+--R +
+--R 6 4 2 7 3
+--R 26306674688a b x + 7516192768a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 11 16 10 14 2 9 12
+--R - 229376b x - 29360128a b x - 616562688a b x
+--R +
+--R 3 8 10 4 7 8 5 6 6
+--R - 4932501504a b x - 19377684480a b x - 41339060224a b x
+--R +
+--R 6 5 4 7 4 2 8 3
+--R - 48855252992a b x - 30064771072a b x - 7516192768a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 8 7 14 9 6 12 10 5 10
+--R - 10080a b x - 423360a b x - 5080320a b x
+--R +
+--R 11 4 8 12 3 6 13 2 4
+--R - 26611200a b x - 70963200a b x - 100638720a b x
+--R +
+--R 14 2 15
+--R - 72253440a b x - 20643840a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 8 16 9 7 14 10 6 12 11 5 10
+--R 630a b x + 80640a b x + 1693440a b x + 13547520a b x
+--R +
+--R 12 4 8 13 3 6 14 2 4
+--R 53222400a b x + 113541120a b x + 134184960a b x
+--R +
+--R 15 2 16
+--R 82575360a b x + 20643840a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 15 31 14 29 2 13 27
+--R - 14336b x - 1901568a b x - 47173888a b x
+--R +
+--R 3 12 25 4 11 23 5 10 21
+--R - 502530176a b x - 2975022960a b x - 11035277480a b x
+--R +
+--R 6 9 19 7 8 17 8 7 15
+--R - 27310058286a b x - 46527167547a b x - 55047454848a b x
+--R +
+--R 9 6 13 10 5 11 11 4 9
+--R - 44639228800a b x - 23770343424a b x - 7526059520a b x
+--R +
+--R 12 3 7 13 2 5 14 3
+--R - 1103085568a b x - 45072384a b x - 34406400a b x
+--R +
+--R 15
+--R - 10321920a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 15 31 14 29 2 13 27
+--R 229376b x + 10928128a b x + 172937216a b x
+--R +
+--R 3 12 25 4 11 23 5 10 21
+--R 1386100736a b x + 6676770560a b x + 21084247936a b x
+--R +
+--R 6 9 19 7 8 17 8 7 15
+--R 45737690208a b x + 69692308560a b x + 74823758928a b x
+--R +
+--R 9 6 13 10 5 11 11 4 9
+--R 55651554400a b x + 27397242752a b x + 8073715456a b x
+--R +
+--R 12 3 7 13 2 5 14 3 15
+--R 1121966080a b x + 60985344a b x + 39567360a b x + 10321920a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 10 14 9 12 2 8 10
+--R 3670016b x + 154140672a b x + 1849688064a b x
+--R +
+--R 3 7 8 4 6 6 5 5 4
+--R 9688842240a b x + 25836912640a b x + 36641439744a b x
+--R +
+--R 6 4 2 7 3
+--R 26306674688a b x + 7516192768a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 11 16 10 14 2 9 12
+--R - 229376b x - 29360128a b x - 616562688a b x
+--R +
+--R 3 8 10 4 7 8 5 6 6
+--R - 4932501504a b x - 19377684480a b x - 41339060224a b x
+--R +
+--R 6 5 4 7 4 2 8 3
+--R - 48855252992a b x - 30064771072a b x - 7516192768a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 491
+
+--S 492 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 8 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R 45a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 8 x\|b
+--R 45a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 32768b \|b
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 8 +---+ x\|b 8 +-+ \|- b \|b x + a - \|- b \|a
+--R 45a \|- b atanh(-----------) - 90a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ---------------------------------------------------------------------------
+--R 3 +---+ +-+
+--R 32768b \|- b \|b
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 495
+
+)clear all
+
+--S 496 of 1369
+t0:=x^4*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 12 3 10 2 2 8 3 6 4 4 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 1369
+r0:=3/128*a^3*x^5*(a+b*x^2)^(3/2)+3/80*a^2*x^5*(a+b*x^2)^(5/2)+_
+ 3/56*a*x^5*(a+b*x^2)^(7/2)+1/14*x^5*(a+b*x^2)^(9/2)+_
+ 9/2048*a^7*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_
+ 9/2048*a^6*x*sqrt(a+b*x^2)/b^2+3/1024*a^5*x^3*sqrt(a+b*x^2)/b+_
+ 3/256*a^4*x^5*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 7 x\|b
+--R 315a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 13 5 11 2 4 9 3 3 7 4 2 5
+--R 5120b x + 24320a b x + 44928a b x + 39056a b x + 14168a b x
+--R +
+--R 5 3 6
+--R 210a b x - 315a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 2 +-+
+--R 71680b \|b
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 7 6 12 8 5 10 9 4 8 10 3 6
+--R 4410a b x + 141120a b x + 1270080a b x + 4838400a b x
+--R +
+--R 11 2 4 12 2 13
+--R 8870400a b x + 7741440a b x + 2580480a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 7 14 8 6 12 9 5 10 10 4 8
+--R - 315a b x - 30870a b x - 493920a b x - 2963520a b x
+--R +
+--R 11 3 6 12 2 4 13 2 14
+--R - 8467200a b x - 12418560a b x - 9031680a b x - 2580480a
+--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 13 27 12 25 2 11 23 3 10 21
+--R - 5120b x - 526080a b x - 10456448a b x - 90744720a b x
+--R +
+--R 4 9 19 5 8 17 6 7 15
+--R - 440716920a b x - 1340883586a b x - 2702931497a b x
+--R +
+--R 7 6 13 8 5 11 9 4 9
+--R - 3693903786a b x - 3409466400a b x - 2049104320a b x
+--R +
+--R 10 3 7 11 2 5 12 3 13
+--R - 725983488a b x - 109666816a b x + 7311360a b x + 2580480a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 13 27 12 25 2 11 23
+--R 71680b x + 2705920a b x + 34802432a b x
+--R +
+--R 3 10 21 4 9 19 5 8 17
+--R 229544160a b x + 913955504a b x + 2381177932a b x
+--R +
+--R 6 7 15 7 6 13 8 5 11
+--R 4226517442a b x + 5183442054a b x + 4350339840a b x
+--R +
+--R 9 4 9 10 3 7 11 2 5
+--R 2398031552a b x + 781569536a b x + 106333696a b x
+--R +
+--R 12 3 13
+--R - 8601600a b x - 2580480a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 8 12 7 10 2 6 8 3 5 6
+--R 1003520b x + 32112640a b x + 289013760a b x + 1101004800a b x
+--R +
+--R 4 4 4 5 3 2 6 2
+--R 2018508800a b x + 1761607680a b x + 587202560a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 9 14 8 12 2 7 10 3 6 8
+--R - 71680b x - 7024640a b x - 112394240a b x - 674365440a b x
+--R +
+--R 4 5 6 5 4 4 6 3 2
+--R - 1926758400a b x - 2825912320a b x - 2055208960a b x
+--R +
+--R 7 2
+--R - 587202560a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 7 6 12 8 5 10 9 4 8 10 3 6
+--R 8820a b x + 282240a b x + 2540160a b x + 9676800a b x
+--R +
+--R 11 2 4 12 2 13
+--R 17740800a b x + 15482880a b x + 5160960a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 7 14 8 6 12 9 5 10 10 4 8
+--R - 630a b x - 61740a b x - 987840a b x - 5927040a b x
+--R +
+--R 11 3 6 12 2 4 13 2 14
+--R - 16934400a b x - 24837120a b x - 18063360a b x - 5160960a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 13 27 12 25 2 11 23 3 10 21
+--R - 5120b x - 526080a b x - 10456448a b x - 90744720a b x
+--R +
+--R 4 9 19 5 8 17 6 7 15
+--R - 440716920a b x - 1340883586a b x - 2702931497a b x
+--R +
+--R 7 6 13 8 5 11 9 4 9
+--R - 3693903786a b x - 3409466400a b x - 2049104320a b x
+--R +
+--R 10 3 7 11 2 5 12 3 13
+--R - 725983488a b x - 109666816a b x + 7311360a b x + 2580480a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 13 27 12 25 2 11 23
+--R 71680b x + 2705920a b x + 34802432a b x
+--R +
+--R 3 10 21 4 9 19 5 8 17
+--R 229544160a b x + 913955504a b x + 2381177932a b x
+--R +
+--R 6 7 15 7 6 13 8 5 11
+--R 4226517442a b x + 5183442054a b x + 4350339840a b x
+--R +
+--R 9 4 9 10 3 7 11 2 5
+--R 2398031552a b x + 781569536a b x + 106333696a b x
+--R +
+--R 12 3 13
+--R - 8601600a b x - 2580480a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 8 12 7 10 2 6 8 3 5 6
+--R 1003520b x + 32112640a b x + 289013760a b x + 1101004800a b x
+--R +
+--R 4 4 4 5 3 2 6 2
+--R 2018508800a b x + 1761607680a b x + 587202560a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 9 14 8 12 2 7 10 3 6 8
+--R - 71680b x - 7024640a b x - 112394240a b x - 674365440a b x
+--R +
+--R 4 5 6 5 4 4 6 3 2
+--R - 1926758400a b x - 2825912320a b x - 2055208960a b x
+--R +
+--R 7 2
+--R - 587202560a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 498
+
+--S 499 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 7 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R 9a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 7 x\|b
+--R - 9a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 2048b \|b
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 500
+
+--S 501 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 7 +---+ x\|b 7 +-+ \|- b \|b x + a - \|- b \|a
+--R - 9a \|- b atanh(-----------) + 18a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ----------------------------------------------------------------------------
+--R 2 +---+ +-+
+--R 2048b \|- b \|b
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 502
+
+)clear all
+
+--S 503 of 1369
+t0:=x^2*(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 10 3 8 2 2 6 3 4 4 2 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 503
+
+--S 504 of 1369
+r0:=7/128*a^3*x^3*(a+b*x^2)^(3/2)+21/320*a^2*x^3*(a+b*x^2)^(5/2)+_
+ 3/40*a*x^3*(a+b*x^2)^(7/2)+1/12*x^3*(a+b*x^2)^(9/2)-_
+ 21/1024*a^6*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_
+ 21/1024*a^5*x*sqrt(a+b*x^2)/b+21/512*a^4*x^3*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 6 x\|b
+--R - 315a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 11 4 9 2 3 7 3 2 5 4 3
+--R 1280b x + 6272a b x + 12144a b x + 11432a b x + 4910a b x
+--R +
+--R 5
+--R 315a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R +-+
+--R 15360b\|b
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 6 5 10 7 4 8 8 3 6 9 2 4
+--R 3780a b x + 88200a b x + 564480a b x + 1451520a b x
+--R +
+--R 10 2 11
+--R 1612800a b x + 645120a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 6 12 7 5 10 8 4 8 9 3 6
+--R - 315a b x - 22680a b x - 264600a b x - 1128960a b x
+--R +
+--R 10 2 4 11 2 12
+--R - 2177280a b x - 1935360a b x - 645120a
+--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 11 23 10 21 2 9 19 3 8 17
+--R - 1280b x - 98432a b x - 1538928a b x - 10741800a b x
+--R +
+--R 4 7 15 5 6 13 6 5 11
+--R - 42355182a b x - 104697195a b x - 170215304a b x
+--R +
+--R 7 4 9 8 3 7 9 2 5
+--R - 184337816a b x - 130176000a b x - 55757056a b x
+--R +
+--R 10 3 11
+--R - 11991040a b x - 645120a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 11 23 10 21 2 9 19 3 8 17
+--R 15360b x + 449024a b x + 4629312a b x + 24870816a b x
+--R +
+--R 4 7 15 5 6 13 6 5 11
+--R 81152072a b x + 173035260a b x + 249146268a b x
+--R +
+--R 7 4 9 8 3 7 9 2 5
+--R 243180424a b x + 156595968a b x + 61671936a b x
+--R +
+--R 10 3 11
+--R 12313600a b x + 645120a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 6 10 5 8 2 4 6 3 3 4
+--R 184320b x + 4300800a b x + 27525120a b x + 70778880a b x
+--R +
+--R 4 2 2 5
+--R 78643200a b x + 31457280a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 7 12 6 10 2 5 8 3 4 6
+--R - 15360b x - 1105920a b x - 12902400a b x - 55050240a b x
+--R +
+--R 4 3 4 5 2 2 6
+--R - 106168320a b x - 94371840a b x - 31457280a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 6 5 10 7 4 8 8 3 6 9 2 4
+--R - 7560a b x - 176400a b x - 1128960a b x - 2903040a b x
+--R +
+--R 10 2 11
+--R - 3225600a b x - 1290240a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 6 12 7 5 10 8 4 8 9 3 6
+--R 630a b x + 45360a b x + 529200a b x + 2257920a b x
+--R +
+--R 10 2 4 11 2 12
+--R 4354560a b x + 3870720a b x + 1290240a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 11 23 10 21 2 9 19 3 8 17
+--R - 1280b x - 98432a b x - 1538928a b x - 10741800a b x
+--R +
+--R 4 7 15 5 6 13 6 5 11
+--R - 42355182a b x - 104697195a b x - 170215304a b x
+--R +
+--R 7 4 9 8 3 7 9 2 5
+--R - 184337816a b x - 130176000a b x - 55757056a b x
+--R +
+--R 10 3 11
+--R - 11991040a b x - 645120a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 11 23 10 21 2 9 19 3 8 17
+--R 15360b x + 449024a b x + 4629312a b x + 24870816a b x
+--R +
+--R 4 7 15 5 6 13 6 5 11
+--R 81152072a b x + 173035260a b x + 249146268a b x
+--R +
+--R 7 4 9 8 3 7 9 2 5
+--R 243180424a b x + 156595968a b x + 61671936a b x
+--R +
+--R 10 3 11
+--R 12313600a b x + 645120a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 6 10 5 8 2 4 6 3 3 4
+--R 184320b x + 4300800a b x + 27525120a b x + 70778880a b x
+--R +
+--R 4 2 2 5
+--R 78643200a b x + 31457280a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 7 12 6 10 2 5 8 3 4 6
+--R - 15360b x - 1105920a b x - 12902400a b x - 55050240a b x
+--R +
+--R 4 3 4 5 2 2 6
+--R - 106168320a b x - 94371840a b x - 31457280a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 505
+
+--S 506 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 6 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R 21a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 6 x\|b
+--R 21a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 1024b\|b
+--R Type: Expression(Integer)
+--E 506
+
+--S 507 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 507
+
+--S 508 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 6 +---+ x\|b 6 +-+ \|- b \|b x + a - \|- b \|a
+--R 21a \|- b atanh(-----------) - 42a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ---------------------------------------------------------------------------
+--R +---+ +-+
+--R 1024b\|- b \|b
+--R Type: Expression(Integer)
+--E 508
+
+--S 509 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 509
+
+)clear all
+
+--S 510 of 1369
+t0:=(a+b*x^2)^(9/2)
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (1) (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 510
+
+--S 511 of 1369
+r0:=21/128*a^3*x*(a+b*x^2)^(3/2)+21/160*a^2*x*(a+b*x^2)^(5/2)+_
+ 9/80*a*x*(a+b*x^2)^(7/2)+1/10*x*(a+b*x^2)^(9/2)+_
+ 63/256*a^5*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+_
+ 63/256*a^4*x*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 5 x\|b
+--R 315a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2
+--R (128b x + 656a b x + 1368a b x + 1490a b x + 965a x)\|b \|b x + a
+--R /
+--R +-+
+--R 1280\|b
+--R Type: Expression(Integer)
+--E 511
+
+--S 512 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R 3150a b x + 50400a b x + 211680a b x + 322560a b x
+--R +
+--R 9
+--R 161280a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R - 315a b x - 15750a b x - 126000a b x - 352800a b x
+--R +
+--R 9 2 10
+--R - 403200a b x - 161280a
+--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 19 8 17 2 7 15 3 6 13
+--R - 128b x - 7056a b x - 85368a b x - 475650a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7 7 2 5
+--R - 1521225a b x - 3081626a b x - 4141712a b x - 3688416a b x
+--R +
+--R 8 3 9
+--R - 1998080a b x - 494080a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 9 19 8 17 2 7 15 3 6 13
+--R 1280b x + 28320a b x + 231696a b x + 1010340a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7 7 2 5
+--R 2710310a b x + 4797010a b x + 5767040a b x + 4625696a b x
+--R +
+--R 8 3 9
+--R 2245120a b x + 494080a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 4 8 3 6 2 2 4 3 2 4
+--R (12800b x + 204800a b x + 860160a b x + 1310720a b x + 655360a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 2 5
+--R - 1638400a b x - 655360a
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R 6300a b x + 100800a b x + 423360a b x + 645120a b x
+--R +
+--R 9
+--R 322560a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R - 630a b x - 31500a b x - 252000a b x - 705600a b x
+--R +
+--R 9 2 10
+--R - 806400a b x - 322560a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 9 19 8 17 2 7 15 3 6 13
+--R - 128b x - 7056a b x - 85368a b x - 475650a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7 7 2 5
+--R - 1521225a b x - 3081626a b x - 4141712a b x - 3688416a b x
+--R +
+--R 8 3 9
+--R - 1998080a b x - 494080a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 9 19 8 17 2 7 15 3 6 13
+--R 1280b x + 28320a b x + 231696a b x + 1010340a b x
+--R +
+--R 4 5 11 5 4 9 6 3 7 7 2 5
+--R 2710310a b x + 4797010a b x + 5767040a b x + 4625696a b x
+--R +
+--R 8 3 9
+--R 2245120a b x + 494080a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 4 8 3 6 2 2 4 3 2 4
+--R (12800b x + 204800a b x + 860160a b x + 1310720a b x + 655360a )
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 2 5
+--R - 1638400a b x - 655360a
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 512
+
+--S 513 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 5 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R 63a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 5 x\|b
+--R - 63a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 256\|b
+--R Type: Expression(Integer)
+--E 513
+
+--S 514 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 514
+
+--S 515 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 5 +---+ x\|b
+--R - 63a \|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 5 +-+ \|- b \|b x + a - \|- b \|a
+--R 126a \|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 256\|- b \|b
+--R Type: Expression(Integer)
+--E 515
+
+--S 516 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 516
+
+)clear all
+
+--S 517 of 1369
+t0:=(a+b*x^2)^(9/2)/x^2
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 1369
+r0:=105/64*a^2*b*x*(a+b*x^2)^(3/2)+21/16*a*b*x*(a+b*x^2)^(5/2)+_
+ 9/8*b*x*(a+b*x^2)^(7/2)-(a+b*x^2)^(9/2)/x+_
+ 315/128*a^4*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+_
+ 315/128*a^3*b*x*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 4 +-+ x\|b
+--R 315a x\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (16b x + 88a b x + 210a b x + 325a b x - 128a )\|b x + a
+--R /
+--R 128x
+--R Type: Expression(Integer)
+--E 518
+
+--S 519 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 4 9 5 3 7 6 2 5 7 3 8
+--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x)
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 8
+--R - 80640a x
+--R *
+--R +-+ +-+
+--R \|a \|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 8 16 7 14 2 6 12 3 5 10
+--R - 144b x - 2712a b x - 19362a b x - 75357a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R - 183352a b x - 268528a b x - 185664a b x - 9472a b x + 32768a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 16b x + 744a b x + 8298a b x + 44583a b x + 143805a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 296280a b x + 358128a b x + 194496a b x - 6912a b x - 32768a
+--R /
+--R 4 9 3 7 2 2 5 3 3 4
+--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a x)
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (- 1152b x - 15360a b x - 55296a b x - 73728a b x - 32768a x)\|a
+--R ,
+--R
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 630a b x + 25200a b x + 151200a b x + 282240a b x
+--R +
+--R 8
+--R 161280a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x
+--R +
+--R 8
+--R - 161280a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 8 16 7 14 2 6 12 3 5 10
+--R - 144b x - 2712a b x - 19362a b x - 75357a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R - 183352a b x - 268528a b x - 185664a b x - 9472a b x + 32768a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 16b x + 744a b x + 8298a b x + 44583a b x + 143805a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 296280a b x + 358128a b x + 194496a b x - 6912a b x - 32768a
+--R /
+--R 4 9 3 7 2 2 5 3 3 4
+--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a x)
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (- 1152b x - 15360a b x - 55296a b x - 73728a b x - 32768a x)\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 519
+
+--S 520 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 4 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 315a \|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 4 +-+ x\|b
+--R - 315a \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 128
+--R Type: Expression(Integer)
+--E 520
+
+--S 521 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 521
+
+--S 522 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R 4 +-+ x\|b 4 +---+ \|b x + a - \|a
+--R - 315a \|b atanh(-----------) + 630a \|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R (6) -------------------------------------------------------------------
+--R 128
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 523
+
+)clear all
+
+--S 524 of 1369
+t0:=(a+b*x^2)^(9/2)/x^4
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 524
+
+--S 525 of 1369
+r0:=35/8*a*b^2*x*(a+b*x^2)^(3/2)+7/2*b^2*x*(a+b*x^2)^(5/2)-_
+ 3*b*(a+b*x^2)^(7/2)/x-1/3*(a+b*x^2)^(9/2)/x^3+_
+ 105/16*a^3*b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+_
+ 105/16*a^2*b^2*x*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 +-+ x\|b
+--R 315a b x \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (8b x + 50a b x + 165a b x - 208a b x - 16a )\|b x + a
+--R /
+--R 3
+--R 48x
+--R Type: Expression(Integer)
+--E 525
+
+--S 526 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 11 4 4 9 5 3 7 6 2 5
+--R 315a b x + 12600a b x + 75600a b x + 141120a b x
+--R +
+--R 7 3
+--R 80640a b x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 3 5 11 4 4 9 5 3 7 6 2 5
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 7 3
+--R - 80640a b x
+--R *
+--R +-+ +-+
+--R \|a \|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 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 72b x - 1410a b x - 10941a b x - 44136a b x - 77024a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 16064a b x + 84480a b x + 62464a b x + 4096a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 8b x + 378a b x + 4455a b x + 26061a b x + 77688a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 91872a b x - 18624a b x - 115200a b x - 64512a b x - 4096a
+--R /
+--R 4 11 3 9 2 2 7 3 5 4 3
+--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 11 3 9 2 2 7 3 5 4 3 +-+
+--R (- 432b x - 5760a b x - 20736a b x - 27648a b x - 12288a x )\|a
+--R ,
+--R
+--R 3 5 11 4 4 9 5 3 7 6 2 5
+--R 630a b x + 25200a b x + 151200a b x + 282240a b x
+--R +
+--R 7 3
+--R 161280a b x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 3 5 11 4 4 9 5 3 7 6 2 5
+--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x
+--R +
+--R 7 3
+--R - 161280a b x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 72b x - 1410a b x - 10941a b x - 44136a b x - 77024a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 16064a b x + 84480a b x + 62464a b x + 4096a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 8b x + 378a b x + 4455a b x + 26061a b x + 77688a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R 91872a b x - 18624a b x - 115200a b x - 64512a b x - 4096a
+--R /
+--R 4 11 3 9 2 2 7 3 5 4 3
+--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 11 3 9 2 2 7 3 5 4 3 +-+
+--R (- 432b x - 5760a b x - 20736a b x - 27648a b x - 12288a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 526
+
+--S 527 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 3 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 105a b\|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 +-+ x\|b
+--R - 105a b\|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 16
+--R Type: Expression(Integer)
+--E 527
+
+--S 528 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 528
+
+--S 529 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R 3 +-+ x\|b 3 +---+ \|b x + a - \|a
+--R - 105a b\|b atanh(-----------) + 210a b\|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R (6) ---------------------------------------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 530
+
+)clear all
+
+--S 531 of 1369
+t0:=(a+b*x^2)^(9/2)/x^6
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 531
+
+--S 532 of 1369
+r0:=21/4*b^3*x*(a+b*x^2)^(3/2)-21/5*b^2*(a+b*x^2)^(5/2)/x-_
+ 3/5*b*(a+b*x^2)^(7/2)/x^3-1/5*(a+b*x^2)^(9/2)/x^5+_
+ 63/8*a^2*b^(5/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+_
+ 63/8*a*b^3*x*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 5 +-+ x\|b
+--R 315a b x \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (10b x + 85a b x - 288a b x - 56a b x - 8a )\|b x + a
+--R /
+--R 5
+--R 40x
+--R Type: Expression(Integer)
+--E 532
+
+--S 533 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 6 13 3 5 11 4 4 9 5 3 7
+--R 315a b x + 12600a b x + 75600a b x + 141120a b x
+--R +
+--R 6 2 5
+--R 80640a b x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 2 6 13 3 5 11 4 4 9 5 3 7
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 6 2 5
+--R - 80640a b x
+--R *
+--R +-+ +-+
+--R \|a \|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 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 90b x - 1965a b x - 11928a b x - 7416a b x + 79688a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 169280a b x + 109440a b x + 18944a b x + 2048a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 10b x + 495a b x + 5997a b x + 18816a b x - 17424a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 151752a b x - 221760a b x - 118656a b x - 19968a b x - 2048a
+--R /
+--R 4 13 3 11 2 2 9 3 7 4 5
+--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 13 3 11 2 2 9 3 7 4 5 +-+
+--R (- 360b x - 4800a b x - 17280a b x - 23040a b x - 10240a x )\|a
+--R ,
+--R
+--R 2 6 13 3 5 11 4 4 9 5 3 7
+--R 630a b x + 25200a b x + 151200a b x + 282240a b x
+--R +
+--R 6 2 5
+--R 161280a b x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 2 6 13 3 5 11 4 4 9 5 3 7
+--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x
+--R +
+--R 6 2 5
+--R - 161280a b x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 90b x - 1965a b x - 11928a b x - 7416a b x + 79688a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 169280a b x + 109440a b x + 18944a b x + 2048a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 10b x + 495a b x + 5997a b x + 18816a b x - 17424a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 151752a b x - 221760a b x - 118656a b x - 19968a b x - 2048a
+--R /
+--R 4 13 3 11 2 2 9 3 7 4 5
+--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 13 3 11 2 2 9 3 7 4 5 +-+
+--R (- 360b x - 4800a b x - 17280a b x - 23040a b x - 10240a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 533
+
+--S 534 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 2 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 63a b \|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 2 +-+ x\|b
+--R - 63a b \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 8
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 535
+
+--S 536 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R 2 2 +-+ x\|b 2 2 +---+ \|b x + a - \|a
+--R - 63a b \|b atanh(-----------) + 126a b \|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R (6) ----------------------------------------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 536
+
+--S 537 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 537
+
+)clear all
+
+--S 538 of 1369
+t0:=(a+b*x^2)^(9/2)/x^8
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 538
+
+--S 539 of 1369
+r0:=-3*b^3*(a+b*x^2)^(3/2)/x-3/5*b^2*(a+b*x^2)^(5/2)/x^3-_
+ 9/35*b*(a+b*x^2)^(7/2)/x^5-1/7*(a+b*x^2)^(9/2)/x^7+_
+ 9/2*a*b^(7/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+9/2*b^4*x*sqrt(a+b*x^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 7 +-+ x\|b
+--R 315a b x \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (35b x - 388a b x - 156a b x - 58a b x - 10a )\|b x + a
+--R /
+--R 7
+--R 70x
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 7 15 2 6 13 3 5 11 4 4 9
+--R 315a b x + 12600a b x + 75600a b x + 141120a b x
+--R +
+--R 5 3 7
+--R 80640a b x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 15 2 6 13 3 5 11 4 4 9
+--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 5 3 7
+--R - 80640a b x
+--R *
+--R +-+ +-+
+--R \|a \|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 8 16 7 14 2 6 12 3 5 10
+--R - 315b x - 708a b x + 32844a b x + 166698a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R 288970a b x + 215440a b x + 77664a b x + 20608a b x + 2560a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 35b x + 1047a b x - 6264a b x - 91014a b x - 288372a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 388170a b x - 251856a b x - 87648a b x - 21888a b x - 2560a
+--R /
+--R 4 15 3 13 2 2 11 3 9 4 7
+--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 15 3 13 2 2 11 3 9 4 7 +-+
+--R (- 630b x - 8400a b x - 30240a b x - 40320a b x - 17920a x )\|a
+--R ,
+--R
+--R 7 15 2 6 13 3 5 11 4 4 9
+--R 630a b x + 25200a b x + 151200a b x + 282240a b x
+--R +
+--R 5 3 7
+--R 161280a b x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 15 2 6 13 3 5 11 4 4 9
+--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x
+--R +
+--R 5 3 7
+--R - 161280a b x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 8 16 7 14 2 6 12 3 5 10
+--R - 315b x - 708a b x + 32844a b x + 166698a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R 288970a b x + 215440a b x + 77664a b x + 20608a b x + 2560a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R 35b x + 1047a b x - 6264a b x - 91014a b x - 288372a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 388170a b x - 251856a b x - 87648a b x - 21888a b x - 2560a
+--R /
+--R 4 15 3 13 2 2 11 3 9 4 7
+--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 15 3 13 2 2 11 3 9 4 7 +-+
+--R (- 630b x - 8400a b x - 30240a b x - 40320a b x - 17920a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 540
+
+--S 541 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 3 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 9a b \|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 +-+ x\|b
+--R - 9a b \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 542
+
+--S 543 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R 3 +-+ x\|b 3 +---+ \|b x + a - \|a
+--R - 9a b \|b atanh(-----------) + 18a b \|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R (6) --------------------------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 543
+
+--S 544 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 544
+
+)clear all
+
+--S 545 of 1369
+t0:=(a+b*x^2)^(9/2)/x^10
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 545
+
+--S 546 of 1369
+r0:=-1/3*b^3*(a+b*x^2)^(3/2)/x^3-1/5*b^2*(a+b*x^2)^(5/2)/x^5-_
+ 1/7*b*(a+b*x^2)^(7/2)/x^7-1/9*(a+b*x^2)^(9/2)/x^9+_
+ b^(9/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))-b^4*sqrt(a+b*x^2)/x
+--R
+--R
+--R (2)
+--R +-+
+--R 4 9 +-+ x\|b
+--R 315b x \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (- 563b x - 506a b x - 408a b x - 185a b x - 35a )\|b x + a
+--R /
+--R 9
+--R 315x
+--R Type: Expression(Integer)
+--E 546
+
+--S 547 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 8 17 7 15 2 6 13 3 5 11
+--R 315b x + 12600a b x + 75600a b x + 141120a b x
+--R +
+--R 4 4 9
+--R 80640a b x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R - 2835b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 4 4 9
+--R - 80640a b x
+--R *
+--R +-+ +-+
+--R \|a \|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 8 16 7 14 2 6 12 3 5 10
+--R 5067b x + 72114a b x + 307608a b x + 593505a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R 634355a b x + 448664a b x + 226128a b x + 67520a b x + 8960a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12
+--R - 563b x - 23589a b x - 178794a b x - 545937a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R - 866340a b x - 834291a b x - 553848a b x - 258768a b x
+--R +
+--R 8 2 9
+--R - 72000a b x - 8960a
+--R /
+--R 4 17 3 15 2 2 13 3 11 4 9
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 17 3 15 2 2 13 3 11
+--R - 2835b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 4 9
+--R - 80640a x
+--R *
+--R +-+
+--R \|a
+--R ,
+--R
+--R 8 17 7 15 2 6 13 3 5 11
+--R 630b x + 25200a b x + 151200a b x + 282240a b x
+--R +
+--R 4 4 9
+--R 161280a b x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R - 5670b x - 75600a b x - 272160a b x - 362880a b x
+--R +
+--R 4 4 9
+--R - 161280a b x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R 8 16 7 14 2 6 12 3 5 10
+--R 5067b x + 72114a b x + 307608a b x + 593505a b x
+--R +
+--R 4 4 8 5 3 6 6 2 4 7 2 8
+--R 634355a b x + 448664a b x + 226128a b x + 67520a b x + 8960a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12
+--R - 563b x - 23589a b x - 178794a b x - 545937a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R - 866340a b x - 834291a b x - 553848a b x - 258768a b x
+--R +
+--R 8 2 9
+--R - 72000a b x - 8960a
+--R /
+--R 4 17 3 15 2 2 13 3 11 4 9
+--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 17 3 15 2 2 13 3 11
+--R - 2835b x - 37800a b x - 136080a b x - 181440a b x
+--R +
+--R 4 9
+--R - 80640a x
+--R *
+--R +-+
+--R \|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 547
+
+--S 548 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R 4 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R b \|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 4 +-+ x\|b
+--R - b \|b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 548
+
+--S 549 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 +-+
+--R 4 +-+ x\|b 4 +---+ \|b x + a - \|a
+--R (6) - b \|b atanh(-----------) + 2b \|- b atan(------------------)
+--R +--------+ +---+
+--R | 2 x\|- b
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 550
+
+--S 551 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 551
+
+)clear all
+
+--S 552 of 1369
+t0:=(a+b*x^2)^(9/2)/x^12
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 12
+--R x
+--R Type: Expression(Integer)
+--E 552
+
+--S 553 of 1369
+r0:=-1/11*(a+b*x^2)^(11/2)/(a*x^11)
+--R
+--R
+--R +--------+
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2
+--R (- b x - 5a b x - 10a b x - 10a b x - 5a b x - a )\|b x + a
+--R (2) -------------------------------------------------------------------
+--R 11
+--R 11a x
+--R Type: Expression(Integer)
+--E 553
+
+--S 554 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12
+--R 11b x + 275a b x + 2442a b x + 11286a b x + 31471a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2
+--R 56695a b x + 67820a b x + 53712a b x + 27136a b x + 7936a b x
+--R +
+--R 10
+--R 1024a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 11 22 10 20 2 9 18 3 8 16 4 7 14
+--R - b x - 66a b x - 935a b x - 6072a b x - 22671a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8 8 3 6 9 2 4
+--R - 53834a b x - 85305a b x - 91740a b x - 66352a b x - 30976a b x
+--R +
+--R 10 2 11
+--R - 8448a b x - 1024a
+--R /
+--R 5 21 2 4 19 3 3 17 4 2 15 5 13
+--R 11a b x + 660a b x + 6160a b x + 19712a b x + 25344a b x
+--R +
+--R 6 11
+--R 11264a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 21 2 4 19 3 3 17 4 2 15
+--R - 121a b x - 2420a b x - 13552a b x - 30976a b x
+--R +
+--R 5 13 6 11
+--R - 30976a b x - 11264a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 554
+
+--S 555 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 555
+
+--S 556 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 556
+
+)clear all
+
+--S 557 of 1369
+t0:=(a+b*x^2)^(9/2)/x^14
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 14
+--R x
+--R Type: Expression(Integer)
+--E 557
+
+--S 558 of 1369
+r0:=-1/13*(a+b*x^2)^(11/2)/(a*x^13)+2/143*b*(a+b*x^2)^(11/2)/(a^2*x^11)
+--R
+--R
+--R (2)
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6
+--R (2b x - a b x - 35a b x - 90a b x - 100a b x - 53a b x - 11a )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 13
+--R 143a x
+--R Type: Expression(Integer)
+--E 558
+
+--S 559 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 12 24 11 22 2 10 20 3 9 18 4 8 16
+--R - 26b x - 715a b x - 5005a b x - 3146a b x + 112684a b x
+--R +
+--R 5 7 14 6 6 12 7 5 10 8 4 8
+--R 638625a b x + 1796715a b x + 3124356a b x + 3566624a b x
+--R +
+--R 9 3 6 10 2 4 11 2 12
+--R 2691584a b x + 1298176a b x + 363520a b x + 45056a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 13 26 12 24 2 11 22 3 10 20 4 9 18
+--R 2b x + 169a b x + 2288a b x + 8723a b x - 22594a b x
+--R +
+--R 5 8 16 6 7 14 7 6 12 8 5 10
+--R - 315601a b x - 1292980a b x - 3039595a b x - 4639388a b x
+--R +
+--R 9 4 8 10 3 6 11 2 4 12 2
+--R - 4771104a b x - 3298048a b x - 1474304a b x - 386048a b x
+--R +
+--R 13
+--R - 45056a
+--R /
+--R 2 6 25 3 5 23 4 4 21 5 3 19
+--R 143a b x + 12012a b x + 160160a b x + 768768a b x
+--R +
+--R 6 2 17 7 15 8 13
+--R 1647360a b x + 1610752a b x + 585728a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 6 25 3 5 23 4 4 21 5 3 19
+--R - 1859a b x - 52052a b x - 416416a b x - 1427712a b x
+--R +
+--R 6 2 17 7 15 8 13
+--R - 2379520a b x - 1903616a b x - 585728a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 559
+
+--S 560 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 560
+
+--S 561 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 561
+
+)clear all
+
+--S 562 of 1369
+t0:=(a+b*x^2)^(9/2)/x^16
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 16
+--R x
+--R Type: Expression(Integer)
+--E 562
+
+--S 563 of 1369
+r0:=-1/15*(a+b*x^2)^(11/2)/(a*x^15)+4/195*b*(a+b*x^2)^(11/2)/(a^2*x^13)-_
+ 8/2145*b^2*(a+b*x^2)^(11/2)/(a^3*x^11)
+--R
+--R
+--R (2)
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R - 8b x + 4a b x - 3a b x - 355a b x - 1030a b x - 1218a b x
+--R +
+--R 6 2 7
+--R - 671a b x - 143a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 15
+--R 2145a x
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 14 28 13 26 2 12 24 3 11 22
+--R 120b x + 4420a b x + 46189a b x + 213213a b x
+--R +
+--R 4 10 20 5 9 18 6 8 16 7 7 14
+--R 680394a b x + 3284190a b x + 17479665a b x + 62562161a b x
+--R +
+--R 8 6 12 9 5 10 10 4 8
+--R 144564272a b x + 222722016a b x + 232707200a b x
+--R +
+--R 11 3 6 12 2 4 13 2 14
+--R 163616000a b x + 74360832a b x + 19779584a b x + 2342912a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 15 30 14 28 2 13 26 3 12 24 4 11 22
+--R - 8b x - 900a b x - 16575a b x - 115830a b x - 431145a b x
+--R +
+--R 5 10 20 6 9 18 7 8 16 8 7 14
+--R - 1575288a b x - 8511425a b x - 38757150a b x - 116822415a b x
+--R +
+--R 9 6 12 10 5 10 11 4 8
+--R - 234650960a b x - 322562592a b x - 306364800a b x
+--R +
+--R 12 3 6 13 2 4 14 2 15
+--R - 198470400a b x - 83957760a b x - 20951040a b x - 2342912a
+--R /
+--R 3 7 29 4 6 27 5 5 25 6 4 23
+--R 2145a b x + 240240a b x + 4324320a b x + 28828800a b x
+--R +
+--R 7 3 21 8 2 19 9 17 10 15
+--R 90604800a b x + 144967680a b x + 114216960a b x + 35143680a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 7 29 4 6 27 5 5 25 6 4 23
+--R - 32175a b x - 1201200a b x - 12972960a b x - 61776000a b x
+--R +
+--R 7 3 21 8 2 19 9 17
+--R - 151008000a b x - 197683200a b x - 131788800a b x
+--R +
+--R 10 15
+--R - 35143680a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 564
+
+--S 565 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 565
+
+--S 566 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 566
+
+)clear all
+
+--S 567 of 1369
+t0:=(a+b*x^2)^(9/2)/x^18
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 18
+--R x
+--R Type: Expression(Integer)
+--E 567
+
+--S 568 of 1369
+r0:=-1/17*(a+b*x^2)^(11/2)/(a*x^17)+2/85*b*(a+b*x^2)^(11/2)/(a^2*x^15)-_
+ 8/1105*b^2*(a+b*x^2)^(11/2)/(a^3*x^13)+_
+ 16/12155*b^3*(a+b*x^2)^(11/2)/(a^4*x^11)
+--R
+--R
+--R (2)
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R 16b x - 8a b x + 6a b x - 5a b x - 1515a b x - 4714a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 5808a b x - 3289a b x - 715a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4 17
+--R 12155a x
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 16 32 15 30 2 14 28 3 13 26
+--R - 272b x - 12920a b x - 176358a b x - 1062347a b x
+--R +
+--R 4 12 24 5 11 22 6 10 20
+--R - 3294005a b x - 4384198a b x + 15997680a b x
+--R +
+--R 7 9 18 8 8 16 9 7 14
+--R 165361193a b x + 770698027a b x + 2270552240a b x
+--R +
+--R 10 6 12 11 5 10 12 4 8
+--R 4507588448a b x + 6187359360a b x + 5902996736a b x
+--R +
+--R 13 3 6 14 2 4 15 2 16
+--R 3853379584a b x + 1645219840a b x + 414695424a b x + 46858240a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 17 34 16 32 2 15 30 3 14 28
+--R 16b x + 2312a b x + 54910a b x + 499681a b x
+--R +
+--R 4 13 26 5 12 24 6 11 22 7 10 20
+--R 2255968a b x + 5418699a b x + 2068118a b x - 60942025a b x
+--R +
+--R 8 9 18 9 8 16 10 7 14
+--R - 410899316a b x - 1576344363a b x - 4006578224a b x
+--R +
+--R 11 6 12 12 5 10 13 4 8
+--R - 7050341728a b x - 8745093760a b x - 7648122112a b x
+--R +
+--R 14 3 6 15 2 4 16 2 17
+--R - 4627081216a b x - 1846710272a b x - 438124544a b x - 46858240a
+--R /
+--R 4 8 33 5 7 31 6 6 29 7 5 27
+--R 12155a b x + 1750320a b x + 40840800a b x + 359399040a b x
+--R +
+--R 8 4 25 9 3 23 10 2 21
+--R 1540281600a b x + 3559761920a b x + 4530606080a b x
+--R +
+--R 11 19 12 17
+--R 2987212800a b x + 796590080a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 8 33 5 7 31 6 6 29
+--R - 206635a b x - 9918480a b x - 138858720a b x
+--R +
+--R 7 5 27 8 4 25 9 3 23
+--R - 872826240a b x - 2909420800a b x - 5501450240a b x
+--R +
+--R 10 2 21 11 19 12 17
+--R - 5924638720a b x - 3385507840a b x - 796590080a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 569
+
+--S 570 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 570
+
+--S 571 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 571
+
+)clear all
+
+--S 572 of 1369
+t0:=(a+b*x^2)^(9/2)/x^20
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 20
+--R x
+--R Type: Expression(Integer)
+--E 572
+
+--S 573 of 1369
+r0:=-1/19*(a+b*x^2)^(11/2)/(a*x^19)+8/323*b*(a+b*x^2)^(11/2)/(a^2*x^17)-_
+ 16/1615*b^2*(a+b*x^2)^(11/2)/(a^3*x^15)+_
+ 64/20995*b^3*(a+b*x^2)^(11/2)/(a^4*x^13)-_
+ 128/230945*b^4*(a+b*x^2)^(11/2)/(a^5*x^11)
+--R
+--R
+--R (2)
+--R 9 18 8 16 2 7 14 3 6 12 4 5 10
+--R - 128b x + 64a b x - 48a b x + 40a b x - 35a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 23063a b x - 75086a b x - 95238a b x - 55055a b x - 12155a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 5 19
+--R 230945a x
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 18 36 17 34 2 16 32 3 15 30
+--R 2432b x + 144704a b x + 2496144a b x + 19315400a b x
+--R +
+--R 4 14 28 5 13 26 6 12 24
+--R 79676025a b x + 189488273a b x + 290726486a b x
+--R +
+--R 7 11 22 8 10 20 9 9 18
+--R 757364586a b x + 5402299925a b x + 30093982765a b x
+--R +
+--R 10 8 16 11 7 14 12 6 12
+--R 109503200092a b x + 271133170464a b x + 470853839872a b x
+--R +
+--R 13 5 10 14 4 8 15 3 6
+--R 581060791040a b x + 508200770560a b x + 308487663616a b x
+--R +
+--R 16 2 4 17 2 18
+--R 123790098432a b x + 29567549440a b x + 3186360320a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 19 38 18 36 2 17 34 3 16 32
+--R - 128b x - 23104a b x - 687344a b x - 7904456a b x
+--R +
+--R 4 15 30 5 14 28 6 13 26
+--R - 45874075a b x - 151407542a b x - 303583501a b x
+--R +
+--R 7 12 24 8 11 22 9 10 20
+--R - 496668056a b x - 2160128069a b x - 14423898830a b x
+--R +
+--R 10 9 18 11 8 16 12 7 14
+--R - 66896650403a b x - 209009021884a b x - 456469602784a b x
+--R +
+--R 13 6 12 14 5 10 15 4 8
+--R - 713047209728a b x - 803269244160a b x - 648694344704a b x
+--R +
+--R 16 3 6 17 2 4 18 2
+--R - 366885916672a b x - 138175578112a b x - 31160729600a b x
+--R +
+--R 19
+--R - 3186360320a
+--R /
+--R 5 9 37 6 8 35 7 7 33
+--R 230945a b x + 41570100a b x + 1219389600a b x
+--R +
+--R 8 6 31 9 5 29 10 4 27
+--R 13657163520a b x + 76089911040a b x + 236724167680a b x
+--R +
+--R 11 3 25 12 2 23 13 21
+--R 430407577600a b x + 454056345600a b x + 257298595840a b x
+--R +
+--R 14 19
+--R 60540846080a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 9 37 6 8 35 7 7 33
+--R - 4387955a b x - 263277300a b x - 4633680480a b x
+--R +
+--R 8 6 31 9 5 29 10 4 27
+--R - 37069443840a b x - 160634256640a b x - 408887198720a b x
+--R +
+--R 11 3 25 12 2 23 13 21
+--R - 629057228800a b x - 575138037760a b x - 287569018880a b x
+--R +
+--R 14 19
+--R - 60540846080a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 574
+
+--S 575 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 575
+
+--S 576 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 576
+
+)clear all
+
+--S 577 of 1369
+t0:=(a+b*x^2)^(9/2)/x^22
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 22
+--R x
+--R Type: Expression(Integer)
+--E 577
+
+--S 578 of 1369
+r0:=-1/21*(a+b*x^2)^(11/2)/(a*x^21)+10/399*b*(a+b*x^2)^(11/2)/(a^2*x^19)-_
+ 80/6783*b^2*(a+b*x^2)^(11/2)/(a^3*x^17)+_
+ 32/6783*b^3*(a+b*x^2)^(11/2)/(a^4*x^15)-_
+ 128/88179*b^4*(a+b*x^2)^(11/2)/(a^5*x^13)+_
+ 256/969969*b^5*(a+b*x^2)^(11/2)/(a^6*x^11)
+--R
+--R
+--R (2)
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10
+--R 256b x - 128a b x + 96a b x - 80a b x + 70a b x - 63a b x
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R - 80773a b x - 271414a b x - 351780a b x - 206635a b x - 46189a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 6 21
+--R 969969a x
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 20 40 19 38 2 18 36 3 17 34
+--R - 5376b x - 391552a b x - 8320480a b x - 80233200a b x
+--R +
+--R 4 16 32 5 15 30 6 14 28
+--R - 420109950a b x - 1302340845a b x - 2477759163a b x
+--R +
+--R 7 13 26 8 12 24 9 11 22
+--R - 2762521454a b x + 1146576508a b x + 35531078583a b x
+--R +
+--R 10 10 20 11 9 18 12 8 16
+--R 246355890781a b x + 1084155358468a b x + 3267141080112a b x
+--R +
+--R 13 7 14 14 6 12
+--R 6979808804864a b x + 10766293094144a b x
+--R +
+--R 15 5 10 16 4 8 17 3 6
+--R 12052957185024a b x + 9715313721344a b x + 5501035544576a b x
+--R +
+--R 18 2 4 19 2 20
+--R 2078509694976a b x + 470944055296a b x + 48432676864a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 21 42 20 40 2 19 38 3 18 36
+--R 256b x + 56448a b x + 2055648a b x + 29121680a b x
+--R +
+--R 4 17 34 5 16 32 6 15 30
+--R 210612150a b x + 882230895a b x + 2279015648a b x
+--R +
+--R 7 14 28 8 13 26 9 12 24
+--R 3701049957a b x + 3078383154a b x - 9508799223a b x
+--R +
+--R 10 11 22 11 10 20 12 9 18
+--R - 105171174108a b x - 592170549789a b x - 2228017774892a b x
+--R +
+--R 13 8 16 14 7 14 15 6 12
+--R - 5899811852592a b x - 11296615236864a b x - 15852864536320a b x
+--R +
+--R 16 5 10 17 4 8 18 3 6
+--R - 16335819537408a b x - 12233559883776a b x - 6484449427456a b x
+--R +
+--R 19 2 4 20 2 21
+--R - 2307927638016a b x - 495160393728a b x - 48432676864a
+--R /
+--R 6 10 41 7 9 39 8 8 37
+--R 969969a b x + 213393180a b x + 7682154480a b x
+--R +
+--R 9 7 35 10 6 33 11 5 31
+--R 106525875456a b x + 745681128192a b x + 2982724512768a b x
+--R +
+--R 12 4 29 13 3 27
+--R 7230847303680a b x + 10806541025280a b x
+--R +
+--R 14 2 25 15 23 16 21
+--R 9725886922752a b x + 4831159517184a b x + 1017086214144a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 10 41 7 9 39 8 8 37
+--R - 20369349a b x - 1493752260a b x - 32265048816a b x
+--R +
+--R 9 7 35 10 6 33 11 5 31
+--R - 319577626368a b x - 1739922632448a b x - 5694292251648a b x
+--R +
+--R 12 4 29 13 3 27
+--R - 11680599490560a b x - 15129157435392a b x
+--R +
+--R 14 2 25 15 23 16 21
+--R - 12014330904576a b x - 5339702624256a b x - 1017086214144a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 579
+
+--S 580 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 580
+
+--S 581 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 581
+
+)clear all
+
+--S 582 of 1369
+t0:=(a+b*x^2)^(9/2)/x^24
+--R
+--R
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R (1) ----------------------------------------------------
+--R 24
+--R x
+--R Type: Expression(Integer)
+--E 582
+
+--S 583 of 1369
+r0:=-1/23*(a+b*x^2)^(11/2)/(a*x^23)+4/161*b*(a+b*x^2)^(11/2)/(a^2*x^21)-_
+ 40/3059*b^2*(a+b*x^2)^(11/2)/(a^3*x^19)+_
+ 320/52003*b^3*(a+b*x^2)^(11/2)/(a^4*x^17)-_
+ 128/52003*b^4*(a+b*x^2)^(11/2)/(a^5*x^15)+_
+ 512/676039*b^5*(a+b*x^2)^(11/2)/(a^6*x^13)-_
+ 1024/7436429*b^6*(a+b*x^2)^(11/2)/(a^7*x^11)
+--R
+--R
+--R (2)
+--R 11 22 10 20 2 9 18 3 8 16 4 7 14
+--R - 1024b x + 512a b x - 384a b x + 320a b x - 280a b x
+--R +
+--R 5 6 12 6 5 10 7 4 8 8 3 6 9 2 4
+--R 252a b x - 231a b x - 530959a b x - 1826110a b x - 2406690a b x
+--R +
+--R 10 2 11
+--R - 1431859a b x - 323323a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 7 23
+--R 7436429a x
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 22 44 21 42 2 20 40 3 19 38
+--R 23552b x + 2060800a b x + 52859520a b x + 620470080a b x
+--R +
+--R 4 18 36 5 17 34 6 16 32
+--R 4007202600a b x + 15628090140a b x + 38569325025a b x
+--R +
+--R 7 15 30 8 14 28 9 13 26
+--R 61172146673a b x + 62501873434a b x + 68498444014a b x
+--R +
+--R 10 12 24 11 11 22
+--R 447722087813a b x + 3519807368805a b x
+--R +
+--R 12 10 20 13 9 18
+--R 18390187227048a b x + 66180088214128a b x
+--R +
+--R 14 8 16 15 7 14
+--R 170212073470272a b x + 319842513071872a b x
+--R +
+--R 16 6 12 17 5 10
+--R 443676599296000a b x + 454256483090432a b x
+--R +
+--R 18 4 8 19 3 6
+--R 339251670810624a b x + 179812413800448a b x
+--R +
+--R 20 2 4 21 2 22
+--R 64121040535552a b x + 13803312906240a b x + 1356114952192a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 23 46 22 44 2 21 42 3 20 40
+--R - 1024b x - 270848a b x - 11849600a b x - 202628160a b x
+--R +
+--R 4 19 38 5 18 36 6 17 34
+--R - 1783851480a b x - 9216565980a b x - 29953839435a b x
+--R +
+--R 7 16 32 8 15 30 9 14 28
+--R - 63364422286a b x - 88059985805a b x - 85139238184a b x
+--R +
+--R 10 13 26 11 12 24 12 11 22
+--R - 172487832517a b x - 1389299606422a b x - 9097536087003a b x
+--R +
+--R 13 10 20 14 9 18
+--R - 40522439458872a b x - 127747340088848a b x
+--R +
+--R 15 8 16 16 7 14
+--R - 293619192660032a b x - 500570144755968a b x
+--R +
+--R 17 6 12 18 5 10
+--R - 637481553092608a b x - 604911221161984a b x
+--R +
+--R 19 4 8 20 3 6 21 2 4
+--R - 421952481460224a b x - 210232277139456a b x - 70853182619648a b x
+--R +
+--R 22 2 23
+--R - 14481370382336a b x - 1356114952192a
+--R /
+--R 7 11 45 8 10 43 9 9 41
+--R 7436429a b x + 1963217256a b x + 85072747760a b x
+--R +
+--R 10 8 39 11 7 37
+--R 1429222162368a b x + 12250475677440a b x
+--R +
+--R 12 6 35 13 5 33
+--R 60980145594368a b x + 188484086382592a b x
+--R +
+--R 14 4 31 15 3 29
+--R 372825665372160a b x + 472245842804736a b x
+--R +
+--R 16 2 27 17 25
+--R 370388896317440a b x + 163750880477184a b x
+--R +
+--R 18 23
+--R 31190643900416a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 11 45 8 10 43 9 9 41
+--R - 171037867a b x - 15051332296a b x - 391334639696a b x
+--R +
+--R 10 8 39 11 7 37
+--R - 4696015676352a b x - 31306771175680a b x
+--R +
+--R 12 6 35 13 5 33
+--R - 127503940788224a b x - 333471845138432a b x
+--R +
+--R 14 4 31 15 3 29
+--R - 571666020237312a b x - 638920846147584a b x
+--R +
+--R 16 2 27 17 25
+--R - 448365506068480a b x - 179346202427392a b x
+--R +
+--R 18 23
+--R - 31190643900416a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 584
+
+--S 585 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 585
+
+--S 586 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 586
+
+)clear all
+
+--S 587 of 1369
+t0:=x^5*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R 5 | 2
+--R (1) x \|4x + 9
+--R Type: Expression(Integer)
+--E 587
+
+--S 588 of 1369
+r0:=27/64*(9+4*x^2)^(3/2)-9/160*(9+4*x^2)^(5/2)+1/448*(9+4*x^2)^(7/2)
+--R
+--R
+--R +-------+
+--R 6 4 2 | 2
+--R (40x + 18x - 54x + 243)\|4x + 9
+--R (2) ------------------------------------
+--R 280
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 13 11 9 7 5
+--R - 327680x - 1437696x - 1589760x - 1310256x - 6062364x
+--R +
+--R 3
+--R - 8266860x - 2480058x
+--R *
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R +
+--R 14 12 10 8 6 4
+--R 655360x + 3612672x + 5999616x + 4844448x + 14451696x + 28934010x
+--R +
+--R 2
+--R 17360406x + 1594323
+--R /
+--R +-------+
+--R 6 4 2 | 2 7
+--R (1146880x + 3225600x + 2177280x + 204120)\|4x + 9 - 2293760x
+--R +
+--R 5 3
+--R - 9031680x - 10160640x - 2857680x
+--R Type: Union(Expression(Integer),...)
+--E 589
+
+--S 590 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 590
+
+--S 591 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 591
+
+)clear all
+
+--S 592 of 1369
+t0:=x^4*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R 4 | 2
+--R (1) x \|4x + 9
+--R Type: Expression(Integer)
+--E 592
+
+--S 593 of 1369
+r0:=729/512*asinh(2/3*x)-81/256*x*sqrt(9+4*x^2)+_
+ 3/32*x^3*sqrt(9+4*x^2)+1/6*x^5*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R 5 3 | 2 2x
+--R (256x + 144x - 486x)\|4x + 9 + 2187asinh(--)
+--R 3
+--R (2) ------------------------------------------------
+--R 1536
+--R Type: Expression(Integer)
+--E 593
+
+--S 594 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 5 3 | 2 6
+--R (- 2239488x - 5038848x - 2125764x)\|4x + 9 + 4478976x
+--R +
+--R 4 2
+--R 15116544x + 12754584x + 1594323
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x + 9 - 2x)
+--R +
+--R 11 9 7 5 3
+--R (- 524288x - 2064384x - 1492992x + 2332800x + 2729376x + 354294x)
+--R *
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R +
+--R 12 10 8 6 4 2
+--R 1048576x + 5308416x + 6967296x - 3172608x - 10707552x - 4251528x
+--R /
+--R +-------+
+--R 5 3 | 2 6 4
+--R (1572864x + 3538944x + 1492992x)\|4x + 9 - 3145728x - 10616832x
+--R +
+--R 2
+--R - 8957952x - 1119744
+--R Type: Union(Expression(Integer),...)
+--E 594
+
+--S 595 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R - 729log(\|4x + 9 - 2x) - 729asinh(--)
+--R 3
+--R (4) ----------------------------------------
+--R 512
+--R Type: Expression(Integer)
+--E 595
+
+--S 596 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 596
+
+)clear all
+
+--S 597 of 1369
+t0:=x^3*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R 3 | 2
+--R (1) x \|4x + 9
+--R Type: Expression(Integer)
+--E 597
+
+--S 598 of 1369
+r0:=-3/16*(9+4*x^2)^(3/2)+1/80*(9+4*x^2)^(5/2)
+--R
+--R
+--R +-------+
+--R 4 2 | 2
+--R (8x + 6x - 27)\|4x + 9
+--R (2) --------------------------
+--R 40
+--R Type: Expression(Integer)
+--E 598
+
+--S 599 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 9 7 5 3 | 2 10
+--R (- 4096x - 14592x - 1296x + 34020x + 21870x)\|4x + 9 + 8192x
+--R +
+--R 8 6 4 2
+--R 38400x + 30240x - 77760x - 109350x - 19683
+--R /
+--R +-------+
+--R 4 2 | 2 5 3
+--R (10240x + 17280x + 3240)\|4x + 9 - 20480x - 57600x - 32400x
+--R Type: Union(Expression(Integer),...)
+--E 599
+
+--S 600 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 600
+
+--S 601 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 601
+
+)clear all
+
+--S 602 of 1369
+t0:=x^2*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (1) x \|4x + 9
+--R Type: Expression(Integer)
+--E 602
+
+--S 603 of 1369
+r0:=-81/64*asinh(2/3*x)+9/32*x*sqrt(9+4*x^2)+1/4*x^3*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R 3 | 2 2x
+--R (16x + 18x)\|4x + 9 - 81asinh(--)
+--R 3
+--R (2) ------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 603
+
+--S 604 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 3 | 2 4 2
+--R ((5184x + 5832x)\|4x + 9 - 10368x - 23328x - 6561)
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x + 9 - 2x)
+--R +
+--R +-------+
+--R 7 5 3 | 2 8 6
+--R (- 2048x - 6912x - 6480x - 1458x)\|4x + 9 + 4096x + 18432x
+--R +
+--R 4 2
+--R 25920x + 11664x
+--R /
+--R +-------+
+--R 3 | 2 4 2
+--R (4096x + 4608x)\|4x + 9 - 8192x - 18432x - 5184
+--R Type: Union(Expression(Integer),...)
+--E 604
+
+--S 605 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R 81log(\|4x + 9 - 2x) + 81asinh(--)
+--R 3
+--R (4) ------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 605
+
+--S 606 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 606
+
+)clear all
+
+--S 607 of 1369
+t0:=x*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R (1) x\|4x + 9
+--R Type: Expression(Integer)
+--E 607
+
+--S 608 of 1369
+r0:=1/12*(9+4*x^2)^(3/2)
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (4x + 9)\|4x + 9
+--R (2) -------------------
+--R 12
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 5 3 | 2 6 4 2
+--R (- 128x - 504x - 486x)\|4x + 9 + 256x + 1296x + 1944x + 729
+--R (3) ------------------------------------------------------------------
+--R +-------+
+--R 2 | 2 3
+--R (192x + 108)\|4x + 9 - 384x - 648x
+--R Type: Union(Expression(Integer),...)
+--E 609
+
+--S 610 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 610
+
+--S 611 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 611
+
+)clear all
+
+--S 612 of 1369
+t0:=sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R (1) \|4x + 9
+--R Type: Expression(Integer)
+--E 612
+
+--S 613 of 1369
+r0:=9/4*asinh(2/3*x)+1/2*x*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R 2x\|4x + 9 + 9asinh(--)
+--R 3
+--R (2) -------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 613
+
+--S 614 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R | 2 2 | 2
+--R (- 36x\|4x + 9 + 72x + 81)log(\|4x + 9 - 2x)
+--R +
+--R +-------+
+--R 3 | 2 4 2
+--R (- 16x - 18x)\|4x + 9 + 32x + 72x
+--R /
+--R +-------+
+--R | 2 2
+--R 16x\|4x + 9 - 32x - 36
+--R Type: Union(Expression(Integer),...)
+--E 614
+
+--S 615 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R - 9log(\|4x + 9 - 2x) - 9asinh(--)
+--R 3
+--R (4) ------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 615
+
+--S 616 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 616
+
+)clear all
+
+--S 617 of 1369
+t0:=sqrt(9+4*x^2)/x
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R (1) ----------
+--R x
+--R Type: Expression(Integer)
+--E 617
+
+--S 618 of 1369
+r0:=-3*atanh(1/3*sqrt(9+4*x^2))+sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R \|4x + 9 | 2
+--R (2) - 3atanh(----------) + \|4x + 9
+--R 3
+--R Type: Expression(Integer)
+--E 618
+
+--S 619 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R | 2 | 2
+--R (- 3\|4x + 9 + 6x)log(\|4x + 9 - 2x + 3)
+--R +
+--R +-------+ +-------+ +-------+
+--R | 2 | 2 | 2 2
+--R (3\|4x + 9 - 6x)log(\|4x + 9 - 2x - 3) - 2x\|4x + 9 + 4x + 9
+--R /
+--R +-------+
+--R | 2
+--R \|4x + 9 - 2x
+--R Type: Union(Expression(Integer),...)
+--E 619
+
+--S 620 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-------+
+--R +-------+ +-------+ | 2
+--R | 2 | 2 \|4x + 9
+--R - 3log(\|4x + 9 - 2x + 3) + 3log(\|4x + 9 - 2x - 3) + 3atanh(----------)
+--R 3
+--R Type: Expression(Integer)
+--E 620
+
+--S 621 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 621
+
+)clear all
+
+--S 622 of 1369
+t0:=sqrt(9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R (1) ----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 622
+
+--S 623 of 1369
+r0:=2*asinh(2/3*x)-sqrt(9+4*x^2)/x
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R - \|4x + 9 + 2x asinh(--)
+--R 3
+--R (2) ---------------------------
+--R x
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+ +-------+
+--R | 2 2 | 2
+--R (- 2x\|4x + 9 + 4x )log(\|4x + 9 - 2x) - 9
+--R (3) ----------------------------------------------
+--R +-------+
+--R | 2 2
+--R x\|4x + 9 - 2x
+--R Type: Union(Expression(Integer),...)
+--E 624
+
+--S 625 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R (4) - 2log(\|4x + 9 - 2x) - 2asinh(--) - 2
+--R 3
+--R Type: Expression(Integer)
+--E 625
+
+--S 626 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 626
+
+)clear all
+
+--S 627 of 1369
+t0:=sqrt(9+4*x^2)/x^3
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R (1) ----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 627
+
+--S 628 of 1369
+r0:=-2/3*atanh(1/3*sqrt(9+4*x^2))-1/2*sqrt(9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R 2 \|4x + 9 | 2
+--R - 4x atanh(----------) - 3\|4x + 9
+--R 3
+--R (2) ------------------------------------
+--R 2
+--R 6x
+--R Type: Expression(Integer)
+--E 628
+
+--S 629 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R 3 | 2 4 2 | 2
+--R (- 16x \|4x + 9 + 32x + 36x )log(\|4x + 9 - 2x + 3)
+--R +
+--R +-------+ +-------+
+--R 3 | 2 4 2 | 2
+--R (16x \|4x + 9 - 32x - 36x )log(\|4x + 9 - 2x - 3)
+--R +
+--R +-------+
+--R 2 | 2 3
+--R (24x + 27)\|4x + 9 - 48x - 108x
+--R /
+--R +-------+
+--R 3 | 2 4 2
+--R 24x \|4x + 9 - 48x - 54x
+--R Type: Union(Expression(Integer),...)
+--E 629
+
+--S 630 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-------+
+--R +-------+ +-------+ | 2
+--R | 2 | 2 \|4x + 9
+--R - 2log(\|4x + 9 - 2x + 3) + 2log(\|4x + 9 - 2x - 3) + 2atanh(----------)
+--R 3
+--R ----------------------------------------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 630
+
+--S 631 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 631
+
+)clear all
+
+--S 632 of 1369
+t0:=sqrt(9+4*x^2)/x^4
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R (1) ----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 632
+
+--S 633 of 1369
+r0:=-1/27*(9+4*x^2)^(3/2)/x^3
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (- 4x - 9)\|4x + 9
+--R (2) ---------------------
+--R 3
+--R 27x
+--R Type: Expression(Integer)
+--E 633
+
+--S 634 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 | 2 4 2
+--R (16x + 18x)\|4x + 9 - 32x - 72x - 27
+--R (3) -----------------------------------------
+--R +-------+
+--R 5 3 | 2 6 4
+--R (16x + 9x )\|4x + 9 - 32x - 54x
+--R Type: Union(Expression(Integer),...)
+--E 634
+
+--S 635 of 1369
+m0:=a0-r0
+--R
+--R
+--R 8
+--R (4) - --
+--R 27
+--R Type: Expression(Integer)
+--E 635
+
+--S 636 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 636
+
+)clear all
+
+--S 637 of 1369
+t0:=sqrt(9+4*x^2)/x^5
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R (1) ----------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 637
+
+--S 638 of 1369
+r0:=2/27*atanh(1/3*sqrt(9+4*x^2))-1/4*sqrt(9+4*x^2)/x^4-1/18*sqrt(9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R 4 \|4x + 9 2 | 2
+--R 8x atanh(----------) + (- 6x - 27)\|4x + 9
+--R 3
+--R (2) ---------------------------------------------
+--R 4
+--R 108x
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R ((512x + 576x )\|4x + 9 - 1024x - 2304x - 648x )
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x + 9 - 2x + 3)
+--R +
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R ((- 512x - 576x )\|4x + 9 + 1024x + 2304x + 648x )
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x + 9 - 2x - 3)
+--R +
+--R +-------+
+--R 6 4 2 | 2 7 5 3
+--R (768x + 5184x + 8262x + 2187)\|4x + 9 - 1536x - 12096x - 27216x
+--R +
+--R - 17496x
+--R /
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R (6912x + 7776x )\|4x + 9 - 13824x - 31104x - 8748x
+--R Type: Union(Expression(Integer),...)
+--E 639
+
+--S 640 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-------+
+--R +-------+ +-------+ | 2
+--R | 2 | 2 \|4x + 9
+--R 2log(\|4x + 9 - 2x + 3) - 2log(\|4x + 9 - 2x - 3) - 2atanh(----------)
+--R 3
+--R --------------------------------------------------------------------------
+--R 27
+--R Type: Expression(Integer)
+--E 640
+
+--S 641 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 641
+
+)clear all
+
+--S 642 of 1369
+t0:=x^5*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R 5 | 2
+--R (1) x \|- 4x + 9
+--R Type: Expression(Integer)
+--E 642
+
+--S 643 of 1369
+r0:=-27/64*(9-4*x^2)^(3/2)+9/160*(9-4*x^2)^(5/2)-1/448*(9-4*x^2)^(7/2)
+--R
+--R
+--R +---------+
+--R 6 4 2 | 2
+--R (40x - 18x - 54x - 243)\|- 4x + 9
+--R (2) --------------------------------------
+--R 280
+--R Type: Expression(Integer)
+--E 643
+
+--S 644 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 12 10 8 6 | 2 14 12
+--R (- 420x + 7749x - 36855x + 51030x )\|- 4x + 9 - 80x + 4536x
+--R +
+--R 10 8 6
+--R - 44037x + 144585x - 153090x
+--R /
+--R +---------+
+--R 6 4 2 | 2 6 4
+--R (140x - 7560x + 56700x - 102060)\|- 4x + 9 - 2940x + 52920x
+--R +
+--R 2
+--R - 238140x + 306180
+--R Type: Union(Expression(Integer),...)
+--E 644
+
+--S 645 of 1369
+m0:=a0-r0
+--R
+--R
+--R 729
+--R (4) - ---
+--R 280
+--R Type: Expression(Integer)
+--E 645
+
+--S 646 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 646
+
+)clear all
+
+--S 647 of 1369
+t0:=x^4*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R 4 | 2
+--R (1) x \|- 4x + 9
+--R Type: Expression(Integer)
+--E 647
+
+--S 648 of 1369
+r0:=729/512*asin(2/3*x)-81/256*x*sqrt(9-4*x^2)-_
+ 3/32*x^3*sqrt(9-4*x^2)+1/6*x^5*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R 5 3 | 2 2x
+--R (256x - 144x - 486x)\|- 4x + 9 + 2187asin(--)
+--R 3
+--R (2) -------------------------------------------------
+--R 1536
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 4 2 | 2 6 4
+--R (- 19683x + 236196x - 531441)\|- 4x + 9 - 4374x + 177147x
+--R +
+--R 2
+--R - 1062882x + 1594323
+--R *
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3
+--R atan(----------------)
+--R 2x
+--R +
+--R +---------+
+--R 11 9 7 5 3 | 2
+--R (256x - 10512x + 67554x - 108621x - 65610x + 177147x)\|- 4x + 9
+--R +
+--R 11 9 7 5 3
+--R - 4608x + 68256x - 277020x + 295245x + 314928x - 531441x
+--R /
+--R +---------+
+--R 4 2 | 2 6 4 2
+--R (6912x - 82944x + 186624)\|- 4x + 9 + 1536x - 62208x + 373248x
+--R +
+--R - 559872
+--R Type: Union(Expression(Integer),...)
+--E 649
+
+--S 650 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3 2x
+--R - 1458atan(----------------) - 729asin(--)
+--R 2x 3
+--R (4) ------------------------------------------
+--R 512
+--R Type: Expression(Integer)
+--E 650
+
+--S 651 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 651
+
+)clear all
+
+--S 652 of 1369
+t0:=x^3*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R 3 | 2
+--R (1) x \|- 4x + 9
+--R Type: Expression(Integer)
+--E 652
+
+--S 653 of 1369
+r0:=-3/16*(9-4*x^2)^(3/2)+1/80*(9-4*x^2)^(5/2)
+--R
+--R
+--R +---------+
+--R 4 2 | 2
+--R (8x - 6x - 27)\|- 4x + 9
+--R (2) ----------------------------
+--R 40
+--R Type: Expression(Integer)
+--E 653
+
+--S 654 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 8 6 4 | 2 10 8 6 4
+--R (- 60x + 585x - 1215x )\|- 4x + 9 - 16x + 480x - 2565x + 3645x
+--R -----------------------------------------------------------------------
+--R +---------+
+--R 4 2 | 2 4 2
+--R (20x - 540x + 1620)\|- 4x + 9 - 300x + 2700x - 4860
+--R Type: Union(Expression(Integer),...)
+--E 654
+
+--S 655 of 1369
+m0:=a0-r0
+--R
+--R
+--R 81
+--R (4) - --
+--R 40
+--R Type: Expression(Integer)
+--E 655
+
+--S 656 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 656
+
+)clear all
+
+--S 657 of 1369
+t0:=x^2*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (1) x \|- 4x + 9
+--R Type: Expression(Integer)
+--E 657
+
+--S 658 of 1369
+r0:=81/64*asin(2/3*x)-9/32*x*sqrt(9-4*x^2)+1/4*x^3*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R 3 | 2 2x
+--R (16x - 18x)\|- 4x + 9 + 81asin(--)
+--R 3
+--R (2) -------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 2 | 2 4 2
+--R ((- 486x + 2187)\|- 4x + 9 - 162x + 2916x - 6561)
+--R *
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3
+--R atan(----------------)
+--R 2x
+--R +
+--R +---------+
+--R 7 5 3 | 2 7 5 3
+--R (16x - 306x + 972x - 729x)\|- 4x + 9 - 192x + 1512x - 3402x + 2187x
+--R /
+--R +---------+
+--R 2 | 2 4 2
+--R (192x - 864)\|- 4x + 9 + 64x - 1152x + 2592
+--R Type: Union(Expression(Integer),...)
+--E 659
+
+--S 660 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3 2x
+--R - 162atan(----------------) - 81asin(--)
+--R 2x 3
+--R (4) ----------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 660
+
+--S 661 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 661
+
+)clear all
+
+--S 662 of 1369
+t0:=x*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2
+--R (1) x\|- 4x + 9
+--R Type: Expression(Integer)
+--E 662
+
+--S 663 of 1369
+r0:=-1/12*(9-4*x^2)^(3/2)
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (4x - 9)\|- 4x + 9
+--R (2) ---------------------
+--R 12
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 4 2 | 2 6 4 2
+--R (- 18x + 81x )\|- 4x + 9 - 8x + 108x - 243x
+--R (3) -------------------------------------------------
+--R +---------+
+--R 2 | 2 2
+--R (6x - 54)\|- 4x + 9 - 54x + 162
+--R Type: Union(Expression(Integer),...)
+--E 664
+
+--S 665 of 1369
+m0:=a0-r0
+--R
+--R
+--R 9
+--R (4) - -
+--R 4
+--R Type: Expression(Integer)
+--E 665
+
+--S 666 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 666
+
+)clear all
+
+--S 667 of 1369
+t0:=sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2
+--R (1) \|- 4x + 9
+--R Type: Expression(Integer)
+--E 667
+
+--S 668 of 1369
+r0:=9/4*asin(2/3*x)+1/2*x*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2 2x
+--R 2x\|- 4x + 9 + 9asin(--)
+--R 3
+--R (2) --------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2
+--R | 2 2 \|- 4x + 9 - 3
+--R (- 27\|- 4x + 9 - 18x + 81)atan(----------------)
+--R 2x
+--R +
+--R +---------+
+--R 3 | 2 3
+--R (2x - 9x)\|- 4x + 9 - 12x + 27x
+--R /
+--R +---------+
+--R | 2 2
+--R 6\|- 4x + 9 + 4x - 18
+--R Type: Union(Expression(Integer),...)
+--E 669
+
+--S 670 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3 2x
+--R - 18atan(----------------) - 9asin(--)
+--R 2x 3
+--R (4) --------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 670
+
+--S 671 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 671
+
+)clear all
+
+--S 672 of 1369
+t0:=sqrt(9-4*x^2)/x
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R (1) ------------
+--R x
+--R Type: Expression(Integer)
+--E 672
+
+--S 673 of 1369
+r0:=-3*atanh(1/3*sqrt(9-4*x^2))+sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R \|- 4x + 9 | 2
+--R (2) - 3atanh(------------) + \|- 4x + 9
+--R 3
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R +---------+ | 2
+--R | 2 \|- 4x + 9 - 3 2
+--R (3\|- 4x + 9 - 9)log(----------------) - 4x
+--R x
+--R (3) ----------------------------------------------
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3
+--R Type: Union(Expression(Integer),...)
+--E 674
+
+--S 675 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+ +---------+
+--R | 2 | 2
+--R \|- 4x + 9 - 3 \|- 4x + 9
+--R (4) 3log(----------------) + 3atanh(------------) + 3
+--R x 3
+--R Type: Expression(Integer)
+--E 675
+
+--S 676 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 676
+
+)clear all
+
+--S 677 of 1369
+t0:=sqrt(9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R (1) ------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 677
+
+--S 678 of 1369
+r0:=-2*asin(2/3*x)-sqrt(9-4*x^2)/x
+--R
+--R
+--R +---------+
+--R | 2 2x
+--R - \|- 4x + 9 - 2x asin(--)
+--R 3
+--R (2) ----------------------------
+--R x
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R +---------+ | 2 +---------+
+--R | 2 \|- 4x + 9 - 3 | 2 2
+--R (4x\|- 4x + 9 - 12x)atan(----------------) + 3\|- 4x + 9 + 4x - 9
+--R 2x
+--R (3) ----------------------------------------------------------------------
+--R +---------+
+--R | 2
+--R x\|- 4x + 9 - 3x
+--R Type: Union(Expression(Integer),...)
+--E 679
+
+--S 680 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3 2x
+--R (4) 4atan(----------------) + 2asin(--)
+--R 2x 3
+--R Type: Expression(Integer)
+--E 680
+
+--S 681 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 681
+
+)clear all
+
+--S 682 of 1369
+t0:=sqrt(9-4*x^2)/x^3
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R (1) ------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 682
+
+--S 683 of 1369
+r0:=2/3*atanh(1/3*sqrt(9-4*x^2))-1/2*sqrt(9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R 2 \|- 4x + 9 | 2
+--R 4x atanh(------------) - 3\|- 4x + 9
+--R 3
+--R (2) --------------------------------------
+--R 2
+--R 6x
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2
+--R 2 | 2 4 2 \|- 4x + 9 - 3
+--R (- 12x \|- 4x + 9 - 8x + 36x )log(----------------)
+--R x
+--R +
+--R +---------+
+--R 2 | 2 2
+--R (- 6x + 27)\|- 4x + 9 + 36x - 81
+--R /
+--R +---------+
+--R 2 | 2 4 2
+--R 18x \|- 4x + 9 + 12x - 54x
+--R Type: Union(Expression(Integer),...)
+--E 684
+
+--S 685 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+ +---------+
+--R | 2 | 2
+--R \|- 4x + 9 - 3 \|- 4x + 9
+--R - 2log(----------------) - 2atanh(------------)
+--R x 3
+--R (4) -----------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 685
+
+--S 686 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 686
+
+)clear all
+
+--S 687 of 1369
+t0:=sqrt(9-4*x^2)/x^4
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R (1) ------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 687
+
+--S 688 of 1369
+r0:=-1/27*(9-4*x^2)^(3/2)/x^3
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (4x - 9)\|- 4x + 9
+--R (2) ---------------------
+--R 3
+--R 27x
+--R Type: Expression(Integer)
+--E 688
+
+--S 689 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 4 2 | 2 6 4 2
+--R (- 36x + 189x - 243)\|- 4x + 9 - 16x + 216x - 729x + 729
+--R (3) ---------------------------------------------------------------
+--R +---------+
+--R 5 3 | 2 5 3
+--R (27x - 243x )\|- 4x + 9 - 243x + 729x
+--R Type: Union(Expression(Integer),...)
+--E 689
+
+--S 690 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 690
+
+--S 691 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 691
+
+)clear all
+
+--S 692 of 1369
+t0:=sqrt(9-4*x^2)/x^5
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R (1) ------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 692
+
+--S 693 of 1369
+r0:=2/27*atanh(1/3*sqrt(9-4*x^2))-1/4*sqrt(9-4*x^2)/x^4+1/18*sqrt(9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R 4 \|- 4x + 9 2 | 2
+--R 8x atanh(------------) + (6x - 27)\|- 4x + 9
+--R 3
+--R (2) -----------------------------------------------
+--R 4
+--R 108x
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 6 4 | 2 8 6 4
+--R ((- 48x + 216x )\|- 4x + 9 - 16x + 288x - 648x )
+--R *
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3
+--R log(----------------)
+--R x
+--R +
+--R +---------+
+--R 6 4 2 | 2 6 4 2
+--R (12x - 270x + 1458x - 2187)\|- 4x + 9 - 144x + 1620x - 5832x + 6561
+--R /
+--R +---------+
+--R 6 4 | 2 8 6 4
+--R (648x - 2916x )\|- 4x + 9 + 216x - 3888x + 8748x
+--R Type: Union(Expression(Integer),...)
+--E 694
+
+--S 695 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+ +---------+
+--R | 2 | 2
+--R \|- 4x + 9 - 3 \|- 4x + 9
+--R - 2log(----------------) - 2atanh(------------)
+--R x 3
+--R (4) -----------------------------------------------
+--R 27
+--R Type: Expression(Integer)
+--E 695
+
+--S 696 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 696
+
+)clear all
+
+--S 697 of 1369
+t0:=x^5*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 5 | 2
+--R (1) x \|4x - 9
+--R Type: Expression(Integer)
+--E 697
+
+--S 698 of 1369
+r0:=27/64*(-9+4*x^2)^(3/2)+9/160*(-9+4*x^2)^(5/2)+1/448*(-9+4*x^2)^(7/2)
+--R
+--R
+--R +-------+
+--R 6 4 2 | 2
+--R (40x - 18x - 54x - 243)\|4x - 9
+--R (2) ------------------------------------
+--R 280
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 13 11 9 7 5
+--R - 327680x + 1437696x - 1589760x + 1310256x - 6062364x
+--R +
+--R 3
+--R 8266860x - 2480058x
+--R *
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R +
+--R 14 12 10 8 6 4
+--R 655360x - 3612672x + 5999616x - 4844448x + 14451696x - 28934010x
+--R +
+--R 2
+--R 17360406x - 1594323
+--R /
+--R +-------+
+--R 6 4 2 | 2 7
+--R (1146880x - 3225600x + 2177280x - 204120)\|4x - 9 - 2293760x
+--R +
+--R 5 3
+--R 9031680x - 10160640x + 2857680x
+--R Type: Union(Expression(Integer),...)
+--E 699
+
+--S 700 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 700
+
+--S 701 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 701
+
+)clear all
+
+--S 702 of 1369
+t0:=x^4*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 4 | 2
+--R (1) x \|4x - 9
+--R Type: Expression(Integer)
+--E 702
+
+--S 703 of 1369
+r0:=-729/512*atanh(2*x/sqrt(-9+4*x^2))-81/256*x*sqrt(-9+4*x^2)-_
+ 3/32*x^3*sqrt(-9+4*x^2)+1/6*x^5*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 2x 5 3 | 2
+--R - 2187atanh(----------) + (256x - 144x - 486x)\|4x - 9
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (2) ----------------------------------------------------------
+--R 1536
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 5 3 | 2 6 4
+--R (2239488x - 5038848x + 2125764x)\|4x - 9 - 4478976x + 15116544x
+--R +
+--R 2
+--R - 12754584x + 1594323
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x - 9 - 2x)
+--R +
+--R 11 9 7 5 3
+--R (- 524288x + 2064384x - 1492992x - 2332800x + 2729376x - 354294x)
+--R *
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R +
+--R 12 10 8 6 4 2
+--R 1048576x - 5308416x + 6967296x + 3172608x - 10707552x + 4251528x
+--R /
+--R +-------+
+--R 5 3 | 2 6 4
+--R (1572864x - 3538944x + 1492992x)\|4x - 9 - 3145728x + 10616832x
+--R +
+--R 2
+--R - 8957952x + 1119744
+--R Type: Union(Expression(Integer),...)
+--E 704
+
+--S 705 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R 729log(\|4x - 9 - 2x) + 729atanh(----------)
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (4) ----------------------------------------------
+--R 512
+--R Type: Expression(Integer)
+--E 705
+
+--S 706 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 706
+
+)clear all
+
+--S 707 of 1369
+t0:=x^3*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 3 | 2
+--R (1) x \|4x - 9
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 1369
+r0:=3/16*(-9+4*x^2)^(3/2)+1/80*(-9+4*x^2)^(5/2)
+--R
+--R
+--R +-------+
+--R 4 2 | 2
+--R (8x - 6x - 27)\|4x - 9
+--R (2) --------------------------
+--R 40
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 9 7 5 3 | 2 10
+--R (- 4096x + 14592x - 1296x - 34020x + 21870x)\|4x - 9 + 8192x
+--R +
+--R 8 6 4 2
+--R - 38400x + 30240x + 77760x - 109350x + 19683
+--R /
+--R +-------+
+--R 4 2 | 2 5 3
+--R (10240x - 17280x + 3240)\|4x - 9 - 20480x + 57600x - 32400x
+--R Type: Union(Expression(Integer),...)
+--E 709
+
+--S 710 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 710
+
+--S 711 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 711
+
+)clear all
+
+--S 712 of 1369
+t0:=x^2*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (1) x \|4x - 9
+--R Type: Expression(Integer)
+--E 712
+
+--S 713 of 1369
+r0:=-81/64*atanh(2*x/sqrt(-9+4*x^2))-9/32*x*sqrt(-9+4*x^2)+_
+ 1/4*x^3*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 2x 3 | 2
+--R - 81atanh(----------) + (16x - 18x)\|4x - 9
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (2) ----------------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 713
+
+--S 714 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 3 | 2 4 2
+--R ((5184x - 5832x)\|4x - 9 - 10368x + 23328x - 6561)
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x - 9 - 2x)
+--R +
+--R +-------+
+--R 7 5 3 | 2 8 6
+--R (- 2048x + 6912x - 6480x + 1458x)\|4x - 9 + 4096x - 18432x
+--R +
+--R 4 2
+--R 25920x - 11664x
+--R /
+--R +-------+
+--R 3 | 2 4 2
+--R (4096x - 4608x)\|4x - 9 - 8192x + 18432x - 5184
+--R Type: Union(Expression(Integer),...)
+--E 714
+
+--S 715 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R 81log(\|4x - 9 - 2x) + 81atanh(----------)
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (4) --------------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 715
+
+--S 716 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 716
+
+)clear all
+
+--S 717 of 1369
+t0:=x*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R (1) x\|4x - 9
+--R Type: Expression(Integer)
+--E 717
+
+--S 718 of 1369
+r0:=1/12*(-9+4*x^2)^(3/2)
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (4x - 9)\|4x - 9
+--R (2) -------------------
+--R 12
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 5 3 | 2 6 4 2
+--R (- 128x + 504x - 486x)\|4x - 9 + 256x - 1296x + 1944x - 729
+--R (3) ------------------------------------------------------------------
+--R +-------+
+--R 2 | 2 3
+--R (192x - 108)\|4x - 9 - 384x + 648x
+--R Type: Union(Expression(Integer),...)
+--E 719
+
+--S 720 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 720
+
+--S 721 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 721
+
+)clear all
+
+--S 722 of 1369
+t0:=sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R (1) \|4x - 9
+--R Type: Expression(Integer)
+--E 722
+
+--S 723 of 1369
+r0:=-9/4*atanh(2*x/sqrt(-9+4*x^2))+1/2*x*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 2x | 2
+--R - 9atanh(----------) + 2x\|4x - 9
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (2) -----------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R | 2 2 | 2
+--R (36x\|4x - 9 - 72x + 81)log(\|4x - 9 - 2x)
+--R +
+--R +-------+
+--R 3 | 2 4 2
+--R (- 16x + 18x)\|4x - 9 + 32x - 72x
+--R /
+--R +-------+
+--R | 2 2
+--R 16x\|4x - 9 - 32x + 36
+--R Type: Union(Expression(Integer),...)
+--E 724
+
+--S 725 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R 9log(\|4x - 9 - 2x) + 9atanh(----------)
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (4) ------------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 725
+
+--S 726 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 726
+
+)clear all
+
+--S 727 of 1369
+t0:=sqrt(-9+4*x^2)/x
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (1) ----------
+--R x
+--R Type: Expression(Integer)
+--E 727
+
+--S 728 of 1369
+r0:=-3*atan(1/3*sqrt(-9+4*x^2))+sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R \|4x - 9 | 2
+--R (2) - 3atan(----------) + \|4x - 9
+--R 3
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R +-------+ | 2 +-------+
+--R | 2 \|4x - 9 - 2x | 2 2
+--R (- 6\|4x - 9 + 12x)atan(---------------) - 2x\|4x - 9 + 4x - 9
+--R 3
+--R (3) -------------------------------------------------------------------
+--R +-------+
+--R | 2
+--R \|4x - 9 - 2x
+--R Type: Union(Expression(Integer),...)
+--E 729
+
+--S 730 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|4x - 9 \|4x - 9 - 2x
+--R (4) 3atan(----------) - 6atan(---------------)
+--R 3 3
+--R Type: Expression(Integer)
+--E 730
+
+--S 731 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 731
+
+)clear all
+
+--S 732 of 1369
+t0:=sqrt(-9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (1) ----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 732
+
+--S 733 of 1369
+r0:=2*atanh(2*x/sqrt(-9+4*x^2))-sqrt(-9+4*x^2)/x
+--R
+--R
+--R +-------+
+--R 2x | 2
+--R 2x atanh(----------) - \|4x - 9
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (2) ---------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+ +-------+
+--R | 2 2 | 2
+--R (- 2x\|4x - 9 + 4x )log(\|4x - 9 - 2x) + 9
+--R (3) ----------------------------------------------
+--R +-------+
+--R | 2 2
+--R x\|4x - 9 - 2x
+--R Type: Union(Expression(Integer),...)
+--E 734
+
+--S 735 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R (4) - 2log(\|4x - 9 - 2x) - 2atanh(----------) - 2
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R Type: Expression(Integer)
+--E 735
+
+--S 736 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 736
+
+)clear all
+
+--S 737 of 1369
+t0:=sqrt(-9+4*x^2)/x^3
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (1) ----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 737
+
+--S 738 of 1369
+r0:=2/3*atan(1/3*sqrt(-9+4*x^2))-1/2*sqrt(-9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R 2 \|4x - 9 | 2
+--R 4x atan(----------) - 3\|4x - 9
+--R 3
+--R (2) ---------------------------------
+--R 2
+--R 6x
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R +-------+ | 2
+--R 3 | 2 4 2 \|4x - 9 - 2x
+--R (32x \|4x - 9 - 64x + 72x )atan(---------------)
+--R 3
+--R +
+--R +-------+
+--R 2 | 2 3
+--R (24x - 27)\|4x - 9 - 48x + 108x
+--R /
+--R +-------+
+--R 3 | 2 4 2
+--R 24x \|4x - 9 - 48x + 54x
+--R Type: Union(Expression(Integer),...)
+--E 739
+
+--S 740 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|4x - 9 \|4x - 9 - 2x
+--R - 2atan(----------) + 4atan(---------------)
+--R 3 3
+--R (4) --------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 740
+
+--S 741 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 741
+
+)clear all
+
+--S 742 of 1369
+t0:=sqrt(-9+4*x^2)/x^4
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (1) ----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 742
+
+--S 743 of 1369
+r0:=1/27*(-9+4*x^2)^(3/2)/x^3
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (4x - 9)\|4x - 9
+--R (2) -------------------
+--R 3
+--R 27x
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 | 2 4 2
+--R (16x - 18x)\|4x - 9 - 32x + 72x - 27
+--R (3) -----------------------------------------
+--R +-------+
+--R 5 3 | 2 6 4
+--R (16x - 9x )\|4x - 9 - 32x + 54x
+--R Type: Union(Expression(Integer),...)
+--E 744
+
+--S 745 of 1369
+m0:=a0-r0
+--R
+--R
+--R 8
+--R (4) --
+--R 27
+--R Type: Expression(Integer)
+--E 745
+
+--S 746 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 746
+
+)clear all
+
+--S 747 of 1369
+t0:=sqrt(-9+4*x^2)/x^5
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (1) ----------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 747
+
+--S 748 of 1369
+r0:=2/27*atan(1/3*sqrt(-9+4*x^2))-1/4*sqrt(-9+4*x^2)/x^4+_
+ 1/18*sqrt(-9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R 4 \|4x - 9 2 | 2
+--R 8x atan(----------) + (6x - 27)\|4x - 9
+--R 3
+--R (2) ------------------------------------------
+--R 4
+--R 108x
+--R Type: Expression(Integer)
+--E 748
+
+--S 749 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R ((1024x - 1152x )\|4x - 9 - 2048x + 4608x - 1296x )
+--R *
+--R +-------+
+--R | 2
+--R \|4x - 9 - 2x
+--R atan(---------------)
+--R 3
+--R +
+--R +-------+
+--R 6 4 2 | 2 7 5 3
+--R (- 768x + 5184x - 8262x + 2187)\|4x - 9 + 1536x - 12096x + 27216x
+--R +
+--R - 17496x
+--R /
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R (6912x - 7776x )\|4x - 9 - 13824x + 31104x - 8748x
+--R Type: Union(Expression(Integer),...)
+--E 749
+
+--S 750 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|4x - 9 \|4x - 9 - 2x
+--R - 2atan(----------) + 4atan(---------------)
+--R 3 3
+--R (4) --------------------------------------------
+--R 27
+--R Type: Expression(Integer)
+--E 750
+
+--S 751 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 751
+
+)clear all
+
+--S 752 of 1369
+t0:=x^5*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 5 | 2
+--R (1) x \|- 4x - 9
+--R Type: Expression(Integer)
+--E 752
+
+--S 753 of 1369
+r0:=-27/64*(-9-4*x^2)^(3/2)-9/160*(-9-4*x^2)^(5/2)-1/448*(-9-4*x^2)^(7/2)
+--R
+--R
+--R +---------+
+--R 6 4 2 | 2
+--R (40x + 18x - 54x + 243)\|- 4x - 9
+--R (2) --------------------------------------
+--R 280
+--R Type: Expression(Integer)
+--E 753
+
+--S 754 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 12 10 8 6 | 2
+--R (420x + 7749x + 36855x + 51030x )\|- 4x - 9
+--R +
+--R 14 12 10 8 6 +---+
+--R (- 80x - 4536x - 44037x - 144585x - 153090x )\|- 1
+--R /
+--R +---------+
+--R 6 4 2 +---+ | 2 6 4
+--R (140x + 7560x + 56700x + 102060)\|- 1 \|- 4x - 9 + 2940x + 52920x
+--R +
+--R 2
+--R 238140x + 306180
+--R Type: Union(Expression(Integer),...)
+--E 754
+
+--S 755 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 6 4 2 | 2
+--R (- 729x - 39366x - 295245x - 531441)\|- 4x - 9
+--R +
+--R 6 4 2 +---+
+--R (15309x + 275562x + 1240029x + 1594323)\|- 1
+--R /
+--R +---------+
+--R 6 4 2 +---+ | 2 6
+--R (280x + 15120x + 113400x + 204120)\|- 1 \|- 4x - 9 + 5880x
+--R +
+--R 4 2
+--R 105840x + 476280x + 612360
+--R Type: Expression(Integer)
+--E 755
+
+--S 756 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 756
+
+)clear all
+
+--S 757 of 1369
+t0:=x^4*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 4 | 2
+--R (1) x \|- 4x - 9
+--R Type: Expression(Integer)
+--E 757
+
+--S 758 of 1369
+r0:=-729/512*atan(2*x/sqrt(-9-4*x^2))-81/256*x*sqrt(-9-4*x^2)+_
+ 3/32*x^3*sqrt(-9-4*x^2)+1/6*x^5*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 2x 5 3 | 2
+--R - 2187atan(------------) + (256x + 144x - 486x)\|- 4x - 9
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (2) -------------------------------------------------------------
+--R 1536
+--R Type: Expression(Integer)
+--E 758
+
+--S 759 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 4 2 | 2
+--R (- 19683x - 236196x - 531441)\|- 4x - 9
+--R +
+--R 6 4 2 +---+
+--R (4374x + 177147x + 1062882x + 1594323)\|- 1
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (2x - 3)\|- 1
+--R log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R 4 2 | 2
+--R (19683x + 236196x + 531441)\|- 4x - 9
+--R +
+--R 6 4 2 +---+
+--R (- 4374x - 177147x - 1062882x - 1594323)\|- 1
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R 11 9 7 5 3 | 2
+--R (512x + 21024x + 135108x + 217242x - 131220x - 354294x)\|- 4x - 9
+--R +
+--R 11 9 7 5 3 +---+
+--R (- 9216x - 136512x - 554040x - 590490x + 629856x + 1062882x)\|- 1
+--R /
+--R +---------+
+--R 4 2 +---+ | 2 6 4
+--R (13824x + 165888x + 373248)\|- 1 \|- 4x - 9 + 3072x + 124416x
+--R +
+--R 2
+--R 746496x + 1119744
+--R Type: Union(Expression(Integer),...)
+--E 759
+
+--S 760 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 4 2 | 2
+--R (- 6561x - 78732x - 177147)\|- 4x - 9
+--R +
+--R 6 4 2 +---+
+--R (1458x + 59049x + 354294x + 531441)\|- 1
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (2x - 3)\|- 1
+--R log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R 4 2 | 2
+--R (6561x + 78732x + 177147)\|- 4x - 9
+--R +
+--R 6 4 2 +---+
+--R (- 1458x - 59049x - 354294x - 531441)\|- 1
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R 4 2 +---+ | 2 6 4
+--R (6561x + 78732x + 177147)\|- 1 \|- 4x - 9 + 1458x + 59049x
+--R +
+--R 2
+--R 354294x + 531441
+--R *
+--R 2x
+--R atan(------------)
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R /
+--R +---------+
+--R 4 2 +---+ | 2 6 4
+--R (4608x + 55296x + 124416)\|- 1 \|- 4x - 9 + 1024x + 41472x
+--R +
+--R 2
+--R 248832x + 373248
+--R Type: Expression(Integer)
+--E 760
+
+--S 761 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 761
+
+)clear all
+
+--S 762 of 1369
+t0:=x^3*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 3 | 2
+--R (1) x \|- 4x - 9
+--R Type: Expression(Integer)
+--E 762
+
+--S 763 of 1369
+r0:=3/16*(-9-4*x^2)^(3/2)+1/80*(-9-4*x^2)^(5/2)
+--R
+--R
+--R +---------+
+--R 4 2 | 2
+--R (8x + 6x - 27)\|- 4x - 9
+--R (2) ----------------------------
+--R 40
+--R Type: Expression(Integer)
+--E 763
+
+--S 764 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 8 6 4 | 2
+--R (60x + 585x + 1215x )\|- 4x - 9
+--R +
+--R 10 8 6 4 +---+
+--R (- 16x - 480x - 2565x - 3645x )\|- 1
+--R /
+--R +---------+
+--R 4 2 +---+ | 2 4 2
+--R (20x + 540x + 1620)\|- 1 \|- 4x - 9 + 300x + 2700x + 4860
+--R Type: Union(Expression(Integer),...)
+--E 764
+
+--S 765 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 4 2 | 2 4 2 +---+
+--R (81x + 2187x + 6561)\|- 4x - 9 + (- 1215x - 10935x - 19683)\|- 1
+--R -----------------------------------------------------------------------
+--R +---------+
+--R 4 2 +---+ | 2 4 2
+--R (40x + 1080x + 3240)\|- 1 \|- 4x - 9 + 600x + 5400x + 9720
+--R Type: Expression(Integer)
+--E 765
+
+--S 766 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 766
+
+)clear all
+
+--S 767 of 1369
+t0:=x^2*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (1) x \|- 4x - 9
+--R Type: Expression(Integer)
+--E 767
+
+--S 768 of 1369
+r0:=81/64*atan(2*x/sqrt(-9-4*x^2))+9/32*x*sqrt(-9-4*x^2)+1/4*x^3*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 2x 3 | 2
+--R 81atan(------------) + (16x + 18x)\|- 4x - 9
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (2) -----------------------------------------------
+--R 64
+--R Type: Expression(Integer)
+--E 768
+
+--S 769 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((486x + 2187)\|- 4x - 9 + (- 162x - 2916x - 6561)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (2x - 3)\|- 1
+--R log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((- 486x - 2187)\|- 4x - 9 + (162x + 2916x + 6561)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R 7 5 3 | 2
+--R (32x + 612x + 1944x + 1458x)\|- 4x - 9
+--R +
+--R 7 5 3 +---+
+--R (- 384x - 3024x - 6804x - 4374x)\|- 1
+--R /
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R (384x + 1728)\|- 1 \|- 4x - 9 + 128x + 2304x + 5184
+--R Type: Union(Expression(Integer),...)
+--E 769
+
+--S 770 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((486x + 2187)\|- 4x - 9 + (- 162x - 2916x - 6561)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (2x - 3)\|- 1
+--R log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((- 486x - 2187)\|- 4x - 9 + (162x + 2916x + 6561)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R ((- 486x - 2187)\|- 1 \|- 4x - 9 - 162x - 2916x - 6561)
+--R *
+--R 2x
+--R atan(------------)
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R /
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R (384x + 1728)\|- 1 \|- 4x - 9 + 128x + 2304x + 5184
+--R Type: Expression(Integer)
+--E 770
+
+--S 771 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 771
+
+)clear all
+
+--S 772 of 1369
+t0:=x*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2
+--R (1) x\|- 4x - 9
+--R Type: Expression(Integer)
+--E 772
+
+--S 773 of 1369
+r0:=-1/12*(-9-4*x^2)^(3/2)
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (4x + 9)\|- 4x - 9
+--R (2) ---------------------
+--R 12
+--R Type: Expression(Integer)
+--E 773
+
+--S 774 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 4 2 | 2 6 4 2 +---+
+--R (18x + 81x )\|- 4x - 9 + (- 8x - 108x - 243x )\|- 1
+--R (3) ---------------------------------------------------------
+--R +---------+
+--R 2 +---+ | 2 2
+--R (6x + 54)\|- 1 \|- 4x - 9 + 54x + 162
+--R Type: Union(Expression(Integer),...)
+--E 774
+
+--S 775 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R 2 | 2 2 +---+
+--R (- 9x - 81)\|- 4x - 9 + (81x + 243)\|- 1
+--R (4) ---------------------------------------------
+--R +---------+
+--R 2 +---+ | 2 2
+--R (4x + 36)\|- 1 \|- 4x - 9 + 36x + 108
+--R Type: Expression(Integer)
+--E 775
+
+--S 776 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 776
+
+)clear all
+
+--S 777 of 1369
+t0:=sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2
+--R (1) \|- 4x - 9
+--R Type: Expression(Integer)
+--E 777
+
+--S 778 of 1369
+r0:=-9/4*atan(2*x/sqrt(-9-4*x^2))+1/2*x*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 2x | 2
+--R - 9atan(------------) + 2x\|- 4x - 9
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (2) --------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 778
+
+--S 779 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2 +---+
+--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1
+--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R | 2 2 +---+
+--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R 3 | 2 3 +---+
+--R (4x + 18x)\|- 4x - 9 + (- 24x - 54x)\|- 1
+--R /
+--R +---------+
+--R +---+ | 2 2
+--R 12\|- 1 \|- 4x - 9 + 8x + 36
+--R Type: Union(Expression(Integer),...)
+--E 779
+
+--S 780 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +---------+ | 2 +---+
+--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1
+--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R | 2 2 +---+
+--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R +---+ | 2 2 2x
+--R (27\|- 1 \|- 4x - 9 + 18x + 81)atan(------------)
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R /
+--R +---------+
+--R +---+ | 2 2
+--R 12\|- 1 \|- 4x - 9 + 8x + 36
+--R Type: Expression(Integer)
+--E 780
+
+--S 781 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 781
+
+)clear all
+
+--S 782 of 1369
+t0:=sqrt(-9-4*x^2)/x
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (1) ------------
+--R x
+--R Type: Expression(Integer)
+--E 782
+
+--S 783 of 1369
+r0:=-3*atan(1/3*sqrt(-9-4*x^2))+sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R \|- 4x - 9 | 2
+--R (2) - 3atan(------------) + \|- 4x - 9
+--R 3
+--R Type: Expression(Integer)
+--E 783
+
+--S 784 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R +---------+ | 2 +---+
+--R | 2 +---+ \|- 4x - 9 - 3\|- 1 2 +---+
+--R (- 3\|- 4x - 9 + 9\|- 1 )log(----------------------) - 4x \|- 1
+--R x
+--R (3) ------------------------------------------------------------------
+--R +---------+
+--R +---+ | 2
+--R \|- 1 \|- 4x - 9 + 3
+--R Type: Union(Expression(Integer),...)
+--E 784
+
+--S 785 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +---------+ | 2 +---+
+--R | 2 +---+ \|- 4x - 9 - 3\|- 1
+--R (- 3\|- 4x - 9 + 9\|- 1 )log(----------------------)
+--R x
+--R +
+--R +---------+
+--R +---------+ | 2 +---------+
+--R +---+ | 2 \|- 4x - 9 | 2 +---+
+--R (3\|- 1 \|- 4x - 9 + 9)atan(------------) - 3\|- 4x - 9 + 9\|- 1
+--R 3
+--R /
+--R +---------+
+--R +---+ | 2
+--R \|- 1 \|- 4x - 9 + 3
+--R Type: Expression(Integer)
+--E 785
+
+--S 786 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 786
+
+)clear all
+
+--S 787 of 1369
+t0:=sqrt(-9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (1) ------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 787
+
+--S 788 of 1369
+r0:=-2*atan(2*x/sqrt(-9-4*x^2))-sqrt(-9-4*x^2)/x
+--R
+--R
+--R +---------+
+--R 2x | 2
+--R - 2x atan(------------) - \|- 4x - 9
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (2) --------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 788
+
+--S 789 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2 +---+
+--R +---+ | 2 \|- 4x - 9 + (2x - 3)\|- 1
+--R (2x\|- 1 \|- 4x - 9 + 6x)log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R +---------+ | 2 +---+
+--R +---+ | 2 \|- 4x - 9 + (- 2x - 3)\|- 1
+--R (- 2x\|- 1 \|- 4x - 9 - 6x)log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R +---+ | 2 2
+--R 3\|- 1 \|- 4x - 9 + 4x + 9
+--R /
+--R +---------+
+--R | 2 +---+
+--R x\|- 4x - 9 - 3x\|- 1
+--R Type: Union(Expression(Integer),...)
+--E 789
+
+--S 790 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +---------+ | 2 +---+
+--R +---+ | 2 \|- 4x - 9 + (2x - 3)\|- 1
+--R (2\|- 1 \|- 4x - 9 + 6)log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R +---------+ | 2 +---+
+--R +---+ | 2 \|- 4x - 9 + (- 2x - 3)\|- 1
+--R (- 2\|- 1 \|- 4x - 9 - 6)log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R | 2 +---+ 2x
+--R (2\|- 4x - 9 - 6\|- 1 )atan(------------)
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R /
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 - 3\|- 1
+--R Type: Expression(Integer)
+--E 790
+
+--S 791 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 791
+
+)clear all
+
+--S 792 of 1369
+t0:=sqrt(-9-4*x^2)/x^3
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (1) ------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 792
+
+--S 793 of 1369
+r0:=-2/3*atan(1/3*sqrt(-9-4*x^2))-1/2*sqrt(-9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R 2 \|- 4x - 9 | 2
+--R - 4x atan(------------) - 3\|- 4x - 9
+--R 3
+--R (2) ---------------------------------------
+--R 2
+--R 6x
+--R Type: Expression(Integer)
+--E 793
+
+--S 794 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2 +---+
+--R 2 | 2 4 2 +---+ \|- 4x - 9 - 3\|- 1
+--R (- 12x \|- 4x - 9 + (8x + 36x )\|- 1 )log(----------------------)
+--R x
+--R +
+--R +---------+
+--R 2 | 2 2 +---+
+--R (- 6x - 27)\|- 4x - 9 + (36x + 81)\|- 1
+--R /
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R 18x \|- 1 \|- 4x - 9 + 12x + 54x
+--R Type: Union(Expression(Integer),...)
+--E 794
+
+--S 795 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +---------+ | 2 +---+
+--R | 2 2 +---+ \|- 4x - 9 - 3\|- 1
+--R (- 6\|- 4x - 9 + (4x + 18)\|- 1 )log(----------------------)
+--R x
+--R +
+--R +---------+
+--R +---------+ | 2
+--R +---+ | 2 2 \|- 4x - 9
+--R (6\|- 1 \|- 4x - 9 + 4x + 18)atan(------------)
+--R 3
+--R /
+--R +---------+
+--R +---+ | 2 2
+--R 9\|- 1 \|- 4x - 9 + 6x + 27
+--R Type: Expression(Integer)
+--E 795
+
+--S 796 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 796
+
+)clear all
+
+--S 797 of 1369
+t0:=sqrt(-9-4*x^2)/x^4
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (1) ------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 797
+
+--S 798 of 1369
+r0:=1/27*(-9-4*x^2)^(3/2)/x^3
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (- 4x - 9)\|- 4x - 9
+--R (2) -----------------------
+--R 3
+--R 27x
+--R Type: Expression(Integer)
+--E 798
+
+--S 799 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 4 2 +---+ | 2 6 4 2
+--R (36x + 189x + 243)\|- 1 \|- 4x - 9 + 16x + 216x + 729x + 729
+--R (3) -------------------------------------------------------------------
+--R +---------+
+--R 5 3 | 2 5 3 +---+
+--R (27x + 243x )\|- 4x - 9 + (- 243x - 729x )\|- 1
+--R Type: Union(Expression(Integer),...)
+--E 799
+
+--S 800 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 800
+
+--S 801 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 801
+
+)clear all
+
+--S 802 of 1369
+t0:=sqrt(-9-4*x^2)/x^5
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (1) ------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 802
+
+--S 803 of 1369
+r0:=2/27*atan(1/3*sqrt(-9-4*x^2))-1/4*sqrt(-9-4*x^2)/x^4-_
+ 1/18*sqrt(-9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R 4 \|- 4x - 9 2 | 2
+--R 8x atan(------------) + (- 6x - 27)\|- 4x - 9
+--R 3
+--R (2) ------------------------------------------------
+--R 4
+--R 108x
+--R Type: Expression(Integer)
+--E 803
+
+--S 804 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 6 4 | 2 8 6 4 +---+
+--R ((48x + 216x )\|- 4x - 9 + (- 16x - 288x - 648x )\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 - 3\|- 1
+--R log(----------------------)
+--R x
+--R +
+--R +---------+
+--R 6 4 2 | 2
+--R (- 12x - 270x - 1458x - 2187)\|- 4x - 9
+--R +
+--R 6 4 2 +---+
+--R (144x + 1620x + 5832x + 6561)\|- 1
+--R /
+--R +---------+
+--R 6 4 +---+ | 2 8 6 4
+--R (648x + 2916x )\|- 1 \|- 4x - 9 + 216x + 3888x + 8748x
+--R Type: Union(Expression(Integer),...)
+--E 804
+
+--S 805 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((12x + 54)\|- 4x - 9 + (- 4x - 72x - 162)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 - 3\|- 1
+--R log(----------------------)
+--R x
+--R +
+--R +---------+
+--R +---------+ | 2
+--R 2 +---+ | 2 4 2 \|- 4x - 9
+--R ((- 12x - 54)\|- 1 \|- 4x - 9 - 4x - 72x - 162)atan(------------)
+--R 3
+--R /
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R (162x + 729)\|- 1 \|- 4x - 9 + 54x + 972x + 2187
+--R Type: Expression(Integer)
+--E 805
+
+--S 806 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 806
+
+)clear all
+
+--S 807 of 1369
+t0:=x^m/(a+b*x^2)^(1/2)
+--R
+--R
+--R m
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 807
+
+--S 808 of 1369
+--r0:=x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+-- sqrt((a+b*x^2)/a)/((1+m)*sqrt(a+b*x^2))
+--E 808
+
+--S 809 of 1369
+--a0:=integrate(t0,x)
+--E 809
+
+--S 810 of 1369
+--m0:=a0-r0
+--E 810
+
+--S 811 of 1369
+--d0:=D(m0,x)
+--E 811
+
+)clear all
+
+--S 812 of 1369
+t0:=x^5/sqrt(a+b*x^2)
+--R
+--R
+--R 5
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 812
+
+--S 813 of 1369
+r0:=8/15*a^2*sqrt(a+b*x^2)/b^3-4/15*a*x^2*sqrt(a+b*x^2)/b^2+_
+ 1/5*x^4*sqrt(a+b*x^2)/b
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (3b x - 4a b x + 8a )\|b x + a
+--R (2) ----------------------------------
+--R 3
+--R 15b
+--R Type: Expression(Integer)
+--E 813
+
+--S 814 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 8 2 6 | 2 2 10 8 2 6 +-+
+--R (- 15a b x - 40a x )\|b x + a + (3b x + 35a b x + 40a x )\|a
+--R --------------------------------------------------------------------------
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a
+--R Type: Union(Expression(Integer),...)
+--E 814
+
+--S 815 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 2 4 4 2 5 | 2
+--R (8a b x + 96a b x + 128a )\|b x + a
+--R +
+--R 3 2 4 4 2 5 +-+
+--R (- 40a b x - 160a b x - 128a )\|a
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +-+ | 2 5 4 2 4 2
+--R (15b x + 180a b x + 240a b )\|a \|b x + a - 75a b x - 300a b x
+--R +
+--R 3 3
+--R - 240a b
+--R Type: Expression(Integer)
+--E 815
+
+--S 816 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 816
+
+)clear all
+
+--S 817 of 1369
+t0:=x^4/sqrt(a+b*x^2)
+--R
+--R
+--R 4
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 817
+
+--S 818 of 1369
+r0:=3/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_
+ 3/8*a*x*sqrt(a+b*x^2)/b^2+1/4*x^3*sqrt(a+b*x^2)/b
+--R
+--R
+--R +-+ +--------+
+--R 2 x\|b 3 +-+ | 2
+--R 3a atanh(-----------) + (2b x - 3a x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------------------------------------------------
+--R 2 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 818
+
+--S 819 of 1369
+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 - 13a b x + 8a b x + 24a x)\|b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8b x + 12a b x - 20a b x - 24a x)\|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 +--------+
+--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 - 13a b x + 8a b x + 24a x)\|- b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (8b x + 12a b x - 20a b x - 24a x)\|- 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 819
+
+--S 820 of 1369
+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 2 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 820
+
+--S 821 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 821
+
+--S 822 of 1369
+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 2 +---+ +-+
+--R 8b \|- b \|b
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 823
+
+)clear all
+
+--S 824 of 1369
+t0:=x^3/sqrt(a+b*x^2)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 824
+
+--S 825 of 1369
+r0:=-2/3*a*sqrt(a+b*x^2)/b^2+1/3*x^2*sqrt(a+b*x^2)/b
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x - 2a)\|b x + a
+--R (2) ----------------------
+--R 2
+--R 3b
+--R Type: Expression(Integer)
+--E 825
+
+--S 826 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 4 | 2 6 4 +-+
+--R - 3a x \|b x + a + (b x + 3a x )\|a
+--R (3) ---------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 826
+
+--S 827 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R 2 2 3 | 2 2 2 3 +-+
+--R (- 2a b x - 8a )\|b x + a + (6a b x + 8a )\|a
+--R (4) --------------------------------------------------
+--R +--------+
+--R 3 2 2 +-+ | 2 3 2 2 2
+--R (3b x + 12a b )\|a \|b x + a - 9a b x - 12a b
+--R Type: Expression(Integer)
+--E 827
+
+--S 828 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 828
+
+)clear all
+
+--S 829 of 1369
+t0:=x^2/sqrt(a+b*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 829
+
+--S 830 of 1369
+r0:=-1/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+1/2*x*sqrt(a+b*x^2)/b
+--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 2b\|b
+--R Type: Expression(Integer)
+--E 830
+
+--S 831 of 1369
+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 2 +-+
+--R 4b\|a \|b \|b x + a + (- 2b x - 4a b)\|b
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (- 4a\|a \|b x + a + 2a b x + 4a )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R 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 2 +---+
+--R 4b\|- b \|a \|b x + a + (- 2b x - 4a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 831
+
+--S 832 of 1369
+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 2b\|b
+--R Type: Expression(Integer)
+--E 832
+
+--S 833 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 833
+
+--S 834 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--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 (6) ----------------------------------------------------------------------
+--R +---+ +-+
+--R 2b\|- b \|b
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 835
+
+)clear all
+
+--S 836 of 1369
+t0:=x/sqrt(a+b*x^2)
+--R
+--R
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 836
+
+--S 837 of 1369
+r0:=sqrt(a+b*x^2)/b
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------
+--R b
+--R Type: Expression(Integer)
+--E 837
+
+--S 838 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R x \|a
+--R (3) -------------------
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R Type: Union(Expression(Integer),...)
+--E 838
+
+--S 839 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R a\|b x + a - a\|a
+--R (4) ----------------------
+--R +--------+
+--R +-+ | 2
+--R b\|a \|b x + a - a b
+--R Type: Expression(Integer)
+--E 839
+
+--S 840 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 840
+
+)clear all
+
+--S 841 of 1369
+t0:=1/sqrt(a+b*x^2)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 1369
+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 842
+
+--S 843 of 1369
+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 843
+
+--S 844 of 1369
+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 844
+
+--S 845 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 845
+
+--S 846 of 1369
+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 846
+
+--S 847 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 847
+
+)clear all
+
+--S 848 of 1369
+t0:=1/(x*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +--------+
+--R | 2
+--R x\|b x + a
+--R Type: Expression(Integer)
+--E 848
+
+--S 849 of 1369
+r0:=-atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R (2) - ------------------
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R +-+ \|b x + a - \|a
+--R \|a log(------------------)
+--R x
+--R (3) ---------------------------
+--R a
+--R Type: Union(Expression(Integer),...)
+--E 850
+
+--S 851 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a - \|a \|b x + a
+--R log(------------------) + atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 851
+
+--S 852 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 852
+
+)clear all
+
+--S 853 of 1369
+t0:=1/(x^2*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 2 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 853
+
+--S 854 of 1369
+r0:=-sqrt(a+b*x^2)/(a*x)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) - -----------
+--R a x
+--R Type: Expression(Integer)
+--E 854
+
+--S 855 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +-+ | 2 2
+--R \|a \|b x + a - b x - a
+--R (3) --------------------------
+--R +--------+
+--R | 2 +-+
+--R a x\|b x + a - a x\|a
+--R Type: Union(Expression(Integer),...)
+--E 855
+
+--S 856 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 856
+
+--S 857 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 857
+
+)clear all
+
+--S 858 of 1369
+t0:=1/(x^3*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 3 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 858
+
+--S 859 of 1369
+r0:=1/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-1/2*sqrt(a+b*x^2)/(a*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 \|b x + a +-+ | 2
+--R b x atanh(-----------) - \|a \|b x + a
+--R +-+
+--R \|a
+--R (2) ----------------------------------------
+--R 2 +-+
+--R 2a x \|a
+--R Type: Expression(Integer)
+--E 859
+
+--S 860 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 | 2 2 4 2 +-+ \|b x + a - \|a
+--R (- 2a b x \|b x + a + (b x + 2a b x )\|a )log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a b x + 2a )\|b x + a + (- 2a b x - 2a )\|a
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 4 3 2
+--R 4a x \|a \|b x + a - 2a b x - 4a x
+--R Type: Union(Expression(Integer),...)
+--E 860
+
+--S 861 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a - \|a \|b x + a
+--R - b log(------------------) - b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------------
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 861
+
+--S 862 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 862
+
+)clear all
+
+--S 863 of 1369
+t0:=1/(x^4*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 4 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 863
+
+--S 864 of 1369
+r0:=-1/3*sqrt(a+b*x^2)/(a*x^3)+2/3*b*sqrt(a+b*x^2)/(a^2*x)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (2b x - a)\|b x + a
+--R (2) ----------------------
+--R 2 3
+--R 3a x
+--R Type: Expression(Integer)
+--E 864
+
+--S 865 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3
+--R (- 6b x - 5a b x + 4a )\|a \|b x + a + 2b x + 9a b x + 3a b x - 4a
+--R --------------------------------------------------------------------------
+--R +--------+
+--R 2 5 3 3 | 2 2 5 3 3 +-+
+--R (3a b x + 12a x )\|b x + a + (- 9a b x - 12a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 865
+
+--S 866 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 866
+
+--S 867 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 867
+
+)clear all
+
+--S 868 of 1369
+t0:=1/(x^5*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 5 | 2
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 868
+
+--S 869 of 1369
+r0:=-3/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_
+ 1/4*sqrt(a+b*x^2)/(a*x^4)+3/8*b*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R +--------+
+--R | 2 +--------+
+--R 2 4 \|b x + a 2 +-+ | 2
+--R - 3b x atanh(-----------) + (3b x - 2a)\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------
+--R 2 4 +-+
+--R 8a x \|a
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 6 2 2 4 | 2
+--R (12a b x + 24a b x )\|b x + a
+--R +
+--R 4 8 3 6 2 2 4 +-+
+--R (- 3b x - 24a b x - 24a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 6 2 2 4 3 2 4 | 2
+--R (- 3a b x - 22a b x - 8a b x + 16a )\|b x + a
+--R +
+--R 3 6 2 2 4 4 +-+
+--R (12a b x + 28a b x - 16a )\|a
+--R /
+--R +--------+
+--R 3 6 4 4 +-+ | 2 3 2 8 4 6 5 4
+--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x
+--R Type: Union(Expression(Integer),...)
+--E 870
+
+--S 871 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R 2 \|b x + a - \|a 2 \|b x + a
+--R 3b log(------------------) + 3b atanh(-----------)
+--R x +-+
+--R \|a
+--R (4) --------------------------------------------------
+--R 2 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 872
+
+)clear all
+
+--S 873 of 1369
+t0:=x^m/(a+b*x^2)^(3/2)
+--R
+--R
+--R m
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 873
+
+--S 874 of 1369
+--r0:=x^(1+m)/(a*sqrt(a+b*x^2))-m*x^(1+m)*_
+-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+-- sqrt((a+b*x^2)/a)/(a*(1+m)*sqrt(a+b*x^2))
+--E 874
+
+--S 875 of 1369
+--a0:=integrate(t0,x)
+--E 875
+
+--S 876 of 1369
+--m0:=a0-r0
+--E 876
+
+--S 877 of 1369
+--d0:=D(m0,x)
+--E 877
+
+)clear all
+
+--S 878 of 1369
+t0:=x^5/(a+b*x^2)^(3/2)
+--R
+--R
+--R 5
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 878
+
+--S 879 of 1369
+r0:=1/3*(a+b*x^2)^(3/2)/b^3-a^2/(b^3*sqrt(a+b*x^2))-2*a*sqrt(a+b*x^2)/b^3
+--R
+--R
+--R 2 4 2 2
+--R b x - 4a b x - 8a
+--R (2) --------------------
+--R +--------+
+--R 3 | 2
+--R 3b \|b x + a
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 6 | 2 8 6 +-+
+--R - 4a x \|b x + a + (b x + 4a x )\|a
+--R (3) ---------------------------------------------------------------------
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (3b x + 24a b x + 24a )\|a \|b x + a - 12a b x - 36a b x - 24a
+--R Type: Union(Expression(Integer),...)
+--E 880
+
+--S 881 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R (- 32a b x - 64a )\|a \|b x + a + 8a b x + 64a b x + 64a
+--R (4) ------------------------------------------------------------------
+--R +--------+
+--R 4 2 2 3 | 2 5 4 4 2 2 3 +-+
+--R (12a b x + 24a b )\|b x + a + (- 3b x - 24a b x - 24a b )\|a
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 882
+
+)clear all
+
+--S 883 of 1369
+t0:=x^4/(a+b*x^2)^(3/2)
+--R
+--R
+--R 4
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 883
+
+--S 884 of 1369
+r0:=-3/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_
+ x^3/(b*sqrt(a+b*x^2))+3/2*x*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R +--------+ +-+
+--R | 2 x\|b 3 +-+
+--R - 3a\|b x + a atanh(-----------) + (b x + 3a x)\|b
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------------------------------------------------
+--R +--------+
+--R 2 +-+ | 2
+--R 2b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 884
+
+--S 885 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 +-+ | 2 2 4 2 2 3
+--R ((9a b x + 12a )\|a \|b x + a - 3a b x - 15a b x - 12a )
+--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 5 3 2 +-+ | 2
+--R (- b x - 7a b x - 12a x)\|b \|b x + a
+--R +
+--R 2 5 3 2 +-+ +-+
+--R (3b x + 13a b x + 12a x)\|a \|b
+--R /
+--R +--------+
+--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+
+--R (6b x + 8a b )\|a \|b \|b x + a + (- 2b x - 10a b x - 8a b )\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 +-+ | 2 2 4 2 2 3
+--R ((- 18a b x - 24a )\|a \|b x + a + 6a b x + 30a b x + 24a )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 2 5 3 2 +---+ | 2
+--R (- b x - 7a b x - 12a x)\|- b \|b x + a
+--R +
+--R 2 5 3 2 +---+ +-+
+--R (3b x + 13a b x + 12a x)\|- b \|a
+--R /
+--R +--------+
+--R 3 2 2 +---+ +-+ | 2 4 4 3 2 2 2 +---+
+--R (6b x + 8a b )\|- b \|a \|b x + a + (- 2b x - 10a b x - 8a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 885
+
+--S 886 of 1369
+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 3a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R 3a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 886
+
+--S 887 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 887
+
+--S 888 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R 3a\|- b atanh(-----------) - 6a\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R -----------------------------------------------------------------------
+--R 2 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 888
+
+--S 889 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 889
+
+)clear all
+
+--S 890 of 1369
+t0:=x^3/(a+b*x^2)^(3/2)
+--R
+--R
+--R 3
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 890
+
+--S 891 of 1369
+r0:=a/(b^2*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^2
+--R
+--R
+--R 2
+--R b x + 2a
+--R (2) -------------
+--R +--------+
+--R 2 | 2
+--R b \|b x + a
+--R Type: Expression(Integer)
+--E 891
+
+--S 892 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 +-+
+--R x \|a
+--R (3) ------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (b x + 2a)\|a \|b x + a - 2a b x - 2a
+--R Type: Union(Expression(Integer),...)
+--E 892
+
+--S 893 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R 4a\|a \|b x + a - 2a b x - 4a
+--R (4) ---------------------------------------
+--R +--------+
+--R 2 | 2 3 2 2 +-+
+--R 2a b \|b x + a + (- b x - 2a b )\|a
+--R Type: Expression(Integer)
+--E 893
+
+--S 894 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 894
+
+)clear all
+
+--S 895 of 1369
+t0:=x^2/(a+b*x^2)^(3/2)
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 895
+
+--S 896 of 1369
+r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)-x/(b*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+ +-+
+--R | 2 x\|b +-+
+--R \|b x + a atanh(-----------) - x\|b
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -------------------------------------
+--R +--------+
+--R +-+ | 2
+--R b\|b \|b x + a
+--R Type: Expression(Integer)
+--E 896
+
+--S 897 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2
+--R (\|a \|b x + a - b x - a)
+--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 x\|b \|b x + a - x\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 +-+
+--R b\|a \|b \|b x + a + (- b x - a b)\|b
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 2 +---+ +-+
+--R +-+ | 2 2 \|- b \|b x + a - \|- b \|a
+--R (2\|a \|b x + a - 2b x - 2a)atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R x\|- b \|b x + a - x\|- b \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 2 +---+
+--R b\|- b \|a \|b x + a + (- b x - a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 897
+
+--S 898 of 1369
+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\|b
+--R Type: Expression(Integer)
+--E 898
+
+--S 899 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 899
+
+--S 900 of 1369
+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 \|b
+--R Type: Expression(Integer)
+--E 900
+
+--S 901 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 901
+
+)clear all
+
+--S 902 of 1369
+t0:=x/(a+b*x^2)^(3/2)
+--R
+--R
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 902
+
+--S 903 of 1369
+r0:=(-1)/(b*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (2) - ------------
+--R +--------+
+--R | 2
+--R b\|b x + a
+--R Type: Expression(Integer)
+--E 903
+
+--S 904 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R 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 904
+
+--S 905 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R - \|a \|b x + a + a
+--R (4) ------------------------
+--R +--------+
+--R | 2 +-+
+--R a b\|b x + a - a b\|a
+--R Type: Expression(Integer)
+--E 905
+
+--S 906 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 906
+
+)clear all
+
+--S 907 of 1369
+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 907
+
+--S 908 of 1369
+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 908
+
+--S 909 of 1369
+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 909
+
+--S 910 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 910
+
+--S 911 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 911
+
+)clear all
+
+--S 912 of 1369
+t0:=1/(x*(a+b*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +--------+
+--R 3 | 2
+--R (b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 912
+
+--S 913 of 1369
+r0:=-atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)+1/(a*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+
+--R +--------+ | 2
+--R | 2 \|b x + a +-+
+--R - \|b x + a atanh(-----------) + \|a
+--R +-+
+--R \|a
+--R (2) --------------------------------------
+--R +--------+
+--R +-+ | 2
+--R a\|a \|b x + a
+--R Type: Expression(Integer)
+--E 913
+
+--S 914 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 2 +-+ \|b x + a - \|a 2 +-+
+--R (a\|b x + a + (- b x - a)\|a )log(------------------) - b x \|a
+--R x
+--R (3) -------------------------------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2 3
+--R a \|a \|b x + a - a b x - a
+--R Type: Union(Expression(Integer),...)
+--E 914
+
+--S 915 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 +-+ \|b x + a - \|a
+--R (\|b x + a - \|a )log(------------------)
+--R x
+--R +
+--R +--------+
+--R +--------+ | 2 +--------+
+--R | 2 +-+ \|b x + a | 2 +-+
+--R (\|b x + a - \|a )atanh(-----------) + \|b x + a - \|a
+--R +-+
+--R \|a
+--R /
+--R +--------+
+--R +-+ | 2 2
+--R a\|a \|b x + a - a
+--R Type: Expression(Integer)
+--E 915
+
+--S 916 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 916
+
+)clear all
+
+--S 917 of 1369
+t0:=1/(x^2*(a+b*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 917
+
+--S 918 of 1369
+r0:=1/(a*x*sqrt(a+b*x^2))-2*sqrt(a+b*x^2)/(a^2*x)
+--R
+--R
+--R 2
+--R - 2b x - a
+--R (2) --------------
+--R +--------+
+--R 2 | 2
+--R a x\|b x + a
+--R Type: Expression(Integer)
+--E 918
+
+--S 919 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2 2 4 2 2
+--R (4b x + 2a)\|a \|b x + a - 2b x - 5a b x - 2a
+--R (3) ---------------------------------------------------
+--R +--------+
+--R 2 3 3 | 2 2 3 3 +-+
+--R (a b x + 2a x)\|b x + a + (- 2a b x - 2a x)\|a
+--R Type: Union(Expression(Integer),...)
+--E 919
+
+--S 920 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 920
+
+--S 921 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 921
+
+)clear all
+
+--S 922 of 1369
+t0:=1/(x^3*(a+b*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 5 3 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 922
+
+--S 923 of 1369
+r0:=3/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+_
+ 1/(a*x^2*sqrt(a+b*x^2))-3/2*sqrt(a+b*x^2)/(a^2*x^2)
+--R
+--R
+--R +--------+
+--R +--------+ | 2
+--R 2 | 2 \|b x + a 2 +-+
+--R 3b x \|b x + a atanh(-----------) + (- 3b x - a)\|a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------
+--R +--------+
+--R 2 2 +-+ | 2
+--R 2a x \|a \|b x + a
+--R Type: Expression(Integer)
+--E 923
+
+--S 924 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+
+--R ((- 9a b x - 12a b x )\|b x + a + (3b x + 15a b x + 12a b x )\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 2 3 | 2
+--R (- 3a b x + 5a b x + 4a )\|b x + a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (2b x + a b x - 7a b x - 4a )\|a
+--R /
+--R +--------+
+--R 3 4 4 2 +-+ | 2 3 2 6 4 4 5 2
+--R (6a b x + 8a x )\|a \|b x + a - 2a b x - 10a b x - 8a x
+--R Type: Union(Expression(Integer),...)
+--E 924
+
+--S 925 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R ((- 3b x - 12a b)\|b x + a + (9b x + 12a b)\|a )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R +--------+ | 2
+--R 2 2 | 2 2 2 +-+ \|b x + a
+--R ((- 3b x - 12a b)\|b x + a + (9b x + 12a b)\|a )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (- 2b x - 8a b)\|b x + a + (6b x + 8a b)\|a
+--R /
+--R +--------+
+--R 2 2 3 +-+ | 2 3 2 4
+--R (2a b x + 8a )\|a \|b x + a - 6a b x - 8a
+--R Type: Expression(Integer)
+--E 925
+
+--S 926 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 926
+
+)clear all
+
+--S 927 of 1369
+t0:=1/(x^4*(a+b*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 6 4 | 2
+--R (b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 927
+
+--S 928 of 1369
+r0:=1/(a*x^3*sqrt(a+b*x^2))-4/3*sqrt(a+b*x^2)/(a^2*x^3)+_
+ 8/3*b*sqrt(a+b*x^2)/(a^3*x)
+--R
+--R
+--R 2 4 2 2
+--R 8b x + 4a b x - a
+--R (2) --------------------
+--R +--------+
+--R 3 3 | 2
+--R 3a x \|b x + a
+--R Type: Expression(Integer)
+--E 928
+
+--S 929 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6
+--R (- 32b x - 80a b x - 28a b x + 8a )\|a \|b x + a + 8b x + 68a b x
+--R +
+--R 2 2 4 3 2 4
+--R 95a b x + 24a b x - 8a
+--R /
+--R +--------+
+--R 3 2 7 4 5 5 3 | 2
+--R (3a b x + 24a b x + 24a x )\|b x + a
+--R +
+--R 3 2 7 4 5 5 3 +-+
+--R (- 12a b x - 36a b x - 24a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 929
+
+--S 930 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 930
+
+--S 931 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 931
+
+)clear all
+
+--S 932 of 1369
+t0:=x^m/(a+b*x^2)^(5/2)
+--R
+--R
+--R m
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 932
+
+--S 933 of 1369
+--r0:=1/3*x^(1+m)/(a*(a+b*x^2)^(3/2))+1/3*(2-m)*x^(1+m)/_
+-- (a^2*sqrt(a+b*x^2))-1/3*(2-m)*m*x^(1+m)*_
+-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+-- sqrt((a+b*x^2)/a)/(a^2*(1+m)*sqrt(a+b*x^2))
+--E 933
+
+--S 934 of 1369
+--a0:=integrate(t0,x)
+--E 934
+
+--S 935 of 1369
+--m0:=a0-r0
+--E 935
+
+--S 936 of 1369
+--d0:=D(m0,x)
+--E 936
+
+)clear all
+
+--S 937 of 1369
+t0:=x^6/(a+b*x^2)^(5/2)
+--R
+--R
+--R 6
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 937
+
+--S 938 of 1369
+r0:=-1/3*x^5/(b*(a+b*x^2)^(3/2))-5/2*a*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(7/2)-5/3*x^3/(b^2*sqrt(a+b*x^2))+_
+ 5/2*x*sqrt(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 | 2 x\|b
+--R (- 15a b x - 15a )\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 5 3 2 +-+
+--R (3b x + 20a b x + 15a x)\|b
+--R /
+--R +--------+
+--R 4 2 3 +-+ | 2
+--R (6b x + 6a b )\|b \|b x + a
+--R Type: Expression(Integer)
+--E 938
+
+--S 939 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 6 2 2 4 3 2 4 +-+ | 2
+--R (75a b x + 375a b x + 540a b x + 240a )\|a \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 15a b x - 210a b x - 615a b x - 660a b x - 240a
+--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 9 3 7 2 2 5 3 3 4 +-+ | 2
+--R (- 3b x - 56a b x - 303a b x - 500a b x - 240a x)\|b \|b x + a
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+ +-+
+--R (15b x + 160a b x + 523a b x + 620a b x + 240a x)\|a \|b
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +-+ +-+ | 2
+--R (30b x + 150a b x + 216a b x + 96a b )\|a \|b \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+
+--R (- 6b x - 84a b x - 246a b x - 264a b x - 96a b )\|b
+--R ,
+--R
+--R +--------+
+--R 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 150a b x - 750a b x - 1080a b x - 480a )\|a \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R 30a b x + 420a b x + 1230a b x + 1320a b x + 480a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 4 9 3 7 2 2 5 3 3 4 +---+ | 2
+--R (- 3b x - 56a b x - 303a b x - 500a b x - 240a x)\|- b \|b x + a
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+
+--R (15b x + 160a b x + 523a b x + 620a b x + 240a x)\|- b \|a
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +---+ +-+ | 2
+--R (30b x + 150a b x + 216a b x + 96a b )\|- b \|a \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +---+
+--R (- 6b x - 84a b x - 246a b x - 264a b x - 96a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 939
+
+--S 940 of 1369
+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 5a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R 5a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 940
+
+--S 941 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R 5a\|- b atanh(-----------) - 10a\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ------------------------------------------------------------------------
+--R 3 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 942
+
+--S 943 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 943
+
+)clear all
+
+--S 944 of 1369
+t0:=x^5/(a+b*x^2)^(5/2)
+--R
+--R
+--R 5
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 1369
+r0:=-1/3*a^2/(b^3*(a+b*x^2)^(3/2))+2*a/(b^3*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^3
+--R
+--R
+--R 2 4 2 2
+--R 3b x + 12a b x + 8a
+--R (2) --------------------------
+--R +--------+
+--R 4 2 3 | 2
+--R (3b x + 3a b )\|b x + a
+--R Type: Expression(Integer)
+--E 945
+
+--S 946 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 6 | 2 8 6 +-+
+--R - 4a x \|b x + a + (3b x + 4a x )\|a
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4
+--R (3b x + 27a b x + 48a b x + 24a )\|a \|b x + a - 12a b x - 48a b x
+--R +
+--R 3 2 4
+--R - 60a b x - 24a
+--R Type: Union(Expression(Integer),...)
+--E 946
+
+--S 947 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R 2 2 +-+ | 2 2 4 2 2 3
+--R (32a b x + 64a )\|a \|b x + a - 8a b x - 64a b x - 64a
+--R (4) ------------------------------------------------------------------
+--R +--------+
+--R 4 2 2 3 | 2 5 4 4 2 2 3 +-+
+--R (12a b x + 24a b )\|b x + a + (- 3b x - 24a b x - 24a b )\|a
+--R Type: Expression(Integer)
+--E 947
+
+--S 948 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 948
+
+)clear all
+
+--S 949 of 1369
+t0:=x^4/(a+b*x^2)^(5/2)
+--R
+--R
+--R 4
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 1369
+r0:=-1/3*x^3/(b*(a+b*x^2)^(3/2))+atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_
+ x/(b^2*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+ +-+
+--R 2 | 2 x\|b 3 +-+
+--R (3b x + 3a)\|b x + a atanh(-----------) + (- 4b x - 3a x)\|b
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ----------------------------------------------------------------
+--R +--------+
+--R 3 2 2 +-+ | 2
+--R (3b x + 3a b )\|b \|b x + a
+--R Type: Expression(Integer)
+--E 950
+
+--S 951 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4
+--R (9b x + 21a b x + 12a )\|a \|b x + a - 3b x - 18a b x
+--R +
+--R 2 2 3
+--R - 27a b x - 12a
+--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 5 3 2 +-+ | 2
+--R (4b x + 19a b x + 12a x)\|b \|b x + a
+--R +
+--R 2 5 3 2 +-+ +-+
+--R (- 12b x - 25a b x - 12a x)\|a \|b
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ +-+ | 2
+--R (9b x + 21a b x + 12a b )\|a \|b \|b x + a
+--R +
+--R 5 6 4 4 2 3 2 3 2 +-+
+--R (- 3b x - 18a b x - 27a b x - 12a b )\|b
+--R ,
+--R
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4
+--R (18b x + 42a b x + 24a )\|a \|b x + a - 6b x - 36a b x
+--R +
+--R 2 2 3
+--R - 54a b x - 24a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 2 5 3 2 +---+ | 2
+--R (4b x + 19a b x + 12a x)\|- b \|b x + a
+--R +
+--R 2 5 3 2 +---+ +-+
+--R (- 12b x - 25a b x - 12a x)\|- b \|a
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +---+ +-+ | 2
+--R (9b x + 21a b x + 12a b )\|- b \|a \|b x + a
+--R +
+--R 5 6 4 4 2 3 2 3 2 +---+
+--R (- 3b x - 18a b x - 27a b x - 12a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 951
+
+--S 952 of 1369
+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 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 952
+
+--S 953 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 953
+
+--S 954 of 1369
+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 2 +---+ +-+
+--R b \|- b \|b
+--R Type: Expression(Integer)
+--E 954
+
+--S 955 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 955
+
+)clear all
+
+--S 956 of 1369
+t0:=x^3/(a+b*x^2)^(5/2)
+--R
+--R
+--R 3
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 956
+
+--S 957 of 1369
+r0:=1/3*a/(b^2*(a+b*x^2)^(3/2))+(-1)/(b^2*sqrt(a+b*x^2))
+--R
+--R
+--R 2
+--R - 3b x - 2a
+--R (2) --------------------------
+--R +--------+
+--R 3 2 2 | 2
+--R (3b x + 3a b )\|b x + a
+--R Type: Expression(Integer)
+--E 957
+
+--S 958 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 | 2 6 4 +-+
+--R - 3a x \|b x + a + (2b x + 3a x )\|a
+--R /
+--R +--------+
+--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4
+--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x
+--R +
+--R 3 2 4
+--R - 27a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 958
+
+--S 959 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (- 2b x - 8a)\|a \|b x + a + 6a b x + 8a
+--R (4) --------------------------------------------------------
+--R +--------+
+--R 3 2 2 2 | 2 3 2 2 2 +-+
+--R (3a b x + 12a b )\|b x + a + (- 9a b x - 12a b )\|a
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 960
+
+)clear all
+
+--S 961 of 1369
+t0:=x^2/(a+b*x^2)^(5/2)
+--R
+--R
+--R 2
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 961
+
+--S 962 of 1369
+r0:=1/3*x^3/(a*(a+b*x^2)^(3/2))
+--R
+--R
+--R 3
+--R x
+--R (2) --------------------------
+--R +--------+
+--R 2 2 | 2
+--R (3a b x + 3a )\|b x + a
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 5 3 | 2 5 3 +-+
+--R (- b x - 4a x )\|b x + a + (3b x + 4a x )\|a
+--R /
+--R +--------+
+--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4
+--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x
+--R +
+--R 3 2 4
+--R - 27a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 963
+
+--S 964 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 964
+
+--S 965 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 965
+
+)clear all
+
+--S 966 of 1369
+t0:=x/(a+b*x^2)^(5/2)
+--R
+--R
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 1369
+r0:=(-1/3)/(b*(a+b*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (2) - -------------------------
+--R +--------+
+--R 2 2 | 2
+--R (3b x + 3a b)\|b x + a
+--R Type: Expression(Integer)
+--E 967
+
+--S 968 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 2 2 | 2 2 6 4 2 2 +-+
+--R (- 3a b x - 6a x )\|b x + a + (b x + 6a b x + 6a x )\|a
+--R /
+--R +--------+
+--R 2 2 4 3 2 4 +-+ | 2 2 3 6 3 2 4
+--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x
+--R +
+--R 4 2 5
+--R - 27a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 968
+
+--S 969 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (- b x - 4a)\|a \|b x + a + 3a b x + 4a
+--R (4) ------------------------------------------------------
+--R +--------+
+--R 2 2 2 3 | 2 2 2 2 3 +-+
+--R (3a b x + 12a b)\|b x + a + (- 9a b x - 12a b)\|a
+--R Type: Expression(Integer)
+--E 969
+
+--S 970 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 970
+
+)clear all
+
+--S 971 of 1369
+t0:=1/(a+b*x^2)^(5/2)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 1369
+r0:=1/3*x/(a*(a+b*x^2)^(3/2))+2/3*x/(a^2*sqrt(a+b*x^2))
+--R
+--R
+--R 3
+--R 2b x + 3a x
+--R (2) --------------------------
+--R +--------+
+--R 2 2 3 | 2
+--R (3a b x + 3a )\|b x + a
+--R Type: Expression(Integer)
+--E 972
+
+--S 973 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 5 3 2 | 2 2 5 3 2 +-+
+--R (- 2b x - 11a b x - 12a x)\|b x + a + (6b x + 17a b x + 12a x)\|a
+--R /
+--R +--------+
+--R 2 2 4 3 2 4 +-+ | 2 2 3 6 3 2 4
+--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x
+--R +
+--R 4 2 5
+--R - 27a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 973
+
+--S 974 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 975
+
+)clear all
+
+--S 976 of 1369
+t0:=1/(x*(a+b*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R +--------+
+--R 2 5 3 2 | 2
+--R (b x + 2a b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1369
+r0:=1/3/(a*(a+b*x^2)^(3/2))-atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+_
+ 1/(a^2*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+
+--R +--------+ | 2
+--R 2 | 2 \|b x + a 2 +-+
+--R (- 3b x - 3a)\|b x + a atanh(-----------) + (3b x + 4a)\|a
+--R +-+
+--R \|a
+--R (2) --------------------------------------------------------------
+--R +--------+
+--R 2 2 3 +-+ | 2
+--R (3a b x + 3a )\|a \|b x + a
+--R Type: Expression(Integer)
+--E 977
+
+--S 978 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 3 | 2
+--R (9a b x + 21a b x + 12a )\|b x + a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 3b x - 18a b x - 27a b x - 12a )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+
+--R (9a b x + 12a b x )\|b x + a + (- 4b x - 15a b x - 12a b x )\|a
+--R /
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4
+--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x
+--R +
+--R 5 2 6
+--R - 27a b x - 12a
+--R Type: Union(Expression(Integer),...)
+--E 978
+
+--S 979 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 | 2 2 +-+ \|b x + a - \|a
+--R ((3b x + 12a)\|b x + a + (- 9b x - 12a)\|a )log(------------------)
+--R x
+--R +
+--R +--------+
+--R +--------+ | 2
+--R 2 | 2 2 +-+ \|b x + a
+--R ((3b x + 12a)\|b x + a + (- 9b x - 12a)\|a )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 | 2 2 +-+
+--R (4b x + 16a)\|b x + a + (- 12b x - 16a)\|a
+--R /
+--R +--------+
+--R 2 2 3 +-+ | 2 3 2 4
+--R (3a b x + 12a )\|a \|b x + a - 9a b x - 12a
+--R Type: Expression(Integer)
+--E 979
+
+--S 980 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 980
+
+)clear all
+
+--S 981 of 1369
+t0:=1/(x^2*(a+b*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R 2 6 4 2 2 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1369
+r0:=1/3/(a*x*(a+b*x^2)^(3/2))+4/3/(a^2*x*sqrt(a+b*x^2))-_
+ 8/3*sqrt(a+b*x^2)/(a^3*x)
+--R
+--R
+--R 2 4 2 2
+--R - 8b x - 12a b x - 3a
+--R (2) ---------------------------
+--R +--------+
+--R 3 3 4 | 2
+--R (3a b x + 3a x)\|b x + a
+--R Type: Expression(Integer)
+--E 982
+
+--S 983 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6
+--R (32b x + 112a b x + 108a b x + 24a )\|a \|b x + a - 8b x - 76a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 163a b x - 120a b x - 24a
+--R /
+--R +--------+
+--R 3 3 7 4 2 5 5 3 6 | 2
+--R (3a b x + 27a b x + 48a b x + 24a x)\|b x + a
+--R +
+--R 3 3 7 4 2 5 5 3 6 +-+
+--R (- 12a b x - 48a b x - 60a b x - 24a x)\|a
+--R Type: Union(Expression(Integer),...)
+--E 983
+
+--S 984 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 984
+
+--S 985 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 985
+
+)clear all
+
+--S 986 of 1369
+t0:=1/(x^3*(a+b*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1369
+r0:=1/3/(a*x^2*(a+b*x^2)^(3/2))+5/2*b*atanh(sqrt(a+b*x^2)/_
+ sqrt(a))/a^(7/2)+5/3/(a^2*x^2*sqrt(a+b*x^2))-_
+ 5/2*sqrt(a+b*x^2)/(a^3*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 2 4 2 | 2 \|b x + a
+--R (15b x + 15a b x )\|b x + a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 +-+
+--R (- 15b x - 20a b x - 3a )\|a
+--R /
+--R +--------+
+--R 3 4 4 2 +-+ | 2
+--R (6a b x + 6a x )\|a \|b x + a
+--R Type: Expression(Integer)
+--E 987
+
+--S 988 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 8 2 3 6 3 2 4 4 2 | 2
+--R (- 75a b x - 375a b x - 540a b x - 240a b x )\|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 +-+
+--R (15b x + 210a b x + 615a b x + 660a b x + 240a b x )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 8 2 3 6 3 2 4 4 2 5 | 2
+--R (- 55a b x - 150a b x - 21a b x + 132a b x + 48a )\|b x + a
+--R +
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+
+--R (14b x + 121a b x + 174a b x - 39a b x - 156a b x - 48a )\|a
+--R /
+--R +--------+
+--R 4 3 8 5 2 6 6 4 7 2 +-+ | 2 4 4 10
+--R (30a b x + 150a b x + 216a b x + 96a x )\|a \|b x + a - 6a b x
+--R +
+--R 5 3 8 6 2 6 7 4 8 2
+--R - 84a b x - 246a b x - 264a b x - 96a x
+--R Type: Union(Expression(Integer),...)
+--E 988
+
+--S 989 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 4 2 2 2 | 2
+--R (- 15b x - 180a b x - 240a b)\|b x + a
+--R +
+--R 3 4 2 2 2 +-+
+--R (75b x + 300a b x + 240a b)\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 4 2 2 2 | 2
+--R (- 15b x - 180a b x - 240a b)\|b x + a
+--R +
+--R 3 4 2 2 2 +-+
+--R (75b x + 300a b x + 240a b)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 3 4 2 2 2 | 2
+--R (- 14b x - 168a b x - 224a b)\|b x + a
+--R +
+--R 3 4 2 2 2 +-+
+--R (70b x + 280a b x + 224a b)\|a
+--R /
+--R +--------+
+--R 3 2 4 4 2 5 +-+ | 2 4 2 4 5 2 6
+--R (6a b x + 72a b x + 96a )\|a \|b x + a - 30a b x - 120a b x - 96a
+--R Type: Expression(Integer)
+--E 989
+
+--S 990 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 990
+
+)clear all
+
+--S 991 of 1369
+t0:=1/(x^4*(a+b*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R 2 8 6 2 4 | 2
+--R (b x + 2a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1369
+r0:=1/3/(a*x^3*(a+b*x^2)^(3/2))+2/(a^2*x^3*sqrt(a+b*x^2))-_
+ 8/3*sqrt(a+b*x^2)/(a^3*x^3)+16/3*b*sqrt(a+b*x^2)/(a^4*x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 16b x + 24a b x + 6a b x - a
+--R (2) --------------------------------
+--R +--------+
+--R 4 5 5 3 | 2
+--R (3a b x + 3a x )\|b x + a
+--R Type: Expression(Integer)
+--E 992
+
+--S 993 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+
+--R (- 96b x - 656a b x - 1316a b x - 954a b x - 160a b x + 32a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2
+--R 16b x + 312a b x + 1206a b x + 1771a b x + 1038a b x + 144a b x
+--R +
+--R 6
+--R - 32a
+--R /
+--R +--------+
+--R 4 4 11 5 3 9 6 2 7 7 5 8 3 | 2
+--R (3a b x + 57a b x + 198a b x + 240a b x + 96a x )\|b x + a
+--R +
+--R 4 4 11 5 3 9 6 2 7 7 5 8 3 +-+
+--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 993
+
+--S 994 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 994
+
+--S 995 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 995
+
+)clear all
+
+--S 996 of 1369
+t0:=x^m/(a+b*x^2)^(9/2)
+--R
+--R
+--R m
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 996
+
+--S 997 of 1369
+--r0:=1/7*x^(1+m)/(a*(a+b*x^2)^(7/2))+1/35*(6-m)*x^(1+m)/_
+-- (a^2*(a+b*x^2)^(5/2))+1/105*(4-m)*(6-m)*x^(1+m)/_
+-- (a^3*(a+b*x^2)^(3/2))+1/105*(2-m)*(4-m)*(6-m)*x^(1+m)/_
+-- (a^4*sqrt(a+b*x^2))-1/105*(2-m)*(4-m)*(6-m)*m*x^(1+m)*_
+-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+-- sqrt((a+b*x^2)/a)/(a^4*(1+m)*sqrt(a+b*x^2))
+--E 997
+
+--S 998 of 1369
+--a0:=integrate(t0,x)
+--E 998
+
+--S 999 of 1369
+--m0:=a0-r0
+--E 999
+
+--S 1000 of 1369
+--d0:=D(m0,x)
+--E 1000
+
+)clear all
+
+--S 1001 of 1369
+t0:=x^10/(a+b*x^2)^(9/2)
+--R
+--R
+--R 10
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1001
+
+--S 1002 of 1369
+r0:=-1/7*x^9/(b*(a+b*x^2)^(7/2))-9/35*x^7/(b^2*(a+b*x^2)^(5/2))-_
+ 3/5*x^5/(b^3*(a+b*x^2)^(3/2))-9/2*a*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(11/2)-3*x^3/(b^4*sqrt(a+b*x^2))+_
+ 9/2*x*sqrt(a+b*x^2)/b^5
+--R
+--R
+--R (2)
+--R +--------+
+--R 3 6 2 2 4 3 2 4 | 2
+--R (- 315a b x - 945a b x - 945a b x - 315a )\|b x + a
+--R *
+--R +-+
+--R x\|b
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (35b x + 528a b x + 1218a b x + 1050a b x + 315a x)\|b
+--R /
+--R +--------+
+--R 8 6 7 4 2 6 2 3 5 +-+ | 2
+--R (70b x + 210a b x + 210a b x + 70a b )\|b \|b x + a
+--R Type: Expression(Integer)
+--E 1002
+
+--S 1003 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 7 14 2 6 12 3 5 10 4 4 8
+--R 2835a b x + 46305a b x + 257985a b x + 705915a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R 1071000a b x + 922320a b x + 423360a b x + 80640a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R - 315a b x - 13860a b x - 127890a b x - 520380a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R - 1149435a b x - 1484280a b x - 1123920a b x - 463680a b x
+--R +
+--R 9
+--R - 80640a
+--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 8 17 7 15 2 6 13 3 5 11
+--R - 35b x - 1928a b x - 30738a b x - 192170a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 580139a b x - 945432a b x - 857808a b x - 409920a b x
+--R +
+--R 8
+--R - 80640a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 315b x + 8952a b x + 89442a b x + 403866a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 968099a b x + 1328136a b x + 1052688a b x + 450240a b x
+--R +
+--R 8
+--R 80640a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 12 14 11 12 2 10 10 3 9 8
+--R 630b x + 10290a b x + 57330a b x + 156870a b x
+--R +
+--R 4 8 6 5 7 4 6 6 2 7 5
+--R 238000a b x + 204960a b x + 94080a b x + 17920a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 13 16 12 14 2 11 12 3 10 10
+--R - 70b x - 3080a b x - 28420a b x - 115640a b x
+--R +
+--R 4 9 8 5 8 6 6 7 4 7 6 2
+--R - 255430a b x - 329840a b x - 249760a b x - 103040a b x
+--R +
+--R 8 5
+--R - 17920a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 7 14 2 6 12 3 5 10 4 4 8
+--R - 5670a b x - 92610a b x - 515970a b x - 1411830a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 2142000a b x - 1844640a b x - 846720a b x - 161280a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R 630a b x + 27720a b x + 255780a b x + 1040760a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R 2298870a b x + 2968560a b x + 2247840a b x + 927360a b x
+--R +
+--R 9
+--R 161280a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R - 35b x - 1928a b x - 30738a b x - 192170a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R - 580139a b x - 945432a b x - 857808a b x - 409920a b x
+--R +
+--R 8
+--R - 80640a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 8 17 7 15 2 6 13 3 5 11
+--R 315b x + 8952a b x + 89442a b x + 403866a b x
+--R +
+--R 4 4 9 5 3 7 6 2 5 7 3
+--R 968099a b x + 1328136a b x + 1052688a b x + 450240a b x
+--R +
+--R 8
+--R 80640a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 12 14 11 12 2 10 10 3 9 8
+--R 630b x + 10290a b x + 57330a b x + 156870a b x
+--R +
+--R 4 8 6 5 7 4 6 6 2 7 5
+--R 238000a b x + 204960a b x + 94080a b x + 17920a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 13 16 12 14 2 11 12 3 10 10
+--R - 70b x - 3080a b x - 28420a b x - 115640a b x
+--R +
+--R 4 9 8 5 8 6 6 7 4 7 6 2
+--R - 255430a b x - 329840a b x - 249760a b x - 103040a b x
+--R +
+--R 8 5
+--R - 17920a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1003
+
+--S 1004 of 1369
+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 9a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R 9a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 5 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 1004
+
+--S 1005 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1005
+
+--S 1006 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R 9a\|- b atanh(-----------) - 18a\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ------------------------------------------------------------------------
+--R 5 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 1006
+
+--S 1007 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1007
+
+)clear all
+
+--S 1008 of 1369
+t0:=x^9/(a+b*x^2)^(9/2)
+--R
+--R
+--R 9
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1008
+
+--S 1009 of 1369
+r0:=-1/7*a^4/(b^5*(a+b*x^2)^(7/2))+4/5*a^3/(b^5*(a+b*x^2)^(5/2))-_
+ 2*a^2/(b^5*(a+b*x^2)^(3/2))+4*a/(b^5*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^5
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R 35b x + 280a b x + 560a b x + 448a b x + 128a
+--R (2) ----------------------------------------------------
+--R +--------+
+--R 8 6 7 4 2 6 2 3 5 | 2
+--R (35b x + 105a b x + 105a b x + 35a b )\|b x + a
+--R Type: Expression(Integer)
+--E 1009
+
+--S 1010 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 14 2 12 3 10 | 2
+--R (- 152a b x - 560a b x - 448a x )\|b x + a
+--R +
+--R 3 16 2 14 2 12 3 10 +-+
+--R (35b x + 376a b x + 784a b x + 448a x )\|a
+--R /
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6
+--R 35b x + 1225a b x + 9065a b x + 29155a b x + 49280a b x
+--R +
+--R 5 2 4 6 2 7
+--R 45920a b x + 22400a b x + 4480a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R - 280a b x - 3920a b x - 19600a b x - 49280a b x - 69720a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 56560a b x - 24640a b x - 4480a
+--R Type: Union(Expression(Integer),...)
+--E 1010
+
+--S 1011 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 6 2 2 4 3 2 4 +-+ | 2
+--R (1024a b x + 10240a b x + 24576a b x + 16384a )\|a \|b x + a
+--R +
+--R 4 8 2 3 6 3 2 4 4 2 5
+--R - 128a b x - 4096a b x - 20480a b x - 32768a b x - 16384a
+--R /
+--R +--------+
+--R 8 6 2 7 4 3 6 2 4 5 | 2
+--R (280a b x + 2800a b x + 6720a b x + 4480a b )\|b x + a
+--R +
+--R 9 8 8 6 2 7 4 3 6 2 4 5 +-+
+--R (- 35b x - 1120a b x - 5600a b x - 8960a b x - 4480a b )\|a
+--R Type: Expression(Integer)
+--E 1011
+
+--S 1012 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1012
+
+)clear all
+
+--S 1013 of 1369
+t0:=x^8/(a+b*x^2)^(9/2)
+--R
+--R
+--R 8
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1013
+
+--S 1014 of 1369
+r0:=-1/7*x^7/(b*(a+b*x^2)^(7/2))-1/5*x^5/(b^2*(a+b*x^2)^(5/2))-_
+ 1/3*x^3/(b^3*(a+b*x^2)^(3/2))+atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(9/2)-x/(b^4*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 3 6 2 4 2 2 3 | 2 x\|b
+--R (105b x + 315a b x + 315a b x + 105a )\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (- 176b x - 406a b x - 350a b x - 105a x)\|b
+--R /
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 +-+ | 2
+--R (105b x + 315a b x + 315a b x + 105a b )\|b \|b x + a
+--R Type: Expression(Integer)
+--E 1014
+
+--S 1015 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 6 12 5 10 2 4 8 3 3 6
+--R 735b x + 8085a b x + 31605a b x + 60375a b x
+--R +
+--R 4 2 4 5 2 6
+--R 61320a b x + 31920a b x + 6720a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6
+--R - 105b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x
+--R +
+--R 5 2 4 6 2 7
+--R - 76440a b x - 35280a b x - 6720a
+--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 13 5 11 2 4 9 3 3 7 4 2 5
+--R 176b x + 4630a b x + 24174a b x + 52249a b x + 56504a b x
+--R +
+--R 5 3 6
+--R 30800a b x + 6720a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 6 13 5 11 2 4 9 3 3 7
+--R - 1232b x - 12698a b x - 44898a b x - 77071a b x
+--R +
+--R 4 2 5 5 3 6
+--R - 71064a b x - 34160a b x - 6720a x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 10 12 9 10 2 8 8 3 7 6 4 6 4
+--R 735b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x
+--R +
+--R 5 5 2 6 4
+--R 31920a b x + 6720a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 11 14 10 12 2 9 10 3 8 8
+--R - 105b x - 2940a b x - 19110a b x - 55860a b x
+--R +
+--R 4 7 6 5 6 4 6 5 2 7 4
+--R - 87465a b x - 76440a b x - 35280a b x - 6720a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 6 12 5 10 2 4 8 3 3 6
+--R 1470b x + 16170a b x + 63210a b x + 120750a b x
+--R +
+--R 4 2 4 5 2 6
+--R 122640a b x + 63840a b x + 13440a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 14 6 12 2 5 10 3 4 8
+--R - 210b x - 5880a b x - 38220a b x - 111720a b x
+--R +
+--R 4 3 6 5 2 4 6 2 7
+--R - 174930a b x - 152880a b x - 70560a b x - 13440a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 6 13 5 11 2 4 9 3 3 7 4 2 5
+--R 176b x + 4630a b x + 24174a b x + 52249a b x + 56504a b x
+--R +
+--R 5 3 6
+--R 30800a b x + 6720a x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 6 13 5 11 2 4 9 3 3 7
+--R - 1232b x - 12698a b x - 44898a b x - 77071a b x
+--R +
+--R 4 2 5 5 3 6
+--R - 71064a b x - 34160a b x - 6720a x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 10 12 9 10 2 8 8 3 7 6 4 6 4
+--R 735b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x
+--R +
+--R 5 5 2 6 4
+--R 31920a b x + 6720a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 11 14 10 12 2 9 10 3 8 8
+--R - 105b x - 2940a b x - 19110a b x - 55860a b x
+--R +
+--R 4 7 6 5 6 4 6 5 2 7 4
+--R - 87465a b x - 76440a b x - 35280a b x - 6720a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1015
+
+--S 1016 of 1369
+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 4 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 1016
+
+--S 1017 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1017
+
+--S 1018 of 1369
+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 4 +---+ +-+
+--R b \|- b \|b
+--R Type: Expression(Integer)
+--E 1018
+
+--S 1019 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1019
+
+)clear all
+
+--S 1020 of 1369
+t0:=x^7/(a+b*x^2)^(9/2)
+--R
+--R
+--R 7
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1020
+
+--S 1021 of 1369
+r0:=1/7*a^3/(b^4*(a+b*x^2)^(7/2))-3/5*a^2/(b^4*(a+b*x^2)^(5/2))+_
+ a/(b^4*(a+b*x^2)^(3/2))+(-1)/(b^4*sqrt(a+b*x^2))
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 35b x - 70a b x - 56a b x - 16a
+--R (2) ----------------------------------------------------
+--R +--------+
+--R 7 6 6 4 2 5 2 3 4 | 2
+--R (35b x + 105a b x + 105a b x + 35a b )\|b x + a
+--R Type: Expression(Integer)
+--E 1021
+
+--S 1022 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 12 2 10 3 8 | 2
+--R (- 77a b x - 322a b x - 280a x )\|b x + a
+--R +
+--R 3 14 2 12 2 10 3 8 +-+
+--R (16b x + 203a b x + 462a b x + 280a x )\|a
+--R /
+--R 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x
+--R +
+--R 6 2 7
+--R 10640a b x + 2240a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 25480a b x - 11760a b x - 2240a
+--R Type: Union(Expression(Integer),...)
+--E 1022
+
+--S 1023 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (- 16b x - 384a b x - 1280a b x - 1024a )\|a \|b x + a + 112a b x
+--R +
+--R 2 2 4 3 2 4
+--R 896a b x + 1792a b x + 1024a
+--R /
+--R +--------+
+--R 7 6 2 6 4 3 5 2 4 4 | 2
+--R (35a b x + 840a b x + 2800a b x + 2240a b )\|b x + a
+--R +
+--R 7 6 2 6 4 3 5 2 4 4 +-+
+--R (- 245a b x - 1960a b x - 3920a b x - 2240a b )\|a
+--R Type: Expression(Integer)
+--E 1023
+
+--S 1024 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1024
+
+)clear all
+
+--S 1025 of 1369
+t0:=x^6/(a+b*x^2)^(9/2)
+--R
+--R
+--R 6
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1025
+
+--S 1026 of 1369
+r0:=1/7*x^7/(a*(a+b*x^2)^(7/2))
+--R
+--R
+--R 7
+--R x
+--R (2) ------------------------------------------------
+--R +--------+
+--R 3 6 2 2 4 3 2 4 | 2
+--R (7a b x + 21a b x + 21a b x + 7a )\|b x + a
+--R Type: Expression(Integer)
+--E 1026
+
+--S 1027 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 13 2 11 2 9 3 7 | 2
+--R (- b x - 24a b x - 80a b x - 64a x )\|b x + a
+--R +
+--R 3 13 2 11 2 9 3 7 +-+
+--R (7b x + 56a b x + 112a b x + 64a x )\|a
+--R /
+--R 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R 49a b x + 539a b x + 2107a b x + 4025a b x + 4088a b x
+--R +
+--R 6 2 7
+--R 2128a b x + 448a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6
+--R - 7a b x - 196a b x - 1274a b x - 3724a b x - 5831a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 5096a b x - 2352a b x - 448a
+--R Type: Union(Expression(Integer),...)
+--E 1027
+
+--S 1028 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1028
+
+--S 1029 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1029
+
+)clear all
+
+--S 1030 of 1369
+t0:=x^5/(a+b*x^2)^(9/2)
+--R
+--R
+--R 5
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1030
+
+--S 1031 of 1369
+r0:=-1/7*a^2/(b^3*(a+b*x^2)^(7/2))+2/5*a/(b^3*(a+b*x^2)^(5/2))+_
+ (-1/3)/(b^3*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2 4 2 2
+--R - 35b x - 28a b x - 8a
+--R (2) ------------------------------------------------------
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 | 2
+--R (105b x + 315a b x + 315a b x + 105a b )\|b x + a
+--R Type: Expression(Integer)
+--E 1031
+
+--S 1032 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 12 2 2 10 3 8 4 6 | 2
+--R (- 56a b x - 581a b x - 1540a b x - 1120a x )\|b x + a
+--R +
+--R 4 14 3 12 2 2 10 3 8 4 6 +-+
+--R (8b x + 224a b x + 1211a b x + 2100a b x + 1120a x )\|a
+--R /
+--R 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R 735a b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x
+--R +
+--R 7 2 8
+--R 31920a b x + 6720a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 7 14 3 6 12 4 5 10 5 4 8 6 3 6
+--R - 105a b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x
+--R +
+--R 7 2 4 8 2 9
+--R - 76440a b x - 35280a b x - 6720a
+--R Type: Union(Expression(Integer),...)
+--E 1032
+
+--S 1033 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (- 8b x - 192a b x - 640a b x - 512a )\|a \|b x + a + 56a b x
+--R +
+--R 2 2 4 3 2 4
+--R 448a b x + 896a b x + 512a
+--R /
+--R +--------+
+--R 2 6 6 3 5 4 4 4 2 5 3 | 2
+--R (105a b x + 2520a b x + 8400a b x + 6720a b )\|b x + a
+--R +
+--R 2 6 6 3 5 4 4 4 2 5 3 +-+
+--R (- 735a b x - 5880a b x - 11760a b x - 6720a b )\|a
+--R Type: Expression(Integer)
+--E 1033
+
+--S 1034 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1034
+
+)clear all
+
+--S 1035 of 1369
+t0:=x^4/(a+b*x^2)^(9/2)
+--R
+--R
+--R 4
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1035
+
+--S 1036 of 1369
+r0:=1/7*x^5/(a*(a+b*x^2)^(7/2))+2/35*x^5/(a^2*(a+b*x^2)^(5/2))
+--R
+--R
+--R 7 5
+--R 2b x + 7a x
+--R (2) ----------------------------------------------------
+--R +--------+
+--R 2 3 6 3 2 4 4 2 5 | 2
+--R (35a b x + 105a b x + 105a b x + 35a )\|b x + a
+--R Type: Expression(Integer)
+--E 1036
+
+--S 1037 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 13 3 11 2 2 9 3 7 4 5 | 2
+--R (- 2b x - 55a b x - 328a b x - 688a b x - 448a x )\|b x + a
+--R +
+--R 4 13 3 11 2 2 9 3 7 4 5 +-+
+--R (14b x + 161a b x + 616a b x + 912a b x + 448a x )\|a
+--R /
+--R 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4
+--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x
+--R +
+--R 7 2 8
+--R 10640a b x + 2240a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 7 14 3 6 12 4 5 10 5 4 8 6 3 6
+--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x
+--R +
+--R 7 2 4 8 2 9
+--R - 25480a b x - 11760a b x - 2240a
+--R Type: Union(Expression(Integer),...)
+--E 1037
+
+--S 1038 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1038
+
+--S 1039 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1039
+
+)clear all
+
+--S 1040 of 1369
+t0:=x^3/(a+b*x^2)^(9/2)
+--R
+--R
+--R 3
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1040
+
+--S 1041 of 1369
+r0:=1/7*a/(b^2*(a+b*x^2)^(7/2))+(-1/5)/(b^2*(a+b*x^2)^(5/2))
+--R
+--R
+--R 2
+--R - 7b x - 2a
+--R (2) ----------------------------------------------------
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 | 2
+--R (35b x + 105a b x + 105a b x + 35a b )\|b x + a
+--R Type: Expression(Integer)
+--E 1041
+
+--S 1042 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 12 2 3 10 3 2 8 4 6 5 4 | 2
+--R (- 14a b x - 154a b x - 595a b x - 980a b x - 560a x )\|b x + a
+--R +
+--R 5 14 4 12 2 3 10 3 2 8 4 6 5 4 +-+
+--R (2b x + 56a b x + 364a b x + 1015a b x + 1260a b x + 560a x )\|a
+--R /
+--R 3 6 12 4 5 10 5 4 8 6 3 6 7 2 4
+--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x
+--R +
+--R 8 2 9
+--R 10640a b x + 2240a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 7 14 4 6 12 5 5 10 6 4 8 7 3 6
+--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x
+--R +
+--R 8 2 4 9 2 10
+--R - 25480a b x - 11760a b x - 2240a
+--R Type: Union(Expression(Integer),...)
+--E 1042
+
+--S 1043 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6
+--R (- 2b x - 48a b x - 160a b x - 128a )\|a \|b x + a + 14a b x
+--R +
+--R 2 2 4 3 2 4
+--R 112a b x + 224a b x + 128a
+--R /
+--R +--------+
+--R 3 5 6 4 4 4 5 3 2 6 2 | 2
+--R (35a b x + 840a b x + 2800a b x + 2240a b )\|b x + a
+--R +
+--R 3 5 6 4 4 4 5 3 2 6 2 +-+
+--R (- 245a b x - 1960a b x - 3920a b x - 2240a b )\|a
+--R Type: Expression(Integer)
+--E 1043
+
+--S 1044 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1044
+
+)clear all
+
+--S 1045 of 1369
+t0:=x^2/(a+b*x^2)^(9/2)
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1045
+
+--S 1046 of 1369
+r0:=1/7*x^3/(a*(a+b*x^2)^(7/2))+4/35*x^3/(a^2*(a+b*x^2)^(5/2))+_
+ 8/105*x^3/(a^3*(a+b*x^2)^(3/2))
+--R
+--R
+--R 2 7 5 2 3
+--R 8b x + 28a b x + 35a x
+--R (2) ------------------------------------------------------
+--R +--------+
+--R 3 3 6 4 2 4 5 2 6 | 2
+--R (105a b x + 315a b x + 315a b x + 105a )\|b x + a
+--R Type: Expression(Integer)
+--E 1046
+
+--S 1047 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 13 4 11 2 3 9 3 2 7 4 5
+--R - 8b x - 220a b x - 1347a b x - 3592a b x - 4592a b x
+--R +
+--R 5 3
+--R - 2240a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 13 4 11 2 3 9 3 2 7 4 5
+--R 56b x + 644a b x + 2709a b x + 5608a b x + 5712a b x
+--R +
+--R 5 3
+--R 2240a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 3 6 12 4 5 10 5 4 8 6 3 6 7 2 4
+--R 735a b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x
+--R +
+--R 8 2 9
+--R 31920a b x + 6720a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 7 14 4 6 12 5 5 10 6 4 8 7 3 6
+--R - 105a b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x
+--R +
+--R 8 2 4 9 2 10
+--R - 76440a b x - 35280a b x - 6720a
+--R Type: Union(Expression(Integer),...)
+--E 1047
+
+--S 1048 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1048
+
+--S 1049 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1049
+
+)clear all
+
+--S 1050 of 1369
+t0:=x/(a+b*x^2)^(9/2)
+--R
+--R
+--R x
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1050
+
+--S 1051 of 1369
+r0:=(-1/7)/(b*(a+b*x^2)^(7/2))
+--R
+--R
+--R 1
+--R (2) - -----------------------------------------------
+--R +--------+
+--R 4 6 3 4 2 2 2 3 | 2
+--R (7b x + 21a b x + 21a b x + 7a b)\|b x + a
+--R Type: Expression(Integer)
+--E 1051
+
+--S 1052 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 2 4 10 3 3 8 4 2 6 5 4 6 2
+--R (- 7a b x - 77a b x - 301a b x - 574a b x - 560a b x - 224a x )
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 14 5 12 2 4 10 3 3 8 4 2 6 5 4
+--R b x + 28a b x + 182a b x + 532a b x + 826a b x + 672a b x
+--R +
+--R 6 2
+--R 224a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 6 12 5 5 10 6 4 8 7 3 6 8 2 4
+--R 49a b x + 539a b x + 2107a b x + 4025a b x + 4088a b x
+--R +
+--R 9 2 10
+--R 2128a b x + 448a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 7 14 5 6 12 6 5 10 7 4 8 8 3 6
+--R - 7a b x - 196a b x - 1274a b x - 3724a b x - 5831a b x
+--R +
+--R 9 2 4 10 2 11
+--R - 5096a b x - 2352a b x - 448a
+--R Type: Union(Expression(Integer),...)
+--E 1052
+
+--S 1053 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4
+--R (- b x - 24a b x - 80a b x - 64a )\|a \|b x + a + 7a b x + 56a b x
+--R +
+--R 3 2 4
+--R 112a b x + 64a
+--R /
+--R +--------+
+--R 4 4 6 5 3 4 6 2 2 7 | 2
+--R (7a b x + 168a b x + 560a b x + 448a b)\|b x + a
+--R +
+--R 4 4 6 5 3 4 6 2 2 7 +-+
+--R (- 49a b x - 392a b x - 784a b x - 448a b)\|a
+--R Type: Expression(Integer)
+--E 1053
+
+--S 1054 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1054
+
+)clear all
+
+--S 1055 of 1369
+t0:=1/(a+b*x^2)^(9/2)
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 1055
+
+--S 1056 of 1369
+r0:=1/7*x/(a*(a+b*x^2)^(7/2))+6/35*x/(a^2*(a+b*x^2)^(5/2))+_
+ 8/35*x/(a^3*(a+b*x^2)^(3/2))+16/35*x/(a^4*sqrt(a+b*x^2))
+--R
+--R
+--R 3 7 2 5 2 3 3
+--R 16b x + 56a b x + 70a b x + 35a x
+--R (2) ----------------------------------------------------
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 | 2
+--R (35a b x + 105a b x + 105a b x + 35a )\|b x + a
+--R Type: Expression(Integer)
+--E 1056
+
+--S 1057 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 13 5 11 2 4 9 3 3 7 4 2 5
+--R - 16b x - 440a b x - 2694a b x - 7219a b x - 10024a b x
+--R +
+--R 5 3 6
+--R - 7280a b x - 2240a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 13 5 11 2 4 9 3 3 7 4 2 5
+--R 112b x + 1288a b x + 5418a b x + 11461a b x + 13384a b x
+--R +
+--R 5 3 6
+--R 8400a b x + 2240a x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 6 12 5 5 10 6 4 8 7 3 6 8 2 4
+--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x
+--R +
+--R 9 2 10
+--R 10640a b x + 2240a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 7 14 5 6 12 6 5 10 7 4 8 8 3 6
+--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x
+--R +
+--R 9 2 4 10 2 11
+--R - 25480a b x - 11760a b x - 2240a
+--R Type: Union(Expression(Integer),...)
+--E 1057
+
+--S 1058 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1058
+
+--S 1059 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1059
+
+)clear all
+
+--S 1060 of 1369
+t0:=1/(x*(a+b*x^2)^(9/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R +--------+
+--R 4 9 3 7 2 2 5 3 3 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a x)\|b x + a
+--R Type: Expression(Integer)
+--E 1060
+
+--S 1061 of 1369
+r0:=1/7/(a*(a+b*x^2)^(7/2))+1/5/(a^2*(a+b*x^2)^(5/2))+_
+ 1/3/(a^3*(a+b*x^2)^(3/2))-atanh(sqrt(a+b*x^2)/sqrt(a))/_
+ a^(9/2)+1/(a^4*sqrt(a+b*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R +--------+ | 2
+--R 3 6 2 4 2 2 3 | 2 \|b x + a
+--R (- 105b x - 315a b x - 315a b x - 105a )\|b x + a atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (105b x + 350a b x + 406a b x + 176a )\|a
+--R /
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2
+--R (105a b x + 315a b x + 315a b x + 105a )\|a \|b x + a
+--R Type: Expression(Integer)
+--E 1061
+
+--S 1062 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 12 2 5 10 3 4 8 4 3 6
+--R 735a b x + 8085a b x + 31605a b x + 60375a b x
+--R +
+--R 5 2 4 6 2 7
+--R 61320a b x + 31920a b x + 6720a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 14 6 12 2 5 10 3 4 8
+--R - 105b x - 2940a b x - 19110a b x - 55860a b x
+--R +
+--R 4 3 6 5 2 4 6 2 7
+--R - 87465a b x - 76440a b x - 35280a b x - 6720a
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 6 12 2 5 10 3 4 8 4 3 6 5 2 4
+--R 1127a b x + 10682a b x + 35770a b x + 56560a b x + 43680a b x
+--R +
+--R 6 2
+--R 13440a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6
+--R - 176b x - 4193a b x - 23702a b x - 59430a b x - 76720a b x
+--R +
+--R 5 2 4 6 2
+--R - 50400a b x - 13440a b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 5 6 12 6 5 10 7 4 8 8 3 6 9 2 4
+--R 735a b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x
+--R +
+--R 10 2 11
+--R 31920a b x + 6720a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 7 14 6 6 12 7 5 10 8 4 8 9 3 6
+--R - 105a b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x
+--R +
+--R 10 2 4 11 2 12
+--R - 76440a b x - 35280a b x - 6720a
+--R Type: Union(Expression(Integer),...)
+--E 1062
+
+--S 1063 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (105b x + 2520a b x + 8400a b x + 6720a )\|b x + a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 735b x - 5880a b x - 11760a b x - 6720a )\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (105b x + 2520a b x + 8400a b x + 6720a )\|b x + a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 735b x - 5880a b x - 11760a b x - 6720a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (176b x + 4224a b x + 14080a b x + 11264a )\|b x + a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 1232b x - 9856a b x - 19712a b x - 11264a )\|a
+--R /
+--R +--------+
+--R 4 3 6 5 2 4 6 2 7 +-+ | 2 5 3 6
+--R (105a b x + 2520a b x + 8400a b x + 6720a )\|a \|b x + a - 735a b x
+--R +
+--R 6 2 4 7 2 8
+--R - 5880a b x - 11760a b x - 6720a
+--R Type: Expression(Integer)
+--E 1063
+
+--S 1064 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1064
+
+)clear all
+
+--S 1065 of 1369
+t0:=1/(x^2*(a+b*x^2)^(9/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------
+--R +--------+
+--R 4 10 3 8 2 2 6 3 4 4 2 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1065
+
+--S 1066 of 1369
+r0:=1/7/(a*x*(a+b*x^2)^(7/2))+8/35/(a^2*x*(a+b*x^2)^(5/2))+_
+ 16/35/(a^3*x*(a+b*x^2)^(3/2))+64/35/(a^4*x*sqrt(a+b*x^2))-_
+ 128/35*sqrt(a+b*x^2)/(a^5*x)
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R - 128b x - 448a b x - 560a b x - 280a b x - 35a
+--R (2) -----------------------------------------------------
+--R +--------+
+--R 5 3 7 6 2 5 7 3 8 | 2
+--R (35a b x + 105a b x + 105a b x + 35a x)\|b x + a
+--R Type: Expression(Integer)
+--E 1066
+
+--S 1067 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 14 6 12 2 5 10 3 4 8 4 3 6
+--R 1024b x + 13824a b x + 64896a b x + 149440a b x + 187544a b x
+--R +
+--R 5 2 4 6 2 7
+--R 128240a b x + 42560a b x + 4480a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 8 16 7 14 2 6 12 3 5 10 4 4 8
+--R - 128b x - 4544a b x - 35376a b x - 122648a b x - 229667a b x
+--R +
+--R 5 3 6 6 2 4 7 2 8
+--R - 246624a b x - 148960a b x - 44800a b x - 4480a
+--R /
+--R 5 7 15 6 6 13 7 5 11 8 4 9 9 3 7
+--R 35a b x + 1225a b x + 9065a b x + 29155a b x + 49280a b x
+--R +
+--R 10 2 5 11 3 12
+--R 45920a b x + 22400a b x + 4480a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 7 15 6 6 13 7 5 11 8 4 9 9 3 7
+--R - 280a b x - 3920a b x - 19600a b x - 49280a b x - 69720a b x
+--R +
+--R 10 2 5 11 3 12
+--R - 56560a b x - 24640a b x - 4480a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 1067
+
+--S 1068 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1068
+
+--S 1069 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1069
+
+)clear all
+
+--S 1070 of 1369
+t0:=1/(x^3*(a+b*x^2)^(9/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------------------
+--R +--------+
+--R 4 11 3 9 2 2 7 3 5 4 3 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1070
+
+--S 1071 of 1369
+r0:=1/7/(a*x^2*(a+b*x^2)^(7/2))+9/35/(a^2*x^2*(a+b*x^2)^(5/2))+_
+ 3/5/(a^3*x^2*(a+b*x^2)^(3/2))+9/2*b*atanh(sqrt(a+b*x^2)/_
+ sqrt(a))/a^(11/2)+3/(a^4*x^2*sqrt(a+b*x^2))-9/2*sqrt(a+b*x^2)/(a^5*x^2)
+--R
+--R
+--R (2)
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 | 2
+--R (315b x + 945a b x + 945a b x + 315a b x )\|b x + a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- 315b x - 1050a b x - 1218a b x - 528a b x - 35a )\|a
+--R /
+--R +--------+
+--R 5 3 8 6 2 6 7 4 8 2 +-+ | 2
+--R (70a b x + 210a b x + 210a b x + 70a x )\|a \|b x + a
+--R Type: Expression(Integer)
+--E 1071
+
+--S 1072 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R - 2835a b x - 46305a b x - 257985a b x - 705915a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2
+--R - 1071000a b x - 922320a b x - 423360a b x - 80640a b x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12
+--R 315b x + 13860a b x + 127890a b x + 520380a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 1149435a b x + 1484280a b x + 1123920a b x + 463680a b x
+--R +
+--R 8 2
+--R 80640a b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 8 16 2 7 14 3 6 12 4 5 10
+--R - 3177a b x - 43386a b x - 198954a b x - 427140a b x
+--R +
+--R 5 4 8 6 3 6 7 2 4 8 2 9
+--R - 454685a b x - 193480a b x + 35280a b x + 51520a b x + 8960a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 9 18 8 16 2 7 14 3 6 12
+--R 388b x + 14237a b x + 110278a b x + 367934a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R 629860a b x + 552965a b x + 181720a b x - 59920a b x
+--R +
+--R 8 2 9
+--R - 56000a b x - 8960a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 7 16 7 6 14 8 5 12 9 4 10
+--R 630a b x + 10290a b x + 57330a b x + 156870a b x
+--R +
+--R 10 3 8 11 2 6 12 4 13 2
+--R 238000a b x + 204960a b x + 94080a b x + 17920a x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 6 8 18 7 7 16 8 6 14 9 5 12 10 4 10
+--R - 70a b x - 3080a b x - 28420a b x - 115640a b x - 255430a b x
+--R +
+--R 11 3 8 12 2 6 13 4 14 2
+--R - 329840a b x - 249760a b x - 103040a b x - 17920a x
+--R Type: Union(Expression(Integer),...)
+--E 1072
+
+--S 1073 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 8 4 6 2 3 4 3 2 2 4
+--R (- 315b x - 12600a b x - 75600a b x - 141120a b x - 80640a b)
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 8 4 6 2 3 4 3 2 2 4 +-+
+--R (2835b x + 37800a b x + 136080a b x + 181440a b x + 80640a b)\|a
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R log(------------------)
+--R x
+--R +
+--R 5 8 4 6 2 3 4 3 2 2 4
+--R (- 315b x - 12600a b x - 75600a b x - 141120a b x - 80640a b)
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 8 4 6 2 3 4 3 2 2 4 +-+
+--R (2835b x + 37800a b x + 136080a b x + 181440a b x + 80640a b)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 5 8 4 6 2 3 4 3 2 2 4
+--R (- 388b x - 15520a b x - 93120a b x - 173824a b x - 99328a b)
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 8 4 6 2 3 4 3 2 2 4 +-+
+--R (3492b x + 46560a b x + 167616a b x + 223488a b x + 99328a b)\|a
+--R /
+--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+
+--R (70a b x + 2800a b x + 16800a b x + 31360a b x + 17920a )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 4 8 7 3 6 8 2 4 9 2 10
+--R - 630a b x - 8400a b x - 30240a b x - 40320a b x - 17920a
+--R Type: Expression(Integer)
+--E 1073
+
+--S 1074 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1074
+
+)clear all
+
+--S 1075 of 1369
+t0:=1/(x^4*(a+b*x^2)^(9/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------------
+--R +--------+
+--R 4 12 3 10 2 2 8 3 6 4 4 | 2
+--R (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1075
+
+--S 1076 of 1369
+r0:=1/7/(a*x^3*(a+b*x^2)^(7/2))+2/7/(a^2*x^3*(a+b*x^2)^(5/2))+_
+ 16/21/(a^3*x^3*(a+b*x^2)^(3/2))+32/7/(a^4*x^3*sqrt(a+b*x^2))-_
+ 128/21*sqrt(a+b*x^2)/(a^5*x^3)+256/21*b*sqrt(a+b*x^2)/(a^6*x)
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R 256b x + 896a b x + 1120a b x + 560a b x + 70a b x - 7a
+--R (2) --------------------------------------------------------------
+--R +--------+
+--R 6 3 9 7 2 7 8 5 9 3 | 2
+--R (21a b x + 63a b x + 63a b x + 21a x )\|b x + a
+--R Type: Expression(Integer)
+--E 1076
+
+--S 1077 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 18 8 16 2 7 14 3 6 12
+--R - 2560b x - 49920a b x - 326592a b x - 1049056a b x
+--R +
+--R 4 5 10 5 4 8 6 3 6 7 2 4
+--R - 1891516a b x - 1993082a b x - 1192800a b x - 353696a b x
+--R +
+--R 8 2 9
+--R - 28672a b x + 3584a
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 10 20 9 18 2 8 16 3 7 14 4 6 12
+--R 256b x + 13696a b x + 148320a b x + 701680a b x + 1807270a b x
+--R +
+--R 5 5 10 6 4 8 7 3 6 8 2 4
+--R 2759845a b x + 2547202a b x + 1365840a b x + 368480a b x
+--R +
+--R 9 2 10
+--R 26880a b x - 3584a
+--R /
+--R 6 8 19 7 7 17 8 6 15 9 5 13
+--R 21a b x + 1113a b x + 11613a b x + 51891a b x
+--R +
+--R 10 4 11 11 3 9 12 2 7 13 5
+--R 123690a b x + 170352a b x + 136416a b x + 59136a b x
+--R +
+--R 14 3
+--R 10752a x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 6 8 19 7 7 17 8 6 15 9 5 13
+--R - 210a b x - 4200a b x - 28812a b x - 98952a b x
+--R +
+--R 10 4 11 11 3 9 12 2 7 13 5
+--R - 195090a b x - 231840a b x - 164640a b x - 64512a b x
+--R +
+--R 14 3
+--R - 10752a x
+--R *
+--R +-+
+--R \|a
+--R Type: Union(Expression(Integer),...)
+--E 1077
+
+--S 1078 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1078
+
+--S 1079 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1079
+
+)clear all
+
+--S 1080 of 1369
+t0:=x^5/sqrt(9+4*x^2)
+--R
+--R
+--R 5
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R Type: Expression(Integer)
+--E 1080
+
+--S 1081 of 1369
+r0:=27/40*sqrt(9+4*x^2)-3/20*x^2*sqrt(9+4*x^2)+1/20*x^4*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R 4 2 | 2
+--R (2x - 6x + 27)\|4x + 9
+--R (2) --------------------------
+--R 40
+--R Type: Expression(Integer)
+--E 1081
+
+--S 1082 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 9 7 5 3 | 2 10
+--R (- 1024x + 192x - 6804x - 34020x - 21870x)\|4x + 9 + 2048x
+--R +
+--R 8 6 4 2
+--R 1920x + 11880x + 85050x + 109350x + 19683
+--R /
+--R +-------+
+--R 4 2 | 2 5 3
+--R (10240x + 17280x + 3240)\|4x + 9 - 20480x - 57600x - 32400x
+--R Type: Union(Expression(Integer),...)
+--E 1082
+
+--S 1083 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1083
+
+--S 1084 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1084
+
+)clear all
+
+--S 1085 of 1369
+t0:=x^4/sqrt(9+4*x^2)
+--R
+--R
+--R 4
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R Type: Expression(Integer)
+--E 1085
+
+--S 1086 of 1369
+r0:=243/256*asinh(2/3*x)-27/128*x*sqrt(9+4*x^2)+1/16*x^3*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R 3 | 2 2x
+--R (16x - 54x)\|4x + 9 + 243asinh(--)
+--R 3
+--R (2) -------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 1086
+
+--S 1087 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 3 | 2 4 2
+--R ((- 15552x - 17496x)\|4x + 9 + 31104x + 69984x + 19683)
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x + 9 - 2x)
+--R +
+--R +-------+
+--R 7 5 3 | 2 8 4
+--R (- 2048x + 2304x + 14256x + 4374x)\|4x + 9 + 4096x - 36288x
+--R +
+--R 2
+--R - 34992x
+--R /
+--R +-------+
+--R 3 | 2 4 2
+--R (16384x + 18432x)\|4x + 9 - 32768x - 73728x - 20736
+--R Type: Union(Expression(Integer),...)
+--E 1087
+
+--S 1088 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R - 243log(\|4x + 9 - 2x) - 243asinh(--)
+--R 3
+--R (4) ----------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 1088
+
+--S 1089 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1089
+
+)clear all
+
+--S 1090 of 1369
+t0:=x^3/sqrt(9+4*x^2)
+--R
+--R
+--R 3
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R Type: Expression(Integer)
+--E 1090
+
+--S 1091 of 1369
+r0:=-3/8*sqrt(9+4*x^2)+1/12*x^2*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (2x - 9)\|4x + 9
+--R (2) -------------------
+--R 24
+--R Type: Expression(Integer)
+--E 1091
+
+--S 1092 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 5 3 | 2 6 4 2
+--R (- 64x + 180x + 486x)\|4x + 9 + 128x - 216x - 1458x - 729
+--R (3) ----------------------------------------------------------------
+--R +-------+
+--R 2 | 2 3
+--R (384x + 216)\|4x + 9 - 768x - 1296x
+--R Type: Union(Expression(Integer),...)
+--E 1092
+
+--S 1093 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1093
+
+--S 1094 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1094
+
+)clear all
+
+--S 1095 of 1369
+t0:=x^2/sqrt(9+4*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R Type: Expression(Integer)
+--E 1095
+
+--S 1096 of 1369
+r0:=-9/16*asinh(2/3*x)+1/8*x*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R 2x\|4x + 9 - 9asinh(--)
+--R 3
+--R (2) -------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 1096
+
+--S 1097 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R | 2 2 | 2
+--R (36x\|4x + 9 - 72x - 81)log(\|4x + 9 - 2x)
+--R +
+--R +-------+
+--R 3 | 2 4 2
+--R (- 16x - 18x)\|4x + 9 + 32x + 72x
+--R /
+--R +-------+
+--R | 2 2
+--R 64x\|4x + 9 - 128x - 144
+--R Type: Union(Expression(Integer),...)
+--E 1097
+
+--S 1098 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R 9log(\|4x + 9 - 2x) + 9asinh(--)
+--R 3
+--R (4) ----------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 1098
+
+--S 1099 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1099
+
+)clear all
+
+--S 1100 of 1369
+t0:=x/sqrt(9+4*x^2)
+--R
+--R
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R Type: Expression(Integer)
+--E 1100
+
+--S 1101 of 1369
+r0:=1/4*sqrt(9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R (2) ----------
+--R 4
+--R Type: Expression(Integer)
+--E 1101
+
+--S 1102 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 2 2
+--R - 2x\|4x + 9 + 4x + 9
+--R (3) ------------------------
+--R +-------+
+--R | 2
+--R 4\|4x + 9 - 8x
+--R Type: Union(Expression(Integer),...)
+--E 1102
+
+--S 1103 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1103
+
+--S 1104 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1104
+
+)clear all
+
+--S 1105 of 1369
+t0:=1/sqrt(9+4*x^2)
+--R
+--R
+--R 1
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R Type: Expression(Integer)
+--E 1105
+
+--S 1106 of 1369
+r0:=1/2*asinh(2/3*x)
+--R
+--R
+--R 2x
+--R asinh(--)
+--R 3
+--R (2) ---------
+--R 2
+--R Type: Expression(Integer)
+--E 1106
+
+--S 1107 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 2
+--R log(\|4x + 9 - 2x)
+--R (3) - --------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 1107
+
+--S 1108 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R - log(\|4x + 9 - 2x) - asinh(--)
+--R 3
+--R (4) ----------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 1108
+
+--S 1109 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1109
+
+)clear all
+
+--S 1110 of 1369
+t0:=1/(x*sqrt(9+4*x^2))
+--R
+--R
+--R 1
+--R (1) -----------
+--R +-------+
+--R | 2
+--R x\|4x + 9
+--R Type: Expression(Integer)
+--E 1110
+
+--S 1111 of 1369
+r0:=-1/3*atanh(1/3*sqrt(9+4*x^2))
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R atanh(----------)
+--R 3
+--R (2) - -----------------
+--R 3
+--R Type: Expression(Integer)
+--E 1111
+
+--S 1112 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+ +-------+
+--R | 2 | 2
+--R - log(\|4x + 9 - 2x + 3) + log(\|4x + 9 - 2x - 3)
+--R (3) -----------------------------------------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 1112
+
+--S 1113 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-------+
+--R +-------+ +-------+ | 2
+--R | 2 | 2 \|4x + 9
+--R - log(\|4x + 9 - 2x + 3) + log(\|4x + 9 - 2x - 3) + atanh(----------)
+--R 3
+--R -------------------------------------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 1113
+
+--S 1114 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1114
+
+)clear all
+
+--S 1115 of 1369
+t0:=1/(x^2*sqrt(9+4*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 2 | 2
+--R x \|4x + 9
+--R Type: Expression(Integer)
+--E 1115
+
+--S 1116 of 1369
+r0:=-1/9*sqrt(9+4*x^2)/x
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x + 9
+--R (2) - ----------
+--R 9x
+--R Type: Expression(Integer)
+--E 1116
+
+--S 1117 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - -----------------
+--R +-------+
+--R | 2 2
+--R x\|4x + 9 - 2x
+--R Type: Union(Expression(Integer),...)
+--E 1117
+
+--S 1118 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2
+--R (4) - -
+--R 9
+--R Type: Expression(Integer)
+--E 1118
+
+--S 1119 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1119
+
+)clear all
+
+--S 1120 of 1369
+t0:=1/(x^3*sqrt(9+4*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 3 | 2
+--R x \|4x + 9
+--R Type: Expression(Integer)
+--E 1120
+
+--S 1121 of 1369
+r0:=2/27*atanh(1/3*sqrt(9+4*x^2))-1/18*sqrt(9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R 2 \|4x + 9 | 2
+--R 4x atanh(----------) - 3\|4x + 9
+--R 3
+--R (2) ----------------------------------
+--R 2
+--R 54x
+--R Type: Expression(Integer)
+--E 1121
+
+--S 1122 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R 3 | 2 4 2 | 2
+--R (16x \|4x + 9 - 32x - 36x )log(\|4x + 9 - 2x + 3)
+--R +
+--R +-------+ +-------+
+--R 3 | 2 4 2 | 2
+--R (- 16x \|4x + 9 + 32x + 36x )log(\|4x + 9 - 2x - 3)
+--R +
+--R +-------+
+--R 2 | 2 3
+--R (24x + 27)\|4x + 9 - 48x - 108x
+--R /
+--R +-------+
+--R 3 | 2 4 2
+--R 216x \|4x + 9 - 432x - 486x
+--R Type: Union(Expression(Integer),...)
+--E 1122
+
+--S 1123 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-------+
+--R +-------+ +-------+ | 2
+--R | 2 | 2 \|4x + 9
+--R 2log(\|4x + 9 - 2x + 3) - 2log(\|4x + 9 - 2x - 3) - 2atanh(----------)
+--R 3
+--R --------------------------------------------------------------------------
+--R 27
+--R Type: Expression(Integer)
+--E 1123
+
+--S 1124 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1124
+
+)clear all
+
+--S 1125 of 1369
+t0:=1/(x^4*sqrt(9+4*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 4 | 2
+--R x \|4x + 9
+--R Type: Expression(Integer)
+--E 1125
+
+--S 1126 of 1369
+r0:=-1/27*sqrt(9+4*x^2)/x^3+8/243*sqrt(9+4*x^2)/x
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (8x - 9)\|4x + 9
+--R (2) -------------------
+--R 3
+--R 243x
+--R Type: Expression(Integer)
+--E 1126
+
+--S 1127 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 2 2
+--R 2x\|4x + 9 - 4x - 3
+--R (3) ------------------------------------
+--R +-------+
+--R 5 3 | 2 6 4
+--R (16x + 9x )\|4x + 9 - 32x - 54x
+--R Type: Union(Expression(Integer),...)
+--E 1127
+
+--S 1128 of 1369
+m0:=a0-r0
+--R
+--R
+--R 16
+--R (4) ---
+--R 243
+--R Type: Expression(Integer)
+--E 1128
+
+--S 1129 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1129
+
+)clear all
+
+--S 1130 of 1369
+t0:=1/(x^5*sqrt(9+4*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 5 | 2
+--R x \|4x + 9
+--R Type: Expression(Integer)
+--E 1130
+
+--S 1131 of 1369
+r0:=-2/81*atanh(1/3*sqrt(9+4*x^2))-1/36*sqrt(9+4*x^2)/x^4+_
+ 1/54*sqrt(9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R 4 \|4x + 9 2 | 2
+--R - 8x atanh(----------) + (6x - 9)\|4x + 9
+--R 3
+--R (2) --------------------------------------------
+--R 4
+--R 324x
+--R Type: Expression(Integer)
+--E 1131
+
+--S 1132 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R ((- 512x - 576x )\|4x + 9 + 1024x + 2304x + 648x )
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x + 9 - 2x + 3)
+--R +
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R ((512x + 576x )\|4x + 9 - 1024x - 2304x - 648x )
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x + 9 - 2x - 3)
+--R +
+--R +-------+
+--R 6 4 2 | 2 7 5 3
+--R (- 768x - 576x + 2106x + 729)\|4x + 9 + 1536x + 2880x - 3888x
+--R +
+--R - 5832x
+--R /
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R (20736x + 23328x )\|4x + 9 - 41472x - 93312x - 26244x
+--R Type: Union(Expression(Integer),...)
+--E 1132
+
+--S 1133 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-------+
+--R +-------+ +-------+ | 2
+--R | 2 | 2 \|4x + 9
+--R - 2log(\|4x + 9 - 2x + 3) + 2log(\|4x + 9 - 2x - 3) + 2atanh(----------)
+--R 3
+--R ----------------------------------------------------------------------------
+--R 81
+--R Type: Expression(Integer)
+--E 1133
+
+--S 1134 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1134
+
+)clear all
+
+--S 1135 of 1369
+t0:=x^5/sqrt(9-4*x^2)
+--R
+--R
+--R 5
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1135
+
+--S 1136 of 1369
+r0:=-27/40*sqrt(9-4*x^2)-3/20*x^2*sqrt(9-4*x^2)-1/20*x^4*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R 4 2 | 2
+--R (- 2x - 6x - 27)\|- 4x + 9
+--R (2) ------------------------------
+--R 40
+--R Type: Expression(Integer)
+--E 1136
+
+--S 1137 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 8 6 | 2 10 8 6
+--R (15x - 90x )\|- 4x + 9 + 4x - 105x + 270x
+--R (3) ---------------------------------------------------------
+--R +---------+
+--R 4 2 | 2 4 2
+--R (20x - 540x + 1620)\|- 4x + 9 - 300x + 2700x - 4860
+--R Type: Union(Expression(Integer),...)
+--E 1137
+
+--S 1138 of 1369
+m0:=a0-r0
+--R
+--R
+--R 81
+--R (4) - --
+--R 40
+--R Type: Expression(Integer)
+--E 1138
+
+--S 1139 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1139
+
+)clear all
+
+--S 1140 of 1369
+t0:=x^4/sqrt(9-4*x^2)
+--R
+--R
+--R 4
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1140
+
+--S 1141 of 1369
+r0:=243/256*asin(2/3*x)-27/128*x*sqrt(9-4*x^2)-1/16*x^3*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R 3 | 2 2x
+--R (- 16x - 54x)\|- 4x + 9 + 243asin(--)
+--R 3
+--R (2) ----------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 1141
+
+--S 1142 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 2 | 2 4 2
+--R ((- 1458x + 6561)\|- 4x + 9 - 486x + 8748x - 19683)
+--R *
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3
+--R atan(----------------)
+--R 2x
+--R +
+--R +---------+
+--R 7 5 3 | 2 7 5 3
+--R (- 16x + 234x + 324x - 2187x)\|- 4x + 9 + 192x - 648x - 2430x
+--R +
+--R 6561x
+--R /
+--R +---------+
+--R 2 | 2 4 2
+--R (768x - 3456)\|- 4x + 9 + 256x - 4608x + 10368
+--R Type: Union(Expression(Integer),...)
+--E 1142
+
+--S 1143 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3 2x
+--R - 486atan(----------------) - 243asin(--)
+--R 2x 3
+--R (4) -----------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 1143
+
+--S 1144 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1144
+
+)clear all
+
+--S 1145 of 1369
+t0:=x^3/sqrt(9-4*x^2)
+--R
+--R
+--R 3
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1145
+
+--S 1146 of 1369
+r0:=-3/8*sqrt(9-4*x^2)-1/12*x^2*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (- 2x - 9)\|- 4x + 9
+--R (2) -----------------------
+--R 24
+--R Type: Expression(Integer)
+--E 1146
+
+--S 1147 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 4 | 2 6 4
+--R 9x \|- 4x + 9 + 4x - 27x
+--R (3) --------------------------------------
+--R +---------+
+--R 2 | 2 2
+--R (12x - 108)\|- 4x + 9 - 108x + 324
+--R Type: Union(Expression(Integer),...)
+--E 1147
+
+--S 1148 of 1369
+m0:=a0-r0
+--R
+--R
+--R 9
+--R (4) - -
+--R 8
+--R Type: Expression(Integer)
+--E 1148
+
+--S 1149 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1149
+
+)clear all
+
+--S 1150 of 1369
+t0:=x^2/sqrt(9-4*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1150
+
+--S 1151 of 1369
+r0:=9/16*asin(2/3*x)-1/8*x*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2 2x
+--R - 2x\|- 4x + 9 + 9asin(--)
+--R 3
+--R (2) ----------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 1151
+
+--S 1152 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2
+--R | 2 2 \|- 4x + 9 - 3
+--R (- 27\|- 4x + 9 - 18x + 81)atan(----------------)
+--R 2x
+--R +
+--R +---------+
+--R 3 | 2 3
+--R (- 2x + 9x)\|- 4x + 9 + 12x - 27x
+--R /
+--R +---------+
+--R | 2 2
+--R 24\|- 4x + 9 + 16x - 72
+--R Type: Union(Expression(Integer),...)
+--E 1152
+
+--S 1153 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3 2x
+--R - 18atan(----------------) - 9asin(--)
+--R 2x 3
+--R (4) --------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 1153
+
+--S 1154 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1154
+
+)clear all
+
+--S 1155 of 1369
+t0:=x/sqrt(9-4*x^2)
+--R
+--R
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1155
+
+--S 1156 of 1369
+r0:=-1/4*sqrt(9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R (2) - ------------
+--R 4
+--R Type: Expression(Integer)
+--E 1156
+
+--S 1157 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R x
+--R (3) ----------------
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3
+--R Type: Union(Expression(Integer),...)
+--E 1157
+
+--S 1158 of 1369
+m0:=a0-r0
+--R
+--R
+--R 3
+--R (4) - -
+--R 4
+--R Type: Expression(Integer)
+--E 1158
+
+--S 1159 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1159
+
+)clear all
+
+--S 1160 of 1369
+t0:=1/sqrt(9-4*x^2)
+--R
+--R
+--R 1
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1160
+
+--S 1161 of 1369
+r0:=1/2*asin(2/3*x)
+--R
+--R
+--R 2x
+--R asin(--)
+--R 3
+--R (2) --------
+--R 2
+--R Type: Expression(Integer)
+--E 1161
+
+--S 1162 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3
+--R (3) - atan(----------------)
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 1162
+
+--S 1163 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3 2x
+--R - 2atan(----------------) - asin(--)
+--R 2x 3
+--R (4) ------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 1163
+
+--S 1164 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1164
+
+)clear all
+
+--S 1165 of 1369
+t0:=1/(x*sqrt(9-4*x^2))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +---------+
+--R | 2
+--R x\|- 4x + 9
+--R Type: Expression(Integer)
+--E 1165
+
+--S 1166 of 1369
+r0:=-1/3*atanh(1/3*sqrt(9-4*x^2))
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R atanh(------------)
+--R 3
+--R (2) - -------------------
+--R 3
+--R Type: Expression(Integer)
+--E 1166
+
+--S 1167 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9 - 3
+--R log(----------------)
+--R x
+--R (3) ---------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 1167
+
+--S 1168 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+ +---------+
+--R | 2 | 2
+--R \|- 4x + 9 - 3 \|- 4x + 9
+--R log(----------------) + atanh(------------)
+--R x 3
+--R (4) -------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 1168
+
+--S 1169 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1169
+
+)clear all
+
+--S 1170 of 1369
+t0:=1/(x^2*sqrt(9-4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 2 | 2
+--R x \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1170
+
+--S 1171 of 1369
+r0:=-1/9*sqrt(9-4*x^2)/x
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x + 9
+--R (2) - ------------
+--R 9x
+--R Type: Expression(Integer)
+--E 1171
+
+--S 1172 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R | 2 2
+--R 3\|- 4x + 9 + 4x - 9
+--R (3) -----------------------
+--R +---------+
+--R | 2
+--R 9x\|- 4x + 9 - 27x
+--R Type: Union(Expression(Integer),...)
+--E 1172
+
+--S 1173 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1173
+
+--S 1174 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1174
+
+)clear all
+
+--S 1175 of 1369
+t0:=1/(x^3*sqrt(9-4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 3 | 2
+--R x \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1175
+
+--S 1176 of 1369
+r0:=-2/27*atanh(1/3*sqrt(9-4*x^2))-1/18*sqrt(9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R 2 \|- 4x + 9 | 2
+--R - 4x atanh(------------) - 3\|- 4x + 9
+--R 3
+--R (2) ----------------------------------------
+--R 2
+--R 54x
+--R Type: Expression(Integer)
+--E 1176
+
+--S 1177 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2
+--R 2 | 2 4 2 \|- 4x + 9 - 3
+--R (12x \|- 4x + 9 + 8x - 36x )log(----------------)
+--R x
+--R +
+--R +---------+
+--R 2 | 2 2
+--R (- 6x + 27)\|- 4x + 9 + 36x - 81
+--R /
+--R +---------+
+--R 2 | 2 4 2
+--R 162x \|- 4x + 9 + 108x - 486x
+--R Type: Union(Expression(Integer),...)
+--E 1177
+
+--S 1178 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+ +---------+
+--R | 2 | 2
+--R \|- 4x + 9 - 3 \|- 4x + 9
+--R 2log(----------------) + 2atanh(------------)
+--R x 3
+--R (4) ---------------------------------------------
+--R 27
+--R Type: Expression(Integer)
+--E 1178
+
+--S 1179 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1179
+
+)clear all
+
+--S 1180 of 1369
+t0:=1/(x^4*sqrt(9-4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 4 | 2
+--R x \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1180
+
+--S 1181 of 1369
+r0:=-1/27*sqrt(9-4*x^2)/x^3-8/243*sqrt(9-4*x^2)/x
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (- 8x - 9)\|- 4x + 9
+--R (2) -----------------------
+--R 3
+--R 243x
+--R Type: Expression(Integer)
+--E 1181
+
+--S 1182 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 4 2 | 2 6 4 2
+--R (72x - 135x - 243)\|- 4x + 9 + 32x - 324x + 243x + 729
+--R (3) -------------------------------------------------------------
+--R +---------+
+--R 5 3 | 2 5 3
+--R (243x - 2187x )\|- 4x + 9 - 2187x + 6561x
+--R Type: Union(Expression(Integer),...)
+--E 1182
+
+--S 1183 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1183
+
+--S 1184 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1184
+
+)clear all
+
+--S 1185 of 1369
+t0:=1/(x^5*sqrt(9-4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 5 | 2
+--R x \|- 4x + 9
+--R Type: Expression(Integer)
+--E 1185
+
+--S 1186 of 1369
+r0:=-2/81*atanh(1/3*sqrt(9-4*x^2))-1/36*sqrt(9-4*x^2)/x^4-_
+ 1/54*sqrt(9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R 4 \|- 4x + 9 2 | 2
+--R - 8x atanh(------------) + (- 6x - 9)\|- 4x + 9
+--R 3
+--R (2) --------------------------------------------------
+--R 4
+--R 324x
+--R Type: Expression(Integer)
+--E 1186
+
+--S 1187 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2
+--R 6 4 | 2 8 6 4 \|- 4x + 9 - 3
+--R ((48x - 216x )\|- 4x + 9 + 16x - 288x + 648x )log(----------------)
+--R x
+--R +
+--R +---------+
+--R 6 4 2 | 2 6 4
+--R (- 12x + 198x - 162x - 729)\|- 4x + 9 + 144x - 756x + 2187
+--R /
+--R +---------+
+--R 6 4 | 2 8 6 4
+--R (1944x - 8748x )\|- 4x + 9 + 648x - 11664x + 26244x
+--R Type: Union(Expression(Integer),...)
+--E 1187
+
+--S 1188 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+ +---------+
+--R | 2 | 2
+--R \|- 4x + 9 - 3 \|- 4x + 9
+--R 2log(----------------) + 2atanh(------------)
+--R x 3
+--R (4) ---------------------------------------------
+--R 81
+--R Type: Expression(Integer)
+--E 1188
+
+--S 1189 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1189
+
+)clear all
+
+--S 1190 of 1369
+t0:=x^5/sqrt(-9+4*x^2)
+--R
+--R
+--R 5
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R Type: Expression(Integer)
+--E 1190
+
+--S 1191 of 1369
+r0:=27/40*sqrt(-9+4*x^2)+3/20*x^2*sqrt(-9+4*x^2)+1/20*x^4*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 4 2 | 2
+--R (2x + 6x + 27)\|4x - 9
+--R (2) --------------------------
+--R 40
+--R Type: Expression(Integer)
+--E 1191
+
+--S 1192 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 9 7 5 3 | 2 10
+--R (- 1024x - 192x - 6804x + 34020x - 21870x)\|4x - 9 + 2048x
+--R +
+--R 8 6 4 2
+--R - 1920x + 11880x - 85050x + 109350x - 19683
+--R /
+--R +-------+
+--R 4 2 | 2 5 3
+--R (10240x - 17280x + 3240)\|4x - 9 - 20480x + 57600x - 32400x
+--R Type: Union(Expression(Integer),...)
+--E 1192
+
+--S 1193 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1193
+
+--S 1194 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1194
+
+)clear all
+
+--S 1195 of 1369
+t0:=x^4/sqrt(-9+4*x^2)
+--R
+--R
+--R 4
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R Type: Expression(Integer)
+--E 1195
+
+--S 1196 of 1369
+r0:=243/256*atanh(2*x/sqrt(-9+4*x^2))+27/128*x*sqrt(-9+4*x^2)+_
+ 1/16*x^3*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 2x 3 | 2
+--R 243atanh(----------) + (16x + 54x)\|4x - 9
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (2) ---------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 1196
+
+--S 1197 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 3 | 2 4 2
+--R ((- 15552x + 17496x)\|4x - 9 + 31104x - 69984x + 19683)
+--R *
+--R +-------+
+--R | 2
+--R log(\|4x - 9 - 2x)
+--R +
+--R +-------+
+--R 7 5 3 | 2 8 4
+--R (- 2048x - 2304x + 14256x - 4374x)\|4x - 9 + 4096x - 36288x
+--R +
+--R 2
+--R 34992x
+--R /
+--R +-------+
+--R 3 | 2 4 2
+--R (16384x - 18432x)\|4x - 9 - 32768x + 73728x - 20736
+--R Type: Union(Expression(Integer),...)
+--E 1197
+
+--S 1198 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R - 243log(\|4x - 9 - 2x) - 243atanh(----------)
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (4) ------------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 1198
+
+--S 1199 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1199
+
+)clear all
+
+--S 1200 of 1369
+t0:=x^3/sqrt(-9+4*x^2)
+--R
+--R
+--R 3
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R Type: Expression(Integer)
+--E 1200
+
+--S 1201 of 1369
+r0:=3/8*sqrt(-9+4*x^2)+1/12*x^2*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (2x + 9)\|4x - 9
+--R (2) -------------------
+--R 24
+--R Type: Expression(Integer)
+--E 1201
+
+--S 1202 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 5 3 | 2 6 4 2
+--R (- 64x - 180x + 486x)\|4x - 9 + 128x + 216x - 1458x + 729
+--R (3) ----------------------------------------------------------------
+--R +-------+
+--R 2 | 2 3
+--R (384x - 216)\|4x - 9 - 768x + 1296x
+--R Type: Union(Expression(Integer),...)
+--E 1202
+
+--S 1203 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1203
+
+--S 1204 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1204
+
+)clear all
+
+--S 1205 of 1369
+t0:=x^2/sqrt(-9+4*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R Type: Expression(Integer)
+--E 1205
+
+--S 1206 of 1369
+r0:=9/16*atanh(2*x/sqrt(-9+4*x^2))+1/8*x*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R 2x | 2
+--R 9atanh(----------) + 2x\|4x - 9
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (2) ---------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 1206
+
+--S 1207 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R | 2 2 | 2
+--R (- 36x\|4x - 9 + 72x - 81)log(\|4x - 9 - 2x)
+--R +
+--R +-------+
+--R 3 | 2 4 2
+--R (- 16x + 18x)\|4x - 9 + 32x - 72x
+--R /
+--R +-------+
+--R | 2 2
+--R 64x\|4x - 9 - 128x + 144
+--R Type: Union(Expression(Integer),...)
+--E 1207
+
+--S 1208 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R - 9log(\|4x - 9 - 2x) - 9atanh(----------)
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (4) --------------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 1208
+
+--S 1209 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1209
+
+)clear all
+
+--S 1210 of 1369
+t0:=x/sqrt(-9+4*x^2)
+--R
+--R
+--R x
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R Type: Expression(Integer)
+--E 1210
+
+--S 1211 of 1369
+r0:=1/4*sqrt(-9+4*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (2) ----------
+--R 4
+--R Type: Expression(Integer)
+--E 1211
+
+--S 1212 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 2 2
+--R - 2x\|4x - 9 + 4x - 9
+--R (3) ------------------------
+--R +-------+
+--R | 2
+--R 4\|4x - 9 - 8x
+--R Type: Union(Expression(Integer),...)
+--E 1212
+
+--S 1213 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1213
+
+--S 1214 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1214
+
+)clear all
+
+--S 1215 of 1369
+t0:=1/sqrt(-9+4*x^2)
+--R
+--R
+--R 1
+--R (1) ----------
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R Type: Expression(Integer)
+--E 1215
+
+--S 1216 of 1369
+r0:=1/2*atanh(2*x/sqrt(-9+4*x^2))
+--R
+--R
+--R 2x
+--R atanh(----------)
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (2) -----------------
+--R 2
+--R Type: Expression(Integer)
+--E 1216
+
+--S 1217 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 2
+--R log(\|4x - 9 - 2x)
+--R (3) - --------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 1217
+
+--S 1218 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 2x
+--R - log(\|4x - 9 - 2x) - atanh(----------)
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (4) ------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 1218
+
+--S 1219 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1219
+
+)clear all
+
+--S 1220 of 1369
+t0:=1/(x*sqrt(-9+4*x^2))
+--R
+--R
+--R 1
+--R (1) -----------
+--R +-------+
+--R | 2
+--R x\|4x - 9
+--R Type: Expression(Integer)
+--E 1220
+
+--S 1221 of 1369
+r0:=1/3*atan(1/3*sqrt(-9+4*x^2))
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R atan(----------)
+--R 3
+--R (2) ----------------
+--R 3
+--R Type: Expression(Integer)
+--E 1221
+
+--S 1222 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x - 9 - 2x
+--R 2atan(---------------)
+--R 3
+--R (3) ----------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 1222
+
+--S 1223 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|4x - 9 \|4x - 9 - 2x
+--R - atan(----------) + 2atan(---------------)
+--R 3 3
+--R (4) -------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 1223
+
+--S 1224 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1224
+
+)clear all
+
+--S 1225 of 1369
+t0:=1/(x^2*sqrt(-9+4*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 2 | 2
+--R x \|4x - 9
+--R Type: Expression(Integer)
+--E 1225
+
+--S 1226 of 1369
+r0:=1/9*sqrt(-9+4*x^2)/x
+--R
+--R
+--R +-------+
+--R | 2
+--R \|4x - 9
+--R (2) ----------
+--R 9x
+--R Type: Expression(Integer)
+--E 1226
+
+--S 1227 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - -----------------
+--R +-------+
+--R | 2 2
+--R x\|4x - 9 - 2x
+--R Type: Union(Expression(Integer),...)
+--E 1227
+
+--S 1228 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2
+--R (4) -
+--R 9
+--R Type: Expression(Integer)
+--E 1228
+
+--S 1229 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1229
+
+)clear all
+
+--S 1230 of 1369
+t0:=1/(x^3*sqrt(-9+4*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 3 | 2
+--R x \|4x - 9
+--R Type: Expression(Integer)
+--E 1230
+
+--S 1231 of 1369
+r0:=2/27*atan(1/3*sqrt(-9+4*x^2))+1/18*sqrt(-9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R 2 \|4x - 9 | 2
+--R 4x atan(----------) + 3\|4x - 9
+--R 3
+--R (2) ---------------------------------
+--R 2
+--R 54x
+--R Type: Expression(Integer)
+--E 1231
+
+--S 1232 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R +-------+ | 2
+--R 3 | 2 4 2 \|4x - 9 - 2x
+--R (32x \|4x - 9 - 64x + 72x )atan(---------------)
+--R 3
+--R +
+--R +-------+
+--R 2 | 2 3
+--R (- 24x + 27)\|4x - 9 + 48x - 108x
+--R /
+--R +-------+
+--R 3 | 2 4 2
+--R 216x \|4x - 9 - 432x + 486x
+--R Type: Union(Expression(Integer),...)
+--E 1232
+
+--S 1233 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|4x - 9 \|4x - 9 - 2x
+--R - 2atan(----------) + 4atan(---------------)
+--R 3 3
+--R (4) --------------------------------------------
+--R 27
+--R Type: Expression(Integer)
+--E 1233
+
+--S 1234 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1234
+
+)clear all
+
+--S 1235 of 1369
+t0:=1/(x^4*sqrt(-9+4*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 4 | 2
+--R x \|4x - 9
+--R Type: Expression(Integer)
+--E 1235
+
+--S 1236 of 1369
+r0:=1/27*sqrt(-9+4*x^2)/x^3+8/243*sqrt(-9+4*x^2)/x
+--R
+--R
+--R +-------+
+--R 2 | 2
+--R (8x + 9)\|4x - 9
+--R (2) -------------------
+--R 3
+--R 243x
+--R Type: Expression(Integer)
+--E 1236
+
+--S 1237 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 2 2
+--R 2x\|4x - 9 - 4x + 3
+--R (3) ------------------------------------
+--R +-------+
+--R 5 3 | 2 6 4
+--R (16x - 9x )\|4x - 9 - 32x + 54x
+--R Type: Union(Expression(Integer),...)
+--E 1237
+
+--S 1238 of 1369
+m0:=a0-r0
+--R
+--R
+--R 16
+--R (4) ---
+--R 243
+--R Type: Expression(Integer)
+--E 1238
+
+--S 1239 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1239
+
+)clear all
+
+--S 1240 of 1369
+t0:=1/(x^5*sqrt(-9+4*x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 5 | 2
+--R x \|4x - 9
+--R Type: Expression(Integer)
+--E 1240
+
+--S 1241 of 1369
+r0:=2/81*atan(1/3*sqrt(-9+4*x^2))+1/36*sqrt(-9+4*x^2)/x^4+_
+ 1/54*sqrt(-9+4*x^2)/x^2
+--R
+--R
+--R +-------+
+--R | 2 +-------+
+--R 4 \|4x - 9 2 | 2
+--R 8x atan(----------) + (6x + 9)\|4x - 9
+--R 3
+--R (2) -----------------------------------------
+--R 4
+--R 324x
+--R Type: Expression(Integer)
+--E 1241
+
+--S 1242 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R ((1024x - 1152x )\|4x - 9 - 2048x + 4608x - 1296x )
+--R *
+--R +-------+
+--R | 2
+--R \|4x - 9 - 2x
+--R atan(---------------)
+--R 3
+--R +
+--R +-------+
+--R 6 4 2 | 2 7 5 3
+--R (- 768x + 576x + 2106x - 729)\|4x - 9 + 1536x - 2880x - 3888x
+--R +
+--R 5832x
+--R /
+--R +-------+
+--R 7 5 | 2 8 6 4
+--R (20736x - 23328x )\|4x - 9 - 41472x + 93312x - 26244x
+--R Type: Union(Expression(Integer),...)
+--E 1242
+
+--S 1243 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|4x - 9 \|4x - 9 - 2x
+--R - 2atan(----------) + 4atan(---------------)
+--R 3 3
+--R (4) --------------------------------------------
+--R 81
+--R Type: Expression(Integer)
+--E 1243
+
+--S 1244 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1244
+
+)clear all
+
+--S 1245 of 1369
+t0:=x^5/sqrt(-9-4*x^2)
+--R
+--R
+--R 5
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1245
+
+--S 1246 of 1369
+r0:=-27/40*sqrt(-9-4*x^2)+3/20*x^2*sqrt(-9-4*x^2)-1/20*x^4*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 4 2 | 2
+--R (- 2x + 6x - 27)\|- 4x - 9
+--R (2) ------------------------------
+--R 40
+--R Type: Expression(Integer)
+--E 1246
+
+--S 1247 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 8 6 | 2 10 8 6 +---+
+--R (- 15x - 90x )\|- 4x - 9 + (4x + 105x + 270x )\|- 1
+--R (3) ---------------------------------------------------------------
+--R +---------+
+--R 4 2 +---+ | 2 4 2
+--R (20x + 540x + 1620)\|- 1 \|- 4x - 9 + 300x + 2700x + 4860
+--R Type: Union(Expression(Integer),...)
+--E 1247
+
+--S 1248 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 4 2 | 2 4 2 +---+
+--R (81x + 2187x + 6561)\|- 4x - 9 + (- 1215x - 10935x - 19683)\|- 1
+--R -----------------------------------------------------------------------
+--R +---------+
+--R 4 2 +---+ | 2 4 2
+--R (40x + 1080x + 3240)\|- 1 \|- 4x - 9 + 600x + 5400x + 9720
+--R Type: Expression(Integer)
+--E 1248
+
+--S 1249 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1249
+
+)clear all
+
+--S 1250 of 1369
+t0:=x^4/sqrt(-9-4*x^2)
+--R
+--R
+--R 4
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1250
+
+--S 1251 of 1369
+r0:=243/256*atan(2*x/sqrt(-9-4*x^2))+27/128*x*sqrt(-9-4*x^2)-_
+ 1/16*x^3*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 2x 3 | 2
+--R 243atan(------------) + (- 16x + 54x)\|- 4x - 9
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (2) --------------------------------------------------
+--R 256
+--R Type: Expression(Integer)
+--E 1251
+
+--S 1252 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((1458x + 6561)\|- 4x - 9 + (- 486x - 8748x - 19683)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (2x - 3)\|- 1
+--R log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((- 1458x - 6561)\|- 4x - 9 + (486x + 8748x + 19683)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R 7 5 3 | 2
+--R (- 32x - 468x + 648x + 4374x)\|- 4x - 9
+--R +
+--R 7 5 3 +---+
+--R (384x + 1296x - 4860x - 13122x)\|- 1
+--R /
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R (1536x + 6912)\|- 1 \|- 4x - 9 + 512x + 9216x + 20736
+--R Type: Union(Expression(Integer),...)
+--E 1252
+
+--S 1253 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((1458x + 6561)\|- 4x - 9 + (- 486x - 8748x - 19683)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (2x - 3)\|- 1
+--R log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((- 1458x - 6561)\|- 4x - 9 + (486x + 8748x + 19683)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R ((- 1458x - 6561)\|- 1 \|- 4x - 9 - 486x - 8748x - 19683)
+--R *
+--R 2x
+--R atan(------------)
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R /
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R (1536x + 6912)\|- 1 \|- 4x - 9 + 512x + 9216x + 20736
+--R Type: Expression(Integer)
+--E 1253
+
+--S 1254 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1254
+
+)clear all
+
+--S 1255 of 1369
+t0:=x^3/sqrt(-9-4*x^2)
+--R
+--R
+--R 3
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1255
+
+--S 1256 of 1369
+r0:=3/8*sqrt(-9-4*x^2)-1/12*x^2*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (- 2x + 9)\|- 4x - 9
+--R (2) -----------------------
+--R 24
+--R Type: Expression(Integer)
+--E 1256
+
+--S 1257 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 4 | 2 6 4 +---+
+--R - 9x \|- 4x - 9 + (4x + 27x )\|- 1
+--R (3) --------------------------------------------
+--R +---------+
+--R 2 +---+ | 2 2
+--R (12x + 108)\|- 1 \|- 4x - 9 + 108x + 324
+--R Type: Union(Expression(Integer),...)
+--E 1257
+
+--S 1258 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R 2 | 2 2 +---+
+--R (- 9x - 81)\|- 4x - 9 + (81x + 243)\|- 1
+--R (4) ---------------------------------------------
+--R +---------+
+--R 2 +---+ | 2 2
+--R (8x + 72)\|- 1 \|- 4x - 9 + 72x + 216
+--R Type: Expression(Integer)
+--E 1258
+
+--S 1259 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1259
+
+)clear all
+
+--S 1260 of 1369
+t0:=x^2/sqrt(-9-4*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1260
+
+--S 1261 of 1369
+r0:=-9/16*atan(2*x/sqrt(-9-4*x^2))-1/8*x*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R 2x | 2
+--R - 9atan(------------) - 2x\|- 4x - 9
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (2) --------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 1261
+
+--S 1262 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2 +---+
+--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1
+--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R | 2 2 +---+
+--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R 3 | 2 3 +---+
+--R (- 4x - 18x)\|- 4x - 9 + (24x + 54x)\|- 1
+--R /
+--R +---------+
+--R +---+ | 2 2
+--R 48\|- 1 \|- 4x - 9 + 32x + 144
+--R Type: Union(Expression(Integer),...)
+--E 1262
+
+--S 1263 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +---------+ | 2 +---+
+--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1
+--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R | 2 2 +---+
+--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 + (- 2x - 3)\|- 1
+--R log(-------------------------------)
+--R x
+--R +
+--R +---------+
+--R +---+ | 2 2 2x
+--R (27\|- 1 \|- 4x - 9 + 18x + 81)atan(------------)
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R /
+--R +---------+
+--R +---+ | 2 2
+--R 48\|- 1 \|- 4x - 9 + 32x + 144
+--R Type: Expression(Integer)
+--E 1263
+
+--S 1264 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1264
+
+)clear all
+
+--S 1265 of 1369
+t0:=x/sqrt(-9-4*x^2)
+--R
+--R
+--R x
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1265
+
+--S 1266 of 1369
+r0:=-1/4*sqrt(-9-4*x^2)
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (2) - ------------
+--R 4
+--R Type: Expression(Integer)
+--E 1266
+
+--S 1267 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +---+
+--R x \|- 1
+--R (3) ----------------------
+--R +---------+
+--R +---+ | 2
+--R \|- 1 \|- 4x - 9 + 3
+--R Type: Union(Expression(Integer),...)
+--E 1267
+
+--S 1268 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 2 +---+
+--R 3\|- 4x - 9 - 9\|- 1
+--R (4) ------------------------
+--R +---------+
+--R +---+ | 2
+--R 4\|- 1 \|- 4x - 9 + 12
+--R Type: Expression(Integer)
+--E 1268
+
+--S 1269 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1269
+
+)clear all
+
+--S 1270 of 1369
+t0:=1/sqrt(-9-4*x^2)
+--R
+--R
+--R 1
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1270
+
+--S 1271 of 1369
+r0:=1/2*atan(2*x/sqrt(-9-4*x^2))
+--R
+--R
+--R 2x
+--R atan(------------)
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (2) ------------------
+--R 2
+--R Type: Expression(Integer)
+--E 1271
+
+--S 1272 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R | 2 +---+
+--R +---+ \|- 4x - 9 + (2x - 3)\|- 1
+--R - \|- 1 log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R | 2 +---+
+--R +---+ \|- 4x - 9 + (- 2x - 3)\|- 1
+--R \|- 1 log(-------------------------------)
+--R x
+--R /
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 1272
+
+--S 1273 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R | 2 +---+
+--R +---+ \|- 4x - 9 + (2x - 3)\|- 1
+--R - \|- 1 log(-----------------------------)
+--R x
+--R +
+--R +---------+
+--R | 2 +---+
+--R +---+ \|- 4x - 9 + (- 2x - 3)\|- 1 2x
+--R \|- 1 log(-------------------------------) - atan(------------)
+--R x +---------+
+--R | 2
+--R \|- 4x - 9
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 1273
+
+--S 1274 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1274
+
+)clear all
+
+--S 1275 of 1369
+t0:=1/(x*sqrt(-9-4*x^2))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +---------+
+--R | 2
+--R x\|- 4x - 9
+--R Type: Expression(Integer)
+--E 1275
+
+--S 1276 of 1369
+r0:=1/3*atan(1/3*sqrt(-9-4*x^2))
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R atan(------------)
+--R 3
+--R (2) ------------------
+--R 3
+--R Type: Expression(Integer)
+--E 1276
+
+--S 1277 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R | 2 +---+
+--R +---+ \|- 4x - 9 - 3\|- 1
+--R \|- 1 log(----------------------)
+--R x
+--R (3) - ---------------------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 1277
+
+--S 1278 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+ +---------+
+--R | 2 +---+ | 2
+--R +---+ \|- 4x - 9 - 3\|- 1 \|- 4x - 9
+--R - \|- 1 log(----------------------) - atan(------------)
+--R x 3
+--R (4) --------------------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 1278
+
+--S 1279 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1279
+
+)clear all
+
+--S 1280 of 1369
+t0:=1/(x^2*sqrt(-9-4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 2 | 2
+--R x \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1280
+
+--S 1281 of 1369
+r0:=1/9*sqrt(-9-4*x^2)/x
+--R
+--R
+--R +---------+
+--R | 2
+--R \|- 4x - 9
+--R (2) ------------
+--R 9x
+--R Type: Expression(Integer)
+--E 1281
+
+--S 1282 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R +---+ | 2 2
+--R - 3\|- 1 \|- 4x - 9 - 4x - 9
+--R (3) -------------------------------
+--R +---------+
+--R | 2 +---+
+--R 9x\|- 4x - 9 - 27x\|- 1
+--R Type: Union(Expression(Integer),...)
+--E 1282
+
+--S 1283 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1283
+
+--S 1284 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1284
+
+)clear all
+
+--S 1285 of 1369
+t0:=1/(x^3*sqrt(-9-4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 3 | 2
+--R x \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1285
+
+--S 1286 of 1369
+r0:=-2/27*atan(1/3*sqrt(-9-4*x^2))+1/18*sqrt(-9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R 2 \|- 4x - 9 | 2
+--R - 4x atan(------------) + 3\|- 4x - 9
+--R 3
+--R (2) ---------------------------------------
+--R 2
+--R 54x
+--R Type: Expression(Integer)
+--E 1286
+
+--S 1287 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 2 +---+
+--R 2 | 2 4 2 +---+ \|- 4x - 9 - 3\|- 1
+--R (- 12x \|- 4x - 9 + (8x + 36x )\|- 1 )log(----------------------)
+--R x
+--R +
+--R +---------+
+--R 2 | 2 2 +---+
+--R (6x + 27)\|- 4x - 9 + (- 36x - 81)\|- 1
+--R /
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R 162x \|- 1 \|- 4x - 9 + 108x + 486x
+--R Type: Union(Expression(Integer),...)
+--E 1287
+
+--S 1288 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R +---------+ | 2 +---+
+--R | 2 2 +---+ \|- 4x - 9 - 3\|- 1
+--R (- 6\|- 4x - 9 + (4x + 18)\|- 1 )log(----------------------)
+--R x
+--R +
+--R +---------+
+--R +---------+ | 2
+--R +---+ | 2 2 \|- 4x - 9
+--R (6\|- 1 \|- 4x - 9 + 4x + 18)atan(------------)
+--R 3
+--R /
+--R +---------+
+--R +---+ | 2 2
+--R 81\|- 1 \|- 4x - 9 + 54x + 243
+--R Type: Expression(Integer)
+--E 1288
+
+--S 1289 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1289
+
+)clear all
+
+--S 1290 of 1369
+t0:=1/(x^4*sqrt(-9-4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 4 | 2
+--R x \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1290
+
+--S 1291 of 1369
+r0:=1/27*sqrt(-9-4*x^2)/x^3-8/243*sqrt(-9-4*x^2)/x
+--R
+--R
+--R +---------+
+--R 2 | 2
+--R (- 8x + 9)\|- 4x - 9
+--R (2) -----------------------
+--R 3
+--R 243x
+--R Type: Expression(Integer)
+--E 1291
+
+--S 1292 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 4 2 +---+ | 2 6 4 2
+--R (72x + 135x - 243)\|- 1 \|- 4x - 9 + 32x + 324x + 243x - 729
+--R (3) -------------------------------------------------------------------
+--R +---------+
+--R 5 3 | 2 5 3 +---+
+--R (243x + 2187x )\|- 4x - 9 + (- 2187x - 6561x )\|- 1
+--R Type: Union(Expression(Integer),...)
+--E 1292
+
+--S 1293 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1293
+
+--S 1294 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1294
+
+)clear all
+
+--S 1295 of 1369
+t0:=1/(x^5*sqrt(-9-4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 5 | 2
+--R x \|- 4x - 9
+--R Type: Expression(Integer)
+--E 1295
+
+--S 1296 of 1369
+r0:=2/81*atan(1/3*sqrt(-9-4*x^2))+1/36*sqrt(-9-4*x^2)/x^4-_
+ 1/54*sqrt(-9-4*x^2)/x^2
+--R
+--R
+--R +---------+
+--R | 2 +---------+
+--R 4 \|- 4x - 9 2 | 2
+--R 8x atan(------------) + (- 6x + 9)\|- 4x - 9
+--R 3
+--R (2) -----------------------------------------------
+--R 4
+--R 324x
+--R Type: Expression(Integer)
+--E 1296
+
+--S 1297 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R 6 4 | 2 8 6 4 +---+
+--R ((48x + 216x )\|- 4x - 9 + (- 16x - 288x - 648x )\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 - 3\|- 1
+--R log(----------------------)
+--R x
+--R +
+--R +---------+
+--R 6 4 2 | 2 6 4 +---+
+--R (- 12x - 198x - 162x + 729)\|- 4x - 9 + (144x + 756x - 2187)\|- 1
+--R /
+--R +---------+
+--R 6 4 +---+ | 2 8 6 4
+--R (1944x + 8748x )\|- 1 \|- 4x - 9 + 648x + 11664x + 26244x
+--R Type: Union(Expression(Integer),...)
+--E 1297
+
+--S 1298 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------+
+--R 2 | 2 4 2 +---+
+--R ((12x + 54)\|- 4x - 9 + (- 4x - 72x - 162)\|- 1 )
+--R *
+--R +---------+
+--R | 2 +---+
+--R \|- 4x - 9 - 3\|- 1
+--R log(----------------------)
+--R x
+--R +
+--R +---------+
+--R +---------+ | 2
+--R 2 +---+ | 2 4 2 \|- 4x - 9
+--R ((- 12x - 54)\|- 1 \|- 4x - 9 - 4x - 72x - 162)atan(------------)
+--R 3
+--R /
+--R +---------+
+--R 2 +---+ | 2 4 2
+--R (486x + 2187)\|- 1 \|- 4x - 9 + 162x + 2916x + 6561
+--R Type: Expression(Integer)
+--E 1298
+
+--S 1299 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1299
+
+)clear all
+
+--S 1300 of 1369
+t0:=1/sqrt(9+b*x^2)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + 9
+--R Type: Expression(Integer)
+--E 1300
+
+--S 1301 of 1369
+r0:=asinh(1/3*x*sqrt(b))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R asinh(-----)
+--R 3
+--R (2) ------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1301
+
+--S 1302 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ | 2 2 +-+
+--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x
+--R log(--------------------------------------------------)
+--R +--------+
+--R | 2
+--R \|b x + 9 - 3
+--R [-------------------------------------------------------,
+--R +-+
+--R \|b
+--R +--------+
+--R +---+ | 2 +---+
+--R \|- b \|b x + 9 - 3\|- b
+--R 2atan(---------------------------)
+--R b x
+--R ----------------------------------]
+--R +---+
+--R \|- b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1302
+
+--S 1303 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+
+--R +-+ | 2 2 +-+ +-+
+--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x x\|b
+--R log(--------------------------------------------------) - asinh(-----)
+--R +--------+ 3
+--R | 2
+--R \|b x + 9 - 3
+--R (4) ----------------------------------------------------------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1303
+
+--S 1304 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1304
+
+--S 1305 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R +-+ \|- b \|b x + 9 - 3\|- b +---+ x\|b
+--R 2\|b atan(---------------------------) - \|- b asinh(-----)
+--R b x 3
+--R (6) -----------------------------------------------------------
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 1305
+
+--S 1306 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1306
+
+)clear all
+
+--S 1307 of 1369
+t0:=1/sqrt(9-b*x^2)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +----------+
+--R | 2
+--R \|- b x + 9
+--R Type: Expression(Integer)
+--E 1307
+
+--S 1308 of 1369
+r0:=asin(1/3*x*sqrt(b))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R asin(-----)
+--R 3
+--R (2) -----------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1308
+
+--S 1309 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+
+--R | 2 2 +---+ | 2
+--R (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x
+--R log(-----------------------------------------------------------)
+--R +----------+
+--R | 2
+--R \|- b x + 9 - 3
+--R [----------------------------------------------------------------,
+--R +---+
+--R \|- b
+--R +----------+
+--R | 2 +-+
+--R (\|- b x + 9 - 3)\|b
+--R 2atan(-----------------------)
+--R b x
+--R - ------------------------------]
+--R +-+
+--R \|b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1309
+
+--S 1310 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +----------+ +----------+
+--R | 2 2 +---+ | 2
+--R +-+ (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x
+--R \|b log(-----------------------------------------------------------)
+--R +----------+
+--R | 2
+--R \|- b x + 9 - 3
+--R +
+--R +-+
+--R +---+ x\|b
+--R - \|- b asin(-----)
+--R 3
+--R /
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 1310
+
+--S 1311 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1311
+
+--S 1312 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +----------+
+--R | 2 +-+ +-+
+--R (\|- b x + 9 - 3)\|b x\|b
+--R - 2atan(-----------------------) - asin(-----)
+--R b x 3
+--R (6) ----------------------------------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1312
+
+--S 1313 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1313
+
+)clear all
+
+--S 1314 of 1369
+t0:=1/sqrt(-9+b*x^2)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x - 9
+--R Type: Expression(Integer)
+--E 1314
+
+--S 1315 of 1369
+r0:=atanh(x*sqrt(b)/sqrt(-9+b*x^2))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x - 9
+--R (2) ------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1315
+
+--S 1316 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +---+ | 2
+--R +--------+ \|- b \|b x - 9
+--R +-+ | 2 2 atan(-----------------)
+--R log(2x\|b \|b x - 9 + 2b x - 9) b x
+--R (3) [----------------------------------,-----------------------]
+--R +-+ +---+
+--R 2\|b \|- b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1316
+
+--S 1317 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +-+
+--R +-+ | 2 2 x\|b
+--R log(2x\|b \|b x - 9 + 2b x - 9) - 2atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x - 9
+--R (4) --------------------------------------------------------
+--R +-+
+--R 2\|b
+--R Type: Expression(Integer)
+--E 1317
+
+--S 1318 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1318
+
+--S 1319 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ +---+ | 2
+--R +---+ x\|b +-+ \|- b \|b x - 9
+--R - \|- b atanh(-----------) + \|b atan(-----------------)
+--R +--------+ b x
+--R | 2
+--R \|b x - 9
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 1319
+
+--S 1320 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1320
+
+)clear all
+
+--S 1321 of 1369
+t0:=1/sqrt(-9-b*x^2)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +----------+
+--R | 2
+--R \|- b x - 9
+--R Type: Expression(Integer)
+--E 1321
+
+--S 1322 of 1369
+r0:=atan(x*sqrt(b)/sqrt(-9-b*x^2))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R atan(-------------)
+--R +----------+
+--R | 2
+--R \|- b x - 9
+--R (2) -------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1322
+
+--S 1323 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +----------+
+--R | 2 +-+
+--R +----------+ \|- b x - 9 \|b
+--R | 2 +---+ 2 atan(-----------------)
+--R log(2x\|- b x - 9 \|- b - 2b x - 9) b x
+--R (3) [--------------------------------------,- -----------------------]
+--R +---+ +-+
+--R 2\|- b \|b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1323
+
+--S 1324 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +----------+ +-+
+--R +-+ | 2 +---+ 2 +---+ x\|b
+--R \|b log(2x\|- b x - 9 \|- b - 2b x - 9) - 2\|- b atan(-------------)
+--R +----------+
+--R | 2
+--R \|- b x - 9
+--R -----------------------------------------------------------------------
+--R +---+ +-+
+--R 2\|- b \|b
+--R Type: Expression(Integer)
+--E 1324
+
+--S 1325 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1325
+
+--S 1326 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +----------+
+--R | 2 +-+ +-+
+--R \|- b x - 9 \|b x\|b
+--R - atan(-----------------) - atan(-------------)
+--R b x +----------+
+--R | 2
+--R \|- b x - 9
+--R (6) -----------------------------------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1326
+
+--S 1327 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1327
+
+)clear all
+
+--S 1328 of 1369
+t0:=1/sqrt(%pi+b*x^2)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +----------+
+--R | 2
+--R \|b x + %pi
+--R Type: Expression(Integer)
+--E 1328
+
+--S 1329 of 1369
+r0:=asinh(x*sqrt(b)/sqrt(%pi))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R asinh(------)
+--R +---+
+--R \|%pi
+--R (2) -------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1329
+
+--S 1330 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+
+--R +-+ +---+ | 2 +---+ 2 +-+
+--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b
+--R log(----------------------------------------------------------------)
+--R +----------+
+--R +---+ | 2
+--R \|%pi \|b x + %pi - %pi
+--R [---------------------------------------------------------------------,
+--R +-+
+--R \|b
+--R +----------+
+--R +---+ | 2 +---+ +---+
+--R \|- b \|b x + %pi - \|- b \|%pi
+--R 2atan(----------------------------------)
+--R b x
+--R -----------------------------------------]
+--R +---+
+--R \|- b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1330
+
+--S 1331 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +----------+
+--R +-+ +---+ | 2 +---+ 2 +-+
+--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b
+--R log(----------------------------------------------------------------)
+--R +----------+
+--R +---+ | 2
+--R \|%pi \|b x + %pi - %pi
+--R +
+--R +-+
+--R x\|b
+--R - asinh(------)
+--R +---+
+--R \|%pi
+--R /
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1331
+
+--S 1332 of 1369
+d0a:=normalize(D(m0a,x))
+--R
+--R
+--R (5)
+--R +----------+
+--R | 2
+--R 2 2 +-+ +---+ 2 3 2 |b x + %pi
+--R ((3b %pi x + 4%pi )\|b \|%pi - b %pi x - 4b %pi x) |----------
+--R \| %pi
+--R +
+--R 2 4 2 2 +-+ +---+ 2 3 2
+--R (b x + 5b %pi x + 4%pi )\|b \|%pi - 3b %pi x - 4b %pi x
+--R *
+--R +----------+
+--R | 2
+--R \|b x + %pi
+--R +
+--R 2 3 2 +---+ 2 4 2 2 3 +-+
+--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b )
+--R *
+--R +----------+
+--R | 2
+--R |b x + %pi
+--R |----------
+--R \| %pi
+--R +
+--R 3 5 2 3 2 +---+ 2 4 2 2 3 +-+
+--R (b x + 5b %pi x + 4b %pi x)\|%pi + (- 3b %pi x - 7b %pi x - 4%pi )\|b
+--R /
+--R 2 3 2 +---+ 2 4 2 2 3 +-+
+--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b )
+--R *
+--R +----------+
+--R | 2 +----------+
+--R |b x + %pi | 2
+--R |---------- \|b x + %pi
+--R \| %pi
+--R +
+--R 2 4 2 2 3 +-+ +---+ 3 5 2 2 3
+--R (3b %pi x + 7b %pi x + 4%pi )\|b \|%pi - b %pi x - 5b %pi x
+--R +
+--R 3
+--R - 4b %pi x
+--R *
+--R +----------+
+--R | 2
+--R |b x + %pi
+--R |----------
+--R \| %pi
+--R Type: Expression(Integer)
+--E 1332
+
+--S 1333 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +----------+
+--R +---+ | 2 +---+ +---+ +-+
+--R +-+ \|- b \|b x + %pi - \|- b \|%pi +---+ x\|b
+--R 2\|b atan(----------------------------------) - \|- b asinh(------)
+--R b x +---+
+--R \|%pi
+--R (6) -------------------------------------------------------------------
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 1333
+
+--S 1334 of 1369
+d0b:=normalize(D(m0b,x))
+--R
+--R
+--R +----------+
+--R +----------+ | 2
+--R +---+ | 2 |b x + %pi
+--R - \|%pi \|b x + %pi + %pi |----------
+--R \| %pi
+--R (7) ----------------------------------------
+--R +----------+
+--R | 2 +----------+
+--R |b x + %pi | 2
+--R %pi |---------- \|b x + %pi
+--R \| %pi
+--R Type: Expression(Integer)
+--E 1334
+
+)clear all
+
+--S 1335 of 1369
+t0:=1/sqrt(%pi-b*x^2)
+--R
+--R
+--R 1
+--R (1) ---------------
+--R +------------+
+--R | 2
+--R \|- b x + %pi
+--R Type: Expression(Integer)
+--E 1335
+
+--S 1336 of 1369
+r0:=asin(x*sqrt(b)/sqrt(%pi))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R asin(------)
+--R +---+
+--R \|%pi
+--R (2) ------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1336
+
+--S 1337 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R log
+--R +------------+
+--R | 2 +---+ +---+ 2 +---+
+--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b
+--R +
+--R +------------+
+--R | 2
+--R b x\|- b x + %pi
+--R /
+--R +------------+
+--R | 2 +---+
+--R \|- b x + %pi \|%pi - %pi
+--R /
+--R +---+
+--R \|- b
+--R ,
+--R +------------+
+--R +-+ +---+ | 2 +-+
+--R \|b \|%pi - \|- b x + %pi \|b
+--R 2atan(--------------------------------)
+--R b x
+--R ---------------------------------------]
+--R +-+
+--R \|b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1337
+
+--S 1338 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-+
+--R \|b
+--R *
+--R log
+--R +------------+
+--R | 2 +---+ +---+ 2 +---+
+--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b
+--R +
+--R +------------+
+--R | 2
+--R b x\|- b x + %pi
+--R /
+--R +------------+
+--R | 2 +---+
+--R \|- b x + %pi \|%pi - %pi
+--R +
+--R +-+
+--R +---+ x\|b
+--R - \|- b asin(------)
+--R +---+
+--R \|%pi
+--R /
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 1338
+
+--S 1339 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +------------+
+--R +------------+ | 2
+--R 2 2 | 2 |- b x + %pi
+--R (- 3b %pi x + 4%pi )\|- b x + %pi |------------
+--R \| %pi
+--R +
+--R +------------+
+--R 2 4 2 2 | 2
+--R (b x - 5b %pi x + 4%pi )\|- b x + %pi
+--R *
+--R +---+
+--R \|- b
+--R +
+--R +------------+
+--R | 2
+--R 2 3 2 |- b x + %pi 3 5 2 3 2
+--R (3b %pi x - 4b %pi x) |------------ - b x + 5b %pi x - 4b %pi x
+--R \| %pi
+--R *
+--R +---+
+--R \|%pi
+--R +
+--R +------------+
+--R | 2
+--R 2 4 2 2 3 |- b x + %pi 2 4
+--R (- b %pi x + 5b %pi x - 4%pi ) |------------ - 3b %pi x
+--R \| %pi
+--R +
+--R 2 2 3
+--R 7b %pi x - 4%pi
+--R *
+--R +---+
+--R \|- b
+--R +
+--R +------------+
+--R +------------+ | 2
+--R 2 3 2 | 2 |- b x + %pi
+--R (- b %pi x + 4b %pi x)\|- b x + %pi |------------
+--R \| %pi
+--R +
+--R +------------+
+--R 2 3 2 | 2
+--R (- 3b %pi x + 4b %pi x)\|- b x + %pi
+--R /
+--R +------------+
+--R | 2
+--R 2 4 2 2 3 |- b x + %pi +---+
+--R (3b %pi x - 7b %pi x + 4%pi ) |------------ \|- b
+--R \| %pi
+--R +
+--R +------------+
+--R +------------+ | 2
+--R 2 3 2 | 2 |- b x + %pi
+--R (3b %pi x - 4b %pi x)\|- b x + %pi |------------
+--R \| %pi
+--R *
+--R +---+
+--R \|%pi
+--R +
+--R +------------+
+--R +------------+ | 2
+--R 2 4 2 2 3 | 2 |- b x + %pi +---+
+--R (- b %pi x + 5b %pi x - 4%pi )\|- b x + %pi |------------ \|- b
+--R \| %pi
+--R +
+--R +------------+
+--R | 2
+--R 3 5 2 2 3 3 |- b x + %pi
+--R (b %pi x - 5b %pi x + 4b %pi x) |------------
+--R \| %pi
+--R Type: Expression(Integer)
+--E 1339
+
+--S 1340 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +------------+
+--R +-+ +---+ | 2 +-+ +-+
+--R \|b \|%pi - \|- b x + %pi \|b x\|b
+--R 2atan(--------------------------------) - asin(------)
+--R b x +---+
+--R \|%pi
+--R (6) ------------------------------------------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1340
+
+--S 1341 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R +------------+
+--R +------------+ | 2
+--R | 2 +---+ |- b x + %pi
+--R - \|- b x + %pi \|%pi + %pi |------------
+--R \| %pi
+--R (7) --------------------------------------------
+--R +------------+
+--R +------------+ | 2
+--R | 2 |- b x + %pi
+--R %pi\|- b x + %pi |------------
+--R \| %pi
+--R Type: Expression(Integer)
+--E 1341
+
+)clear all
+
+--S 1342 of 1369
+t0:=1/sqrt(-%pi+b*x^2)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +----------+
+--R | 2
+--R \|b x - %pi
+--R Type: Expression(Integer)
+--E 1342
+
+--S 1343 of 1369
+r0:=atanh(x*sqrt(b)/sqrt(-%pi+b*x^2))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R atanh(-------------)
+--R +----------+
+--R | 2
+--R \|b x - %pi
+--R (2) --------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1343
+
+--S 1344 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +----------+
+--R +---+ | 2
+--R +----------+ \|- b \|b x - %pi
+--R +-+ | 2 2 atan(-------------------)
+--R log(2x\|b \|b x - %pi + 2b x - %pi) b x
+--R (3) [--------------------------------------,-------------------------]
+--R +-+ +---+
+--R 2\|b \|- b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1344
+
+--S 1345 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +----------+ +-+
+--R +-+ | 2 2 x\|b
+--R log(2x\|b \|b x - %pi + 2b x - %pi) - 2atanh(-------------)
+--R +----------+
+--R | 2
+--R \|b x - %pi
+--R (4) --------------------------------------------------------------
+--R +-+
+--R 2\|b
+--R Type: Expression(Integer)
+--E 1345
+
+--S 1346 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1346
+
+--S 1347 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +----------+
+--R +-+ +---+ | 2
+--R +---+ x\|b +-+ \|- b \|b x - %pi
+--R - \|- b atanh(-------------) + \|b atan(-------------------)
+--R +----------+ b x
+--R | 2
+--R \|b x - %pi
+--R (6) ------------------------------------------------------------
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 1347
+
+--S 1348 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1348
+
+)clear all
+
+--S 1349 of 1369
+t0:=1/sqrt(-%pi-b*x^2)
+--R
+--R
+--R 1
+--R (1) ---------------
+--R +------------+
+--R | 2
+--R \|- b x - %pi
+--R Type: Expression(Integer)
+--E 1349
+
+--S 1350 of 1369
+r0:=atan(x*sqrt(b)/sqrt(-%pi-b*x^2))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R atan(---------------)
+--R +------------+
+--R | 2
+--R \|- b x - %pi
+--R (2) ---------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1350
+
+--S 1351 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------------+
+--R | 2 +-+
+--R +------------+ \|- b x - %pi \|b
+--R | 2 +---+ 2 atan(-------------------)
+--R log(2x\|- b x - %pi \|- b - 2b x - %pi) b x
+--R [------------------------------------------,- -------------------------]
+--R +---+ +-+
+--R 2\|- b \|b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1351
+
+--S 1352 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +------------+ +-+
+--R +-+ | 2 +---+ 2 +---+ x\|b
+--R \|b log(2x\|- b x - %pi \|- b - 2b x - %pi) - 2\|- b atan(---------------)
+--R +------------+
+--R | 2
+--R \|- b x - %pi
+--R -----------------------------------------------------------------------------
+--R +---+ +-+
+--R 2\|- b \|b
+--R Type: Expression(Integer)
+--E 1352
+
+--S 1353 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1353
+
+--S 1354 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +------------+
+--R | 2 +-+ +-+
+--R \|- b x - %pi \|b x\|b
+--R - atan(-------------------) - atan(---------------)
+--R b x +------------+
+--R | 2
+--R \|- b x - %pi
+--R (6) ---------------------------------------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1354
+
+--S 1355 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1355
+
+)clear all
+
+--S 1356 of 1369
+t0:=1/sqrt(a+b*x^2)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 1356
+
+--S 1357 of 1369
+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 1357
+
+--S 1358 of 1369
+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 1358
+
+--S 1359 of 1369
+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 1359
+
+--S 1360 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1360
+
+--S 1361 of 1369
+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 1361
+
+--S 1362 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1362
+
+)clear all
+
+--S 1363 of 1369
+t0:=1/sqrt(a-b*x^2)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +----------+
+--R | 2
+--R \|- b x + a
+--R Type: Expression(Integer)
+--E 1363
+
+--S 1364 of 1369
+r0:=atan(x*sqrt(b)/sqrt(a-b*x^2))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R atan(-------------)
+--R +----------+
+--R | 2
+--R \|- b x + a
+--R (2) -------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1364
+
+--S 1365 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+
+--R | 2 +---+ +-+ 2 +---+ | 2
+--R (\|- b x + a \|- b - b x)\|a + (b x - a)\|- b + b x\|- b x + a
+--R log(---------------------------------------------------------------------)
+--R +----------+
+--R | 2 +-+
+--R \|- b x + a \|a - a
+--R [--------------------------------------------------------------------------,
+--R +---+
+--R \|- b
+--R +----------+
+--R +-+ | 2 +-+
+--R (\|a - \|- b x + a )\|b
+--R 2atan(--------------------------)
+--R b x
+--R ---------------------------------]
+--R +-+
+--R \|b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1365
+
+--S 1366 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-+
+--R \|b
+--R *
+--R log
+--R +----------+
+--R | 2 +---+ +-+ 2 +---+
+--R (\|- b x + a \|- b - b x)\|a + (b x - a)\|- b
+--R +
+--R +----------+
+--R | 2
+--R b x\|- b x + a
+--R /
+--R +----------+
+--R | 2 +-+
+--R \|- b x + a \|a - a
+--R +
+--R +-+
+--R +---+ x\|b
+--R - \|- b atan(-------------)
+--R +----------+
+--R | 2
+--R \|- b x + a
+--R /
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 1366
+
+--S 1367 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1367
+
+--S 1368 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +----------+
+--R +-+ | 2 +-+ +-+
+--R (\|a - \|- b x + a )\|b x\|b
+--R 2atan(--------------------------) - atan(-------------)
+--R b x +----------+
+--R | 2
+--R \|- b x + a
+--R (6) -------------------------------------------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1368
+
+--S 1369 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1369
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich4b.input.pdf b/src/axiom-website/CATS/rich4b.input.pdf
new file mode 100644
index 0000000..5c18802
Binary files /dev/null and b/src/axiom-website/CATS/rich4b.input.pdf differ
diff --git a/src/axiom-website/CATS/rich4c.input.pamphlet b/src/axiom-website/CATS/rich4c.input.pamphlet
new file mode 100644
index 0000000..ea77292
--- /dev/null
+++ b/src/axiom-website/CATS/rich4c.input.pamphlet
@@ -0,0 +1,16055 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich4c.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 257 supplied "optimal results".
+\item 187 matching answers.
+\item 2 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 70 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich4c.output
+)spool rich4c.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1285
+t0:=1/sqrt(-a+b*x^2)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x - a
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1285
+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 2
+
+--S 3 of 1285
+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 3
+
+--S 4 of 1285
+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 4
+
+--S 5 of 1285
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+--S 6 of 1285
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--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 ------------------------------------------------------------------------
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 1285
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 7
+
+)clear all
+
+--S 8 of 1285
+t0:=1/sqrt(-a-b*x^2)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +----------+
+--R | 2
+--R \|- b x - a
+--R Type: Expression(Integer)
+--E 8
+
+--S 9 of 1285
+r0:=atan(x*sqrt(b)/sqrt(-a-b*x^2))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R atan(-------------)
+--R +----------+
+--R | 2
+--R \|- b x - a
+--R (2) -------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+
+--R | 2 +---+ +---+ 2 +---+ | 2
+--R (\|- b x - a \|- b - b x)\|- a + (b x + a)\|- b + b x\|- b x - a
+--R log(-----------------------------------------------------------------------)
+--R +----------+
+--R | 2 +---+
+--R \|- b x - a \|- a + a
+--R [----------------------------------------------------------------------------
+--R +---+
+--R \|- b
+--R ,
+--R +----------+
+--R +---+ | 2 +-+
+--R (\|- a - \|- b x - a )\|b
+--R 2atan(----------------------------)
+--R b x
+--R -----------------------------------]
+--R +-+
+--R \|b
+--R Type: Union(List(Expression(Integer)),...)
+--E 10
+
+--S 11 of 1285
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-+
+--R \|b
+--R *
+--R log
+--R +----------+
+--R | 2 +---+ +---+ 2 +---+
+--R (\|- b x - a \|- b - b x)\|- a + (b x + a)\|- b
+--R +
+--R +----------+
+--R | 2
+--R b x\|- b x - a
+--R /
+--R +----------+
+--R | 2 +---+
+--R \|- b x - a \|- a + a
+--R +
+--R +-+
+--R +---+ x\|b
+--R - \|- b atan(-------------)
+--R +----------+
+--R | 2
+--R \|- b x - a
+--R /
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1285
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 1285
+m0b:=a0.2-r0
+--R
+--R
+--R +----------+
+--R +---+ | 2 +-+ +-+
+--R (\|- a - \|- b x - a )\|b x\|b
+--R 2atan(----------------------------) - atan(-------------)
+--R b x +----------+
+--R | 2
+--R \|- b x - a
+--R (6) ---------------------------------------------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 13
+
+--S 14 of 1285
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 14
+
+)clear all
+
+--S 15 of 1285
+t0:=1/sqrt(a^2-x^2)
+--R
+--R
+--R 1
+--R (1) ------------
+--R +---------+
+--R | 2 2
+--R \|- x + a
+--R Type: Expression(Integer)
+--E 15
+
+--S 16 of 1285
+r0:=atan(x/sqrt(a^2-x^2))
+--R
+--R
+--R x
+--R (2) atan(------------)
+--R +---------+
+--R | 2 2
+--R \|- x + a
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R | 2 2
+--R \|- x + a - a
+--R (3) - 2atan(----------------)
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 17
+
+--S 18 of 1285
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 2 2
+--R \|- x + a - a x
+--R (4) - 2atan(----------------) - atan(------------)
+--R x +---------+
+--R | 2 2
+--R \|- x + a
+--R Type: Expression(Integer)
+--E 18
+
+--S 19 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 19
+
+)clear all
+
+--S 20 of 1285
+t0:=x^(3+m)/sqrt(a+b*x^2)
+--R
+--R
+--R m + 3
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 20
+
+--S 21 of 1285
+--r0:=x^(2+m)*sqrt(a+b*x^2)/(b*(3+m))-a*x^(2+m)*_
+--hypergeometric(1/2,1/2*(2+m),1/2*(4+m),-b*x^2/a)*sqrt((a+b*x^2)/a)/_
+--(b*(3+m)*sqrt(a+b*x^2))
+--E 21
+
+--S 22 of 1285
+--a0:=integrate(t0,x)
+--E 22
+
+--S 23 of 1285
+--m0:=a0-r0
+--E 23
+
+--S 24 of 1285
+--d0:=D(m0,x)
+--E 24
+
+)clear all
+
+--S 25 of 1285
+t0:=x^(2+m)/sqrt(a+b*x^2)
+--R
+--R
+--R m + 2
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 25
+
+--S 26 of 1285
+--r0:=x^(1+m)*sqrt(a+b*x^2)/(b*(2+m))-a*x^(1+m)*_
+--hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+--sqrt((a+b*x^2)/a)/(b*(2+m)*sqrt(a+b*x^2))
+--E 26
+
+--S 27 of 1285
+--a0:=integrate(t0,x)
+--E 27
+
+--S 28 of 1285
+--m0:=a0-r0
+--E 28
+
+--S 29 of 1285
+--d0:=D(m0,x)
+--E 29
+
+)clear all
+
+--S 30 of 1285
+t0:=x^(1+m)/sqrt(a+b*x^2)
+--R
+--R
+--R m + 1
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 30
+
+--S 31 of 1285
+--r0:=x^(2+m)*hypergeometric(1/2,1/2*(2+m),1/2*(4+m),-b*x^2/a)*_
+--sqrt((a+b*x^2)/a)/((2+m)*sqrt(a+b*x^2))
+--E 31
+
+--S 32 of 1285
+--a0:=integrate(t0,x)
+--E 32
+
+--S 33 of 1285
+--m0:=a0-r0
+--E 33
+
+--S 34 of 1285
+--d0:=D(m0,x)
+--E 34
+
+)clear all
+
+--S 35 of 1285
+t0:=x^m/sqrt(a+b*x^2)
+--R
+--R
+--R m
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 35
+
+--S 36 of 1285
+--r0:=x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+--sqrt((a+b*x^2)/a)/((1+m)*sqrt(a+b*x^2))
+--E 36
+
+--S 37 of 1285
+--a0:=integrate(t0,x)
+--E 37
+
+--S 38 of 1285
+--m0:=a0-r0
+--E 38
+
+--S 39 of 1285
+--d0:=D(m0,x)
+--E 39
+
+)clear all
+
+--S 40 of 1285
+t0:=x^(-1+m)/sqrt(a+b*x^2)
+--R
+--R
+--R m - 1
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 40
+
+--S 41 of 1285
+--r0:=x^m*sqrt(a+b*x^2)/(a*m)-b*(1+m)*x^(2+m)*_
+--hypergeometric(1/2,1/2*(2+m),1/2*(4+m),-b*x^2/a)*_
+--sqrt((a+b*x^2)/a)/(a*m*(2+m)*sqrt(a+b*x^2))
+--E 41
+
+--S 42 of 1285
+--a0:=integrate(t0,x)
+--E 42
+
+--S 43 of 1285
+--m0:=a0-r0
+--E 43
+
+--S 44 of 1285
+--d0:=D(m0,x)
+--E 44
+
+)clear all
+
+--S 45 of 1285
+t0:=x^(-2+m)/sqrt(a+b*x^2)
+--R
+--R
+--R m - 2
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 45
+
+--S 46 of 1285
+--r0:=-x^(-1+m)*sqrt(a+b*x^2)/(a*(1-m))+b*m*x^(1+m)*_
+--hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_
+--sqrt((a+b*x^2)/a)/(a*(1-m^2)*sqrt(a+b*x^2))
+--E 46
+
+--S 47 of 1285
+--a0:=integrate(t0,x)
+--E 47
+
+--S 48 of 1285
+--m0:=a0-r0
+--E 48
+
+--S 49 of 1285
+--d0:=D(m0,x)
+--E 49
+
+)clear all
+
+--S 50 of 1285
+t0:=x^(1+m)*(a*(2+m)+b*(3+m)*x^2)/sqrt(a+b*x^2)
+--R
+--R
+--R 2 m + 1
+--R ((b m + 3b)x + a m + 2a)x
+--R (1) -------------------------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 50
+
+--S 51 of 1285
+r0:=x^(2+m)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R m + 2 | 2
+--R (2) x \|b x + a
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 | 2 3 +-+ (m + 1)log(x)
+--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e
+--R (3) ----------------------------------------------------------------
+--R +--------+
+--R +-+ | 2 2
+--R 2\|a \|b x + a - b x - 2a
+--R Type: Union(Expression(Integer),...)
+--E 52
+
+--S 53 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 | 2 3 +-+ (m + 1)log(x)
+--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e
+--R +
+--R +--------+
+--R 2 m + 2 | 2 2 m + 2 +-+
+--R (b x + 2a)x \|b x + a + (- 2b x - 2a)x \|a
+--R /
+--R +--------+
+--R +-+ | 2 2
+--R 2\|a \|b x + a - b x - 2a
+--R Type: Expression(Integer)
+--E 53
+
+--S 54 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 54
+
+)clear all
+
+--S 55 of 1285
+t0:=a*(2+m)*x^(1+m)/sqrt(a+b*x^2)+b*(3+m)*x^(3+m)/sqrt(a+b*x^2)
+--R
+--R
+--R m + 3 m + 1
+--R (b m + 3b)x + (a m + 2a)x
+--R (1) -----------------------------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 55
+
+--S 56 of 1285
+r0:=x^(2+m)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R m + 2 | 2
+--R (2) x \|b x + a
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 | 2 3 +-+ (m + 1)log(x)
+--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e
+--R (3) ----------------------------------------------------------------
+--R +--------+
+--R +-+ | 2 2
+--R 2\|a \|b x + a - b x - 2a
+--R Type: Union(Expression(Integer),...)
+--E 57
+
+--S 58 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 | 2 3 +-+ (m + 1)log(x)
+--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e
+--R +
+--R +--------+
+--R 2 m + 2 | 2 2 m + 2 +-+
+--R (b x + 2a)x \|b x + a + (- 2b x - 2a)x \|a
+--R /
+--R +--------+
+--R +-+ | 2 2
+--R 2\|a \|b x + a - b x - 2a
+--R Type: Expression(Integer)
+--E 58
+
+--S 59 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 59
+
+)clear all
+
+--S 60 of 1285
+t0:=x^(-1+m)*(a*m+b*(-1+m)*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 2 m - 1
+--R ((b m - b)x + a m)x
+--R (1) -------------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 60
+
+--S 61 of 1285
+r0:=x^m/sqrt(a+b*x^2)
+--R
+--R
+--R m
+--R x
+--R (2) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 2 +-+ (m - 1)log(x)
+--R (- x\|b x + a + x\|a )%e
+--R (3) ---------------------------------------
+--R +--------+
+--R +-+ | 2 2
+--R \|a \|b x + a - b x - a
+--R Type: Union(Expression(Integer),...)
+--E 62
+
+--S 63 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R +-+ | 2 3 (m - 1)log(x) m +-+ | 2
+--R (- x\|a \|b x + a + b x + a x)%e + x \|a \|b x + a
+--R +
+--R 2 m
+--R (- b x - a)x
+--R /
+--R +--------+
+--R 2 | 2 2 +-+
+--R (b x + a)\|b x + a + (- b x - a)\|a
+--R Type: Expression(Integer)
+--E 63
+
+--S 64 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 64
+
+)clear all
+
+--S 65 of 1285
+t0:=-b*x^(1+m)/(a+b*x^2)^(3/2)+m*x^(-1+m)/sqrt(a+b*x^2)
+--R
+--R
+--R m + 1 2 m - 1
+--R - b x + (b m x + a m)x
+--R (1) ---------------------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 65
+
+--S 66 of 1285
+r0a:=x^m/sqrt(a+b*x^2)
+--R
+--R
+--R m
+--R x
+--R (2) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 1285
+r0b:=-b*x^(2+m)/(a*sqrt(a+b*x^2))+x^m*sqrt(a+b*x^2)/a
+--R
+--R
+--R m + 2 2 m
+--R - b x + (b x + a)x
+--R (3) -------------------------
+--R +--------+
+--R | 2
+--R a\|b x + a
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 2 +-+ (m - 1)log(x)
+--R (- x\|b x + a + x\|a )%e
+--R (4) ---------------------------------------
+--R +--------+
+--R +-+ | 2 2
+--R \|a \|b x + a - b x - a
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 1285
+m0a:=a0-r0a
+--R
+--R
+--R (5)
+--R +--------+ +--------+
+--R +-+ | 2 3 (m - 1)log(x) m +-+ | 2
+--R (- x\|a \|b x + a + b x + a x)%e + x \|a \|b x + a
+--R +
+--R 2 m
+--R (- b x - a)x
+--R /
+--R +--------+
+--R 2 | 2 2 +-+
+--R (b x + a)\|b x + a + (- b x - a)\|a
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 1285
+--d0:=normalize m0a
+--E 70
+
+--S 71 of 1285
+m0b:=a0-r0b
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ | 2 3 2 (m - 1)log(x)
+--R (- a x\|a \|b x + a + a b x + a x)%e
+--R +
+--R +--------+
+--R m + 2 2 m +-+ | 2 2 2 m + 2
+--R (- b x + (b x + a)x )\|a \|b x + a + (b x + a b)x
+--R +
+--R 2 4 2 2 m
+--R (- b x - 2a b x - a )x
+--R /
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a b x + a )\|b x + a + (- a b x - a )\|a
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 1285
+--d0:=normalize m0b
+--E 72
+
+)clear all
+
+--S 73 of 1285
+t0:=x*(-1+x^2)^(7/3)
+--R
+--R
+--R +------+
+--R 5 3 3| 2
+--R (1) (x - 2x + x)\|x - 1
+--R Type: Expression(Integer)
+--E 73
+
+--S 74 of 1285
+r0:=3/20*(-1+x^2)^(10/3)
+--R
+--R
+--R +------+
+--R 6 4 2 3| 2
+--R (3x - 9x + 9x - 3)\|x - 1
+--R (2) ------------------------------
+--R 20
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R 6 4 2 3| 2
+--R (3x - 9x + 9x - 3)\|x - 1
+--R (3) ------------------------------
+--R 20
+--R Type: Union(Expression(Integer),...)
+--E 75
+
+--S 76 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 77
+
+)clear all
+
+--S 78 of 1285
+t0:=x*(1+x^2)^(1/3)
+--R
+--R
+--R +------+
+--R 3| 2
+--R (1) x\|x + 1
+--R Type: Expression(Integer)
+--E 78
+
+--S 79 of 1285
+r0:=3/8*(1+x^2)^(4/3)
+--R
+--R
+--R +------+
+--R 2 3| 2
+--R (3x + 3)\|x + 1
+--R (2) ------------------
+--R 8
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R 2 3| 2
+--R (3x + 3)\|x + 1
+--R (3) ------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 80
+
+--S 81 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 82
+
+)clear all
+
+--S 83 of 1285
+t0:=x*(1-x^2)^(1/3)
+--R
+--R
+--R +--------+
+--R 3| 2
+--R (1) x\|- x + 1
+--R Type: Expression(Integer)
+--E 83
+
+--S 84 of 1285
+r0:=-3/8*(1-x^2)^(4/3)
+--R
+--R
+--R +--------+
+--R 2 3| 2
+--R (3x - 3)\|- x + 1
+--R (2) --------------------
+--R 8
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 3| 2
+--R (3x - 3)\|- x + 1
+--R (3) --------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 85
+
+--S 86 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 87
+
+)clear all
+
+--S 88 of 1285
+t0:=x^3*(1+x^2)^(1/3)
+--R
+--R
+--R +------+
+--R 3 3| 2
+--R (1) x \|x + 1
+--R Type: Expression(Integer)
+--E 88
+
+--S 89 of 1285
+r0:=-3/8*(1+x^2)^(4/3)+3/14*(1+x^2)^(7/3)
+--R
+--R
+--R +------+
+--R 4 2 3| 2
+--R (12x + 3x - 9)\|x + 1
+--R (2) -------------------------
+--R 56
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R 4 2 3| 2
+--R (12x + 3x - 9)\|x + 1
+--R (3) -------------------------
+--R 56
+--R Type: Union(Expression(Integer),...)
+--E 90
+
+--S 91 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 92
+
+)clear all
+
+--S 93 of 1285
+t0:=x/(3+2*x^2)^(1/3)
+--R
+--R
+--R x
+--R (1) ----------
+--R +-------+
+--R 3| 2
+--R \|2x + 3
+--R Type: Expression(Integer)
+--E 93
+
+--S 94 of 1285
+r0:=3/8*(3+2*x^2)^(2/3)
+--R
+--R
+--R +-------+2
+--R 3| 2
+--R 3\|2x + 3
+--R (2) ------------
+--R 8
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+2
+--R 3| 2
+--R 3\|2x + 3
+--R (3) ------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 95
+
+--S 96 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 97
+
+)clear all
+
+--S 98 of 1285
+t0:=x^3/(4+x^2)^(1/3)
+--R
+--R
+--R 3
+--R x
+--R (1) ---------
+--R +------+
+--R 3| 2
+--R \|x + 4
+--R Type: Expression(Integer)
+--E 98
+
+--S 99 of 1285
+r0:=-9/5*(4+x^2)^(2/3)+3/10*x^2*(4+x^2)^(2/3)
+--R
+--R
+--R +------+2
+--R 2 3| 2
+--R (3x - 18)\|x + 4
+--R (2) --------------------
+--R 10
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+2
+--R 2 3| 2
+--R (3x - 18)\|x + 4
+--R (3) --------------------
+--R 10
+--R Type: Union(Expression(Integer),...)
+--E 100
+
+--S 101 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 102
+
+)clear all
+
+--S 103 of 1285
+t0:=x^3/(1+x^2)^(1/3)
+--R
+--R
+--R 3
+--R x
+--R (1) ---------
+--R +------+
+--R 3| 2
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 103
+
+--S 104 of 1285
+r0:=-9/20*(1+x^2)^(2/3)+3/10*x^2*(1+x^2)^(2/3)
+--R
+--R
+--R +------+2
+--R 2 3| 2
+--R (6x - 9)\|x + 1
+--R (2) -------------------
+--R 20
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+2
+--R 2 3| 2
+--R (6x - 9)\|x + 1
+--R (3) -------------------
+--R 20
+--R Type: Union(Expression(Integer),...)
+--E 105
+
+--S 106 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 107
+
+)clear all
+
+--S 108 of 1285
+t0:=x^3/(-1+x^2)^(4/3)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------------
+--R +------+
+--R 2 3| 2
+--R (x - 1)\|x - 1
+--R Type: Expression(Integer)
+--E 108
+
+--S 109 of 1285
+r0:=(-3/2)/(-1+x^2)^(1/3)+3/4*(-1+x^2)^(2/3)
+--R
+--R
+--R 2
+--R 3x - 9
+--R (2) ----------
+--R +------+
+--R 3| 2
+--R 4\|x - 1
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 3x - 9
+--R (3) ----------
+--R +------+
+--R 3| 2
+--R 4\|x - 1
+--R Type: Union(Expression(Integer),...)
+--E 110
+
+--S 111 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 112
+
+)clear all
+
+--S 113 of 1285
+t0:=x^(7/2)*(a+b*x^2)
+--R
+--R
+--R 5 3 +-+
+--R (1) (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 113
+
+--S 114 of 1285
+r0:=2/9*a*x^(9/2)+2/13*b*x^(13/2)
+--R
+--R
+--R 6 4 +-+
+--R (18b x + 26a x )\|x
+--R (2) ---------------------
+--R 117
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 4 +-+
+--R (18b x + 26a x )\|x
+--R (3) ---------------------
+--R 117
+--R Type: Union(Expression(Integer),...)
+--E 115
+
+--S 116 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 117
+
+)clear all
+
+--S 118 of 1285
+t0:=x^(5/2)*(a+b*x^2)
+--R
+--R
+--R 4 2 +-+
+--R (1) (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 118
+
+--S 119 of 1285
+r0:=2/7*a*x^(7/2)+2/11*b*x^(11/2)
+--R
+--R
+--R 5 3 +-+
+--R (14b x + 22a x )\|x
+--R (2) ---------------------
+--R 77
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 3 +-+
+--R (14b x + 22a x )\|x
+--R (3) ---------------------
+--R 77
+--R Type: Union(Expression(Integer),...)
+--E 120
+
+--S 121 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 122
+
+)clear all
+
+--S 123 of 1285
+t0:=x^(3/2)*(a+b*x^2)
+--R
+--R
+--R 3 +-+
+--R (1) (b x + a x)\|x
+--R Type: Expression(Integer)
+--E 123
+
+--S 124 of 1285
+r0:=2/5*a*x^(5/2)+2/9*b*x^(9/2)
+--R
+--R
+--R 4 2 +-+
+--R (10b x + 18a x )\|x
+--R (2) ---------------------
+--R 45
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2 +-+
+--R (10b x + 18a x )\|x
+--R (3) ---------------------
+--R 45
+--R Type: Union(Expression(Integer),...)
+--E 125
+
+--S 126 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 127
+
+)clear all
+
+--S 128 of 1285
+t0:=(a+b*x^2)*sqrt(x)
+--R
+--R
+--R 2 +-+
+--R (1) (b x + a)\|x
+--R Type: Expression(Integer)
+--E 128
+
+--S 129 of 1285
+r0:=2/3*a*x^(3/2)+2/7*b*x^(7/2)
+--R
+--R
+--R 3 +-+
+--R (6b x + 14a x)\|x
+--R (2) -------------------
+--R 21
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 +-+
+--R (6b x + 14a x)\|x
+--R (3) -------------------
+--R 21
+--R Type: Union(Expression(Integer),...)
+--E 130
+
+--S 131 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 132
+
+)clear all
+
+--S 133 of 1285
+t0:=(a+b*x^2)/sqrt(x)
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 133
+
+--S 134 of 1285
+r0:=2/5*b*x^(5/2)+2*a*sqrt(x)
+--R
+--R
+--R 2 +-+
+--R (2b x + 10a)\|x
+--R (2) -----------------
+--R 5
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R (2b x + 10a)\|x
+--R (3) -----------------
+--R 5
+--R Type: Union(Expression(Integer),...)
+--E 135
+
+--S 136 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 137
+
+)clear all
+
+--S 138 of 1285
+t0:=(a+b*x^2)/x^(3/2)
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 138
+
+--S 139 of 1285
+r0:=2/3*b*x^(3/2)-2*a/sqrt(x)
+--R
+--R
+--R 2
+--R 2b x - 6a
+--R (2) ----------
+--R +-+
+--R 3\|x
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 2b x - 6a
+--R (3) ----------
+--R +-+
+--R 3\|x
+--R Type: Union(Expression(Integer),...)
+--E 140
+
+--S 141 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 142
+
+)clear all
+
+--S 143 of 1285
+t0:=(a+b*x^2)/x^(5/2)
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 143
+
+--S 144 of 1285
+r0:=-2/3*a/x^(3/2)+2*b*sqrt(x)
+--R
+--R
+--R 2
+--R 6b x - 2a
+--R (2) ----------
+--R +-+
+--R 3x\|x
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 6b x - 2a
+--R (3) ----------
+--R +-+
+--R 3x\|x
+--R Type: Union(Expression(Integer),...)
+--E 145
+
+--S 146 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 147
+
+)clear all
+
+--S 148 of 1285
+t0:=(a+b*x^2)/x^(7/2)
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 148
+
+--S 149 of 1285
+r0:=-2/5*a/x^(5/2)-2*b/sqrt(x)
+--R
+--R
+--R 2
+--R - 10b x - 2a
+--R (2) -------------
+--R 2 +-+
+--R 5x \|x
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 10b x - 2a
+--R (3) -------------
+--R 2 +-+
+--R 5x \|x
+--R Type: Union(Expression(Integer),...)
+--E 150
+
+--S 151 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 152
+
+)clear all
+
+--S 153 of 1285
+t0:=x^(7/2)*(a+b*x^2)^2
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (1) (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 153
+
+--S 154 of 1285
+r0:=2/9*a^2*x^(9/2)+4/13*a*b*x^(13/2)+2/17*b^2*x^(17/2)
+--R
+--R
+--R 2 8 6 2 4 +-+
+--R (234b x + 612a b x + 442a x )\|x
+--R (2) -----------------------------------
+--R 1989
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 6 2 4 +-+
+--R (234b x + 612a b x + 442a x )\|x
+--R (3) -----------------------------------
+--R 1989
+--R Type: Union(Expression(Integer),...)
+--E 155
+
+--S 156 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 157
+
+)clear all
+
+--S 158 of 1285
+t0:=x^(5/2)*(a+b*x^2)^2
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (1) (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 158
+
+--S 159 of 1285
+r0:=2/7*a^2*x^(7/2)+4/11*a*b*x^(11/2)+2/15*b^2*x^(15/2)
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (154b x + 420a b x + 330a x )\|x
+--R (2) -----------------------------------
+--R 1155
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 7 5 2 3 +-+
+--R (154b x + 420a b x + 330a x )\|x
+--R (3) -----------------------------------
+--R 1155
+--R Type: Union(Expression(Integer),...)
+--E 160
+
+--S 161 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 162
+
+)clear all
+
+--S 163 of 1285
+t0:=x^(3/2)*(a+b*x^2)^2
+--R
+--R
+--R 2 5 3 2 +-+
+--R (1) (b x + 2a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 163
+
+--S 164 of 1285
+r0:=2/5*a^2*x^(5/2)+4/9*a*b*x^(9/2)+2/13*b^2*x^(13/2)
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (90b x + 260a b x + 234a x )\|x
+--R (2) ----------------------------------
+--R 585
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 4 2 2 +-+
+--R (90b x + 260a b x + 234a x )\|x
+--R (3) ----------------------------------
+--R 585
+--R Type: Union(Expression(Integer),...)
+--E 165
+
+--S 166 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 167
+
+)clear all
+
+--S 168 of 1285
+t0:=(a+b*x^2)^2*sqrt(x)
+--R
+--R
+--R 2 4 2 2 +-+
+--R (1) (b x + 2a b x + a )\|x
+--R Type: Expression(Integer)
+--E 168
+
+--S 169 of 1285
+r0:=2/3*a^2*x^(3/2)+4/7*a*b*x^(7/2)+2/11*b^2*x^(11/2)
+--R
+--R
+--R 2 5 3 2 +-+
+--R (42b x + 132a b x + 154a x)\|x
+--R (2) ---------------------------------
+--R 231
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 5 3 2 +-+
+--R (42b x + 132a b x + 154a x)\|x
+--R (3) ---------------------------------
+--R 231
+--R Type: Union(Expression(Integer),...)
+--E 170
+
+--S 171 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 172
+
+)clear all
+
+--S 173 of 1285
+t0:=(a+b*x^2)^2/sqrt(x)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 173
+
+--S 174 of 1285
+r0:=4/5*a*b*x^(5/2)+2/9*b^2*x^(9/2)+2*a^2*sqrt(x)
+--R
+--R
+--R 2 4 2 2 +-+
+--R (10b x + 36a b x + 90a )\|x
+--R (2) ------------------------------
+--R 45
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2 +-+
+--R (10b x + 36a b x + 90a )\|x
+--R (3) ------------------------------
+--R 45
+--R Type: Union(Expression(Integer),...)
+--E 175
+
+--S 176 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 177
+
+)clear all
+
+--S 178 of 1285
+t0:=(a+b*x^2)^2/x^(3/2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 178
+
+--S 179 of 1285
+r0:=4/3*a*b*x^(3/2)+2/7*b^2*x^(7/2)-2*a^2/sqrt(x)
+--R
+--R
+--R 2 4 2 2
+--R 6b x + 28a b x - 42a
+--R (2) -----------------------
+--R +-+
+--R 21\|x
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R 6b x + 28a b x - 42a
+--R (3) -----------------------
+--R +-+
+--R 21\|x
+--R Type: Union(Expression(Integer),...)
+--E 180
+
+--S 181 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 182
+
+)clear all
+
+--S 183 of 1285
+t0:=(a+b*x^2)^2/x^(5/2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 183
+
+--S 184 of 1285
+r0:=-2/3*a^2/x^(3/2)+2/5*b^2*x^(5/2)+4*a*b*sqrt(x)
+--R
+--R
+--R 2 4 2 2
+--R 6b x + 60a b x - 10a
+--R (2) -----------------------
+--R +-+
+--R 15x\|x
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R 6b x + 60a b x - 10a
+--R (3) -----------------------
+--R +-+
+--R 15x\|x
+--R Type: Union(Expression(Integer),...)
+--E 185
+
+--S 186 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 187
+
+)clear all
+
+--S 188 of 1285
+t0:=(a+b*x^2)^2/x^(7/2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 188
+
+--S 189 of 1285
+r0:=-2/5*a^2/x^(5/2)+2/3*b^2*x^(3/2)-4*a*b/sqrt(x)
+--R
+--R
+--R 2 4 2 2
+--R 10b x - 60a b x - 6a
+--R (2) -----------------------
+--R 2 +-+
+--R 15x \|x
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R 10b x - 60a b x - 6a
+--R (3) -----------------------
+--R 2 +-+
+--R 15x \|x
+--R Type: Union(Expression(Integer),...)
+--E 190
+
+--S 191 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 192
+
+)clear all
+
+--S 193 of 1285
+t0:=x^(7/2)*(a+b*x^2)^3
+--R
+--R
+--R 3 9 2 7 2 5 3 3 +-+
+--R (1) (b x + 3a b x + 3a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 193
+
+--S 194 of 1285
+r0:=2/9*a^3*x^(9/2)+6/13*a^2*b*x^(13/2)+6/17*a*b^2*x^(17/2)+2/21*b^3*x^(21/2)
+--R
+--R
+--R 3 10 2 8 2 6 3 4 +-+
+--R (1326b x + 4914a b x + 6426a b x + 3094a x )\|x
+--R (2) ----------------------------------------------------
+--R 13923
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 10 2 8 2 6 3 4 +-+
+--R (1326b x + 4914a b x + 6426a b x + 3094a x )\|x
+--R (3) ----------------------------------------------------
+--R 13923
+--R Type: Union(Expression(Integer),...)
+--E 195
+
+--S 196 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 197
+
+)clear all
+
+--S 198 of 1285
+t0:=x^(5/2)*(a+b*x^2)^3
+--R
+--R
+--R 3 8 2 6 2 4 3 2 +-+
+--R (1) (b x + 3a b x + 3a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 198
+
+--S 199 of 1285
+r0:=2/7*a^3*x^(7/2)+6/11*a^2*b*x^(11/2)+2/5*a*b^2*x^(15/2)+2/19*b^3*x^(19/2)
+--R
+--R
+--R 3 9 2 7 2 5 3 3 +-+
+--R (770b x + 2926a b x + 3990a b x + 2090a x )\|x
+--R (2) --------------------------------------------------
+--R 7315
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 7 2 5 3 3 +-+
+--R (770b x + 2926a b x + 3990a b x + 2090a x )\|x
+--R (3) --------------------------------------------------
+--R 7315
+--R Type: Union(Expression(Integer),...)
+--E 200
+
+--S 201 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 202
+
+)clear all
+
+--S 203 of 1285
+t0:=x^(3/2)*(a+b*x^2)^3
+--R
+--R
+--R 3 7 2 5 2 3 3 +-+
+--R (1) (b x + 3a b x + 3a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 203
+
+--S 204 of 1285
+r0:=2/5*a^3*x^(5/2)+2/3*a^2*b*x^(9/2)+6/13*a*b^2*x^(13/2)+2/17*b^3*x^(17/2)
+--R
+--R
+--R 3 8 2 6 2 4 3 2 +-+
+--R (390b x + 1530a b x + 2210a b x + 1326a x )\|x
+--R (2) --------------------------------------------------
+--R 3315
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 8 2 6 2 4 3 2 +-+
+--R (390b x + 1530a b x + 2210a b x + 1326a x )\|x
+--R (3) --------------------------------------------------
+--R 3315
+--R Type: Union(Expression(Integer),...)
+--E 205
+
+--S 206 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 207
+
+)clear all
+
+--S 208 of 1285
+t0:=(a+b*x^2)^3*sqrt(x)
+--R
+--R
+--R 3 6 2 4 2 2 3 +-+
+--R (1) (b x + 3a b x + 3a b x + a )\|x
+--R Type: Expression(Integer)
+--E 208
+
+--S 209 of 1285
+r0:=2/3*a^3*x^(3/2)+6/7*a^2*b*x^(7/2)+6/11*a*b^2*x^(11/2)+2/15*b^3*x^(15/2)
+--R
+--R
+--R 3 7 2 5 2 3 3 +-+
+--R (154b x + 630a b x + 990a b x + 770a x)\|x
+--R (2) ----------------------------------------------
+--R 1155
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 7 2 5 2 3 3 +-+
+--R (154b x + 630a b x + 990a b x + 770a x)\|x
+--R (3) ----------------------------------------------
+--R 1155
+--R Type: Union(Expression(Integer),...)
+--E 210
+
+--S 211 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 212
+
+)clear all
+
+--S 213 of 1285
+t0:=(a+b*x^2)^3/sqrt(x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 213
+
+--S 214 of 1285
+r0:=6/5*a^2*b*x^(5/2)+2/3*a*b^2*x^(9/2)+2/13*b^3*x^(13/2)+2*a^3*sqrt(x)
+--R
+--R
+--R 3 6 2 4 2 2 3 +-+
+--R (30b x + 130a b x + 234a b x + 390a )\|x
+--R (2) --------------------------------------------
+--R 195
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3 +-+
+--R (30b x + 130a b x + 234a b x + 390a )\|x
+--R (3) --------------------------------------------
+--R 195
+--R Type: Union(Expression(Integer),...)
+--E 215
+
+--S 216 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 217
+
+)clear all
+
+--S 218 of 1285
+t0:=(a+b*x^2)^3/x^(3/2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 218
+
+--S 219 of 1285
+r0:=2*a^2*b*x^(3/2)+6/7*a*b^2*x^(7/2)+2/11*b^3*x^(11/2)-2*a^3/sqrt(x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 14b x + 66a b x + 154a b x - 154a
+--R (2) -------------------------------------
+--R +-+
+--R 77\|x
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 14b x + 66a b x + 154a b x - 154a
+--R (3) -------------------------------------
+--R +-+
+--R 77\|x
+--R Type: Union(Expression(Integer),...)
+--E 220
+
+--S 221 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 222
+
+)clear all
+
+--S 223 of 1285
+t0:=(a+b*x^2)^3/x^(5/2)
+--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 x \|x
+--R Type: Expression(Integer)
+--E 223
+
+--S 224 of 1285
+r0:=-2/3*a^3/x^(3/2)+6/5*a*b^2*x^(5/2)+2/9*b^3*x^(9/2)+6*a^2*b*sqrt(x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 10b x + 54a b x + 270a b x - 30a
+--R (2) ------------------------------------
+--R +-+
+--R 45x\|x
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 10b x + 54a b x + 270a b x - 30a
+--R (3) ------------------------------------
+--R +-+
+--R 45x\|x
+--R Type: Union(Expression(Integer),...)
+--E 225
+
+--S 226 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 227
+
+)clear all
+
+--S 228 of 1285
+t0:=(a+b*x^2)^3/x^(7/2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 228
+
+--S 229 of 1285
+r0:=-2/5*a^3/x^(5/2)+2*a*b^2*x^(3/2)+2/7*b^3*x^(7/2)-6*a^2*b/sqrt(x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 10b x + 70a b x - 210a b x - 14a
+--R (2) ------------------------------------
+--R 2 +-+
+--R 35x \|x
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 10b x + 70a b x - 210a b x - 14a
+--R (3) ------------------------------------
+--R 2 +-+
+--R 35x \|x
+--R Type: Union(Expression(Integer),...)
+--E 230
+
+--S 231 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 232
+
+)clear all
+
+--S 233 of 1285
+t0:=x^(7/2)/(a+b*x^2)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 233
+
+--S 234 of 1285
+r0:=2/5*x^(5/2)/b-a^(5/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*_
+ sqrt(2))+a^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*_
+ sqrt(2))-1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(b^(9/4)*sqrt(2))+1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))-2*a*sqrt(x)/b^2
+--R
+--R
+--R (2)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 5a\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 5a\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R 10a\|a atan(-------------------) + 10a\|a atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R 2 +-+4+-+ +-+
+--R (4b x - 20a)\|2 \|b \|x
+--R /
+--R 2 +-+4+-+
+--R 10b \|2 \|b
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+
+--R | 5 | 5
+--R 2 | a +-+ 2 | a
+--R 5b |- ---- log(a\|x + 2b |- ----)
+--R 4| 9 4| 9
+--R \| 16b \| 16b
+--R +
+--R +------+
+--R | 5
+--R 2 | a
+--R +------+ +------+ +------+ 2b |- ----
+--R | 5 | 5 | 5 4| 9
+--R 2 | a +-+ 2 | a 2 | a \| 16b
+--R - 5b |- ---- log(a\|x - 2b |- ---- - 10b |- ---- atan(------------)
+--R 4| 9 4| 9 4| 9 +-+
+--R \| 16b \| 16b \| 16b a\|x
+--R +
+--R 2 +-+
+--R (2b x - 10a)\|x
+--R /
+--R 2
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 235
+
+--S 236 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - a\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------+ +------+
+--R | 5 | 5
+--R 2 +-+ | a 4+-+ +-+ 2 | a
+--R 2b \|2 |- ---- \|b log(a\|x + 2b |- ----)
+--R 4| 9 4| 9
+--R \| 16b \| 16b
+--R +
+--R +------+ +------+
+--R | 5 | 5
+--R 2 +-+ | a 4+-+ +-+ 2 | a
+--R - 2b \|2 |- ---- \|b log(a\|x - 2b |- ----)
+--R 4| 9 4| 9
+--R \| 16b \| 16b
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R a\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R - 2a\|a atan(-------------------) - 2a\|a atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +------+
+--R | 5
+--R 2 | a
+--R +------+ 2b |- ----
+--R | 5 4| 9
+--R 2 +-+ | a 4+-+ \| 16b
+--R - 4b \|2 |- ---- \|b atan(------------)
+--R 4| 9 +-+
+--R \| 16b a\|x
+--R /
+--R 2 +-+4+-+
+--R 2b \|2 \|b
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 237
+
+)clear all
+
+--S 238 of 1285
+t0:=x^(5/2)/(a+b*x^2)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 238
+
+--S 239 of 1285
+r0:=2/3*x^(3/2)/b+a^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(7/4)*_
+ sqrt(2))-a^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(7/4)*_
+ sqrt(2))-1/2*a^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(b^(7/4)*sqrt(2))+1/2*a^(3/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(b^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R 3\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - 3\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a
+--R - 6\|a atan(-------------------) - 6\|a atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+4+-+3 +-+
+--R 4x\|2 \|b \|x
+--R /
+--R +-+4+-+3
+--R 6b\|2 \|b
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+3
+--R | 3 | 3
+--R | a 2 +-+ 5 | a
+--R - 3b |- ---- log(a \|x + 8b |- ---- )
+--R 4| 7 4| 7
+--R \| 16b \| 16b
+--R +
+--R +------+3
+--R | 3
+--R 5 | a
+--R +------+ +------+3 +------+ 8b |- ----
+--R | 3 | 3 | 3 4| 7
+--R | a 2 +-+ 5 | a | a \| 16b
+--R 3b |- ---- log(a \|x - 8b |- ---- - 6b |- ---- atan(-------------)
+--R 4| 7 4| 7 4| 7 2 +-+
+--R \| 16b \| 16b \| 16b a \|x
+--R +
+--R +-+
+--R 2x\|x
+--R /
+--R 3b
+--R Type: Union(Expression(Integer),...)
+--E 240
+
+--S 241 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------+ +------+3
+--R | 3 | 3
+--R +-+ | a 4+-+3 2 +-+ 5 | a
+--R - 2b\|2 |- ---- \|b log(a \|x + 8b |- ---- )
+--R 4| 7 4| 7
+--R \| 16b \| 16b
+--R +
+--R +------+ +------+3
+--R | 3 | 3
+--R +-+ | a 4+-+3 2 +-+ 5 | a
+--R 2b\|2 |- ---- \|b log(a \|x - 8b |- ---- )
+--R 4| 7 4| 7
+--R \| 16b \| 16b
+--R +
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a
+--R 2\|a atan(-------------------) + 2\|a atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +------+3
+--R | 3
+--R 5 | a
+--R +------+ 8b |- ----
+--R | 3 4| 7
+--R +-+ | a 4+-+3 \| 16b
+--R - 4b\|2 |- ---- \|b atan(-------------)
+--R 4| 7 2 +-+
+--R \| 16b a \|x
+--R /
+--R +-+4+-+3
+--R 2b\|2 \|b
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 242
+
+)clear all
+
+--S 243 of 1285
+t0:=x^(3/2)/(a+b*x^2)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 243
+
+--S 244 of 1285
+r0:=a^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*sqrt(2))-_
+ a^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*sqrt(2))+_
+ 1/2*a^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (b^(5/4)*sqrt(2))-1/2*a^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(b^(5/4)*sqrt(2))+2*sqrt(x)/b
+--R
+--R
+--R (2)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R - 2\|a atan(-------------------) - 2\|a atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+4+-+ +-+
+--R 4\|2 \|b \|x
+--R /
+--R +-+4+-+
+--R 2b\|2 \|b
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+ +------+ +------+
+--R | a +-+ | a | a +-+ | a
+--R - b |- ---- log(\|x + 2b |- ---- + b |- ---- log(\|x - 2b |- ----)
+--R 4| 5 4| 5 4| 5 4| 5
+--R \| 16b \| 16b \| 16b \| 16b
+--R +
+--R +------+
+--R | a
+--R 2b |- ----
+--R +------+ 4| 5
+--R | a \| 16b +-+
+--R 2b |- ---- atan(----------- + 2\|x
+--R 4| 5 +-+
+--R \| 16b \|x
+--R /
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 245
+
+--S 246 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------+ +------+
+--R +-+ | a 4+-+ +-+ | a
+--R - 2b\|2 |- ---- \|b log(\|x + 2b |- ----)
+--R 4| 5 4| 5
+--R \| 16b \| 16b
+--R +
+--R +------+ +------+
+--R +-+ | a 4+-+ +-+ | a
+--R 2b\|2 |- ---- \|b log(\|x - 2b |- ----)
+--R 4| 5 4| 5
+--R \| 16b \| 16b
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R 2\|a atan(-------------------) + 2\|a atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +------+
+--R | a
+--R 2b |- ----
+--R +------+ 4| 5
+--R +-+ | a 4+-+ \| 16b
+--R 4b\|2 |- ---- \|b atan(-----------)
+--R 4| 5 +-+
+--R \| 16b \|x
+--R /
+--R +-+4+-+
+--R 2b\|2 \|b
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 247
+
+)clear all
+
+--S 248 of 1285
+t0:=sqrt(x)/(a+b*x^2)
+--R
+--R
+--R +-+
+--R \|x
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Expression(Integer)
+--E 248
+
+--S 249 of 1285
+r0:=-atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_
+ 1/2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*_
+ b^(3/4)*sqrt(2))-1/2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(1/4)*b^(3/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R - log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R log(- \|2 \|a \|b \|x + x\|b + \|a ) + 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+4+-+3
+--R 2\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+3
+--R | 1 +-+ 2 | 1
+--R |- ------ log(\|x + 8a b |- ------ )
+--R 4| 3 4| 3
+--R \| 16a b \| 16a b
+--R +
+--R +--------+ +--------+3
+--R | 1 +-+ 2 | 1
+--R - |- ------ log(\|x - 8a b |- ------ )
+--R 4| 3 4| 3
+--R \| 16a b \| 16a b
+--R +
+--R +--------+3
+--R 2 | 1
+--R 8a b |- ------
+--R +--------+ 4| 3
+--R | 1 \| 16a b
+--R 2 |- ------ atan(-----------------)
+--R 4| 3 +-+
+--R \| 16a b \|x
+--R Type: Union(Expression(Integer),...)
+--E 250
+
+--S 251 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------+ +--------+3
+--R +-+ | 1 4+-+4+-+3 +-+ 2 | 1
+--R 2\|2 |- ------ \|a \|b log(\|x + 8a b |- ------ )
+--R 4| 3 4| 3
+--R \| 16a b \| 16a b
+--R +
+--R +--------+ +--------+3
+--R +-+ | 1 4+-+4+-+3 +-+ 2 | 1
+--R - 2\|2 |- ------ \|a \|b log(\|x - 8a b |- ------ )
+--R 4| 3 4| 3
+--R \| 16a b \| 16a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R - log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------+3
+--R 2 | 1
+--R 8a b |- ------
+--R +--------+ 4| 3
+--R +-+ | 1 4+-+4+-+3 \| 16a b
+--R 4\|2 |- ------ \|a \|b atan(-----------------)
+--R 4| 3 +-+
+--R \| 16a b \|x
+--R /
+--R +-+4+-+4+-+3
+--R 2\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 252
+
+)clear all
+
+--S 253 of 1285
+t0:=1/((a+b*x^2)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) --------------
+--R 2 +-+
+--R (b x + a)\|x
+--R Type: Expression(Integer)
+--E 253
+
+--S 254 of 1285
+r0:=-atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))+_
+ atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))-_
+ 1/2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*_
+ b^(1/4)*sqrt(2))+1/2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(3/4)*b^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R - log(- \|2 \|a \|b \|x + x\|b + \|a ) + 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+3 4+-+
+--R 2\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+ +-------+ +-------+
+--R | 1 +-+ | 1 | 1 +-+ | 1
+--R |- ----- log(\|x + 2a |- -----) - |- ----- log(\|x - 2a |- -----)
+--R 4| 3 4| 3 4| 3 4| 3
+--R \| 16a b \| 16a b \| 16a b \| 16a b
+--R +
+--R +-------+
+--R | 1
+--R 2a |- -----
+--R +-------+ 4| 3
+--R | 1 \| 16a b
+--R - 2 |- ----- atan(------------)
+--R 4| 3 +-+
+--R \| 16a b \|x
+--R Type: Union(Expression(Integer),...)
+--E 255
+
+--S 256 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R - log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-------+ +-------+
+--R +-+ | 1 4+-+3 4+-+ +-+ | 1
+--R 2\|2 |- ----- \|a \|b log(\|x + 2a |- -----)
+--R 4| 3 4| 3
+--R \| 16a b \| 16a b
+--R +
+--R +-------+ +-------+
+--R +-+ | 1 4+-+3 4+-+ +-+ | 1
+--R - 2\|2 |- ----- \|a \|b log(\|x - 2a |- -----)
+--R 4| 3 4| 3
+--R \| 16a b \| 16a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-------+
+--R | 1
+--R 2a |- -----
+--R +-+4+-+ +-+ 4+-+ +-------+ 4| 3
+--R \|2 \|b \|x - \|a +-+ | 1 4+-+3 4+-+ \| 16a b
+--R - 2atan(-------------------) - 4\|2 |- ----- \|a \|b atan(------------)
+--R 4+-+ 4| 3 +-+
+--R \|a \| 16a b \|x
+--R /
+--R +-+4+-+3 4+-+
+--R 2\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 257
+
+)clear all
+
+--S 258 of 1285
+t0:=1/(x^(3/2)*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------
+--R 3 +-+
+--R (b x + a x)\|x
+--R Type: Expression(Integer)
+--E 258
+
+--S 259 of 1285
+r0:=b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*sqrt(2))-_
+ b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*sqrt(2))-_
+ 1/2*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(5/4)*sqrt(2))+1/2*b^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(5/4)*sqrt(2))+(-2)/(a*sqrt(x))
+--R
+--R
+--R (2)
+--R 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ +-+ \|2 \|b \|x + \|a 4+-+ +-+ \|2 \|b \|x - \|a
+--R - 2\|b \|x atan(-------------------) - 2\|b \|x atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+4+-+
+--R - 4\|2 \|a
+--R /
+--R +-+4+-+ +-+
+--R 2a\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+3
+--R | b +-+ +-+ 4 | b
+--R - a |- ---- \|x log(b\|x + 8a |- ---- )
+--R 4| 5 4| 5
+--R \| 16a \| 16a
+--R +
+--R +------+ +------+3
+--R | b +-+ +-+ 4 | b
+--R a |- ---- \|x log(b\|x - 8a |- ---- )
+--R 4| 5 4| 5
+--R \| 16a \| 16a
+--R +
+--R +------+3
+--R 4 | b
+--R 8a |- ----
+--R +------+ 4| 5
+--R | b +-+ \| 16a
+--R - 2a |- ---- \|x atan(------------- - 2
+--R 4| 5 +-+
+--R \| 16a b\|x
+--R /
+--R +-+
+--R a\|x
+--R Type: Union(Expression(Integer),...)
+--E 260
+
+--S 261 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------+ +------+3
+--R +-+ | b 4+-+ +-+ 4 | b
+--R - 2a\|2 |- ---- \|a log(b\|x + 8a |- ---- )
+--R 4| 5 4| 5
+--R \| 16a \| 16a
+--R +
+--R +------+ +------+3
+--R +-+ | b 4+-+ +-+ 4 | b
+--R 2a\|2 |- ---- \|a log(b\|x - 8a |- ---- )
+--R 4| 5 4| 5
+--R \| 16a \| 16a
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R 2\|b atan(-------------------) + 2\|b atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +------+3
+--R 4 | b
+--R 8a |- ----
+--R +------+ 4| 5
+--R +-+ | b 4+-+ \| 16a
+--R - 4a\|2 |- ---- \|a atan(-------------)
+--R 4| 5 +-+
+--R \| 16a b\|x
+--R /
+--R +-+4+-+
+--R 2a\|2 \|a
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 262
+
+)clear all
+
+--S 263 of 1285
+t0:=1/(x^(5/2)*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R 4 2 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 263
+
+--S 264 of 1285
+r0:=(-2/3)/(a*x^(3/2))+b^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(7/4)*sqrt(2))-b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(7/4)*sqrt(2))+1/2*b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(7/4)*sqrt(2))-1/2*b^(3/4)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 3x \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 3x \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 +-+ \|2 \|b \|x + \|a
+--R - 6x \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 4+-+3 +-+ \|2 \|b \|x - \|a +-+4+-+3
+--R - 6x \|b \|x atan(-------------------) - 4\|2 \|a
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+3 +-+
+--R 6a x\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+
+--R | 3 | 3
+--R | b +-+ +-+ 2 | b
+--R - 3a x |- ---- \|x log(b\|x + 2a |- ----)
+--R 4| 7 4| 7
+--R \| 16a \| 16a
+--R +
+--R +------+ +------+
+--R | 3 | 3
+--R | b +-+ +-+ 2 | b
+--R 3a x |- ---- \|x log(b\|x - 2a |- ----)
+--R 4| 7 4| 7
+--R \| 16a \| 16a
+--R +
+--R +------+
+--R | 3
+--R 2 | b
+--R +------+ 2a |- ----
+--R | 3 4| 7
+--R | b +-+ \| 16a
+--R 6a x |- ---- \|x atan(------------ - 2
+--R 4| 7 +-+
+--R \| 16a b\|x
+--R /
+--R +-+
+--R 3a x\|x
+--R Type: Union(Expression(Integer),...)
+--E 265
+
+--S 266 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R \|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------+ +------+
+--R | 3 | 3
+--R +-+ | b 4+-+3 +-+ 2 | b
+--R - 2a\|2 |- ---- \|a log(b\|x + 2a |- ----)
+--R 4| 7 4| 7
+--R \| 16a \| 16a
+--R +
+--R +------+ +------+
+--R | 3 | 3
+--R +-+ | b 4+-+3 +-+ 2 | b
+--R 2a\|2 |- ---- \|a log(b\|x - 2a |- ----)
+--R 4| 7 4| 7
+--R \| 16a \| 16a
+--R +
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - \|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a
+--R 2\|b atan(-------------------) + 2\|b atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +------+
+--R | 3
+--R 2 | b
+--R +------+ 2a |- ----
+--R | 3 4| 7
+--R +-+ | b 4+-+3 \| 16a
+--R 4a\|2 |- ---- \|a atan(------------)
+--R 4| 7 +-+
+--R \| 16a b\|x
+--R /
+--R +-+4+-+3
+--R 2a\|2 \|a
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 267
+
+)clear all
+
+--S 268 of 1285
+t0:=1/(x^(7/2)*(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R 5 3 +-+
+--R (b x + a x )\|x
+--R Type: Expression(Integer)
+--E 268
+
+--S 269 of 1285
+r0:=(-2/5)/(a*x^(5/2))-b^(5/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(9/4)*sqrt(2))+b^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(9/4)*sqrt(2))+1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))-1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+2*b/(a^2*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 5b x \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 5b x \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ +-+ \|2 \|b \|x + \|a
+--R 10b x \|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ +-+ \|2 \|b \|x - \|a 2 +-+4+-+
+--R 10b x \|b \|x atan(------------------- + (20b x - 4a)\|2 \|a
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 +-+4+-+ +-+
+--R 10a x \|2 \|a \|x
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+3
+--R | 5 | 5
+--R 2 2 | b +-+ 4 +-+ 7 | b
+--R 5a x |- ---- \|x log(b \|x + 8a |- ---- )
+--R 4| 9 4| 9
+--R \| 16a \| 16a
+--R +
+--R +------+ +------+3
+--R | 5 | 5
+--R 2 2 | b +-+ 4 +-+ 7 | b
+--R - 5a x |- ---- \|x log(b \|x - 8a |- ---- )
+--R 4| 9 4| 9
+--R \| 16a \| 16a
+--R +
+--R +------+3
+--R | 5
+--R 7 | b
+--R +------+ 8a |- ----
+--R | 5 4| 9
+--R 2 2 | b +-+ \| 16a 2
+--R 10a x |- ---- \|x atan(------------- + 10b x - 2a
+--R 4| 9 4 +-+
+--R \| 16a b \|x
+--R /
+--R 2 2 +-+
+--R 5a x \|x
+--R Type: Union(Expression(Integer),...)
+--E 270
+
+--S 271 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R b\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +------+ +------+3
+--R | 5 | 5
+--R 2 +-+ | b 4+-+ 4 +-+ 7 | b
+--R 2a \|2 |- ---- \|a log(b \|x + 8a |- ---- )
+--R 4| 9 4| 9
+--R \| 16a \| 16a
+--R +
+--R +------+ +------+3
+--R | 5 | 5
+--R 2 +-+ | b 4+-+ 4 +-+ 7 | b
+--R - 2a \|2 |- ---- \|a log(b \|x - 8a |- ---- )
+--R 4| 9 4| 9
+--R \| 16a \| 16a
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - b\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R - 2b\|b atan(-------------------) - 2b\|b atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +------+3
+--R | 5
+--R 7 | b
+--R +------+ 8a |- ----
+--R | 5 4| 9
+--R 2 +-+ | b 4+-+ \| 16a
+--R 4a \|2 |- ---- \|a atan(-------------)
+--R 4| 9 4 +-+
+--R \| 16a b \|x
+--R /
+--R 2 +-+4+-+
+--R 2a \|2 \|a
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 272
+
+)clear all
+
+--S 273 of 1285
+t0:=x^(7/2)/(a+b*x^2)^2
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 273
+
+--S 274 of 1285
+r0:=-1/2*x^(5/2)/(b*(a+b*x^2))+5/4*a^(1/4)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))-5/4*a^(1/4)*atan(1+b^(1/4)*_
+ sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))+5/8*a^(1/4)*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))-_
+ 5/8*a^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (b^(9/4)*sqrt(2))+5/2*sqrt(x)/b^2
+--R
+--R
+--R (2)
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5b x - 5a)\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5b x + 5a)\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x + \|a
+--R (- 10b x - 10a)\|a atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ \|2 \|b \|x - \|a 2 +-+4+-+ +-+
+--R (- 10b x - 10a)\|a atan(-------------------) + (16b x + 20a)\|2 \|b \|x
+--R 4+-+
+--R \|a
+--R /
+--R 3 2 2 +-+4+-+
+--R (8b x + 8a b )\|2 \|b
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+
+--R 3 2 2 | 625a +-+ 2 | 625a
+--R (- 2b x - 2a b ) |- ------ log(5\|x + 8b |- ------)
+--R 4| 9 4| 9
+--R \| 4096b \| 4096b
+--R +
+--R +--------+ +--------+
+--R 3 2 2 | 625a +-+ 2 | 625a
+--R (2b x + 2a b ) |- ------ log(5\|x - 8b |- ------)
+--R 4| 9 4| 9
+--R \| 4096b \| 4096b
+--R +
+--R +--------+
+--R 2 | 625a
+--R 8b |- ------
+--R +--------+ 4| 9
+--R 3 2 2 | 625a \| 4096b 2 +-+
+--R (4b x + 4a b ) |- ------ atan(-------------- + (4b x + 5a)\|x
+--R 4| 9 +-+
+--R \| 4096b 5\|x
+--R /
+--R 3 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 275
+
+--S 276 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 5\|a log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------+ +--------+
+--R 2 +-+ | 625a 4+-+ +-+ 2 | 625a
+--R - 8b \|2 |- ------ \|b log(5\|x + 8b |- ------)
+--R 4| 9 4| 9
+--R \| 4096b \| 4096b
+--R +
+--R +--------+ +--------+
+--R 2 +-+ | 625a 4+-+ +-+ 2 | 625a
+--R 8b \|2 |- ------ \|b log(5\|x - 8b |- ------)
+--R 4| 9 4| 9
+--R \| 4096b \| 4096b
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 5\|a log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R 10\|a atan(-------------------) + 10\|a atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +--------+
+--R 2 | 625a
+--R 8b |- ------
+--R +--------+ 4| 9
+--R 2 +-+ | 625a 4+-+ \| 4096b
+--R 16b \|2 |- ------ \|b atan(--------------)
+--R 4| 9 +-+
+--R \| 4096b 5\|x
+--R /
+--R 2 +-+4+-+
+--R 8b \|2 \|b
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 277
+
+)clear all
+
+--S 278 of 1285
+t0:=x^(5/2)/(a+b*x^2)^2
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 278
+
+--S 279 of 1285
+r0:=-1/2*x^(3/2)/(b*(a+b*x^2))-3/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+3/4*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+3/8*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(7/4)*_
+ sqrt(2))-3/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(1/4)*b^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3b x - 3a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (3b x + 3a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 \|2 \|b \|x + \|a
+--R (6b x + 6a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 \|2 \|b \|x - \|a +-+4+-+4+-+3 +-+
+--R (6b x + 6a)atan(-------------------) - 4x\|2 \|a \|b \|x
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 +-+4+-+4+-+3
+--R (8b x + 8a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+3
+--R 2 2 | 1 +-+ 5 | 1
+--R (6b x + 6a b) |- -------- log(\|x + 512a b |- -------- )
+--R 4| 7 4| 7
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+ +----------+3
+--R 2 2 | 1 +-+ 5 | 1
+--R (- 6b x - 6a b) |- -------- log(\|x - 512a b |- -------- )
+--R 4| 7 4| 7
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+3
+--R 5 | 1
+--R 512a b |- --------
+--R +----------+ 4| 7
+--R 2 2 | 1 \| 4096a b +-+
+--R (12b x + 12a b) |- -------- atan(--------------------- - x\|x
+--R 4| 7 +-+
+--R \| 4096a b \|x
+--R /
+--R 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 280
+
+--S 281 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R 3log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +----------+ +----------+3
+--R +-+ | 1 4+-+4+-+3 +-+ 5 | 1
+--R 24b\|2 |- -------- \|a \|b log(\|x + 512a b |- -------- )
+--R 4| 7 4| 7
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+ +----------+3
+--R +-+ | 1 4+-+4+-+3 +-+ 5 | 1
+--R - 24b\|2 |- -------- \|a \|b log(\|x - 512a b |- -------- )
+--R 4| 7 4| 7
+--R \| 4096a b \| 4096a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R - 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 6atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +----------+3
+--R 5 | 1
+--R 512a b |- --------
+--R +----------+ 4| 7
+--R +-+ | 1 4+-+4+-+3 \| 4096a b
+--R 48b\|2 |- -------- \|a \|b atan(---------------------)
+--R 4| 7 +-+
+--R \| 4096a b \|x
+--R /
+--R +-+4+-+4+-+3
+--R 8b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 282
+
+)clear all
+
+--S 283 of 1285
+t0:=x^(3/2)/(a+b*x^2)^2
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 283
+
+--S 284 of 1285
+r0:=-1/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(5/4)*_
+ sqrt(2))+1/4*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*_
+ b^(5/4)*sqrt(2))-1/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*sqrt(2))+1/8*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*_
+ sqrt(2))-1/2*sqrt(x)/(b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (b x + a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- b x - a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 \|2 \|b \|x + \|a
+--R (2b x + 2a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 \|2 \|b \|x - \|a +-+4+-+3 4+-+ +-+
+--R (2b x + 2a)atan(-------------------) - 4\|2 \|a \|b \|x
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 +-+4+-+3 4+-+
+--R (8b x + 8a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+
+--R 2 2 | 1 +-+ | 1
+--R (2b x + 2a b) |- -------- log(\|x + 8a b |- --------)
+--R 4| 3 5 4| 3 5
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+ +----------+
+--R 2 2 | 1 +-+ | 1
+--R (- 2b x - 2a b) |- -------- log(\|x - 8a b |- --------)
+--R 4| 3 5 4| 3 5
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+
+--R | 1
+--R 8a b |- --------
+--R +----------+ 4| 3 5
+--R 2 2 | 1 \| 4096a b +-+
+--R (- 4b x - 4a b) |- -------- atan(----------------- - \|x
+--R 4| 3 5 +-+
+--R \| 4096a b \|x
+--R /
+--R 2 2
+--R 2b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 285
+
+--S 286 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R - log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +----------+ +----------+
+--R +-+ | 1 4+-+3 4+-+ +-+ | 1
+--R 8b\|2 |- -------- \|a \|b log(\|x + 8a b |- --------)
+--R 4| 3 5 4| 3 5
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+ +----------+
+--R +-+ | 1 4+-+3 4+-+ +-+ | 1
+--R - 8b\|2 |- -------- \|a \|b log(\|x - 8a b |- --------)
+--R 4| 3 5 4| 3 5
+--R \| 4096a b \| 4096a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +----------+
+--R | 1
+--R 8a b |- --------
+--R +----------+ 4| 3 5
+--R +-+ | 1 4+-+3 4+-+ \| 4096a b
+--R - 16b\|2 |- -------- \|a \|b atan(-----------------)
+--R 4| 3 5 +-+
+--R \| 4096a b \|x
+--R /
+--R +-+4+-+3 4+-+
+--R 8b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 287
+
+)clear all
+
+--S 288 of 1285
+t0:=sqrt(x)/(a+b*x^2)^2
+--R
+--R
+--R +-+
+--R \|x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 288
+
+--S 289 of 1285
+r0:=1/2*x^(3/2)/(a*(a+b*x^2))-1/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(5/4)*b^(3/4)*sqrt(2))+1/4*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(5/4)*b^(3/4)*sqrt(2))+1/8*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(3/4)*sqrt(2))-_
+ 1/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(5/4)*b^(3/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- b x - a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (b x + a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 \|2 \|b \|x + \|a
+--R (2b x + 2a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 \|2 \|b \|x - \|a +-+4+-+4+-+3 +-+
+--R (2b x + 2a)atan(-------------------) + 4x\|2 \|a \|b \|x
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 +-+4+-+4+-+3
+--R (8a b x + 8a )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+3
+--R 2 2 | 1 +-+ 4 2 | 1
+--R (2a b x + 2a ) |- -------- log(\|x + 512a b |- -------- )
+--R 4| 5 3 4| 5 3
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+ +----------+3
+--R 2 2 | 1 +-+ 4 2 | 1
+--R (- 2a b x - 2a ) |- -------- log(\|x - 512a b |- -------- )
+--R 4| 5 3 4| 5 3
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+3
+--R 4 2 | 1
+--R 512a b |- --------
+--R +----------+ 4| 5 3
+--R 2 2 | 1 \| 4096a b +-+
+--R (4a b x + 4a ) |- -------- atan(--------------------- + x\|x
+--R 4| 5 3 +-+
+--R \| 4096a b \|x
+--R /
+--R 2 2
+--R 2a b x + 2a
+--R Type: Union(Expression(Integer),...)
+--E 290
+
+--S 291 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +----------+ +----------+3
+--R +-+ | 1 4+-+4+-+3 +-+ 4 2 | 1
+--R 8a\|2 |- -------- \|a \|b log(\|x + 512a b |- -------- )
+--R 4| 5 3 4| 5 3
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+ +----------+3
+--R +-+ | 1 4+-+4+-+3 +-+ 4 2 | 1
+--R - 8a\|2 |- -------- \|a \|b log(\|x - 512a b |- -------- )
+--R 4| 5 3 4| 5 3
+--R \| 4096a b \| 4096a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R - log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 2atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +----------+3
+--R 4 2 | 1
+--R 512a b |- --------
+--R +----------+ 4| 5 3
+--R +-+ | 1 4+-+4+-+3 \| 4096a b
+--R 16a\|2 |- -------- \|a \|b atan(---------------------)
+--R 4| 5 3 +-+
+--R \| 4096a b \|x
+--R /
+--R +-+4+-+4+-+3
+--R 8a\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 292
+
+)clear all
+
+--S 293 of 1285
+t0:=1/((a+b*x^2)^2*sqrt(x))
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R 2 4 2 2 +-+
+--R (b x + 2a b x + a )\|x
+--R Type: Expression(Integer)
+--E 293
+
+--S 294 of 1285
+r0:=-3/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*sqrt(2))+_
+ 3/4*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*_
+ sqrt(2))-3/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))+3/8*log(sqrt(a)+x*sqrt(b)+_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))+_
+ 1/2*sqrt(x)/(a*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (3b x + 3a)log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3b x - 3a)log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 \|2 \|b \|x + \|a
+--R (6b x + 6a)atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 \|2 \|b \|x - \|a +-+4+-+3 4+-+ +-+
+--R (6b x + 6a)atan(-------------------) + 4\|2 \|a \|b \|x
+--R 4+-+
+--R \|a
+--R /
+--R 2 2 +-+4+-+3 4+-+
+--R (8a b x + 8a )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+
+--R 2 2 | 1 +-+ 2 | 1
+--R (6a b x + 6a ) |- ------- log(\|x + 8a |- -------)
+--R 4| 7 4| 7
+--R \| 4096a b \| 4096a b
+--R +
+--R +---------+ +---------+
+--R 2 2 | 1 +-+ 2 | 1
+--R (- 6a b x - 6a ) |- ------- log(\|x - 8a |- -------)
+--R 4| 7 4| 7
+--R \| 4096a b \| 4096a b
+--R +
+--R +---------+
+--R 2 | 1
+--R 8a |- -------
+--R +---------+ 4| 7
+--R 2 2 | 1 \| 4096a b +-+
+--R (- 12a b x - 12a ) |- ------- atan(--------------- + \|x
+--R 4| 7 +-+
+--R \| 4096a b \|x
+--R /
+--R 2 2
+--R 2a b x + 2a
+--R Type: Union(Expression(Integer),...)
+--E 295
+
+--S 296 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R - 3log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +---------+ +---------+
+--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1
+--R 24a\|2 |- ------- \|a \|b log(\|x + 8a |- -------)
+--R 4| 7 4| 7
+--R \| 4096a b \| 4096a b
+--R +
+--R +---------+ +---------+
+--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1
+--R - 24a\|2 |- ------- \|a \|b log(\|x - 8a |- -------)
+--R 4| 7 4| 7
+--R \| 4096a b \| 4096a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 6atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +---------+
+--R 2 | 1
+--R 8a |- -------
+--R +---------+ 4| 7
+--R +-+ | 1 4+-+3 4+-+ \| 4096a b
+--R - 48a\|2 |- ------- \|a \|b atan(---------------)
+--R 4| 7 +-+
+--R \| 4096a b \|x
+--R /
+--R +-+4+-+3 4+-+
+--R 8a\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 297
+
+)clear all
+
+--S 298 of 1285
+t0:=1/(x^(3/2)*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) --------------------------
+--R 2 5 3 2 +-+
+--R (b x + 2a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 298
+
+--S 299 of 1285
+r0:=5/4*b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))-_
+ 5/4*b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_
+ sqrt(2))-5/8*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+5/8*b^(1/4)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+_
+ (-5/2)/(a^2*sqrt(x))+1/2/(a*(a+b*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (5b x + 5a)\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5b x - 5a)\|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ +-+ \|2 \|b \|x + \|a
+--R (- 10b x - 10a)\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4+-+ +-+ \|2 \|b \|x - \|a
+--R (- 10b x - 10a)\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+
+--R (- 20b x - 16a)\|2 \|a
+--R /
+--R 2 2 3 +-+4+-+ +-+
+--R (8a b x + 8a )\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+3
+--R 2 2 3 | 625b +-+ +-+ 7 | 625b
+--R (- 2a b x - 2a ) |- ------ \|x log(125b\|x + 512a |- ------ )
+--R 4| 9 4| 9
+--R \| 4096a \| 4096a
+--R +
+--R +--------+ +--------+3
+--R 2 2 3 | 625b +-+ +-+ 7 | 625b
+--R (2a b x + 2a ) |- ------ \|x log(125b\|x - 512a |- ------ )
+--R 4| 9 4| 9
+--R \| 4096a \| 4096a
+--R +
+--R +--------+3
+--R 7 | 625b
+--R 512a |- ------
+--R +--------+ 4| 9
+--R 2 2 3 | 625b +-+ \| 4096a 2
+--R (- 4a b x - 4a ) |- ------ \|x atan(----------------- - 5b x - 4a
+--R 4| 9 +-+
+--R \| 4096a 125b\|x
+--R /
+--R 2 2 3 +-+
+--R (2a b x + 2a )\|x
+--R Type: Union(Expression(Integer),...)
+--E 300
+
+--S 301 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 5\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------+ +--------+3
+--R 2 +-+ | 625b 4+-+ +-+ 7 | 625b
+--R - 8a \|2 |- ------ \|a log(125b\|x + 512a |- ------ )
+--R 4| 9 4| 9
+--R \| 4096a \| 4096a
+--R +
+--R +--------+ +--------+3
+--R 2 +-+ | 625b 4+-+ +-+ 7 | 625b
+--R 8a \|2 |- ------ \|a log(125b\|x - 512a |- ------ )
+--R 4| 9 4| 9
+--R \| 4096a \| 4096a
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 5\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R 10\|b atan(-------------------) + 10\|b atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +--------+3
+--R 7 | 625b
+--R 512a |- ------
+--R +--------+ 4| 9
+--R 2 +-+ | 625b 4+-+ \| 4096a
+--R - 16a \|2 |- ------ \|a atan(-----------------)
+--R 4| 9 +-+
+--R \| 4096a 125b\|x
+--R /
+--R 2 +-+4+-+
+--R 8a \|2 \|a
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 302
+
+)clear all
+
+--S 303 of 1285
+t0:=1/(x^(5/2)*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R 2 6 4 2 2 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 303
+
+--S 304 of 1285
+r0:=(-7/6)/(a^2*x^(3/2))+1/2/(a*x^(3/2)*(a+b*x^2))+7/4*b^(3/4)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*sqrt(2))-_
+ 7/4*b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*_
+ sqrt(2))+7/8*b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(11/4)*sqrt(2))-7/8*b^(3/4)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 21b x - 21a x)\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (21b x + 21a x)\|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 4+-+3 +-+ \|2 \|b \|x + \|a
+--R (- 42b x - 42a x)\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 4+-+3 +-+ \|2 \|b \|x - \|a
+--R (- 42b x - 42a x)\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3
+--R (- 28b x - 16a)\|2 \|a
+--R /
+--R 2 3 3 +-+4+-+3 +-+
+--R (24a b x + 24a x)\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+
+--R | 3 | 3
+--R 2 3 3 | 2401b +-+ +-+ 3 | 2401b
+--R (- 6a b x - 6a x) |- ------- \|x log(7b\|x + 8a |- -------)
+--R 4| 11 4| 11
+--R \| 4096a \| 4096a
+--R +
+--R +---------+ +---------+
+--R | 3 | 3
+--R 2 3 3 | 2401b +-+ +-+ 3 | 2401b
+--R (6a b x + 6a x) |- ------- \|x log(7b\|x - 8a |- -------)
+--R 4| 11 4| 11
+--R \| 4096a \| 4096a
+--R +
+--R +---------+
+--R | 3
+--R 3 | 2401b
+--R +---------+ 8a |- -------
+--R | 3 4| 11
+--R 2 3 3 | 2401b +-+ \| 4096a 2
+--R (12a b x + 12a x) |- ------- \|x atan(--------------- - 7b x - 4a
+--R 4| 11 +-+
+--R \| 4096a 7b\|x
+--R /
+--R 2 3 3 +-+
+--R (6a b x + 6a x)\|x
+--R Type: Union(Expression(Integer),...)
+--E 305
+
+--S 306 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R 7\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +---------+ +---------+
+--R | 3 | 3
+--R 2 +-+ | 2401b 4+-+3 +-+ 3 | 2401b
+--R - 8a \|2 |- ------- \|a log(7b\|x + 8a |- -------)
+--R 4| 11 4| 11
+--R \| 4096a \| 4096a
+--R +
+--R +---------+ +---------+
+--R | 3 | 3
+--R 2 +-+ | 2401b 4+-+3 +-+ 3 | 2401b
+--R 8a \|2 |- ------- \|a log(7b\|x - 8a |- -------)
+--R 4| 11 4| 11
+--R \| 4096a \| 4096a
+--R +
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - 7\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a
+--R 14\|b atan(-------------------) + 14\|b atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +---------+
+--R | 3
+--R 3 | 2401b
+--R +---------+ 8a |- -------
+--R | 3 4| 11
+--R 2 +-+ | 2401b 4+-+3 \| 4096a
+--R 16a \|2 |- ------- \|a atan(---------------)
+--R 4| 11 +-+
+--R \| 4096a 7b\|x
+--R /
+--R 2 +-+4+-+3
+--R 8a \|2 \|a
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 307
+
+)clear all
+
+--S 308 of 1285
+t0:=1/(x^(7/2)*(a+b*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R 2 7 5 2 3 +-+
+--R (b x + 2a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 1285
+r0:=(-9/10)/(a^2*x^(5/2))+1/2/(a*x^(5/2)*(a+b*x^2))-9/4*b^(5/4)*_
+ atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))+_
+ 9/4*b^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*_
+ sqrt(2))+9/8*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))-9/8*b^(5/4)*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+_
+ 9/2*b/(a^3*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 45b x - 45a b x )\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (45b x + 45a b x )\|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 4+-+ +-+ \|2 \|b \|x + \|a
+--R (90b x + 90a b x )\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 4+-+ +-+ \|2 \|b \|x - \|a
+--R (90b x + 90a b x )\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 +-+4+-+
+--R (180b x + 144a b x - 16a )\|2 \|a
+--R /
+--R 3 4 4 2 +-+4+-+ +-+
+--R (40a b x + 40a x )\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+3
+--R | 5 | 5
+--R 3 4 4 2 | 6561b +-+ 4 +-+ 10 | 6561b
+--R (10a b x + 10a x ) |- ------- \|x log(729b \|x + 512a |- ------- )
+--R 4| 13 4| 13
+--R \| 4096a \| 4096a
+--R +
+--R +---------+ +---------+3
+--R | 5 | 5
+--R 3 4 4 2 | 6561b +-+ 4 +-+ 10 | 6561b
+--R (- 10a b x - 10a x ) |- ------- \|x log(729b \|x - 512a |- ------- )
+--R 4| 13 4| 13
+--R \| 4096a \| 4096a
+--R +
+--R +---------+3
+--R | 5
+--R 10 | 6561b
+--R +---------+ 512a |- -------
+--R | 5 4| 13
+--R 3 4 4 2 | 6561b +-+ \| 4096a 2 4
+--R (20a b x + 20a x ) |- ------- \|x atan(------------------- + 45b x
+--R 4| 13 4 +-+
+--R \| 4096a 729b \|x
+--R +
+--R 2 2
+--R 36a b x - 4a
+--R /
+--R 3 4 4 2 +-+
+--R (10a b x + 10a x )\|x
+--R Type: Union(Expression(Integer),...)
+--E 310
+
+--S 311 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 9b\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +---------+ +---------+3
+--R | 5 | 5
+--R 3 +-+ | 6561b 4+-+ 4 +-+ 10 | 6561b
+--R 8a \|2 |- ------- \|a log(729b \|x + 512a |- ------- )
+--R 4| 13 4| 13
+--R \| 4096a \| 4096a
+--R +
+--R +---------+ +---------+3
+--R | 5 | 5
+--R 3 +-+ | 6561b 4+-+ 4 +-+ 10 | 6561b
+--R - 8a \|2 |- ------- \|a log(729b \|x - 512a |- ------- )
+--R 4| 13 4| 13
+--R \| 4096a \| 4096a
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 9b\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R - 18b\|b atan(-------------------) - 18b\|b atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +---------+3
+--R | 5
+--R 10 | 6561b
+--R +---------+ 512a |- -------
+--R | 5 4| 13
+--R 3 +-+ | 6561b 4+-+ \| 4096a
+--R 16a \|2 |- ------- \|a atan(-------------------)
+--R 4| 13 4 +-+
+--R \| 4096a 729b \|x
+--R /
+--R 3 +-+4+-+
+--R 8a \|2 \|a
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 312
+
+)clear all
+
+--S 313 of 1285
+t0:=x^(7/2)/(a+b*x^2)^3
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 1285
+r0:=-1/4*x^(5/2)/(b*(a+b*x^2)^2)-5/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))+5/32*atan(1+b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))-5/64*log(sqrt(a)+_
+ x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(9/4)*_
+ sqrt(2))+5/64*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_
+ sqrt(x))/(a^(3/4)*b^(9/4)*sqrt(2))-5/16*sqrt(x)/(b^2*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (5b x + 10a b x + 5a )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5b x - 10a b x - 5a )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x + \|a
+--R (10b x + 20a b x + 10a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x - \|a
+--R (10b x + 20a b x + 10a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3 4+-+ +-+
+--R (- 36b x - 20a)\|2 \|a \|b \|x
+--R /
+--R 4 4 3 2 2 2 +-+4+-+3 4+-+
+--R (64b x + 128a b x + 64a b )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R 4 4 3 2 2 2 | 1
+--R (80b x + 160a b x + 80a b ) |- ------------
+--R 4| 3 9
+--R \| 16777216a b
+--R *
+--R +--------------+
+--R +-+ 2 | 1
+--R log(\|x + 64a b |- ------------)
+--R 4| 3 9
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 4 4 3 2 2 2 | 1
+--R (- 80b x - 160a b x - 80a b ) |- ------------
+--R 4| 3 9
+--R \| 16777216a b
+--R *
+--R +--------------+
+--R +-+ 2 | 1
+--R log(\|x - 64a b |- ------------)
+--R 4| 3 9
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 4 4 3 2 2 2 | 1
+--R (- 160b x - 320a b x - 160a b ) |- ------------
+--R 4| 3 9
+--R \| 16777216a b
+--R *
+--R +--------------+
+--R 2 | 1
+--R 64a b |- ------------
+--R 4| 3 9
+--R \| 16777216a b
+--R atan(-----------------------)
+--R +-+
+--R \|x
+--R +
+--R 2 +-+
+--R (- 9b x - 5a)\|x
+--R /
+--R 4 4 3 2 2 2
+--R 16b x + 32a b x + 16a b
+--R Type: Union(Expression(Integer),...)
+--E 315
+
+--S 316 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R - 5log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------+ +--------------+
+--R 2 +-+ | 1 4+-+3 4+-+ +-+ 2 | 1
+--R 320b \|2 |- ------------ \|a \|b log(\|x + 64a b |- ------------)
+--R 4| 3 9 4| 3 9
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+
+--R 2 +-+ | 1 4+-+3 4+-+ +-+ 2 | 1
+--R - 320b \|2 |- ------------ \|a \|b log(\|x - 64a b |- ------------)
+--R 4| 3 9 4| 3 9
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R 5log(- \|2 \|a \|b \|x + x\|b + \|a ) - 10atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 10atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------+
+--R 2 | 1
+--R 64a b |- ------------
+--R +--------------+ 4| 3 9
+--R 2 +-+ | 1 4+-+3 4+-+ \| 16777216a b
+--R - 640b \|2 |- ------------ \|a \|b atan(-----------------------)
+--R 4| 3 9 +-+
+--R \| 16777216a b \|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 64b \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 317
+
+)clear all
+
+--S 318 of 1285
+t0:=x^(5/2)/(a+b*x^2)^3
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 1285
+r0:=-1/4*x^(3/2)/(b*(a+b*x^2)^2)+3/16*x^(3/2)/(a*b*(a+b*x^2))-_
+ 3/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(7/4)*_
+ sqrt(2))+3/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*_
+ b^(7/4)*sqrt(2))+3/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))-3/64*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3b x - 6a b x - 3a )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (3b x + 6a b x + 3a )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x + \|a
+--R (6b x + 12a b x + 6a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x - \|a
+--R (6b x + 12a b x + 6a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+4+-+4+-+3 +-+
+--R (12b x - 4a x)\|2 \|a \|b \|x
+--R /
+--R 3 4 2 2 2 3 +-+4+-+4+-+3
+--R (64a b x + 128a b x + 64a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R 3 4 2 2 2 3 | 1
+--R (48a b x + 96a b x + 48a b) |- ------------
+--R 4| 5 7
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R +-+ 4 5 | 1
+--R log(\|x + 262144a b |- ------------ )
+--R 4| 5 7
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 3 4 2 2 2 3 | 1
+--R (- 48a b x - 96a b x - 48a b) |- ------------
+--R 4| 5 7
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R +-+ 4 5 | 1
+--R log(\|x - 262144a b |- ------------ )
+--R 4| 5 7
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 3 4 2 2 2 3 | 1
+--R (96a b x + 192a b x + 96a b) |- ------------
+--R 4| 5 7
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R 4 5 | 1
+--R 262144a b |- ------------
+--R 4| 5 7
+--R \| 16777216a b
+--R atan(----------------------------)
+--R +-+
+--R \|x
+--R +
+--R 3 +-+
+--R (3b x - a x)\|x
+--R /
+--R 3 4 2 2 2 3
+--R 16a b x + 32a b x + 16a b
+--R Type: Union(Expression(Integer),...)
+--E 320
+
+--S 321 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R 3log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------+
+--R +-+ | 1 4+-+4+-+3
+--R 192a b\|2 |- ------------ \|a \|b
+--R 4| 5 7
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R +-+ 4 5 | 1
+--R log(\|x + 262144a b |- ------------ )
+--R 4| 5 7
+--R \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R +-+ | 1 4+-+4+-+3
+--R 192a b\|2 |- ------------ \|a \|b
+--R 4| 5 7
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R +-+ 4 5 | 1
+--R log(\|x - 262144a b |- ------------ )
+--R 4| 5 7
+--R \| 16777216a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R - 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 6atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------+3
+--R 4 5 | 1
+--R 262144a b |- ------------
+--R +--------------+ 4| 5 7
+--R +-+ | 1 4+-+4+-+3 \| 16777216a b
+--R 384a b\|2 |- ------------ \|a \|b atan(----------------------------)
+--R 4| 5 7 +-+
+--R \| 16777216a b \|x
+--R /
+--R +-+4+-+4+-+3
+--R 64a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 322
+
+)clear all
+
+--S 323 of 1285
+t0:=x^(3/2)/(a+b*x^2)^3
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Expression(Integer)
+--E 323
+
+--S 324 of 1285
+r0:=-3/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(5/4)*_
+ sqrt(2))+3/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*_
+ b^(5/4)*sqrt(2))-3/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*sqrt(2))+3/64*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*_
+ sqrt(2))-1/4*sqrt(x)/(b*(a+b*x^2)^2)+1/16*sqrt(x)/(a*b*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (3b x + 6a b x + 3a )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 3b x - 6a b x - 3a )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x + \|a
+--R (6b x + 12a b x + 6a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x - \|a
+--R (6b x + 12a b x + 6a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3 4+-+ +-+
+--R (4b x - 12a)\|2 \|a \|b \|x
+--R /
+--R 3 4 2 2 2 3 +-+4+-+3 4+-+
+--R (64a b x + 128a b x + 64a b)\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R 3 4 2 2 2 3 | 1
+--R (48a b x + 96a b x + 48a b) |- ------------
+--R 4| 7 5
+--R \| 16777216a b
+--R *
+--R +--------------+
+--R +-+ 2 | 1
+--R log(\|x + 64a b |- ------------)
+--R 4| 7 5
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 3 4 2 2 2 3 | 1
+--R (- 48a b x - 96a b x - 48a b) |- ------------
+--R 4| 7 5
+--R \| 16777216a b
+--R *
+--R +--------------+
+--R +-+ 2 | 1
+--R log(\|x - 64a b |- ------------)
+--R 4| 7 5
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 3 4 2 2 2 3 | 1
+--R (- 96a b x - 192a b x - 96a b) |- ------------
+--R 4| 7 5
+--R \| 16777216a b
+--R *
+--R +--------------+
+--R 2 | 1
+--R 64a b |- ------------
+--R 4| 7 5
+--R \| 16777216a b
+--R atan(----------------------)
+--R +-+
+--R \|x
+--R +
+--R 2 +-+
+--R (b x - 3a)\|x
+--R /
+--R 3 4 2 2 2 3
+--R 16a b x + 32a b x + 16a b
+--R Type: Union(Expression(Integer),...)
+--E 325
+
+--S 326 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R - 3log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------+ +--------------+
+--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1
+--R 192a b\|2 |- ------------ \|a \|b log(\|x + 64a b |- ------------)
+--R 4| 7 5 4| 7 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+
+--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1
+--R - 192a b\|2 |- ------------ \|a \|b log(\|x - 64a b |- ------------)
+--R 4| 7 5 4| 7 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 6atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------+
+--R 2 | 1
+--R 64a b |- ------------
+--R +--------------+ 4| 7 5
+--R +-+ | 1 4+-+3 4+-+ \| 16777216a b
+--R - 384a b\|2 |- ------------ \|a \|b atan(----------------------)
+--R 4| 7 5 +-+
+--R \| 16777216a b \|x
+--R /
+--R +-+4+-+3 4+-+
+--R 64a b\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 327
+
+)clear all
+
+--S 328 of 1285
+t0:=sqrt(x)/(a+b*x^2)^3
+--R
+--R
+--R +-+
+--R \|x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Expression(Integer)
+--E 328
+
+--S 329 of 1285
+r0:=1/4*x^(3/2)/(a*(a+b*x^2)^2)+5/16*x^(3/2)/(a^2*(a+b*x^2))-_
+ 5/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(3/4)*_
+ sqrt(2))+5/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_
+ b^(3/4)*sqrt(2))+5/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2))-5/64*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 5b x - 10a b x - 5a )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (5b x + 10a b x + 5a )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x + \|a
+--R (10b x + 20a b x + 10a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x - \|a
+--R (10b x + 20a b x + 10a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 +-+4+-+4+-+3 +-+
+--R (20b x + 36a x)\|2 \|a \|b \|x
+--R /
+--R 2 2 4 3 2 4 +-+4+-+4+-+3
+--R (64a b x + 128a b x + 64a )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R 2 2 4 3 2 4 | 1
+--R (80a b x + 160a b x + 80a ) |- ------------
+--R 4| 9 3
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R +-+ 7 2 | 1
+--R log(\|x + 262144a b |- ------------ )
+--R 4| 9 3
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 2 2 4 3 2 4 | 1
+--R (- 80a b x - 160a b x - 80a ) |- ------------
+--R 4| 9 3
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R +-+ 7 2 | 1
+--R log(\|x - 262144a b |- ------------ )
+--R 4| 9 3
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 2 2 4 3 2 4 | 1
+--R (160a b x + 320a b x + 160a ) |- ------------
+--R 4| 9 3
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R 7 2 | 1
+--R 262144a b |- ------------
+--R 4| 9 3
+--R \| 16777216a b
+--R atan(----------------------------)
+--R +-+
+--R \|x
+--R +
+--R 3 +-+
+--R (5b x + 9a x)\|x
+--R /
+--R 2 2 4 3 2 4
+--R 16a b x + 32a b x + 16a
+--R Type: Union(Expression(Integer),...)
+--E 330
+
+--S 331 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R 5log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------+
+--R 2 +-+ | 1 4+-+4+-+3
+--R 320a \|2 |- ------------ \|a \|b
+--R 4| 9 3
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R +-+ 7 2 | 1
+--R log(\|x + 262144a b |- ------------ )
+--R 4| 9 3
+--R \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R 2 +-+ | 1 4+-+4+-+3
+--R 320a \|2 |- ------------ \|a \|b
+--R 4| 9 3
+--R \| 16777216a b
+--R *
+--R +--------------+3
+--R +-+ 7 2 | 1
+--R log(\|x - 262144a b |- ------------ )
+--R 4| 9 3
+--R \| 16777216a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R - 5log(- \|2 \|a \|b \|x + x\|b + \|a ) - 10atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 10atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------+3
+--R 7 2 | 1
+--R 262144a b |- ------------
+--R +--------------+ 4| 9 3
+--R 2 +-+ | 1 4+-+4+-+3 \| 16777216a b
+--R 640a \|2 |- ------------ \|a \|b atan(----------------------------)
+--R 4| 9 3 +-+
+--R \| 16777216a b \|x
+--R /
+--R 2 +-+4+-+4+-+3
+--R 64a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 332
+
+)clear all
+
+--S 333 of 1285
+t0:=1/((a+b*x^2)^3*sqrt(x))
+--R
+--R
+--R 1
+--R (1) -----------------------------------
+--R 3 6 2 4 2 2 3 +-+
+--R (b x + 3a b x + 3a b x + a )\|x
+--R Type: Expression(Integer)
+--E 333
+
+--S 334 of 1285
+r0:=-21/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(1/4)*_
+ sqrt(2))+21/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*_
+ b^(1/4)*sqrt(2))-21/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_
+ sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*sqrt(2))+21/64*log(sqrt(a)+_
+ x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*_
+ sqrt(2))+1/4*sqrt(x)/(a*(a+b*x^2)^2)+7/16*sqrt(x)/(a^2*(a+b*x^2))
+--R
+--R
+--R (2)
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (21b x + 42a b x + 21a )log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+
+--R (- 21b x - 42a b x - 21a )log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x + \|a
+--R (42b x + 84a b x + 42a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 \|2 \|b \|x - \|a
+--R (42b x + 84a b x + 42a )atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+3 4+-+ +-+
+--R (28b x + 44a)\|2 \|a \|b \|x
+--R /
+--R 2 2 4 3 2 4 +-+4+-+3 4+-+
+--R (64a b x + 128a b x + 64a )\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R 2 2 4 3 2 4 | 1
+--R (336a b x + 672a b x + 336a ) |- ------------
+--R 4| 11
+--R \| 16777216a b
+--R *
+--R +--------------+
+--R +-+ 3 | 1
+--R log(\|x + 64a |- ------------)
+--R 4| 11
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 2 2 4 3 2 4 | 1
+--R (- 336a b x - 672a b x - 336a ) |- ------------
+--R 4| 11
+--R \| 16777216a b
+--R *
+--R +--------------+
+--R +-+ 3 | 1
+--R log(\|x - 64a |- ------------)
+--R 4| 11
+--R \| 16777216a b
+--R +
+--R +--------------+
+--R 2 2 4 3 2 4 | 1
+--R (- 672a b x - 1344a b x - 672a ) |- ------------
+--R 4| 11
+--R \| 16777216a b
+--R *
+--R +--------------+
+--R 3 | 1
+--R 64a |- ------------
+--R 4| 11
+--R \| 16777216a b
+--R atan(---------------------)
+--R +-+
+--R \|x
+--R +
+--R 2 +-+
+--R (7b x + 11a)\|x
+--R /
+--R 2 2 4 3 2 4
+--R 16a b x + 32a b x + 16a
+--R Type: Union(Expression(Integer),...)
+--E 335
+
+--S 336 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R - 21log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +--------------+ +--------------+
+--R 2 +-+ | 1 4+-+3 4+-+ +-+ 3 | 1
+--R 1344a \|2 |- ------------ \|a \|b log(\|x + 64a |- ------------)
+--R 4| 11 4| 11
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+
+--R 2 +-+ | 1 4+-+3 4+-+ +-+ 3 | 1
+--R - 1344a \|2 |- ------------ \|a \|b log(\|x - 64a |- ------------)
+--R 4| 11 4| 11
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a
+--R 21log(- \|2 \|a \|b \|x + x\|b + \|a ) - 42atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R \|2 \|b \|x - \|a
+--R - 42atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------+
+--R 3 | 1
+--R 64a |- ------------
+--R +--------------+ 4| 11
+--R 2 +-+ | 1 4+-+3 4+-+ \| 16777216a b
+--R - 2688a \|2 |- ------------ \|a \|b atan(---------------------)
+--R 4| 11 +-+
+--R \| 16777216a b \|x
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 64a \|2 \|a \|b
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 337
+
+)clear all
+
+--S 338 of 1285
+t0:=1/(x^(3/2)*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R 3 7 2 5 2 3 3 +-+
+--R (b x + 3a b x + 3a b x + a x)\|x
+--R Type: Expression(Integer)
+--E 338
+
+--S 339 of 1285
+r0:=45/32*b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*_
+ sqrt(2))-45/32*b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(13/4)*sqrt(2))-45/64*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+45/64*b^(1/4)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*_
+ sqrt(2))+(-45/16)/(a^3*sqrt(x))+1/4/(a*(a+b*x^2)^2*sqrt(x))+_
+ 9/16/(a^2*(a+b*x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 4 2 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R (45b x + 90a b x + 45a )\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 4 2 2 4+-+ +-+
+--R (- 45b x - 90a b x - 45a )\|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 4+-+ +-+ \|2 \|b \|x + \|a
+--R (- 90b x - 180a b x - 90a )\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 4 2 2 4+-+ +-+ \|2 \|b \|x - \|a
+--R (- 90b x - 180a b x - 90a )\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 +-+4+-+
+--R (- 180b x - 324a b x - 128a )\|2 \|a
+--R /
+--R 3 2 4 4 2 5 +-+4+-+ +-+
+--R (64a b x + 128a b x + 64a )\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------------+
+--R 3 2 4 4 2 5 | 4100625b +-+
+--R (- 16a b x - 32a b x - 16a ) |- ----------- \|x
+--R 4| 13
+--R \| 16777216a
+--R *
+--R +-------------+3
+--R +-+ 10 | 4100625b
+--R log(91125b\|x + 262144a |- ----------- )
+--R 4| 13
+--R \| 16777216a
+--R +
+--R +-------------+
+--R 3 2 4 4 2 5 | 4100625b +-+
+--R (16a b x + 32a b x + 16a ) |- ----------- \|x
+--R 4| 13
+--R \| 16777216a
+--R *
+--R +-------------+3
+--R +-+ 10 | 4100625b
+--R log(91125b\|x - 262144a |- ----------- )
+--R 4| 13
+--R \| 16777216a
+--R +
+--R +-------------+
+--R 3 2 4 4 2 5 | 4100625b +-+
+--R (- 32a b x - 64a b x - 32a ) |- ----------- \|x
+--R 4| 13
+--R \| 16777216a
+--R *
+--R +-------------+3
+--R 10 | 4100625b
+--R 262144a |- -----------
+--R 4| 13
+--R \| 16777216a
+--R atan(--------------------------)
+--R +-+
+--R 91125b\|x
+--R +
+--R 2 4 2 2
+--R - 45b x - 81a b x - 32a
+--R /
+--R 3 2 4 4 2 5 +-+
+--R (16a b x + 32a b x + 16a )\|x
+--R Type: Union(Expression(Integer),...)
+--E 340
+
+--S 341 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 45\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R -
+--R +-------------+
+--R 3 +-+ | 4100625b 4+-+
+--R 64a \|2 |- ----------- \|a
+--R 4| 13
+--R \| 16777216a
+--R *
+--R +-------------+3
+--R +-+ 10 | 4100625b
+--R log(91125b\|x + 262144a |- ----------- )
+--R 4| 13
+--R \| 16777216a
+--R +
+--R +-------------+ +-------------+3
+--R 3 +-+ | 4100625b 4+-+ +-+ 10 | 4100625b
+--R 64a \|2 |- ----------- \|a log(91125b\|x - 262144a |- ----------- )
+--R 4| 13 4| 13
+--R \| 16777216a \| 16777216a
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 45\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R 90\|b atan(-------------------) + 90\|b atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-------------+3
+--R 10 | 4100625b
+--R 262144a |- -----------
+--R +-------------+ 4| 13
+--R 3 +-+ | 4100625b 4+-+ \| 16777216a
+--R - 128a \|2 |- ----------- \|a atan(--------------------------)
+--R 4| 13 +-+
+--R \| 16777216a 91125b\|x
+--R /
+--R 3 +-+4+-+
+--R 64a \|2 \|a
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 342
+
+)clear all
+
+--S 343 of 1285
+t0:=1/(x^(5/2)*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R 3 8 2 6 2 4 3 2 +-+
+--R (b x + 3a b x + 3a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 343
+
+--S 344 of 1285
+r0:=(-77/48)/(a^3*x^(3/2))+1/4/(a*x^(3/2)*(a+b*x^2)^2)+11/16/(a^2*x^(3/2)*_
+ (a+b*x^2))+77/32*b^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_
+ (a^(15/4)*sqrt(2))-77/32*b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_
+ a^(1/4))/(a^(15/4)*sqrt(2))+77/64*b^(3/4)*log(sqrt(a)+x*sqrt(b)-_
+ a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*sqrt(2))-77/64*b^(3/4)*_
+ log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 5 3 2 4+-+3 +-+
+--R (- 231b x - 462a b x - 231a x)\|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 2 5 3 2 4+-+3 +-+
+--R (231b x + 462a b x + 231a x)\|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 5 3 2 4+-+3 +-+ \|2 \|b \|x + \|a
+--R (- 462b x - 924a b x - 462a x)\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 2 5 3 2 4+-+3 +-+ \|2 \|b \|x - \|a
+--R (- 462b x - 924a b x - 462a x)\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 4 2 2 +-+4+-+3
+--R (- 308b x - 484a b x - 128a )\|2 \|a
+--R /
+--R 3 2 5 4 3 5 +-+4+-+3 +-+
+--R (192a b x + 384a b x + 192a x)\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------------+
+--R | 3
+--R 3 2 5 4 3 5 | 35153041b +-+
+--R (- 48a b x - 96a b x - 48a x) |- ----------- \|x
+--R 4| 15
+--R \| 16777216a
+--R *
+--R +-------------+
+--R | 3
+--R +-+ 4 | 35153041b
+--R log(77b\|x + 64a |- -----------)
+--R 4| 15
+--R \| 16777216a
+--R +
+--R +-------------+
+--R | 3
+--R 3 2 5 4 3 5 | 35153041b +-+
+--R (48a b x + 96a b x + 48a x) |- ----------- \|x
+--R 4| 15
+--R \| 16777216a
+--R *
+--R +-------------+
+--R | 3
+--R +-+ 4 | 35153041b
+--R log(77b\|x - 64a |- -----------)
+--R 4| 15
+--R \| 16777216a
+--R +
+--R +-------------+
+--R | 3
+--R 3 2 5 4 3 5 | 35153041b +-+
+--R (96a b x + 192a b x + 96a x) |- ----------- \|x
+--R 4| 15
+--R \| 16777216a
+--R *
+--R +-------------+
+--R | 3
+--R 4 | 35153041b
+--R 64a |- -----------
+--R 4| 15
+--R \| 16777216a
+--R atan(--------------------)
+--R +-+
+--R 77b\|x
+--R +
+--R 2 4 2 2
+--R - 77b x - 121a b x - 32a
+--R /
+--R 3 2 5 4 3 5 +-+
+--R (48a b x + 96a b x + 48a x)\|x
+--R Type: Union(Expression(Integer),...)
+--E 345
+
+--S 346 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R 77\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-------------+ +-------------+
+--R | 3 | 3
+--R 3 +-+ | 35153041b 4+-+3 +-+ 4 | 35153041b
+--R - 64a \|2 |- ----------- \|a log(77b\|x + 64a |- -----------)
+--R 4| 15 4| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+
+--R | 3 | 3
+--R 3 +-+ | 35153041b 4+-+3 +-+ 4 | 35153041b
+--R 64a \|2 |- ----------- \|a log(77b\|x - 64a |- -----------)
+--R 4| 15 4| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+
+--R - 77\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a
+--R 154\|b atan(-------------------) + 154\|b atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-------------+
+--R | 3
+--R 4 | 35153041b
+--R +-------------+ 64a |- -----------
+--R | 3 4| 15
+--R 3 +-+ | 35153041b 4+-+3 \| 16777216a
+--R 128a \|2 |- ----------- \|a atan(--------------------)
+--R 4| 15 +-+
+--R \| 16777216a 77b\|x
+--R /
+--R 3 +-+4+-+3
+--R 64a \|2 \|a
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 347
+
+)clear all
+
+--S 348 of 1285
+t0:=1/(x^(7/2)*(a+b*x^2)^3)
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R 3 9 2 7 2 5 3 3 +-+
+--R (b x + 3a b x + 3a b x + a x )\|x
+--R Type: Expression(Integer)
+--E 348
+
+--S 349 of 1285
+r0:=(-117/80)/(a^3*x^(5/2))+1/4/(a*x^(5/2)*(a+b*x^2)^2)+13/16/(a^2*_
+ x^(5/2)*(a+b*x^2))-117/32*b^(5/4)*atan(1-b^(1/4)*sqrt(2)*_
+ sqrt(x)/a^(1/4))/(a^(17/4)*sqrt(2))+117/32*b^(5/4)*atan(1+_
+ b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(17/4)*sqrt(2))+117/64*_
+ b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_
+ (a^(17/4)*sqrt(2))-117/64*b^(5/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_
+ b^(1/4)*sqrt(2)*sqrt(x))/(a^(17/4)*sqrt(2))+117/16*b/(a^4*sqrt(x))
+--R
+--R
+--R (2)
+--R 3 6 2 4 2 2 4+-+ +-+
+--R (- 585b x - 1170a b x - 585a b x )\|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R 3 6 2 4 2 2 4+-+ +-+
+--R (585b x + 1170a b x + 585a b x )\|b \|x
+--R *
+--R +-+4+-+4+-+ +-+ +-+ +-+
+--R log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 6 2 4 2 2 4+-+ +-+ \|2 \|b \|x + \|a
+--R (1170b x + 2340a b x + 1170a b x )\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ +-+ 4+-+
+--R 3 6 2 4 2 2 4+-+ +-+ \|2 \|b \|x - \|a
+--R (1170b x + 2340a b x + 1170a b x )\|b \|x atan(-------------------)
+--R 4+-+
+--R \|a
+--R +
+--R 3 6 2 4 2 2 3 +-+4+-+
+--R (2340b x + 4212a b x + 1664a b x - 128a )\|2 \|a
+--R /
+--R 4 2 6 5 4 6 2 +-+4+-+ +-+
+--R (320a b x + 640a b x + 320a x )\|2 \|a \|x
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------------+
+--R | 5
+--R 4 2 6 5 4 6 2 | 187388721b +-+
+--R (80a b x + 160a b x + 80a x ) |- ----------- \|x
+--R 4| 17
+--R \| 16777216a
+--R *
+--R +-------------+3
+--R | 5
+--R 4 +-+ 13 | 187388721b
+--R log(1601613b \|x + 262144a |- ----------- )
+--R 4| 17
+--R \| 16777216a
+--R +
+--R +-------------+
+--R | 5
+--R 4 2 6 5 4 6 2 | 187388721b +-+
+--R (- 80a b x - 160a b x - 80a x ) |- ----------- \|x
+--R 4| 17
+--R \| 16777216a
+--R *
+--R +-------------+3
+--R | 5
+--R 4 +-+ 13 | 187388721b
+--R log(1601613b \|x - 262144a |- ----------- )
+--R 4| 17
+--R \| 16777216a
+--R +
+--R +-------------+
+--R | 5
+--R 4 2 6 5 4 6 2 | 187388721b +-+
+--R (160a b x + 320a b x + 160a x ) |- ----------- \|x
+--R 4| 17
+--R \| 16777216a
+--R *
+--R +-------------+3
+--R | 5
+--R 13 | 187388721b
+--R 262144a |- -----------
+--R 4| 17
+--R \| 16777216a
+--R atan(--------------------------)
+--R 4 +-+
+--R 1601613b \|x
+--R +
+--R 3 6 2 4 2 2 3
+--R 585b x + 1053a b x + 416a b x - 32a
+--R /
+--R 4 2 6 5 4 6 2 +-+
+--R (80a b x + 160a b x + 80a x )\|x
+--R Type: Union(Expression(Integer),...)
+--E 350
+
+--S 351 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R 117b\|b log(\|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-------------+
+--R | 5
+--R 4 +-+ | 187388721b 4+-+
+--R 64a \|2 |- ----------- \|a
+--R 4| 17
+--R \| 16777216a
+--R *
+--R +-------------+3
+--R | 5
+--R 4 +-+ 13 | 187388721b
+--R log(1601613b \|x + 262144a |- ----------- )
+--R 4| 17
+--R \| 16777216a
+--R +
+--R -
+--R +-------------+
+--R | 5
+--R 4 +-+ | 187388721b 4+-+
+--R 64a \|2 |- ----------- \|a
+--R 4| 17
+--R \| 16777216a
+--R *
+--R +-------------+3
+--R | 5
+--R 4 +-+ 13 | 187388721b
+--R log(1601613b \|x - 262144a |- ----------- )
+--R 4| 17
+--R \| 16777216a
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+
+--R - 117b\|b log(- \|2 \|a \|b \|x + x\|b + \|a )
+--R +
+--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+
+--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a
+--R - 234b\|b atan(-------------------) - 234b\|b atan(-------------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-------------+3
+--R | 5
+--R 13 | 187388721b
+--R +-------------+ 262144a |- -----------
+--R | 5 4| 17
+--R 4 +-+ | 187388721b 4+-+ \| 16777216a
+--R 128a \|2 |- ----------- \|a atan(--------------------------)
+--R 4| 17 4 +-+
+--R \| 16777216a 1601613b \|x
+--R /
+--R 4 +-+4+-+
+--R 64a \|2 \|a
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1285
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 352
+
+)clear all
+
+--S 353 of 1285
+t0:=x^(7/2)/(1+x^2)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ------
+--R 2
+--R x + 1
+--R Type: Expression(Integer)
+--E 353
+
+--S 354 of 1285
+r0:=2/5*x^(5/2)-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*sqrt(x))/_
+ sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*_
+ sqrt(x))/sqrt(2)-2*sqrt(x)
+--R
+--R
+--R (2)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R 5log(\|2 \|x + x + 1) - 5log(- \|2 \|x + x + 1) + 10atan(\|2 \|x + 1)
+--R +
+--R +-+ +-+ 2 +-+ +-+
+--R 10atan(\|2 \|x - 1) + (4x - 20)\|2 \|x
+--R /
+--R +-+
+--R 10\|2
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R 5\|2 log(\|2 \|x + x + 1) - 5\|2 log(- \|2 \|x + x + 1)
+--R +
+--R +-+ 1 +-+ 1 2 +-+
+--R - 10\|2 atan(------------) - 10\|2 atan(------------) + (8x - 40)\|x
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R /
+--R 20
+--R Type: Union(Expression(Integer),...)
+--E 355
+
+--S 356 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 357
+
+)clear all
+
+--S 358 of 1285
+t0:=x^(5/2)/(1+x^2)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ------
+--R 2
+--R x + 1
+--R Type: Expression(Integer)
+--E 358
+
+--S 359 of 1285
+r0:=2/3*x^(3/2)+atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*sqrt(x))/_
+ sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*_
+ sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R 3log(\|2 \|x + x + 1) - 3log(- \|2 \|x + x + 1) - 6atan(\|2 \|x + 1)
+--R +
+--R +-+ +-+ +-+ +-+
+--R - 6atan(\|2 \|x - 1) + 4x\|2 \|x
+--R /
+--R +-+
+--R 6\|2
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R 3\|2 log(\|2 \|x + x + 1) - 3\|2 log(- \|2 \|x + x + 1)
+--R +
+--R +-+ 1 +-+ 1 +-+
+--R 6\|2 atan(------------) + 6\|2 atan(------------) + 8x\|x
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R /
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 360
+
+--S 361 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 362
+
+)clear all
+
+--S 363 of 1285
+t0:=x^(3/2)/(1+x^2)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ------
+--R 2
+--R x + 1
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 1285
+r0:=atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*sqrt(x))/sqrt(2)+_
+ 1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/_
+ sqrt(2)+2*sqrt(x)
+--R
+--R
+--R (2)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R - log(\|2 \|x + x + 1) + log(- \|2 \|x + x + 1) - 2atan(\|2 \|x + 1)
+--R +
+--R +-+ +-+ +-+ +-+
+--R - 2atan(\|2 \|x - 1) + 4\|2 \|x
+--R /
+--R +-+
+--R 2\|2
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R - \|2 log(\|2 \|x + x + 1) + \|2 log(- \|2 \|x + x + 1)
+--R +
+--R +-+ 1 +-+ 1 +-+
+--R 2\|2 atan(------------) + 2\|2 atan(------------) + 8\|x
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R /
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 365
+
+--S 366 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 367
+
+)clear all
+
+--S 368 of 1285
+t0:=sqrt(x)/(1+x^2)
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ------
+--R 2
+--R x + 1
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1285
+r0:=-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*sqrt(x))/sqrt(2)+_
+ 1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R - log(\|2 \|x + x + 1) + log(- \|2 \|x + x + 1) + 2atan(\|2 \|x + 1)
+--R +
+--R +-+ +-+
+--R 2atan(\|2 \|x - 1)
+--R /
+--R +-+
+--R 2\|2
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R - \|2 log(\|2 \|x + x + 1) + \|2 log(- \|2 \|x + x + 1)
+--R +
+--R +-+ 1 +-+ 1
+--R - 2\|2 atan(------------) - 2\|2 atan(------------)
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R /
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 370
+
+--S 371 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 372
+
+)clear all
+
+--S 373 of 1285
+t0:=1/((1+x^2)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 2 +-+
+--R (x + 1)\|x
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 1285
+r0:=-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*_
+ log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R log(\|2 \|x + x + 1) - log(- \|2 \|x + x + 1) + 2atan(\|2 \|x + 1)
+--R +
+--R +-+ +-+
+--R 2atan(\|2 \|x - 1)
+--R /
+--R +-+
+--R 2\|2
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R \|2 log(\|2 \|x + x + 1) - \|2 log(- \|2 \|x + x + 1)
+--R +
+--R +-+ 1 +-+ 1
+--R - 2\|2 atan(------------) - 2\|2 atan(------------)
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R /
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 375
+
+--S 376 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 377
+
+)clear all
+
+--S 378 of 1285
+t0:=1/(x^(3/2)*(1+x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 3 +-+
+--R (x + x)\|x
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 1285
+r0:=atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*_
+ log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/_
+ sqrt(2)+(-2)/sqrt(x)
+--R
+--R
+--R (2)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R \|x log(\|2 \|x + x + 1) - \|x log(- \|2 \|x + x + 1)
+--R +
+--R +-+ +-+ +-+ +-+ +-+ +-+ +-+
+--R - 2\|x atan(\|2 \|x + 1) - 2\|x atan(\|2 \|x - 1) - 4\|2
+--R /
+--R +-+ +-+
+--R 2\|2 \|x
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R x\|2 log(\|2 \|x + x + 1) - x\|2 log(- \|2 \|x + x + 1)
+--R +
+--R +-+ 1 +-+ 1 +-+
+--R 2x\|2 atan(------------) + 2x\|2 atan(------------) - 8\|x
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R /
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 380
+
+--S 381 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 382
+
+)clear all
+
+--S 383 of 1285
+t0:=1/(x^(5/2)*(1+x^2))
+--R
+--R
+--R 1
+--R (1) -------------
+--R 4 2 +-+
+--R (x + x )\|x
+--R Type: Expression(Integer)
+--E 383
+
+--S 384 of 1285
+r0:=(-2/3)/x^(3/2)+atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*_
+ sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*_
+ log(1+x+sqrt(2)*sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ +-+ +-+ +-+ +-+ +-+
+--R - 3x\|x log(\|2 \|x + x + 1) + 3x\|x log(- \|2 \|x + x + 1)
+--R +
+--R +-+ +-+ +-+ +-+ +-+ +-+ +-+
+--R - 6x\|x atan(\|2 \|x + 1) - 6x\|x atan(\|2 \|x - 1) - 4\|2
+--R /
+--R +-+ +-+
+--R 6x\|2 \|x
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+
+--R - 3x \|2 log(\|2 \|x + x + 1) + 3x \|2 log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ 1 2 +-+ 1 +-+
+--R 6x \|2 atan(------------) + 6x \|2 atan(------------) - 8\|x
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R /
+--R 2
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 385
+
+--S 386 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 387
+
+)clear all
+
+--S 388 of 1285
+t0:=1/(x^(7/2)*(1+x^2))
+--R
+--R
+--R 1
+--R (1) -------------
+--R 5 3 +-+
+--R (x + x )\|x
+--R Type: Expression(Integer)
+--E 388
+
+--S 389 of 1285
+r0:=(-2/5)/x^(5/2)-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*_
+ sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*_
+ log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+2/sqrt(x)
+--R
+--R
+--R (2)
+--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+
+--R - 5x \|x log(\|2 \|x + x + 1) + 5x \|x log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ 2 +-+
+--R 10x \|x atan(\|2 \|x + 1) + 10x \|x atan(\|2 \|x - 1) + (20x - 4)\|2
+--R /
+--R 2 +-+ +-+
+--R 10x \|2 \|x
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 +-+ +-+ +-+ 3 +-+ +-+ +-+
+--R - 5x \|2 log(\|2 \|x + x + 1) + 5x \|2 log(- \|2 \|x + x + 1)
+--R +
+--R 3 +-+ 1 3 +-+ 1 2 +-+
+--R - 10x \|2 atan(------------) - 10x \|2 atan(------------) + (40x - 8)\|x
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R /
+--R 3
+--R 20x
+--R Type: Union(Expression(Integer),...)
+--E 390
+
+--S 391 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 392
+
+)clear all
+
+--S 393 of 1285
+t0:=x^(7/2)/(1+x^2)^2
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ------------
+--R 4 2
+--R x + 2x + 1
+--R Type: Expression(Integer)
+--E 393
+
+--S 394 of 1285
+r0:=-1/2*x^(5/2)/(1+x^2)+5/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-5/4*_
+ atan(1+sqrt(2)*sqrt(x))/sqrt(2)+5/8*log(1+x-sqrt(2)*sqrt(x))/_
+ sqrt(2)-5/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+5/2*sqrt(x)
+--R
+--R
+--R (2)
+--R 2 +-+ +-+ 2 +-+ +-+
+--R (- 5x - 5)log(\|2 \|x + x + 1) + (5x + 5)log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ 2 +-+ +-+
+--R (- 10x - 10)atan(\|2 \|x + 1) + (- 10x - 10)atan(\|2 \|x - 1)
+--R +
+--R 2 +-+ +-+
+--R (16x + 20)\|2 \|x
+--R /
+--R 2 +-+
+--R (8x + 8)\|2
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +-+ +-+
+--R (- 5x - 5)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ +-+ 2 +-+ 1
+--R (5x + 5)\|2 log(- \|2 \|x + x + 1) + (10x + 10)\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 2 +-+ 1 2 +-+
+--R (10x + 10)\|2 atan(------------) + (32x + 40)\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 2
+--R 16x + 16
+--R Type: Union(Expression(Integer),...)
+--E 395
+
+--S 396 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R 5atan(\|2 \|x + 1) + 5atan(\|2 \|x - 1) + 5atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R 5atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 397
+
+)clear all
+
+--S 398 of 1285
+t0:=x^(5/2)/(1+x^2)^2
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ------------
+--R 4 2
+--R x + 2x + 1
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 1285
+r0:=-1/2*x^(3/2)/(1+x^2)-3/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+_
+ 3/4*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+3/8*log(1+x-sqrt(2)*_
+ sqrt(x))/sqrt(2)-3/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R 2 +-+ +-+ 2 +-+ +-+
+--R (- 3x - 3)log(\|2 \|x + x + 1) + (3x + 3)log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+
+--R (6x + 6)atan(\|2 \|x + 1) + (6x + 6)atan(\|2 \|x - 1) - 4x\|2 \|x
+--R /
+--R 2 +-+
+--R (8x + 8)\|2
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +-+ +-+
+--R (- 3x - 3)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ +-+ 2 +-+ 1
+--R (3x + 3)\|2 log(- \|2 \|x + x + 1) + (- 6x - 6)\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 2 +-+ 1 +-+
+--R (- 6x - 6)\|2 atan(------------) - 8x\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 2
+--R 16x + 16
+--R Type: Union(Expression(Integer),...)
+--E 400
+
+--S 401 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - 3atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 402
+
+)clear all
+
+--S 403 of 1285
+t0:=x^(3/2)/(1+x^2)^2
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ------------
+--R 4 2
+--R x + 2x + 1
+--R Type: Expression(Integer)
+--E 403
+
+--S 404 of 1285
+r0:=-1/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+1/4*atan(1+sqrt(2)*sqrt(x))/_
+ sqrt(2)-1/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/8*log(1+x+sqrt(2)*_
+ sqrt(x))/sqrt(2)-1/2*sqrt(x)/(1+x^2)
+--R
+--R
+--R (2)
+--R 2 +-+ +-+ 2 +-+ +-+
+--R (x + 1)log(\|2 \|x + x + 1) + (- x - 1)log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+
+--R (2x + 2)atan(\|2 \|x + 1) + (2x + 2)atan(\|2 \|x - 1) - 4\|2 \|x
+--R /
+--R 2 +-+
+--R (8x + 8)\|2
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+
+--R (x + 1)\|2 log(\|2 \|x + x + 1) + (- x - 1)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ 1 2 +-+ 1
+--R (- 2x - 2)\|2 atan(------------) + (- 2x - 2)\|2 atan(------------)
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R +
+--R +-+
+--R - 8\|x
+--R /
+--R 2
+--R 16x + 16
+--R Type: Union(Expression(Integer),...)
+--E 405
+
+--S 406 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 407
+
+)clear all
+
+--S 408 of 1285
+t0:=sqrt(x)/(1+x^2)^2
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ------------
+--R 4 2
+--R x + 2x + 1
+--R Type: Expression(Integer)
+--E 408
+
+--S 409 of 1285
+r0:=1/2*x^(3/2)/(1+x^2)-1/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+1/4*_
+ atan(1+sqrt(2)*sqrt(x))/sqrt(2)+1/8*log(1+x-sqrt(2)*sqrt(x))/_
+ sqrt(2)-1/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R 2 +-+ +-+ 2 +-+ +-+
+--R (- x - 1)log(\|2 \|x + x + 1) + (x + 1)log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+
+--R (2x + 2)atan(\|2 \|x + 1) + (2x + 2)atan(\|2 \|x - 1) + 4x\|2 \|x
+--R /
+--R 2 +-+
+--R (8x + 8)\|2
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+
+--R (- x - 1)\|2 log(\|2 \|x + x + 1) + (x + 1)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ 1 2 +-+ 1
+--R (- 2x - 2)\|2 atan(------------) + (- 2x - 2)\|2 atan(------------)
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R +
+--R +-+
+--R 8x\|x
+--R /
+--R 2
+--R 16x + 16
+--R Type: Union(Expression(Integer),...)
+--E 410
+
+--S 411 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 412
+
+)clear all
+
+--S 413 of 1285
+t0:=1/((1+x^2)^2*sqrt(x))
+--R
+--R
+--R 1
+--R (1) ------------------
+--R 4 2 +-+
+--R (x + 2x + 1)\|x
+--R Type: Expression(Integer)
+--E 413
+
+--S 414 of 1285
+r0:=-3/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/4*atan(1+sqrt(2)*sqrt(x))/_
+ sqrt(2)-3/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+3/8*log(1+x+sqrt(2)*_
+ sqrt(x))/sqrt(2)+1/2*sqrt(x)/(1+x^2)
+--R
+--R
+--R (2)
+--R 2 +-+ +-+ 2 +-+ +-+
+--R (3x + 3)log(\|2 \|x + x + 1) + (- 3x - 3)log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+
+--R (6x + 6)atan(\|2 \|x + 1) + (6x + 6)atan(\|2 \|x - 1) + 4\|2 \|x
+--R /
+--R 2 +-+
+--R (8x + 8)\|2
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ +-+ +-+
+--R (3x + 3)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ +-+
+--R (- 3x - 3)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ 1 2 +-+ 1
+--R (- 6x - 6)\|2 atan(------------) + (- 6x - 6)\|2 atan(------------)
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R +
+--R +-+
+--R 8\|x
+--R /
+--R 2
+--R 16x + 16
+--R Type: Union(Expression(Integer),...)
+--E 415
+
+--S 416 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - 3atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 417
+
+)clear all
+
+--S 418 of 1285
+t0:=1/(x^(3/2)*(1+x^2)^2)
+--R
+--R
+--R 1
+--R (1) ------------------
+--R 5 3 +-+
+--R (x + 2x + x)\|x
+--R Type: Expression(Integer)
+--E 418
+
+--S 419 of 1285
+r0:=5/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-5/4*atan(1+sqrt(2)*sqrt(x))/_
+ sqrt(2)-5/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+5/8*log(1+x+sqrt(2)*_
+ sqrt(x))/sqrt(2)+(-5/2)/sqrt(x)+1/2/((1+x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 2 +-+ +-+ +-+
+--R (5x + 5)\|x log(\|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ +-+
+--R (- 5x - 5)\|x log(- \|2 \|x + x + 1)
+--R +
+--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+
+--R (- 10x - 10)\|x atan(\|2 \|x + 1) + (- 10x - 10)\|x atan(\|2 \|x - 1)
+--R +
+--R 2 +-+
+--R (- 20x - 16)\|2
+--R /
+--R 2 +-+ +-+
+--R (8x + 8)\|2 \|x
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 +-+ +-+ +-+
+--R (5x + 5x)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 3 +-+ +-+ +-+
+--R (- 5x - 5x)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 3 +-+ 1 3 +-+ 1
+--R (10x + 10x)\|2 atan(------------) + (10x + 10x)\|2 atan(------------)
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R +
+--R 2 +-+
+--R (- 40x - 32)\|x
+--R /
+--R 3
+--R 16x + 16x
+--R Type: Union(Expression(Integer),...)
+--E 420
+
+--S 421 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R 5atan(\|2 \|x + 1) + 5atan(\|2 \|x - 1) + 5atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R 5atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 422
+
+)clear all
+
+--S 423 of 1285
+t0:=1/(x^(5/2)*(1+x^2)^2)
+--R
+--R
+--R 1
+--R (1) -------------------
+--R 6 4 2 +-+
+--R (x + 2x + x )\|x
+--R Type: Expression(Integer)
+--E 423
+
+--S 424 of 1285
+r0:=(-7/6)/x^(3/2)+1/2/(x^(3/2)*(1+x^2))+7/4*atan(1-sqrt(2)*sqrt(x))/_
+ sqrt(2)-7/4*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+7/8*log(1+x-sqrt(2)*_
+ sqrt(x))/sqrt(2)-7/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R 3 +-+ +-+ +-+
+--R (- 21x - 21x)\|x log(\|2 \|x + x + 1)
+--R +
+--R 3 +-+ +-+ +-+
+--R (21x + 21x)\|x log(- \|2 \|x + x + 1)
+--R +
+--R 3 +-+ +-+ +-+
+--R (- 42x - 42x)\|x atan(\|2 \|x + 1)
+--R +
+--R 3 +-+ +-+ +-+ 2 +-+
+--R (- 42x - 42x)\|x atan(\|2 \|x - 1) + (- 28x - 16)\|2
+--R /
+--R 3 +-+ +-+
+--R (24x + 24x)\|2 \|x
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 +-+ +-+ +-+
+--R (- 21x - 21x )\|2 log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+
+--R (21x + 21x )\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ 1 4 2 +-+ 1
+--R (42x + 42x )\|2 atan(------------) + (42x + 42x )\|2 atan(------------)
+--R +-+ +-+ +-+ +-+
+--R \|2 \|x - 1 \|2 \|x + 1
+--R +
+--R 2 +-+
+--R (- 56x - 32)\|x
+--R /
+--R 4 2
+--R 48x + 48x
+--R Type: Union(Expression(Integer),...)
+--E 425
+
+--S 426 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R 7atan(\|2 \|x + 1) + 7atan(\|2 \|x - 1) + 7atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R 7atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 426
+
+--S 427 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 427
+
+)clear all
+
+--S 428 of 1285
+t0:=1/(x^(7/2)*(1+x^2)^2)
+--R
+--R
+--R 1
+--R (1) -------------------
+--R 7 5 3 +-+
+--R (x + 2x + x )\|x
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 1285
+r0:=(-9/10)/x^(5/2)+1/2/(x^(5/2)*(1+x^2))-9/4*atan(1-sqrt(2)*sqrt(x))/_
+ sqrt(2)+9/4*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+9/8*log(1+x-sqrt(2)*_
+ sqrt(x))/sqrt(2)-9/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+9/2/sqrt(x)
+--R
+--R
+--R (2)
+--R 4 2 +-+ +-+ +-+
+--R (- 45x - 45x )\|x log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+
+--R (45x + 45x )\|x log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+ 4 2 +-+ +-+ +-+
+--R (90x + 90x )\|x atan(\|2 \|x + 1) + (90x + 90x )\|x atan(\|2 \|x - 1)
+--R +
+--R 4 2 +-+
+--R (180x + 144x - 16)\|2
+--R /
+--R 4 2 +-+ +-+
+--R (40x + 40x )\|2 \|x
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 3 +-+ +-+ +-+
+--R (- 45x - 45x )\|2 log(\|2 \|x + x + 1)
+--R +
+--R 5 3 +-+ +-+ +-+
+--R (45x + 45x )\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 5 3 +-+ 1
+--R (- 90x - 90x )\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 5 3 +-+ 1 4 2 +-+
+--R (- 90x - 90x )\|2 atan(------------) + (360x + 288x - 32)\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 5 3
+--R 80x + 80x
+--R Type: Union(Expression(Integer),...)
+--E 430
+
+--S 431 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - 9atan(\|2 \|x + 1) - 9atan(\|2 \|x - 1) - 9atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - 9atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 432
+
+)clear all
+
+--S 433 of 1285
+t0:=x^(7/2)/(1+x^2)^3
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ------------------
+--R 6 4 2
+--R x + 3x + 3x + 1
+--R Type: Expression(Integer)
+--E 433
+
+--S 434 of 1285
+r0:=-1/4*x^(5/2)/(1+x^2)^2-5/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+5/32*_
+ atan(1+sqrt(2)*sqrt(x))/sqrt(2)-5/64*log(1+x-sqrt(2)*sqrt(x))/_
+ sqrt(2)+5/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)-5/16*sqrt(x)/(1+x^2)
+--R
+--R
+--R (2)
+--R 4 2 +-+ +-+
+--R (5x + 10x + 5)log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+
+--R (- 5x - 10x - 5)log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+
+--R (10x + 20x + 10)atan(\|2 \|x + 1)
+--R +
+--R 4 2 +-+ +-+ 2 +-+ +-+
+--R (10x + 20x + 10)atan(\|2 \|x - 1) + (- 36x - 20)\|2 \|x
+--R /
+--R 4 2 +-+
+--R (64x + 128x + 64)\|2
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 +-+ +-+ +-+
+--R (5x + 10x + 5)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+
+--R (- 5x - 10x - 5)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ 1
+--R (- 10x - 20x - 10)\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 4 2 +-+ 1 2 +-+
+--R (- 10x - 20x - 10)\|2 atan(------------) + (- 72x - 40)\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 4 2
+--R 128x + 256x + 128
+--R Type: Union(Expression(Integer),...)
+--E 435
+
+--S 436 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - 5atan(\|2 \|x + 1) - 5atan(\|2 \|x - 1) - 5atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - 5atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 32\|2
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 437
+
+)clear all
+
+--S 438 of 1285
+t0:=x^(5/2)/(1+x^2)^3
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ------------------
+--R 6 4 2
+--R x + 3x + 3x + 1
+--R Type: Expression(Integer)
+--E 438
+
+--S 439 of 1285
+r0:=-1/4*x^(3/2)/(1+x^2)^2+3/16*x^(3/2)/(1+x^2)-3/32*atan(1-sqrt(2)*_
+ sqrt(x))/sqrt(2)+3/32*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+3/64*_
+ log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-3/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R 4 2 +-+ +-+
+--R (- 3x - 6x - 3)log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+
+--R (3x + 6x + 3)log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ 4 2 +-+ +-+
+--R (6x + 12x + 6)atan(\|2 \|x + 1) + (6x + 12x + 6)atan(\|2 \|x - 1)
+--R +
+--R 3 +-+ +-+
+--R (12x - 4x)\|2 \|x
+--R /
+--R 4 2 +-+
+--R (64x + 128x + 64)\|2
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 +-+ +-+ +-+
+--R (- 3x - 6x - 3)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+
+--R (3x + 6x + 3)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ 1
+--R (- 6x - 12x - 6)\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 4 2 +-+ 1 3 +-+
+--R (- 6x - 12x - 6)\|2 atan(------------) + (24x - 8x)\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 4 2
+--R 128x + 256x + 128
+--R Type: Union(Expression(Integer),...)
+--E 440
+
+--S 441 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - 3atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 32\|2
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 442
+
+)clear all
+
+--S 443 of 1285
+t0:=x^(3/2)/(1+x^2)^3
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ------------------
+--R 6 4 2
+--R x + 3x + 3x + 1
+--R Type: Expression(Integer)
+--E 443
+
+--S 444 of 1285
+r0:=-3/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/32*atan(1+sqrt(2)*sqrt(x))/_
+ sqrt(2)-3/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+3/64*log(1+x+sqrt(2)*_
+ sqrt(x))/sqrt(2)-1/4*sqrt(x)/(1+x^2)^2+1/16*sqrt(x)/(1+x^2)
+--R
+--R
+--R (2)
+--R 4 2 +-+ +-+
+--R (3x + 6x + 3)log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+
+--R (- 3x - 6x - 3)log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ 4 2 +-+ +-+
+--R (6x + 12x + 6)atan(\|2 \|x + 1) + (6x + 12x + 6)atan(\|2 \|x - 1)
+--R +
+--R 2 +-+ +-+
+--R (4x - 12)\|2 \|x
+--R /
+--R 4 2 +-+
+--R (64x + 128x + 64)\|2
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 +-+ +-+ +-+
+--R (3x + 6x + 3)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+
+--R (- 3x - 6x - 3)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ 1
+--R (- 6x - 12x - 6)\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 4 2 +-+ 1 2 +-+
+--R (- 6x - 12x - 6)\|2 atan(------------) + (8x - 24)\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 4 2
+--R 128x + 256x + 128
+--R Type: Union(Expression(Integer),...)
+--E 445
+
+--S 446 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - 3atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 32\|2
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 447
+
+)clear all
+
+--S 448 of 1285
+t0:=sqrt(x)/(1+x^2)^3
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ------------------
+--R 6 4 2
+--R x + 3x + 3x + 1
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 1285
+r0:=1/4*x^(3/2)/(1+x^2)^2+5/16*x^(3/2)/(1+x^2)-5/32*atan(1-sqrt(2)*_
+ sqrt(x))/sqrt(2)+5/32*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+5/64*_
+ log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-5/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R 4 2 +-+ +-+
+--R (- 5x - 10x - 5)log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+
+--R (5x + 10x + 5)log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+
+--R (10x + 20x + 10)atan(\|2 \|x + 1)
+--R +
+--R 4 2 +-+ +-+ 3 +-+ +-+
+--R (10x + 20x + 10)atan(\|2 \|x - 1) + (20x + 36x)\|2 \|x
+--R /
+--R 4 2 +-+
+--R (64x + 128x + 64)\|2
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 +-+ +-+ +-+
+--R (- 5x - 10x - 5)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+
+--R (5x + 10x + 5)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ 1
+--R (- 10x - 20x - 10)\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 4 2 +-+ 1 3 +-+
+--R (- 10x - 20x - 10)\|2 atan(------------) + (40x + 72x)\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 4 2
+--R 128x + 256x + 128
+--R Type: Union(Expression(Integer),...)
+--E 450
+
+--S 451 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - 5atan(\|2 \|x + 1) - 5atan(\|2 \|x - 1) - 5atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - 5atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 32\|2
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 452
+
+)clear all
+
+--S 453 of 1285
+t0:=1/((1+x^2)^3*sqrt(x))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R 6 4 2 +-+
+--R (x + 3x + 3x + 1)\|x
+--R Type: Expression(Integer)
+--E 453
+
+--S 454 of 1285
+r0:=-21/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+21/32*atan(1+sqrt(2)*sqrt(x))/_
+ sqrt(2)-21/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+21/64*log(1+x+_
+ sqrt(2)*sqrt(x))/sqrt(2)+1/4*sqrt(x)/(1+x^2)^2+7/16*sqrt(x)/(1+x^2)
+--R
+--R
+--R (2)
+--R 4 2 +-+ +-+
+--R (21x + 42x + 21)log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+
+--R (- 21x - 42x - 21)log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+
+--R (42x + 84x + 42)atan(\|2 \|x + 1)
+--R +
+--R 4 2 +-+ +-+ 2 +-+ +-+
+--R (42x + 84x + 42)atan(\|2 \|x - 1) + (28x + 44)\|2 \|x
+--R /
+--R 4 2 +-+
+--R (64x + 128x + 64)\|2
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 +-+ +-+ +-+
+--R (21x + 42x + 21)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+
+--R (- 21x - 42x - 21)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ 1
+--R (- 42x - 84x - 42)\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 4 2 +-+ 1 2 +-+
+--R (- 42x - 84x - 42)\|2 atan(------------) + (56x + 88)\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 4 2
+--R 128x + 256x + 128
+--R Type: Union(Expression(Integer),...)
+--E 455
+
+--S 456 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - 21atan(\|2 \|x + 1) - 21atan(\|2 \|x - 1) - 21atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - 21atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 32\|2
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 457
+
+)clear all
+
+--S 458 of 1285
+t0:=1/(x^(3/2)*(1+x^2)^3)
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R 7 5 3 +-+
+--R (x + 3x + 3x + x)\|x
+--R Type: Expression(Integer)
+--E 458
+
+--S 459 of 1285
+r0:=45/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-45/32*atan(1+sqrt(2)*sqrt(x))/_
+ sqrt(2)-45/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+45/64*log(1+x+_
+ sqrt(2)*sqrt(x))/sqrt(2)+(-45/16)/sqrt(x)+1/4/((1+x^2)^2*sqrt(x))+_
+ 9/16/((1+x^2)*sqrt(x))
+--R
+--R
+--R (2)
+--R 4 2 +-+ +-+ +-+
+--R (45x + 90x + 45)\|x log(\|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+
+--R (- 45x - 90x - 45)\|x log(- \|2 \|x + x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+
+--R (- 90x - 180x - 90)\|x atan(\|2 \|x + 1)
+--R +
+--R 4 2 +-+ +-+ +-+ 4 2 +-+
+--R (- 90x - 180x - 90)\|x atan(\|2 \|x - 1) + (- 180x - 324x - 128)\|2
+--R /
+--R 4 2 +-+ +-+
+--R (64x + 128x + 64)\|2 \|x
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 3 +-+ +-+ +-+
+--R (45x + 90x + 45x)\|2 log(\|2 \|x + x + 1)
+--R +
+--R 5 3 +-+ +-+ +-+
+--R (- 45x - 90x - 45x)\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 5 3 +-+ 1
+--R (90x + 180x + 90x)\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 5 3 +-+ 1 4 2 +-+
+--R (90x + 180x + 90x)\|2 atan(------------) + (- 360x - 648x - 256)\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 5 3
+--R 128x + 256x + 128x
+--R Type: Union(Expression(Integer),...)
+--E 460
+
+--S 461 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R 45atan(\|2 \|x + 1) + 45atan(\|2 \|x - 1) + 45atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R 45atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 32\|2
+--R Type: Expression(Integer)
+--E 461
+
+--S 462 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 462
+
+)clear all
+
+--S 463 of 1285
+t0:=1/(x^(5/2)*(1+x^2)^3)
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R 8 6 4 2 +-+
+--R (x + 3x + 3x + x )\|x
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 1285
+r0:=(-77/48)/x^(3/2)+1/4/(x^(3/2)*(1+x^2)^2)+11/16/(x^(3/2)*(1+x^2))+_
+ 77/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-77/32*atan(1+sqrt(2)*_
+ sqrt(x))/sqrt(2)+77/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-77/64*_
+ log(1+x+sqrt(2)*sqrt(x))/sqrt(2)
+--R
+--R
+--R (2)
+--R 5 3 +-+ +-+ +-+
+--R (- 231x - 462x - 231x)\|x log(\|2 \|x + x + 1)
+--R +
+--R 5 3 +-+ +-+ +-+
+--R (231x + 462x + 231x)\|x log(- \|2 \|x + x + 1)
+--R +
+--R 5 3 +-+ +-+ +-+
+--R (- 462x - 924x - 462x)\|x atan(\|2 \|x + 1)
+--R +
+--R 5 3 +-+ +-+ +-+
+--R (- 462x - 924x - 462x)\|x atan(\|2 \|x - 1)
+--R +
+--R 4 2 +-+
+--R (- 308x - 484x - 128)\|2
+--R /
+--R 5 3 +-+ +-+
+--R (192x + 384x + 192x)\|2 \|x
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 4 2 +-+ +-+ +-+
+--R (- 231x - 462x - 231x )\|2 log(\|2 \|x + x + 1)
+--R +
+--R 6 4 2 +-+ +-+ +-+
+--R (231x + 462x + 231x )\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 6 4 2 +-+ 1
+--R (462x + 924x + 462x )\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 6 4 2 +-+ 1 4 2 +-+
+--R (462x + 924x + 462x )\|2 atan(------------) + (- 616x - 968x - 256)\|x
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R 6 4 2
+--R 384x + 768x + 384x
+--R Type: Union(Expression(Integer),...)
+--E 465
+
+--S 466 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R 77atan(\|2 \|x + 1) + 77atan(\|2 \|x - 1) + 77atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R 77atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 32\|2
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 467
+
+)clear all
+
+--S 468 of 1285
+t0:=1/(x^(7/2)*(1+x^2)^3)
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R 9 7 5 3 +-+
+--R (x + 3x + 3x + x )\|x
+--R Type: Expression(Integer)
+--E 468
+
+--S 469 of 1285
+r0:=(-117/80)/x^(5/2)+1/4/(x^(5/2)*(1+x^2)^2)+13/16/(x^(5/2)*(1+x^2))-_
+ 117/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+117/32*atan(1+sqrt(2)*_
+ sqrt(x))/sqrt(2)+117/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-117/64*_
+ log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+117/16/sqrt(x)
+--R
+--R
+--R (2)
+--R 6 4 2 +-+ +-+ +-+
+--R (- 585x - 1170x - 585x )\|x log(\|2 \|x + x + 1)
+--R +
+--R 6 4 2 +-+ +-+ +-+
+--R (585x + 1170x + 585x )\|x log(- \|2 \|x + x + 1)
+--R +
+--R 6 4 2 +-+ +-+ +-+
+--R (1170x + 2340x + 1170x )\|x atan(\|2 \|x + 1)
+--R +
+--R 6 4 2 +-+ +-+ +-+
+--R (1170x + 2340x + 1170x )\|x atan(\|2 \|x - 1)
+--R +
+--R 6 4 2 +-+
+--R (2340x + 4212x + 1664x - 128)\|2
+--R /
+--R 6 4 2 +-+ +-+
+--R (320x + 640x + 320x )\|2 \|x
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 5 3 +-+ +-+ +-+
+--R (- 585x - 1170x - 585x )\|2 log(\|2 \|x + x + 1)
+--R +
+--R 7 5 3 +-+ +-+ +-+
+--R (585x + 1170x + 585x )\|2 log(- \|2 \|x + x + 1)
+--R +
+--R 7 5 3 +-+ 1
+--R (- 1170x - 2340x - 1170x )\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 7 5 3 +-+ 1
+--R (- 1170x - 2340x - 1170x )\|2 atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R +
+--R 6 4 2 +-+
+--R (4680x + 8424x + 3328x - 256)\|x
+--R /
+--R 7 5 3
+--R 640x + 1280x + 640x
+--R Type: Union(Expression(Integer),...)
+--E 470
+
+--S 471 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+ 1
+--R - 117atan(\|2 \|x + 1) - 117atan(\|2 \|x - 1) - 117atan(------------)
+--R +-+ +-+
+--R \|2 \|x - 1
+--R +
+--R 1
+--R - 117atan(------------)
+--R +-+ +-+
+--R \|2 \|x + 1
+--R /
+--R +-+
+--R 32\|2
+--R Type: Expression(Integer)
+--E 471
+
+--S 472 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 472
+
+)clear all
+
+--S 473 of 1285
+t0:=x^(2/3)/(1+x^2)
+--R
+--R
+--R 3+-+2
+--R \|x
+--R (1) ------
+--R 2
+--R x + 1
+--R Type: Expression(Integer)
+--E 473
+
+--S 474 of 1285
+r0a:=atan(x^(1/3))-1/2*atan(-2*x^(1/3)+sqrt(3))+1/2*atan(2*x^(1/3)+sqrt(3))-_
+ 1/2*atanh(x^(1/3)*sqrt(3)/(1+x^(2/3)))*sqrt(3)
+--R
+--R
+--R (2)
+--R +-+3+-+
+--R +-+ \|3 \|x 3+-+ +-+ 3+-+ +-+
+--R - \|3 atanh(---------) + atan(2\|x + \|3 ) + atan(2\|x - \|3 )
+--R 3+-+2
+--R \|x + 1
+--R +
+--R 3+-+
+--R 2atan(\|x )
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 1285
+r0b:=atan(x^(1/3))-1/2*atan(-2*x^(1/3)+sqrt(3))+1/2*atan(2*x^(1/3)+sqrt(3))+_
+ 1/4*log(1+x^(2/3)-x^(1/3)*sqrt(3))*sqrt(3)-1/4*log(1+x^(2/3)+_
+ x^(1/3)*sqrt(3))*sqrt(3)
+--R
+--R
+--R (3)
+--R +-+ 3+-+2 +-+3+-+ +-+ 3+-+2 +-+3+-+
+--R - \|3 log(\|x + \|3 \|x + 1) + \|3 log(\|x - \|3 \|x + 1)
+--R +
+--R 3+-+ +-+ 3+-+ +-+ 3+-+
+--R 2atan(2\|x + \|3 ) + 2atan(2\|x - \|3 ) + 4atan(\|x )
+--R /
+--R 4
+--R Type: Expression(Integer)
+--E 475
+
+--S 476 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R +-+ 3+-+2 +-+3+-+ +-+ 3+-+2 +-+3+-+
+--R - \|3 log(\|x + \|3 \|x + 1) + \|3 log(\|x - \|3 \|x + 1)
+--R +
+--R 3+-+
+--R 2\|x 1 1
+--R - 2atan(---------) - 2atan(------------) - 2atan(------------)
+--R 3+-+2 3+-+ +-+ 3+-+ +-+
+--R \|x - 1 2\|x - \|3 2\|x + \|3
+--R /
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 476
+
+--S 477 of 1285
+m0a:=a0-r0a
+--R
+--R
+--R (5)
+--R +-+ 3+-+2 +-+3+-+ +-+ 3+-+2 +-+3+-+
+--R - \|3 log(\|x + \|3 \|x + 1) + \|3 log(\|x - \|3 \|x + 1)
+--R +
+--R +-+3+-+
+--R +-+ \|3 \|x 3+-+ +-+ 3+-+ +-+
+--R 2\|3 atanh(---------) - 2atan(2\|x + \|3 ) - 2atan(2\|x - \|3 )
+--R 3+-+2
+--R \|x + 1
+--R +
+--R 3+-+
+--R 3+-+ 2\|x 1
+--R - 4atan(\|x ) - 2atan(---------) - 2atan(------------)
+--R 3+-+2 3+-+ +-+
+--R \|x - 1 2\|x - \|3
+--R +
+--R 1
+--R - 2atan(------------)
+--R 3+-+ +-+
+--R 2\|x + \|3
+--R /
+--R 4
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 1285
+d0:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 478
+
+--S 479 of 1285
+m0b:=a0-r0b
+--R
+--R
+--R (7)
+--R 3+-+
+--R 3+-+ +-+ 3+-+ +-+ 3+-+ 2\|x
+--R - atan(2\|x + \|3 ) - atan(2\|x - \|3 ) - 2atan(\|x ) - atan(---------)
+--R 3+-+2
+--R \|x - 1
+--R +
+--R 1 1
+--R - atan(------------) - atan(------------)
+--R 3+-+ +-+ 3+-+ +-+
+--R 2\|x - \|3 2\|x + \|3
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 1285
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 480
+
+)clear all
+
+--S 481 of 1285
+t0:=x^(7/2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 3 +-+ | 2
+--R (1) x \|x \|b x + a
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 1285
+--r0:=4/77*a*x^(5/2)*sqrt(a+b*x^2)/b+2/11*x^(9/2)*sqrt(a+b*x^2)-_
+-- 20/231*a^2*sqrt(x)*sqrt(a+b*x^2)/b^2+20/231*a^(13/4)*_
+-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+-- ((-b)^(9/4)*sqrt(a+b*x^2))
+--E 482
+
+--S 483 of 1285
+--a0:=integrate(t0,x)
+--E 483
+
+--S 484 of 1285
+--m0:=a0-r0
+--E 484
+
+--S 485 of 1285
+--d0:=D(m0,x)
+--E 485
+
+)clear all
+
+--S 486 of 1285
+t0:=x^(5/2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2
+--R (1) x \|x \|b x + a
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 1285
+--r0:=4/45*a*x^(3/2)*sqrt(a+b*x^2)/b+2/9*x^(7/2)*sqrt(a+b*x^2)+4/15*_
+--a^(11/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_
+--b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))-4/15*a^(11/4)*elliptic_f(_
+--asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(7/4)*sqrt(a+b*x^2))
+--E 487
+
+--S 488 of 1285
+--a0:=integrate(t0,x)
+--E 488
+
+--S 489 of 1285
+--m0:=a0-r0
+--E 489
+
+--S 490 of 1285
+--d0:=D(m0,x)
+--E 490
+
+)clear all
+
+--S 491 of 1285
+t0:=x^(3/2)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R (1) x\|x \|b x + a
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 1285
+--r0:=2/7*x^(5/2)*sqrt(a+b*x^2)+4/21*a*sqrt(x)*sqrt(a+b*x^2)/b+4/21*_
+--a^(9/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2))
+--E 492
+
+--S 493 of 1285
+--a0:=integrate(t0,x)
+--E 493
+
+--S 494 of 1285
+--m0:=a0-r0
+--E 494
+
+--S 495 of 1285
+--d0:=D(m0,x)
+--E 495
+
+)clear all
+
+--S 496 of 1285
+t0:=sqrt(x)*sqrt(a+b*x^2)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R (1) \|x \|b x + a
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 1285
+--r0:=2/5*x^(3/2)*sqrt(a+b*x^2)+4/5*a^(7/4)*elliptic_e(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-_
+--4/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))
+--E 497
+
+--S 498 of 1285
+--a0:=integrate(t0,x)
+--E 498
+
+--S 499 of 1285
+--m0:=a0-r0
+--E 499
+
+--S 500 of 1285
+--d0:=D(m0,x)
+--E 500
+
+)clear all
+
+--S 501 of 1285
+t0:=sqrt(a+b*x^2)/sqrt(x)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 1285
+--r0:=2/3*sqrt(x)*sqrt(a+b*x^2)+4/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2))
+--E 502
+
+--S 503 of 1285
+--a0:=integrate(t0,x)
+--E 503
+
+--S 504 of 1285
+--m0:=a0-r0
+--E 504
+
+--S 505 of 1285
+--d0:=D(m0,x)
+--E 505
+
+)clear all
+
+--S 506 of 1285
+t0:=sqrt(a+b*x^2)/x^(3/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 506
+
+--S 507 of 1285
+--r0:=-2*sqrt(a+b*x^2)/sqrt(x)-4*a^(3/4)*(-b)^(1/4)*_
+--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--sqrt(a+b*x^2)+4*a^(3/4)*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)
+--E 507
+
+--S 508 of 1285
+--a0:=integrate(t0,x)
+--E 508
+
+--S 509 of 1285
+--m0:=a0-r0
+--E 509
+
+--S 510 of 1285
+--d0:=D(m0,x)
+--E 510
+
+)clear all
+
+--S 511 of 1285
+t0:=sqrt(a+b*x^2)/x^(5/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 511
+
+--S 512 of 1285
+--r0:=-2/3*sqrt(a+b*x^2)/x^(3/2)-4/3*a^(1/4)*(-b)^(3/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--sqrt(a+b*x^2)
+--E 512
+
+--S 513 of 1285
+--a0:=integrate(t0,x)
+--E 513
+
+--S 514 of 1285
+--m0:=a0-r0
+--E 514
+
+--S 515 of 1285
+--d0:=D(m0,x)
+--E 515
+
+)clear all
+
+--S 516 of 1285
+t0:=sqrt(a+b*x^2)/x^(7/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 516
+
+--S 517 of 1285
+--r0:=-2/5*sqrt(a+b*x^2)/x^(5/2)-4/5*b*sqrt(a+b*x^2)/(a*sqrt(x))+4/5*_
+--(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/(a^(1/4)*sqrt(a+b*x^2))-4/5*(-b)^(5/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(1/4)*sqrt(a+b*x^2))
+--E 517
+
+--S 518 of 1285
+--a0:=integrate(t0,x)
+--E 518
+
+--S 519 of 1285
+--m0:=a0-r0
+--E 519
+
+--S 520 of 1285
+--d0:=D(m0,x)
+--E 520
+
+)clear all
+
+--S 521 of 1285
+t0:=x^(7/2)*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 5 3 +-+ | 2
+--R (1) (b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 521
+
+--S 522 of 1285
+--r0:=2/15*x^(9/2)*(a+b*x^2)^(3/2)+8/385*a^2*x^(5/2)*sqrt(a+b*x^2)/b+_
+--4/55*a*x^(9/2)*sqrt(a+b*x^2)-8/231*a^3*sqrt(x)*sqrt(a+b*x^2)/b^2+_
+--8/231*a^(17/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2))
+--E 522
+
+--S 523 of 1285
+--a0:=integrate(t0,x)
+--E 523
+
+--S 524 of 1285
+--m0:=a0-r0
+--E 524
+
+--S 525 of 1285
+--d0:=D(m0,x)
+--E 525
+
+)clear all
+
+--S 526 of 1285
+t0:=x^(5/2)*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 4 2 +-+ | 2
+--R (1) (b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 526
+
+--S 527 of 1285
+--r0:=2/13*x^(7/2)*(a+b*x^2)^(3/2)+8/195*a^2*x^(3/2)*sqrt(a+b*x^2)/b+_
+--4/39*a*x^(7/2)*sqrt(a+b*x^2)+8/65*a^(15/4)*elliptic_e(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))-_
+--8/65*a^(15/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))
+--E 527
+
+--S 528 of 1285
+--a0:=integrate(t0,x)
+--E 528
+
+--S 529 of 1285
+--m0:=a0-r0
+--E 529
+
+--S 530 of 1285
+--d0:=D(m0,x)
+--E 530
+
+)clear all
+
+--S 531 of 1285
+t0:=x^(3/2)*(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 3 +-+ | 2
+--R (1) (b x + a x)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 531
+
+--S 532 of 1285
+--r0:=2/11*x^(5/2)*(a+b*x^2)^(3/2)+12/77*a*x^(5/2)*sqrt(a+b*x^2)+_
+--8/77*a^2*sqrt(x)*sqrt(a+b*x^2)/b+8/77*a^(13/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(5/4)*sqrt(a+b*x^2))
+--E 532
+
+--S 533 of 1285
+--a0:=integrate(t0,x)
+--E 533
+
+--S 534 of 1285
+--m0:=a0-r0
+--E 534
+
+--S 535 of 1285
+--d0:=D(m0,x)
+--E 535
+
+)clear all
+
+--S 536 of 1285
+t0:=(a+b*x^2)^(3/2)*sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2
+--R (1) (b x + a)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 536
+
+--S 537 of 1285
+--r0:=2/9*x^(3/2)*(a+b*x^2)^(3/2)+4/15*a*x^(3/2)*sqrt(a+b*x^2)+_
+--8/15*a^(11/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-8/15*a^(11/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(3/4)*sqrt(a+b*x^2))
+--E 537
+
+--S 538 of 1285
+--a0:=integrate(t0,x)
+--E 538
+
+--S 539 of 1285
+--m0:=a0-r0
+--E 539
+
+--S 540 of 1285
+--d0:=D(m0,x)
+--E 540
+
+)clear all
+
+--S 541 of 1285
+t0:=(a+b*x^2)^(3/2)/sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 1285
+--r0:=2/7*(a+b*x^2)^(3/2)*sqrt(x)+4/7*a*sqrt(x)*sqrt(a+b*x^2)+_
+--8/7*a^(9/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2))
+--E 542
+
+--S 543 of 1285
+--a0:=integrate(t0,x)
+--E 543
+
+--S 544 of 1285
+--m0:=a0-r0
+--E 544
+
+--S 545 of 1285
+--d0:=D(m0,x)
+--E 545
+
+)clear all
+
+--S 546 of 1285
+t0:=(a+b*x^2)^(3/2)/x^(3/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 546
+
+--S 547 of 1285
+--r0:=-2*(a+b*x^2)^(3/2)/sqrt(x)+12/5*b*x^(3/2)*sqrt(a+b*x^2)-_
+--24/5*a^(7/4)*(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)+24/5*a^(7/4)*(-b)^(1/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--sqrt(a+b*x^2)
+--E 547
+
+--S 548 of 1285
+--a0:=integrate(t0,x)
+--E 548
+
+--S 549 of 1285
+--m0:=a0-r0
+--E 549
+
+--S 550 of 1285
+--d0:=D(m0,x)
+--E 550
+
+)clear all
+
+--S 551 of 1285
+t0:=(a+b*x^2)^(3/2)/x^(5/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 551
+
+--S 552 of 1285
+--r0:=-2/3*(a+b*x^2)^(3/2)/x^(3/2)+4/3*b*sqrt(x)*sqrt(a+b*x^2)-_
+--8/3*a^(5/4)*(-b)^(3/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)
+--E 552
+
+--S 553 of 1285
+--a0:=integrate(t0,x)
+--E 553
+
+--S 554 of 1285
+--m0:=a0-r0
+--E 554
+
+--S 555 of 1285
+--d0:=D(m0,x)
+--E 555
+
+)clear all
+
+--S 556 of 1285
+t0:=(a+b*x^2)^(3/2)/x^(7/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 1285
+--r0:=-2/5*(a+b*x^2)^(3/2)/x^(5/2)-12/5*b*sqrt(a+b*x^2)/sqrt(x)+_
+--24/5*a^(3/4)*(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)-24/5*a^(3/4)*(-b)^(5/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--sqrt(a+b*x^2)
+--E 557
+
+--S 558 of 1285
+--a0:=integrate(t0,x)
+--E 558
+
+--S 559 of 1285
+--m0:=a0-r0
+--E 559
+
+--S 560 of 1285
+--d0:=D(m0,x)
+--E 560
+
+)clear all
+
+--S 561 of 1285
+t0:=x^(7/2)*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 7 5 2 3 +-+ | 2
+--R (1) (b x + 2a b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 561
+
+--S 562 of 1285
+--r0:=4/57*a*x^(9/2)*(a+b*x^2)^(3/2)+2/19*x^(9/2)*(a+b*x^2)^(5/2)+_
+--16/1463*a^3*x^(5/2)*sqrt(a+b*x^2)/b+8/209*a^2*x^(9/2)*sqrt(a+b*x^2)-_
+--80/4389*a^4*sqrt(x)*sqrt(a+b*x^2)/b^2+80/4389*a^(21/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(9/4)*sqrt(a+b*x^2))
+--E 562
+
+--S 563 of 1285
+--a0:=integrate(t0,x)
+--E 563
+
+--S 564 of 1285
+--m0:=a0-r0
+--E 564
+
+--S 565 of 1285
+--d0:=D(m0,x)
+--E 565
+
+)clear all
+
+--S 566 of 1285
+t0:=x^(5/2)*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2
+--R (1) (b x + 2a b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 566
+
+--S 567 of 1285
+--r0:=20/221*a*x^(7/2)*(a+b*x^2)^(3/2)+2/17*x^(7/2)*(a+b*x^2)^(5/2)+_
+--16/663*a^3*x^(3/2)*sqrt(a+b*x^2)/b+40/663*a^2*x^(7/2)*sqrt(a+b*x^2)+_
+--16/221*a^(19/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))-16/221*a^(19/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(7/4)*sqrt(a+b*x^2))
+--E 567
+
+--S 568 of 1285
+--a0:=integrate(t0,x)
+--E 568
+
+--S 569 of 1285
+--m0:=a0-r0
+--E 569
+
+--S 570 of 1285
+--d0:=D(m0,x)
+--E 570
+
+)clear all
+
+--S 571 of 1285
+t0:=x^(3/2)*(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (1) (b x + 2a b x + a x)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 1285
+--r0:=4/33*a*x^(5/2)*(a+b*x^2)^(3/2)+2/15*x^(5/2)*(a+b*x^2)^(5/2)+_
+--8/77*a^2*x^(5/2)*sqrt(a+b*x^2)+16/231*a^3*sqrt(x)*sqrt(a+b*x^2)/_
+--b+16/231*a^(17/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2))
+--E 572
+
+--S 573 of 1285
+--a0:=integrate(t0,x)
+--E 573
+
+--S 574 of 1285
+--m0:=a0-r0
+--E 574
+
+--S 575 of 1285
+--d0:=D(m0,x)
+--E 575
+
+)clear all
+
+--S 576 of 1285
+t0:=(a+b*x^2)^(5/2)*sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 +-+ | 2
+--R (1) (b x + 2a b x + a )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 576
+
+--S 577 of 1285
+--r0:=20/117*a*x^(3/2)*(a+b*x^2)^(3/2)+2/13*x^(3/2)*(a+b*x^2)^(5/2)+_
+--8/39*a^2*x^(3/2)*sqrt(a+b*x^2)+16/39*a^(15/4)*_
+--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(3/4)*sqrt(a+b*x^2))-16/39*a^(15/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(3/4)*sqrt(a+b*x^2))
+--E 577
+
+--S 578 of 1285
+--a0:=integrate(t0,x)
+--E 578
+
+--S 579 of 1285
+--m0:=a0-r0
+--E 579
+
+--S 580 of 1285
+--d0:=D(m0,x)
+--E 580
+
+)clear all
+
+--S 581 of 1285
+t0:=(a+b*x^2)^(5/2)/sqrt(x)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 581
+
+--S 582 of 1285
+--r0:=20/77*a*(a+b*x^2)^(3/2)*sqrt(x)+2/11*(a+b*x^2)^(5/2)*sqrt(x)+_
+--40/77*a^2*sqrt(x)*sqrt(a+b*x^2)+80/77*a^(13/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(1/4)*sqrt(a+b*x^2))
+--E 582
+
+--S 583 of 1285
+--a0:=integrate(t0,x)
+--E 583
+
+--S 584 of 1285
+--m0:=a0-r0
+--E 584
+
+--S 585 of 1285
+--d0:=D(m0,x)
+--E 585
+
+)clear all
+
+--S 586 of 1285
+t0:=(a+b*x^2)^(5/2)/x^(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 x\|x
+--R Type: Expression(Integer)
+--E 586
+
+--S 587 of 1285
+--r0:=20/9*b*x^(3/2)*(a+b*x^2)^(3/2)-2*(a+b*x^2)^(5/2)/sqrt(x)+_
+--8/3*a*b*x^(3/2)*sqrt(a+b*x^2)-16/3*a^(11/4)*(-b)^(1/4)*_
+--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--sqrt(a+b*x^2)+16/3*a^(11/4)*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)
+--E 587
+
+--S 588 of 1285
+--a0:=integrate(t0,x)
+--E 588
+
+--S 589 of 1285
+--m0:=a0-r0
+--E 589
+
+--S 590 of 1285
+--d0:=D(m0,x)
+--E 590
+
+)clear all
+
+--S 591 of 1285
+t0:=(a+b*x^2)^(5/2)/x^(5/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 591
+
+--S 592 of 1285
+--r0:=-2/3*(a+b*x^2)^(5/2)/x^(3/2)+20/21*b*(a+b*x^2)^(3/2)*sqrt(x)+_
+--40/21*a*b*sqrt(x)*sqrt(a+b*x^2)-80/21*a^(9/4)*(-b)^(3/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--sqrt(a+b*x^2)
+--E 592
+
+--S 593 of 1285
+--a0:=integrate(t0,x)
+--E 593
+
+--S 594 of 1285
+--m0:=a0-r0
+--E 594
+
+--S 595 of 1285
+--d0:=D(m0,x)
+--E 595
+
+)clear all
+
+--S 596 of 1285
+t0:=(a+b*x^2)^(5/2)/x^(7/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 596
+
+--S 597 of 1285
+--r0:=-2/5*(a+b*x^2)^(5/2)/x^(5/2)-4*b*(a+b*x^2)^(3/2)/sqrt(x)+_
+--24/5*b^2*x^(3/2)*sqrt(a+b*x^2)+48/5*a^(7/4)*(-b)^(5/4)*_
+--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--sqrt(a+b*x^2)-48/5*a^(7/4)*(-b)^(5/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)
+--E 597
+
+--S 598 of 1285
+--a0:=integrate(t0,x)
+--E 598
+
+--S 599 of 1285
+--m0:=a0-r0
+--E 599
+
+--S 600 of 1285
+--d0:=D(m0,x)
+--E 600
+
+)clear all
+
+--S 601 of 1285
+t0:=x^(7/2)/sqrt(a+b*x^2)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 601
+
+--S 602 of 1285
+--r0:=2/7*x^(5/2)*sqrt(a+b*x^2)/b-10/21*a*sqrt(x)*sqrt(a+b*x^2)/b^2+_
+--10/21*a^(9/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2))
+--E 602
+
+--S 603 of 1285
+--a0:=integrate(t0,x)
+--E 603
+
+--S 604 of 1285
+--m0:=a0-r0
+--E 604
+
+--S 605 of 1285
+--d0:=D(m0,x)
+--E 605
+
+)clear all
+
+--S 606 of 1285
+t0:=x^(5/2)/sqrt(a+b*x^2)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 606
+
+--S 607 of 1285
+--r0:=2/5*x^(3/2)*sqrt(a+b*x^2)/b+6/5*a^(7/4)*_
+--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(7/4)*sqrt(a+b*x^2))-6/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))
+--E 607
+
+--S 608 of 1285
+--a0:=integrate(t0,x)
+--E 608
+
+--S 609 of 1285
+--m0:=a0-r0
+--E 609
+
+--S 610 of 1285
+--d0:=D(m0,x)
+--E 610
+
+)clear all
+
+--S 611 of 1285
+t0:=x^(3/2)/sqrt(a+b*x^2)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 611
+
+--S 612 of 1285
+--r0:=2/3*sqrt(x)*sqrt(a+b*x^2)/b+2/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2))
+--E 612
+
+--S 613 of 1285
+--a0:=integrate(t0,x)
+--E 613
+
+--S 614 of 1285
+--m0:=a0-r0
+--E 614
+
+--S 615 of 1285
+--d0:=D(m0,x)
+--E 615
+
+)clear all
+
+--S 616 of 1285
+t0:=sqrt(x)/sqrt(a+b*x^2)
+--R
+--R
+--R +-+
+--R \|x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 616
+
+--S 617 of 1285
+--r0:=2*a^(3/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-2*a^(3/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--((-b)^(3/4)*sqrt(a+b*x^2))
+--E 617
+
+--S 618 of 1285
+--a0:=integrate(t0,x)
+--E 618
+
+--S 619 of 1285
+--m0:=a0-r0
+--E 619
+
+--S 620 of 1285
+--d0:=D(m0,x)
+--E 620
+
+)clear all
+
+--S 621 of 1285
+t0:=1/(sqrt(x)*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------
+--R +--------+
+--R +-+ | 2
+--R \|x \|b x + a
+--R Type: Expression(Integer)
+--E 621
+
+--S 622 of 1285
+--r0:=2*a^(1/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2))
+--E 622
+
+--S 623 of 1285
+--a0:=integrate(t0,x)
+--E 623
+
+--S 624 of 1285
+--m0:=a0-r0
+--E 624
+
+--S 625 of 1285
+--d0:=D(m0,x)
+--E 625
+
+)clear all
+
+--S 626 of 1285
+t0:=1/(x^(3/2)*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------
+--R +--------+
+--R +-+ | 2
+--R x\|x \|b x + a
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 1285
+--r0:=-2*sqrt(a+b*x^2)/(a*sqrt(x))-2*(-b)^(1/4)*_
+--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(1/4)*sqrt(a+b*x^2))+2*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(1/4)*sqrt(a+b*x^2))
+--E 627
+
+--S 628 of 1285
+--a0:=integrate(t0,x)
+--E 628
+
+--S 629 of 1285
+--m0:=a0-r0
+--E 629
+
+--S 630 of 1285
+--d0:=D(m0,x)
+--E 630
+
+)clear all
+
+--S 631 of 1285
+t0:=1/(x^(5/2)*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R +--------+
+--R 2 +-+ | 2
+--R x \|x \|b x + a
+--R Type: Expression(Integer)
+--E 631
+
+--S 632 of 1285
+--r0:=-2/3*sqrt(a+b*x^2)/(a*x^(3/2))+2/3*(-b)^(3/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(3/4)*sqrt(a+b*x^2))
+--E 632
+
+--S 633 of 1285
+--a0:=integrate(t0,x)
+--E 633
+
+--S 634 of 1285
+--m0:=a0-r0
+--E 634
+
+--S 635 of 1285
+--d0:=D(m0,x)
+--E 635
+
+)clear all
+
+--S 636 of 1285
+t0:=1/(x^(7/2)*sqrt(a+b*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R +--------+
+--R 3 +-+ | 2
+--R x \|x \|b x + a
+--R Type: Expression(Integer)
+--E 636
+
+--S 637 of 1285
+--r0:=-2/5*sqrt(a+b*x^2)/(a*x^(5/2))+6/5*b*sqrt(a+b*x^2)/(a^2*sqrt(x))-_
+--6/5*(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/(a^(5/4)*sqrt(a+b*x^2))+6/5*(-b)^(5/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(5/4)*sqrt(a+b*x^2))
+--E 637
+
+--S 638 of 1285
+--a0:=integrate(t0,x)
+--E 638
+
+--S 639 of 1285
+--m0:=a0-r0
+--E 639
+
+--S 640 of 1285
+--d0:=D(m0,x)
+--E 640
+
+)clear all
+
+--S 641 of 1285
+t0:=x^(7/2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 641
+
+--S 642 of 1285
+--r0:=-x^(5/2)/(b*sqrt(a+b*x^2))+5/3*sqrt(x)*sqrt(a+b*x^2)/b^2-_
+--5/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2))
+--E 642
+
+--S 643 of 1285
+--a0:=integrate(t0,x)
+--E 643
+
+--S 644 of 1285
+--m0:=a0-r0
+--E 644
+
+--S 645 of 1285
+--d0:=D(m0,x)
+--E 645
+
+)clear all
+
+--S 646 of 1285
+t0:=x^(5/2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 646
+
+--S 647 of 1285
+--r0:=-x^(3/2)/(b*sqrt(a+b*x^2))-3*a^(3/4)*elliptic_e(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))+_
+--3*a^(3/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))
+--E 647
+
+--S 648 of 1285
+--a0:=integrate(t0,x)
+--E 648
+
+--S 649 of 1285
+--m0:=a0-r0
+--E 649
+
+--S 650 of 1285
+--d0:=D(m0,x)
+--E 650
+
+)clear all
+
+--S 651 of 1285
+t0:=x^(3/2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 651
+
+--S 652 of 1285
+--r0:=-sqrt(x)/(b*sqrt(a+b*x^2))-a^(1/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2))
+--E 652
+
+--S 653 of 1285
+--a0:=integrate(t0,x)
+--E 653
+
+--S 654 of 1285
+--m0:=a0-r0
+--E 654
+
+--S 655 of 1285
+--d0:=D(m0,x)
+--E 655
+
+)clear all
+
+--S 656 of 1285
+t0:=sqrt(x)/(a+b*x^2)^(3/2)
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 656
+
+--S 657 of 1285
+--r0:=x^(3/2)/(a*sqrt(a+b*x^2))-elliptic_e(asin((-b)^(1/4)*sqrt(x)/_
+--a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(3/4)*sqrt(a+b*x^2))+_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(1/4)*(-b)^(3/4)*sqrt(a+b*x^2))
+--E 657
+
+--S 658 of 1285
+--a0:=integrate(t0,x)
+--E 658
+
+--S 659 of 1285
+--m0:=a0-r0
+--E 659
+
+--S 660 of 1285
+--d0:=D(m0,x)
+--E 660
+
+)clear all
+
+--S 661 of 1285
+t0:=1/((a+b*x^2)^(3/2)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R +--------+
+--R 2 +-+ | 2
+--R (b x + a)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1285
+--r0:=sqrt(x)/(a*sqrt(a+b*x^2))+elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(3/4)*(-b)^(1/4)*sqrt(a+b*x^2))
+--E 662
+
+--S 663 of 1285
+--a0:=integrate(t0,x)
+--E 663
+
+--S 664 of 1285
+--m0:=a0-r0
+--E 664
+
+--S 665 of 1285
+--d0:=D(m0,x)
+--E 665
+
+)clear all
+
+--S 666 of 1285
+t0:=1/(x^(3/2)*(a+b*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R +--------+
+--R 3 +-+ | 2
+--R (b x + a x)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 666
+
+--S 667 of 1285
+--r0:=1/(a*sqrt(x)*sqrt(a+b*x^2))-3*sqrt(a+b*x^2)/(a^2*sqrt(x))-3*_
+--(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/(a^(5/4)*sqrt(a+b*x^2))+3*(-b)^(1/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(5/4)*sqrt(a+b*x^2))
+--E 667
+
+--S 668 of 1285
+--a0:=integrate(t0,x)
+--E 668
+
+--S 669 of 1285
+--m0:=a0-r0
+--E 669
+
+--S 670 of 1285
+--d0:=D(m0,x)
+--E 670
+
+)clear all
+
+--S 671 of 1285
+t0:=1/(x^(5/2)*(a+b*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R +--------+
+--R 4 2 +-+ | 2
+--R (b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 671
+
+--S 672 of 1285
+--r0:=1/(a*x^(3/2)*sqrt(a+b*x^2))-5/3*sqrt(a+b*x^2)/(a^2*x^(3/2))+_
+--5/3*(-b)^(3/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/(a^(7/4)*sqrt(a+b*x^2))
+--E 672
+
+--S 673 of 1285
+--a0:=integrate(t0,x)
+--E 673
+
+--S 674 of 1285
+--m0:=a0-r0
+--E 674
+
+--S 675 of 1285
+--d0:=D(m0,x)
+--E 675
+
+)clear all
+
+--S 676 of 1285
+t0:=1/(x^(7/2)*(a+b*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R +--------+
+--R 5 3 +-+ | 2
+--R (b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 676
+
+--S 677 of 1285
+--r0:=1/(a*x^(5/2)*sqrt(a+b*x^2))-7/5*sqrt(a+b*x^2)/(a^2*x^(5/2))+_
+--21/5*b*sqrt(a+b*x^2)/(a^3*sqrt(x))-21/5*(-b)^(5/4)*_
+--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(9/4)*sqrt(a+b*x^2))+21/5*(-b)^(5/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(9/4)*sqrt(a+b*x^2))
+--E 677
+
+--S 678 of 1285
+--a0:=integrate(t0,x)
+--E 678
+
+--S 679 of 1285
+--m0:=a0-r0
+--E 679
+
+--S 680 of 1285
+--d0:=D(m0,x)
+--E 680
+
+)clear all
+
+--S 681 of 1285
+t0:=x^(7/2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 681
+
+--S 682 of 1285
+--r0:=-1/3*x^(5/2)/(b*(a+b*x^2)^(3/2))-5/6*sqrt(x)/(b^2*sqrt(a+b*x^2))+_
+--5/6*a^(1/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2))
+--E 682
+
+--S 683 of 1285
+--a0:=integrate(t0,x)
+--E 683
+
+--S 684 of 1285
+--m0:=a0-r0
+--E 684
+
+--S 685 of 1285
+--d0:=D(m0,x)
+--E 685
+
+)clear all
+
+--S 686 of 1285
+t0:=x^(5/2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 686
+
+--S 687 of 1285
+--r0:=-1/3*x^(3/2)/(b*(a+b*x^2)^(3/2))+1/2*x^(3/2)/(a*b*sqrt(a+b*x^2))+_
+--1/2*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(1/4)*(-b)^(7/4)*sqrt(a+b*x^2))-1/2*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(7/4)*sqrt(a+b*x^2))
+--E 687
+
+--S 688 of 1285
+--a0:=integrate(t0,x)
+--E 688
+
+--S 689 of 1285
+--m0:=a0-r0
+--E 689
+
+--S 690 of 1285
+--d0:=D(m0,x)
+--E 690
+
+)clear all
+
+--S 691 of 1285
+t0:=x^(3/2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 691
+
+--S 692 of 1285
+--r0:=-1/3*sqrt(x)/(b*(a+b*x^2)^(3/2))+1/6*sqrt(x)/(a*b*sqrt(a+b*x^2))-_
+--1/6*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(3/4)*(-b)^(5/4)*sqrt(a+b*x^2))
+--E 692
+
+--S 693 of 1285
+--a0:=integrate(t0,x)
+--E 693
+
+--S 694 of 1285
+--m0:=a0-r0
+--E 694
+
+--S 695 of 1285
+--d0:=D(m0,x)
+--E 695
+
+)clear all
+
+--S 696 of 1285
+t0:=sqrt(x)/(a+b*x^2)^(5/2)
+--R
+--R
+--R +-+
+--R \|x
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 696
+
+--S 697 of 1285
+--r0:=1/3*x^(3/2)/(a*(a+b*x^2)^(3/2))+1/2*x^(3/2)/(a^2*sqrt(a+b*x^2))-_
+--1/2*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(5/4)*(-b)^(3/4)*sqrt(a+b*x^2))+1/2*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(5/4)*(-b)^(3/4)*sqrt(a+b*x^2))
+--E 697
+
+--S 698 of 1285
+--a0:=integrate(t0,x)
+--E 698
+
+--S 699 of 1285
+--m0:=a0-r0
+--E 699
+
+--S 700 of 1285
+--d0:=D(m0,x)
+--E 700
+
+)clear all
+
+--S 701 of 1285
+t0:=1/((a+b*x^2)^(5/2)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R +--------+
+--R 2 4 2 2 +-+ | 2
+--R (b x + 2a b x + a )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 701
+
+--S 702 of 1285
+--r0:=1/3*sqrt(x)/(a*(a+b*x^2)^(3/2))+5/6*sqrt(x)/(a^2*sqrt(a+b*x^2))+_
+--5/6*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(7/4)*(-b)^(1/4)*sqrt(a+b*x^2))
+--E 702
+
+--S 703 of 1285
+--a0:=integrate(t0,x)
+--E 703
+
+--S 704 of 1285
+--m0:=a0-r0
+--E 704
+
+--S 705 of 1285
+--d0:=D(m0,x)
+--E 705
+
+)clear all
+
+--S 706 of 1285
+t0:=1/(x^(3/2)*(a+b*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (b x + 2a b x + a x)\|x \|b x + a
+--R Type: Expression(Integer)
+--E 706
+
+--S 707 of 1285
+--r0:=1/3/(a*(a+b*x^2)^(3/2)*sqrt(x))+7/6/(a^2*sqrt(x)*sqrt(a+b*x^2))-_
+--7/2*sqrt(a+b*x^2)/(a^3*sqrt(x))-7/2*(-b)^(1/4)*_
+--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(9/4)*sqrt(a+b*x^2))+7/2*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_
+--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(9/4)*sqrt(a+b*x^2))
+--E 707
+
+--S 708 of 1285
+--a0:=integrate(t0,x)
+--E 708
+
+--S 709 of 1285
+--m0:=a0-r0
+--E 709
+
+--S 710 of 1285
+--d0:=D(m0,x)
+--E 710
+
+)clear all
+
+--S 711 of 1285
+t0:=1/(x^(5/2)*(a+b*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2
+--R (b x + 2a b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1285
+--r0:=1/3/(a*x^(3/2)*(a+b*x^2)^(3/2))+3/2/(a^2*x^(3/2)*sqrt(a+b*x^2))-_
+--5/2*sqrt(a+b*x^2)/(a^3*x^(3/2))+5/2*(-b)^(3/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(11/4)*sqrt(a+b*x^2))
+--E 712
+
+--S 713 of 1285
+--a0:=integrate(t0,x)
+--E 713
+
+--S 714 of 1285
+--m0:=a0-r0
+--E 714
+
+--S 715 of 1285
+--d0:=D(m0,x)
+--E 715
+
+)clear all
+
+--S 716 of 1285
+t0:=1/(x^(7/2)*(a+b*x^2)^(5/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------
+--R +--------+
+--R 2 7 5 2 3 +-+ | 2
+--R (b x + 2a b x + a x )\|x \|b x + a
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1285
+--r0:=1/3/(a*x^(5/2)*(a+b*x^2)^(3/2))+11/6/(a^2*x^(5/2)*sqrt(a+b*x^2))-_
+--77/30*sqrt(a+b*x^2)/(a^3*x^(5/2))+77/10*b*sqrt(a+b*x^2)/(a^4*sqrt(x))-_
+--77/10*(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_
+--sqrt((a+b*x^2)/a)/(a^(13/4)*sqrt(a+b*x^2))+77/10*(-b)^(5/4)*_
+--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_
+--(a^(13/4)*sqrt(a+b*x^2))
+--E 717
+
+--S 718 of 1285
+--a0:=integrate(t0,x)
+--E 718
+
+--S 719 of 1285
+--m0:=a0-r0
+--E 719
+
+--S 720 of 1285
+--d0:=D(m0,x)
+--E 720
+
+)clear all
+
+--S 721 of 1285
+t0:=x^m*(a+b*x^2)^p
+--R
+--R
+--R m 2 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 721
+
+--S 722 of 1285
+--r0:=x^(1+m)*(a+b*x^2)^p*hypergeometric(1/2*(1+m),-p,1/2*(3+m),-b*x^2/a)/_
+--((1+m)*((a+b*x^2)/a)^p)
+--E 722
+
+--S 723 of 1285
+--a0:=integrate(t0,x)
+--E 723
+
+--S 724 of 1285
+--m0:=a0-r0
+--E 724
+
+--S 725 of 1285
+--d0:=D(m0,x)
+--E 725
+
+)clear all
+
+--S 726 of 1285
+t0:=x^7*(a+b*x^2)^p
+--R
+--R
+--R 7 2 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1285
+r0:=-1/2*a^3*(a+b*x^2)^(1+p)/(b^4*(1+p))+3/2*a^2*(a+b*x^2)^(2+p)/_
+ (b^4*(2+p))-3/2*a*(a+b*x^2)^(3+p)/(b^4*(3+p))+1/2*(a+b*x^2)^(4+p)/_
+ (b^4*(4+p))
+--R
+--R
+--R (2)
+--R 3 2 2 p + 4
+--R (p + 6p + 11p + 6)(b x + a)
+--R +
+--R 3 2 2 p + 3
+--R (- 3a p - 21a p - 42a p - 24a)(b x + a)
+--R +
+--R 2 3 2 2 2 2 2 p + 2
+--R (3a p + 24a p + 57a p + 36a )(b x + a)
+--R +
+--R 3 3 3 2 3 3 2 p + 1
+--R (- a p - 9a p - 26a p - 24a )(b x + a)
+--R /
+--R 4 4 4 3 4 2 4 4
+--R 2b p + 20b p + 70b p + 100b p + 48b
+--R Type: Expression(Integer)
+--E 727
+
+--S 728 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 4 2 4 4 8 3 3 3 2 3 6
+--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x
+--R +
+--R 2 2 2 2 2 4 3 2 4
+--R (- 3a b p - 3a b p)x + 6a b p x - 6a
+--R *
+--R 2
+--R p log(b x + a)
+--R %e
+--R /
+--R 4 4 4 3 4 2 4 4
+--R 2b p + 20b p + 70b p + 100b p + 48b
+--R Type: Union(Expression(Integer),...)
+--E 728
+
+--S 729 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 3 4 2 4 4 8 3 3 3 2 3 6
+--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x
+--R +
+--R 2 2 2 2 2 4 3 2 4
+--R (- 3a b p - 3a b p)x + 6a b p x - 6a
+--R *
+--R 2
+--R p log(b x + a)
+--R %e
+--R +
+--R 3 2 2 p + 4
+--R (- p - 6p - 11p - 6)(b x + a)
+--R +
+--R 3 2 2 p + 3
+--R (3a p + 21a p + 42a p + 24a)(b x + a)
+--R +
+--R 2 3 2 2 2 2 2 p + 2
+--R (- 3a p - 24a p - 57a p - 36a )(b x + a)
+--R +
+--R 3 3 3 2 3 3 2 p + 1
+--R (a p + 9a p + 26a p + 24a )(b x + a)
+--R /
+--R 4 4 4 3 4 2 4 4
+--R 2b p + 20b p + 70b p + 100b p + 48b
+--R Type: Expression(Integer)
+--E 729
+
+--S 730 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 730
+
+)clear all
+
+--S 731 of 1285
+t0:=x^5*(a+b*x^2)^p
+--R
+--R
+--R 5 2 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1285
+r0:=1/2*a^2*(a+b*x^2)^(1+p)/(b^3*(1+p))-a*(a+b*x^2)^(2+p)/(b^3*(2+p))+_
+ 1/2*(a+b*x^2)^(3+p)/(b^3*(3+p))
+--R
+--R
+--R (2)
+--R 2 2 p + 3 2 2 p + 2
+--R (p + 3p + 2)(b x + a) + (- 2a p - 8a p - 6a)(b x + a)
+--R +
+--R 2 2 2 2 2 p + 1
+--R (a p + 5a p + 6a )(b x + a)
+--R /
+--R 3 3 3 2 3 3
+--R 2b p + 12b p + 22b p + 12b
+--R Type: Expression(Integer)
+--E 732
+
+--S 733 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 3 3 6 2 2 2 4 2 2 3
+--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a )
+--R *
+--R 2
+--R p log(b x + a)
+--R %e
+--R /
+--R 3 3 3 2 3 3
+--R 2b p + 12b p + 22b p + 12b
+--R Type: Union(Expression(Integer),...)
+--E 733
+
+--S 734 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 2 3 3 6 2 2 2 4 2 2 3
+--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a )
+--R *
+--R 2
+--R p log(b x + a)
+--R %e
+--R +
+--R 2 2 p + 3 2 2 p + 2
+--R (- p - 3p - 2)(b x + a) + (2a p + 8a p + 6a)(b x + a)
+--R +
+--R 2 2 2 2 2 p + 1
+--R (- a p - 5a p - 6a )(b x + a)
+--R /
+--R 3 3 3 2 3 3
+--R 2b p + 12b p + 22b p + 12b
+--R Type: Expression(Integer)
+--E 734
+
+--S 735 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 735
+
+)clear all
+
+--S 736 of 1285
+t0:=x^4*(a+b*x^2)^p
+--R
+--R
+--R 4 2 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 736
+
+--S 737 of 1285
+--r0:=-3*a*x*(a+b*x^2)^(1+p)/(b^2*(3+2*p)*(5+2*p))+x^3*(a+b*x^2)^(1+p)/_
+-- (b*(5+2*p))+3*a^2*x*(a+b*x^2)^p*hypergeometric(1/2,-p,3/2,_
+-- -b*x^2/a)/(b^2*(3+2*p)*(5+2*p)*((a+b*x^2)/a)^p)
+--E 737
+
+--S 738 of 1285
+--a0:=integrate(t0,x)
+--E 738
+
+--S 739 of 1285
+--m0:=a0-r0
+--E 739
+
+--S 740 of 1285
+--d0:=normalize m0
+--E 740
+
+)clear all
+
+--S 741 of 1285
+t0:=x^3*(a+b*x^2)^p
+--R
+--R
+--R 3 2 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 741
+
+--S 742 of 1285
+r0:=-1/2*a*(a+b*x^2)^(1+p)/(b^2*(1+p))+1/2*(a+b*x^2)^(2+p)/(b^2*(2+p))
+--R
+--R
+--R 2 p + 2 2 p + 1
+--R (p + 1)(b x + a) + (- a p - 2a)(b x + a)
+--R (2) ----------------------------------------------------
+--R 2 2 2 2
+--R 2b p + 6b p + 4b
+--R Type: Expression(Integer)
+--E 742
+
+--S 743 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 2 2 4 2 2 p log(b x + a)
+--R ((b p + b )x + a b p x - a )%e
+--R (3) -----------------------------------------------
+--R 2 2 2 2
+--R 2b p + 6b p + 4b
+--R Type: Union(Expression(Integer),...)
+--E 743
+
+--S 744 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2
+--R 2 2 4 2 2 p log(b x + a)
+--R ((b p + b )x + a b p x - a )%e
+--R +
+--R 2 p + 2 2 p + 1
+--R (- p - 1)(b x + a) + (a p + 2a)(b x + a)
+--R /
+--R 2 2 2 2
+--R 2b p + 6b p + 4b
+--R Type: Expression(Integer)
+--E 744
+
+--S 745 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 745
+
+)clear all
+
+--S 746 of 1285
+t0:=x^2*(a+b*x^2)^p
+--R
+--R
+--R 2 2 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 746
+
+--S 747 of 1285
+--r0:=x*(a+b*x^2)^(1+p)/(b*(3+2*p))-a*x*(a+b*x^2)^p*_
+-- hypergeometric(1/2,-p,3/2,-b*x^2/a)/(b*(3+2*p)*((a+b*x^2)/a)^p)
+--E 747
+
+--S 748 of 1285
+--a0:=integrate(t0,x)
+--E 748
+
+--S 749 of 1285
+--m0:=a0-r0
+--E 749
+
+--S 750 of 1285
+--d0:=D(m0,x)
+--E 750
+
+)clear all
+
+--S 751 of 1285
+t0:=x*(a+b*x^2)^p
+--R
+--R
+--R 2 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 751
+
+--S 752 of 1285
+r0:=1/2*(a+b*x^2)^(1+p)/(b*(1+p))
+--R
+--R
+--R 2 p + 1
+--R (b x + a)
+--R (2) ---------------
+--R 2b p + 2b
+--R Type: Expression(Integer)
+--E 752
+
+--S 753 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 2 p log(b x + a)
+--R (b x + a)%e
+--R (3) ---------------------------
+--R 2b p + 2b
+--R Type: Union(Expression(Integer),...)
+--E 753
+
+--S 754 of 1285
+m0:=a0-r0
+--R
+--R
+--R 2
+--R 2 p log(b x + a) 2 p + 1
+--R (b x + a)%e - (b x + a)
+--R (4) ---------------------------------------------
+--R 2b p + 2b
+--R Type: Expression(Integer)
+--E 754
+
+--S 755 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 755
+
+)clear all
+
+--S 756 of 1285
+t0:=(a+b*x^2)^p
+--R
+--R
+--R 2 p
+--R (1) (b x + a)
+--R Type: Expression(Integer)
+--E 756
+
+--S 757 of 1285
+--r0:=x*(a+b*x^2)^p*hypergeometric(1/2,-p,3/2,-b*x^2/a)/((a+b*x^2)/a)^p
+--E 757
+
+--S 758 of 1285
+--a0:=integrate(t0,x)
+--E 758
+
+--S 759 of 1285
+--m0:=a0-r0
+--E 759
+
+--S 760 of 1285
+--d0:=D(m0,x)
+--E 760
+
+)clear all
+
+--S 761 of 1285
+t0:=(a+b*x^2)^p/x
+--R
+--R
+--R 2 p
+--R (b x + a)
+--R (1) -----------
+--R x
+--R Type: Expression(Integer)
+--E 761
+
+--S 762 of 1285
+--r0:=1/2*(a+b*x^2)^p*_
+-- hypergeometric(-p,-p,1-p,-a/(b*x^2))/(p*((a+b*x^2)/(b*x^2))^p)
+--E 762
+
+--S 763 of 1285
+--a0:=integrate(t0,x)
+--E 763
+
+--S 764 of 1285
+--m0:=a0-r0
+--E 764
+
+--S 765 of 1285
+--d0:=D(m0,x)
+--E 765
+
+)clear all
+
+--S 766 of 1285
+t0:=(a+b*x^2)^p/x^2
+--R
+--R
+--R 2 p
+--R (b x + a)
+--R (1) -----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 766
+
+--S 767 of 1285
+--r0:=-(a+b*x^2)^(1+p)/(a*x)+b*(1+2*p)*x*(a+b*x^2)^p*_
+-- hypergeometric(1/2,-p,3/2,-b*x^2/a)/(a*((a+b*x^2)/a)^p)
+--E 767
+
+--S 768 of 1285
+--a0:=integrate(t0,x)
+--E 768
+
+--S 769 of 1285
+--m0:=a0-r0
+--E 769
+
+--S 770 of 1285
+--d0:=D(m0,x)
+--E 770
+
+)clear all
+
+--S 771 of 1285
+t0:=(a+b*x^2)^p/x^3
+--R
+--R
+--R 2 p
+--R (b x + a)
+--R (1) -----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 771
+
+--S 772 of 1285
+--r0:=-1/2*(a+b*x^2)^(1+p)/(a*x^2)-1/2*b*p*(a+b*x^2)^(1+p)*_
+-- hypergeometric(1,1+p,2+p,(a+b*x^2)/a)/(a^2*(1+p))
+--E 772
+
+--S 773 of 1285
+--a0:=integrate(t0,x)
+--E 773
+
+--S 774 of 1285
+--m0:=a0-r0
+--E 774
+
+--S 775 of 1285
+--d0:=D(m0,x)
+--E 775
+
+)clear all
+
+--S 776 of 1285
+t0:=x^(9/2)*(a+b*x^2)^p
+--R
+--R
+--R 4 2 p +-+
+--R (1) x (b x + a) \|x
+--R Type: Expression(Integer)
+--E 776
+
+--S 777 of 1285
+--r0:=-14*a*x^(3/2)*(a+b*x^2)^(1+p)/(b^2*(7+4*p)*(11+4*p))+2*x^(7/2)*_
+-- (a+b*x^2)^(1+p)/(b*(11+4*p))+14*a^2*x^(3/2)*(a+b*x^2)^p*_
+-- hypergeometric(3/4,-p,7/4,-b*x^2/a)/(b^2*(7+4*p)*(11+4*p)*_
+-- ((a+b*x^2)/a)^p)
+--E 777
+
+--S 778 of 1285
+--a0:=integrate(t0,x)
+--E 778
+
+--S 779 of 1285
+--m0:=a0-r0
+--E 779
+
+--S 780 of 1285
+--d0:=D(m0,x)
+--E 780
+
+)clear all
+
+--S 781 of 1285
+t0:=x^(7/2)*(a+b*x^2)^p
+--R
+--R
+--R 3 2 p +-+
+--R (1) x (b x + a) \|x
+--R Type: Expression(Integer)
+--E 781
+
+--S 782 of 1285
+--r0:=2*x^(5/2)*(a+b*x^2)^(1+p)/(b*(9+4*p))-2*a*x^(5/2)*(a+b*x^2)^p*_
+-- hypergeometric(5/4,-p,9/4,-b*x^2/a)/(b*(9+4*p)*((a+b*x^2)/a)^p)
+--E 782
+
+--S 783 of 1285
+--a0:=integrate(t0,x)
+--E 783
+
+--S 784 of 1285
+--m0:=a0-r0
+--E 784
+
+--S 785 of 1285
+--d0:=D(m0,x)
+--E 785
+
+)clear all
+
+--S 786 of 1285
+t0:=x^(5/2)*(a+b*x^2)^p
+--R
+--R
+--R 2 2 p +-+
+--R (1) x (b x + a) \|x
+--R Type: Expression(Integer)
+--E 786
+
+--S 787 of 1285
+--r0:=2*x^(3/2)*(a+b*x^2)^(1+p)/(b*(7+4*p))-2*a*x^(3/2)*(a+b*x^2)^p*_
+-- hypergeometric(3/4,-p,7/4,-b*x^2/a)/(b*(7+4*p)*((a+b*x^2)/a)^p)
+--E 787
+
+--S 788 of 1285
+--a0:=integrate(t0,x)
+--E 788
+
+--S 789 of 1285
+--m0:=a0-r0
+--E 789
+
+--S 790 of 1285
+--d0:=D(m0,x)
+--E 790
+
+)clear all
+
+--S 791 of 1285
+t0:=x^(3/2)*(a+b*x^2)^p
+--R
+--R
+--R 2 p +-+
+--R (1) x (b x + a) \|x
+--R Type: Expression(Integer)
+--E 791
+
+--S 792 of 1285
+--r0:=2/5*x^(5/2)*(a+b*x^2)^p*hypergeometric(5/4,-p,9/4,-b*x^2/a)/_
+-- ((a+b*x^2)/a)^p
+--E 792
+
+--S 793 of 1285
+--a0:=integrate(t0,x)
+--E 793
+
+--S 794 of 1285
+--m0:=a0-r0
+--E 794
+
+--S 795 of 1285
+--d0:=D(m0,x)
+--E 795
+
+)clear all
+
+--S 796 of 1285
+t0:=x^(1/2)*(a+b*x^2)^p
+--R
+--R
+--R 2 p +-+
+--R (1) (b x + a) \|x
+--R Type: Expression(Integer)
+--E 796
+
+--S 797 of 1285
+--r0:=2/3*x^(3/2)*(a+b*x^2)^p*hypergeometric(3/4,-p,7/4,-b*x^2/a)/_
+-- ((a+b*x^2)/a)^p
+--E 797
+
+--S 798 of 1285
+--a0:=integrate(t0,x)
+--E 798
+
+--S 799 of 1285
+--m0:=a0-r0
+--E 799
+
+--S 800 of 1285
+--d0:=D(m0,x)
+--E 800
+
+)clear all
+
+--S 801 of 1285
+t0:=(a+b*x^2)^p/x^(1/2)
+--R
+--R
+--R 2 p
+--R (b x + a)
+--R (1) -----------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 801
+
+--S 802 of 1285
+--r0:=2*(a+b*x^2)^p*hypergeometric(1/4,-p,5/4,-b*x^2/a)*sqrt(x)/((a+b*x^2)/a)^p
+--E 802
+
+--S 803 of 1285
+--a0:=integrate(t0,x)
+--E 803
+
+--S 804 of 1285
+--m0:=a0-r0
+--E 804
+
+--S 805 of 1285
+--d0:=D(m0,x)
+--E 805
+
+)clear all
+
+--S 806 of 1285
+t0:=(a+b*x^2)^p/x^(3/2)
+--R
+--R
+--R 2 p
+--R (b x + a)
+--R (1) -----------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 806
+
+--S 807 of 1285
+--r0:=2/3*b*(3+4*p)*x^(3/2)*(a+b*x^2)^p*_
+-- hypergeometric(3/4,-p,7/4,-b*x^2/a)/(a*((a+b*x^2)/a)^p)-_
+-- 2*(a+b*x^2)^(1+p)/(a*sqrt(x))
+--E 807
+
+--S 808 of 1285
+--a0:=integrate(t0,x)
+--E 808
+
+--S 809 of 1285
+--m0:=a0-r0
+--E 809
+
+--S 810 of 1285
+--d0:=D(m0,x)
+--E 810
+
+)clear all
+
+--S 811 of 1285
+t0:=(a+b*x^2)^p/x^(5/2)
+--R
+--R
+--R 2 p
+--R (b x + a)
+--R (1) -----------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 811
+
+--S 812 of 1285
+--r0:=-2/3*(a+b*x^2)^(1+p)/(a*x^(3/2))+2/3*b*(1+4*p)*(a+b*x^2)^p*_
+-- hypergeometric(1/4,-p,5/4,-b*x^2/a)*sqrt(x)/(a*((a+b*x^2)/a)^p)
+--E 812
+
+--S 813 of 1285
+--a0:=integrate(t0,x)
+--E 813
+
+--S 814 of 1285
+--m0:=a0-r0
+--E 814
+
+--S 815 of 1285
+--d0:=D(m0,x)
+--E 815
+
+)clear all
+
+--S 816 of 1285
+t0:=(a+b*x^2)^p/x^(7/2)
+--R
+--R
+--R 2 p
+--R (b x + a)
+--R (1) -----------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 816
+
+--S 817 of 1285
+--r0:=-2/5*(a+b*x^2)^(1+p)/(a*x^(5/2))-2/15*b^2*(1-4*p)*(3+4*p)*x^(3/2)*_
+-- (a+b*x^2)^p*hypergeometric(3/4,-p,7/4,-b*x^2/a)/(a^2*((a+b*x^2)/a)^p)+_
+-- 2/5*b*(1-4*p)*(a+b*x^2)^(1+p)/(a^2*sqrt(x))
+--E 817
+
+--S 818 of 1285
+--a0:=integrate(t0,x)
+--E 818
+
+--S 819 of 1285
+--m0:=a0-r0
+--E 819
+
+--S 820 of 1285
+--d0:=D(m0,x)
+--E 820
+
+)clear all
+
+--S 821 of 1285
+t0:=x^m*(a+b*x^3)
+--R
+--R
+--R 3 m
+--R (1) (b x + a)x
+--R Type: Expression(Integer)
+--E 821
+
+--S 822 of 1285
+r0:=a*x^(1+m)/(1+m)+b*x^(4+m)/(4+m)
+--R
+--R
+--R m + 4 m + 1
+--R (b m + b)x + (a m + 4a)x
+--R (2) ----------------------------------
+--R 2
+--R m + 5m + 4
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 m log(x)
+--R ((b m + b)x + (a m + 4a)x)%e
+--R (3) -------------------------------------
+--R 2
+--R m + 5m + 4
+--R Type: Union(Expression(Integer),...)
+--E 823
+
+--S 824 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 m log(x) m + 4
+--R ((b m + b)x + (a m + 4a)x)%e + (- b m - b)x
+--R +
+--R m + 1
+--R (- a m - 4a)x
+--R /
+--R 2
+--R m + 5m + 4
+--R Type: Expression(Integer)
+--E 824
+
+--S 825 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 825
+
+)clear all
+
+--S 826 of 1285
+t0:=x^3*(a+b*x^3)
+--R
+--R
+--R 6 3
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 826
+
+--S 827 of 1285
+r0:=1/4*a*x^4+1/7*b*x^7
+--R
+--R
+--R 1 7 1 4
+--R (2) - b x + - a x
+--R 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 827
+
+--S 828 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 7 1 4
+--R (3) - b x + - a x
+--R 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 828
+
+--S 829 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 829
+
+--S 830 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 830
+
+)clear all
+
+--S 831 of 1285
+t0:=x^2*(a+b*x^3)
+--R
+--R
+--R 5 2
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 831
+
+--S 832 of 1285
+r0:=1/3*a*x^3+1/6*b*x^6
+--R
+--R
+--R 1 6 1 3
+--R (2) - b x + - a x
+--R 6 3
+--R Type: Polynomial(Fraction(Integer))
+--E 832
+
+--S 833 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 6 1 3
+--R (3) - b x + - a x
+--R 6 3
+--R Type: Polynomial(Fraction(Integer))
+--E 833
+
+--S 834 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 834
+
+--S 835 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 835
+
+)clear all
+
+--S 836 of 1285
+t0:=x*(a+b*x^3)
+--R
+--R
+--R 4
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 836
+
+--S 837 of 1285
+r0:=1/2*a*x^2+1/5*b*x^5
+--R
+--R
+--R 1 5 1 2
+--R (2) - b x + - a x
+--R 5 2
+--R Type: Polynomial(Fraction(Integer))
+--E 837
+
+--S 838 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 1 2
+--R (3) - b x + - a x
+--R 5 2
+--R Type: Polynomial(Fraction(Integer))
+--E 838
+
+--S 839 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 839
+
+--S 840 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 840
+
+)clear all
+
+--S 841 of 1285
+t0:=a+b*x^3
+--R
+--R
+--R 3
+--R (1) b x + a
+--R Type: Polynomial(Integer)
+--E 841
+
+--S 842 of 1285
+r0:=a*x+1/4*b*x^4
+--R
+--R
+--R 1 4
+--R (2) - b x + a x
+--R 4
+--R Type: Polynomial(Fraction(Integer))
+--E 842
+
+--S 843 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 4
+--R (3) - b x + a x
+--R 4
+--R Type: Polynomial(Fraction(Integer))
+--E 843
+
+--S 844 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 844
+
+--S 845 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 845
+
+)clear all
+
+--S 846 of 1285
+t0:=(a+b*x^3)/x
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 846
+
+--S 847 of 1285
+r0:=1/3*b*x^3+a*log(x)
+--R
+--R
+--R 3
+--R 3a log(x) + b x
+--R (2) ----------------
+--R 3
+--R Type: Expression(Integer)
+--E 847
+
+--S 848 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R 3a log(x) + b x
+--R (3) ----------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 848
+
+--S 849 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 850
+
+)clear all
+
+--S 851 of 1285
+t0:=(a+b*x^3)/x^2
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 851
+
+--S 852 of 1285
+r0:=-a/x+1/2*b*x^2
+--R
+--R
+--R 3
+--R b x - 2a
+--R (2) ---------
+--R 2x
+--R Type: Fraction(Polynomial(Integer))
+--E 852
+
+--S 853 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R b x - 2a
+--R (3) ---------
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 853
+
+--S 854 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 854
+
+--S 855 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 855
+
+)clear all
+
+--S 856 of 1285
+t0:=(a+b*x^3)/x^3
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 856
+
+--S 857 of 1285
+r0:=-1/2*a/x^2+b*x
+--R
+--R
+--R 3 1
+--R b x - - a
+--R 2
+--R (2) ----------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 857
+
+--S 858 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R 2b x - a
+--R (3) ---------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 858
+
+--S 859 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 859
+
+--S 860 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 860
+
+)clear all
+
+--S 861 of 1285
+t0:=(a+b*x^3)/x^4
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 861
+
+--S 862 of 1285
+r0:=-1/3*a/x^3+b*log(x)
+--R
+--R
+--R 3
+--R 3b x log(x) - a
+--R (2) ---------------
+--R 3
+--R 3x
+--R Type: Expression(Integer)
+--E 862
+
+--S 863 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R 3b x log(x) - a
+--R (3) ---------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 863
+
+--S 864 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 864
+
+--S 865 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 865
+
+)clear all
+
+--S 866 of 1285
+t0:=(a+b*x^3)/x^5
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 866
+
+--S 867 of 1285
+r0:=-1/4*a/x^4-b/x
+--R
+--R
+--R 3 1
+--R - b x - - a
+--R 4
+--R (2) ------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 867
+
+--S 868 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R - 4b x - a
+--R (3) -----------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 868
+
+--S 869 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 870
+
+)clear all
+
+--S 871 of 1285
+t0:=(a+b*x^3)/x^6
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 871
+
+--S 872 of 1285
+r0:=-1/5*a/x^5-1/2*b/x^2
+--R
+--R
+--R 1 3 1
+--R - - b x - - a
+--R 2 5
+--R (2) --------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 872
+
+--S 873 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R - 5b x - 2a
+--R (3) ------------
+--R 5
+--R 10x
+--R Type: Union(Expression(Integer),...)
+--E 873
+
+--S 874 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 875
+
+)clear all
+
+--S 876 of 1285
+t0:=(a+b*x^3)/x^7
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 876
+
+--S 877 of 1285
+r0:=-1/6*a/x^6-1/3*b/x^3
+--R
+--R
+--R 1 3 1
+--R - - b x - - a
+--R 3 6
+--R (2) --------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 877
+
+--S 878 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R - 2b x - a
+--R (3) -----------
+--R 6
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 878
+
+--S 879 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 880
+
+)clear all
+
+--S 881 of 1285
+t0:=(a+b*x^3)/x^8
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 881
+
+--S 882 of 1285
+r0:=-1/7*a/x^7-1/4*b/x^4
+--R
+--R
+--R 1 3 1
+--R - - b x - - a
+--R 4 7
+--R (2) --------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 882
+
+--S 883 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R - 7b x - 4a
+--R (3) ------------
+--R 7
+--R 28x
+--R Type: Union(Expression(Integer),...)
+--E 883
+
+--S 884 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 884
+
+--S 885 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 885
+
+)clear all
+
+--S 886 of 1285
+t0:=x^m*(a+b*x^3)^2
+--R
+--R
+--R 2 6 3 2 m
+--R (1) (b x + 2a b x + a )x
+--R Type: Expression(Integer)
+--E 886
+
+--S 887 of 1285
+r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(4+m)/(4+m)+b^2*x^(7+m)/(7+m)
+--R
+--R
+--R (2)
+--R 2 2 2 2 m + 7 2 m + 4
+--R (b m + 5b m + 4b )x + (2a b m + 16a b m + 14a b)x
+--R +
+--R 2 2 2 2 m + 1
+--R (a m + 11a m + 28a )x
+--R /
+--R 3 2
+--R m + 12m + 39m + 28
+--R Type: Expression(Integer)
+--E 887
+
+--S 888 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 7 2 4
+--R (b m + 5b m + 4b )x + (2a b m + 16a b m + 14a b)x
+--R +
+--R 2 2 2 2
+--R (a m + 11a m + 28a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 3 2
+--R m + 12m + 39m + 28
+--R Type: Union(Expression(Integer),...)
+--E 888
+
+--S 889 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 7 2 4
+--R (b m + 5b m + 4b )x + (2a b m + 16a b m + 14a b)x
+--R +
+--R 2 2 2 2
+--R (a m + 11a m + 28a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 2 2 2 m + 7 2 m + 4
+--R (- b m - 5b m - 4b )x + (- 2a b m - 16a b m - 14a b)x
+--R +
+--R 2 2 2 2 m + 1
+--R (- a m - 11a m - 28a )x
+--R /
+--R 3 2
+--R m + 12m + 39m + 28
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 890
+
+)clear all
+
+--S 891 of 1285
+t0:=x^4*(a+b*x^3)^2
+--R
+--R
+--R 2 10 7 2 4
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 891
+
+--S 892 of 1285
+r0:=1/5*a^2*x^5+1/4*a*b*x^8+1/11*b^2*x^11
+--R
+--R
+--R 1 2 11 1 8 1 2 5
+--R (2) -- b x + - a b x + - a x
+--R 11 4 5
+--R Type: Polynomial(Fraction(Integer))
+--E 892
+
+--S 893 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 11 1 8 1 2 5
+--R (3) -- b x + - a b x + - a x
+--R 11 4 5
+--R Type: Polynomial(Fraction(Integer))
+--E 893
+
+--S 894 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 894
+
+--S 895 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 895
+
+)clear all
+
+--S 896 of 1285
+t0:=x^3*(a+b*x^3)^2
+--R
+--R
+--R 2 9 6 2 3
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 896
+
+--S 897 of 1285
+r0:=1/4*a^2*x^4+2/7*a*b*x^7+1/10*b^2*x^10
+--R
+--R
+--R 1 2 10 2 7 1 2 4
+--R (2) -- b x + - a b x + - a x
+--R 10 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 897
+
+--S 898 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 10 2 7 1 2 4
+--R (3) -- b x + - a b x + - a x
+--R 10 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 898
+
+--S 899 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 899
+
+--S 900 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 900
+
+)clear all
+
+--S 901 of 1285
+t0:=x^2*(a+b*x^3)^2
+--R
+--R
+--R 2 8 5 2 2
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 901
+
+--S 902 of 1285
+r0:=1/9*(a+b*x^3)^3/b
+--R
+--R
+--R 1 3 9 1 2 6 1 2 3 1 3
+--R - b x + - a b x + - a b x + - a
+--R 9 3 3 9
+--R (2) -----------------------------------
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 902
+
+--S 903 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 9 1 6 1 2 3
+--R (3) - b x + - a b x + - a x
+--R 9 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 903
+
+--S 904 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 3
+--R - a
+--R 9
+--R (4) - ----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 904
+
+--S 905 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 905
+
+)clear all
+
+--S 906 of 1285
+t0:=x*(a+b*x^3)^2
+--R
+--R
+--R 2 7 4 2
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 906
+
+--S 907 of 1285
+r0:=1/2*a^2*x^2+2/5*a*b*x^5+1/8*b^2*x^8
+--R
+--R
+--R 1 2 8 2 5 1 2 2
+--R (2) - b x + - a b x + - a x
+--R 8 5 2
+--R Type: Polynomial(Fraction(Integer))
+--E 907
+
+--S 908 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 8 2 5 1 2 2
+--R (3) - b x + - a b x + - a x
+--R 8 5 2
+--R Type: Polynomial(Fraction(Integer))
+--E 908
+
+--S 909 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 909
+
+--S 910 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 910
+
+)clear all
+
+--S 911 of 1285
+t0:=(a+b*x^3)^2
+--R
+--R
+--R 2 6 3 2
+--R (1) b x + 2a b x + a
+--R Type: Polynomial(Integer)
+--E 911
+
+--S 912 of 1285
+r0:=a^2*x+1/2*a*b*x^4+1/7*b^2*x^7
+--R
+--R
+--R 1 2 7 1 4 2
+--R (2) - b x + - a b x + a x
+--R 7 2
+--R Type: Polynomial(Fraction(Integer))
+--E 912
+
+--S 913 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 7 1 4 2
+--R (3) - b x + - a b x + a x
+--R 7 2
+--R Type: Polynomial(Fraction(Integer))
+--E 913
+
+--S 914 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 914
+
+--S 915 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 915
+
+)clear all
+
+--S 916 of 1285
+t0:=(a+b*x^3)^2/x
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 916
+
+--S 917 of 1285
+r0:=2/3*a*b*x^3+1/6*b^2*x^6+a^2*log(x)
+--R
+--R
+--R 2 2 6 3
+--R 6a log(x) + b x + 4a b x
+--R (2) --------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 917
+
+--S 918 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 6 3
+--R 6a log(x) + b x + 4a b x
+--R (3) --------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 918
+
+--S 919 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 919
+
+--S 920 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 920
+
+)clear all
+
+--S 921 of 1285
+t0:=(a+b*x^3)^2/x^2
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 921
+
+--S 922 of 1285
+r0:=-a^2/x+a*b*x^2+1/5*b^2*x^5
+--R
+--R
+--R 2 6 3 2
+--R b x + 5a b x - 5a
+--R (2) --------------------
+--R 5x
+--R Type: Fraction(Polynomial(Integer))
+--E 922
+
+--S 923 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R b x + 5a b x - 5a
+--R (3) --------------------
+--R 5x
+--R Type: Union(Expression(Integer),...)
+--E 923
+
+--S 924 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 924
+
+--S 925 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 925
+
+)clear all
+
+--S 926 of 1285
+t0:=(a+b*x^3)^2/x^3
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 926
+
+--S 927 of 1285
+r0:=-1/2*a^2/x^2+2*a*b*x+1/4*b^2*x^4
+--R
+--R
+--R 1 2 6 3 1 2
+--R - b x + 2a b x - - a
+--R 4 2
+--R (2) -----------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 927
+
+--S 928 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R b x + 8a b x - 2a
+--R (3) --------------------
+--R 2
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 928
+
+--S 929 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 929
+
+--S 930 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 930
+
+)clear all
+
+--S 931 of 1285
+t0:=(a+b*x^3)^2/x^4
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 931
+
+--S 932 of 1285
+r0:=-1/3*a^2/x^3+1/3*b^2*x^3+2*a*b*log(x)
+--R
+--R
+--R 3 2 6 2
+--R 6a b x log(x) + b x - a
+--R (2) -------------------------
+--R 3
+--R 3x
+--R Type: Expression(Integer)
+--E 932
+
+--S 933 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 6 2
+--R 6a b x log(x) + b x - a
+--R (3) -------------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 933
+
+--S 934 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 935
+
+)clear all
+
+--S 936 of 1285
+t0:=(a+b*x^3)^2/x^5
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 936
+
+--S 937 of 1285
+r0:=-1/4*a^2/x^4-2*a*b/x+1/2*b^2*x^2
+--R
+--R
+--R 1 2 6 3 1 2
+--R - b x - 2a b x - - a
+--R 2 4
+--R (2) -----------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 937
+
+--S 938 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R 2b x - 8a b x - a
+--R (3) --------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 938
+
+--S 939 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 940
+
+)clear all
+
+--S 941 of 1285
+t0:=(a+b*x^3)^2/x^6
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 941
+
+--S 942 of 1285
+r0:=-1/5*a^2/x^5-a*b/x^2+b^2*x
+--R
+--R
+--R 2 6 3 1 2
+--R b x - a b x - - a
+--R 5
+--R (2) --------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 942
+
+--S 943 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R 5b x - 5a b x - a
+--R (3) --------------------
+--R 5
+--R 5x
+--R Type: Union(Expression(Integer),...)
+--E 943
+
+--S 944 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 945
+
+)clear all
+
+--S 946 of 1285
+t0:=(a+b*x^3)^2/x^7
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 946
+
+--S 947 of 1285
+r0:=-1/6*a^2/x^6-2/3*a*b/x^3+b^2*log(x)
+--R
+--R
+--R 2 6 3 2
+--R 6b x log(x) - 4a b x - a
+--R (2) --------------------------
+--R 6
+--R 6x
+--R Type: Expression(Integer)
+--E 947
+
+--S 948 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R 6b x log(x) - 4a b x - a
+--R (3) --------------------------
+--R 6
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 948
+
+--S 949 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 950
+
+)clear all
+
+--S 951 of 1285
+t0:=(a+b*x^3)^2/x^8
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 951
+
+--S 952 of 1285
+r0:=-1/7*a^2/x^7-1/2*a*b/x^4-b^2/x
+--R
+--R
+--R 2 6 1 3 1 2
+--R - b x - - a b x - - a
+--R 2 7
+--R (2) ------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 952
+
+--S 953 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R - 14b x - 7a b x - 2a
+--R (3) ------------------------
+--R 7
+--R 14x
+--R Type: Union(Expression(Integer),...)
+--E 953
+
+--S 954 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 954
+
+--S 955 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 955
+
+)clear all
+
+--S 956 of 1285
+t0:=(a+b*x^3)^2/x^9
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 956
+
+--S 957 of 1285
+r0:=-1/8*a^2/x^8-2/5*a*b/x^5-1/2*b^2/x^2
+--R
+--R
+--R 1 2 6 2 3 1 2
+--R - - b x - - a b x - - a
+--R 2 5 8
+--R (2) --------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 957
+
+--S 958 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R - 20b x - 16a b x - 5a
+--R (3) -------------------------
+--R 8
+--R 40x
+--R Type: Union(Expression(Integer),...)
+--E 958
+
+--S 959 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 960
+
+)clear all
+
+--S 961 of 1285
+t0:=(a+b*x^3)^2/x^10
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 961
+
+--S 962 of 1285
+r0:=-1/9*(a+b*x^3)^3/(a*x^9)
+--R
+--R
+--R 1 3 9 1 2 6 1 2 3 1 3
+--R - - b x - - a b x - - a b x - - a
+--R 9 3 3 9
+--R (2) -------------------------------------
+--R 9
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 962
+
+--S 963 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R - 3b x - 3a b x - a
+--R (3) ----------------------
+--R 9
+--R 9x
+--R Type: Union(Expression(Integer),...)
+--E 963
+
+--S 964 of 1285
+m0:=a0-r0
+--R
+--R
+--R 3
+--R b
+--R (4) --
+--R 9a
+--R Type: Expression(Integer)
+--E 964
+
+--S 965 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 965
+
+)clear all
+
+--S 966 of 1285
+t0:=(a+b*x^3)^2/x^11
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 966
+
+--S 967 of 1285
+r0:=-1/10*a^2/x^10-2/7*a*b/x^7-1/4*b^2/x^4
+--R
+--R
+--R 1 2 6 2 3 1 2
+--R - - b x - - a b x - -- a
+--R 4 7 10
+--R (2) ---------------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 967
+
+--S 968 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R - 35b x - 40a b x - 14a
+--R (3) --------------------------
+--R 10
+--R 140x
+--R Type: Union(Expression(Integer),...)
+--E 968
+
+--S 969 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 969
+
+--S 970 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 970
+
+)clear all
+
+--S 971 of 1285
+t0:=(a+b*x^3)^2/x^12
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 12
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 971
+
+--S 972 of 1285
+r0:=-1/11*a^2/x^11-1/4*a*b/x^8-1/5*b^2/x^5
+--R
+--R
+--R 1 2 6 1 3 1 2
+--R - - b x - - a b x - -- a
+--R 5 4 11
+--R (2) ---------------------------
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 972
+
+--S 973 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R - 44b x - 55a b x - 20a
+--R (3) --------------------------
+--R 11
+--R 220x
+--R Type: Union(Expression(Integer),...)
+--E 973
+
+--S 974 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 975
+
+)clear all
+
+--S 976 of 1285
+t0:=(a+b*x^3)^2/x^13
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 976
+
+--S 977 of 1285
+r0:=-1/12*a^2/x^12-2/9*a*b/x^9-1/6*b^2/x^6
+--R
+--R
+--R 1 2 6 2 3 1 2
+--R - - b x - - a b x - -- a
+--R 6 9 12
+--R (2) ---------------------------
+--R 12
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 977
+
+--S 978 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2
+--R - 6b x - 8a b x - 3a
+--R (3) -----------------------
+--R 12
+--R 36x
+--R Type: Union(Expression(Integer),...)
+--E 978
+
+--S 979 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 979
+
+--S 980 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 980
+
+)clear all
+
+--S 981 of 1285
+t0:=x^m*(a+b*x^3)^3
+--R
+--R
+--R 3 9 2 6 2 3 3 m
+--R (1) (b x + 3a b x + 3a b x + a )x
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1285
+r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(4+m)/(4+m)+3*a*b^2*x^(7+m)/(7+m)+_
+ b^3*x^(10+m)/(10+m)
+--R
+--R
+--R (2)
+--R 3 3 3 2 3 3 m + 10
+--R (b m + 12b m + 39b m + 28b )x
+--R +
+--R 2 3 2 2 2 2 m + 7
+--R (3a b m + 45a b m + 162a b m + 120a b )x
+--R +
+--R 2 3 2 2 2 2 m + 4
+--R (3a b m + 54a b m + 261a b m + 210a b)x
+--R +
+--R 3 3 3 2 3 3 m + 1
+--R (a m + 21a m + 138a m + 280a )x
+--R /
+--R 4 3 2
+--R m + 22m + 159m + 418m + 280
+--R Type: Expression(Integer)
+--E 982
+
+--S 983 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 3 2 3 3 10
+--R (b m + 12b m + 39b m + 28b )x
+--R +
+--R 2 3 2 2 2 2 7
+--R (3a b m + 45a b m + 162a b m + 120a b )x
+--R +
+--R 2 3 2 2 2 2 4
+--R (3a b m + 54a b m + 261a b m + 210a b)x
+--R +
+--R 3 3 3 2 3 3
+--R (a m + 21a m + 138a m + 280a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 4 3 2
+--R m + 22m + 159m + 418m + 280
+--R Type: Union(Expression(Integer),...)
+--E 983
+
+--S 984 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 3 2 3 3 10
+--R (b m + 12b m + 39b m + 28b )x
+--R +
+--R 2 3 2 2 2 2 7
+--R (3a b m + 45a b m + 162a b m + 120a b )x
+--R +
+--R 2 3 2 2 2 2 4
+--R (3a b m + 54a b m + 261a b m + 210a b)x
+--R +
+--R 3 3 3 2 3 3
+--R (a m + 21a m + 138a m + 280a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 3 3 3 2 3 3 m + 10
+--R (- b m - 12b m - 39b m - 28b )x
+--R +
+--R 2 3 2 2 2 2 m + 7
+--R (- 3a b m - 45a b m - 162a b m - 120a b )x
+--R +
+--R 2 3 2 2 2 2 m + 4
+--R (- 3a b m - 54a b m - 261a b m - 210a b)x
+--R +
+--R 3 3 3 2 3 3 m + 1
+--R (- a m - 21a m - 138a m - 280a )x
+--R /
+--R 4 3 2
+--R m + 22m + 159m + 418m + 280
+--R Type: Expression(Integer)
+--E 984
+
+--S 985 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 985
+
+)clear all
+
+--S 986 of 1285
+t0:=x^14*(a+b*x^3)^3
+--R
+--R
+--R 3 23 2 20 2 17 3 14
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 986
+
+--S 987 of 1285
+r0:=1/15*a^3*x^15+1/6*a^2*b*x^18+1/7*a*b^2*x^21+1/24*b^3*x^24
+--R
+--R
+--R 1 3 24 1 2 21 1 2 18 1 3 15
+--R (2) -- b x + - a b x + - a b x + -- a x
+--R 24 7 6 15
+--R Type: Polynomial(Fraction(Integer))
+--E 987
+
+--S 988 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 24 1 2 21 1 2 18 1 3 15
+--R (3) -- b x + - a b x + - a b x + -- a x
+--R 24 7 6 15
+--R Type: Polynomial(Fraction(Integer))
+--E 988
+
+--S 989 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 989
+
+--S 990 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 990
+
+)clear all
+
+--S 991 of 1285
+t0:=x^11*(a+b*x^3)^3
+--R
+--R
+--R 3 20 2 17 2 14 3 11
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 991
+
+--S 992 of 1285
+r0:=1/12*a^3*x^12+1/5*a^2*b*x^15+1/6*a*b^2*x^18+1/21*b^3*x^21
+--R
+--R
+--R 1 3 21 1 2 18 1 2 15 1 3 12
+--R (2) -- b x + - a b x + - a b x + -- a x
+--R 21 6 5 12
+--R Type: Polynomial(Fraction(Integer))
+--E 992
+
+--S 993 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 21 1 2 18 1 2 15 1 3 12
+--R (3) -- b x + - a b x + - a b x + -- a x
+--R 21 6 5 12
+--R Type: Polynomial(Fraction(Integer))
+--E 993
+
+--S 994 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 994
+
+--S 995 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 995
+
+)clear all
+
+--S 996 of 1285
+t0:=x^8*(a+b*x^3)^3
+--R
+--R
+--R 3 17 2 14 2 11 3 8
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 996
+
+--S 997 of 1285
+r0:=1/9*a^3*x^9+1/4*a^2*b*x^12+1/5*a*b^2*x^15+1/18*b^3*x^18
+--R
+--R
+--R 1 3 18 1 2 15 1 2 12 1 3 9
+--R (2) -- b x + - a b x + - a b x + - a x
+--R 18 5 4 9
+--R Type: Polynomial(Fraction(Integer))
+--E 997
+
+--S 998 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 18 1 2 15 1 2 12 1 3 9
+--R (3) -- b x + - a b x + - a b x + - a x
+--R 18 5 4 9
+--R Type: Polynomial(Fraction(Integer))
+--E 998
+
+--S 999 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 999
+
+--S 1000 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1000
+
+)clear all
+
+--S 1001 of 1285
+t0:=x^5*(a+b*x^3)^3
+--R
+--R
+--R 3 14 2 11 2 8 3 5
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 1001
+
+--S 1002 of 1285
+r0:=-1/12*a*(a+b*x^3)^4/b^2+1/15*(a+b*x^3)^5/b^2
+--R
+--R
+--R 1 5 15 1 4 12 1 2 3 9 1 3 2 6 1 5
+--R -- b x + - a b x + - a b x + - a b x - -- a
+--R 15 4 3 6 60
+--R (2) --------------------------------------------------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1002
+
+--S 1003 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 15 1 2 12 1 2 9 1 3 6
+--R (3) -- b x + - a b x + - a b x + - a x
+--R 15 4 3 6
+--R Type: Polynomial(Fraction(Integer))
+--E 1003
+
+--S 1004 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 5
+--R -- a
+--R 60
+--R (4) -----
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1004
+
+--S 1005 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1005
+
+)clear all
+
+--S 1006 of 1285
+t0:=x^2*(a+b*x^3)^3
+--R
+--R
+--R 3 11 2 8 2 5 3 2
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 1006
+
+--S 1007 of 1285
+r0:=1/12*(a+b*x^3)^4/b
+--R
+--R
+--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4
+--R -- b x + - a b x + - a b x + - a b x + -- a
+--R 12 3 2 3 12
+--R (2) -------------------------------------------------
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1007
+
+--S 1008 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 12 1 2 9 1 2 6 1 3 3
+--R (3) -- b x + - a b x + - a b x + - a x
+--R 12 3 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 1008
+
+--S 1009 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 4
+--R -- a
+--R 12
+--R (4) - -----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1009
+
+--S 1010 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1010
+
+)clear all
+
+--S 1011 of 1285
+t0:=(a+b*x^3)^3/x
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1011
+
+--S 1012 of 1285
+r0:=a^2*b*x^3+1/2*a*b^2*x^6+1/9*b^3*x^9+a^3*log(x)
+--R
+--R
+--R 3 3 9 2 6 2 3
+--R 18a log(x) + 2b x + 9a b x + 18a b x
+--R (2) ---------------------------------------
+--R 18
+--R Type: Expression(Integer)
+--E 1012
+
+--S 1013 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 9 2 6 2 3
+--R 18a log(x) + 2b x + 9a b x + 18a b x
+--R (3) ---------------------------------------
+--R 18
+--R Type: Union(Expression(Integer),...)
+--E 1013
+
+--S 1014 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1014
+
+--S 1015 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1015
+
+)clear all
+
+--S 1016 of 1285
+t0:=(a+b*x^3)^3/x^4
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1016
+
+--S 1017 of 1285
+r0:=-1/3*a^3/x^3+a*b^2*x^3+1/6*b^3*x^6+3*a^2*b*log(x)
+--R
+--R
+--R 2 3 3 9 2 6 3
+--R 18a b x log(x) + b x + 6a b x - 2a
+--R (2) -------------------------------------
+--R 3
+--R 6x
+--R Type: Expression(Integer)
+--E 1017
+
+--S 1018 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 3 9 2 6 3
+--R 18a b x log(x) + b x + 6a b x - 2a
+--R (3) -------------------------------------
+--R 3
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 1018
+
+--S 1019 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1019
+
+--S 1020 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1020
+
+)clear all
+
+--S 1021 of 1285
+t0:=(a+b*x^3)^3/x^7
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1021
+
+--S 1022 of 1285
+r0:=-1/6*a^3/x^6-a^2*b/x^3+1/3*b^3*x^3+3*a*b^2*log(x)
+--R
+--R
+--R 2 6 3 9 2 3 3
+--R 18a b x log(x) + 2b x - 6a b x - a
+--R (2) -------------------------------------
+--R 6
+--R 6x
+--R Type: Expression(Integer)
+--E 1022
+
+--S 1023 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 9 2 3 3
+--R 18a b x log(x) + 2b x - 6a b x - a
+--R (3) -------------------------------------
+--R 6
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 1023
+
+--S 1024 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1024
+
+--S 1025 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1025
+
+)clear all
+
+--S 1026 of 1285
+t0:=(a+b*x^3)^3/x^10
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1026
+
+--S 1027 of 1285
+r0:=-1/9*a^3/x^9-1/2*a^2*b/x^6-a*b^2/x^3+b^3*log(x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R 18b x log(x) - 18a b x - 9a b x - 2a
+--R (2) ---------------------------------------
+--R 9
+--R 18x
+--R Type: Expression(Integer)
+--E 1027
+
+--S 1028 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R 18b x log(x) - 18a b x - 9a b x - 2a
+--R (3) ---------------------------------------
+--R 9
+--R 18x
+--R Type: Union(Expression(Integer),...)
+--E 1028
+
+--S 1029 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1029
+
+--S 1030 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1030
+
+)clear all
+
+--S 1031 of 1285
+t0:=(a+b*x^3)^3/x^13
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1031
+
+--S 1032 of 1285
+r0:=-1/12*(a+b*x^3)^4/(a*x^12)
+--R
+--R
+--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4
+--R - -- b x - - a b x - - a b x - - a b x - -- a
+--R 12 3 2 3 12
+--R (2) ---------------------------------------------------
+--R 12
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1032
+
+--S 1033 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R - 4b x - 6a b x - 4a b x - a
+--R (3) --------------------------------
+--R 12
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 1033
+
+--S 1034 of 1285
+m0:=a0-r0
+--R
+--R
+--R 4
+--R b
+--R (4) ---
+--R 12a
+--R Type: Expression(Integer)
+--E 1034
+
+--S 1035 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1035
+
+)clear all
+
+--S 1036 of 1285
+t0:=(a+b*x^3)^3/x^16
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 16
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1036
+
+--S 1037 of 1285
+r0:=-1/15*a^3/x^15-1/4*a^2*b/x^12-1/3*a*b^2/x^9-1/6*b^3/x^6
+--R
+--R
+--R 1 3 9 1 2 6 1 2 3 1 3
+--R - - b x - - a b x - - a b x - -- a
+--R 6 3 4 15
+--R (2) --------------------------------------
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1037
+
+--S 1038 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R - 10b x - 20a b x - 15a b x - 4a
+--R (3) ------------------------------------
+--R 15
+--R 60x
+--R Type: Union(Expression(Integer),...)
+--E 1038
+
+--S 1039 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1039
+
+--S 1040 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1040
+
+)clear all
+
+--S 1041 of 1285
+t0:=(a+b*x^3)^3/x^19
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1041
+
+--S 1042 of 1285
+r0:=-1/18*a^3/x^18-1/5*a^2*b/x^15-1/4*a*b^2/x^12-1/9*b^3/x^9
+--R
+--R
+--R 1 3 9 1 2 6 1 2 3 1 3
+--R - - b x - - a b x - - a b x - -- a
+--R 9 4 5 18
+--R (2) --------------------------------------
+--R 18
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1042
+
+--S 1043 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R - 20b x - 45a b x - 36a b x - 10a
+--R (3) -------------------------------------
+--R 18
+--R 180x
+--R Type: Union(Expression(Integer),...)
+--E 1043
+
+--S 1044 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1044
+
+--S 1045 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1045
+
+)clear all
+
+--S 1046 of 1285
+t0:=(a+b*x^3)^3/x^22
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 22
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1046
+
+--S 1047 of 1285
+r0:=-1/21*a^3/x^21-1/6*a^2*b/x^18-1/5*a*b^2/x^15-1/12*b^3/x^12
+--R
+--R
+--R 1 3 9 1 2 6 1 2 3 1 3
+--R - -- b x - - a b x - - a b x - -- a
+--R 12 5 6 21
+--R (2) ---------------------------------------
+--R 21
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1047
+
+--S 1048 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R - 35b x - 84a b x - 70a b x - 20a
+--R (3) -------------------------------------
+--R 21
+--R 420x
+--R Type: Union(Expression(Integer),...)
+--E 1048
+
+--S 1049 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1049
+
+--S 1050 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1050
+
+)clear all
+
+--S 1051 of 1285
+t0:=(a+b*x^3)^3/x^25
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 25
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1051
+
+--S 1052 of 1285
+r0:=-1/24*a^3/x^24-1/7*a^2*b/x^21-1/6*a*b^2/x^18-1/15*b^3/x^15
+--R
+--R
+--R 1 3 9 1 2 6 1 2 3 1 3
+--R - -- b x - - a b x - - a b x - -- a
+--R 15 6 7 24
+--R (2) ---------------------------------------
+--R 24
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1052
+
+--S 1053 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R - 56b x - 140a b x - 120a b x - 35a
+--R (3) ---------------------------------------
+--R 24
+--R 840x
+--R Type: Union(Expression(Integer),...)
+--E 1053
+
+--S 1054 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1054
+
+--S 1055 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1055
+
+)clear all
+
+--S 1056 of 1285
+t0:=x^4*(a+b*x^3)^3
+--R
+--R
+--R 3 13 2 10 2 7 3 4
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 1056
+
+--S 1057 of 1285
+r0:=1/5*a^3*x^5+3/8*a^2*b*x^8+3/11*a*b^2*x^11+1/14*b^3*x^14
+--R
+--R
+--R 1 3 14 3 2 11 3 2 8 1 3 5
+--R (2) -- b x + -- a b x + - a b x + - a x
+--R 14 11 8 5
+--R Type: Polynomial(Fraction(Integer))
+--E 1057
+
+--S 1058 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 14 3 2 11 3 2 8 1 3 5
+--R (3) -- b x + -- a b x + - a b x + - a x
+--R 14 11 8 5
+--R Type: Polynomial(Fraction(Integer))
+--E 1058
+
+--S 1059 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1059
+
+--S 1060 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1060
+
+)clear all
+
+--S 1061 of 1285
+t0:=x^3*(a+b*x^3)^3
+--R
+--R
+--R 3 12 2 9 2 6 3 3
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 1061
+
+--S 1062 of 1285
+r0:=1/4*a^3*x^4+3/7*a^2*b*x^7+3/10*a*b^2*x^10+1/13*b^3*x^13
+--R
+--R
+--R 1 3 13 3 2 10 3 2 7 1 3 4
+--R (2) -- b x + -- a b x + - a b x + - a x
+--R 13 10 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 1062
+
+--S 1063 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 13 3 2 10 3 2 7 1 3 4
+--R (3) -- b x + -- a b x + - a b x + - a x
+--R 13 10 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 1063
+
+--S 1064 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1064
+
+--S 1065 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1065
+
+)clear all
+
+--S 1066 of 1285
+t0:=x*(a+b*x^3)^3
+--R
+--R
+--R 3 10 2 7 2 4 3
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 1066
+
+--S 1067 of 1285
+r0:=1/2*a^3*x^2+3/5*a^2*b*x^5+3/8*a*b^2*x^8+1/11*b^3*x^11
+--R
+--R
+--R 1 3 11 3 2 8 3 2 5 1 3 2
+--R (2) -- b x + - a b x + - a b x + - a x
+--R 11 8 5 2
+--R Type: Polynomial(Fraction(Integer))
+--E 1067
+
+--S 1068 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 11 3 2 8 3 2 5 1 3 2
+--R (3) -- b x + - a b x + - a b x + - a x
+--R 11 8 5 2
+--R Type: Polynomial(Fraction(Integer))
+--E 1068
+
+--S 1069 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1069
+
+--S 1070 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1070
+
+)clear all
+
+--S 1071 of 1285
+t0:=(a+b*x^3)^3
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R (1) b x + 3a b x + 3a b x + a
+--R Type: Polynomial(Integer)
+--E 1071
+
+--S 1072 of 1285
+r0:=a^3*x+3/4*a^2*b*x^4+3/7*a*b^2*x^7+1/10*b^3*x^10
+--R
+--R
+--R 1 3 10 3 2 7 3 2 4 3
+--R (2) -- b x + - a b x + - a b x + a x
+--R 10 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 1072
+
+--S 1073 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 10 3 2 7 3 2 4 3
+--R (3) -- b x + - a b x + - a b x + a x
+--R 10 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 1073
+
+--S 1074 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1074
+
+--S 1075 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1075
+
+)clear all
+
+--S 1076 of 1285
+t0:=(a+b*x^3)^3/x^2
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1076
+
+--S 1077 of 1285
+r0:=-a^3/x+3/2*a^2*b*x^2+3/5*a*b^2*x^5+1/8*b^3*x^8
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R 5b x + 24a b x + 60a b x - 40a
+--R (2) ----------------------------------
+--R 40x
+--R Type: Fraction(Polynomial(Integer))
+--E 1077
+
+--S 1078 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R 5b x + 24a b x + 60a b x - 40a
+--R (3) ----------------------------------
+--R 40x
+--R Type: Union(Expression(Integer),...)
+--E 1078
+
+--S 1079 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1079
+
+--S 1080 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1080
+
+)clear all
+
+--S 1081 of 1285
+t0:=(a+b*x^3)^3/x^3
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1081
+
+--S 1082 of 1285
+r0:=-1/2*a^3/x^2+3*a^2*b*x+3/4*a*b^2*x^4+1/7*b^3*x^7
+--R
+--R
+--R 1 3 9 3 2 6 2 3 1 3
+--R - b x + - a b x + 3a b x - - a
+--R 7 4 2
+--R (2) ----------------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1082
+
+--S 1083 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R 4b x + 21a b x + 84a b x - 14a
+--R (3) ----------------------------------
+--R 2
+--R 28x
+--R Type: Union(Expression(Integer),...)
+--E 1083
+
+--S 1084 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1084
+
+--S 1085 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1085
+
+)clear all
+
+--S 1086 of 1285
+t0:=(a+b*x^3)^3/x^5
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1086
+
+--S 1087 of 1285
+r0:=-1/4*a^3/x^4-3*a^2*b/x+3/2*a*b^2*x^2+1/5*b^3*x^5
+--R
+--R
+--R 1 3 9 3 2 6 2 3 1 3
+--R - b x + - a b x - 3a b x - - a
+--R 5 2 4
+--R (2) ----------------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1087
+
+--S 1088 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R 4b x + 30a b x - 60a b x - 5a
+--R (3) ---------------------------------
+--R 4
+--R 20x
+--R Type: Union(Expression(Integer),...)
+--E 1088
+
+--S 1089 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1089
+
+--S 1090 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1090
+
+)clear all
+
+--S 1091 of 1285
+t0:=(a+b*x^3)^3/x^6
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1091
+
+--S 1092 of 1285
+r0:=-1/5*a^3/x^5-3/2*a^2*b/x^2+3*a*b^2*x+1/4*b^3*x^4
+--R
+--R
+--R 1 3 9 2 6 3 2 3 1 3
+--R - b x + 3a b x - - a b x - - a
+--R 4 2 5
+--R (2) ----------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1092
+
+--S 1093 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R 5b x + 60a b x - 30a b x - 4a
+--R (3) ---------------------------------
+--R 5
+--R 20x
+--R Type: Union(Expression(Integer),...)
+--E 1093
+
+--S 1094 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1094
+
+--S 1095 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1095
+
+)clear all
+
+--S 1096 of 1285
+t0:=(a+b*x^3)^3/x^8
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1096
+
+--S 1097 of 1285
+r0:=-1/7*a^3/x^7-3/4*a^2*b/x^4-3*a*b^2/x+1/2*b^3*x^2
+--R
+--R
+--R 1 3 9 2 6 3 2 3 1 3
+--R - b x - 3a b x - - a b x - - a
+--R 2 4 7
+--R (2) ----------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1097
+
+--S 1098 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R 14b x - 84a b x - 21a b x - 4a
+--R (3) ----------------------------------
+--R 7
+--R 28x
+--R Type: Union(Expression(Integer),...)
+--E 1098
+
+--S 1099 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1099
+
+--S 1100 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1100
+
+)clear all
+
+--S 1101 of 1285
+t0:=x^m*(a+b*x^3)^5
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5 m
+--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )x
+--R Type: Expression(Integer)
+--E 1101
+
+--S 1102 of 1285
+r0:=a^5*x^(1+m)/(1+m)+5*a^4*b*x^(4+m)/(4+m)+10*a^3*b^2*x^(7+m)/(7+m)+_
+ 10*a^2*b^3*x^(10+m)/(10+m)+5*a*b^4*x^(13+m)/(13+m)+b^5*x^(16+m)/(16+m)
+--R
+--R
+--R (2)
+--R 5 5 5 4 5 3 5 2 5 5 m + 16
+--R (b m + 35b m + 445b m + 2485b m + 5714b m + 3640b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 190a b m + 2555a b m + 14810a b m + 34840a b m
+--R +
+--R 4
+--R 22400a b
+--R *
+--R m + 13
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R 10a b m + 410a b m + 5950a b m + 36550a b m + 89240a b m
+--R +
+--R 2 3
+--R 58240a b
+--R *
+--R m + 10
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R 10a b m + 440a b m + 6970a b m + 47260a b m + 123920a b m
+--R +
+--R 3 2
+--R 83200a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 235a b m + 4085a b m + 31685a b m + 100630a b m
+--R +
+--R 4
+--R 72800a b
+--R *
+--R m + 4
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5 m + 1
+--R (a m + 50a m + 955a m + 8650a m + 36824a m + 58240a )x
+--R /
+--R 6 5 4 3 2
+--R m + 51m + 1005m + 9605m + 45474m + 95064m + 58240
+--R Type: Expression(Integer)
+--E 1102
+
+--S 1103 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 5 4 5 3 5 2 5 5 16
+--R (b m + 35b m + 445b m + 2485b m + 5714b m + 3640b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 190a b m + 2555a b m + 14810a b m + 34840a b m
+--R +
+--R 4
+--R 22400a b
+--R *
+--R 13
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R 10a b m + 410a b m + 5950a b m + 36550a b m + 89240a b m
+--R +
+--R 2 3
+--R 58240a b
+--R *
+--R 10
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R 10a b m + 440a b m + 6970a b m + 47260a b m + 123920a b m
+--R +
+--R 3 2
+--R 83200a b
+--R *
+--R 7
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 235a b m + 4085a b m + 31685a b m + 100630a b m
+--R +
+--R 4
+--R 72800a b
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5
+--R (a m + 50a m + 955a m + 8650a m + 36824a m + 58240a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 6 5 4 3 2
+--R m + 51m + 1005m + 9605m + 45474m + 95064m + 58240
+--R Type: Union(Expression(Integer),...)
+--E 1103
+
+--S 1104 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 5 5 4 5 3 5 2 5 5 16
+--R (b m + 35b m + 445b m + 2485b m + 5714b m + 3640b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 190a b m + 2555a b m + 14810a b m + 34840a b m
+--R +
+--R 4
+--R 22400a b
+--R *
+--R 13
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R 10a b m + 410a b m + 5950a b m + 36550a b m + 89240a b m
+--R +
+--R 2 3
+--R 58240a b
+--R *
+--R 10
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R 10a b m + 440a b m + 6970a b m + 47260a b m + 123920a b m
+--R +
+--R 3 2
+--R 83200a b
+--R *
+--R 7
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 5a b m + 235a b m + 4085a b m + 31685a b m + 100630a b m
+--R +
+--R 4
+--R 72800a b
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5
+--R (a m + 50a m + 955a m + 8650a m + 36824a m + 58240a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 5 5 5 4 5 3 5 2 5 5 m + 16
+--R (- b m - 35b m - 445b m - 2485b m - 5714b m - 3640b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R - 5a b m - 190a b m - 2555a b m - 14810a b m - 34840a b m
+--R +
+--R 4
+--R - 22400a b
+--R *
+--R m + 13
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R - 10a b m - 410a b m - 5950a b m - 36550a b m - 89240a b m
+--R +
+--R 2 3
+--R - 58240a b
+--R *
+--R m + 10
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R - 10a b m - 440a b m - 6970a b m - 47260a b m - 123920a b m
+--R +
+--R 3 2
+--R - 83200a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R - 5a b m - 235a b m - 4085a b m - 31685a b m - 100630a b m
+--R +
+--R 4
+--R - 72800a b
+--R *
+--R m + 4
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5 m + 1
+--R (- a m - 50a m - 955a m - 8650a m - 36824a m - 58240a )x
+--R /
+--R 6 5 4 3 2
+--R m + 51m + 1005m + 9605m + 45474m + 95064m + 58240
+--R Type: Expression(Integer)
+--E 1104
+
+--S 1105 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1105
+
+)clear all
+
+--S 1106 of 1285
+t0:=x^17*(a+b*x^3)^5
+--R
+--R
+--R 5 32 4 29 2 3 26 3 2 23 4 20 5 17
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 1106
+
+--S 1107 of 1285
+r0:=1/18*a^5*x^18+5/21*a^4*b*x^21+5/12*a^3*b^2*x^24+10/27*a^2*b^3*x^27+_
+ 1/6*a*b^4*x^30+1/33*b^5*x^33
+--R
+--R
+--R 1 5 33 1 4 30 10 2 3 27 5 3 2 24 5 4 21 1 5 18
+--R (2) -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a x
+--R 33 6 27 12 21 18
+--R Type: Polynomial(Fraction(Integer))
+--E 1107
+
+--S 1108 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 33 1 4 30 10 2 3 27 5 3 2 24 5 4 21 1 5 18
+--R (3) -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a x
+--R 33 6 27 12 21 18
+--R Type: Polynomial(Fraction(Integer))
+--E 1108
+
+--S 1109 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1109
+
+--S 1110 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1110
+
+)clear all
+
+--S 1111 of 1285
+t0:=x^14*(a+b*x^3)^5
+--R
+--R
+--R 5 29 4 26 2 3 23 3 2 20 4 17 5 14
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 1111
+
+--S 1112 of 1285
+r0:=1/15*a^5*x^15+5/18*a^4*b*x^18+10/21*a^3*b^2*x^21+5/12*a^2*b^3*x^24+_
+ 5/27*a*b^4*x^27+1/30*b^5*x^30
+--R
+--R
+--R (2)
+--R 1 5 30 5 4 27 5 2 3 24 10 3 2 21 5 4 18 1 5 15
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x
+--R 30 27 12 21 18 15
+--R Type: Polynomial(Fraction(Integer))
+--E 1112
+
+--S 1113 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 30 5 4 27 5 2 3 24 10 3 2 21 5 4 18 1 5 15
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x
+--R 30 27 12 21 18 15
+--R Type: Polynomial(Fraction(Integer))
+--E 1113
+
+--S 1114 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1114
+
+--S 1115 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1115
+
+)clear all
+
+--S 1116 of 1285
+t0:=x^11*(a+b*x^3)^5
+--R
+--R
+--R 5 26 4 23 2 3 20 3 2 17 4 14 5 11
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 1116
+
+--S 1117 of 1285
+r0:=1/12*a^5*x^12+1/3*a^4*b*x^15+5/9*a^3*b^2*x^18+10/21*a^2*b^3*x^21+_
+ 5/24*a*b^4*x^24+1/27*b^5*x^27
+--R
+--R
+--R 1 5 27 5 4 24 10 2 3 21 5 3 2 18 1 4 15 1 5 12
+--R (2) -- b x + -- a b x + -- a b x + - a b x + - a b x + -- a x
+--R 27 24 21 9 3 12
+--R Type: Polynomial(Fraction(Integer))
+--E 1117
+
+--S 1118 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 27 5 4 24 10 2 3 21 5 3 2 18 1 4 15 1 5 12
+--R (3) -- b x + -- a b x + -- a b x + - a b x + - a b x + -- a x
+--R 27 24 21 9 3 12
+--R Type: Polynomial(Fraction(Integer))
+--E 1118
+
+--S 1119 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1119
+
+--S 1120 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1120
+
+)clear all
+
+--S 1121 of 1285
+t0:=x^8*(a+b*x^3)^5
+--R
+--R
+--R 5 23 4 20 2 3 17 3 2 14 4 11 5 8
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 1121
+
+--S 1122 of 1285
+r0:=1/18*a^2*(a+b*x^3)^6/b^3-2/21*a*(a+b*x^3)^7/b^3+1/24*(a+b*x^3)^8/b^3
+--R
+--R
+--R (2)
+--R 1 8 24 5 7 21 5 2 6 18 2 3 5 15 5 4 4 12 1 5 3 9
+--R -- b x + -- a b x + - a b x + - a b x + -- a b x + - a b x
+--R 24 21 9 3 12 9
+--R +
+--R 1 8
+--R --- a
+--R 504
+--R /
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1122
+
+--S 1123 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 24 5 4 21 5 2 3 18 2 3 2 15 5 4 12 1 5 9
+--R (3) -- b x + -- a b x + - a b x + - a b x + -- a b x + - a x
+--R 24 21 9 3 12 9
+--R Type: Polynomial(Fraction(Integer))
+--E 1123
+
+--S 1124 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 8
+--R --- a
+--R 504
+--R (4) - ------
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1124
+
+--S 1125 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1125
+
+)clear all
+
+--S 1126 of 1285
+t0:=x^5*(a+b*x^3)^5
+--R
+--R
+--R 5 20 4 17 2 3 14 3 2 11 4 8 5 5
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 1126
+
+--S 1127 of 1285
+r0:=-1/18*a*(a+b*x^3)^6/b^2+1/21*(a+b*x^3)^7/b^2
+--R
+--R
+--R (2)
+--R 1 7 21 5 6 18 2 2 5 15 5 3 4 12 5 4 3 9 1 5 2 6 1 7
+--R -- b x + -- a b x + - a b x + - a b x + - a b x + - a b x - --- a
+--R 21 18 3 6 9 6 126
+--R ----------------------------------------------------------------------------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1127
+
+--S 1128 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 21 5 4 18 2 2 3 15 5 3 2 12 5 4 9 1 5 6
+--R (3) -- b x + -- a b x + - a b x + - a b x + - a b x + - a x
+--R 21 18 3 6 9 6
+--R Type: Polynomial(Fraction(Integer))
+--E 1128
+
+--S 1129 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 7
+--R --- a
+--R 126
+--R (4) ------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1129
+
+--S 1130 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1130
+
+)clear all
+
+--S 1131 of 1285
+t0:=x^2*(a+b*x^3)^5
+--R
+--R
+--R 5 17 4 14 2 3 11 3 2 8 4 5 5 2
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 1131
+
+--S 1132 of 1285
+r0:=1/18*(a+b*x^3)^6/b
+--R
+--R
+--R (2)
+--R 1 6 18 1 5 15 5 2 4 12 10 3 3 9 5 4 2 6 1 5 3 1 6
+--R -- b x + - a b x + - a b x + -- a b x + - a b x + - a b x + -- a
+--R 18 3 6 9 6 3 18
+--R --------------------------------------------------------------------------
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1132
+
+--S 1133 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 18 1 4 15 5 2 3 12 10 3 2 9 5 4 6 1 5 3
+--R (3) -- b x + - a b x + - a b x + -- a b x + - a b x + - a x
+--R 18 3 6 9 6 3
+--R Type: Polynomial(Fraction(Integer))
+--E 1133
+
+--S 1134 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 6
+--R -- a
+--R 18
+--R (4) - -----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1134
+
+--S 1135 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1135
+
+)clear all
+
+--S 1136 of 1285
+t0:=(a+b*x^3)^5/x
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1136
+
+--S 1137 of 1285
+r0:=5/3*a^4*b*x^3+5/3*a^3*b^2*x^6+10/9*a^2*b^3*x^9+5/12*a*b^4*x^12+_
+ 1/15*b^5*x^15+a^5*log(x)
+--R
+--R
+--R 5 5 15 4 12 2 3 9 3 2 6 4 3
+--R 180a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x
+--R (2) ---------------------------------------------------------------------
+--R 180
+--R Type: Expression(Integer)
+--E 1137
+
+--S 1138 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5 15 4 12 2 3 9 3 2 6 4 3
+--R 180a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x
+--R (3) ---------------------------------------------------------------------
+--R 180
+--R Type: Union(Expression(Integer),...)
+--E 1138
+
+--S 1139 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1139
+
+--S 1140 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1140
+
+)clear all
+
+--S 1141 of 1285
+t0:=(a+b*x^3)^5/x^4
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1141
+
+--S 1142 of 1285
+r0:=-1/3*a^5/x^3+10/3*a^3*b^2*x^3+5/3*a^2*b^3*x^6+5/9*a*b^4*x^9+_
+ 1/12*b^5*x^12+5*a^4*b*log(x)
+--R
+--R
+--R 4 3 5 15 4 12 2 3 9 3 2 6 5
+--R 180a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a
+--R (2) ------------------------------------------------------------------
+--R 3
+--R 36x
+--R Type: Expression(Integer)
+--E 1142
+
+--S 1143 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3 5 15 4 12 2 3 9 3 2 6 5
+--R 180a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a
+--R (3) ------------------------------------------------------------------
+--R 3
+--R 36x
+--R Type: Union(Expression(Integer),...)
+--E 1143
+
+--S 1144 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1144
+
+--S 1145 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1145
+
+)clear all
+
+--S 1146 of 1285
+t0:=(a+b*x^3)^5/x^7
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1146
+
+--S 1147 of 1285
+r0:=-1/6*a^5/x^6-5/3*a^4*b/x^3+10/3*a^2*b^3*x^3+5/6*a*b^4*x^6+_
+ 1/9*b^5*x^9+10*a^3*b^2*log(x)
+--R
+--R
+--R 3 2 6 5 15 4 12 2 3 9 4 3 5
+--R 180a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a
+--R (2) ----------------------------------------------------------------
+--R 6
+--R 18x
+--R Type: Expression(Integer)
+--E 1147
+
+--S 1148 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 6 5 15 4 12 2 3 9 4 3 5
+--R 180a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a
+--R (3) ----------------------------------------------------------------
+--R 6
+--R 18x
+--R Type: Union(Expression(Integer),...)
+--E 1148
+
+--S 1149 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1149
+
+--S 1150 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1150
+
+)clear all
+
+--S 1151 of 1285
+t0:=(a+b*x^3)^5/x^10
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1151
+
+--S 1152 of 1285
+r0:=-1/9*a^5/x^9-5/6*a^4*b/x^6-10/3*a^3*b^2/x^3+5/3*a*b^4*x^3+_
+ 1/6*b^5*x^6+10*a^2*b^3*log(x)
+--R
+--R
+--R 2 3 9 5 15 4 12 3 2 6 4 3 5
+--R 180a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a
+--R (2) ----------------------------------------------------------------
+--R 9
+--R 18x
+--R Type: Expression(Integer)
+--E 1152
+
+--S 1153 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 9 5 15 4 12 3 2 6 4 3 5
+--R 180a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a
+--R (3) ----------------------------------------------------------------
+--R 9
+--R 18x
+--R Type: Union(Expression(Integer),...)
+--E 1153
+
+--S 1154 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1154
+
+--S 1155 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1155
+
+)clear all
+
+--S 1156 of 1285
+t0:=(a+b*x^3)^5/x^13
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1156
+
+--S 1157 of 1285
+r0:=-1/12*a^5/x^12-5/9*a^4*b/x^9-5/3*a^3*b^2/x^6-10/3*a^2*b^3/x^3+_
+ 1/3*b^5*x^3+5*a*b^4*log(x)
+--R
+--R
+--R 4 12 5 15 2 3 9 3 2 6 4 3 5
+--R 180a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a
+--R (2) ------------------------------------------------------------------
+--R 12
+--R 36x
+--R Type: Expression(Integer)
+--E 1157
+
+--S 1158 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 12 5 15 2 3 9 3 2 6 4 3 5
+--R 180a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a
+--R (3) ------------------------------------------------------------------
+--R 12
+--R 36x
+--R Type: Union(Expression(Integer),...)
+--E 1158
+
+--S 1159 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1159
+
+--S 1160 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1160
+
+)clear all
+
+--S 1161 of 1285
+t0:=(a+b*x^3)^5/x^16
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 16
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1161
+
+--S 1162 of 1285
+r0:=-1/15*a^5/x^15-5/12*a^4*b/x^12-10/9*a^3*b^2/x^9-5/3*a^2*b^3/x^6-_
+ 5/3*a*b^4/x^3+b^5*log(x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R 180b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a
+--R (2) ---------------------------------------------------------------------
+--R 15
+--R 180x
+--R Type: Expression(Integer)
+--E 1162
+
+--S 1163 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R 180b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a
+--R (3) ---------------------------------------------------------------------
+--R 15
+--R 180x
+--R Type: Union(Expression(Integer),...)
+--E 1163
+
+--S 1164 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1164
+
+--S 1165 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1165
+
+)clear all
+
+--S 1166 of 1285
+t0:=(a+b*x^3)^5/x^19
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1166
+
+--S 1167 of 1285
+r0:=-1/18*(a+b*x^3)^6/(a*x^18)
+--R
+--R
+--R (2)
+--R 1 6 18 1 5 15 5 2 4 12 10 3 3 9 5 4 2 6 1 5 3 1 6
+--R - -- b x - - a b x - - a b x - -- a b x - - a b x - - a b x - -- a
+--R 18 3 6 9 6 3 18
+--R ----------------------------------------------------------------------------
+--R 18
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1167
+
+--S 1168 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a
+--R (3) ---------------------------------------------------------
+--R 18
+--R 18x
+--R Type: Union(Expression(Integer),...)
+--E 1168
+
+--S 1169 of 1285
+m0:=a0-r0
+--R
+--R
+--R 6
+--R b
+--R (4) ---
+--R 18a
+--R Type: Expression(Integer)
+--E 1169
+
+--S 1170 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1170
+
+)clear all
+
+--S 1171 of 1285
+t0:=(a+b*x^3)^5/x^22
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 22
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1171
+
+--S 1172 of 1285
+r0:=-1/21*(a+b*x^3)^6/(a*x^21)+1/126*b*(a+b*x^3)^6/(a^2*x^18)
+--R
+--R
+--R (2)
+--R 1 7 21 1 2 5 15 5 3 4 12 5 4 3 9 2 5 2 6 5 6 3 1 7
+--R --- b x - - a b x - - a b x - - a b x - - a b x - -- a b x - -- a
+--R 126 6 9 6 3 18 21
+--R ---------------------------------------------------------------------------
+--R 2 21
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1172
+
+--S 1173 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R - 21b x - 70a b x - 105a b x - 84a b x - 35a b x - 6a
+--R (3) -------------------------------------------------------------
+--R 21
+--R 126x
+--R Type: Union(Expression(Integer),...)
+--E 1173
+
+--S 1174 of 1285
+m0:=a0-r0
+--R
+--R
+--R 7
+--R b
+--R (4) - -----
+--R 2
+--R 126a
+--R Type: Expression(Integer)
+--E 1174
+
+--S 1175 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1175
+
+)clear all
+
+--S 1176 of 1285
+t0:=(a+b*x^3)^5/x^25
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 25
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1176
+
+--S 1177 of 1285
+r0:=-1/24*a^5/x^24-5/21*a^4*b/x^21-5/9*a^3*b^2/x^18-2/3*a^2*b^3/x^15-_
+ 5/12*a*b^4/x^12-1/9*b^5/x^9
+--R
+--R
+--R 1 5 15 5 4 12 2 2 3 9 5 3 2 6 5 4 3 1 5
+--R - - b x - -- a b x - - a b x - - a b x - -- a b x - -- a
+--R 9 12 3 9 21 24
+--R (2) ----------------------------------------------------------------
+--R 24
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1177
+
+--S 1178 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R - 56b x - 210a b x - 336a b x - 280a b x - 120a b x - 21a
+--R (3) -----------------------------------------------------------------
+--R 24
+--R 504x
+--R Type: Union(Expression(Integer),...)
+--E 1178
+
+--S 1179 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1179
+
+--S 1180 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1180
+
+)clear all
+
+--S 1181 of 1285
+t0:=(a+b*x^3)^5/x^28
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 28
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1181
+
+--S 1182 of 1285
+r0:=-1/27*a^5/x^27-5/24*a^4*b/x^24-10/21*a^3*b^2/x^21-5/9*a^2*b^3/x^18-_
+ 1/3*a*b^4/x^15-1/12*b^5/x^12
+--R
+--R
+--R 1 5 15 1 4 12 5 2 3 9 10 3 2 6 5 4 3 1 5
+--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a
+--R 12 3 9 21 24 27
+--R (2) -----------------------------------------------------------------
+--R 27
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1182
+
+--S 1183 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R - 126b x - 504a b x - 840a b x - 720a b x - 315a b x - 56a
+--R (3) ------------------------------------------------------------------
+--R 27
+--R 1512x
+--R Type: Union(Expression(Integer),...)
+--E 1183
+
+--S 1184 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1184
+
+--S 1185 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1185
+
+)clear all
+
+--S 1186 of 1285
+t0:=(a+b*x^3)^5/x^31
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 31
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1186
+
+--S 1187 of 1285
+r0:=-1/30*a^5/x^30-5/27*a^4*b/x^27-5/12*a^3*b^2/x^24-10/21*a^2*b^3/x^21-_
+ 5/18*a*b^4/x^18-1/15*b^5/x^15
+--R
+--R
+--R 1 5 15 5 4 12 10 2 3 9 5 3 2 6 5 4 3 1 5
+--R - -- b x - -- a b x - -- a b x - -- a b x - -- a b x - -- a
+--R 15 18 21 12 27 30
+--R (2) -------------------------------------------------------------------
+--R 30
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1187
+
+--S 1188 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R - 252b x - 1050a b x - 1800a b x - 1575a b x - 700a b x - 126a
+--R (3) ----------------------------------------------------------------------
+--R 30
+--R 3780x
+--R Type: Union(Expression(Integer),...)
+--E 1188
+
+--S 1189 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1189
+
+--S 1190 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1190
+
+)clear all
+
+--S 1191 of 1285
+t0:=(a+b*x^3)^5/x^34
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 34
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1191
+
+--S 1192 of 1285
+r0:=-1/33*a^5/x^33-1/6*a^4*b/x^30-10/27*a^3*b^2/x^27-5/12*a^2*b^3/x^24-_
+ 5/21*a*b^4/x^21-1/18*b^5/x^18
+--R
+--R
+--R 1 5 15 5 4 12 5 2 3 9 10 3 2 6 1 4 3 1 5
+--R - -- b x - -- a b x - -- a b x - -- a b x - - a b x - -- a
+--R 18 21 12 27 6 33
+--R (2) ------------------------------------------------------------------
+--R 33
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1192
+
+--S 1193 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R - 462b x - 1980a b x - 3465a b x - 3080a b x - 1386a b x - 252a
+--R -----------------------------------------------------------------------
+--R 33
+--R 8316x
+--R Type: Union(Expression(Integer),...)
+--E 1193
+
+--S 1194 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1194
+
+--S 1195 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1195
+
+)clear all
+
+--S 1196 of 1285
+t0:=x^4*(a+b*x^3)^5
+--R
+--R
+--R 5 19 4 16 2 3 13 3 2 10 4 7 5 4
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 1196
+
+--S 1197 of 1285
+r0:=1/5*a^5*x^5+5/8*a^4*b*x^8+10/11*a^3*b^2*x^11+5/7*a^2*b^3*x^14+_
+ 5/17*a*b^4*x^17+1/20*b^5*x^20
+--R
+--R
+--R 1 5 20 5 4 17 5 2 3 14 10 3 2 11 5 4 8 1 5 5
+--R (2) -- b x + -- a b x + - a b x + -- a b x + - a b x + - a x
+--R 20 17 7 11 8 5
+--R Type: Polynomial(Fraction(Integer))
+--E 1197
+
+--S 1198 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 20 5 4 17 5 2 3 14 10 3 2 11 5 4 8 1 5 5
+--R (3) -- b x + -- a b x + - a b x + -- a b x + - a b x + - a x
+--R 20 17 7 11 8 5
+--R Type: Polynomial(Fraction(Integer))
+--E 1198
+
+--S 1199 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1199
+
+--S 1200 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1200
+
+)clear all
+
+--S 1201 of 1285
+t0:=x^3*(a+b*x^3)^5
+--R
+--R
+--R 5 18 4 15 2 3 12 3 2 9 4 6 5 3
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 1201
+
+--S 1202 of 1285
+r0:=1/4*a^5*x^4+5/7*a^4*b*x^7+a^3*b^2*x^10+10/13*a^2*b^3*x^13+_
+ 5/16*a*b^4*x^16+1/19*b^5*x^19
+--R
+--R
+--R 1 5 19 5 4 16 10 2 3 13 3 2 10 5 4 7 1 5 4
+--R (2) -- b x + -- a b x + -- a b x + a b x + - a b x + - a x
+--R 19 16 13 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 1202
+
+--S 1203 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 19 5 4 16 10 2 3 13 3 2 10 5 4 7 1 5 4
+--R (3) -- b x + -- a b x + -- a b x + a b x + - a b x + - a x
+--R 19 16 13 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 1203
+
+--S 1204 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1204
+
+--S 1205 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1205
+
+)clear all
+
+--S 1206 of 1285
+t0:=x*(a+b*x^3)^5
+--R
+--R
+--R 5 16 4 13 2 3 10 3 2 7 4 4 5
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x
+--R Type: Polynomial(Integer)
+--E 1206
+
+--S 1207 of 1285
+r0:=1/2*a^5*x^2+a^4*b*x^5+5/4*a^3*b^2*x^8+10/11*a^2*b^3*x^11+_
+ 5/14*a*b^4*x^14+1/17*b^5*x^17
+--R
+--R
+--R 1 5 17 5 4 14 10 2 3 11 5 3 2 8 4 5 1 5 2
+--R (2) -- b x + -- a b x + -- a b x + - a b x + a b x + - a x
+--R 17 14 11 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 1207
+
+--S 1208 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 17 5 4 14 10 2 3 11 5 3 2 8 4 5 1 5 2
+--R (3) -- b x + -- a b x + -- a b x + - a b x + a b x + - a x
+--R 17 14 11 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 1208
+
+--S 1209 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1209
+
+--S 1210 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1210
+
+)clear all
+
+--S 1211 of 1285
+t0:=(a+b*x^3)^5
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R Type: Polynomial(Integer)
+--E 1211
+
+--S 1212 of 1285
+r0:=a^5*x+5/4*a^4*b*x^4+10/7*a^3*b^2*x^7+a^2*b^3*x^10+5/13*a*b^4*x^13+_
+ 1/16*b^5*x^16
+--R
+--R
+--R 1 5 16 5 4 13 2 3 10 10 3 2 7 5 4 4 5
+--R (2) -- b x + -- a b x + a b x + -- a b x + - a b x + a x
+--R 16 13 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 1212
+
+--S 1213 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 16 5 4 13 2 3 10 10 3 2 7 5 4 4 5
+--R (3) -- b x + -- a b x + a b x + -- a b x + - a b x + a x
+--R 16 13 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 1213
+
+--S 1214 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1214
+
+--S 1215 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1215
+
+)clear all
+
+--S 1216 of 1285
+t0:=(a+b*x^3)^5/x^2
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1216
+
+--S 1217 of 1285
+r0:=-a^5/x+5/2*a^4*b*x^2+2*a^3*b^2*x^5+5/4*a^2*b^3*x^8+5/11*a*b^4*x^11+_
+ 1/14*b^5*x^14
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R 22b x + 140a b x + 385a b x + 616a b x + 770a b x - 308a
+--R (2) ----------------------------------------------------------------
+--R 308x
+--R Type: Fraction(Polynomial(Integer))
+--E 1217
+
+--S 1218 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R 22b x + 140a b x + 385a b x + 616a b x + 770a b x - 308a
+--R (3) ----------------------------------------------------------------
+--R 308x
+--R Type: Union(Expression(Integer),...)
+--E 1218
+
+--S 1219 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1219
+
+--S 1220 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1220
+
+)clear all
+
+--S 1221 of 1285
+t0:=(a+b*x^3)^5/x^3
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1221
+
+--S 1222 of 1285
+r0:=-1/2*a^5/x^2+5*a^4*b*x+5/2*a^3*b^2*x^4+10/7*a^2*b^3*x^7+_
+ 1/2*a*b^4*x^10+1/13*b^5*x^13
+--R
+--R
+--R 1 5 15 1 4 12 10 2 3 9 5 3 2 6 4 3 1 5
+--R -- b x + - a b x + -- a b x + - a b x + 5a b x - - a
+--R 13 2 7 2 2
+--R (2) ------------------------------------------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1222
+
+--S 1223 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R 14b x + 91a b x + 260a b x + 455a b x + 910a b x - 91a
+--R (3) --------------------------------------------------------------
+--R 2
+--R 182x
+--R Type: Union(Expression(Integer),...)
+--E 1223
+
+--S 1224 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1224
+
+--S 1225 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1225
+
+)clear all
+
+--S 1226 of 1285
+t0:=(a+b*x^3)^5/x^5
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1226
+
+--S 1227 of 1285
+r0:=-1/4*a^5/x^4-5*a^4*b/x+5*a^3*b^2*x^2+2*a^2*b^3*x^5+5/8*a*b^4*x^8+_
+ 1/11*b^5*x^11
+--R
+--R
+--R 1 5 15 5 4 12 2 3 9 3 2 6 4 3 1 5
+--R -- b x + - a b x + 2a b x + 5a b x - 5a b x - - a
+--R 11 8 4
+--R (2) ---------------------------------------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1227
+
+--S 1228 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R 8b x + 55a b x + 176a b x + 440a b x - 440a b x - 22a
+--R (3) -------------------------------------------------------------
+--R 4
+--R 88x
+--R Type: Union(Expression(Integer),...)
+--E 1228
+
+--S 1229 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1229
+
+--S 1230 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1230
+
+)clear all
+
+--S 1231 of 1285
+t0:=(a+b*x^3)^5/x^6
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1231
+
+--S 1232 of 1285
+r0:=-1/5*a^5/x^5-5/2*a^4*b/x^2+10*a^3*b^2*x+5/2*a^2*b^3*x^4+5/7*a*b^4*x^7+_
+ 1/10*b^5*x^10
+--R
+--R
+--R 1 5 15 5 4 12 5 2 3 9 3 2 6 5 4 3 1 5
+--R -- b x + - a b x + - a b x + 10a b x - - a b x - - a
+--R 10 7 2 2 5
+--R (2) ------------------------------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1232
+
+--S 1233 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R 7b x + 50a b x + 175a b x + 700a b x - 175a b x - 14a
+--R (3) -------------------------------------------------------------
+--R 5
+--R 70x
+--R Type: Union(Expression(Integer),...)
+--E 1233
+
+--S 1234 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1234
+
+--S 1235 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1235
+
+)clear all
+
+--S 1236 of 1285
+t0:=(a+b*x^3)^5/x^8
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1236
+
+--S 1237 of 1285
+r0:=-1/7*a^5/x^7-5/4*a^4*b/x^4-10*a^3*b^2/x+5*a^2*b^3*x^2+a*b^4*x^5+1/8*b^5*x^8
+--R
+--R
+--R 1 5 15 4 12 2 3 9 3 2 6 5 4 3 1 5
+--R - b x + a b x + 5a b x - 10a b x - - a b x - - a
+--R 8 4 7
+--R (2) --------------------------------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1237
+
+--S 1238 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R 7b x + 56a b x + 280a b x - 560a b x - 70a b x - 8a
+--R (3) -----------------------------------------------------------
+--R 7
+--R 56x
+--R Type: Union(Expression(Integer),...)
+--E 1238
+
+--S 1239 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1239
+
+--S 1240 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1240
+
+)clear all
+
+--S 1241 of 1285
+t0:=(a+b*x^3)^5/x^9
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a
+--R (1) -----------------------------------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1241
+
+--S 1242 of 1285
+r0:=-1/8*a^5/x^8-a^4*b/x^5-5*a^3*b^2/x^2+10*a^2*b^3*x+5/4*a*b^4*x^4+1/7*b^5*x^7
+--R
+--R
+--R 1 5 15 5 4 12 2 3 9 3 2 6 4 3 1 5
+--R - b x + - a b x + 10a b x - 5a b x - a b x - - a
+--R 7 4 8
+--R (2) --------------------------------------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1242
+
+--S 1243 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R 8b x + 70a b x + 560a b x - 280a b x - 56a b x - 7a
+--R (3) -----------------------------------------------------------
+--R 8
+--R 56x
+--R Type: Union(Expression(Integer),...)
+--E 1243
+
+--S 1244 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1244
+
+--S 1245 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1245
+
+)clear all
+
+--S 1246 of 1285
+t0:=x^m*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R *
+--R m
+--R x
+--R Type: Expression(Integer)
+--E 1246
+
+--S 1247 of 1285
+r0:=a^8*x^(1+m)/(1+m)+8*a^7*b*x^(4+m)/(4+m)+28*a^6*b^2*x^(7+m)/(7+m)+_
+ 56*a^5*b^3*x^(10+m)/(10+m)+70*a^4*b^4*x^(13+m)/(13+m)+_
+ 56*a^3*b^5*x^(16+m)/(16+m)+28*a^2*b^6*x^(19+m)/(19+m)+_
+ 8*a*b^7*x^(22+m)/(22+m)+b^8*x^(25+m)/(25+m)
+--R
+--R
+--R (2)
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R b m + 92b m + 3514b m + 72128b m + 859369b m + 5974388b m
+--R +
+--R 8 2 8 8
+--R 22963996b m + 42124592b m + 24344320b
+--R *
+--R m + 25
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 760a b m + 29792a b m + 624400a b m + 7563752a b m
+--R +
+--R 7 3 7 2 7 7
+--R 53266360a b m + 206729648a b m + 381743680a b m + 221312000a b
+--R *
+--R m + 22
+--R x
+--R +
+--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4
+--R 28a b m + 2744a b m + 110656a b m + 2376920a b m + 29390452a b m
+--R +
+--R 2 6 3 2 6 2 2 6 2 6
+--R 210422576a b m + 827034544a b m + 1540629440a b m + 896896000a b
+--R *
+--R m + 19
+--R x
+--R +
+--R 3 5 8 3 5 7 3 5 6 3 5 5 3 5 4
+--R 56a b m + 5656a b m + 235088a b m + 5197360a b m + 65946104a b m
+--R +
+--R 3 5 3 3 5 2 3 5 3 5
+--R 482544664a b m + 1929412352a b m + 3637973920a b m + 2130128000a b
+--R *
+--R m + 16
+--R x
+--R +
+--R 4 4 8 4 4 7 4 4 6 4 4 5 4 4 4
+--R 70a b m + 7280a b m + 312340a b m + 7138040a b m + 93585310a b m
+--R +
+--R 4 4 3 4 4 2 4 4 4 4
+--R 705493880a b m + 2891238280a b m + 5549616800a b m + 3277120000a b
+--R *
+--R m + 13
+--R x
+--R +
+--R 5 3 8 5 3 7 5 3 6 5 3 5 5 3 4
+--R 56a b m + 5992a b m + 265664a b m + 6302128a b m + 86082584a b m
+--R +
+--R 5 3 3 5 3 2 5 3 5 3
+--R 676856488a b m + 2881562096a b m + 5692950592a b m + 3408204800a b
+--R *
+--R m + 10
+--R x
+--R +
+--R 6 2 8 6 2 7 6 2 6 6 2 5 6 2 4
+--R 28a b m + 3080a b m + 141232a b m + 3490760a b m + 50116612a b m
+--R +
+--R 6 2 3 6 2 2 6 2 6 2
+--R 418024880a b m + 1898889328a b m + 3962060480a b m + 2434432000a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 904a b m + 42896a b m + 1108240a b m + 16867592a b m
+--R +
+--R 7 3 7 2 7 7
+--R 152198536a b m + 769795424a b m + 1850614240a b m + 1217216000a b
+--R *
+--R m + 4
+--R x
+--R +
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R a m + 116a m + 5698a m + 154280a m + 2508289a m + 24950324a m
+--R +
+--R 8 2 8 8
+--R 147373372a m + 468851120a m + 608608000a
+--R *
+--R m + 1
+--R x
+--R /
+--R 9 8 7 6 5 4 3
+--R m + 117m + 5814m + 159978m + 2662569m + 27458613m + 172323696m
+--R +
+--R 2
+--R 616224492m + 1077459120m + 608608000
+--R Type: Expression(Integer)
+--E 1247
+
+--S 1248 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R b m + 92b m + 3514b m + 72128b m + 859369b m + 5974388b m
+--R +
+--R 8 2 8 8
+--R 22963996b m + 42124592b m + 24344320b
+--R *
+--R 25
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 760a b m + 29792a b m + 624400a b m + 7563752a b m
+--R +
+--R 7 3 7 2 7 7
+--R 53266360a b m + 206729648a b m + 381743680a b m + 221312000a b
+--R *
+--R 22
+--R x
+--R +
+--R 2 6 8 2 6 7 2 6 6 2 6 5
+--R 28a b m + 2744a b m + 110656a b m + 2376920a b m
+--R +
+--R 2 6 4 2 6 3 2 6 2
+--R 29390452a b m + 210422576a b m + 827034544a b m
+--R +
+--R 2 6 2 6
+--R 1540629440a b m + 896896000a b
+--R *
+--R 19
+--R x
+--R +
+--R 3 5 8 3 5 7 3 5 6 3 5 5
+--R 56a b m + 5656a b m + 235088a b m + 5197360a b m
+--R +
+--R 3 5 4 3 5 3 3 5 2
+--R 65946104a b m + 482544664a b m + 1929412352a b m
+--R +
+--R 3 5 3 5
+--R 3637973920a b m + 2130128000a b
+--R *
+--R 16
+--R x
+--R +
+--R 4 4 8 4 4 7 4 4 6 4 4 5
+--R 70a b m + 7280a b m + 312340a b m + 7138040a b m
+--R +
+--R 4 4 4 4 4 3 4 4 2
+--R 93585310a b m + 705493880a b m + 2891238280a b m
+--R +
+--R 4 4 4 4
+--R 5549616800a b m + 3277120000a b
+--R *
+--R 13
+--R x
+--R +
+--R 5 3 8 5 3 7 5 3 6 5 3 5
+--R 56a b m + 5992a b m + 265664a b m + 6302128a b m
+--R +
+--R 5 3 4 5 3 3 5 3 2
+--R 86082584a b m + 676856488a b m + 2881562096a b m
+--R +
+--R 5 3 5 3
+--R 5692950592a b m + 3408204800a b
+--R *
+--R 10
+--R x
+--R +
+--R 6 2 8 6 2 7 6 2 6 6 2 5
+--R 28a b m + 3080a b m + 141232a b m + 3490760a b m
+--R +
+--R 6 2 4 6 2 3 6 2 2
+--R 50116612a b m + 418024880a b m + 1898889328a b m
+--R +
+--R 6 2 6 2
+--R 3962060480a b m + 2434432000a b
+--R *
+--R 7
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 904a b m + 42896a b m + 1108240a b m + 16867592a b m
+--R +
+--R 7 3 7 2 7 7
+--R 152198536a b m + 769795424a b m + 1850614240a b m + 1217216000a b
+--R *
+--R 4
+--R x
+--R +
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R a m + 116a m + 5698a m + 154280a m + 2508289a m + 24950324a m
+--R +
+--R 8 2 8 8
+--R 147373372a m + 468851120a m + 608608000a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 9 8 7 6 5 4 3
+--R m + 117m + 5814m + 159978m + 2662569m + 27458613m + 172323696m
+--R +
+--R 2
+--R 616224492m + 1077459120m + 608608000
+--R Type: Union(Expression(Integer),...)
+--E 1248
+
+--S 1249 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R b m + 92b m + 3514b m + 72128b m + 859369b m + 5974388b m
+--R +
+--R 8 2 8 8
+--R 22963996b m + 42124592b m + 24344320b
+--R *
+--R 25
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R 8a b m + 760a b m + 29792a b m + 624400a b m + 7563752a b m
+--R +
+--R 7 3 7 2 7 7
+--R 53266360a b m + 206729648a b m + 381743680a b m + 221312000a b
+--R *
+--R 22
+--R x
+--R +
+--R 2 6 8 2 6 7 2 6 6 2 6 5
+--R 28a b m + 2744a b m + 110656a b m + 2376920a b m
+--R +
+--R 2 6 4 2 6 3 2 6 2
+--R 29390452a b m + 210422576a b m + 827034544a b m
+--R +
+--R 2 6 2 6
+--R 1540629440a b m + 896896000a b
+--R *
+--R 19
+--R x
+--R +
+--R 3 5 8 3 5 7 3 5 6 3 5 5
+--R 56a b m + 5656a b m + 235088a b m + 5197360a b m
+--R +
+--R 3 5 4 3 5 3 3 5 2
+--R 65946104a b m + 482544664a b m + 1929412352a b m
+--R +
+--R 3 5 3 5
+--R 3637973920a b m + 2130128000a b
+--R *
+--R 16
+--R x
+--R +
+--R 4 4 8 4 4 7 4 4 6 4 4 5
+--R 70a b m + 7280a b m + 312340a b m + 7138040a b m
+--R +
+--R 4 4 4 4 4 3 4 4 2
+--R 93585310a b m + 705493880a b m + 2891238280a b m
+--R +
+--R 4 4 4 4
+--R 5549616800a b m + 3277120000a b
+--R *
+--R 13
+--R x
+--R +
+--R 5 3 8 5 3 7 5 3 6 5 3 5
+--R 56a b m + 5992a b m + 265664a b m + 6302128a b m
+--R +
+--R 5 3 4 5 3 3 5 3 2
+--R 86082584a b m + 676856488a b m + 2881562096a b m
+--R +
+--R 5 3 5 3
+--R 5692950592a b m + 3408204800a b
+--R *
+--R 10
+--R x
+--R +
+--R 6 2 8 6 2 7 6 2 6 6 2 5
+--R 28a b m + 3080a b m + 141232a b m + 3490760a b m
+--R +
+--R 6 2 4 6 2 3 6 2 2
+--R 50116612a b m + 418024880a b m + 1898889328a b m
+--R +
+--R 6 2 6 2
+--R 3962060480a b m + 2434432000a b
+--R *
+--R 7
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5
+--R 8a b m + 904a b m + 42896a b m + 1108240a b m
+--R +
+--R 7 4 7 3 7 2
+--R 16867592a b m + 152198536a b m + 769795424a b m
+--R +
+--R 7 7
+--R 1850614240a b m + 1217216000a b
+--R *
+--R 4
+--R x
+--R +
+--R 8 8 8 7 8 6 8 5 8 4
+--R a m + 116a m + 5698a m + 154280a m + 2508289a m
+--R +
+--R 8 3 8 2 8 8
+--R 24950324a m + 147373372a m + 468851120a m + 608608000a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R - b m - 92b m - 3514b m - 72128b m - 859369b m - 5974388b m
+--R +
+--R 8 2 8 8
+--R - 22963996b m - 42124592b m - 24344320b
+--R *
+--R m + 25
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R - 8a b m - 760a b m - 29792a b m - 624400a b m - 7563752a b m
+--R +
+--R 7 3 7 2 7 7
+--R - 53266360a b m - 206729648a b m - 381743680a b m - 221312000a b
+--R *
+--R m + 22
+--R x
+--R +
+--R 2 6 8 2 6 7 2 6 6 2 6 5
+--R - 28a b m - 2744a b m - 110656a b m - 2376920a b m
+--R +
+--R 2 6 4 2 6 3 2 6 2
+--R - 29390452a b m - 210422576a b m - 827034544a b m
+--R +
+--R 2 6 2 6
+--R - 1540629440a b m - 896896000a b
+--R *
+--R m + 19
+--R x
+--R +
+--R 3 5 8 3 5 7 3 5 6 3 5 5
+--R - 56a b m - 5656a b m - 235088a b m - 5197360a b m
+--R +
+--R 3 5 4 3 5 3 3 5 2
+--R - 65946104a b m - 482544664a b m - 1929412352a b m
+--R +
+--R 3 5 3 5
+--R - 3637973920a b m - 2130128000a b
+--R *
+--R m + 16
+--R x
+--R +
+--R 4 4 8 4 4 7 4 4 6 4 4 5
+--R - 70a b m - 7280a b m - 312340a b m - 7138040a b m
+--R +
+--R 4 4 4 4 4 3 4 4 2
+--R - 93585310a b m - 705493880a b m - 2891238280a b m
+--R +
+--R 4 4 4 4
+--R - 5549616800a b m - 3277120000a b
+--R *
+--R m + 13
+--R x
+--R +
+--R 5 3 8 5 3 7 5 3 6 5 3 5
+--R - 56a b m - 5992a b m - 265664a b m - 6302128a b m
+--R +
+--R 5 3 4 5 3 3 5 3 2
+--R - 86082584a b m - 676856488a b m - 2881562096a b m
+--R +
+--R 5 3 5 3
+--R - 5692950592a b m - 3408204800a b
+--R *
+--R m + 10
+--R x
+--R +
+--R 6 2 8 6 2 7 6 2 6 6 2 5
+--R - 28a b m - 3080a b m - 141232a b m - 3490760a b m
+--R +
+--R 6 2 4 6 2 3 6 2 2
+--R - 50116612a b m - 418024880a b m - 1898889328a b m
+--R +
+--R 6 2 6 2
+--R - 3962060480a b m - 2434432000a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 7 8 7 7 7 6 7 5 7 4
+--R - 8a b m - 904a b m - 42896a b m - 1108240a b m - 16867592a b m
+--R +
+--R 7 3 7 2 7 7
+--R - 152198536a b m - 769795424a b m - 1850614240a b m - 1217216000a b
+--R *
+--R m + 4
+--R x
+--R +
+--R 8 8 8 7 8 6 8 5 8 4 8 3
+--R - a m - 116a m - 5698a m - 154280a m - 2508289a m - 24950324a m
+--R +
+--R 8 2 8 8
+--R - 147373372a m - 468851120a m - 608608000a
+--R *
+--R m + 1
+--R x
+--R /
+--R 9 8 7 6 5 4 3
+--R m + 117m + 5814m + 159978m + 2662569m + 27458613m + 172323696m
+--R +
+--R 2
+--R 616224492m + 1077459120m + 608608000
+--R Type: Expression(Integer)
+--E 1249
+
+--S 1250 of 1285
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1250
+
+)clear all
+
+--S 1251 of 1285
+t0:=x^20*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 44 7 41 2 6 38 3 5 35 4 4 32 5 3 29
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 26 7 23 8 20
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 1251
+
+--S 1252 of 1285
+r0:=1/21*a^8*x^21+1/3*a^7*b*x^24+28/27*a^6*b^2*x^27+28/15*a^5*b^3*x^30+_
+ 70/33*a^4*b^4*x^33+14/9*a^3*b^5*x^36+28/39*a^2*b^6*x^39+_
+ 4/21*a*b^7*x^42+1/45*b^8*x^45
+--R
+--R
+--R (2)
+--R 1 8 45 4 7 42 28 2 6 39 14 3 5 36 70 4 4 33 28 5 3 30
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 45 21 39 9 33 15
+--R +
+--R 28 6 2 27 1 7 24 1 8 21
+--R -- a b x + - a b x + -- a x
+--R 27 3 21
+--R Type: Polynomial(Fraction(Integer))
+--E 1252
+
+--S 1253 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 45 4 7 42 28 2 6 39 14 3 5 36 70 4 4 33 28 5 3 30
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 45 21 39 9 33 15
+--R +
+--R 28 6 2 27 1 7 24 1 8 21
+--R -- a b x + - a b x + -- a x
+--R 27 3 21
+--R Type: Polynomial(Fraction(Integer))
+--E 1253
+
+--S 1254 of 1285
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1254
+
+--S 1255 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 1255
+
+)clear all
+
+--S 1256 of 1285
+t0:=x^17*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 41 7 38 2 6 35 3 5 32 4 4 29 5 3 26
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 23 7 20 8 17
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 1256
+
+--S 1257 of 1285
+r0:=-1/27*a^5*(a+b*x^3)^9/b^6+1/6*a^4*(a+b*x^3)^10/b^6-_
+ 10/33*a^3*(a+b*x^3)^11/b^6+5/18*a^2*(a+b*x^3)^12/b^6-_
+ 5/39*a*(a+b*x^3)^13/b^6+1/42*(a+b*x^3)^14/b^6
+--R
+--R
+--R (2)
+--R 1 14 42 8 13 39 7 2 12 36 56 3 11 33 7 4 10 30
+--R -- b x + -- a b x + - a b x + -- a b x + - a b x
+--R 42 39 9 33 3
+--R +
+--R 56 5 9 27 7 6 8 24 8 7 7 21 1 8 6 18 1 14
+--R -- a b x + - a b x + -- a b x + -- a b x - ----- a
+--R 27 6 21 18 54054
+--R /
+--R 6
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1257
+
+--S 1258 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 42 8 7 39 7 2 6 36 56 3 5 33 7 4 4 30 56 5 3 27
+--R -- b x + -- a b x + - a b x + -- a b x + - a b x + -- a b x
+--R 42 39 9 33 3 27
+--R +
+--R 7 6 2 24 8 7 21 1 8 18
+--R - a b x + -- a b x + -- a x
+--R 6 21 18
+--R Type: Polynomial(Fraction(Integer))
+--E 1258
+
+--S 1259 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 14
+--R ----- a
+--R 54054
+--R (4) ---------
+--R 6
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1259
+
+--S 1260 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1260
+
+)clear all
+
+--S 1261 of 1285
+t0:=x^14*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 38 7 35 2 6 32 3 5 29 4 4 26 5 3 23
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 20 7 17 8 14
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 1261
+
+--S 1262 of 1285
+r0:=1/27*a^4*(a+b*x^3)^9/b^5-2/15*a^3*(a+b*x^3)^10/b^5+_
+ 2/11*a^2*(a+b*x^3)^11/b^5-1/9*a*(a+b*x^3)^12/b^5+_
+ 1/39*(a+b*x^3)^13/b^5
+--R
+--R
+--R (2)
+--R 1 13 39 2 12 36 28 2 11 33 28 3 10 30 70 4 9 27
+--R -- b x + - a b x + -- a b x + -- a b x + -- a b x
+--R 39 9 33 15 27
+--R +
+--R 7 5 8 24 4 6 7 21 4 7 6 18 1 8 5 15 1 13
+--R - a b x + - a b x + - a b x + -- a b x + ----- a
+--R 3 3 9 15 19305
+--R /
+--R 5
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1262
+
+--S 1263 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 39 2 7 36 28 2 6 33 28 3 5 30 70 4 4 27 7 5 3 24
+--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + - a b x
+--R 39 9 33 15 27 3
+--R +
+--R 4 6 2 21 4 7 18 1 8 15
+--R - a b x + - a b x + -- a x
+--R 3 9 15
+--R Type: Polynomial(Fraction(Integer))
+--E 1263
+
+--S 1264 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 13
+--R ----- a
+--R 19305
+--R (4) - ---------
+--R 5
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1264
+
+--S 1265 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1265
+
+)clear all
+
+--S 1266 of 1285
+t0:=x^11*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 35 7 32 2 6 29 3 5 26 4 4 23 5 3 20
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 17 7 14 8 11
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 1266
+
+--S 1267 of 1285
+r0:=-1/27*a^3*(a+b*x^3)^9/b^4+1/10*a^2*(a+b*x^3)^10/b^4-_
+ 1/11*a*(a+b*x^3)^11/b^4+1/36*(a+b*x^3)^12/b^4
+--R
+--R
+--R (2)
+--R 1 12 36 8 11 33 14 2 10 30 56 3 9 27 35 4 8 24
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 36 33 15 27 12
+--R +
+--R 8 5 7 21 14 6 6 18 8 7 5 15 1 8 4 12 1 12
+--R - a b x + -- a b x + -- a b x + -- a b x - ---- a
+--R 3 9 15 12 5940
+--R /
+--R 4
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1267
+
+--S 1268 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 36 8 7 33 14 2 6 30 56 3 5 27 35 4 4 24 8 5 3 21
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + - a b x
+--R 36 33 15 27 12 3
+--R +
+--R 14 6 2 18 8 7 15 1 8 12
+--R -- a b x + -- a b x + -- a x
+--R 9 15 12
+--R Type: Polynomial(Fraction(Integer))
+--E 1268
+
+--S 1269 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 12
+--R ---- a
+--R 5940
+--R (4) --------
+--R 4
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1269
+
+--S 1270 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1270
+
+)clear all
+
+--S 1271 of 1285
+t0:=x^8*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 32 7 29 2 6 26 3 5 23 4 4 20 5 3 17
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 14 7 11 8 8
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 1271
+
+--S 1272 of 1285
+r0:=1/27*a^2*(a+b*x^3)^9/b^3-1/15*a*(a+b*x^3)^10/b^3+1/33*(a+b*x^3)^11/b^3
+--R
+--R
+--R (2)
+--R 1 11 33 4 10 30 28 2 9 27 7 3 8 24 10 4 7 21
+--R -- b x + -- a b x + -- a b x + - a b x + -- a b x
+--R 33 15 27 3 3
+--R +
+--R 28 5 6 18 28 6 5 15 2 7 4 12 1 8 3 9 1 11
+--R -- a b x + -- a b x + - a b x + - a b x + ---- a
+--R 9 15 3 9 1485
+--R /
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1272
+
+--S 1273 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 33 4 7 30 28 2 6 27 7 3 5 24 10 4 4 21 28 5 3 18
+--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x
+--R 33 15 27 3 3 9
+--R +
+--R 28 6 2 15 2 7 12 1 8 9
+--R -- a b x + - a b x + - a x
+--R 15 3 9
+--R Type: Polynomial(Fraction(Integer))
+--E 1273
+
+--S 1274 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 11
+--R ---- a
+--R 1485
+--R (4) - --------
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1274
+
+--S 1275 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1275
+
+)clear all
+
+--S 1276 of 1285
+t0:=x^5*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 29 7 26 2 6 23 3 5 20 4 4 17 5 3 14
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 11 7 8 8 5
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 1276
+
+--S 1277 of 1285
+r0:=-1/27*a*(a+b*x^3)^9/b^2+1/30*(a+b*x^3)^10/b^2
+--R
+--R
+--R (2)
+--R 1 10 30 8 9 27 7 2 8 24 8 3 7 21 35 4 6 18 56 5 5 15
+--R -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a b x
+--R 30 27 6 3 9 15
+--R +
+--R 7 6 4 12 8 7 3 9 1 8 2 6 1 10
+--R - a b x + - a b x + - a b x - --- a
+--R 3 9 6 270
+--R /
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1277
+
+--S 1278 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 30 8 7 27 7 2 6 24 8 3 5 21 35 4 4 18 56 5 3 15
+--R -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a b x
+--R 30 27 6 3 9 15
+--R +
+--R 7 6 2 12 8 7 9 1 8 6
+--R - a b x + - a b x + - a x
+--R 3 9 6
+--R Type: Polynomial(Fraction(Integer))
+--E 1278
+
+--S 1279 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 10
+--R --- a
+--R 270
+--R (4) -------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1279
+
+--S 1280 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1280
+
+)clear all
+
+--S 1281 of 1285
+t0:=x^2*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 26 7 23 2 6 20 3 5 17 4 4 14 5 3 11 6 2 8
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 5 8 2
+--R 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 1281
+
+--S 1282 of 1285
+r0:=1/27*(a+b*x^3)^9/b
+--R
+--R
+--R (2)
+--R 1 9 27 1 8 24 4 2 7 21 28 3 6 18 14 4 5 15 14 5 4 12
+--R -- b x + - a b x + - a b x + -- a b x + -- a b x + -- a b x
+--R 27 3 3 9 3 3
+--R +
+--R 28 6 3 9 4 7 2 6 1 8 3 1 9
+--R -- a b x + - a b x + - a b x + -- a
+--R 9 3 3 27
+--R /
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1282
+
+--S 1283 of 1285
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 27 1 7 24 4 2 6 21 28 3 5 18 14 4 4 15 14 5 3 12
+--R -- b x + - a b x + - a b x + -- a b x + -- a b x + -- a b x
+--R 27 3 3 9 3 3
+--R +
+--R 28 6 2 9 4 7 6 1 8 3
+--R -- a b x + - a b x + - a x
+--R 9 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 1283
+
+--S 1284 of 1285
+m0:=a0-r0
+--R
+--R
+--R 1 9
+--R -- a
+--R 27
+--R (4) - -----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1284
+
+--S 1285 of 1285
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1285
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich4c.input.pdf b/src/axiom-website/CATS/rich4c.input.pdf
new file mode 100644
index 0000000..d5d9361
Binary files /dev/null and b/src/axiom-website/CATS/rich4c.input.pdf differ
diff --git a/src/axiom-website/CATS/rich4d.input.pamphlet b/src/axiom-website/CATS/rich4d.input.pamphlet
new file mode 100644
index 0000000..895334e
--- /dev/null
+++ b/src/axiom-website/CATS/rich4d.input.pamphlet
@@ -0,0 +1,19462 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich4d.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 255 supplied "optimal results".
+\item 232 matching answers.
+\item 10 cases where Axiom's result differs from Rubi
+\item 17 cases where Axiom supplied 2 results.
+\item 2 cases that Axiom failed to integrate.
+\item 28 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich4d.output
+)spool rich4d.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1309
+t0:=(a+b*x^3)^8/x
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 1
+
+--S 2 of 1309
+r0:=8/3*a^7*b*x^3+14/3*a^6*b^2*x^6+56/9*a^5*b^3*x^9+35/6*a^4*b^4*x^12+_
+ 56/15*a^3*b^5*x^15+14/9*a^2*b^6*x^18+8/21*a*b^7*x^21+_
+ 1/24*b^8*x^24+a^8*log(x)
+--R
+--R
+--R (2)
+--R 8 8 24 7 21 2 6 18 3 5 15
+--R 2520a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x
+--R +
+--R 4 4 12 5 3 9 6 2 6 7 3
+--R 14700a b x + 15680a b x + 11760a b x + 6720a b x
+--R /
+--R 2520
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 8 24 7 21 2 6 18 3 5 15
+--R 2520a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x
+--R +
+--R 4 4 12 5 3 9 6 2 6 7 3
+--R 14700a b x + 15680a b x + 11760a b x + 6720a b x
+--R /
+--R 2520
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1309
+t0:=(a+b*x^3)^8/x^4
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 6
+
+--S 7 of 1309
+r0:=-1/3*a^8/x^3+28/3*a^6*b^2*x^3+28/3*a^5*b^3*x^6+70/9*a^4*b^4*x^9+_
+ 14/3*a^3*b^5*x^12+28/15*a^2*b^6*x^15+4/9*a*b^7*x^18+1/21*b^8*x^21+_
+ 8*a^7*b*log(x)
+--R
+--R
+--R (2)
+--R 7 3 8 24 7 21 2 6 18 3 5 15
+--R 2520a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x
+--R +
+--R 4 4 12 5 3 9 6 2 6 8
+--R 2450a b x + 2940a b x + 2940a b x - 105a
+--R /
+--R 3
+--R 315x
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 3 8 24 7 21 2 6 18 3 5 15
+--R 2520a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x
+--R +
+--R 4 4 12 5 3 9 6 2 6 8
+--R 2450a b x + 2940a b x + 2940a b x - 105a
+--R /
+--R 3
+--R 315x
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 1309
+t0:=(a+b*x^3)^8/x^7
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 11
+
+--S 12 of 1309
+r0:=-1/6*a^8/x^6-8/3*a^7*b/x^3+56/3*a^5*b^3*x^3+35/3*a^4*b^4*x^6+_
+ 56/9*a^3*b^5*x^9+7/3*a^2*b^6*x^12+8/15*a*b^7*x^15+_
+ 1/18*b^8*x^18+28*a^6*b^2*log(x)
+--R
+--R
+--R (2)
+--R 6 2 6 8 24 7 21 2 6 18 3 5 15
+--R 2520a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x
+--R +
+--R 4 4 12 5 3 9 7 3 8
+--R 1050a b x + 1680a b x - 240a b x - 15a
+--R /
+--R 6
+--R 90x
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 2 6 8 24 7 21 2 6 18 3 5 15
+--R 2520a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x
+--R +
+--R 4 4 12 5 3 9 7 3 8
+--R 1050a b x + 1680a b x - 240a b x - 15a
+--R /
+--R 6
+--R 90x
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 1309
+t0:=(a+b*x^3)^8/x^10
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 16
+
+--S 17 of 1309
+r0:=-1/9*a^8/x^9-4/3*a^7*b/x^6-28/3*a^6*b^2/x^3+70/3*a^4*b^4*x^3+_
+ 28/3*a^3*b^5*x^6+28/9*a^2*b^6*x^9+2/3*a*b^7*x^12+_
+ 1/15*b^8*x^15+56*a^5*b^3*log(x)
+--R
+--R
+--R (2)
+--R 5 3 9 8 24 7 21 2 6 18 3 5 15
+--R 2520a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x
+--R +
+--R 4 4 12 6 2 6 7 3 8
+--R 1050a b x - 420a b x - 60a b x - 5a
+--R /
+--R 9
+--R 45x
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 3 9 8 24 7 21 2 6 18 3 5 15
+--R 2520a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x
+--R +
+--R 4 4 12 6 2 6 7 3 8
+--R 1050a b x - 420a b x - 60a b x - 5a
+--R /
+--R 9
+--R 45x
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 1309
+t0:=(a+b*x^3)^8/x^13
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 21
+
+--S 22 of 1309
+r0:=-1/12*a^8/x^12-8/9*a^7*b/x^9-14/3*a^6*b^2/x^6-56/3*a^5*b^3/x^3+_
+ 56/3*a^3*b^5*x^3+14/3*a^2*b^6*x^6+8/9*a*b^7*x^9+_
+ 1/12*b^8*x^12+70*a^4*b^4*log(x)
+--R
+--R
+--R (2)
+--R 4 4 12 8 24 7 21 2 6 18 3 5 15
+--R 2520a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 672a b x - 168a b x - 32a b x - 3a
+--R /
+--R 12
+--R 36x
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 12 8 24 7 21 2 6 18 3 5 15
+--R 2520a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 672a b x - 168a b x - 32a b x - 3a
+--R /
+--R 12
+--R 36x
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 1309
+t0:=(a+b*x^3)^8/x^16
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 16
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 26
+
+--S 27 of 1309
+r0:=-1/15*a^8/x^15-2/3*a^7*b/x^12-28/9*a^6*b^2/x^9-28/3*a^5*b^3/x^6-_
+ 70/3*a^4*b^4/x^3+28/3*a^2*b^6*x^3+4/3*a*b^7*x^6+1/9*b^8*x^9+_
+ 56*a^3*b^5*log(x)
+--R
+--R
+--R (2)
+--R 3 5 15 8 24 7 21 2 6 18 4 4 12
+--R 2520a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 420a b x - 140a b x - 30a b x - 3a
+--R /
+--R 15
+--R 45x
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 5 15 8 24 7 21 2 6 18 4 4 12
+--R 2520a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 420a b x - 140a b x - 30a b x - 3a
+--R /
+--R 15
+--R 45x
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 1309
+t0:=(a+b*x^3)^8/x^19
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 31
+
+--S 32 of 1309
+r0:=-1/18*a^8/x^18-8/15*a^7*b/x^15-7/3*a^6*b^2/x^12-56/9*a^5*b^3/x^9-_
+ 35/3*a^4*b^4/x^6-56/3*a^3*b^5/x^3+8/3*a*b^7*x^3+_
+ 1/6*b^8*x^6+28*a^2*b^6*log(x)
+--R
+--R
+--R (2)
+--R 2 6 18 8 24 7 21 3 5 15 4 4 12
+--R 2520a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 560a b x - 210a b x - 48a b x - 5a
+--R /
+--R 18
+--R 90x
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 18 8 24 7 21 3 5 15 4 4 12
+--R 2520a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 560a b x - 210a b x - 48a b x - 5a
+--R /
+--R 18
+--R 90x
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 1309
+t0:=(a+b*x^3)^8/x^22
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 22
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 36
+
+--S 37 of 1309
+r0:=-1/21*a^8/x^21-4/9*a^7*b/x^18-28/15*a^6*b^2/x^15-14/3*a^5*b^3/x^12-_
+ 70/9*a^4*b^4/x^9-28/3*a^3*b^5/x^6-28/3*a^2*b^6/x^3+_
+ 1/3*b^8*x^3+8*a*b^7*log(x)
+--R
+--R
+--R (2)
+--R 7 21 8 24 2 6 18 3 5 15 4 4 12
+--R 2520a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 1470a b x - 588a b x - 140a b x - 15a
+--R /
+--R 21
+--R 315x
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 21 8 24 2 6 18 3 5 15 4 4 12
+--R 2520a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 1470a b x - 588a b x - 140a b x - 15a
+--R /
+--R 21
+--R 315x
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 1309
+t0:=(a+b*x^3)^8/x^25
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 25
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 41
+
+--S 42 of 1309
+r0:=-1/24*a^8/x^24-8/21*a^7*b/x^21-14/9*a^6*b^2/x^18-_
+ 56/15*a^5*b^3/x^15-35/6*a^4*b^4/x^12-56/9*a^3*b^5/x^9-_
+ 14/3*a^2*b^6/x^6-8/3*a*b^7/x^3+b^8*log(x)
+--R
+--R
+--R (2)
+--R 8 24 7 21 2 6 18 3 5 15
+--R 2520b x log(x) - 6720a b x - 11760a b x - 15680a b x
+--R +
+--R 4 4 12 5 3 9 6 2 6 7 3 8
+--R - 14700a b x - 9408a b x - 3920a b x - 960a b x - 105a
+--R /
+--R 24
+--R 2520x
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15
+--R 2520b x log(x) - 6720a b x - 11760a b x - 15680a b x
+--R +
+--R 4 4 12 5 3 9 6 2 6 7 3 8
+--R - 14700a b x - 9408a b x - 3920a b x - 960a b x - 105a
+--R /
+--R 24
+--R 2520x
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 1309
+t0:=(a+b*x^3)^8/x^28
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 28
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 46
+
+--S 47 of 1309
+r0:=-1/27*(a+b*x^3)^9/(a*x^27)
+--R
+--R
+--R (2)
+--R 1 9 27 1 8 24 4 2 7 21 28 3 6 18 14 4 5 15 14 5 4 12
+--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a b x
+--R 27 3 3 9 3 3
+--R +
+--R 28 6 3 9 4 7 2 6 1 8 3 1 9
+--R - -- a b x - - a b x - - a b x - -- a
+--R 9 3 3 27
+--R /
+--R 27
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 47
+
+--S 48 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x
+--R +
+--R 6 2 6 7 3 8
+--R - 36a b x - 9a b x - a
+--R /
+--R 27
+--R 27x
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 1309
+m0:=a0-r0
+--R
+--R
+--R 9
+--R b
+--R (4) ---
+--R 27a
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 1309
+t0:=(a+b*x^3)^8/x^31
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 31
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 1309
+r0:=-1/30*(a+b*x^3)^9/(a*x^30)+1/270*b*(a+b*x^3)^9/(a^2*x^27)
+--R
+--R
+--R (2)
+--R 1 10 30 1 2 8 24 8 3 7 21 7 4 6 18 56 5 5 15 35 6 4 12
+--R --- b x - - a b x - - a b x - - a b x - -- a b x - -- a b x
+--R 270 6 9 3 15 9
+--R +
+--R 8 7 3 9 7 8 2 6 8 9 3 1 10
+--R - - a b x - - a b x - -- a b x - -- a
+--R 3 6 27 30
+--R /
+--R 2 30
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 52
+
+--S 53 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R - 45b x - 240a b x - 630a b x - 1008a b x - 1050a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 720a b x - 315a b x - 80a b x - 9a
+--R /
+--R 30
+--R 270x
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 1309
+m0:=a0-r0
+--R
+--R
+--R 10
+--R b
+--R (4) - -----
+--R 2
+--R 270a
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 1309
+t0:=(a+b*x^3)^8/x^34
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 34
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 56
+
+--S 57 of 1309
+r0:=-1/33*(a+b*x^3)^9/(a*x^33)+1/165*b*(a+b*x^3)^9/(a^2*x^30)-_
+ 1/1485*b^2*(a+b*x^3)^9/(a^3*x^27)
+--R
+--R
+--R (2)
+--R 1 11 33 1 3 8 24 2 4 7 21 28 5 6 18 28 6 5 15
+--R - ---- b x - - a b x - - a b x - -- a b x - -- a b x
+--R 1485 9 3 15 9
+--R +
+--R 10 7 4 12 7 8 3 9 28 9 2 6 4 10 3 1 11
+--R - -- a b x - - a b x - -- a b x - -- a b x - -- a
+--R 3 3 27 15 33
+--R /
+--R 3 33
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 57
+
+--S 58 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R - 165b x - 990a b x - 2772a b x - 4620a b x - 4950a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 3465a b x - 1540a b x - 396a b x - 45a
+--R /
+--R 33
+--R 1485x
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 1309
+m0:=a0-r0
+--R
+--R
+--R 11
+--R b
+--R (4) ------
+--R 3
+--R 1485a
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 1309
+t0:=(a+b*x^3)^8/x^37
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 37
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 61
+
+--S 62 of 1309
+r0:=-1/36*(a+b*x^3)^9/(a*x^36)+1/132*b*(a+b*x^3)^9/(a^2*x^33)-_
+ 1/660*b^2*(a+b*x^3)^9/(a^3*x^30)+1/5940*b^3*(a+b*x^3)^9/(a^4*x^27)
+--R
+--R
+--R (2)
+--R 1 12 36 1 4 8 24 8 5 7 21 14 6 6 18 8 7 5 15
+--R ---- b x - -- a b x - -- a b x - -- a b x - - a b x
+--R 5940 12 15 9 3
+--R +
+--R 35 8 4 12 56 9 3 9 14 10 2 6 8 11 3 1 12
+--R - -- a b x - -- a b x - -- a b x - -- a b x - -- a
+--R 12 27 15 33 36
+--R /
+--R 4 36
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 62
+
+--S 63 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R - 495b x - 3168a b x - 9240a b x - 15840a b x - 17325a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 12320a b x - 5544a b x - 1440a b x - 165a
+--R /
+--R 36
+--R 5940x
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 1309
+m0:=a0-r0
+--R
+--R
+--R 12
+--R b
+--R (4) - ------
+--R 4
+--R 5940a
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 1309
+t0:=(a+b*x^3)^8/x^40
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 40
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 66
+
+--S 67 of 1309
+r0:=-1/39*a^8/x^39-2/9*a^7*b/x^36-28/33*a^6*b^2/x^33-28/15*a^5*b^3/x^30-_
+ 70/27*a^4*b^4/x^27-7/3*a^3*b^5/x^24-4/3*a^2*b^6/x^21-_
+ 4/9*a*b^7/x^18-1/15*b^8/x^15
+--R
+--R
+--R (2)
+--R 1 8 24 4 7 21 4 2 6 18 7 3 5 15 70 4 4 12 28 5 3 9
+--R - -- b x - - a b x - - a b x - - a b x - -- a b x - -- a b x
+--R 15 9 3 3 27 15
+--R +
+--R 28 6 2 6 2 7 3 1 8
+--R - -- a b x - - a b x - -- a
+--R 33 9 39
+--R /
+--R 39
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 67
+
+--S 68 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R - 1287b x - 8580a b x - 25740a b x - 45045a b x - 50050a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 36036a b x - 16380a b x - 4290a b x - 495a
+--R /
+--R 39
+--R 19305x
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 1309
+t0:=(a+b*x^3)^8/x^43
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 43
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 71
+
+--S 72 of 1309
+r0:=-1/42*a^8/x^42-8/39*a^7*b/x^39-7/9*a^6*b^2/x^36-56/33*a^5*b^3/x^33-_
+ 7/3*a^4*b^4/x^30-56/27*a^3*b^5/x^27-7/6*a^2*b^6/x^24-_
+ 8/21*a*b^7/x^21-1/18*b^8/x^18
+--R
+--R
+--R (2)
+--R 1 8 24 8 7 21 7 2 6 18 56 3 5 15 7 4 4 12 56 5 3 9
+--R - -- b x - -- a b x - - a b x - -- a b x - - a b x - -- a b x
+--R 18 21 6 27 3 33
+--R +
+--R 7 6 2 6 8 7 3 1 8
+--R - - a b x - -- a b x - -- a
+--R 9 39 42
+--R /
+--R 42
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 72
+
+--S 73 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R - 3003b x - 20592a b x - 63063a b x - 112112a b x - 126126a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R - 91728a b x - 42042a b x - 11088a b x - 1287a
+--R /
+--R 42
+--R 54054x
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 1309
+t0:=(a+b*x^3)^8/x^46
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 46
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 76
+
+--S 77 of 1309
+r0:=-1/45*a^8/x^45-4/21*a^7*b/x^42-28/39*a^6*b^2/x^39-_
+ 14/9*a^5*b^3/x^36-70/33*a^4*b^4/x^33-28/15*a^3*b^5/x^30-_
+ 28/27*a^2*b^6/x^27-1/3*a*b^7/x^24-1/21*b^8/x^21
+--R
+--R
+--R (2)
+--R 1 8 24 1 7 21 28 2 6 18 28 3 5 15 70 4 4 12 14 5 3 9
+--R - -- b x - - a b x - -- a b x - -- a b x - -- a b x - -- a b x
+--R 21 3 27 15 33 9
+--R +
+--R 28 6 2 6 4 7 3 1 8
+--R - -- a b x - -- a b x - -- a
+--R 39 21 45
+--R /
+--R 45
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 77
+
+--S 78 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15
+--R - 6435b x - 45045a b x - 140140a b x - 252252a b x
+--R +
+--R 4 4 12 5 3 9 6 2 6 7 3 8
+--R - 286650a b x - 210210a b x - 97020a b x - 25740a b x - 3003a
+--R /
+--R 45
+--R 135135x
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 1309
+t0:=x^4*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 28 7 25 2 6 22 3 5 19 4 4 16 5 3 13
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 10 7 7 8 4
+--R 28a b x + 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 81
+
+--S 82 of 1309
+r0:=1/5*a^8*x^5+a^7*b*x^8+28/11*a^6*b^2*x^11+4*a^5*b^3*x^14+_
+ 70/17*a^4*b^4*x^17+14/5*a^3*b^5*x^20+28/23*a^2*b^6*x^23+_
+ 4/13*a*b^7*x^26+1/29*b^8*x^29
+--R
+--R
+--R (2)
+--R 1 8 29 4 7 26 28 2 6 23 14 3 5 20 70 4 4 17 5 3 14
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 4a b x
+--R 29 13 23 5 17
+--R +
+--R 28 6 2 11 7 8 1 8 5
+--R -- a b x + a b x + - a x
+--R 11 5
+--R Type: Polynomial(Fraction(Integer))
+--E 82
+
+--S 83 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 29 4 7 26 28 2 6 23 14 3 5 20 70 4 4 17 5 3 14
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 4a b x
+--R 29 13 23 5 17
+--R +
+--R 28 6 2 11 7 8 1 8 5
+--R -- a b x + a b x + - a x
+--R 11 5
+--R Type: Polynomial(Fraction(Integer))
+--E 83
+
+--S 84 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 84
+
+--S 85 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 85
+
+)clear all
+
+--S 86 of 1309
+t0:=x^3*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 27 7 24 2 6 21 3 5 18 4 4 15 5 3 12 6 2 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 6 8 3
+--R 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 86
+
+--S 87 of 1309
+r0:=1/4*a^8*x^4+8/7*a^7*b*x^7+14/5*a^6*b^2*x^10+56/13*a^5*b^3*x^13+_
+ 35/8*a^4*b^4*x^16+56/19*a^3*b^5*x^19+14/11*a^2*b^6*x^22+_
+ 8/25*a*b^7*x^25+1/28*b^8*x^28
+--R
+--R
+--R (2)
+--R 1 8 28 8 7 25 14 2 6 22 56 3 5 19 35 4 4 16 56 5 3 13
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 28 25 11 19 8 13
+--R +
+--R 14 6 2 10 8 7 7 1 8 4
+--R -- a b x + - a b x + - a x
+--R 5 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 87
+
+--S 88 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 28 8 7 25 14 2 6 22 56 3 5 19 35 4 4 16 56 5 3 13
+--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x
+--R 28 25 11 19 8 13
+--R +
+--R 14 6 2 10 8 7 7 1 8 4
+--R -- a b x + - a b x + - a x
+--R 5 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 88
+
+--S 89 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 89
+
+--S 90 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 90
+
+)clear all
+
+--S 91 of 1309
+t0:=x*(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 25 7 22 2 6 19 3 5 16 4 4 13 5 3 10 6 2 7
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 4 8
+--R 8a b x + a x
+--R Type: Polynomial(Integer)
+--E 91
+
+--S 92 of 1309
+r0:=1/2*a^8*x^2+8/5*a^7*b*x^5+7/2*a^6*b^2*x^8+56/11*a^5*b^3*x^11+_
+ 5*a^4*b^4*x^14+56/17*a^3*b^5*x^17+7/5*a^2*b^6*x^20+_
+ 8/23*a*b^7*x^23+1/26*b^8*x^26
+--R
+--R
+--R (2)
+--R 1 8 26 8 7 23 7 2 6 20 56 3 5 17 4 4 14 56 5 3 11
+--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + -- a b x
+--R 26 23 5 17 11
+--R +
+--R 7 6 2 8 8 7 5 1 8 2
+--R - a b x + - a b x + - a x
+--R 2 5 2
+--R Type: Polynomial(Fraction(Integer))
+--E 92
+
+--S 93 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 26 8 7 23 7 2 6 20 56 3 5 17 4 4 14 56 5 3 11
+--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + -- a b x
+--R 26 23 5 17 11
+--R +
+--R 7 6 2 8 8 7 5 1 8 2
+--R - a b x + - a b x + - a x
+--R 2 5 2
+--R Type: Polynomial(Fraction(Integer))
+--E 93
+
+--S 94 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 94
+
+--S 95 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 95
+
+)clear all
+
+--S 96 of 1309
+t0:=(a+b*x^3)^8
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 6 2 6
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x
+--R +
+--R 7 3 8
+--R 8a b x + a
+--R Type: Polynomial(Integer)
+--E 96
+
+--S 97 of 1309
+r0:=a^8*x+2*a^7*b*x^4+4*a^6*b^2*x^7+28/5*a^5*b^3*x^10+_
+ 70/13*a^4*b^4*x^13+7/2*a^3*b^5*x^16+28/19*a^2*b^6*x^19+_
+ 4/11*a*b^7*x^22+1/25*b^8*x^25
+--R
+--R
+--R (2)
+--R 1 8 25 4 7 22 28 2 6 19 7 3 5 16 70 4 4 13 28 5 3 10
+--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x
+--R 25 11 19 2 13 5
+--R +
+--R 6 2 7 7 4 8
+--R 4a b x + 2a b x + a x
+--R Type: Polynomial(Fraction(Integer))
+--E 97
+
+--S 98 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 8 25 4 7 22 28 2 6 19 7 3 5 16 70 4 4 13 28 5 3 10
+--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x
+--R 25 11 19 2 13 5
+--R +
+--R 6 2 7 7 4 8
+--R 4a b x + 2a b x + a x
+--R Type: Polynomial(Fraction(Integer))
+--E 98
+
+--S 99 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 99
+
+--S 100 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 100
+
+)clear all
+
+--S 101 of 1309
+t0:=(a+b*x^3)^8/x^2
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 1309
+r0:=-a^8/x+4*a^7*b*x^2+28/5*a^6*b^2*x^5+7*a^5*b^3*x^8+_
+ 70/11*a^4*b^4*x^11+4*a^3*b^5*x^14+28/17*a^2*b^6*x^17+_
+ 2/5*a*b^7*x^20+1/23*b^8*x^23
+--R
+--R
+--R (2)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R 935b x + 8602a b x + 35420a b x + 86020a b x + 136850a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R 150535a b x + 120428a b x + 86020a b x - 21505a
+--R /
+--R 21505x
+--R Type: Fraction(Polynomial(Integer))
+--E 102
+
+--S 103 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R 935b x + 8602a b x + 35420a b x + 86020a b x + 136850a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R 150535a b x + 120428a b x + 86020a b x - 21505a
+--R /
+--R 21505x
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 1309
+t0:=(a+b*x^3)^8/x^3
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 106
+
+--S 107 of 1309
+r0:=-1/2*a^8/x^2+8*a^7*b*x+7*a^6*b^2*x^4+8*a^5*b^3*x^7+7*a^4*b^4*x^10+_
+ 56/13*a^3*b^5*x^13+7/4*a^2*b^6*x^16+8/19*a*b^7*x^19+1/22*b^8*x^22
+--R
+--R
+--R (2)
+--R 1 8 24 8 7 21 7 2 6 18 56 3 5 15 4 4 12 5 3 9
+--R -- b x + -- a b x + - a b x + -- a b x + 7a b x + 8a b x
+--R 22 19 4 13
+--R +
+--R 6 2 6 7 3 1 8
+--R 7a b x + 8a b x - - a
+--R 2
+--R /
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 107
+
+--S 108 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R 494b x + 4576a b x + 19019a b x + 46816a b x + 76076a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R 86944a b x + 76076a b x + 86944a b x - 5434a
+--R /
+--R 2
+--R 10868x
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 1309
+t0:=(a+b*x^3)^8/x^5
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 111
+
+--S 112 of 1309
+r0:=-1/4*a^8/x^4-8*a^7*b/x+14*a^6*b^2*x^2+56/5*a^5*b^3*x^5+_
+ 35/4*a^4*b^4*x^8+56/11*a^3*b^5*x^11+2*a^2*b^6*x^14+_
+ 8/17*a*b^7*x^17+1/20*b^8*x^20
+--R
+--R
+--R (2)
+--R 1 8 24 8 7 21 2 6 18 56 3 5 15 35 4 4 12 56 5 3 9
+--R -- b x + -- a b x + 2a b x + -- a b x + -- a b x + -- a b x
+--R 20 17 11 4 5
+--R +
+--R 6 2 6 7 3 1 8
+--R 14a b x - 8a b x - - a
+--R 4
+--R /
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 112
+
+--S 113 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R 187b x + 1760a b x + 7480a b x + 19040a b x + 32725a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R 41888a b x + 52360a b x - 29920a b x - 935a
+--R /
+--R 4
+--R 3740x
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 1309
+t0:=(a+b*x^3)^8/x^6
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 116
+
+--S 117 of 1309
+r0:=-1/5*a^8/x^5-4*a^7*b/x^2+28*a^6*b^2*x+14*a^5*b^3*x^4+10*a^4*b^4*x^7+_
+ 28/5*a^3*b^5*x^10+28/13*a^2*b^6*x^13+1/2*a*b^7*x^16+1/19*b^8*x^19
+--R
+--R
+--R (2)
+--R 1 8 24 1 7 21 28 2 6 18 28 3 5 15 4 4 12 5 3 9
+--R -- b x + - a b x + -- a b x + -- a b x + 10a b x + 14a b x
+--R 19 2 13 5
+--R +
+--R 6 2 6 7 3 1 8
+--R 28a b x - 4a b x - - a
+--R 5
+--R /
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 117
+
+--S 118 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R 130b x + 1235a b x + 5320a b x + 13832a b x + 24700a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R 34580a b x + 69160a b x - 9880a b x - 494a
+--R /
+--R 5
+--R 2470x
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 1309
+t0:=(a+b*x^3)^8/x^8
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 121
+
+--S 122 of 1309
+r0:=-1/7*a^8/x^7-2*a^7*b/x^4-28*a^6*b^2/x+28*a^5*b^3*x^2+_
+ 14*a^4*b^4*x^5+7*a^3*b^5*x^8+28/11*a^2*b^6*x^11+4/7*a*b^7*x^14+_
+ 1/17*b^8*x^17
+--R
+--R
+--R (2)
+--R 1 8 24 4 7 21 28 2 6 18 3 5 15 4 4 12 5 3 9
+--R -- b x + - a b x + -- a b x + 7a b x + 14a b x + 28a b x
+--R 17 7 11
+--R +
+--R 6 2 6 7 3 1 8
+--R - 28a b x - 2a b x - - a
+--R 7
+--R /
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 122
+
+--S 123 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R 77b x + 748a b x + 3332a b x + 9163a b x + 18326a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R 36652a b x - 36652a b x - 2618a b x - 187a
+--R /
+--R 7
+--R 1309x
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 1309
+t0:=(a+b*x^3)^8/x^9
+--R
+--R
+--R (1)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9
+--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x
+--R +
+--R 6 2 6 7 3 8
+--R 28a b x + 8a b x + a
+--R /
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 126
+
+--S 127 of 1309
+r0:=-1/8*a^8/x^8-8/5*a^7*b/x^5-14*a^6*b^2/x^2+56*a^5*b^3*x+_
+ 35/2*a^4*b^4*x^4+8*a^3*b^5*x^7+14/5*a^2*b^6*x^10+_
+ 8/13*a*b^7*x^13+1/16*b^8*x^16
+--R
+--R
+--R (2)
+--R 1 8 24 8 7 21 14 2 6 18 3 5 15 35 4 4 12 5 3 9
+--R -- b x + -- a b x + -- a b x + 8a b x + -- a b x + 56a b x
+--R 16 13 5 2
+--R +
+--R 6 2 6 8 7 3 1 8
+--R - 14a b x - - a b x - - a
+--R 5 8
+--R /
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 127
+
+--S 128 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 24 7 21 2 6 18 3 5 15 4 4 12
+--R 65b x + 640a b x + 2912a b x + 8320a b x + 18200a b x
+--R +
+--R 5 3 9 6 2 6 7 3 8
+--R 58240a b x - 14560a b x - 1664a b x - 130a
+--R /
+--R 8
+--R 1040x
+--R Type: Union(Expression(Integer),...)
+--E 128
+
+--S 129 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+)clear all
+
+--S 131 of 1309
+t0:=x^5/(a+b*x^3)
+--R
+--R
+--R 5
+--R x
+--R (1) --------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 131
+
+--S 132 of 1309
+r0:=1/3*x^3/b-1/3*a*log(a+b*x^3)/b^2
+--R
+--R
+--R 3 3
+--R - a log(b x + a) + b x
+--R (2) ------------------------
+--R 2
+--R 3b
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R - a log(b x + a) + b x
+--R (3) ------------------------
+--R 2
+--R 3b
+--R Type: Union(Expression(Integer),...)
+--E 133
+
+--S 134 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 135
+
+)clear all
+
+--S 136 of 1309
+t0:=x^4/(a+b*x^3)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 136
+
+--S 137 of 1309
+r0:=1/2*x^2/b+1/3*a^(2/3)*log(a^(1/3)+b^(1/3)*x)/b^(5/3)-_
+ 1/6*a^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(5/3)+_
+ a^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+
+--R - \|3 \|a log(x \|b - x\|a \|b + \|a ) + 2\|3 \|a log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 2x\|b - \|a 2 +-+3+-+2
+--R - 6\|a atan(-------------) + 3x \|3 \|b
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2
+--R | 2 | 2
+--R +-+ |a |a
+--R 2\|3 |-- log(b |-- + a x)
+--R 3| 2 3| 2
+--R \|b \|b
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |a |a |a 2
+--R - \|3 |-- log(- b x |-- + a |-- + a x )
+--R 3| 2 3| 2 3| 2
+--R \|b \|b \|b
+--R +
+--R +--+2
+--R | 2
+--R +-+ |a +-+
+--R +--+ b\|3 |-- - 2a x\|3
+--R | 2 3| 2
+--R |a \|b 2 +-+
+--R 6 |-- atan(---------------------- + 3x \|3
+--R 3| 2 +--+2
+--R \|b | 2
+--R |a
+--R 3b |--
+--R 3| 2
+--R \|b
+--R /
+--R +-+
+--R 6b\|3
+--R Type: Union(Expression(Integer),...)
+--E 138
+
+--S 139 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+
+--R \|3 \|a log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a log(x\|b + \|a )
+--R +
+--R +--+ +--+2
+--R | 2 | 2
+--R +-+ |a 3+-+2 |a
+--R 2\|3 |-- \|b log(b |-- + a x)
+--R 3| 2 3| 2
+--R \|b \|b
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |a 3+-+2 |a |a 2
+--R - \|3 |-- \|b log(- b x |-- + a |-- + a x )
+--R 3| 2 3| 2 3| 2
+--R \|b \|b \|b
+--R +
+--R +--+2
+--R | 2
+--R +-+ |a +-+
+--R +--+ b\|3 |-- - 2a x\|3
+--R 3+-+ 3+-+ | 2 3| 2
+--R 3+-+2 2x\|b - \|a |a 3+-+2 \|b
+--R 6\|a atan(-------------) + 6 |-- \|b atan(----------------------)
+--R +-+3+-+ 3| 2 +--+2
+--R \|3 \|a \|b | 2
+--R |a
+--R 3b |--
+--R 3| 2
+--R \|b
+--R /
+--R +-+3+-+2
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 140
+
+)clear all
+
+--S 141 of 1309
+t0:=x^3/(a+b*x^3)
+--R
+--R
+--R 3
+--R x
+--R (1) --------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 141
+
+--S 142 of 1309
+r0:=x/b-1/3*a^(1/3)*log(a^(1/3)+b^(1/3)*x)/b^(4/3)+1/6*a^(1/3)*_
+ log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(4/3)+a^(1/3)*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R \|3 \|a log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+ 2x\|b - \|a +-+3+-+
+--R - 6\|a atan(-------------) + 6x\|3 \|b
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 142
+
+--S 143 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+2 +---+ +---+ +---+
+--R +-+ | a | a | a 2 +-+ | a | a
+--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x)
+--R \| b \| b \| b \| b \| b
+--R +
+--R +---+
+--R +-+ | a +-+
+--R +---+ \|3 3|- - + 2x\|3
+--R | a \| b +-+
+--R - 6 3|- - atan(------------------- + 6x\|3
+--R \| b +---+
+--R | a
+--R 3 3|- -
+--R \| b
+--R /
+--R +-+
+--R 6b\|3
+--R Type: Union(Expression(Integer),...)
+--E 143
+
+--S 144 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R - \|3 \|a log(x \|b - x\|a \|b + \|a ) + 2\|3 \|a log(x\|b + \|a )
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | a 3+-+ | a | a 2
+--R - \|3 3|- - \|b log(3|- - + x 3|- - + x )
+--R \| b \| b \| b
+--R +
+--R +---+ +---+ 3+-+ 3+-+
+--R +-+ | a 3+-+ | a 3+-+ 2x\|b - \|a
+--R 2\|3 3|- - \|b log(- 3|- - + x + 6\|a atan(-------------)
+--R \| b \| b +-+3+-+
+--R \|3 \|a
+--R +
+--R +---+
+--R +-+ | a +-+
+--R +---+ \|3 3|- - + 2x\|3
+--R | a 3+-+ \| b
+--R - 6 3|- - \|b atan(-------------------)
+--R \| b +---+
+--R | a
+--R 3 3|- -
+--R \| b
+--R /
+--R +-+3+-+
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 145
+
+)clear all
+
+--S 146 of 1309
+t0:=x^2/(a+b*x^3)
+--R
+--R
+--R 2
+--R x
+--R (1) --------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 1309
+r0:=1/3*log(a+b*x^3)/b
+--R
+--R
+--R 3
+--R log(b x + a)
+--R (2) -------------
+--R 3b
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R log(b x + a)
+--R (3) -------------
+--R 3b
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 1309
+t0:=x/(a+b*x^3)
+--R
+--R
+--R x
+--R (1) --------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 151
+
+--S 152 of 1309
+r0:=-1/3*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*b^(2/3))+1/6*log(a^(2/3)-_
+ a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(2/3))-atan((a^(1/3)-_
+ 2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+
+--R \|3 log(x \|b - x\|a \|b + \|a ) - 2\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R 6atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+3+-+2
+--R 6\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R +-+ 3| 2 2 3| 2
+--R - \|3 log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2
+--R +------+2 +-+3| 2 +-+
+--R +-+ 3| 2 2x\|3 \|- a b - a b\|3
+--R 2\|3 log(x \|- a b + a b) - 6atan(--------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2
+--R 6\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 153
+
+--S 154 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +------+
+--R +-+3| 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(x\|b + \|a )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 3| 2 2 3| 2
+--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2 +------+ 3+-+ 3+-+
+--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a
+--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3
+--R - 6\|a \|b atan(--------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2 3+-+3+-+2
+--R 6\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 1309
+t0:=1/(a+b*x^3)
+--R
+--R
+--R 1
+--R (1) --------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 1309
+r0:=1/3*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(1/3))-1/6*log(a^(2/3)-_
+ a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(1/3))-_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+
+--R - \|3 log(x \|b - x\|a \|b + \|a ) + 2\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R 6atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2 3+-+
+--R 6\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+ +---+
+--R +-+ 2 3| 2 3| 2 2 +-+ 3| 2
+--R - \|3 log(x \|a b - a x\|a b + a ) + 2\|3 log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R 6atan(--------------------)
+--R 3a
+--R /
+--R +---+
+--R +-+3| 2
+--R 6\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 158
+
+--S 159 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--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 +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R 2\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+ +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+
+--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 +-+ +---+ 3+-+ 3+-+
+--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a
+--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------)
+--R 3a +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 6\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+)clear all
+
+--S 161 of 1309
+t0:=1/(x*(a+b*x^3))
+--R
+--R
+--R 1
+--R (1) ----------
+--R 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 161
+
+--S 162 of 1309
+r0:=log(x)/a-1/3*log(a+b*x^3)/a
+--R
+--R
+--R 3
+--R - log(b x + a) + 3log(x)
+--R (2) -------------------------
+--R 3a
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R - log(b x + a) + 3log(x)
+--R (3) -------------------------
+--R 3a
+--R Type: Union(Expression(Integer),...)
+--E 163
+
+--S 164 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 165
+
+)clear all
+
+--S 166 of 1309
+t0:=1/(x^2*(a+b*x^3))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 5 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 166
+
+--S 167 of 1309
+r0:=(-1)/(a*x)+1/3*b^(1/3)*log(a^(1/3)+b^(1/3)*x)/a^(4/3)-_
+ 1/6*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(4/3)+_
+ b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R - x\|3 \|b log(x \|b - x\|a \|b + \|a ) + 2x\|3 \|b log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+ 2x\|b - \|a +-+3+-+
+--R - 6x\|b atan(-------------) - 6\|3 \|a
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+
+--R 6a x\|3 \|a
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2 +-+ +-+2 +-+
+--R +-+ |b |b +-+ |b |b |b 2
+--R 2x\|3 3|- log(a 3|- + b x - x\|3 3|- log(- a x 3|- + a 3|- + b x )
+--R \|a \|a \|a \|a \|a
+--R +
+--R +-+2
+--R +-+ |b +-+
+--R +-+ a\|3 3|- - 2b x\|3
+--R |b \|a +-+
+--R 6x 3|- atan(--------------------- - 6\|3
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R /
+--R +-+
+--R 6a x\|3
+--R Type: Union(Expression(Integer),...)
+--E 168
+
+--S 169 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R \|3 \|b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|b log(x\|b + \|a )
+--R +
+--R +-+ +-+2
+--R +-+3+-+ |b |b
+--R 2\|3 \|a 3|- log(a 3|- + b x)
+--R \|a \|a
+--R +
+--R +-+ +-+2 +-+ 3+-+ 3+-+
+--R +-+3+-+ |b |b |b 2 3+-+ 2x\|b - \|a
+--R - \|3 \|a 3|- log(- a x 3|- + a 3|- + b x + 6\|b atan(-------------)
+--R \|a \|a \|a +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+2
+--R +-+ |b +-+
+--R +-+ a\|3 3|- - 2b x\|3
+--R 3+-+ |b \|a
+--R 6\|a 3|- atan(---------------------)
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R /
+--R +-+3+-+
+--R 6a\|3 \|a
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 170
+
+)clear all
+
+--S 171 of 1309
+t0:=1/(x^3*(a+b*x^3))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 6 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 171
+
+--S 172 of 1309
+r0:=(-1/2)/(a*x^2)-1/3*b^(2/3)*log(a^(1/3)+b^(1/3)*x)/a^(5/3)+_
+ 1/6*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(5/3)+_
+ b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R x \|3 \|b log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 +-+3+-+2 3+-+ 3+-+ 2 3+-+2 2x\|b - \|a +-+3+-+2
+--R - 2x \|3 \|b log(x\|b + \|a ) - 6x \|b atan(------------- - 3\|3 \|a
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 2 +-+3+-+2
+--R 6a x \|3 \|a
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R 2 +-+ | b 2 | b | b 2 2
+--R - x \|3 |- -- log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R 2 +-+ | b | b
+--R 2x \|3 |- -- log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R 2 | b \| a +-+
+--R - 6x |- -- atan(----------------------- - 3\|3
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R /
+--R 2 +-+
+--R 6a x \|3
+--R Type: Union(Expression(Integer),...)
+--E 173
+
+--S 174 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+
+--R - \|3 \|b log(x \|b - x\|a \|b + \|a ) + 2\|3 \|b log(x\|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 2 | b | b 2 2
+--R - \|3 |- -- \|a log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2 3+-+ 3+-+
+--R +-+ | b 3+-+2 | b 3+-+2 2x\|b - \|a
+--R 2\|3 |- -- \|a log(- a |- -- + b x + 6\|b atan(-------------)
+--R 3| 2 3| 2 +-+3+-+
+--R \| a \| a \|3 \|a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R | b 3+-+2 \| a
+--R - 6 |- -- \|a atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R /
+--R +-+3+-+2
+--R 6a\|3 \|a
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 175
+
+)clear all
+
+--S 176 of 1309
+t0:=1/(x^4*(a+b*x^3))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 7 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 176
+
+--S 177 of 1309
+r0:=(-1/3)/(a*x^3)-b*log(x)/a^2+1/3*b*log(a+b*x^3)/a^2
+--R
+--R
+--R 3 3 3
+--R b x log(b x + a) - 3b x log(x) - a
+--R (2) -----------------------------------
+--R 2 3
+--R 3a x
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3
+--R b x log(b x + a) - 3b x log(x) - a
+--R (3) -----------------------------------
+--R 2 3
+--R 3a x
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 1309
+t0:=x^4/(a-b*x^3)
+--R
+--R
+--R 4
+--R x
+--R (1) - --------
+--R 3
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 1309
+r0:=-1/2*x^2/b-1/3*a^(2/3)*log(a^(1/3)-b^(1/3)*x)/b^(5/3)+_
+ 1/6*a^(2/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(5/3)-_
+ a^(2/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+
+--R \|3 \|a log(x \|b + x\|a \|b + \|a ) - 2\|3 \|a log(- x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 2x\|b + \|a 2 +-+3+-+2
+--R - 6\|a atan(-------------) - 3x \|3 \|b
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | a | a | a 2
+--R - \|3 |- -- log(b x |- -- - a |- -- + a x )
+--R 3| 2 3| 2 3| 2
+--R \| b \| b \| b
+--R +
+--R +----+ +----+2
+--R | 2 | 2
+--R +-+ | a | a
+--R 2\|3 |- -- log(- b |- -- + a x)
+--R 3| 2 3| 2
+--R \| b \| b
+--R +
+--R +----+2
+--R | 2
+--R +-+ | a +-+
+--R +----+ b\|3 |- -- + 2a x\|3
+--R | 2 3| 2
+--R | a \| b 2 +-+
+--R 6 |- -- atan(------------------------ - 3x \|3
+--R 3| 2 +----+2
+--R \| b | 2
+--R | a
+--R 3b |- --
+--R 3| 2
+--R \| b
+--R /
+--R +-+
+--R 6b\|3
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|a log(x \|b + x\|a \|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | a 3+-+2 | a | a 2
+--R - \|3 |- -- \|b log(b x |- -- - a |- -- + a x )
+--R 3| 2 3| 2 3| 2
+--R \| b \| b \| b
+--R +
+--R +----+ +----+2
+--R | 2 | 2
+--R +-+ | a 3+-+2 | a +-+3+-+2 3+-+ 3+-+
+--R 2\|3 |- -- \|b log(- b |- -- + a x + 2\|3 \|a log(- x\|b + \|a )
+--R 3| 2 3| 2
+--R \| b \| b
+--R +
+--R +----+2
+--R | 2
+--R +-+ | a +-+
+--R +----+ b\|3 |- -- + 2a x\|3
+--R 3+-+ 3+-+ | 2 3| 2
+--R 3+-+2 2x\|b + \|a | a 3+-+2 \| b
+--R 6\|a atan(-------------) + 6 |- -- \|b atan(------------------------)
+--R +-+3+-+ 3| 2 +----+2
+--R \|3 \|a \| b | 2
+--R | a
+--R 3b |- --
+--R 3| 2
+--R \| b
+--R /
+--R +-+3+-+2
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 1309
+t0:=x^3/(a-b*x^3)
+--R
+--R
+--R 3
+--R x
+--R (1) - --------
+--R 3
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 186
+
+--S 187 of 1309
+r0:=-x/b-1/3*a^(1/3)*log(a^(1/3)-b^(1/3)*x)/b^(4/3)+_
+ 1/6*a^(1/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(4/3)+_
+ a^(1/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R \|3 \|a log(x \|b + x\|a \|b + \|a ) - 2\|3 \|a log(- x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+ 2x\|b + \|a +-+3+-+
+--R 6\|a atan(-------------) - 6x\|3 \|b
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+2 +---+ +---+ +---+
+--R +-+ | a | a | a 2 +-+ | a | a
+--R - \|3 3|- - log(3|- - - x 3|- - + x + 2\|3 3|- - log(3|- - + x)
+--R \| b \| b \| b \| b \| b
+--R +
+--R +---+
+--R +-+ | a +-+
+--R +---+ \|3 3|- - - 2x\|3
+--R | a \| b +-+
+--R - 6 3|- - atan(------------------- - 6x\|3
+--R \| b +---+
+--R | a
+--R 3 3|- -
+--R \| b
+--R /
+--R +-+
+--R 6b\|3
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|a log(x \|b + x\|a \|b + \|a )
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | a 3+-+ | a | a 2
+--R - \|3 3|- - \|b log(3|- - - x 3|- - + x )
+--R \| b \| b \| b
+--R +
+--R +---+ +---+
+--R +-+ | a 3+-+ | a +-+3+-+ 3+-+ 3+-+
+--R 2\|3 3|- - \|b log(3|- - + x + 2\|3 \|a log(- x\|b + \|a )
+--R \| b \| b
+--R +
+--R +---+
+--R +-+ | a +-+
+--R 3+-+ 3+-+ +---+ \|3 3|- - - 2x\|3
+--R 3+-+ 2x\|b + \|a | a 3+-+ \| b
+--R - 6\|a atan(-------------) - 6 3|- - \|b atan(-------------------)
+--R +-+3+-+ \| b +---+
+--R \|3 \|a | a
+--R 3 3|- -
+--R \| b
+--R /
+--R +-+3+-+
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 1309
+t0:=x^2/(a-b*x^3)
+--R
+--R
+--R 2
+--R x
+--R (1) - --------
+--R 3
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 1309
+r0:=-1/3*log(a-b*x^3)/b
+--R
+--R
+--R 3
+--R log(- b x + a)
+--R (2) - ---------------
+--R 3b
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R log(b x - a)
+--R (3) - -------------
+--R 3b
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 1309
+m0:=a0-r0
+--R
+--R
+--R 3 3
+--R - log(b x - a) + log(- b x + a)
+--R (4) ---------------------------------
+--R 3b
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 1309
+t0:=x/(a-b*x^3)
+--R
+--R
+--R x
+--R (1) - --------
+--R 3
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 196
+
+--S 197 of 1309
+r0:=-1/3*log(a^(1/3)-b^(1/3)*x)/(a^(1/3)*b^(2/3))+1/6*log(a^(2/3)+_
+ a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(2/3))-_
+ atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+
+--R \|3 log(x \|b + x\|a \|b + \|a ) - 2\|3 log(- x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2x\|b + \|a
+--R - 6atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+3+-+2
+--R 6\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2
+--R +-+ 3| 2
+--R 2\|3 log(x \|- a b - a b)
+--R +
+--R +------+2 +------+
+--R +-+ 3| 2 2 3| 2
+--R - \|3 log(- x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a b\|3
+--R 6atan(--------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2
+--R 6\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|- a b log(x \|b + x\|a \|b + \|a )
+--R +
+--R +------+2
+--R +-+3+-+3+-+2 3| 2
+--R 2\|3 \|a \|b log(x \|- a b - a b)
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 3| 2 2 3| 2
+--R - \|3 \|a \|b log(- x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+ +------+ 3+-+ 3+-+
+--R +-+3| 2 3+-+ 3+-+ 3| 2 2x\|b + \|a
+--R 2\|3 \|- a b log(- x\|b + \|a ) + 6\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 3+-+3+-+2 2x\|3 \|- a b + a b\|3
+--R 6\|a \|b atan(--------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2 3+-+3+-+2
+--R 6\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 1309
+t0:=1/(a-b*x^3)
+--R
+--R
+--R 1
+--R (1) - --------
+--R 3
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 201
+
+--S 202 of 1309
+r0:=-1/3*log(a^(1/3)-b^(1/3)*x)/(a^(2/3)*b^(1/3))+1/6*log(a^(2/3)+_
+ a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(1/3))+_
+ atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+
+--R \|3 log(x \|b + x\|a \|b + \|a ) - 2\|3 log(- x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2x\|b + \|a
+--R 6atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2 3+-+
+--R 6\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----+2 +-----+ +-----+
+--R +-+ 2 3| 2 3| 2 2 +-+ 3| 2
+--R - \|3 log(x \|- a b - a x\|- a b + a ) + 2\|3 log(x\|- a b + a)
+--R +
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b - a\|3
+--R 6atan(----------------------)
+--R 3a
+--R /
+--R +-----+
+--R +-+3| 2
+--R 6\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|- a b log(x \|b + x\|a \|b + \|a )
+--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 +-----+ +-----+
+--R +-+3+-+2 3+-+ 3| 2 +-+3| 2 3+-+ 3+-+
+--R 2\|3 \|a \|b log(x\|- a b + a + 2\|3 \|- a b log(- x\|b + \|a )
+--R +
+--R +-----+
+--R +-----+ 3+-+ 3+-+ +-+3| 2 +-+
+--R 3| 2 2x\|b + \|a 3+-+2 3+-+ 2x\|3 \|- a b - a\|3
+--R - 6\|- a b atan(-------------) + 6\|a \|b atan(----------------------)
+--R +-+3+-+ 3a
+--R \|3 \|a
+--R /
+--R +-----+
+--R +-+3| 2 3+-+2 3+-+
+--R 6\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 1309
+t0:=1/(x*(a-b*x^3))
+--R
+--R
+--R 1
+--R (1) - ----------
+--R 4
+--R b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 206
+
+--S 207 of 1309
+r0:=log(x)/a-1/3*log(a-b*x^3)/a
+--R
+--R
+--R 3
+--R 3log(x) - log(- b x + a)
+--R (2) -------------------------
+--R 3a
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R - log(b x - a) + 3log(x)
+--R (3) -------------------------
+--R 3a
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 1309
+m0:=a0-r0
+--R
+--R
+--R 3 3
+--R - log(b x - a) + log(- b x + a)
+--R (4) ---------------------------------
+--R 3a
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 1309
+t0:=1/(x^2*(a-b*x^3))
+--R
+--R
+--R 1
+--R (1) - -----------
+--R 5 2
+--R b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 211
+
+--S 212 of 1309
+r0:=(-1)/(a*x)-1/3*b^(1/3)*log(a^(1/3)-b^(1/3)*x)/a^(4/3)+_
+ 1/6*b^(1/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(4/3)-_
+ b^(1/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R x\|3 \|b log(x \|b + x\|a \|b + \|a ) - 2x\|3 \|b log(- x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+ 2x\|b + \|a +-+3+-+
+--R - 6x\|b atan(-------------) - 6\|3 \|a
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+
+--R 6a x\|3 \|a
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+2 +---+
+--R +-+ | b | b | b 2
+--R - x\|3 3|- - log(a x 3|- - - a 3|- - + b x )
+--R \| a \| a \| a
+--R +
+--R +---+ +---+2
+--R +-+ | b | b
+--R 2x\|3 3|- - log(- a 3|- - + b x)
+--R \| a \| a
+--R +
+--R +---+2
+--R +-+ | b +-+
+--R +---+ a\|3 3|- - + 2b x\|3
+--R | b \| a +-+
+--R 6x 3|- - atan(----------------------- - 6\|3
+--R \| a +---+2
+--R | b
+--R 3a 3|- -
+--R \| a
+--R /
+--R +-+
+--R 6a x\|3
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|b log(x \|b + x\|a \|b + \|a )
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | b 3+-+ | b | b 2
+--R - \|3 3|- - \|a log(a x 3|- - - a 3|- - + b x )
+--R \| a \| a \| a
+--R +
+--R +---+ +---+2
+--R +-+ | b 3+-+ | b +-+3+-+ 3+-+ 3+-+
+--R 2\|3 3|- - \|a log(- a 3|- - + b x + 2\|3 \|b log(- x\|b + \|a )
+--R \| a \| a
+--R +
+--R +---+2
+--R +-+ | b +-+
+--R 3+-+ 3+-+ +---+ a\|3 3|- - + 2b x\|3
+--R 3+-+ 2x\|b + \|a | b 3+-+ \| a
+--R 6\|b atan(-------------) + 6 3|- - \|a atan(-----------------------)
+--R +-+3+-+ \| a +---+2
+--R \|3 \|a | b
+--R 3a 3|- -
+--R \| a
+--R /
+--R +-+3+-+
+--R 6a\|3 \|a
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 1309
+t0:=1/(x^3*(a-b*x^3))
+--R
+--R
+--R 1
+--R (1) - -----------
+--R 6 3
+--R b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 216
+
+--S 217 of 1309
+r0:=(-1/2)/(a*x^2)-1/3*b^(2/3)*log(a^(1/3)-b^(1/3)*x)/a^(5/3)+_
+ 1/6*b^(2/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(5/3)+_
+ b^(2/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R x \|3 \|b log(x \|b + x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 +-+3+-+2 3+-+ 3+-+ 2 3+-+2 2x\|b + \|a
+--R - 2x \|3 \|b log(- x\|b + \|a ) + 6x \|b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+3+-+2
+--R - 3\|3 \|a
+--R /
+--R 2 +-+3+-+2
+--R 6a x \|3 \|a
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R 2 +-+ | b 2 | b | b 2 2
+--R - x \|3 |- -- log(a |- -- - a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R 2 +-+ | b | b
+--R 2x \|3 |- -- log(a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- - 2b x\|3
+--R | 2 3| 2
+--R 2 | b \| a +-+
+--R - 6x |- -- atan(----------------------- - 3\|3
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R /
+--R 2 +-+
+--R 6a x \|3
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|b log(x \|b + x\|a \|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 2 | b | b 2 2
+--R - \|3 |- -- \|a 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 | b +-+3+-+2 3+-+ 3+-+
+--R 2\|3 |- -- \|a log(a |- -- + b x + 2\|3 \|b log(- x\|b + \|a )
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- - 2b x\|3
+--R 3+-+ 3+-+ | 2 3| 2
+--R 3+-+2 2x\|b + \|a | b 3+-+2 \| a
+--R - 6\|b atan(-------------) - 6 |- -- \|a atan(-----------------------)
+--R +-+3+-+ 3| 2 +----+
+--R \|3 \|a \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R /
+--R +-+3+-+2
+--R 6a\|3 \|a
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 1309
+t0:=1/(x^4*(a-b*x^3))
+--R
+--R
+--R 1
+--R (1) - -----------
+--R 7 4
+--R b x - a x
+--R Type: Fraction(Polynomial(Integer))
+--E 221
+
+--S 222 of 1309
+r0:=(-1/3)/(a*x^3)+b*log(x)/a^2-1/3*b*log(a-b*x^3)/a^2
+--R
+--R
+--R 3 3 3
+--R 3b x log(x) - b x log(- b x + a) - a
+--R (2) -------------------------------------
+--R 2 3
+--R 3a x
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3
+--R - b x log(b x - a) + 3b x log(x) - a
+--R (3) -------------------------------------
+--R 2 3
+--R 3a x
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 1309
+m0:=a0-r0
+--R
+--R
+--R 3 3
+--R - b log(b x - a) + b log(- b x + a)
+--R (4) -------------------------------------
+--R 2
+--R 3a
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 1309
+t0:=1/(1+a+b*x^3)
+--R
+--R
+--R 1
+--R (1) ------------
+--R 3
+--R b x + a + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 226
+
+--S 227 of 1309
+r0:=1/3*log((1+a)^(1/3)+b^(1/3)*x)/((1+a)^(2/3)*b^(1/3))-_
+ 1/6*log((1+a)^(2/3)-(1+a)^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/((1+a)^(2/3)*b^(1/3))-atan(((1+a)^(1/3)-_
+ 2*b^(1/3)*x)/((1+a)^(1/3)*sqrt(3)))/((1+a)^(2/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-----+3+-+ 3+-----+2
+--R - \|3 log(x \|b - x\|a + 1 \|b + \|a + 1 )
+--R +
+--R 3+-+ 3+-----+
+--R +-+ 3+-+ 3+-----+ 2x\|b - \|a + 1
+--R 2\|3 log(x\|b + \|a + 1 ) + 6atan(-----------------)
+--R +-+3+-----+
+--R \|3 \|a + 1
+--R /
+--R +-+3+-----+2 3+-+
+--R 6\|3 \|a + 1 \|b
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-+
+--R \|3
+--R *
+--R +--------------+2 +--------------+
+--R 2 3| 2 3| 2 2
+--R log(x \|(a + 2a + 1)b + (- a - 1)x\|(a + 2a + 1)b + a + 2a + 1)
+--R +
+--R +--------------+
+--R +-+ 3| 2
+--R 2\|3 log(x\|(a + 2a + 1)b + a + 1)
+--R +
+--R +--------------+
+--R +-+3| 2 +-+
+--R 2x\|3 \|(a + 2a + 1)b + (- a - 1)\|3
+--R 6atan(---------------------------------------)
+--R 3a + 3
+--R /
+--R +--------------+
+--R +-+3| 2
+--R 6\|3 \|(a + 2a + 1)b
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R -
+--R +-+3+-----+2 3+-+
+--R \|3 \|a + 1 \|b
+--R *
+--R +--------------+2 +--------------+
+--R 2 3| 2 3| 2 2
+--R log(x \|(a + 2a + 1)b + (- a - 1)x\|(a + 2a + 1)b + a + 2a + 1)
+--R +
+--R +--------------+
+--R +-+3+-----+2 3+-+ 3| 2
+--R 2\|3 \|a + 1 \|b log(x\|(a + 2a + 1)b + a + 1)
+--R +
+--R +--------------+
+--R +-+3| 2 2 3+-+2 3+-----+3+-+ 3+-----+2
+--R \|3 \|(a + 2a + 1)b log(x \|b - x\|a + 1 \|b + \|a + 1 )
+--R +
+--R +--------------+
+--R +-+3| 2 3+-+ 3+-----+
+--R - 2\|3 \|(a + 2a + 1)b log(x\|b + \|a + 1 )
+--R +
+--R +--------------+
+--R +-+3| 2 +-+
+--R 3+-----+2 3+-+ 2x\|3 \|(a + 2a + 1)b + (- a - 1)\|3
+--R 6\|a + 1 \|b atan(---------------------------------------)
+--R 3a + 3
+--R +
+--R +--------------+ 3+-+ 3+-----+
+--R 3| 2 2x\|b - \|a + 1
+--R - 6\|(a + 2a + 1)b atan(-----------------)
+--R +-+3+-----+
+--R \|3 \|a + 1
+--R /
+--R +--------------+
+--R +-+3+-----+2 3+-+3| 2
+--R 6\|3 \|a + 1 \|b \|(a + 2a + 1)b
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 1309
+t0:=1/(1+a-b*x^3)
+--R
+--R
+--R 1
+--R (1) - ------------
+--R 3
+--R b x - a - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 1309
+r0:=-1/3*log((1+a)^(1/3)-b^(1/3)*x)/((1+a)^(2/3)*b^(1/3))+_
+ 1/6*log((1+a)^(2/3)+(1+a)^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/((1+a)^(2/3)*b^(1/3))+atan(((1+a)^(1/3)+_
+ 2*b^(1/3)*x)/((1+a)^(1/3)*sqrt(3)))/((1+a)^(2/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-----+3+-+ 3+-----+2
+--R \|3 log(x \|b + x\|a + 1 \|b + \|a + 1 )
+--R +
+--R 3+-+ 3+-----+
+--R +-+ 3+-+ 3+-----+ 2x\|b + \|a + 1
+--R - 2\|3 log(- x\|b + \|a + 1 ) + 6atan(-----------------)
+--R +-+3+-----+
+--R \|3 \|a + 1
+--R /
+--R +-+3+-----+2 3+-+
+--R 6\|3 \|a + 1 \|b
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-+
+--R \|3
+--R *
+--R log
+--R +----------------+2 +----------------+
+--R 2 3| 2 3| 2 2
+--R x \|(- a - 2a - 1)b + (- a - 1)x\|(- a - 2a - 1)b + a
+--R +
+--R 2a + 1
+--R +
+--R +----------------+
+--R +-+ 3| 2
+--R 2\|3 log(x\|(- a - 2a - 1)b + a + 1)
+--R +
+--R +----------------+
+--R +-+3| 2 +-+
+--R 2x\|3 \|(- a - 2a - 1)b + (- a - 1)\|3
+--R 6atan(-----------------------------------------)
+--R 3a + 3
+--R /
+--R +----------------+
+--R +-+3| 2
+--R 6\|3 \|(- a - 2a - 1)b
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----------------+
+--R +-+3| 2 2 3+-+2 3+-----+3+-+ 3+-----+2
+--R - \|3 \|(- a - 2a - 1)b log(x \|b + x\|a + 1 \|b + \|a + 1 )
+--R +
+--R -
+--R +-+3+-----+2 3+-+
+--R \|3 \|a + 1 \|b
+--R *
+--R log
+--R +----------------+2 +----------------+
+--R 2 3| 2 3| 2 2
+--R x \|(- a - 2a - 1)b + (- a - 1)x\|(- a - 2a - 1)b + a
+--R +
+--R 2a + 1
+--R +
+--R +----------------+
+--R +-+3+-----+2 3+-+ 3| 2
+--R 2\|3 \|a + 1 \|b log(x\|(- a - 2a - 1)b + a + 1)
+--R +
+--R +----------------+
+--R +-+3| 2 3+-+ 3+-----+
+--R 2\|3 \|(- a - 2a - 1)b log(- x\|b + \|a + 1 )
+--R +
+--R +----------------+ 3+-+ 3+-----+
+--R 3| 2 2x\|b + \|a + 1
+--R - 6\|(- a - 2a - 1)b atan(-----------------)
+--R +-+3+-----+
+--R \|3 \|a + 1
+--R +
+--R +----------------+
+--R +-+3| 2 +-+
+--R 3+-----+2 3+-+ 2x\|3 \|(- a - 2a - 1)b + (- a - 1)\|3
+--R 6\|a + 1 \|b atan(-----------------------------------------)
+--R 3a + 3
+--R /
+--R +----------------+
+--R +-+3| 2 3+-----+2 3+-+
+--R 6\|3 \|(- a - 2a - 1)b \|a + 1 \|b
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 1309
+t0:=1/(-1+a+b*x^3)
+--R
+--R
+--R 1
+--R (1) ------------
+--R 3
+--R b x + a - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 1309
+r0:=1/3*log((1-a)^(1/3)-b^(1/3)*x)/((1-a)^(2/3)*b^(1/3))-_
+ 1/6*log((1-a)^(2/3)+(1-a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1-a)^(2/3)*_
+ b^(1/3))-atan(((1-a)^(1/3)+2*b^(1/3)*x)/((1-a)^(1/3)*_
+ sqrt(3)))/((1-a)^(2/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-------+3+-+ 3+-------+2
+--R - \|3 log(x \|b + x\|- a + 1 \|b + \|- a + 1 )
+--R +
+--R 3+-+ 3+-------+
+--R +-+ 3+-+ 3+-------+ 2x\|b + \|- a + 1
+--R 2\|3 log(- x\|b + \|- a + 1 ) - 6atan(-------------------)
+--R +-+3+-------+
+--R \|3 \|- a + 1
+--R /
+--R +-+3+-------+2 3+-+
+--R 6\|3 \|- a + 1 \|b
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-+
+--R \|3
+--R *
+--R +--------------+2 +--------------+
+--R 2 3| 2 3| 2 2
+--R log(x \|(a - 2a + 1)b + (- a + 1)x\|(a - 2a + 1)b + a - 2a + 1)
+--R +
+--R +--------------+
+--R +-+ 3| 2
+--R 2\|3 log(x\|(a - 2a + 1)b + a - 1)
+--R +
+--R +--------------+
+--R +-+3| 2 +-+
+--R 2x\|3 \|(a - 2a + 1)b + (- a + 1)\|3
+--R 6atan(---------------------------------------)
+--R 3a - 3
+--R /
+--R +--------------+
+--R +-+3| 2
+--R 6\|3 \|(a - 2a + 1)b
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R -
+--R +-+3+-------+2 3+-+
+--R \|3 \|- a + 1 \|b
+--R *
+--R +--------------+2 +--------------+
+--R 2 3| 2 3| 2 2
+--R log(x \|(a - 2a + 1)b + (- a + 1)x\|(a - 2a + 1)b + a - 2a + 1)
+--R +
+--R +--------------+
+--R +-+3+-------+2 3+-+ 3| 2
+--R 2\|3 \|- a + 1 \|b log(x\|(a - 2a + 1)b + a - 1)
+--R +
+--R +--------------+
+--R +-+3| 2 2 3+-+2 3+-------+3+-+ 3+-------+2
+--R \|3 \|(a - 2a + 1)b log(x \|b + x\|- a + 1 \|b + \|- a + 1 )
+--R +
+--R +--------------+
+--R +-+3| 2 3+-+ 3+-------+
+--R - 2\|3 \|(a - 2a + 1)b log(- x\|b + \|- a + 1 )
+--R +
+--R +--------------+
+--R +-+3| 2 +-+
+--R 3+-------+2 3+-+ 2x\|3 \|(a - 2a + 1)b + (- a + 1)\|3
+--R 6\|- a + 1 \|b atan(---------------------------------------)
+--R 3a - 3
+--R +
+--R +--------------+ 3+-+ 3+-------+
+--R 3| 2 2x\|b + \|- a + 1
+--R 6\|(a - 2a + 1)b atan(-------------------)
+--R +-+3+-------+
+--R \|3 \|- a + 1
+--R /
+--R +--------------+
+--R +-+3+-------+2 3+-+3| 2
+--R 6\|3 \|- a + 1 \|b \|(a - 2a + 1)b
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 1309
+t0:=1/(-1+a-b*x^3)
+--R
+--R
+--R 1
+--R (1) - ------------
+--R 3
+--R b x - a + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 1309
+r0:=-1/3*log((1-a)^(1/3)+b^(1/3)*x)/((1-a)^(2/3)*b^(1/3))+_
+ 1/6*log((1-a)^(2/3)-(1-a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1-a)^(2/3)*_
+ b^(1/3))+atan(((1-a)^(1/3)-2*b^(1/3)*x)/((1-a)^(1/3)*_
+ sqrt(3)))/((1-a)^(2/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-------+3+-+ 3+-------+2
+--R \|3 log(x \|b - x\|- a + 1 \|b + \|- a + 1 )
+--R +
+--R 3+-+ 3+-------+
+--R +-+ 3+-+ 3+-------+ 2x\|b - \|- a + 1
+--R - 2\|3 log(x\|b + \|- a + 1 ) - 6atan(-------------------)
+--R +-+3+-------+
+--R \|3 \|- a + 1
+--R /
+--R +-+3+-------+2 3+-+
+--R 6\|3 \|- a + 1 \|b
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-+
+--R \|3
+--R *
+--R log
+--R +----------------+2 +----------------+
+--R 2 3| 2 3| 2 2
+--R x \|(- a + 2a - 1)b + (- a + 1)x\|(- a + 2a - 1)b + a
+--R +
+--R - 2a + 1
+--R +
+--R +----------------+
+--R +-+ 3| 2
+--R 2\|3 log(x\|(- a + 2a - 1)b + a - 1)
+--R +
+--R +----------------+
+--R +-+3| 2 +-+
+--R 2x\|3 \|(- a + 2a - 1)b + (- a + 1)\|3
+--R 6atan(-----------------------------------------)
+--R 3a - 3
+--R /
+--R +----------------+
+--R +-+3| 2
+--R 6\|3 \|(- a + 2a - 1)b
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----------------+
+--R +-+3| 2 2 3+-+2 3+-------+3+-+ 3+-------+2
+--R - \|3 \|(- a + 2a - 1)b log(x \|b - x\|- a + 1 \|b + \|- a + 1 )
+--R +
+--R +----------------+
+--R +-+3| 2 3+-+ 3+-------+
+--R 2\|3 \|(- a + 2a - 1)b log(x\|b + \|- a + 1 )
+--R +
+--R -
+--R +-+3+-------+2 3+-+
+--R \|3 \|- a + 1 \|b
+--R *
+--R log
+--R +----------------+2 +----------------+
+--R 2 3| 2 3| 2 2
+--R x \|(- a + 2a - 1)b + (- a + 1)x\|(- a + 2a - 1)b + a
+--R +
+--R - 2a + 1
+--R +
+--R +----------------+
+--R +-+3+-------+2 3+-+ 3| 2
+--R 2\|3 \|- a + 1 \|b log(x\|(- a + 2a - 1)b + a - 1)
+--R +
+--R +----------------+ 3+-+ 3+-------+
+--R 3| 2 2x\|b - \|- a + 1
+--R 6\|(- a + 2a - 1)b atan(-------------------)
+--R +-+3+-------+
+--R \|3 \|- a + 1
+--R +
+--R +----------------+
+--R +-+3| 2 +-+
+--R 3+-------+2 3+-+ 2x\|3 \|(- a + 2a - 1)b + (- a + 1)\|3
+--R 6\|- a + 1 \|b atan(-----------------------------------------)
+--R 3a - 3
+--R /
+--R +----------------+
+--R +-+3| 2 3+-------+2 3+-+
+--R 6\|3 \|(- a + 2a - 1)b \|- a + 1 \|b
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 1309
+t0:=x^5/(a+b*x^3)^2
+--R
+--R
+--R 5
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 1309
+r0:=1/3*a/(b^2*(a+b*x^3))+1/3*log(a+b*x^3)/b^2
+--R
+--R
+--R 3 3
+--R (b x + a)log(b x + a) + a
+--R (2) ---------------------------
+--R 3 3 2
+--R 3b x + 3a b
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R (b x + a)log(b x + a) + a
+--R (3) ---------------------------
+--R 3 3 2
+--R 3b x + 3a b
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 1309
+t0:=x^4/(a+b*x^3)^2
+--R
+--R
+--R 4
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 1309
+r0:=-1/3*x^2/(b*(a+b*x^3))-2/9*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*b^(5/3))+_
+ 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(5/3))-_
+ 2/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_
+ (a^(1/3)*b^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (b x + a)\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a
+--R (- 2b x - 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 +-+3+-+3+-+2
+--R - 3x \|3 \|a \|b
+--R /
+--R 2 3 +-+3+-+3+-+2
+--R (9b x + 9a b)\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R 3 +-+ 3| 2 2 3| 2
+--R (- b x - a)\|3 log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2
+--R 3 +-+ 3| 2
+--R (2b x + 2a)\|3 log(x \|- a b + a b)
+--R +
+--R +------+2
+--R +-+3| 2 +-+ +------+
+--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2
+--R (- 6b x - 6a)atan(--------------------------) - 3x \|3 \|- a b
+--R 3a b
+--R /
+--R +------+
+--R 2 3 +-+3| 2
+--R (9b x + 9a b)\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +------+
+--R +-+3| 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(x\|b + \|a )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 3| 2 2 3| 2
+--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2 +------+ 3+-+ 3+-+
+--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a
+--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3
+--R - 6\|a \|b atan(--------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2 3+-+3+-+2
+--R 9b\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 1309
+t0:=x^3/(a+b*x^3)^2
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 1309
+r0:=-1/3*x/(b*(a+b*x^3))+1/9*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(4/3))-_
+ 1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(4/3))-_
+ 1/3*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 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- b x - a)\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a
+--R (2b x + 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+3+-+2 3+-+
+--R - 6x\|3 \|a \|b
+--R /
+--R 2 3 +-+3+-+2 3+-+
+--R (18b x + 18a b)\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 3 +-+ 2 3| 2 3| 2 2
+--R (- b x - a)\|3 log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R +---+ +-+3| 2 +-+
+--R 3 +-+ 3| 2 3 2x\|3 \|a b - a\|3
+--R (2b x + 2a)\|3 log(x\|a b + a) + (6b x + 6a)atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R +-+3| 2
+--R - 6x\|3 \|a b
+--R /
+--R +---+
+--R 2 3 +-+3| 2
+--R (18b x + 18a b)\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--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 +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R 2\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+ +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+
+--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 +-+ +---+ 3+-+ 3+-+
+--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a
+--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------)
+--R 3a +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 18b\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 1309
+t0:=x^2/(a+b*x^3)^2
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 1309
+r0:=(-1/3)/(b*(a+b*x^3))
+--R
+--R
+--R 1
+--R -
+--R 3
+--R (2) - ----------
+--R 2 3
+--R b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 262
+
+--S 263 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ------------
+--R 2 3
+--R 3b x + 3a b
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 1309
+t0:=x/(a+b*x^3)^2
+--R
+--R
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 266
+
+--S 267 of 1309
+r0:=1/3*x^2/(a*(a+b*x^3))-1/9*log(a^(1/3)+b^(1/3)*x)/(a^(4/3)*b^(2/3))+_
+ 1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(4/3)*b^(2/3))-_
+ 1/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_
+ (a^(4/3)*b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (b x + a)\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a
+--R (- 2b x - 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 +-+3+-+3+-+2
+--R 6x \|3 \|a \|b
+--R /
+--R 3 2 +-+3+-+3+-+2
+--R (18a b x + 18a )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 267
+
+--S 268 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R 3 +-+ 3| 2 2 3| 2
+--R (- b x - a)\|3 log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2
+--R 3 +-+ 3| 2
+--R (2b x + 2a)\|3 log(x \|- a b + a b)
+--R +
+--R +------+2
+--R +-+3| 2 +-+ +------+
+--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2
+--R (- 6b x - 6a)atan(--------------------------) + 6x \|3 \|- a b
+--R 3a b
+--R /
+--R +------+
+--R 3 2 +-+3| 2
+--R (18a b x + 18a )\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +------+
+--R +-+3| 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(x\|b + \|a )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 3| 2 2 3| 2
+--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2 +------+ 3+-+ 3+-+
+--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a
+--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3
+--R - 6\|a \|b atan(--------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2 3+-+3+-+2
+--R 18a\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 1309
+t0:=1/(a+b*x^3)^2
+--R
+--R
+--R 1
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 271
+
+--S 272 of 1309
+r0:=1/3*x/(a*(a+b*x^3))+2/9*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(1/3))-_
+ 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(1/3))-_
+ 2/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_
+ (a^(5/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- b x - a)\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a
+--R (2b x + 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+3+-+2 3+-+
+--R 3x\|3 \|a \|b
+--R /
+--R 3 2 +-+3+-+2 3+-+
+--R (9a b x + 9a )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 3 +-+ 2 3| 2 3| 2 2
+--R (- b x - a)\|3 log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R +---+ +-+3| 2 +-+
+--R 3 +-+ 3| 2 3 2x\|3 \|a b - a\|3
+--R (2b x + 2a)\|3 log(x\|a b + a) + (6b x + 6a)atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R +-+3| 2
+--R 3x\|3 \|a b
+--R /
+--R +---+
+--R 3 2 +-+3| 2
+--R (9a b x + 9a )\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--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 +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R 2\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+ +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+
+--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 +-+ +---+ 3+-+ 3+-+
+--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a
+--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------)
+--R 3a +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 9a\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 1309
+t0:=1/(x*(a+b*x^3)^2)
+--R
+--R
+--R 1
+--R (1) --------------------
+--R 2 7 4 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 276
+
+--S 277 of 1309
+r0:=1/3/(a*(a+b*x^3))+log(x)/a^2-1/3*log(a+b*x^3)/a^2
+--R
+--R
+--R 3 3 3
+--R (- b x - a)log(b x + a) + (3b x + 3a)log(x) + a
+--R (2) --------------------------------------------------
+--R 2 3 3
+--R 3a b x + 3a
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3
+--R (- b x - a)log(b x + a) + (3b x + 3a)log(x) + a
+--R (3) --------------------------------------------------
+--R 2 3 3
+--R 3a b x + 3a
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 1309
+t0:=1/(x^2*(a+b*x^3)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 8 5 2 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 1309
+r0:=(-4/3)/(a^2*x)+1/3/(a*x*(a+b*x^3))+4/9*b^(1/3)*log(a^(1/3)+_
+ b^(1/3)*x)/a^(7/3)-2/9*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/a^(7/3)+4/3*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 4 +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 2b x - 2a x)\|3 \|b log(x \|b - x\|a \|b + \|a )
+--R +
+--R 4 +-+3+-+ 3+-+ 3+-+
+--R (4b x + 4a x)\|3 \|b log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 4 3+-+ 2x\|b - \|a 3 +-+3+-+
+--R (- 12b x - 12a x)\|b atan(-------------) + (- 12b x - 9a)\|3 \|a
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 2 4 3 +-+3+-+
+--R (9a b x + 9a x)\|3 \|a
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2
+--R 4 +-+ |b |b
+--R (4b x + 4a x)\|3 3|- log(a 3|- + b x)
+--R \|a \|a
+--R +
+--R +-+ +-+2 +-+
+--R 4 +-+ |b |b |b 2
+--R (- 2b x - 2a x)\|3 3|- log(- a x 3|- + a 3|- + b x )
+--R \|a \|a \|a
+--R +
+--R +-+2
+--R +-+ |b +-+
+--R +-+ a\|3 3|- - 2b x\|3
+--R 4 |b \|a 3 +-+
+--R (12b x + 12a x) 3|- atan(--------------------- + (- 12b x - 9a)\|3
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R /
+--R 2 4 3 +-+
+--R (9a b x + 9a x)\|3
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R 2\|3 \|b log(x \|b - x\|a \|b + \|a ) - 4\|3 \|b log(x\|b + \|a )
+--R +
+--R +-+ +-+2
+--R +-+3+-+ |b |b
+--R 4\|3 \|a 3|- log(a 3|- + b x)
+--R \|a \|a
+--R +
+--R +-+ +-+2 +-+
+--R +-+3+-+ |b |b |b 2
+--R - 2\|3 \|a 3|- log(- a x 3|- + a 3|- + b x )
+--R \|a \|a \|a
+--R +
+--R +-+2
+--R +-+ |b +-+
+--R 3+-+ 3+-+ +-+ a\|3 3|- - 2b x\|3
+--R 3+-+ 2x\|b - \|a 3+-+ |b \|a
+--R 12\|b atan(-------------) + 12\|a 3|- atan(---------------------)
+--R +-+3+-+ \|a +-+2
+--R \|3 \|a |b
+--R 3a 3|-
+--R \|a
+--R /
+--R 2 +-+3+-+
+--R 9a \|3 \|a
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 1309
+t0:=1/(x^3*(a+b*x^3)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 9 6 2 3
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 1309
+r0:=(-5/6)/(a^2*x^2)+1/3/(a*x^2*(a+b*x^3))-5/9*b^(2/3)*log(a^(1/3)+_
+ b^(1/3)*x)/a^(8/3)+5/18*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/a^(8/3)+5/3*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 5 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (5b x + 5a x )\|3 \|b log(x \|b - x\|a \|b + \|a )
+--R +
+--R 5 2 +-+3+-+2 3+-+ 3+-+
+--R (- 10b x - 10a x )\|3 \|b log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 5 2 3+-+2 2x\|b - \|a 3 +-+3+-+2
+--R (- 30b x - 30a x )\|b atan(-------------) + (- 15b x - 9a)\|3 \|a
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 2 5 3 2 +-+3+-+2
+--R (18a b x + 18a x )\|3 \|a
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R 5 2 +-+ | b 2 | b | b 2 2
+--R (- 5b x - 5a x )\|3 |- -- log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R 5 2 +-+ | b | b
+--R (10b x + 10a x )\|3 |- -- log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R 5 2 | b \| a
+--R (- 30b x - 30a x ) |- -- atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R 3 +-+
+--R (- 15b x - 9a)\|3
+--R /
+--R 2 5 3 2 +-+
+--R (18a b x + 18a x )\|3
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - 5\|3 \|b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+2 3+-+ 3+-+
+--R 10\|3 \|b log(x\|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 2 | b | b 2 2
+--R - 5\|3 |- -- \|a log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2 3+-+ 3+-+
+--R +-+ | b 3+-+2 | b 3+-+2 2x\|b - \|a
+--R 10\|3 |- -- \|a log(- a |- -- + b x + 30\|b atan(-------------)
+--R 3| 2 3| 2 +-+3+-+
+--R \| a \| a \|3 \|a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R | b 3+-+2 \| a
+--R - 30 |- -- \|a atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R /
+--R 2 +-+3+-+2
+--R 18a \|3 \|a
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 1309
+t0:=1/(x^4*(a+b*x^3)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 2 10 7 2 4
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 1309
+r0:=(-2/3)/(a^2*x^3)+1/3/(a*x^3*(a+b*x^3))-2*b*log(x)/a^3+_
+ 2/3*b*log(a+b*x^3)/a^3
+--R
+--R
+--R (2)
+--R 2 6 3 3 2 6 3 3 2
+--R (2b x + 2a b x )log(b x + a) + (- 6b x - 6a b x )log(x) - 2a b x - a
+--R -------------------------------------------------------------------------
+--R 3 6 4 3
+--R 3a b x + 3a x
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 3 3 2 6 3 3 2
+--R (2b x + 2a b x )log(b x + a) + (- 6b x - 6a b x )log(x) - 2a b x - a
+--R -------------------------------------------------------------------------
+--R 3 6 4 3
+--R 3a b x + 3a x
+--R Type: Union(Expression(Integer),...)
+--E 293
+
+--S 294 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+)clear all
+
+--S 296 of 1309
+t0:=x^8/(a+b*x^3)^3
+--R
+--R
+--R 8
+--R x
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 296
+
+--S 297 of 1309
+r0:=-1/6*a^2/(b^3*(a+b*x^3)^2)+2/3*a/(b^3*(a+b*x^3))+1/3*log(a+b*x^3)/b^3
+--R
+--R
+--R 2 6 3 2 3 3 2
+--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a
+--R (2) ----------------------------------------------------
+--R 5 6 4 3 2 3
+--R 6b x + 12a b x + 6a b
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 3 2 3 3 2
+--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a
+--R (3) ----------------------------------------------------
+--R 5 6 4 3 2 3
+--R 6b x + 12a b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 298
+
+--S 299 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 300
+
+)clear all
+
+--S 301 of 1309
+t0:=x^7/(a+b*x^3)^3
+--R
+--R
+--R 7
+--R x
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 301
+
+--S 302 of 1309
+r0:=-1/6*x^5/(b*(a+b*x^3)^2)-5/18*x^2/(b^2*(a+b*x^3))-5/27*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(1/3)*b^(8/3))+5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(1/3)*b^(8/3))-5/9*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(1/3)*b^(8/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (5b x + 10a b x + 5a )\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 6 3 2 +-+ 3+-+ 3+-+
+--R (- 10b x - 20a b x - 10a )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 6 3 2 2x\|b - \|a
+--R (30b x + 60a b x + 30a )atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 5 2 +-+3+-+3+-+2
+--R (- 24b x - 15a x )\|3 \|a \|b
+--R /
+--R 4 6 3 3 2 2 +-+3+-+3+-+2
+--R (54b x + 108a b x + 54a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R 2 6 3 2 +-+ 3| 2 2 3| 2
+--R (- 5b x - 10a b x - 5a )\|3 log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2
+--R 2 6 3 2 +-+ 3| 2
+--R (10b x + 20a b x + 10a )\|3 log(x \|- a b + a b)
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 2 6 3 2 2x\|3 \|- a b - a b\|3
+--R (- 30b x - 60a b x - 30a )atan(--------------------------)
+--R 3a b
+--R +
+--R +------+
+--R 5 2 +-+3| 2
+--R (- 24b x - 15a x )\|3 \|- a b
+--R /
+--R +------+
+--R 4 6 3 3 2 2 +-+3| 2
+--R (54b x + 108a b x + 54a b )\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 303
+
+--S 304 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - 5\|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +------+
+--R +-+3| 2 3+-+ 3+-+
+--R 10\|3 \|- a b log(x\|b + \|a )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 3| 2 2 3| 2
+--R - 5\|3 \|a \|b log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2 +------+ 3+-+ 3+-+
+--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a
+--R 10\|3 \|a \|b log(x \|- a b + a b) - 30\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3
+--R - 30\|a \|b atan(--------------------------)
+--R 3a b
+--R /
+--R +------+
+--R 2 +-+3| 2 3+-+3+-+2
+--R 54b \|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 305
+
+)clear all
+
+--S 306 of 1309
+t0:=x^6/(a+b*x^3)^3
+--R
+--R
+--R 6
+--R x
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 306
+
+--S 307 of 1309
+r0:=-1/6*x^4/(b*(a+b*x^3)^2)-2/9*x/(b^2*(a+b*x^3))+2/27*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(2/3)*b^(7/3))-1/27*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(2/3)*b^(7/3))-2/9*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 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 2b x - 4a b x - 2a )\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 6 3 2 +-+ 3+-+ 3+-+
+--R (4b x + 8a b x + 4a )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 6 3 2 2x\|b - \|a
+--R (12b x + 24a b x + 12a )atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 4 +-+3+-+2 3+-+
+--R (- 21b x - 12a x)\|3 \|a \|b
+--R /
+--R 4 6 3 3 2 2 +-+3+-+2 3+-+
+--R (54b x + 108a b x + 54a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 6 3 2 +-+ 2 3| 2 3| 2 2
+--R (- 2b x - 4a b x - 2a )\|3 log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 2 6 3 2 +-+ 3| 2
+--R (4b x + 8a b x + 4a )\|3 log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 6 3 2 2x\|3 \|a b - a\|3
+--R (12b x + 24a b x + 12a )atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R 4 +-+3| 2
+--R (- 21b x - 12a x)\|3 \|a b
+--R /
+--R +---+
+--R 4 6 3 3 2 2 +-+3| 2
+--R (54b x + 108a b x + 54a b )\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 308
+
+--S 309 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--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 +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R 2\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+ +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+
+--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 +-+ +---+ 3+-+ 3+-+
+--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a
+--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------)
+--R 3a +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 27b \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 310
+
+)clear all
+
+--S 311 of 1309
+t0:=x^5/(a+b*x^3)^3
+--R
+--R
+--R 5
+--R x
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 311
+
+--S 312 of 1309
+r0:=1/6*x^6/(a*(a+b*x^3)^2)
+--R
+--R
+--R 1 6
+--R - x
+--R 6
+--R (2) ---------------------
+--R 2 6 2 3 3
+--R a b x + 2a b x + a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 312
+
+--S 313 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R - 2b x - a
+--R (3) ------------------------
+--R 4 6 3 3 2 2
+--R 6b x + 12a b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 313
+
+--S 314 of 1309
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - -----
+--R 2
+--R 6a b
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 315
+
+)clear all
+
+--S 316 of 1309
+t0:=x^4/(a+b*x^3)^3
+--R
+--R
+--R 4
+--R x
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 316
+
+--S 317 of 1309
+r0:=-1/6*x^2/(b*(a+b*x^3)^2)+1/9*x^2/(a*b*(a+b*x^3))-1/27*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(4/3)*b^(5/3))+1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(4/3)*b^(5/3))-1/9*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(4/3)*b^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (b x + 2a b x + a )\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 6 3 2 +-+ 3+-+ 3+-+
+--R (- 2b x - 4a b x - 2a )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 6 3 2 2x\|b - \|a 5 2 +-+3+-+3+-+2
+--R (6b x + 12a b x + 6a )atan(-------------) + (6b x - 3a x )\|3 \|a \|b
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 3 6 2 2 3 3 +-+3+-+3+-+2
+--R (54a b x + 108a b x + 54a b)\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R 2 6 3 2 +-+ 3| 2 2 3| 2
+--R (- b x - 2a b x - a )\|3 log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2
+--R 2 6 3 2 +-+ 3| 2
+--R (2b x + 4a b x + 2a )\|3 log(x \|- a b + a b)
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 2 6 3 2 2x\|3 \|- a b - a b\|3
+--R (- 6b x - 12a b x - 6a )atan(--------------------------)
+--R 3a b
+--R +
+--R +------+
+--R 5 2 +-+3| 2
+--R (6b x - 3a x )\|3 \|- a b
+--R /
+--R +------+
+--R 3 6 2 2 3 3 +-+3| 2
+--R (54a b x + 108a b x + 54a b)\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 318
+
+--S 319 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +------+
+--R +-+3| 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(x\|b + \|a )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 3| 2 2 3| 2
+--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2 +------+ 3+-+ 3+-+
+--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a
+--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3
+--R - 6\|a \|b atan(--------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2 3+-+3+-+2
+--R 54a b\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 1309
+t0:=x^3/(a+b*x^3)^3
+--R
+--R
+--R 3
+--R x
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 321
+
+--S 322 of 1309
+r0:=-1/6*x/(b*(a+b*x^3)^2)+1/18*x/(a*b*(a+b*x^3))+1/27*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(5/3)*b^(4/3))-1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(5/3)*b^(4/3))-1/9*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 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- b x - 2a b x - a )\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 6 3 2 +-+ 3+-+ 3+-+
+--R (2b x + 4a b x + 2a )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 6 3 2 2x\|b - \|a 4 +-+3+-+2 3+-+
+--R (6b x + 12a b x + 6a )atan(-------------) + (3b x - 6a x)\|3 \|a \|b
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 3 6 2 2 3 3 +-+3+-+2 3+-+
+--R (54a b x + 108a b x + 54a b)\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 6 3 2 +-+ 2 3| 2 3| 2 2
+--R (- b x - 2a b x - a )\|3 log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 2 6 3 2 +-+ 3| 2
+--R (2b x + 4a b x + 2a )\|3 log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 6 3 2 2x\|3 \|a b - a\|3
+--R (6b x + 12a b x + 6a )atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R 4 +-+3| 2
+--R (3b x - 6a x)\|3 \|a b
+--R /
+--R +---+
+--R 3 6 2 2 3 3 +-+3| 2
+--R (54a b x + 108a b x + 54a b)\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 323
+
+--S 324 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--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 +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R 2\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+ +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+
+--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 +-+ +---+ 3+-+ 3+-+
+--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a
+--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------)
+--R 3a +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 54a b\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+)clear all
+
+--S 326 of 1309
+t0:=x^2/(a+b*x^3)^3
+--R
+--R
+--R 2
+--R x
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 326
+
+--S 327 of 1309
+r0:=(-1/6)/(b*(a+b*x^3)^2)
+--R
+--R
+--R 1
+--R -
+--R 6
+--R (2) - --------------------
+--R 3 6 2 3 2
+--R b x + 2a b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 327
+
+--S 328 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - -----------------------
+--R 3 6 2 3 2
+--R 6b x + 12a b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 328
+
+--S 329 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 330
+
+)clear all
+
+--S 331 of 1309
+t0:=x/(a+b*x^3)^3
+--R
+--R
+--R x
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 331
+
+--S 332 of 1309
+r0:=1/6*x^2/(a*(a+b*x^3)^2)+2/9*x^2/(a^2*(a+b*x^3))-2/27*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(7/3)*b^(2/3))+1/27*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(7/3)*b^(2/3))-2/9*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(7/3)*b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (2b x + 4a b x + 2a )\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 6 3 2 +-+ 3+-+ 3+-+
+--R (- 4b x - 8a b x - 4a )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 6 3 2 2x\|b - \|a
+--R (12b x + 24a b x + 12a )atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 5 2 +-+3+-+3+-+2
+--R (12b x + 21a x )\|3 \|a \|b
+--R /
+--R 2 2 6 3 3 4 +-+3+-+3+-+2
+--R (54a b x + 108a b x + 54a )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R 2 6 3 2 +-+ 3| 2 2 3| 2
+--R (- 2b x - 4a b x - 2a )\|3 log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2
+--R 2 6 3 2 +-+ 3| 2
+--R (4b x + 8a b x + 4a )\|3 log(x \|- a b + a b)
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 2 6 3 2 2x\|3 \|- a b - a b\|3
+--R (- 12b x - 24a b x - 12a )atan(--------------------------)
+--R 3a b
+--R +
+--R +------+
+--R 5 2 +-+3| 2
+--R (12b x + 21a x )\|3 \|- a b
+--R /
+--R +------+
+--R 2 2 6 3 3 4 +-+3| 2
+--R (54a b x + 108a b x + 54a )\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 333
+
+--S 334 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +------+
+--R +-+3| 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(x\|b + \|a )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 3| 2 2 3| 2
+--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2 +------+ 3+-+ 3+-+
+--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a
+--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +------+2
+--R +-+3| 2 +-+
+--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3
+--R - 6\|a \|b atan(--------------------------)
+--R 3a b
+--R /
+--R +------+
+--R 2 +-+3| 2 3+-+3+-+2
+--R 27a \|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 1309
+t0:=1/(a+b*x^3)^3
+--R
+--R
+--R 1
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 336
+
+--S 337 of 1309
+r0:=1/6*x/(a*(a+b*x^3)^2)+5/18*x/(a^2*(a+b*x^3))+5/27*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(8/3)*b^(1/3))-5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(8/3)*b^(1/3))-5/9*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(8/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 5b x - 10a b x - 5a )\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 6 3 2 +-+ 3+-+ 3+-+
+--R (10b x + 20a b x + 10a )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 6 3 2 2x\|b - \|a
+--R (30b x + 60a b x + 30a )atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 4 +-+3+-+2 3+-+
+--R (15b x + 24a x)\|3 \|a \|b
+--R /
+--R 2 2 6 3 3 4 +-+3+-+2 3+-+
+--R (54a b x + 108a b x + 54a )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 6 3 2 +-+ 2 3| 2 3| 2 2
+--R (- 5b x - 10a b x - 5a )\|3 log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 2 6 3 2 +-+ 3| 2
+--R (10b x + 20a b x + 10a )\|3 log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 6 3 2 2x\|3 \|a b - a\|3
+--R (30b x + 60a b x + 30a )atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R 4 +-+3| 2
+--R (15b x + 24a x)\|3 \|a b
+--R /
+--R +---+
+--R 2 2 6 3 3 4 +-+3| 2
+--R (54a b x + 108a b x + 54a )\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 338
+
+--S 339 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R - 5\|3 \|a \|b log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R 10\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R 5\|3 \|a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +---+
+--R +---+ +-+3| 2 +-+
+--R +-+3| 2 3+-+ 3+-+ 3+-+2 3+-+ 2x\|3 \|a b - a\|3
+--R - 10\|3 \|a b log(x\|b + \|a ) + 30\|a \|b atan(--------------------)
+--R 3a
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|b - \|a
+--R - 30\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 54a \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 1309
+t0:=1/(x*(a+b*x^3)^3)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 10 2 7 2 4 3
+--R b x + 3a b x + 3a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 1309
+r0:=1/6/(a*(a+b*x^3)^2)+1/3/(a^2*(a+b*x^3))+log(x)/a^3-1/3*log(a+b*x^3)/a^3
+--R
+--R
+--R (2)
+--R 2 6 3 2 3 2 6 3 2
+--R (- 2b x - 4a b x - 2a )log(b x + a) + (6b x + 12a b x + 6a )log(x)
+--R +
+--R 3 2
+--R 2a b x + 3a
+--R /
+--R 3 2 6 4 3 5
+--R 6a b x + 12a b x + 6a
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 6 3 2 3 2 6 3 2
+--R (- 2b x - 4a b x - 2a )log(b x + a) + (6b x + 12a b x + 6a )log(x)
+--R +
+--R 3 2
+--R 2a b x + 3a
+--R /
+--R 3 2 6 4 3 5
+--R 6a b x + 12a b x + 6a
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 1309
+t0:=x^8*sqrt(a+b*x^3)
+--R
+--R
+--R +--------+
+--R 8 | 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 1309
+r0:=2/9*a^2*(a+b*x^3)^(3/2)/b^3-4/15*a*(a+b*x^3)^(5/2)/b^3+_
+ 2/21*(a+b*x^3)^(7/2)/b^3
+--R
+--R
+--R +--------+
+--R 3 9 2 6 2 3 3 | 3
+--R (30b x + 6a b x - 8a b x + 16a )\|b x + a
+--R (2) ----------------------------------------------
+--R 3
+--R 315b
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 9 2 6 2 3 3 | 3
+--R (30b x + 6a b x - 8a b x + 16a )\|b x + a
+--R (3) ----------------------------------------------
+--R 3
+--R 315b
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 1309
+t0:=x^5*sqrt(a+b*x^3)
+--R
+--R
+--R +--------+
+--R 5 | 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1309
+r0:=-2/9*a*(a+b*x^3)^(3/2)/b^2+2/15*(a+b*x^3)^(5/2)/b^2
+--R
+--R
+--R +--------+
+--R 2 6 3 2 | 3
+--R (6b x + 2a b x - 4a )\|b x + a
+--R (2) ----------------------------------
+--R 2
+--R 45b
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 6 3 2 | 3
+--R (6b x + 2a b x - 4a )\|b x + a
+--R (3) ----------------------------------
+--R 2
+--R 45b
+--R Type: Union(Expression(Integer),...)
+--E 353
+
+--S 354 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 1309
+t0:=x^2*sqrt(a+b*x^3)
+--R
+--R
+--R +--------+
+--R 2 | 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1309
+r0:=2/9*(a+b*x^3)^(3/2)/b
+--R
+--R
+--R +--------+
+--R 3 | 3
+--R (2b x + 2a)\|b x + a
+--R (2) -----------------------
+--R 9b
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 | 3
+--R (2b x + 2a)\|b x + a
+--R (3) -----------------------
+--R 9b
+--R Type: Union(Expression(Integer),...)
+--E 358
+
+--S 359 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+)clear all
+
+--S 361 of 1309
+t0:=sqrt(a+b*x^3)/x
+--R
+--R
+--R +--------+
+--R | 3
+--R \|b x + a
+--R (1) -----------
+--R x
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 1309
+r0:=-2/3*atanh(sqrt(a+b*x^3)/sqrt(a))*sqrt(a)+2/3*sqrt(a+b*x^3)
+--R
+--R
+--R +--------+
+--R | 3 +--------+
+--R +-+ \|b x + a | 3
+--R - 2\|a atanh(-----------) + 2\|b x + a
+--R +-+
+--R \|a
+--R (2) ----------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ | 3 3 +--------+
+--R +-+ - 2\|a \|b x + a + b x + 2a | 3
+--R \|a log(------------------------------) + 2\|b x + a
+--R 3
+--R x
+--R [------------------------------------------------------,
+--R 3
+--R +--------+
+--R | 3 +--------+
+--R +---+ \|b x + a | 3
+--R - 2\|- a atan(-----------) + 2\|b x + a
+--R +---+
+--R \|- a
+--R -----------------------------------------]
+--R 3
+--R Type: Union(List(Expression(Integer)),...)
+--E 363
+
+--S 364 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R +-+ | 3 3 | 3
+--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a
+--R \|a log(------------------------------) + 2\|a atanh(-----------)
+--R 3 +-+
+--R x \|a
+--R (4) -----------------------------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 365
+
+--S 366 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R +-+ \|b x + a +---+ \|b x + a
+--R 2\|a atanh(-----------) - 2\|- a atan(-----------)
+--R +-+ +---+
+--R \|a \|- a
+--R (6) --------------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 367
+
+)clear all
+
+--S 368 of 1309
+t0:=sqrt(a+b*x^3)/x^4
+--R
+--R
+--R +--------+
+--R | 3
+--R \|b x + a
+--R (1) -----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1309
+r0:=-1/3*b*atanh(sqrt(a+b*x^3)/sqrt(a))/sqrt(a)-1/3*sqrt(a+b*x^3)/x^3
+--R
+--R
+--R +--------+
+--R | 3 +--------+
+--R 3 \|b x + a +-+ | 3
+--R - b x atanh(-----------) - \|a \|b x + a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------
+--R 3 +-+
+--R 3x \|a
+--R Type: Expression(Integer)
+--E 369
+
+--S 370 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 3 3 +-+ +--------+
+--R 3 - 2a\|b x + a + (b x + 2a)\|a +-+ | 3
+--R b x log(---------------------------------) - 2\|a \|b x + a
+--R 3
+--R x
+--R [-------------------------------------------------------------,
+--R 3 +-+
+--R 6x \|a
+--R +--------+
+--R +---+ | 3 +--------+
+--R 3 \|- a \|b x + a +---+ | 3
+--R - b x atan(-----------------) - \|- a \|b x + a
+--R a
+--R -------------------------------------------------]
+--R 3 +---+
+--R 3x \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 370
+
+--S 371 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 3 +-+ | 3
+--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a
+--R b log(---------------------------------) + 2b atanh(-----------)
+--R 3 +-+
+--R x \|a
+--R (4) ----------------------------------------------------------------
+--R +-+
+--R 6\|a
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 +---+ | 3
+--R +---+ \|b x + a +-+ \|- a \|b x + a
+--R b\|- a atanh(-----------) - b\|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R 3\|- a \|a
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 374
+
+)clear all
+
+--S 375 of 1309
+t0:=sqrt(a+b*x^3)/x^7
+--R
+--R
+--R +--------+
+--R | 3
+--R \|b x + a
+--R (1) -----------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 375
+
+--S 376 of 1309
+r0:=1/12*b^2*atanh(sqrt(a+b*x^3)/sqrt(a))/a^(3/2)-1/6*sqrt(a+b*x^3)/x^6-_
+ 1/12*b*sqrt(a+b*x^3)/(a*x^3)
+--R
+--R
+--R +--------+
+--R | 3 +--------+
+--R 2 6 \|b x + a 3 +-+ | 3
+--R b x atanh(-----------) + (- b x - 2a)\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) -----------------------------------------------------
+--R 6 +-+
+--R 12a x \|a
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 3 3 +-+ +--------+
+--R 2 6 2a\|b x + a + (b x + 2a)\|a 3 +-+ | 3
+--R b x log(-------------------------------) + (- 2b x - 4a)\|a \|b x + a
+--R 3
+--R x
+--R [------------------------------------------------------------------------,
+--R 6 +-+
+--R 24a x \|a
+--R +--------+
+--R +---+ | 3 +--------+
+--R 2 6 \|- a \|b x + a 3 +---+ | 3
+--R b x atan(-----------------) + (- b x - 2a)\|- a \|b x + a
+--R a
+--R ------------------------------------------------------------]
+--R 6 +---+
+--R 12a x \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 377
+
+--S 378 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 3 +-+ | 3
+--R 2 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a
+--R b log(-------------------------------) - 2b atanh(-----------)
+--R 3 +-+
+--R x \|a
+--R (4) --------------------------------------------------------------
+--R +-+
+--R 24a\|a
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 379
+
+--S 380 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 +---+ | 3
+--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a
+--R - b \|- a atanh(-----------) + b \|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R +---+ +-+
+--R 12a\|- a \|a
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 381
+
+)clear all
+
+--S 382 of 1309
+t0:=x^3*sqrt(8+27*x^3)
+--R
+--R
+--R +--------+
+--R 3 | 3
+--R (1) x \|27x + 8
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 1309
+--r0:=16/495*x*sqrt(8+27*x^3)+2/11*x^4*sqrt(8+27*x^3)-256/1485*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 383
+
+--S 384 of 1309
+--a0:=integrate(t0,x)
+--E 384
+
+--S 385 of 1309
+--m0:=a0-r0
+--E 385
+
+--S 386 of 1309
+--d0:=D(m0,x)
+--E 386
+
+)clear all
+
+--S 387 of 1309
+t0:=sqrt(8+27*x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R (1) \|27x + 8
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 1309
+--r0:=2/5*x*sqrt(8+27*x^3)+16/5*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 388
+
+--S 389 of 1309
+--a0:=integrate(t0,x)
+--E 389
+
+--S 390 of 1309
+--m0:=a0-r0
+--E 390
+
+--S 391 of 1309
+--d0:=D(m0,x)
+--E 391
+
+)clear all
+
+--S 392 of 1309
+t0:=sqrt(8+27*x^3)/x^3
+--R
+--R
+--R +--------+
+--R | 3
+--R \|27x + 8
+--R (1) -----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1309
+--r0:=-1/2*sqrt(8+27*x^3)/x^2+27/2*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 393
+
+--S 394 of 1309
+--a0:=integrate(t0,x)
+--E 394
+
+--S 395 of 1309
+--m0:=a0-r0
+--E 395
+
+--S 396 of 1309
+--d0:=D(m0,x)
+--E 396
+
+)clear all
+
+--S 397 of 1309
+t0:=x^4*sqrt(8+27*x^3)
+--R
+--R
+--R +--------+
+--R 4 | 3
+--R (1) x \|27x + 8
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1309
+--r0:=16/819*x^2*sqrt(8+27*x^3)+2/13*x^5*sqrt(8+27*x^3)-_
+-- 512/7371*(-1)^(1/4)*(2+3*x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_
+-- sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_
+-- (3+%i*sqrt(3))))+1024/7371*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 398
+
+--S 399 of 1309
+--a0:=integrate(t0,x)
+--E 399
+
+--S 400 of 1309
+--m0:=a0-r0
+--E 400
+
+--S 401 of 1309
+--d0:=D(m0,x)
+--E 401
+
+)clear all
+
+--S 402 of 1309
+t0:=x*sqrt(8+27*x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R (1) x\|27x + 8
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 1309
+--r0:=2/7*x^2*sqrt(8+27*x^3)+16/21*(-1)^(1/4)*(2+3*x)*_
+-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_
+-- (3+%i*sqrt(3))))-32/21*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 403
+
+--S 404 of 1309
+--a0:=integrate(t0,x)
+--E 404
+
+--S 405 of 1309
+--m0:=a0-r0
+--E 405
+
+--S 406 of 1309
+--d0:=D(m0,x)
+--E 406
+
+)clear all
+
+--R
+--S 407 of 1309
+t0:=sqrt(8+27*x^3)/x^2
+--R
+--R
+--R +--------+
+--R | 3
+--R \|27x + 8
+--R (1) -----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 1309
+--r0:=-sqrt(8+27*x^3)/x+9*(-1)^(1/4)*(2+3*x)*_
+-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_
+-- (3+%i*sqrt(3))))-18*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 408
+
+--S 409 of 1309
+--a0:=integrate(t0,x)
+--E 409
+
+--S 410 of 1309
+--m0:=a0-r0
+--E 410
+
+--S 411 of 1309
+--d0:=D(m0,x)
+--E 411
+
+)clear all
+
+--S 412 of 1309
+t0:=x^8/sqrt(a+b*x^3)
+--R
+--R
+--R 8
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 1309
+r0:=16/45*a^2*sqrt(a+b*x^3)/b^3-8/45*a*x^3*sqrt(a+b*x^3)/b^2+_
+ 2/15*x^6*sqrt(a+b*x^3)/b
+--R
+--R
+--R +--------+
+--R 2 6 3 2 | 3
+--R (6b x - 8a b x + 16a )\|b x + a
+--R (2) -----------------------------------
+--R 3
+--R 45b
+--R Type: Expression(Integer)
+--E 413
+
+--S 414 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 6 3 2 | 3
+--R (6b x - 8a b x + 16a )\|b x + a
+--R (3) -----------------------------------
+--R 3
+--R 45b
+--R Type: Union(Expression(Integer),...)
+--E 414
+
+--S 415 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 415
+
+--S 416 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 416
+
+)clear all
+
+--S 417 of 1309
+t0:=x^5/sqrt(a+b*x^3)
+--R
+--R
+--R 5
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 1309
+r0:=-4/9*a*sqrt(a+b*x^3)/b^2+2/9*x^3*sqrt(a+b*x^3)/b
+--R
+--R
+--R +--------+
+--R 3 | 3
+--R (2b x - 4a)\|b x + a
+--R (2) -----------------------
+--R 2
+--R 9b
+--R Type: Expression(Integer)
+--E 418
+
+--S 419 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 | 3
+--R (2b x - 4a)\|b x + a
+--R (3) -----------------------
+--R 2
+--R 9b
+--R Type: Union(Expression(Integer),...)
+--E 419
+
+--S 420 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 420
+
+--S 421 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 421
+
+)clear all
+
+--S 422 of 1309
+t0:=x^2/sqrt(a+b*x^3)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 1309
+r0:=2/3*sqrt(a+b*x^3)/b
+--R
+--R
+--R +--------+
+--R | 3
+--R 2\|b x + a
+--R (2) ------------
+--R 3b
+--R Type: Expression(Integer)
+--E 423
+
+--S 424 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 2\|b x + a
+--R (3) ------------
+--R 3b
+--R Type: Union(Expression(Integer),...)
+--E 424
+
+--S 425 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 425
+
+--S 426 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 426
+
+)clear all
+
+--S 427 of 1309
+t0:=1/(x*sqrt(a+b*x^3))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +--------+
+--R | 3
+--R x\|b x + a
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 1309
+r0:=-2/3*atanh(sqrt(a+b*x^3)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +--------+
+--R | 3
+--R \|b x + a
+--R 2atanh(-----------)
+--R +-+
+--R \|a
+--R (2) - -------------------
+--R +-+
+--R 3\|a
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3 3 +-+ +--------+
+--R - 2a\|b x + a + (b x + 2a)\|a +---+ | 3
+--R log(---------------------------------) \|- a \|b x + a
+--R 3 2atan(-----------------)
+--R x a
+--R (3) [--------------------------------------,- ------------------------]
+--R +-+ +---+
+--R 3\|a 3\|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 429
+
+--S 430 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 3 +-+ | 3
+--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a
+--R log(---------------------------------) + 2atanh(-----------)
+--R 3 +-+
+--R x \|a
+--R (4) ------------------------------------------------------------
+--R +-+
+--R 3\|a
+--R Type: Expression(Integer)
+--E 430
+
+--S 431 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 +---+ | 3
+--R +---+ \|b x + a +-+ \|- a \|b x + a
+--R 2\|- a atanh(-----------) - 2\|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R 3\|- a \|a
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 433
+
+)clear all
+
+--S 434 of 1309
+t0:=1/(x^4*sqrt(a+b*x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 4 | 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 1309
+r0:=1/3*b*atanh(sqrt(a+b*x^3)/sqrt(a))/a^(3/2)-1/3*sqrt(a+b*x^3)/(a*x^3)
+--R
+--R
+--R +--------+
+--R | 3 +--------+
+--R 3 \|b x + a +-+ | 3
+--R b x atanh(-----------) - \|a \|b x + a
+--R +-+
+--R \|a
+--R (2) ----------------------------------------
+--R 3 +-+
+--R 3a x \|a
+--R Type: Expression(Integer)
+--E 435
+
+--S 436 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 3 3 +-+ +--------+
+--R 3 2a\|b x + a + (b x + 2a)\|a +-+ | 3
+--R b x log(-------------------------------) - 2\|a \|b x + a
+--R 3
+--R x
+--R [-----------------------------------------------------------,
+--R 3 +-+
+--R 6a x \|a
+--R +--------+
+--R +---+ | 3 +--------+
+--R 3 \|- a \|b x + a +---+ | 3
+--R b x atan(-----------------) - \|- a \|b x + a
+--R a
+--R -----------------------------------------------]
+--R 3 +---+
+--R 3a x \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 436
+
+--S 437 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 3 +-+ | 3
+--R 2a\|b x + a + (b x + 2a)\|a \|b x + a
+--R b log(-------------------------------) - 2b atanh(-----------)
+--R 3 +-+
+--R x \|a
+--R (4) --------------------------------------------------------------
+--R +-+
+--R 6a\|a
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 438
+
+--S 439 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 +---+ | 3
+--R +---+ \|b x + a +-+ \|- a \|b x + a
+--R - b\|- a atanh(-----------) + b\|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------------
+--R +---+ +-+
+--R 3a\|- a \|a
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 1309
+t0:=1/(x^7*sqrt(a+b*x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 7 | 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 1309
+r0:=-1/4*b^2*atanh(sqrt(a+b*x^3)/sqrt(a))/a^(5/2)-_
+ 1/6*sqrt(a+b*x^3)/(a*x^6)+1/4*b*sqrt(a+b*x^3)/(a^2*x^3)
+--R
+--R
+--R +--------+
+--R | 3 +--------+
+--R 2 6 \|b x + a 3 +-+ | 3
+--R - 3b x atanh(-----------) + (3b x - 2a)\|a \|b x + a
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------
+--R 2 6 +-+
+--R 12a x \|a
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 3 3 +-+ +--------+
+--R 2 6 - 2a\|b x + a + (b x + 2a)\|a 3 +-+ | 3
+--R 3b x log(---------------------------------) + (6b x - 4a)\|a \|b x + a
+--R 3
+--R x
+--R [-------------------------------------------------------------------------,
+--R 2 6 +-+
+--R 24a x \|a
+--R +--------+
+--R +---+ | 3 +--------+
+--R 2 6 \|- a \|b x + a 3 +---+ | 3
+--R - 3b x atan(-----------------) + (3b x - 2a)\|- a \|b x + a
+--R a
+--R --------------------------------------------------------------]
+--R 2 6 +---+
+--R 12a x \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 443
+
+--S 444 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 3 +-+ | 3
+--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a
+--R b log(---------------------------------) + 2b atanh(-----------)
+--R 3 +-+
+--R x \|a
+--R (4) ----------------------------------------------------------------
+--R 2 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+--S 446 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 +---+ | 3
+--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a
+--R b \|- a atanh(-----------) - b \|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------------
+--R 2 +---+ +-+
+--R 4a \|- a \|a
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 447
+
+)clear all
+
+--S 448 of 1309
+t0:=x^3/sqrt(8+27*x^3)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R \|27x + 8
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 1309
+--r0:=2/135*x*sqrt(8+27*x^3)-32/405*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 449
+
+--S 450 of 1309
+--a0:=integrate(t0,x)
+--E 450
+
+--S 451 of 1309
+--m0:=a0-r0
+--E 451
+
+--S 452 of 1309
+--d0:=D(m0,x)
+--E 452
+
+)clear all
+
+--S 453 of 1309
+t0:=1/sqrt(8+27*x^3)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 3
+--R \|27x + 8
+--R Type: Expression(Integer)
+--E 453
+
+--S 454 of 1309
+--r0:=2/3*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_
+-- sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*_
+-- sqrt(%i*(1-3*x-%i*sqrt(3)))*sqrt((2+3*x)/(3+%i*sqrt(3)))*_
+-- sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 454
+
+--S 455 of 1309
+--a0:=integrate(t0,x)
+--E 455
+
+--S 456 of 1309
+--m0:=a0-r0
+--E 456
+
+--S 457 of 1309
+--d0:=D(m0,x)
+--E 457
+
+)clear all
+
+--S 458 of 1309
+t0:=1/(x^3*sqrt(8+27*x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 3 | 3
+--R x \|27x + 8
+--R Type: Expression(Integer)
+--E 458
+
+--S 459 of 1309
+--r0:=-1/16*sqrt(8+27*x^3)/x^2-9/16*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 459
+
+--S 460 of 1309
+--a0:=integrate(t0,x)
+--E 460
+
+--S 461 of 1309
+--m0:=a0-r0
+--E 461
+
+--S 462 of 1309
+--d0:=D(m0,x)
+--E 462
+
+)clear all
+
+--S 463 of 1309
+t0:=x^4/sqrt(8+27*x^3)
+--R
+--R
+--R 4
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R \|27x + 8
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 1309
+--r0:=2/189*x^2*sqrt(8+27*x^3)-64/1701*(-1)^(1/4)*(2+3*x)*_
+-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_
+-- (3+%i*sqrt(3))))+128/1701*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 464
+
+--S 465 of 1309
+--a0:=integrate(t0,x)
+--E 465
+
+--S 466 of 1309
+--m0:=a0-r0
+--E 466
+
+--S 467 of 1309
+--d0:=D(m0,x)
+--E 467
+
+)clear all
+
+--S 468 of 1309
+t0:=x/sqrt(8+27*x^3)
+--R
+--R
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R \|27x + 8
+--R Type: Expression(Integer)
+--E 468
+
+--S 469 of 1309
+--r0:=2/9*(-1)^(1/4)*(2+3*x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_
+-- sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_
+-- (3+%i*sqrt(3))))-4/9*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 469
+
+--S 470 of 1309
+--a0:=integrate(t0,x)
+--E 470
+
+--S 471 of 1309
+--m0:=a0-r0
+--E 471
+
+--S 472 of 1309
+--d0:=D(m0,x)
+--E 472
+
+)clear all
+
+--S 473 of 1309
+t0:=1/(x^2*sqrt(8+27*x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 2 | 3
+--R x \|27x + 8
+--R Type: Expression(Integer)
+--E 473
+
+--S 474 of 1309
+--r0:=-1/8*sqrt(8+27*x^3)/x+3/8*(-1)^(1/4)*(2+3*x)*_
+-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_
+-- (3+%i*sqrt(3))))-3/4*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_
+-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3)
+--E 474
+
+--S 475 of 1309
+--a0:=integrate(t0,x)
+--E 475
+
+--S 476 of 1309
+--m0:=a0-r0
+--E 476
+
+--S 477 of 1309
+--d0:=D(m0,x)
+--E 477
+
+)clear all
+
+--S 478 of 1309
+t0:=x^5/(1+x^3)^(3/2)
+--R
+--R
+--R 5
+--R x
+--R (1) -----------------
+--R +------+
+--R 3 | 3
+--R (x + 1)\|x + 1
+--R Type: Expression(Integer)
+--E 478
+
+--S 479 of 1309
+r0:=2/3/sqrt(1+x^3)+2/3*sqrt(1+x^3)
+--R
+--R
+--R 3
+--R 2x + 4
+--R (2) ----------
+--R +------+
+--R | 3
+--R 3\|x + 1
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R 2x + 4
+--R (3) ----------
+--R +------+
+--R | 3
+--R 3\|x + 1
+--R Type: Union(Expression(Integer),...)
+--E 480
+
+--S 481 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 482
+
+)clear all
+
+--S 483 of 1309
+t0:=x^8*(1-x^3)^(1/3)
+--R
+--R
+--R +--------+
+--R 8 3| 3
+--R (1) x \|- x + 1
+--R Type: Expression(Integer)
+--E 483
+
+--S 484 of 1309
+r0:=-1/4*(1-x^3)^(4/3)+2/7*(1-x^3)^(7/3)-1/10*(1-x^3)^(10/3)
+--R
+--R
+--R +--------+
+--R 9 6 3 3| 3
+--R (14x - 2x - 3x - 9)\|- x + 1
+--R (2) ---------------------------------
+--R 140
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 9 6 3 3| 3
+--R (14x - 2x - 3x - 9)\|- x + 1
+--R (3) ---------------------------------
+--R 140
+--R Type: Union(Expression(Integer),...)
+--E 485
+
+--S 486 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 487
+
+)clear all
+
+--S 488 of 1309
+t0:=x^5*(a+b*x^3)^(1/3)
+--R
+--R
+--R +--------+
+--R 5 3| 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 488
+
+--S 489 of 1309
+r0:=-1/4*a*(a+b*x^3)^(4/3)/b^2+1/7*(a+b*x^3)^(7/3)/b^2
+--R
+--R
+--R +--------+
+--R 2 6 3 2 3| 3
+--R (4b x + a b x - 3a )\|b x + a
+--R (2) ---------------------------------
+--R 2
+--R 28b
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 6 3 2 3| 3
+--R (4b x + a b x - 3a )\|b x + a
+--R (3) ---------------------------------
+--R 2
+--R 28b
+--R Type: Union(Expression(Integer),...)
+--E 490
+
+--S 491 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 492
+
+)clear all
+
+--S 493 of 1309
+t0:=x^4*(a+b*x^3)^(1/3)
+--R
+--R
+--R +--------+
+--R 4 3| 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 1309
+r0:=1/18*a*x^2*(a+b*x^3)^(1/3)/b+1/6*x^5*(a+b*x^3)^(1/3)+_
+ 1/27*a^2*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(5/3)-_
+ 1/54*a^2*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/b^(5/3)+1/9*a^2*_
+ atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R 2 +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R - a \|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R 3| 3 3+-+ 3| 3 3+-+
+--R 2 +-+ \|b x + a - x\|b 2 \|b x + a + 2x\|b
+--R 2a \|3 log(-------------------) + 6a atan(--------------------)
+--R +--------+ +--------+
+--R 3| 3 +-+3| 3
+--R \|b x + a \|3 \|b x + a
+--R +
+--R +--------+
+--R 5 2 +-+3+-+2 3| 3
+--R (9b x + 3a x )\|3 \|b \|b x + a
+--R /
+--R +-+3+-+2
+--R 54b\|3 \|b
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+2 +--------+2 +--+ +--------+
+--R 3| 2 3| 3 3| 2 3| 3 2 2
+--R 2 +-+ \|b \|b x + a + b x\|b \|b x + a + b x
+--R - a \|3 log(-----------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--+ +--------+
+--R 3| 2 3| 3
+--R 2 +-+ \|b \|b x + a - b x
+--R 2a \|3 log(----------------------)
+--R x
+--R +
+--R +--+ +--------+
+--R +-+3| 2 3| 3 +-+
+--R 2 2\|3 \|b \|b x + a + b x\|3
+--R - 6a atan(-------------------------------)
+--R 3b x
+--R +
+--R +--+ +--------+
+--R 5 2 +-+3| 2 3| 3
+--R (9b x + 3a x )\|3 \|b \|b x + a
+--R /
+--R +--+
+--R +-+3| 2
+--R 54b\|3 \|b
+--R Type: Union(Expression(Integer),...)
+--E 495
+
+--S 496 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+2 +--------+2 +--+ +--------+
+--R 3| 2 3| 3 3| 2 3| 3 2 2
+--R 2 +-+3+-+2 \|b \|b x + a + b x\|b \|b x + a + b x
+--R - a \|3 \|b log(-----------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--+ +--------+
+--R 3| 2 3| 3
+--R 2 +-+3+-+2 \|b \|b x + a - b x
+--R 2a \|3 \|b log(----------------------)
+--R x
+--R +
+--R +--------+2 +--------+
+--R +--+ 3| 3 3+-+3| 3 2 3+-+2
+--R 2 +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b
+--R a \|3 \|b log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R +--+ 3| 3 3+-+
+--R 2 +-+3| 2 \|b x + a - x\|b
+--R - 2a \|3 \|b log(-------------------)
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--+ +--------+
+--R +-+3| 2 3| 3 +-+
+--R 2 3+-+2 2\|3 \|b \|b x + a + b x\|3
+--R - 6a \|b atan(-------------------------------)
+--R 3b x
+--R +
+--R +--------+
+--R +--+ 3| 3 3+-+
+--R 2 3| 2 \|b x + a + 2x\|b
+--R - 6a \|b atan(--------------------)
+--R +--------+
+--R +-+3| 3
+--R \|3 \|b x + a
+--R /
+--R +--+
+--R +-+3+-+2 3| 2
+--R 54b\|3 \|b \|b
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 497
+
+)clear all
+
+--S 498 of 1309
+t0:=x^3*(a+b*x^3)^(1/3)
+--R
+--R
+--R +--------+
+--R 3 3| 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 1309
+--r0:=1/10*a*x*(a+b*x^3)^(1/3)/b+1/5*x^4*(a+b*x^3)^(1/3)-_
+-- 1/10*a^2*x*((a+b*x^3)/a)^(2/3)*_
+-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(b*(a+b*x^3)^(2/3))
+--E 499
+
+--S 500 of 1309
+--a0:=integrate(t0,x)
+--E 500
+
+--S 501 of 1309
+--m0:=a0-r0
+--E 501
+
+--S 502 of 1309
+--d0:=D(m0,x)
+--E 502
+
+)clear all
+
+--S 503 of 1309
+t0:=x^2*(a+b*x^3)^(1/3)
+--R
+--R
+--R +--------+
+--R 2 3| 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 503
+
+--S 504 of 1309
+r0:=1/4*(a+b*x^3)^(4/3)/b
+--R
+--R
+--R +--------+
+--R 3 3| 3
+--R (b x + a)\|b x + a
+--R (2) ---------------------
+--R 4b
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 3| 3
+--R (b x + a)\|b x + a
+--R (3) ---------------------
+--R 4b
+--R Type: Union(Expression(Integer),...)
+--E 505
+
+--S 506 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 506
+
+--S 507 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 507
+
+)clear all
+
+--S 508 of 1309
+t0:=x*(a+b*x^3)^(1/3)
+--R
+--R
+--R +--------+
+--R 3| 3
+--R (1) x\|b x + a
+--R Type: Expression(Integer)
+--E 508
+
+--S 509 of 1309
+r0:=1/3*x^2*(a+b*x^3)^(1/3)-1/9*a*log(1-b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/b^(2/3)+1/18*a*log(1+b^(2/3)*_
+ x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))/b^(2/3)-_
+ 1/3*a*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R a\|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R 3| 3 3+-+ 3| 3 3+-+
+--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b
+--R - 2a\|3 log(-------------------) - 6a atan(--------------------)
+--R +--------+ +--------+
+--R 3| 3 +-+3| 3
+--R \|b x + a \|3 \|b x + a
+--R +
+--R +--------+
+--R 2 +-+3+-+2 3| 3
+--R 6x \|3 \|b \|b x + a
+--R /
+--R +-+3+-+2
+--R 18\|3 \|b
+--R Type: Expression(Integer)
+--E 509
+
+--S 510 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+2 +--------+2 +----+ +--------+
+--R 3| 2 3| 3 3| 2 3| 3 2 2
+--R +-+ \|- b \|b x + a - b x\|- b \|b x + a + b x
+--R - a\|3 log(---------------------------------------------------)
+--R 2
+--R x
+--R +
+--R +----+ +--------+
+--R 3| 2 3| 3
+--R +-+ \|- b \|b x + a + b x
+--R 2a\|3 log(------------------------)
+--R x
+--R +
+--R +----+ +--------+
+--R +-+3| 2 3| 3 +-+ +----+ +--------+
+--R 2\|3 \|- b \|b x + a - b x\|3 2 +-+3| 2 3| 3
+--R 6a atan(---------------------------------) + 6x \|3 \|- b \|b x + a
+--R 3b x
+--R /
+--R +----+
+--R +-+3| 2
+--R 18\|3 \|- b
+--R Type: Union(Expression(Integer),...)
+--E 510
+
+--S 511 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----+2 +--------+2 +----+ +--------+
+--R 3| 2 3| 3 3| 2 3| 3 2 2
+--R +-+3+-+2 \|- b \|b x + a - b x\|- b \|b x + a + b x
+--R - a\|3 \|b log(---------------------------------------------------)
+--R 2
+--R x
+--R +
+--R +----+ +--------+
+--R 3| 2 3| 3
+--R +-+3+-+2 \|- b \|b x + a + b x
+--R 2a\|3 \|b log(------------------------)
+--R x
+--R +
+--R +--------+2 +--------+
+--R +----+ 3| 3 3+-+3| 3 2 3+-+2
+--R +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b
+--R - a\|3 \|- b log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R +----+ 3| 3 3+-+
+--R +-+3| 2 \|b x + a - x\|b
+--R 2a\|3 \|- b log(-------------------)
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R +
+--R +----+ +--------+
+--R +-+3| 2 3| 3 +-+
+--R 3+-+2 2\|3 \|- b \|b x + a - b x\|3
+--R 6a \|b atan(---------------------------------)
+--R 3b x
+--R +
+--R +--------+
+--R +----+ 3| 3 3+-+
+--R 3| 2 \|b x + a + 2x\|b
+--R 6a\|- b atan(--------------------)
+--R +--------+
+--R +-+3| 3
+--R \|3 \|b x + a
+--R /
+--R +----+
+--R +-+3| 2 3+-+2
+--R 18\|3 \|- b \|b
+--R Type: Expression(Integer)
+--E 511
+
+--S 512 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 512
+
+)clear all
+
+--S 513 of 1309
+t0:=(a+b*x^3)^(1/3)
+--R
+--R
+--R +--------+
+--R 3| 3
+--R (1) \|b x + a
+--R Type: Expression(Integer)
+--E 513
+
+--S 514 of 1309
+--r0:=1/2*x*(a+b*x^3)^(1/3)+1/2*a*x*((a+b*x^3)/a)^(2/3)*_
+-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a+b*x^3)^(2/3)
+--E 514
+
+--S 515 of 1309
+--a0:=integrate(t0,x)
+--E 515
+
+--S 516 of 1309
+--m0:=a0-r0
+--E 516
+
+--S 517 of 1309
+--d0:=D(m0,x)
+--E 517
+
+)clear all
+
+--S 518 of 1309
+t0:=(a+b*x^3)^(1/3)/x
+--R
+--R
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R (1) -----------
+--R x
+--R Type: Expression(Integer)
+--E 518
+
+--S 519 of 1309
+r0:=(a+b*x^3)^(1/3)+1/3*a^(1/3)*log(a^(1/3)-(a+b*x^3)^(1/3))-_
+ 1/6*a^(1/3)*log(a^(2/3)+a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))-_
+ a^(1/3)*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3)
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R +-+3+-+ 3| 3 3+-+3| 3 3+-+2
+--R - \|3 \|a log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +--------+ 3| 3 3+-+
+--R +-+3+-+ 3| 3 3+-+ 3+-+ 2\|b x + a + \|a
+--R 2\|3 \|a log(- \|b x + a + \|a ) - 6\|a atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +--------+
+--R +-+3| 3
+--R 6\|3 \|b x + a
+--R /
+--R +-+
+--R 6\|3
+--R Type: Expression(Integer)
+--E 519
+
+--S 520 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+2 +--------+
+--R +-+3+-+ 3| 3 3+-+3| 3 3+-+2
+--R - \|3 \|a log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +--------+ +-+3| 3 +-+3+-+
+--R +-+3+-+ 3| 3 3+-+ 3+-+ 2\|3 \|b x + a + \|3 \|a
+--R 2\|3 \|a log(\|b x + a - \|a ) - 6\|a atan(---------------------------)
+--R 3+-+
+--R 3\|a
+--R +
+--R +--------+
+--R +-+3| 3
+--R 6\|3 \|b x + a
+--R /
+--R +-+
+--R 6\|3
+--R Type: Union(Expression(Integer),...)
+--E 520
+
+--S 521 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R +-+3+-+ 3| 3 3+-+ +-+3+-+ 3| 3 3+-+
+--R \|3 \|a log(\|b x + a - \|a ) - \|3 \|a log(- \|b x + a + \|a )
+--R +
+--R +--------+ +--------+
+--R +-+3| 3 +-+3+-+ 3| 3 3+-+
+--R 3+-+ 2\|3 \|b x + a + \|3 \|a 3+-+ 2\|b x + a + \|a
+--R - 3\|a atan(---------------------------) + 3\|a atan(-------------------)
+--R 3+-+ +-+3+-+
+--R 3\|a \|3 \|a
+--R /
+--R +-+
+--R 3\|3
+--R Type: Expression(Integer)
+--E 521
+
+--S 522 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 522
+
+)clear all
+
+--S 523 of 1309
+t0:=(a+b*x^3)^(1/3)/x^2
+--R
+--R
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R (1) -----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 523
+
+--S 524 of 1309
+r0:=-(a+b*x^3)^(1/3)/x-1/3*b^(1/3)*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))+_
+ 1/6*b^(1/3)*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+_
+ b^(1/3)*x/(a+b*x^3)^(1/3))-b^(1/3)*_
+ atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+3+-+ \|b x + a + x\|b \|b x + a + x \|b
+--R x\|3 \|b log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R 3| 3 3+-+ 3| 3 3+-+
+--R +-+3+-+ \|b x + a - x\|b 3+-+ \|b x + a + 2x\|b
+--R - 2x\|3 \|b log(-------------------) - 6x\|b atan(--------------------)
+--R +--------+ +--------+
+--R 3| 3 +-+3| 3
+--R \|b x + a \|3 \|b x + a
+--R +
+--R +--------+
+--R +-+3| 3
+--R - 6\|3 \|b x + a
+--R /
+--R +-+
+--R 6x\|3
+--R Type: Expression(Integer)
+--E 524
+
+--S 525 of 1309
+--a0:=integrate(t0,x)
+--E 525
+
+--S 526 of 1309
+--m0:=a0-r0
+--E 526
+
+--S 527 of 1309
+--d0:=D(m0,x)
+--E 527
+
+)clear all
+
+--S 528 of 1309
+t0:=(a+b*x^3)^(1/3)/x^3
+--R
+--R
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R (1) -----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 528
+
+--S 529 of 1309
+--r0:=-1/2*(a+b*x^3)^(1/3)/x^2+1/2*b*x*((a+b*x^3)/a)^(2/3)*_
+-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a+b*x^3)^(2/3)
+--E 529
+
+--S 530 of 1309
+--a0:=integrate(t0,x)
+--E 530
+
+--S 531 of 1309
+--m0:=a0-r0
+--E 531
+
+--S 532 of 1309
+--d0:=D(m0,x)
+--E 532
+
+)clear all
+
+--S 533 of 1309
+t0:=(a+b*x^3)^(1/3)/x^4
+--R
+--R
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R (1) -----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 533
+
+--S 534 of 1309
+r0:=-1/3*(a+b*x^3)^(1/3)/x^3+1/9*b*log(a^(1/3)-(a+b*x^3)^(1/3))/a^(2/3)-_
+ 1/18*b*log(a^(2/3)+a^(1/3)*(a+b*x^3)^(1/3)+_
+ (a+b*x^3)^(2/3))/a^(2/3)-1/3*b*atan((a^(1/3)+_
+ 2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3 +-+ 3| 3 3+-+3| 3 3+-+2
+--R - b x \|3 log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +--------+ 3| 3 3+-+
+--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a
+--R 2b x \|3 log(- \|b x + a + \|a ) - 6b x atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +--------+
+--R +-+3+-+2 3| 3
+--R - 6\|3 \|a \|b x + a
+--R /
+--R 3 +-+3+-+2
+--R 18x \|3 \|a
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+2 +--------+2 +--+ +--------+
+--R 3 +-+ 3| 2 3| 3 3| 2 3| 3 2
+--R - b x \|3 log(\|a \|b x + a + a\|a \|b x + a + a )
+--R +
+--R +--+ +--------+
+--R 3 +-+ 3| 2 3| 3
+--R 2b x \|3 log(\|a \|b x + a - a)
+--R +
+--R +--+ +--------+
+--R +-+3| 2 3| 3 +-+ +--+ +--------+
+--R 3 2\|3 \|a \|b x + a + a\|3 +-+3| 2 3| 3
+--R - 6b x atan(-----------------------------) - 6\|3 \|a \|b x + a
+--R 3a
+--R /
+--R +--+
+--R 3 +-+3| 2
+--R 18x \|3 \|a
+--R Type: Union(Expression(Integer),...)
+--E 535
+
+--S 536 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+2 +--------+2 +--+ +--------+
+--R +-+3+-+2 3| 2 3| 3 3| 2 3| 3 2
+--R - b\|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a )
+--R +
+--R +--+ +--------+2 +--------+
+--R +-+3| 2 3| 3 3+-+3| 3 3+-+2
+--R b\|3 \|a log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--+ +--------+
+--R +-+3+-+2 3| 2 3| 3
+--R 2b\|3 \|a log(\|a \|b x + a - a)
+--R +
+--R +--+ +--------+
+--R +-+3| 2 3| 3 3+-+
+--R - 2b\|3 \|a log(- \|b x + a + \|a )
+--R +
+--R +--+ +--------+
+--R +-+3| 2 3| 3 +-+
+--R 3+-+2 2\|3 \|a \|b x + a + a\|3
+--R - 6b \|a atan(-----------------------------)
+--R 3a
+--R +
+--R +--------+
+--R +--+ 3| 3 3+-+
+--R 3| 2 2\|b x + a + \|a
+--R 6b\|a atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +--+
+--R +-+3+-+2 3| 2
+--R 18\|3 \|a \|a
+--R Type: Expression(Integer)
+--E 536
+
+--S 537 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 537
+
+)clear all
+
+--S 538 of 1309
+t0:=x^5*(a+b*x^3)^(2/3)
+--R
+--R
+--R +--------+2
+--R 5 3| 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 538
+
+--S 539 of 1309
+r0:=-1/5*a*(a+b*x^3)^(5/3)/b^2+1/8*(a+b*x^3)^(8/3)/b^2
+--R
+--R
+--R +--------+2
+--R 2 6 3 2 3| 3
+--R (5b x + 2a b x - 3a )\|b x + a
+--R (2) -----------------------------------
+--R 2
+--R 40b
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 2 6 3 2 3| 3
+--R (5b x + 2a b x - 3a )\|b x + a
+--R (3) -----------------------------------
+--R 2
+--R 40b
+--R Type: Union(Expression(Integer),...)
+--E 540
+
+--S 541 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 542
+
+)clear all
+
+--S 543 of 1309
+t0:=x^4*(a+b*x^3)^(2/3)
+--R
+--R
+--R +--------+2
+--R 4 3| 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 543
+
+--S 544 of 1309
+--r0:=1/14*a*x^2*(a+b*x^3)^(2/3)/b+1/7*x^5*(a+b*x^3)^(2/3)-_
+-- 1/14*a^2*x^2*((a+b*x^3)/a)^(1/3)*_
+-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(b*(a+b*x^3)^(1/3))
+--E 544
+
+--S 545 of 1309
+--a0:=integrate(t0,x)
+--E 545
+
+--S 546 of 1309
+--m0:=a0-r0
+--E 546
+
+--S 547 of 1309
+--d0:=D(m0,x)
+--E 547
+
+)clear all
+
+--S 548 of 1309
+t0:=x^3*(a+b*x^3)^(2/3)
+--R
+--R
+--R +--------+2
+--R 3 3| 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 548
+
+--S 549 of 1309
+r0:=1/9*a*x*(a+b*x^3)^(2/3)/b+1/6*x^4*(a+b*x^3)^(2/3)+_
+ 1/27*a^2*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(4/3)-_
+ 1/54*a^2*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+_
+ b^(1/3)*x/(a+b*x^3)^(1/3))/b^(4/3)-_
+ 1/9*a^2*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R 2 +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R - a \|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R 3| 3 3+-+ 3| 3 3+-+
+--R 2 +-+ \|b x + a - x\|b 2 \|b x + a + 2x\|b
+--R 2a \|3 log(-------------------) - 6a atan(--------------------)
+--R +--------+ +--------+
+--R 3| 3 +-+3| 3
+--R \|b x + a \|3 \|b x + a
+--R +
+--R +--------+2
+--R 4 +-+3+-+3| 3
+--R (9b x + 6a x)\|3 \|b \|b x + a
+--R /
+--R +-+3+-+
+--R 54b\|3 \|b
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+2 +--------+
+--R 3+-+3| 3 3+-+2 3| 3 2
+--R 2 +-+ \|b \|b x + a + x \|b \|b x + a + b x
+--R - a \|3 log(--------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R 3+-+2 3| 3
+--R 2 +-+ \|b \|b x + a - b x
+--R 2a \|3 log(----------------------)
+--R x
+--R +
+--R +--------+
+--R +-+3+-+2 3| 3 +-+
+--R 2 2\|3 \|b \|b x + a + b x\|3
+--R 6a atan(-------------------------------)
+--R 3b x
+--R +
+--R +--------+2
+--R 4 +-+3+-+3| 3
+--R (9b x + 6a x)\|3 \|b \|b x + a
+--R /
+--R +-+3+-+
+--R 54b\|3 \|b
+--R Type: Union(Expression(Integer),...)
+--E 550
+
+--S 551 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+2 +--------+
+--R 3+-+3| 3 3+-+2 3| 3 2
+--R 2 +-+ \|b \|b x + a + x \|b \|b x + a + b x
+--R - a \|3 log(--------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R 3+-+2 3| 3
+--R 2 +-+ \|b \|b x + a - b x
+--R 2a \|3 log(----------------------)
+--R x
+--R +
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R 2 +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R a \|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R 3| 3 3+-+
+--R 2 +-+ \|b x + a - x\|b
+--R - 2a \|3 log(-------------------)
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+
+--R 2 2\|3 \|b \|b x + a + b x\|3 2 \|b x + a + 2x\|b
+--R 6a atan(-------------------------------) + 6a atan(--------------------)
+--R 3b x +--------+
+--R +-+3| 3
+--R \|3 \|b x + a
+--R /
+--R +-+3+-+
+--R 54b\|3 \|b
+--R Type: Expression(Integer)
+--E 551
+
+--S 552 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 552
+
+)clear all
+
+--S 553 of 1309
+t0:=x^2*(a+b*x^3)^(2/3)
+--R
+--R
+--R +--------+2
+--R 2 3| 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 553
+
+--S 554 of 1309
+r0:=1/5*(a+b*x^3)^(5/3)/b
+--R
+--R
+--R +--------+2
+--R 3 3| 3
+--R (b x + a)\|b x + a
+--R (2) ----------------------
+--R 5b
+--R Type: Expression(Integer)
+--E 554
+
+--S 555 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 3 3| 3
+--R (b x + a)\|b x + a
+--R (3) ----------------------
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 555
+
+--S 556 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 557
+
+)clear all
+
+--S 558 of 1309
+t0:=x*(a+b*x^3)^(2/3)
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R (1) x \|b x + a
+--R Type: Expression(Integer)
+--E 558
+
+--S 559 of 1309
+--r0:=1/4*x^2*(a+b*x^3)^(2/3)+1/4*a*x^2*((a+b*x^3)/a)^(1/3)*_
+-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a+b*x^3)^(1/3)
+--E 559
+
+--S 560 of 1309
+--a0:=integrate(t0,x)
+--E 560
+
+--S 561 of 1309
+--m0:=a0-r0
+--E 561
+
+--S 562 of 1309
+--d0:=D(m0,x)
+--E 562
+
+)clear all
+
+--S 563 of 1309
+t0:=(a+b*x^3)^(2/3)
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R (1) \|b x + a
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 1309
+r0:=1/3*x*(a+b*x^3)^(2/3)-2/9*a*log(1-b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/b^(1/3)+1/9*a*log(1+b^(2/3)*_
+ x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))/b^(1/3)+_
+ 2/3*a*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R a\|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R 3| 3 3+-+ 3| 3 3+-+
+--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b
+--R - 2a\|3 log(-------------------) + 6a atan(--------------------)
+--R +--------+ +--------+
+--R 3| 3 +-+3| 3
+--R \|b x + a \|3 \|b x + a
+--R +
+--R +--------+2
+--R +-+3+-+3| 3
+--R 3x\|3 \|b \|b x + a
+--R /
+--R +-+3+-+
+--R 9\|3 \|b
+--R Type: Expression(Integer)
+--E 564
+
+--S 565 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+2 +--------+
+--R 3+---+3| 3 3+---+2 3| 3 2
+--R +-+ \|- b \|b x + a - x \|- b \|b x + a - b x
+--R - a\|3 log(------------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R 3+---+2 3| 3
+--R +-+ \|- b \|b x + a - b x
+--R 2a\|3 log(------------------------)
+--R x
+--R +
+--R +--------+
+--R +-+3+---+2 3| 3 +-+ +--------+2
+--R 2\|3 \|- b \|b x + a + b x\|3 +-+3+---+3| 3
+--R 6a atan(---------------------------------) + 3x\|3 \|- b \|b x + a
+--R 3b x
+--R /
+--R +-+3+---+
+--R 9\|3 \|- b
+--R Type: Union(Expression(Integer),...)
+--E 565
+
+--S 566 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+2 +--------+
+--R 3+---+3| 3 3+---+2 3| 3 2
+--R +-+3+-+ \|- b \|b x + a - x \|- b \|b x + a - b x
+--R - a\|3 \|b log(------------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R 3+---+2 3| 3
+--R +-+3+-+ \|- b \|b x + a - b x
+--R 2a\|3 \|b log(------------------------)
+--R x
+--R +
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+3+---+ \|b x + a + x\|b \|b x + a + x \|b
+--R - a\|3 \|- b log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R 3| 3 3+-+
+--R +-+3+---+ \|b x + a - x\|b
+--R 2a\|3 \|- b log(-------------------)
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R +-+3+---+2 3| 3 +-+
+--R 3+-+ 2\|3 \|- b \|b x + a + b x\|3
+--R 6a\|b atan(---------------------------------)
+--R 3b x
+--R +
+--R +--------+
+--R 3| 3 3+-+
+--R 3+---+ \|b x + a + 2x\|b
+--R - 6a\|- b atan(--------------------)
+--R +--------+
+--R +-+3| 3
+--R \|3 \|b x + a
+--R /
+--R +-+3+---+3+-+
+--R 9\|3 \|- b \|b
+--R Type: Expression(Integer)
+--E 566
+
+--S 567 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 567
+
+)clear all
+
+--S 568 of 1309
+t0:=(a+b*x^3)^(2/3)/x
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R (1) ------------
+--R x
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 1309
+r0:=1/2*(a+b*x^3)^(2/3)+1/3*a^(2/3)*log(a^(1/3)-(a+b*x^3)^(1/3))-_
+ 1/6*a^(2/3)*log(a^(2/3)+a^(1/3)*(a+b*x^3)^(1/3)+_
+ (a+b*x^3)^(2/3))+a^(2/3)*atan((a^(1/3)+_
+ 2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3)
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R +-+3+-+2 3| 3 3+-+3| 3 3+-+2
+--R - \|3 \|a log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +--------+ 3| 3 3+-+
+--R +-+3+-+2 3| 3 3+-+ 3+-+2 2\|b x + a + \|a
+--R 2\|3 \|a log(- \|b x + a + \|a ) + 6\|a atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +--------+2
+--R +-+3| 3
+--R 3\|3 \|b x + a
+--R /
+--R +-+
+--R 6\|3
+--R Type: Expression(Integer)
+--E 569
+
+--S 570 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--------+2 +--+2 +--------+ +--+
+--R +-+3| 2 3| 3 3| 2 3| 3 3| 2
+--R - \|3 \|a log(a \|b x + a + \|a \|b x + a + a\|a )
+--R +
+--R +--+ +--------+ +--+2
+--R +-+3| 2 3| 3 3| 2
+--R 2\|3 \|a log(a\|b x + a - \|a )
+--R +
+--R +--------+ +--+2
+--R +--+ +-+3| 3 +-+3| 2 +--------+2
+--R 3| 2 2a\|3 \|b x + a + \|3 \|a +-+3| 3
+--R 6\|a atan(------------------------------) + 3\|3 \|b x + a
+--R +--+2
+--R 3| 2
+--R 3\|a
+--R /
+--R +-+
+--R 6\|3
+--R Type: Union(Expression(Integer),...)
+--E 570
+
+--S 571 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--------+2 +--+2 +--------+ +--+
+--R +-+3| 2 3| 3 3| 2 3| 3 3| 2
+--R - \|3 \|a log(a \|b x + a + \|a \|b x + a + a\|a )
+--R +
+--R +--------+2 +--------+
+--R +-+3+-+2 3| 3 3+-+3| 3 3+-+2
+--R \|3 \|a log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--+ +--------+ +--+2
+--R +-+3| 2 3| 3 3| 2
+--R 2\|3 \|a log(a\|b x + a - \|a )
+--R +
+--R +--------+
+--R +--------+ 3| 3 3+-+
+--R +-+3+-+2 3| 3 3+-+ 3+-+2 2\|b x + a + \|a
+--R - 2\|3 \|a log(- \|b x + a + \|a ) - 6\|a atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +--------+ +--+2
+--R +--+ +-+3| 3 +-+3| 2
+--R 3| 2 2a\|3 \|b x + a + \|3 \|a
+--R 6\|a atan(------------------------------)
+--R +--+2
+--R 3| 2
+--R 3\|a
+--R /
+--R +-+
+--R 6\|3
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 572
+
+)clear all
+
+--S 573 of 1309
+t0:=(a+b*x^3)^(2/3)/x^2
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R (1) ------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 1309
+--r0:=-(a+b*x^3)^(2/3)/x+b*x^2*((a+b*x^3)/a)^(1/3)*_
+-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a+b*x^3)^(1/3)
+--E 574
+
+--S 575 of 1309
+--a0:=integrate(t0,x)
+--E 575
+
+--S 576 of 1309
+--m0:=a0-r0
+--E 576
+
+--S 577 of 1309
+--d0:=D(m0,x)
+--E 577
+
+)clear all
+
+--S 578 of 1309
+t0:=(a+b*x^3)^(2/3)/x^3
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R (1) ------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 1309
+r0:=-1/2*(a+b*x^3)^(2/3)/x^2-1/3*b^(2/3)*log(1-b^(1/3)*_
+ x/(a+b*x^3)^(1/3))+1/6*b^(2/3)*log(1+b^(2/3)*_
+ x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))+_
+ b^(2/3)*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R 2 +-+3+-+2 \|b x + a + x\|b \|b x + a + x \|b
+--R x \|3 \|b log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R 3| 3 3+-+
+--R 2 +-+3+-+2 \|b x + a - x\|b
+--R - 2x \|3 \|b log(-------------------)
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R 3| 3 3+-+ +--------+2
+--R 2 3+-+2 \|b x + a + 2x\|b +-+3| 3
+--R 6x \|b atan(-------------------- - 3\|3 \|b x + a
+--R +--------+
+--R +-+3| 3
+--R \|3 \|b x + a
+--R /
+--R 2 +-+
+--R 6x \|3
+--R Type: Expression(Integer)
+--E 579
+
+--S 580 of 1309
+--a0:=integrate(t0,x)
+--E 580
+
+--S 581 of 1309
+--m0:=a0-r0
+--E 581
+
+--S 582 of 1309
+--d0:=D(m0,x)
+--E 582
+
+)clear all
+
+--S 583 of 1309
+t0:=(a+b*x^3)^(2/3)/x^4
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R (1) ------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 1309
+r0:=-1/3*(a+b*x^3)^(2/3)/x^3+2/9*b*log(a^(1/3)-_
+ (a+b*x^3)^(1/3))/a^(1/3)-1/9*b*log(a^(2/3)+_
+ a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(1/3)+_
+ 2/3*b*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/_
+ (a^(1/3)*sqrt(3)))/(a^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3 +-+ 3| 3 3+-+3| 3 3+-+2
+--R - b x \|3 log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +--------+ 3| 3 3+-+
+--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a
+--R 2b x \|3 log(- \|b x + a + \|a ) + 6b x atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +--------+2
+--R +-+3+-+3| 3
+--R - 3\|3 \|a \|b x + a
+--R /
+--R 3 +-+3+-+
+--R 9x \|3 \|a
+--R Type: Expression(Integer)
+--E 584
+
+--S 585 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+2 +--------+
+--R 3 +-+ 3+-+3| 3 3+-+2 3| 3
+--R - b x \|3 log(\|a \|b x + a + \|a \|b x + a + a)
+--R +
+--R +--------+
+--R 3 +-+ 3+-+2 3| 3
+--R 2b x \|3 log(\|a \|b x + a - a)
+--R +
+--R +--------+
+--R +-+3+-+2 3| 3 +-+ +--------+2
+--R 3 2\|3 \|a \|b x + a + a\|3 +-+3+-+3| 3
+--R 6b x atan(-----------------------------) - 3\|3 \|a \|b x + a
+--R 3a
+--R /
+--R 3 +-+3+-+
+--R 9x \|3 \|a
+--R Type: Union(Expression(Integer),...)
+--E 585
+
+--S 586 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+2 +--------+
+--R +-+ 3+-+3| 3 3+-+2 3| 3
+--R - b\|3 log(\|a \|b x + a + \|a \|b x + a + a)
+--R +
+--R +--------+2 +--------+
+--R +-+ 3| 3 3+-+3| 3 3+-+2
+--R b\|3 log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+ +--------+
+--R +-+ 3+-+2 3| 3 +-+ 3| 3 3+-+
+--R 2b\|3 log(\|a \|b x + a - a) - 2b\|3 log(- \|b x + a + \|a )
+--R +
+--R +--------+ +--------+
+--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+
+--R 2\|3 \|a \|b x + a + a\|3 2\|b x + a + \|a
+--R 6b atan(-----------------------------) - 6b atan(-------------------)
+--R 3a +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+
+--R 9\|3 \|a
+--R Type: Expression(Integer)
+--E 586
+
+--S 587 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 587
+
+)clear all
+
+--S 588 of 1309
+t0:=x^8*(1-x^3)^(6/5)
+--R
+--R
+--R +--------+
+--R 11 8 5| 3
+--R (1) (- x + x )\|- x + 1
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 1309
+r0:=-5/33*(1-x^3)^(11/5)+5/24*(1-x^3)^(16/5)-5/63*(1-x^3)^(21/5)
+--R
+--R
+--R +--------+
+--R 12 9 6 3 5| 3
+--R (- 440x + 605x - 15x - 25x - 125)\|- x + 1
+--R (2) -------------------------------------------------
+--R 5544
+--R Type: Expression(Integer)
+--E 589
+
+--S 590 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 12 9 6 3 5| 3
+--R (- 440x + 605x - 15x - 25x - 125)\|- x + 1
+--R (3) -------------------------------------------------
+--R 5544
+--R Type: Union(Expression(Integer),...)
+--E 590
+
+--S 591 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 591
+
+--S 592 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 592
+
+)clear all
+
+--S 593 of 1309
+t0:=x^11/(a+b*x^3)^(1/3)
+--R
+--R
+--R 11
+--R x
+--R (1) -----------
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 593
+
+--S 594 of 1309
+r0:=-81/440*a^3*(a+b*x^3)^(2/3)/b^4+27/220*a^2*x^3*_
+ (a+b*x^3)^(2/3)/b^3-9/88*a*x^6*(a+b*x^3)^(2/3)/b^2+_
+ 1/11*x^9*(a+b*x^3)^(2/3)/b
+--R
+--R
+--R +--------+2
+--R 3 9 2 6 2 3 3 3| 3
+--R (40b x - 45a b x + 54a b x - 81a )\|b x + a
+--R (2) -------------------------------------------------
+--R 4
+--R 440b
+--R Type: Expression(Integer)
+--E 594
+
+--S 595 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 3 9 2 6 2 3 3 3| 3
+--R (40b x - 45a b x + 54a b x - 81a )\|b x + a
+--R (3) -------------------------------------------------
+--R 4
+--R 440b
+--R Type: Union(Expression(Integer),...)
+--E 595
+
+--S 596 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 596
+
+--S 597 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 597
+
+)clear all
+
+--S 598 of 1309
+t0:=x^8/(a+b*x^3)^(1/3)
+--R
+--R
+--R 8
+--R x
+--R (1) -----------
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 598
+
+--S 599 of 1309
+r0:=9/40*a^2*(a+b*x^3)^(2/3)/b^3-3/20*a*x^3*(a+b*x^3)^(2/3)/b^2+_
+ 1/8*x^6*(a+b*x^3)^(2/3)/b
+--R
+--R
+--R +--------+2
+--R 2 6 3 2 3| 3
+--R (5b x - 6a b x + 9a )\|b x + a
+--R (2) -----------------------------------
+--R 3
+--R 40b
+--R Type: Expression(Integer)
+--E 599
+
+--S 600 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 2 6 3 2 3| 3
+--R (5b x - 6a b x + 9a )\|b x + a
+--R (3) -----------------------------------
+--R 3
+--R 40b
+--R Type: Union(Expression(Integer),...)
+--E 600
+
+--S 601 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 601
+
+--S 602 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 602
+
+)clear all
+
+--S 603 of 1309
+t0:=x^5/(a+b*x^3)^(1/3)
+--R
+--R
+--R 5
+--R x
+--R (1) -----------
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 603
+
+--S 604 of 1309
+r0:=-3/10*a*(a+b*x^3)^(2/3)/b^2+1/5*x^3*(a+b*x^3)^(2/3)/b
+--R
+--R
+--R +--------+2
+--R 3 3| 3
+--R (2b x - 3a)\|b x + a
+--R (2) ------------------------
+--R 2
+--R 10b
+--R Type: Expression(Integer)
+--E 604
+
+--S 605 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 3 3| 3
+--R (2b x - 3a)\|b x + a
+--R (3) ------------------------
+--R 2
+--R 10b
+--R Type: Union(Expression(Integer),...)
+--E 605
+
+--S 606 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 606
+
+--S 607 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 607
+
+)clear all
+
+--S 608 of 1309
+t0:=x^2/(a+b*x^3)^(1/3)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 1309
+r0:=1/2*(a+b*x^3)^(2/3)/b
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R (2) ------------
+--R 2b
+--R Type: Expression(Integer)
+--E 609
+
+--S 610 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R (3) ------------
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 610
+
+--S 611 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 611
+
+--S 612 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 612
+
+)clear all
+
+--S 613 of 1309
+t0:=1/(x*(a+b*x^3)^(1/3))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +--------+
+--R 3| 3
+--R x\|b x + a
+--R Type: Expression(Integer)
+--E 613
+
+--S 614 of 1309
+r0:=1/3*log(a^(1/3)-(a+b*x^3)^(1/3))/a^(1/3)-1/6*log(a^(2/3)+_
+ a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(1/3)+_
+ 1/3*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3)
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 3+-+2
+--R - log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +--------+ 3| 3 3+-+
+--R 3| 3 3+-+ +-+ 2\|b x + a + \|a
+--R 2log(- \|b x + a + \|a ) + 2\|3 atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 3+-+
+--R 6\|a
+--R Type: Expression(Integer)
+--E 614
+
+--S 615 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+2 +--------+
+--R +-+ 3+-+3| 3 3+-+2 3| 3
+--R - \|3 log(\|a \|b x + a + \|a \|b x + a + a)
+--R +
+--R +--------+
+--R +--------+ +-+3+-+2 3| 3 +-+
+--R +-+ 3+-+2 3| 3 2\|3 \|a \|b x + a + a\|3
+--R 2\|3 log(\|a \|b x + a - a) + 6atan(-----------------------------)
+--R 3a
+--R /
+--R +-+3+-+
+--R 6\|3 \|a
+--R Type: Union(Expression(Integer),...)
+--E 615
+
+--S 616 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+2 +--------+
+--R +-+ 3+-+3| 3 3+-+2 3| 3
+--R - \|3 log(\|a \|b x + a + \|a \|b x + a + a)
+--R +
+--R +--------+2 +--------+
+--R +-+ 3| 3 3+-+3| 3 3+-+2
+--R \|3 log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+ +--------+
+--R +-+ 3+-+2 3| 3 +-+ 3| 3 3+-+
+--R 2\|3 log(\|a \|b x + a - a) - 2\|3 log(- \|b x + a + \|a )
+--R +
+--R +--------+ +--------+
+--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+
+--R 2\|3 \|a \|b x + a + a\|3 2\|b x + a + \|a
+--R 6atan(-----------------------------) - 6atan(-------------------)
+--R 3a +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+
+--R 6\|3 \|a
+--R Type: Expression(Integer)
+--E 616
+
+--S 617 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 617
+
+)clear all
+
+--S 618 of 1309
+t0:=1/(x^4*(a+b*x^3)^(1/3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 4 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 618
+
+--S 619 of 1309
+r0:=-1/3*(a+b*x^3)^(2/3)/(a*x^3)-1/9*b*log(a^(1/3)-_
+ (a+b*x^3)^(1/3))/a^(4/3)+1/18*b*log(a^(2/3)+_
+ a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(4/3)-_
+ 1/3*b*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/_
+ (a^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3 +-+ 3| 3 3+-+3| 3 3+-+2
+--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +--------+ 3| 3 3+-+
+--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a
+--R - 2b x \|3 log(- \|b x + a + \|a ) - 6b x atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +--------+2
+--R +-+3+-+3| 3
+--R - 6\|3 \|a \|b x + a
+--R /
+--R 3 +-+3+-+
+--R 18a x \|3 \|a
+--R Type: Expression(Integer)
+--E 619
+
+--S 620 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+2 +--------+
+--R 3 +-+ 3+---+3| 3 3+---+2 3| 3
+--R - b x \|3 log(\|- a \|b x + a - \|- a \|b x + a - a)
+--R +
+--R +--------+
+--R 3 +-+ 3+---+2 3| 3
+--R 2b x \|3 log(\|- a \|b x + a - a)
+--R +
+--R +--------+
+--R +-+3+---+2 3| 3 +-+ +--------+2
+--R 3 2\|3 \|- a \|b x + a + a\|3 +-+3+---+3| 3
+--R 6b x atan(-------------------------------) - 6\|3 \|- a \|b x + a
+--R 3a
+--R /
+--R 3 +-+3+---+
+--R 18a x \|3 \|- a
+--R Type: Union(Expression(Integer),...)
+--E 620
+
+--S 621 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+2 +--------+
+--R +-+3+-+ 3+---+3| 3 3+---+2 3| 3
+--R - b\|3 \|a log(\|- a \|b x + a - \|- a \|b x + a - a)
+--R +
+--R +--------+2 +--------+
+--R +-+3+---+ 3| 3 3+-+3| 3 3+-+2
+--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +-+3+-+ 3+---+2 3| 3
+--R 2b\|3 \|a log(\|- a \|b x + a - a)
+--R +
+--R +--------+
+--R +-+3+---+ 3| 3 3+-+
+--R 2b\|3 \|- a log(- \|b x + a + \|a )
+--R +
+--R +--------+
+--R +-+3+---+2 3| 3 +-+
+--R 3+-+ 2\|3 \|- a \|b x + a + a\|3
+--R 6b\|a atan(-------------------------------)
+--R 3a
+--R +
+--R +--------+
+--R 3| 3 3+-+
+--R 3+---+ 2\|b x + a + \|a
+--R 6b\|- a atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+---+3+-+
+--R 18a\|3 \|- a \|a
+--R Type: Expression(Integer)
+--E 621
+
+--S 622 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 622
+
+)clear all
+
+--S 623 of 1309
+t0:=x^7/(a+b*x^3)^(1/3)
+--R
+--R
+--R 7
+--R x
+--R (1) -----------
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 1309
+--r0:=-5/28*a*x^2*(a+b*x^3)^(2/3)/b^2+1/7*x^5*(a+b*x^3)^(2/3)/b+_
+-- 5/28*a^2*x^2*((a+b*x^3)/a)^(1/3)*_
+-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(b^2*(a+b*x^3)^(1/3))
+--E 624
+
+--S 625 of 1309
+--a0:=integrate(t0,x)
+--E 625
+
+--S 626 of 1309
+--m0:=a0-r0
+--E 626
+
+--S 627 of 1309
+--d0:=D(m0,x)
+--E 627
+
+)clear all
+
+--S 628 of 1309
+t0:=x^4/(a+b*x^3)^(1/3)
+--R
+--R
+--R 4
+--R x
+--R (1) -----------
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 628
+
+--S 629 of 1309
+--r0:=1/4*x^2*(a+b*x^3)^(2/3)/b-1/4*a*x^2*((a+b*x^3)/a)^(1/3)*_
+-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(b*(a+b*x^3)^(1/3))
+--E 629
+
+--S 630 of 1309
+--a0:=integrate(t0,x)
+--E 630
+
+--S 631 of 1309
+--m0:=a0-r0
+--E 631
+
+--S 632 of 1309
+--d0:=D(m0,x)
+--E 632
+
+)clear all
+
+--S 633 of 1309
+t0:=x/(a+b*x^3)^(1/3)
+--R
+--R
+--R x
+--R (1) -----------
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 633
+
+--S 634 of 1309
+--r0:=1/2*x^2*((a+b*x^3)/a)^(1/3)*_
+-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a+b*x^3)^(1/3)
+--E 634
+
+--S 635 of 1309
+--a0:=integrate(t0,x)
+--E 635
+
+--S 636 of 1309
+--m0:=a0-r0
+--E 636
+
+--S 637 of 1309
+--d0:=D(m0,x)
+--E 637
+
+)clear all
+
+--S 638 of 1309
+t0:=1/(x^2*(a+b*x^3)^(1/3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 2 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 1309
+--r0:=-(a+b*x^3)^(2/3)/(a*x)+1/2*b*x^2*((a+b*x^3)/a)^(1/3)*_
+-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a*(a+b*x^3)^(1/3))
+--E 639
+
+--S 640 of 1309
+--a0:=integrate(t0,x)
+--E 640
+
+--S 641 of 1309
+--m0:=a0-r0
+--E 641
+
+--S 642 of 1309
+--d0:=D(m0,x)
+--E 642
+
+)clear all
+
+--S 643 of 1309
+t0:=1/(x^5*(a+b*x^3)^(1/3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 5 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 643
+
+--S 644 of 1309
+--r0:=-1/4*(a+b*x^3)^(2/3)/(a*x^4)+1/2*b*(a+b*x^3)^(2/3)/(a^2*x)-_
+-- 1/4*b^2*x^2*((a+b*x^3)/a)^(1/3)*_
+-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a^2*(a+b*x^3)^(1/3))
+--E 644
+
+--S 645 of 1309
+--a0:=integrate(t0,x)
+--E 645
+
+--S 646 of 1309
+--m0:=a0-r0
+--E 646
+
+--S 647 of 1309
+--d0:=D(m0,x)
+--E 647
+
+)clear all
+
+--S 648 of 1309
+t0:=x^3/(a+b*x^3)^(1/3)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 1309
+r0:=1/3*x*(a+b*x^3)^(2/3)/b+1/9*a*log(1-b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/b^(4/3)-1/18*a*log(1+b^(2/3)*_
+ x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))/b^(4/3)-_
+ 1/3*a*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R - a\|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R 3| 3 3+-+ 3| 3 3+-+
+--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b
+--R 2a\|3 log(-------------------) - 6a atan(--------------------)
+--R +--------+ +--------+
+--R 3| 3 +-+3| 3
+--R \|b x + a \|3 \|b x + a
+--R +
+--R +--------+2
+--R +-+3+-+3| 3
+--R 6x\|3 \|b \|b x + a
+--R /
+--R +-+3+-+
+--R 18b\|3 \|b
+--R Type: Expression(Integer)
+--E 649
+
+--S 650 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+2 +--------+
+--R 3+-+3| 3 3+-+2 3| 3 2
+--R +-+ \|b \|b x + a + x \|b \|b x + a + b x
+--R - a\|3 log(--------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R 3+-+2 3| 3
+--R +-+ \|b \|b x + a - b x
+--R 2a\|3 log(----------------------)
+--R x
+--R +
+--R +--------+
+--R +-+3+-+2 3| 3 +-+ +--------+2
+--R 2\|3 \|b \|b x + a + b x\|3 +-+3+-+3| 3
+--R 6a atan(-------------------------------) + 6x\|3 \|b \|b x + a
+--R 3b x
+--R /
+--R +-+3+-+
+--R 18b\|3 \|b
+--R Type: Union(Expression(Integer),...)
+--E 650
+
+--S 651 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+2 +--------+
+--R 3+-+3| 3 3+-+2 3| 3 2
+--R +-+ \|b \|b x + a + x \|b \|b x + a + b x
+--R - a\|3 log(--------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R 3+-+2 3| 3
+--R +-+ \|b \|b x + a - b x
+--R 2a\|3 log(----------------------)
+--R x
+--R +
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R a\|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R 3| 3 3+-+
+--R +-+ \|b x + a - x\|b
+--R - 2a\|3 log(-------------------)
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+
+--R 2\|3 \|b \|b x + a + b x\|3 \|b x + a + 2x\|b
+--R 6a atan(-------------------------------) + 6a atan(--------------------)
+--R 3b x +--------+
+--R +-+3| 3
+--R \|3 \|b x + a
+--R /
+--R +-+3+-+
+--R 18b\|3 \|b
+--R Type: Expression(Integer)
+--E 651
+
+--S 652 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 652
+
+)clear all
+
+--S 653 of 1309
+t0:=1/(a+b*x^3)^(1/3)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 653
+
+--S 654 of 1309
+r0:=-1/3*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(1/3)+_
+ 1/6*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/b^(1/3)+atan((1+2*b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R \|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R 3| 3 3+-+ 3| 3 3+-+
+--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b
+--R - 2\|3 log(-------------------) + 6atan(--------------------)
+--R +--------+ +--------+
+--R 3| 3 +-+3| 3
+--R \|b x + a \|3 \|b x + a
+--R /
+--R +-+3+-+
+--R 6\|3 \|b
+--R Type: Expression(Integer)
+--E 654
+
+--S 655 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+2 +--------+
+--R 3+---+3| 3 3+---+2 3| 3 2
+--R +-+ \|- b \|b x + a - x \|- b \|b x + a - b x
+--R - \|3 log(------------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R 3+---+2 3| 3
+--R +-+ \|- b \|b x + a - b x
+--R 2\|3 log(------------------------)
+--R x
+--R +
+--R +--------+
+--R +-+3+---+2 3| 3 +-+
+--R 2\|3 \|- b \|b x + a + b x\|3
+--R 6atan(---------------------------------)
+--R 3b x
+--R /
+--R +-+3+---+
+--R 6\|3 \|- b
+--R Type: Union(Expression(Integer),...)
+--E 655
+
+--S 656 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+2 +--------+
+--R 3+---+3| 3 3+---+2 3| 3 2
+--R +-+3+-+ \|- b \|b x + a - x \|- b \|b x + a - b x
+--R - \|3 \|b log(------------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R 3+---+2 3| 3
+--R +-+3+-+ \|- b \|b x + a - b x
+--R 2\|3 \|b log(------------------------)
+--R x
+--R +
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+3+---+ \|b x + a + x\|b \|b x + a + x \|b
+--R - \|3 \|- b log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R 3| 3 3+-+
+--R +-+3+---+ \|b x + a - x\|b
+--R 2\|3 \|- b log(-------------------)
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R +-+3+---+2 3| 3 +-+
+--R 3+-+ 2\|3 \|- b \|b x + a + b x\|3
+--R 6\|b atan(---------------------------------)
+--R 3b x
+--R +
+--R +--------+
+--R 3| 3 3+-+
+--R 3+---+ \|b x + a + 2x\|b
+--R - 6\|- b atan(--------------------)
+--R +--------+
+--R +-+3| 3
+--R \|3 \|b x + a
+--R /
+--R +-+3+---+3+-+
+--R 6\|3 \|- b \|b
+--R Type: Expression(Integer)
+--E 656
+
+--S 657 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 657
+
+)clear all
+
+--S 658 of 1309
+t0:=1/(x^3*(a+b*x^3)^(1/3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 3 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 1309
+r0:=-1/2*(a+b*x^3)^(2/3)/(a*x^2)
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R (2) - ------------
+--R 2
+--R 2a x
+--R Type: Expression(Integer)
+--E 659
+
+--S 660 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R (3) - ------------
+--R 2
+--R 2a x
+--R Type: Union(Expression(Integer),...)
+--E 660
+
+--S 661 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 662
+
+)clear all
+
+--S 663 of 1309
+t0:=1/(x^6*(a+b*x^3)^(1/3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 6 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 1309
+r0:=-1/5*(a+b*x^3)^(2/3)/(a*x^5)+3/10*b*(a+b*x^3)^(2/3)/(a^2*x^2)
+--R
+--R
+--R +--------+2
+--R 3 3| 3
+--R (3b x - 2a)\|b x + a
+--R (2) ------------------------
+--R 2 5
+--R 10a x
+--R Type: Expression(Integer)
+--E 664
+
+--S 665 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 3 3| 3
+--R (3b x - 2a)\|b x + a
+--R (3) ------------------------
+--R 2 5
+--R 10a x
+--R Type: Union(Expression(Integer),...)
+--E 665
+
+--S 666 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 666
+
+--S 667 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 667
+
+)clear all
+
+--S 668 of 1309
+t0:=1/(x^9*(a+b*x^3)^(1/3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 9 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 1309
+r0:=-1/8*(a+b*x^3)^(2/3)/(a*x^8)+3/20*b*(a+b*x^3)^(2/3)/(a^2*x^5)-_
+ 9/40*b^2*(a+b*x^3)^(2/3)/(a^3*x^2)
+--R
+--R
+--R +--------+2
+--R 2 6 3 2 3| 3
+--R (- 9b x + 6a b x - 5a )\|b x + a
+--R (2) -------------------------------------
+--R 3 8
+--R 40a x
+--R Type: Expression(Integer)
+--E 669
+
+--S 670 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 2 6 3 2 3| 3
+--R (- 9b x + 6a b x - 5a )\|b x + a
+--R (3) -------------------------------------
+--R 3 8
+--R 40a x
+--R Type: Union(Expression(Integer),...)
+--E 670
+
+--S 671 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 671
+
+--S 672 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 672
+
+)clear all
+
+--S 673 of 1309
+t0:=1/(x^12*(a+b*x^3)^(1/3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+
+--R 12 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 1309
+r0:=-1/11*(a+b*x^3)^(2/3)/(a*x^11)+9/88*b*(a+b*x^3)^(2/3)/(a^2*x^8)-_
+ 27/220*b^2*(a+b*x^3)^(2/3)/(a^3*x^5)+81/440*b^3*(a+b*x^3)^(2/3)/(a^4*x^2)
+--R
+--R
+--R +--------+2
+--R 3 9 2 6 2 3 3 3| 3
+--R (81b x - 54a b x + 45a b x - 40a )\|b x + a
+--R (2) -------------------------------------------------
+--R 4 11
+--R 440a x
+--R Type: Expression(Integer)
+--E 674
+
+--S 675 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+2
+--R 3 9 2 6 2 3 3 3| 3
+--R (81b x - 54a b x + 45a b x - 40a )\|b x + a
+--R (3) -------------------------------------------------
+--R 4 11
+--R 440a x
+--R Type: Union(Expression(Integer),...)
+--E 675
+
+--S 676 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 676
+
+--S 677 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 677
+
+)clear all
+
+--S 678 of 1309
+t0:=x^11/(a+b*x^3)^(2/3)
+--R
+--R
+--R 11
+--R x
+--R (1) ------------
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 1309
+r0:=-81/140*a^3*(a+b*x^3)^(1/3)/b^4+27/140*a^2*x^3*(a+b*x^3)^(1/3)/b^3-_
+ 9/70*a*x^6*(a+b*x^3)^(1/3)/b^2+1/10*x^9*(a+b*x^3)^(1/3)/b
+--R
+--R
+--R +--------+
+--R 3 9 2 6 2 3 3 3| 3
+--R (14b x - 18a b x + 27a b x - 81a )\|b x + a
+--R (2) ------------------------------------------------
+--R 4
+--R 140b
+--R Type: Expression(Integer)
+--E 679
+
+--S 680 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 9 2 6 2 3 3 3| 3
+--R (14b x - 18a b x + 27a b x - 81a )\|b x + a
+--R (3) ------------------------------------------------
+--R 4
+--R 140b
+--R Type: Union(Expression(Integer),...)
+--E 680
+
+--S 681 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 681
+
+--S 682 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 682
+
+)clear all
+
+--S 683 of 1309
+t0:=x^8/(a+b*x^3)^(2/3)
+--R
+--R
+--R 8
+--R x
+--R (1) ------------
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 1309
+r0:=9/14*a^2*(a+b*x^3)^(1/3)/b^3-3/14*a*x^3*(a+b*x^3)^(1/3)/b^2+_
+ 1/7*x^6*(a+b*x^3)^(1/3)/b
+--R
+--R
+--R +--------+
+--R 2 6 3 2 3| 3
+--R (2b x - 3a b x + 9a )\|b x + a
+--R (2) ----------------------------------
+--R 3
+--R 14b
+--R Type: Expression(Integer)
+--E 684
+
+--S 685 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 6 3 2 3| 3
+--R (2b x - 3a b x + 9a )\|b x + a
+--R (3) ----------------------------------
+--R 3
+--R 14b
+--R Type: Union(Expression(Integer),...)
+--E 685
+
+--S 686 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 686
+
+--S 687 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 687
+
+)clear all
+
+--S 688 of 1309
+t0:=x^5/(a+b*x^3)^(2/3)
+--R
+--R
+--R 5
+--R x
+--R (1) ------------
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 688
+
+--S 689 of 1309
+r0:=-3/4*a*(a+b*x^3)^(1/3)/b^2+1/4*x^3*(a+b*x^3)^(1/3)/b
+--R
+--R
+--R +--------+
+--R 3 3| 3
+--R (b x - 3a)\|b x + a
+--R (2) ----------------------
+--R 2
+--R 4b
+--R Type: Expression(Integer)
+--E 689
+
+--S 690 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 3| 3
+--R (b x - 3a)\|b x + a
+--R (3) ----------------------
+--R 2
+--R 4b
+--R Type: Union(Expression(Integer),...)
+--E 690
+
+--S 691 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 691
+
+--S 692 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 692
+
+)clear all
+
+--S 693 of 1309
+t0:=x^2/(a+b*x^3)^(2/3)
+--R
+--R
+--R 2
+--R x
+--R (1) ------------
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 1309
+r0:=(a+b*x^3)^(1/3)/b
+--R
+--R
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R (2) -----------
+--R b
+--R Type: Expression(Integer)
+--E 694
+
+--S 695 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R (3) -----------
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 695
+
+--S 696 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 696
+
+--S 697 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 697
+
+)clear all
+
+--S 698 of 1309
+t0:=1/(x*(a+b*x^3)^(2/3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+2
+--R 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 1309
+r0:=1/3*log(a^(1/3)-(a+b*x^3)^(1/3))/a^(2/3)-1/6*log(a^(2/3)+_
+ a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(2/3)-_
+ atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R +-+ 3| 3 3+-+3| 3 3+-+2
+--R - \|3 log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +--------+ 3| 3 3+-+
+--R +-+ 3| 3 3+-+ 2\|b x + a + \|a
+--R 2\|3 log(- \|b x + a + \|a ) - 6atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2
+--R 6\|3 \|a
+--R Type: Expression(Integer)
+--E 699
+
+--S 700 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+2 +--------+2 +--+ +--------+
+--R +-+ 3| 2 3| 3 3| 2 3| 3 2
+--R - \|3 log(\|a \|b x + a + a\|a \|b x + a + a )
+--R +
+--R +--+ +--------+
+--R +--+ +--------+ +-+3| 2 3| 3 +-+
+--R +-+ 3| 2 3| 3 2\|3 \|a \|b x + a + a\|3
+--R 2\|3 log(\|a \|b x + a - a) - 6atan(-----------------------------)
+--R 3a
+--R /
+--R +--+
+--R +-+3| 2
+--R 6\|3 \|a
+--R Type: Union(Expression(Integer),...)
+--E 700
+
+--S 701 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+2 +--------+2 +--+ +--------+
+--R +-+3+-+2 3| 2 3| 3 3| 2 3| 3 2
+--R - \|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a )
+--R +
+--R +--+ +--------+2 +--------+
+--R +-+3| 2 3| 3 3+-+3| 3 3+-+2
+--R \|3 \|a log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--+ +--------+ +--+ +--------+
+--R +-+3+-+2 3| 2 3| 3 +-+3| 2 3| 3 3+-+
+--R 2\|3 \|a log(\|a \|b x + a - a) - 2\|3 \|a log(- \|b x + a + \|a )
+--R +
+--R +--+ +--------+
+--R +-+3| 2 3| 3 +-+
+--R 3+-+2 2\|3 \|a \|b x + a + a\|3
+--R - 6\|a atan(-----------------------------)
+--R 3a
+--R +
+--R +--------+
+--R +--+ 3| 3 3+-+
+--R 3| 2 2\|b x + a + \|a
+--R 6\|a atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +--+
+--R +-+3+-+2 3| 2
+--R 6\|3 \|a \|a
+--R Type: Expression(Integer)
+--E 701
+
+--S 702 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 702
+
+)clear all
+
+--S 703 of 1309
+t0:=1/(x^4*(a+b*x^3)^(2/3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+2
+--R 4 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 1309
+r0:=-1/3*(a+b*x^3)^(1/3)/(a*x^3)-2/9*b*log(a^(1/3)-_
+ (a+b*x^3)^(1/3))/a^(5/3)+1/9*b*log(a^(2/3)+a^(1/3)*_
+ (a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(5/3)+2/3*b*_
+ atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3 +-+ 3| 3 3+-+3| 3 3+-+2
+--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +--------+
+--R +--------+ 3| 3 3+-+
+--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a
+--R - 2b x \|3 log(- \|b x + a + \|a ) + 6b x atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +--------+
+--R +-+3+-+2 3| 3
+--R - 3\|3 \|a \|b x + a
+--R /
+--R 3 +-+3+-+2
+--R 9a x \|3 \|a
+--R Type: Expression(Integer)
+--E 704
+
+--S 705 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+2 +--------+2 +----+ +--------+
+--R 3 +-+ 3| 2 3| 3 3| 2 3| 3 2
+--R - b x \|3 log(\|- a \|b x + a - a\|- a \|b x + a + a )
+--R +
+--R +----+ +--------+
+--R 3 +-+ 3| 2 3| 3
+--R 2b x \|3 log(\|- a \|b x + a + a)
+--R +
+--R +----+ +--------+
+--R +-+3| 2 3| 3 +-+ +----+ +--------+
+--R 3 2\|3 \|- a \|b x + a - a\|3 +-+3| 2 3| 3
+--R 6b x atan(-------------------------------) - 3\|3 \|- a \|b x + a
+--R 3a
+--R /
+--R +----+
+--R 3 +-+3| 2
+--R 9a x \|3 \|- a
+--R Type: Union(Expression(Integer),...)
+--E 705
+
+--S 706 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----+2 +--------+2 +----+ +--------+
+--R +-+3+-+2 3| 2 3| 3 3| 2 3| 3 2
+--R - b\|3 \|a log(\|- a \|b x + a - a\|- a \|b x + a + a )
+--R +
+--R +----+ +--------+2 +--------+
+--R +-+3| 2 3| 3 3+-+3| 3 3+-+2
+--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a )
+--R +
+--R +----+ +--------+
+--R +-+3+-+2 3| 2 3| 3
+--R 2b\|3 \|a log(\|- a \|b x + a + a)
+--R +
+--R +----+ +--------+
+--R +-+3| 2 3| 3 3+-+
+--R 2b\|3 \|- a log(- \|b x + a + \|a )
+--R +
+--R +----+ +--------+
+--R +-+3| 2 3| 3 +-+
+--R 3+-+2 2\|3 \|- a \|b x + a - a\|3
+--R 6b \|a atan(-------------------------------)
+--R 3a
+--R +
+--R +--------+
+--R +----+ 3| 3 3+-+
+--R 3| 2 2\|b x + a + \|a
+--R - 6b\|- a atan(-------------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +----+
+--R +-+3| 2 3+-+2
+--R 9a\|3 \|- a \|a
+--R Type: Expression(Integer)
+--E 706
+
+--S 707 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 707
+
+)clear all
+
+--S 708 of 1309
+t0:=x^4/(a+b*x^3)^(2/3)
+--R
+--R
+--R 4
+--R x
+--R (1) ------------
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 1309
+r0:=1/3*x^2*(a+b*x^3)^(1/3)/b+2/9*a*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/_
+ b^(5/3)-1/9*a*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/b^(5/3)+2/3*a*atan((1+2*b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R - a\|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R 3| 3 3+-+ 3| 3 3+-+
+--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b
+--R 2a\|3 log(-------------------) + 6a atan(--------------------)
+--R +--------+ +--------+
+--R 3| 3 +-+3| 3
+--R \|b x + a \|3 \|b x + a
+--R +
+--R +--------+
+--R 2 +-+3+-+2 3| 3
+--R 3x \|3 \|b \|b x + a
+--R /
+--R +-+3+-+2
+--R 9b\|3 \|b
+--R Type: Expression(Integer)
+--E 709
+
+--S 710 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+2 +--------+2 +--+ +--------+
+--R 3| 2 3| 3 3| 2 3| 3 2 2
+--R +-+ \|b \|b x + a + b x\|b \|b x + a + b x
+--R - a\|3 log(-----------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--+ +--------+
+--R 3| 2 3| 3
+--R +-+ \|b \|b x + a - b x
+--R 2a\|3 log(----------------------)
+--R x
+--R +
+--R +--+ +--------+
+--R +-+3| 2 3| 3 +-+ +--+ +--------+
+--R 2\|3 \|b \|b x + a + b x\|3 2 +-+3| 2 3| 3
+--R - 6a atan(-------------------------------) + 3x \|3 \|b \|b x + a
+--R 3b x
+--R /
+--R +--+
+--R +-+3| 2
+--R 9b\|3 \|b
+--R Type: Union(Expression(Integer),...)
+--E 710
+
+--S 711 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+2 +--------+2 +--+ +--------+
+--R 3| 2 3| 3 3| 2 3| 3 2 2
+--R +-+3+-+2 \|b \|b x + a + b x\|b \|b x + a + b x
+--R - a\|3 \|b log(-----------------------------------------------)
+--R 2
+--R x
+--R +
+--R +--+ +--------+
+--R 3| 2 3| 3
+--R +-+3+-+2 \|b \|b x + a - b x
+--R 2a\|3 \|b log(----------------------)
+--R x
+--R +
+--R +--------+2 +--------+
+--R +--+ 3| 3 3+-+3| 3 2 3+-+2
+--R +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b
+--R a\|3 \|b log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R +--+ 3| 3 3+-+
+--R +-+3| 2 \|b x + a - x\|b
+--R - 2a\|3 \|b log(-------------------)
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--+ +--------+
+--R +-+3| 2 3| 3 +-+
+--R 3+-+2 2\|3 \|b \|b x + a + b x\|3
+--R - 6a \|b atan(-------------------------------)
+--R 3b x
+--R +
+--R +--------+
+--R +--+ 3| 3 3+-+
+--R 3| 2 \|b x + a + 2x\|b
+--R - 6a\|b atan(--------------------)
+--R +--------+
+--R +-+3| 3
+--R \|3 \|b x + a
+--R /
+--R +--+
+--R +-+3+-+2 3| 2
+--R 9b\|3 \|b \|b
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 712
+
+)clear all
+
+--S 713 of 1309
+t0:=x/(a+b*x^3)^(2/3)
+--R
+--R
+--R x
+--R (1) ------------
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 713
+
+--S 714 of 1309
+r0:=-1/3*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(2/3)+_
+ 1/6*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/b^(2/3)-atan((1+2*b^(1/3)*_
+ x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +--------+2 +--------+
+--R 3| 3 3+-+3| 3 2 3+-+2
+--R +-+ \|b x + a + x\|b \|b x + a + x \|b
+--R \|3 log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+ +--------+
+--R 3| 3 3+-+ 3| 3 3+-+
+--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b
+--R - 2\|3 log(-------------------) - 6atan(--------------------)
+--R +--------+ +--------+
+--R 3| 3 +-+3| 3
+--R \|b x + a \|3 \|b x + a
+--R /
+--R +-+3+-+2
+--R 6\|3 \|b
+--R Type: Expression(Integer)
+--E 714
+
+--S 715 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+2 +--------+2 +----+ +--------+
+--R 3| 2 3| 3 3| 2 3| 3 2 2
+--R +-+ \|- b \|b x + a - b x\|- b \|b x + a + b x
+--R - \|3 log(---------------------------------------------------)
+--R 2
+--R x
+--R +
+--R +----+ +--------+
+--R 3| 2 3| 3
+--R +-+ \|- b \|b x + a + b x
+--R 2\|3 log(------------------------)
+--R x
+--R +
+--R +----+ +--------+
+--R +-+3| 2 3| 3 +-+
+--R 2\|3 \|- b \|b x + a - b x\|3
+--R 6atan(---------------------------------)
+--R 3b x
+--R /
+--R +----+
+--R +-+3| 2
+--R 6\|3 \|- b
+--R Type: Union(Expression(Integer),...)
+--E 715
+
+--S 716 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----+2 +--------+2 +----+ +--------+
+--R 3| 2 3| 3 3| 2 3| 3 2 2
+--R +-+3+-+2 \|- b \|b x + a - b x\|- b \|b x + a + b x
+--R - \|3 \|b log(---------------------------------------------------)
+--R 2
+--R x
+--R +
+--R +----+ +--------+
+--R 3| 2 3| 3
+--R +-+3+-+2 \|- b \|b x + a + b x
+--R 2\|3 \|b log(------------------------)
+--R x
+--R +
+--R +--------+2 +--------+
+--R +----+ 3| 3 3+-+3| 3 2 3+-+2
+--R +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b
+--R - \|3 \|- b log(-----------------------------------------)
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R +
+--R +--------+
+--R +----+ 3| 3 3+-+
+--R +-+3| 2 \|b x + a - x\|b
+--R 2\|3 \|- b log(-------------------)
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R +
+--R +----+ +--------+
+--R +-+3| 2 3| 3 +-+
+--R 3+-+2 2\|3 \|- b \|b x + a - b x\|3
+--R 6\|b atan(---------------------------------)
+--R 3b x
+--R +
+--R +--------+
+--R +----+ 3| 3 3+-+
+--R 3| 2 \|b x + a + 2x\|b
+--R 6\|- b atan(--------------------)
+--R +--------+
+--R +-+3| 3
+--R \|3 \|b x + a
+--R /
+--R +----+
+--R +-+3| 2 3+-+2
+--R 6\|3 \|- b \|b
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 717
+
+)clear all
+
+--S 718 of 1309
+t0:=1/(x^2*(a+b*x^3)^(2/3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+2
+--R 2 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 1309
+r0:=-(a+b*x^3)^(1/3)/(a*x)
+--R
+--R
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R (2) - -----------
+--R a x
+--R Type: Expression(Integer)
+--E 719
+
+--S 720 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3| 3
+--R \|b x + a
+--R (3) - -----------
+--R a x
+--R Type: Union(Expression(Integer),...)
+--E 720
+
+--S 721 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 721
+
+--S 722 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 722
+
+)clear all
+
+--S 723 of 1309
+t0:=1/(x^5*(a+b*x^3)^(2/3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+2
+--R 5 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 1309
+r0:=-1/4*(a+b*x^3)^(1/3)/(a*x^4)+3/4*b*(a+b*x^3)^(1/3)/(a^2*x)
+--R
+--R
+--R +--------+
+--R 3 3| 3
+--R (3b x - a)\|b x + a
+--R (2) ----------------------
+--R 2 4
+--R 4a x
+--R Type: Expression(Integer)
+--E 724
+
+--S 725 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 3| 3
+--R (3b x - a)\|b x + a
+--R (3) ----------------------
+--R 2 4
+--R 4a x
+--R Type: Union(Expression(Integer),...)
+--E 725
+
+--S 726 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 727
+
+)clear all
+
+--S 728 of 1309
+t0:=1/(x^8*(a+b*x^3)^(2/3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+2
+--R 8 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 1309
+r0:=-1/7*(a+b*x^3)^(1/3)/(a*x^7)+3/14*b*(a+b*x^3)^(1/3)/(a^2*x^4)-_
+ 9/14*b^2*(a+b*x^3)^(1/3)/(a^3*x)
+--R
+--R
+--R +--------+
+--R 2 6 3 2 3| 3
+--R (- 9b x + 3a b x - 2a )\|b x + a
+--R (2) ------------------------------------
+--R 3 7
+--R 14a x
+--R Type: Expression(Integer)
+--E 729
+
+--S 730 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 6 3 2 3| 3
+--R (- 9b x + 3a b x - 2a )\|b x + a
+--R (3) ------------------------------------
+--R 3 7
+--R 14a x
+--R Type: Union(Expression(Integer),...)
+--E 730
+
+--S 731 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 732
+
+)clear all
+
+--S 733 of 1309
+t0:=1/(x^11*(a+b*x^3)^(2/3))
+--R
+--R
+--R 1
+--R (1) ---------------
+--R +--------+2
+--R 11 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 1309
+r0:=-1/10*(a+b*x^3)^(1/3)/(a*x^10)+9/70*b*(a+b*x^3)^(1/3)/(a^2*x^7)-_
+ 27/140*b^2*(a+b*x^3)^(1/3)/(a^3*x^4)+81/140*b^3*(a+b*x^3)^(1/3)/(a^4*x)
+--R
+--R
+--R +--------+
+--R 3 9 2 6 2 3 3 3| 3
+--R (81b x - 27a b x + 18a b x - 14a )\|b x + a
+--R (2) ------------------------------------------------
+--R 4 10
+--R 140a x
+--R Type: Expression(Integer)
+--E 734
+
+--S 735 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 9 2 6 2 3 3 3| 3
+--R (81b x - 27a b x + 18a b x - 14a )\|b x + a
+--R (3) ------------------------------------------------
+--R 4 10
+--R 140a x
+--R Type: Union(Expression(Integer),...)
+--E 735
+
+--S 736 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 736
+
+--S 737 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 737
+
+)clear all
+
+--S 738 of 1309
+t0:=x^6/(a+b*x^3)^(2/3)
+--R
+--R
+--R 6
+--R x
+--R (1) ------------
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 1309
+--r0:=-2/5*a*x*(a+b*x^3)^(1/3)/b^2+1/5*x^4*(a+b*x^3)^(1/3)/b+_
+-- 2/5*a^2*x*((a+b*x^3)/a)^(2/3)*_
+-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(b^2*(a+b*x^3)^(2/3))
+--E 739
+
+--S 740 of 1309
+--a0:=integrate(t0,x)
+--E 740
+
+--S 741 of 1309
+--m0:=a0-r0
+--E 741
+
+--S 742 of 1309
+--d0:=D(m0,x)
+--E 742
+
+)clear all
+
+--S 743 of 1309
+t0:=x^3/(a+b*x^3)^(2/3)
+--R
+--R
+--R 3
+--R x
+--R (1) ------------
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1309
+--r0:=1/2*x*(a+b*x^3)^(1/3)/b-1/2*a*x*((a+b*x^3)/a)^(2/3)*_
+-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(b*(a+b*x^3)^(2/3))
+--E 744
+
+--S 745 of 1309
+--a0:=integrate(t0,x)
+--E 745
+
+--S 746 of 1309
+--m0:=a0-r0
+--E 746
+
+--S 747 of 1309
+--d0:=D(m0,x)
+--E 747
+
+)clear all
+
+--S 748 of 1309
+t0:=1/(a+b*x^3)^(2/3)
+--R
+--R
+--R 1
+--R (1) ------------
+--R +--------+2
+--R 3| 3
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 748
+
+--S 749 of 1309
+--r0:=x*((a+b*x^3)/a)^(2/3)*_
+--hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a+b*x^3)^(2/3)
+--E 749
+
+--S 750 of 1309
+--a0:=integrate(t0,x)
+--E 750
+
+--S 751 of 1309
+--m0:=a0-r0
+--E 751
+
+--S 752 of 1309
+--d0:=D(m0,x)
+--E 752
+
+)clear all
+
+--S 753 of 1309
+t0:=1/(x^3*(a+b*x^3)^(2/3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+2
+--R 3 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 753
+
+--S 754 of 1309
+--r0:=-1/2*(a+b*x^3)^(1/3)/(a*x^2)-1/2*b*x*((a+b*x^3)/a)^(2/3)*_
+-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a*(a+b*x^3)^(2/3))
+--E 754
+
+--S 755 of 1309
+--a0:=integrate(t0,x)
+--E 755
+
+--S 756 of 1309
+--m0:=a0-r0
+--E 756
+
+--S 757 of 1309
+--d0:=D(m0,x)
+--E 757
+
+)clear all
+
+--S 758 of 1309
+t0:=1/(x^6*(a+b*x^3)^(2/3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+2
+--R 6 3| 3
+--R x \|b x + a
+--R Type: Expression(Integer)
+--E 758
+
+--S 759 of 1309
+--r0:=-1/5*(a+b*x^3)^(1/3)/(a*x^5)+2/5*b*(a+b*x^3)^(1/3)/(a^2*x^2)+_
+-- 2/5*b^2*x*((a+b*x^3)/a)^(2/3)*_
+-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a^2*(a+b*x^3)^(2/3))
+--E 759
+
+--S 760 of 1309
+--a0:=integrate(t0,x)
+--E 760
+
+--S 761 of 1309
+--m0:=a0-r0
+--E 761
+
+--S 762 of 1309
+--d0:=D(m0,x)
+--E 762
+
+)clear all
+
+--S 763 of 1309
+t0:=x^2/(2+x^3)^(1/4)
+--R
+--R
+--R 2
+--R x
+--R (1) ---------
+--R +------+
+--R 4| 3
+--R \|x + 2
+--R Type: Expression(Integer)
+--E 763
+
+--S 764 of 1309
+r0:=4/9*(2+x^3)^(3/4)
+--R
+--R
+--R +------+3
+--R 4| 3
+--R 4\|x + 2
+--R (2) -----------
+--R 9
+--R Type: Expression(Integer)
+--E 764
+
+--S 765 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+3
+--R 4| 3
+--R 4\|x + 2
+--R (3) -----------
+--R 9
+--R Type: Union(Expression(Integer),...)
+--E 765
+
+--S 766 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 766
+
+--S 767 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 767
+
+)clear all
+
+--S 768 of 1309
+t0:=sqrt(x)/(1+x^3)
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ------
+--R 3
+--R x + 1
+--R Type: Expression(Integer)
+--E 768
+
+--S 769 of 1309
+r0:=2/3*atan(x^(3/2))
+--R
+--R
+--R +-+
+--R 2atan(x\|x )
+--R (2) ------------
+--R 3
+--R Type: Expression(Integer)
+--E 769
+
+--S 770 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R 2atan(x\|x )
+--R (3) ------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 770
+
+--S 771 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 771
+
+--S 772 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 772
+
+)clear all
+
+--S 773 of 1309
+t0:=x^2*(a+b*x^3)^p
+--R
+--R
+--R 2 3 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 773
+
+--S 774 of 1309
+r0:=1/3*(a+b*x^3)^(1+p)/(b*(1+p))
+--R
+--R
+--R 3 p + 1
+--R (b x + a)
+--R (2) ---------------
+--R 3b p + 3b
+--R Type: Expression(Integer)
+--E 774
+
+--S 775 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R 3 p log(b x + a)
+--R (b x + a)%e
+--R (3) ---------------------------
+--R 3b p + 3b
+--R Type: Union(Expression(Integer),...)
+--E 775
+
+--S 776 of 1309
+m0:=a0-r0
+--R
+--R
+--R 3
+--R 3 p log(b x + a) 3 p + 1
+--R (b x + a)%e - (b x + a)
+--R (4) ---------------------------------------------
+--R 3b p + 3b
+--R Type: Expression(Integer)
+--E 776
+
+--S 777 of 1309
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 777
+
+)clear all
+
+--S 778 of 1309
+t0:=x^5*(a+b*x^3)^p
+--R
+--R
+--R 5 3 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 778
+
+--S 779 of 1309
+r0:=-1/3*a*(a+b*x^3)^(1+p)/(b^2*(1+p))+1/3*(a+b*x^3)^(2+p)/(b^2*(2+p))
+--R
+--R
+--R 3 p + 2 3 p + 1
+--R (p + 1)(b x + a) + (- a p - 2a)(b x + a)
+--R (2) ----------------------------------------------------
+--R 2 2 2 2
+--R 3b p + 9b p + 6b
+--R Type: Expression(Integer)
+--E 779
+
+--S 780 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R 2 2 6 3 2 p log(b x + a)
+--R ((b p + b )x + a b p x - a )%e
+--R (3) -----------------------------------------------
+--R 2 2 2 2
+--R 3b p + 9b p + 6b
+--R Type: Union(Expression(Integer),...)
+--E 780
+
+--S 781 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3
+--R 2 2 6 3 2 p log(b x + a)
+--R ((b p + b )x + a b p x - a )%e
+--R +
+--R 3 p + 2 3 p + 1
+--R (- p - 1)(b x + a) + (a p + 2a)(b x + a)
+--R /
+--R 2 2 2 2
+--R 3b p + 9b p + 6b
+--R Type: Expression(Integer)
+--E 781
+
+--S 782 of 1309
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 782
+
+)clear all
+
+--S 783 of 1309
+t0:=x^8*(a+b*x^3)^p
+--R
+--R
+--R 8 3 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 783
+
+--S 784 of 1309
+r0:=1/3*a^2*(a+b*x^3)^(1+p)/(b^3*(1+p))-_
+ 2/3*a*(a+b*x^3)^(2+p)/(b^3*(2+p))+1/3*(a+b*x^3)^(3+p)/(b^3*(3+p))
+--R
+--R
+--R (2)
+--R 2 3 p + 3 2 3 p + 2
+--R (p + 3p + 2)(b x + a) + (- 2a p - 8a p - 6a)(b x + a)
+--R +
+--R 2 2 2 2 3 p + 1
+--R (a p + 5a p + 6a )(b x + a)
+--R /
+--R 3 3 3 2 3 3
+--R 3b p + 18b p + 33b p + 18b
+--R Type: Expression(Integer)
+--E 784
+
+--S 785 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 3 3 9 2 2 2 6 2 3 3
+--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a )
+--R *
+--R 3
+--R p log(b x + a)
+--R %e
+--R /
+--R 3 3 3 2 3 3
+--R 3b p + 18b p + 33b p + 18b
+--R Type: Union(Expression(Integer),...)
+--E 785
+
+--S 786 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 2 3 3 9 2 2 2 6 2 3 3
+--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a )
+--R *
+--R 3
+--R p log(b x + a)
+--R %e
+--R +
+--R 2 3 p + 3 2 3 p + 2
+--R (- p - 3p - 2)(b x + a) + (2a p + 8a p + 6a)(b x + a)
+--R +
+--R 2 2 2 2 3 p + 1
+--R (- a p - 5a p - 6a )(b x + a)
+--R /
+--R 3 3 3 2 3 3
+--R 3b p + 18b p + 33b p + 18b
+--R Type: Expression(Integer)
+--E 786
+
+--S 787 of 1309
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 787
+
+)clear all
+
+--S 788 of 1309
+t0:=x^11*(a+b*x^3)^p
+--R
+--R
+--R 11 3 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 788
+
+--S 789 of 1309
+r0:=-1/3*a^3*(a+b*x^3)^(1+p)/(b^4*(1+p))+a^2*(a+b*x^3)^(2+p)/(b^4*(2+p))-_
+ a*(a+b*x^3)^(3+p)/(b^4*(3+p))+1/3*(a+b*x^3)^(4+p)/(b^4*(4+p))
+--R
+--R
+--R (2)
+--R 3 2 3 p + 4
+--R (p + 6p + 11p + 6)(b x + a)
+--R +
+--R 3 2 3 p + 3
+--R (- 3a p - 21a p - 42a p - 24a)(b x + a)
+--R +
+--R 2 3 2 2 2 2 3 p + 2
+--R (3a p + 24a p + 57a p + 36a )(b x + a)
+--R +
+--R 3 3 3 2 3 3 3 p + 1
+--R (- a p - 9a p - 26a p - 24a )(b x + a)
+--R /
+--R 4 4 4 3 4 2 4 4
+--R 3b p + 30b p + 105b p + 150b p + 72b
+--R Type: Expression(Integer)
+--E 789
+
+--S 790 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 3 4 2 4 4 12 3 3 3 2 3 9
+--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x
+--R +
+--R 2 2 2 2 2 6 3 3 4
+--R (- 3a b p - 3a b p)x + 6a b p x - 6a
+--R *
+--R 3
+--R p log(b x + a)
+--R %e
+--R /
+--R 4 4 4 3 4 2 4 4
+--R 3b p + 30b p + 105b p + 150b p + 72b
+--R Type: Union(Expression(Integer),...)
+--E 790
+
+--S 791 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 3 4 2 4 4 12 3 3 3 2 3 9
+--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x
+--R +
+--R 2 2 2 2 2 6 3 3 4
+--R (- 3a b p - 3a b p)x + 6a b p x - 6a
+--R *
+--R 3
+--R p log(b x + a)
+--R %e
+--R +
+--R 3 2 3 p + 4
+--R (- p - 6p - 11p - 6)(b x + a)
+--R +
+--R 3 2 3 p + 3
+--R (3a p + 21a p + 42a p + 24a)(b x + a)
+--R +
+--R 2 3 2 2 2 2 3 p + 2
+--R (- 3a p - 24a p - 57a p - 36a )(b x + a)
+--R +
+--R 3 3 3 2 3 3 3 p + 1
+--R (a p + 9a p + 26a p + 24a )(b x + a)
+--R /
+--R 4 4 4 3 4 2 4 4
+--R 3b p + 30b p + 105b p + 150b p + 72b
+--R Type: Expression(Integer)
+--E 791
+
+--S 792 of 1309
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 792
+
+)clear all
+
+--S 793 of 1309
+t0:=x^m*(a+b*x^4)
+--R
+--R
+--R 4 m
+--R (1) (b x + a)x
+--R Type: Expression(Integer)
+--E 793
+
+--S 794 of 1309
+r0:=a*x^(1+m)/(1+m)+b*x^(5+m)/(5+m)
+--R
+--R
+--R m + 5 m + 1
+--R (b m + b)x + (a m + 5a)x
+--R (2) ----------------------------------
+--R 2
+--R m + 6m + 5
+--R Type: Expression(Integer)
+--E 794
+
+--S 795 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 m log(x)
+--R ((b m + b)x + (a m + 5a)x)%e
+--R (3) -------------------------------------
+--R 2
+--R m + 6m + 5
+--R Type: Union(Expression(Integer),...)
+--E 795
+
+--S 796 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 m log(x) m + 5
+--R ((b m + b)x + (a m + 5a)x)%e + (- b m - b)x
+--R +
+--R m + 1
+--R (- a m - 5a)x
+--R /
+--R 2
+--R m + 6m + 5
+--R Type: Expression(Integer)
+--E 796
+
+--S 797 of 1309
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 797
+
+)clear all
+
+--S 798 of 1309
+t0:=x^5*(a+b*x^4)
+--R
+--R
+--R 9 5
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 798
+
+--S 799 of 1309
+r0:=1/6*a*x^6+1/10*b*x^10
+--R
+--R
+--R 1 10 1 6
+--R (2) -- b x + - a x
+--R 10 6
+--R Type: Polynomial(Fraction(Integer))
+--E 799
+
+--S 800 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 10 1 6
+--R (3) -- b x + - a x
+--R 10 6
+--R Type: Polynomial(Fraction(Integer))
+--E 800
+
+--S 801 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 801
+
+--S 802 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 802
+
+)clear all
+
+--S 803 of 1309
+t0:=x^4*(a+b*x^4)
+--R
+--R
+--R 8 4
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 803
+
+--S 804 of 1309
+r0:=1/5*a*x^5+1/9*b*x^9
+--R
+--R
+--R 1 9 1 5
+--R (2) - b x + - a x
+--R 9 5
+--R Type: Polynomial(Fraction(Integer))
+--E 804
+
+--S 805 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 9 1 5
+--R (3) - b x + - a x
+--R 9 5
+--R Type: Polynomial(Fraction(Integer))
+--E 805
+
+--S 806 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 806
+
+--S 807 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 807
+
+)clear all
+
+--S 808 of 1309
+t0:=x^3*(a+b*x^4)
+--R
+--R
+--R 7 3
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 808
+
+--S 809 of 1309
+r0:=1/4*a*x^4+1/8*b*x^8
+--R
+--R
+--R 1 8 1 4
+--R (2) - b x + - a x
+--R 8 4
+--R Type: Polynomial(Fraction(Integer))
+--E 809
+
+--S 810 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 8 1 4
+--R (3) - b x + - a x
+--R 8 4
+--R Type: Polynomial(Fraction(Integer))
+--E 810
+
+--S 811 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 811
+
+--S 812 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 812
+
+)clear all
+
+--S 813 of 1309
+t0:=x^2*(a+b*x^4)
+--R
+--R
+--R 6 2
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 813
+
+--S 814 of 1309
+r0:=1/3*a*x^3+1/7*b*x^7
+--R
+--R
+--R 1 7 1 3
+--R (2) - b x + - a x
+--R 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 814
+
+--S 815 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 7 1 3
+--R (3) - b x + - a x
+--R 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 815
+
+--S 816 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 816
+
+--S 817 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 817
+
+)clear all
+
+--S 818 of 1309
+t0:=x*(a+b*x^4)
+--R
+--R
+--R 5
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 818
+
+--S 819 of 1309
+r0:=1/2*a*x^2+1/6*b*x^6
+--R
+--R
+--R 1 6 1 2
+--R (2) - b x + - a x
+--R 6 2
+--R Type: Polynomial(Fraction(Integer))
+--E 819
+
+--S 820 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 6 1 2
+--R (3) - b x + - a x
+--R 6 2
+--R Type: Polynomial(Fraction(Integer))
+--E 820
+
+--S 821 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 821
+
+--S 822 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 822
+
+)clear all
+
+--S 823 of 1309
+t0:=a+b*x^4
+--R
+--R
+--R 4
+--R (1) b x + a
+--R Type: Polynomial(Integer)
+--E 823
+
+--S 824 of 1309
+r0:=a*x+1/5*b*x^5
+--R
+--R
+--R 1 5
+--R (2) - b x + a x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 824
+
+--S 825 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5
+--R (3) - b x + a x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 825
+
+--S 826 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 826
+
+--S 827 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 827
+
+)clear all
+
+--S 828 of 1309
+t0:=(a+b*x^4)/x
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 828
+
+--S 829 of 1309
+r0:=1/4*b*x^4+a*log(x)
+--R
+--R
+--R 4
+--R 4a log(x) + b x
+--R (2) ----------------
+--R 4
+--R Type: Expression(Integer)
+--E 829
+
+--S 830 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R 4a log(x) + b x
+--R (3) ----------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 830
+
+--S 831 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 831
+
+--S 832 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 832
+
+)clear all
+
+--S 833 of 1309
+t0:=(a+b*x^4)/x^2
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 833
+
+--S 834 of 1309
+r0:=-a/x+1/3*b*x^3
+--R
+--R
+--R 4
+--R b x - 3a
+--R (2) ---------
+--R 3x
+--R Type: Fraction(Polynomial(Integer))
+--E 834
+
+--S 835 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R b x - 3a
+--R (3) ---------
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 835
+
+--S 836 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 836
+
+--S 837 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 837
+
+)clear all
+
+--S 838 of 1309
+t0:=(a+b*x^4)/x^3
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 838
+
+--S 839 of 1309
+r0:=-1/2*a/x^2+1/2*b*x^2
+--R
+--R
+--R 1 4 1
+--R - b x - - a
+--R 2 2
+--R (2) ------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 839
+
+--S 840 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R b x - a
+--R (3) --------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 840
+
+--S 841 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 842
+
+)clear all
+
+--S 843 of 1309
+t0:=(a+b*x^4)/x^4
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 843
+
+--S 844 of 1309
+r0:=-1/3*a/x^3+b*x
+--R
+--R
+--R 4 1
+--R b x - - a
+--R 3
+--R (2) ----------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 844
+
+--S 845 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R 3b x - a
+--R (3) ---------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 845
+
+--S 846 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 847
+
+)clear all
+
+--S 848 of 1309
+t0:=(a+b*x^4)/x^5
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 848
+
+--S 849 of 1309
+r0:=-1/4*a/x^4+b*log(x)
+--R
+--R
+--R 4
+--R 4b x log(x) - a
+--R (2) ---------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R 4b x log(x) - a
+--R (3) ---------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 850
+
+--S 851 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 851
+
+--S 852 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 852
+
+)clear all
+
+--S 853 of 1309
+t0:=(a+b*x^4)/x^6
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 853
+
+--S 854 of 1309
+r0:=-1/5*a/x^5-b/x
+--R
+--R
+--R 4 1
+--R - b x - - a
+--R 5
+--R (2) ------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 854
+
+--S 855 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R - 5b x - a
+--R (3) -----------
+--R 5
+--R 5x
+--R Type: Union(Expression(Integer),...)
+--E 855
+
+--S 856 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 856
+
+--S 857 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 857
+
+)clear all
+
+--S 858 of 1309
+t0:=(a+b*x^4)/x^7
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 858
+
+--S 859 of 1309
+r0:=-1/6*a/x^6-1/2*b/x^2
+--R
+--R
+--R 1 4 1
+--R - - b x - - a
+--R 2 6
+--R (2) --------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 859
+
+--S 860 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R - 3b x - a
+--R (3) -----------
+--R 6
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 860
+
+--S 861 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 861
+
+--S 862 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 862
+
+)clear all
+
+--S 863 of 1309
+t0:=(a+b*x^4)/x^8
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 863
+
+--S 864 of 1309
+r0:=-1/7*a/x^7-1/3*b/x^3
+--R
+--R
+--R 1 4 1
+--R - - b x - - a
+--R 3 7
+--R (2) --------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 864
+
+--S 865 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R - 7b x - 3a
+--R (3) ------------
+--R 7
+--R 21x
+--R Type: Union(Expression(Integer),...)
+--E 865
+
+--S 866 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 866
+
+--S 867 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 867
+
+)clear all
+
+--S 868 of 1309
+t0:=(a+b*x^4)/x^9
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 868
+
+--S 869 of 1309
+r0:=-1/8*a/x^8-1/4*b/x^4
+--R
+--R
+--R 1 4 1
+--R - - b x - - a
+--R 4 8
+--R (2) --------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 869
+
+--S 870 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R - 2b x - a
+--R (3) -----------
+--R 8
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 870
+
+--S 871 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 872
+
+)clear all
+
+--S 873 of 1309
+t0:=(a+b*x^4)/x^10
+--R
+--R
+--R 4
+--R b x + a
+--R (1) --------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 873
+
+--S 874 of 1309
+r0:=-1/9*a/x^9-1/5*b/x^5
+--R
+--R
+--R 1 4 1
+--R - - b x - - a
+--R 5 9
+--R (2) --------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 874
+
+--S 875 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R - 9b x - 5a
+--R (3) ------------
+--R 9
+--R 45x
+--R Type: Union(Expression(Integer),...)
+--E 875
+
+--S 876 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 876
+
+--S 877 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 877
+
+)clear all
+
+--S 878 of 1309
+t0:=x^m*(a+b*x^4)^2
+--R
+--R
+--R 2 8 4 2 m
+--R (1) (b x + 2a b x + a )x
+--R Type: Expression(Integer)
+--E 878
+
+--S 879 of 1309
+r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(5+m)/(5+m)+b^2*x^(9+m)/(9+m)
+--R
+--R
+--R (2)
+--R 2 2 2 2 m + 9 2 m + 5
+--R (b m + 6b m + 5b )x + (2a b m + 20a b m + 18a b)x
+--R +
+--R 2 2 2 2 m + 1
+--R (a m + 14a m + 45a )x
+--R /
+--R 3 2
+--R m + 15m + 59m + 45
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 9 2 5
+--R (b m + 6b m + 5b )x + (2a b m + 20a b m + 18a b)x
+--R +
+--R 2 2 2 2
+--R (a m + 14a m + 45a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 3 2
+--R m + 15m + 59m + 45
+--R Type: Union(Expression(Integer),...)
+--E 880
+
+--S 881 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 9 2 5
+--R (b m + 6b m + 5b )x + (2a b m + 20a b m + 18a b)x
+--R +
+--R 2 2 2 2
+--R (a m + 14a m + 45a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 2 2 2 m + 9 2 m + 5
+--R (- b m - 6b m - 5b )x + (- 2a b m - 20a b m - 18a b)x
+--R +
+--R 2 2 2 2 m + 1
+--R (- a m - 14a m - 45a )x
+--R /
+--R 3 2
+--R m + 15m + 59m + 45
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1309
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 882
+
+)clear all
+
+--S 883 of 1309
+t0:=x^5*(a+b*x^4)^2
+--R
+--R
+--R 2 13 9 2 5
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 883
+
+--S 884 of 1309
+r0:=1/6*a^2*x^6+1/5*a*b*x^10+1/14*b^2*x^14
+--R
+--R
+--R 1 2 14 1 10 1 2 6
+--R (2) -- b x + - a b x + - a x
+--R 14 5 6
+--R Type: Polynomial(Fraction(Integer))
+--E 884
+
+--S 885 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 14 1 10 1 2 6
+--R (3) -- b x + - a b x + - a x
+--R 14 5 6
+--R Type: Polynomial(Fraction(Integer))
+--E 885
+
+--S 886 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 886
+
+--S 887 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 887
+
+)clear all
+
+--S 888 of 1309
+t0:=x^4*(a+b*x^4)^2
+--R
+--R
+--R 2 12 8 2 4
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 888
+
+--S 889 of 1309
+r0:=1/5*a^2*x^5+2/9*a*b*x^9+1/13*b^2*x^13
+--R
+--R
+--R 1 2 13 2 9 1 2 5
+--R (2) -- b x + - a b x + - a x
+--R 13 9 5
+--R Type: Polynomial(Fraction(Integer))
+--E 889
+
+--S 890 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 13 2 9 1 2 5
+--R (3) -- b x + - a b x + - a x
+--R 13 9 5
+--R Type: Polynomial(Fraction(Integer))
+--E 890
+
+--S 891 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 891
+
+--S 892 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 892
+
+)clear all
+
+--S 893 of 1309
+t0:=x^3*(a+b*x^4)^2
+--R
+--R
+--R 2 11 7 2 3
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 893
+
+--S 894 of 1309
+r0:=1/12*(a+b*x^4)^3/b
+--R
+--R
+--R 1 3 12 1 2 8 1 2 4 1 3
+--R -- b x + - a b x + - a b x + -- a
+--R 12 4 4 12
+--R (2) --------------------------------------
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 894
+
+--S 895 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 12 1 8 1 2 4
+--R (3) -- b x + - a b x + - a x
+--R 12 4 4
+--R Type: Polynomial(Fraction(Integer))
+--E 895
+
+--S 896 of 1309
+m0:=a0-r0
+--R
+--R
+--R 1 3
+--R -- a
+--R 12
+--R (4) - -----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 896
+
+--S 897 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 897
+
+)clear all
+
+--S 898 of 1309
+t0:=x^2*(a+b*x^4)^2
+--R
+--R
+--R 2 10 6 2 2
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 898
+
+--S 899 of 1309
+r0:=1/3*a^2*x^3+2/7*a*b*x^7+1/11*b^2*x^11
+--R
+--R
+--R 1 2 11 2 7 1 2 3
+--R (2) -- b x + - a b x + - a x
+--R 11 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 899
+
+--S 900 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 11 2 7 1 2 3
+--R (3) -- b x + - a b x + - a x
+--R 11 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 900
+
+--S 901 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 901
+
+--S 902 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 902
+
+)clear all
+
+--S 903 of 1309
+t0:=x*(a+b*x^4)^2
+--R
+--R
+--R 2 9 5 2
+--R (1) b x + 2a b x + a x
+--R Type: Polynomial(Integer)
+--E 903
+
+--S 904 of 1309
+r0:=1/2*a^2*x^2+1/3*a*b*x^6+1/10*b^2*x^10
+--R
+--R
+--R 1 2 10 1 6 1 2 2
+--R (2) -- b x + - a b x + - a x
+--R 10 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 904
+
+--S 905 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 10 1 6 1 2 2
+--R (3) -- b x + - a b x + - a x
+--R 10 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 905
+
+--S 906 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 906
+
+--S 907 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 907
+
+)clear all
+
+--S 908 of 1309
+t0:=(a+b*x^4)^2
+--R
+--R
+--R 2 8 4 2
+--R (1) b x + 2a b x + a
+--R Type: Polynomial(Integer)
+--E 908
+
+--S 909 of 1309
+r0:=a^2*x+2/5*a*b*x^5+1/9*b^2*x^9
+--R
+--R
+--R 1 2 9 2 5 2
+--R (2) - b x + - a b x + a x
+--R 9 5
+--R Type: Polynomial(Fraction(Integer))
+--E 909
+
+--S 910 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 9 2 5 2
+--R (3) - b x + - a b x + a x
+--R 9 5
+--R Type: Polynomial(Fraction(Integer))
+--E 910
+
+--S 911 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 911
+
+--S 912 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 912
+
+)clear all
+
+--S 913 of 1309
+t0:=(a+b*x^4)^2/x
+--R
+--R
+--R 2 8 4 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 913
+
+--S 914 of 1309
+r0:=1/2*a*b*x^4+1/8*b^2*x^8+a^2*log(x)
+--R
+--R
+--R 2 2 8 4
+--R 8a log(x) + b x + 4a b x
+--R (2) --------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 8 4
+--R 8a log(x) + b x + 4a b x
+--R (3) --------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 915
+
+--S 916 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 916
+
+--S 917 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 917
+
+)clear all
+
+--S 918 of 1309
+t0:=(a+b*x^4)^2/x^2
+--R
+--R
+--R 2 8 4 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 918
+
+--S 919 of 1309
+r0:=-a^2/x+2/3*a*b*x^3+1/7*b^2*x^7
+--R
+--R
+--R 2 8 4 2
+--R 3b x + 14a b x - 21a
+--R (2) -----------------------
+--R 21x
+--R Type: Fraction(Polynomial(Integer))
+--E 919
+
+--S 920 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 4 2
+--R 3b x + 14a b x - 21a
+--R (3) -----------------------
+--R 21x
+--R Type: Union(Expression(Integer),...)
+--E 920
+
+--S 921 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 921
+
+--S 922 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 922
+
+)clear all
+
+--S 923 of 1309
+t0:=(a+b*x^4)^2/x^3
+--R
+--R
+--R 2 8 4 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 923
+
+--S 924 of 1309
+r0:=-1/2*a^2/x^2+a*b*x^2+1/6*b^2*x^6
+--R
+--R
+--R 1 2 8 4 1 2
+--R - b x + a b x - - a
+--R 6 2
+--R (2) ----------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 924
+
+--S 925 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 4 2
+--R b x + 6a b x - 3a
+--R (3) --------------------
+--R 2
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 925
+
+--S 926 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 927
+
+)clear all
+
+--S 928 of 1309
+t0:=(a+b*x^4)^2/x^4
+--R
+--R
+--R 2 8 4 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 928
+
+--S 929 of 1309
+r0:=-1/3*a^2/x^3+2*a*b*x+1/5*b^2*x^5
+--R
+--R
+--R 1 2 8 4 1 2
+--R - b x + 2a b x - - a
+--R 5 3
+--R (2) -----------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 929
+
+--S 930 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 4 2
+--R 3b x + 30a b x - 5a
+--R (3) ----------------------
+--R 3
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 930
+
+--S 931 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 932
+
+)clear all
+
+--S 933 of 1309
+t0:=(a+b*x^4)^2/x^5
+--R
+--R
+--R 2 8 4 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 933
+
+--S 934 of 1309
+r0:=-1/4*a^2/x^4+1/4*b^2*x^4+2*a*b*log(x)
+--R
+--R
+--R 4 2 8 2
+--R 8a b x log(x) + b x - a
+--R (2) -------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2 8 2
+--R 8a b x log(x) + b x - a
+--R (3) -------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 935
+
+--S 936 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 936
+
+--S 937 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 937
+
+)clear all
+
+--S 938 of 1309
+t0:=x^m*(a+b*x^4)^3
+--R
+--R
+--R 3 12 2 8 2 4 3 m
+--R (1) (b x + 3a b x + 3a b x + a )x
+--R Type: Expression(Integer)
+--E 938
+
+--S 939 of 1309
+r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(5+m)/(5+m)+3*a*b^2*x^(9+m)/(9+m)+_
+ b^3*x^(13+m)/(13+m)
+--R
+--R
+--R (2)
+--R 3 3 3 2 3 3 m + 13
+--R (b m + 15b m + 59b m + 45b )x
+--R +
+--R 2 3 2 2 2 2 m + 9
+--R (3a b m + 57a b m + 249a b m + 195a b )x
+--R +
+--R 2 3 2 2 2 2 m + 5
+--R (3a b m + 69a b m + 417a b m + 351a b)x
+--R +
+--R 3 3 3 2 3 3 m + 1
+--R (a m + 27a m + 227a m + 585a )x
+--R /
+--R 4 3 2
+--R m + 28m + 254m + 812m + 585
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 3 2 3 3 13
+--R (b m + 15b m + 59b m + 45b )x
+--R +
+--R 2 3 2 2 2 2 9
+--R (3a b m + 57a b m + 249a b m + 195a b )x
+--R +
+--R 2 3 2 2 2 2 5
+--R (3a b m + 69a b m + 417a b m + 351a b)x
+--R +
+--R 3 3 3 2 3 3
+--R (a m + 27a m + 227a m + 585a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 4 3 2
+--R m + 28m + 254m + 812m + 585
+--R Type: Union(Expression(Integer),...)
+--E 940
+
+--S 941 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 3 2 3 3 13
+--R (b m + 15b m + 59b m + 45b )x
+--R +
+--R 2 3 2 2 2 2 9
+--R (3a b m + 57a b m + 249a b m + 195a b )x
+--R +
+--R 2 3 2 2 2 2 5
+--R (3a b m + 69a b m + 417a b m + 351a b)x
+--R +
+--R 3 3 3 2 3 3
+--R (a m + 27a m + 227a m + 585a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 3 3 3 2 3 3 m + 13
+--R (- b m - 15b m - 59b m - 45b )x
+--R +
+--R 2 3 2 2 2 2 m + 9
+--R (- 3a b m - 57a b m - 249a b m - 195a b )x
+--R +
+--R 2 3 2 2 2 2 m + 5
+--R (- 3a b m - 69a b m - 417a b m - 351a b)x
+--R +
+--R 3 3 3 2 3 3 m + 1
+--R (- a m - 27a m - 227a m - 585a )x
+--R /
+--R 4 3 2
+--R m + 28m + 254m + 812m + 585
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 1309
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 942
+
+)clear all
+
+--S 943 of 1309
+t0:=x^5*(a+b*x^4)^3
+--R
+--R
+--R 3 17 2 13 2 9 3 5
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 943
+
+--S 944 of 1309
+r0:=1/6*a^3*x^6+3/10*a^2*b*x^10+3/14*a*b^2*x^14+1/18*b^3*x^18
+--R
+--R
+--R 1 3 18 3 2 14 3 2 10 1 3 6
+--R (2) -- b x + -- a b x + -- a b x + - a x
+--R 18 14 10 6
+--R Type: Polynomial(Fraction(Integer))
+--E 944
+
+--S 945 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 18 3 2 14 3 2 10 1 3 6
+--R (3) -- b x + -- a b x + -- a b x + - a x
+--R 18 14 10 6
+--R Type: Polynomial(Fraction(Integer))
+--E 945
+
+--S 946 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 946
+
+--S 947 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 947
+
+)clear all
+
+--S 948 of 1309
+t0:=x^4*(a+b*x^4)^3
+--R
+--R
+--R 3 16 2 12 2 8 3 4
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 948
+
+--S 949 of 1309
+r0:=1/5*a^3*x^5+1/3*a^2*b*x^9+3/13*a*b^2*x^13+1/17*b^3*x^17
+--R
+--R
+--R 1 3 17 3 2 13 1 2 9 1 3 5
+--R (2) -- b x + -- a b x + - a b x + - a x
+--R 17 13 3 5
+--R Type: Polynomial(Fraction(Integer))
+--E 949
+
+--S 950 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 17 3 2 13 1 2 9 1 3 5
+--R (3) -- b x + -- a b x + - a b x + - a x
+--R 17 13 3 5
+--R Type: Polynomial(Fraction(Integer))
+--E 950
+
+--S 951 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 951
+
+--S 952 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 952
+
+)clear all
+
+--S 953 of 1309
+t0:=x^3*(a+b*x^4)^3
+--R
+--R
+--R 3 15 2 11 2 7 3 3
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 953
+
+--S 954 of 1309
+r0:=1/16*(a+b*x^4)^4/b
+--R
+--R
+--R 1 4 16 1 3 12 3 2 2 8 1 3 4 1 4
+--R -- b x + - a b x + - a b x + - a b x + -- a
+--R 16 4 8 4 16
+--R (2) --------------------------------------------------
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 954
+
+--S 955 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 16 1 2 12 3 2 8 1 3 4
+--R (3) -- b x + - a b x + - a b x + - a x
+--R 16 4 8 4
+--R Type: Polynomial(Fraction(Integer))
+--E 955
+
+--S 956 of 1309
+m0:=a0-r0
+--R
+--R
+--R 1 4
+--R -- a
+--R 16
+--R (4) - -----
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 956
+
+--S 957 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 957
+
+)clear all
+
+--S 958 of 1309
+t0:=x^2*(a+b*x^4)^3
+--R
+--R
+--R 3 14 2 10 2 6 3 2
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 958
+
+--S 959 of 1309
+r0:=1/3*a^3*x^3+3/7*a^2*b*x^7+3/11*a*b^2*x^11+1/15*b^3*x^15
+--R
+--R
+--R 1 3 15 3 2 11 3 2 7 1 3 3
+--R (2) -- b x + -- a b x + - a b x + - a x
+--R 15 11 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 959
+
+--S 960 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 15 3 2 11 3 2 7 1 3 3
+--R (3) -- b x + -- a b x + - a b x + - a x
+--R 15 11 7 3
+--R Type: Polynomial(Fraction(Integer))
+--E 960
+
+--S 961 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 961
+
+--S 962 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 962
+
+)clear all
+
+--S 963 of 1309
+t0:=x*(a+b*x^4)^3
+--R
+--R
+--R 3 13 2 9 2 5 3
+--R (1) b x + 3a b x + 3a b x + a x
+--R Type: Polynomial(Integer)
+--E 963
+
+--S 964 of 1309
+r0:=1/2*a^3*x^2+1/2*a^2*b*x^6+3/10*a*b^2*x^10+1/14*b^3*x^14
+--R
+--R
+--R 1 3 14 3 2 10 1 2 6 1 3 2
+--R (2) -- b x + -- a b x + - a b x + - a x
+--R 14 10 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 964
+
+--S 965 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 14 3 2 10 1 2 6 1 3 2
+--R (3) -- b x + -- a b x + - a b x + - a x
+--R 14 10 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 965
+
+--S 966 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 966
+
+--S 967 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 967
+
+)clear all
+
+--S 968 of 1309
+t0:=(a+b*x^4)^3
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R (1) b x + 3a b x + 3a b x + a
+--R Type: Polynomial(Integer)
+--E 968
+
+--S 969 of 1309
+r0:=a^3*x+3/5*a^2*b*x^5+1/3*a*b^2*x^9+1/13*b^3*x^13
+--R
+--R
+--R 1 3 13 1 2 9 3 2 5 3
+--R (2) -- b x + - a b x + - a b x + a x
+--R 13 3 5
+--R Type: Polynomial(Fraction(Integer))
+--E 969
+
+--S 970 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 3 13 1 2 9 3 2 5 3
+--R (3) -- b x + - a b x + - a b x + a x
+--R 13 3 5
+--R Type: Polynomial(Fraction(Integer))
+--E 970
+
+--S 971 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 971
+
+--S 972 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 972
+
+)clear all
+
+--S 973 of 1309
+t0:=(a+b*x^4)^3/x
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R b x + 3a b x + 3a b x + a
+--R (1) ------------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 973
+
+--S 974 of 1309
+r0:=3/4*a^2*b*x^4+3/8*a*b^2*x^8+1/12*b^3*x^12+a^3*log(x)
+--R
+--R
+--R 3 3 12 2 8 2 4
+--R 24a log(x) + 2b x + 9a b x + 18a b x
+--R (2) ----------------------------------------
+--R 24
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 12 2 8 2 4
+--R 24a log(x) + 2b x + 9a b x + 18a b x
+--R (3) ----------------------------------------
+--R 24
+--R Type: Union(Expression(Integer),...)
+--E 975
+
+--S 976 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 977
+
+)clear all
+
+--S 978 of 1309
+t0:=(a+b*x^4)^3/x^2
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R b x + 3a b x + 3a b x + a
+--R (1) ------------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 978
+
+--S 979 of 1309
+r0:=-a^3/x+a^2*b*x^3+3/7*a*b^2*x^7+1/11*b^3*x^11
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R 7b x + 33a b x + 77a b x - 77a
+--R (2) -----------------------------------
+--R 77x
+--R Type: Fraction(Polynomial(Integer))
+--E 979
+
+--S 980 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R 7b x + 33a b x + 77a b x - 77a
+--R (3) -----------------------------------
+--R 77x
+--R Type: Union(Expression(Integer),...)
+--E 980
+
+--S 981 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 982
+
+)clear all
+
+--S 983 of 1309
+t0:=(a+b*x^4)^3/x^3
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R b x + 3a b x + 3a b x + a
+--R (1) ------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 983
+
+--S 984 of 1309
+r0:=-1/2*a^3/x^2+3/2*a^2*b*x^2+1/2*a*b^2*x^6+1/10*b^3*x^10
+--R
+--R
+--R 1 3 12 1 2 8 3 2 4 1 3
+--R -- b x + - a b x + - a b x - - a
+--R 10 2 2 2
+--R (2) -------------------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 984
+
+--S 985 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R b x + 5a b x + 15a b x - 5a
+--R (3) --------------------------------
+--R 2
+--R 10x
+--R Type: Union(Expression(Integer),...)
+--E 985
+
+--S 986 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 987
+
+)clear all
+
+--S 988 of 1309
+t0:=(a+b*x^4)^3/x^4
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R b x + 3a b x + 3a b x + a
+--R (1) ------------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 988
+
+--S 989 of 1309
+r0:=-1/3*a^3/x^3+3*a^2*b*x+3/5*a*b^2*x^5+1/9*b^3*x^9
+--R
+--R
+--R 1 3 12 3 2 8 2 4 1 3
+--R - b x + - a b x + 3a b x - - a
+--R 9 5 3
+--R (2) -----------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 989
+
+--S 990 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R 5b x + 27a b x + 135a b x - 15a
+--R (3) ------------------------------------
+--R 3
+--R 45x
+--R Type: Union(Expression(Integer),...)
+--E 990
+
+--S 991 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 992
+
+)clear all
+
+--S 993 of 1309
+t0:=(a+b*x^4)^3/x^5
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R b x + 3a b x + 3a b x + a
+--R (1) ------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 993
+
+--S 994 of 1309
+r0:=-1/4*a^3/x^4+3/4*a*b^2*x^4+1/8*b^3*x^8+3*a^2*b*log(x)
+--R
+--R
+--R 2 4 3 12 2 8 3
+--R 24a b x log(x) + b x + 6a b x - 2a
+--R (2) --------------------------------------
+--R 4
+--R 8x
+--R Type: Expression(Integer)
+--E 994
+
+--S 995 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 3 12 2 8 3
+--R 24a b x log(x) + b x + 6a b x - 2a
+--R (3) --------------------------------------
+--R 4
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 995
+
+--S 996 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 996
+
+--S 997 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 997
+
+)clear all
+
+--S 998 of 1309
+t0:=x^5/(a+c*x^4)
+--R
+--R
+--R 5
+--R x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 998
+
+--S 999 of 1309
+r0:=1/2*x^2/c-1/2*atan(x^2*sqrt(c)/sqrt(a))*sqrt(a)/c^(3/2)
+--R
+--R
+--R 2 +-+
+--R +-+ x \|c 2 +-+
+--R - \|a atan(------) + x \|c
+--R +-+
+--R \|a
+--R (2) ---------------------------
+--R +-+
+--R 2c\|c
+--R Type: Expression(Integer)
+--E 999
+
+--S 1000 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+ +-+
+--R 2 | a 4 |a
+--R +---+ - 2c x |- - + c x - a +-+ |-
+--R | a \| c 2 |a \|c 2
+--R |- - log(------------------------) + 2x |- atan(----) + x
+--R \| c 4 \|c 2
+--R c x + a x
+--R (3) [-----------------------------------------,-------------------]
+--R 4c 2c
+--R Type: Union(List(Expression(Integer)),...)
+--E 1000
+
+--S 1001 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R 2 | a 4
+--R +---+ - 2c x |- - + c x - a 2 +-+
+--R | a +-+ \| c +-+ x \|c
+--R |- - \|c log(------------------------) + 2\|a atan(------)
+--R \| c 4 +-+
+--R c x + a \|a
+--R (4) -----------------------------------------------------------
+--R +-+
+--R 4c\|c
+--R Type: Expression(Integer)
+--E 1001
+
+--S 1002 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1002
+
+--S 1003 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R 2 +-+ +-+ |-
+--R +-+ x \|c |a +-+ \|c
+--R \|a atan(------) + |- \|c atan(----)
+--R +-+ \|c 2
+--R \|a x
+--R (6) -------------------------------------
+--R +-+
+--R 2c\|c
+--R Type: Expression(Integer)
+--E 1003
+
+--S 1004 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1004
+
+)clear all
+
+--S 1005 of 1309
+t0:=x^4/(a+c*x^4)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1005
+
+--S 1006 of 1309
+r0:=x/c+1/2*a^(1/4)*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(c^(5/4)*sqrt(2))-_
+ 1/2*a^(1/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(c^(5/4)*sqrt(2))+_
+ 1/4*a^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(c^(5/4)*sqrt(2))-1/4*a^(1/4)*log(a^(1/4)*c^(1/4)*_
+ x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(c^(5/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|a log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a
+--R \|a log(- x\|2 \|a \|c + x \|c + \|a ) - 2\|a atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+ x\|2 \|c - \|a +-+4+-+
+--R - 2\|a atan(----------------) + 4x\|2 \|c
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+
+--R 4c\|2 \|c
+--R Type: Expression(Integer)
+--E 1006
+
+--S 1007 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+ +-------+ +-------+
+--R | a | a | a | a
+--R - c |- ----- log(4c |- ----- + x + c |- ----- log(- 4c |- ----- + x)
+--R 4| 5 4| 5 4| 5 4| 5
+--R \| 256c \| 256c \| 256c \| 256c
+--R +
+--R +-------+
+--R | a
+--R 4c |- -----
+--R +-------+ 4| 5
+--R | a \| 256c
+--R 2c |- ----- atan(------------ + x
+--R 4| 5 x
+--R \| 256c
+--R /
+--R c
+--R Type: Union(Expression(Integer),...)
+--E 1007
+
+--S 1008 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R \|a log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-------+ +-------+
+--R +-+ | a 4+-+ | a
+--R - 4c\|2 |- ----- \|c log(4c |- ----- + x)
+--R 4| 5 4| 5
+--R \| 256c \| 256c
+--R +
+--R +-------+ +-------+
+--R +-+ | a 4+-+ | a
+--R 4c\|2 |- ----- \|c log(- 4c |- ----- + x)
+--R 4| 5 4| 5
+--R \| 256c \| 256c
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a
+--R - \|a log(- x\|2 \|a \|c + x \|c + \|a ) + 2\|a atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-------+
+--R | a
+--R 4c |- -----
+--R +-+4+-+ 4+-+ +-------+ 4| 5
+--R 4+-+ x\|2 \|c - \|a +-+ | a 4+-+ \| 256c
+--R 2\|a atan(----------------) + 8c\|2 |- ----- \|c atan(------------)
+--R 4+-+ 4| 5 x
+--R \|a \| 256c
+--R /
+--R +-+4+-+
+--R 4c\|2 \|c
+--R Type: Expression(Integer)
+--E 1008
+
+--S 1009 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1009
+
+)clear all
+
+--S 1010 of 1309
+t0:=x^3/(a+c*x^4)
+--R
+--R
+--R 3
+--R x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1010
+
+--S 1011 of 1309
+r0:=1/4*log(a+c*x^4)/c
+--R
+--R
+--R 4
+--R log(c x + a)
+--R (2) -------------
+--R 4c
+--R Type: Expression(Integer)
+--E 1011
+
+--S 1012 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R log(c x + a)
+--R (3) -------------
+--R 4c
+--R Type: Union(Expression(Integer),...)
+--E 1012
+
+--S 1013 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1013
+
+--S 1014 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1014
+
+)clear all
+
+--S 1015 of 1309
+t0:=x^2/(a+c*x^4)
+--R
+--R
+--R 2
+--R x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1015
+
+--S 1016 of 1309
+r0:=-1/2*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(3/4)*sqrt(2))+_
+ 1/2*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(3/4)*sqrt(2))+_
+ 1/4*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(1/4)*c^(3/4)*sqrt(2))-_
+ 1/4*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(1/4)*c^(3/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R - log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R log(- x\|2 \|a \|c + x \|c + \|a ) + 2atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R 2atan(----------------)
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+4+-+3
+--R 4\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1016
+
+--S 1017 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+3
+--R | 1 2 | 1
+--R |- ------- log(64a c |- ------- + x)
+--R 4| 3 4| 3
+--R \| 256a c \| 256a c
+--R +
+--R +---------+ +---------+3
+--R | 1 2 | 1
+--R - |- ------- log(- 64a c |- ------- + x)
+--R 4| 3 4| 3
+--R \| 256a c \| 256a c
+--R +
+--R +---------+3
+--R 2 | 1
+--R 64a c |- -------
+--R +---------+ 4| 3
+--R | 1 \| 256a c
+--R 2 |- ------- atan(-------------------)
+--R 4| 3 x
+--R \| 256a c
+--R Type: Union(Expression(Integer),...)
+--E 1017
+
+--S 1018 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +---------+ +---------+3
+--R +-+ | 1 4+-+4+-+3 2 | 1
+--R 4\|2 |- ------- \|a \|c log(64a c |- ------- + x)
+--R 4| 3 4| 3
+--R \| 256a c \| 256a c
+--R +
+--R +---------+ +---------+3
+--R +-+ | 1 4+-+4+-+3 2 | 1
+--R - 4\|2 |- ------- \|a \|c log(- 64a c |- ------- + x)
+--R 4| 3 4| 3
+--R \| 256a c \| 256a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R - log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 2atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +---------+3
+--R 2 | 1
+--R 64a c |- -------
+--R +---------+ 4| 3
+--R +-+ | 1 4+-+4+-+3 \| 256a c
+--R 8\|2 |- ------- \|a \|c atan(-------------------)
+--R 4| 3 x
+--R \| 256a c
+--R /
+--R +-+4+-+4+-+3
+--R 4\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1018
+
+--S 1019 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1019
+
+)clear all
+
+--S 1020 of 1309
+t0:=x/(a+c*x^4)
+--R
+--R
+--R x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1020
+
+--S 1021 of 1309
+r0:=1/2*atan(x^2*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c))
+--R
+--R
+--R 2 +-+
+--R x \|c
+--R atan(------)
+--R +-+
+--R \|a
+--R (2) ------------
+--R +-+ +-+
+--R 2\|a \|c
+--R Type: Expression(Integer)
+--E 1021
+
+--S 1022 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 +-----+ 2
+--R (c x - a)\|- a c + 2a c x 2 +---+
+--R log(----------------------------) x \|a c
+--R 4 atan(--------)
+--R c x + a a
+--R (3) [---------------------------------,--------------]
+--R +-----+ +---+
+--R 4\|- a c 2\|a c
+--R Type: Union(List(Expression(Integer)),...)
+--E 1022
+
+--S 1023 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R 4 +-----+ 2 2 +-+
+--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c
+--R \|a \|c log(----------------------------) - 2\|- a c atan(------)
+--R 4 +-+
+--R c x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 4\|- a c \|a \|c
+--R Type: Expression(Integer)
+--E 1023
+
+--S 1024 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1024
+
+--S 1025 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R 2 +---+ 2 +-+
+--R +-+ +-+ x \|a c +---+ x \|c
+--R \|a \|c atan(--------) - \|a c atan(------)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 2\|a \|c \|a c
+--R Type: Expression(Integer)
+--E 1025
+
+--S 1026 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1026
+
+)clear all
+
+--S 1027 of 1309
+t0:=1/(a+c*x^4)
+--R
+--R
+--R 1
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1027
+
+--S 1028 of 1309
+r0:=-1/2*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(1/4)*sqrt(2))+_
+ 1/2*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(1/4)*sqrt(2))-_
+ 1/4*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(3/4)*c^(1/4)*sqrt(2))+1/4*log(a^(1/4)*_
+ c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(3/4)*c^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+4+-+4+-+ 2 +-+ +-+ +-+4+-+4+-+ 2 +-+ +-+
+--R log(x\|2 \|a \|c + x \|c + \|a ) - log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R x\|2 \|c + \|a x\|2 \|c - \|a
+--R 2atan(----------------) + 2atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R +-+4+-+3 4+-+
+--R 4\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1028
+
+--S 1029 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+ +--------+ +--------+
+--R | 1 | 1 | 1 | 1
+--R |- ------ log(4a |- ------ + x) - |- ------ log(- 4a |- ------ + x)
+--R 4| 3 4| 3 4| 3 4| 3
+--R \| 256a c \| 256a c \| 256a c \| 256a c
+--R +
+--R +--------+
+--R | 1
+--R 4a |- ------
+--R +--------+ 4| 3
+--R | 1 \| 256a c
+--R - 2 |- ------ atan(-------------)
+--R 4| 3 x
+--R \| 256a c
+--R Type: Union(Expression(Integer),...)
+--E 1029
+
+--S 1030 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R - log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +--------+ +--------+
+--R +-+ | 1 4+-+3 4+-+ | 1
+--R 4\|2 |- ------ \|a \|c log(4a |- ------ + x)
+--R 4| 3 4| 3
+--R \| 256a c \| 256a c
+--R +
+--R +--------+ +--------+
+--R +-+ | 1 4+-+3 4+-+ | 1
+--R - 4\|2 |- ------ \|a \|c log(- 4a |- ------ + x)
+--R 4| 3 4| 3
+--R \| 256a c \| 256a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------+
+--R | 1
+--R 4a |- ------
+--R +-+4+-+ 4+-+ +--------+ 4| 3
+--R x\|2 \|c - \|a +-+ | 1 4+-+3 4+-+ \| 256a c
+--R - 2atan(----------------) - 8\|2 |- ------ \|a \|c atan(-------------)
+--R 4+-+ 4| 3 x
+--R \|a \| 256a c
+--R /
+--R +-+4+-+3 4+-+
+--R 4\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1030
+
+--S 1031 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1031
+
+)clear all
+
+--S 1032 of 1309
+t0:=1/(x*(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) ----------
+--R 5
+--R c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1032
+
+--S 1033 of 1309
+r0:=log(x)/a-1/4*log(a+c*x^4)/a
+--R
+--R
+--R 4
+--R - log(c x + a) + 4log(x)
+--R (2) -------------------------
+--R 4a
+--R Type: Expression(Integer)
+--E 1033
+
+--S 1034 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R - log(c x + a) + 4log(x)
+--R (3) -------------------------
+--R 4a
+--R Type: Union(Expression(Integer),...)
+--E 1034
+
+--S 1035 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1035
+
+--S 1036 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1036
+
+)clear all
+
+--S 1037 of 1309
+t0:=1/(x^2*(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 6 2
+--R c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1037
+
+--S 1038 of 1309
+r0:=(-1)/(a*x)+1/2*c^(1/4)*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*_
+ sqrt(2))-1/2*c^(1/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*_
+ sqrt(2))-1/4*c^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_
+ sqrt(a)+x^2*sqrt(c))/(a^(5/4)*sqrt(2))+1/4*c^(1/4)*_
+ log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(5/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R x\|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - x\|c log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+ x\|2 \|c + \|a 4+-+ x\|2 \|c - \|a +-+4+-+
+--R - 2x\|c atan(----------------) - 2x\|c atan(----------------) - 4\|2 \|a
+--R 4+-+ 4+-+
+--R \|a \|a
+--R /
+--R +-+4+-+
+--R 4a x\|2 \|a
+--R Type: Expression(Integer)
+--E 1038
+
+--S 1039 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+3
+--R | c 4 | c
+--R - a x |- ----- log(64a |- ----- + c x)
+--R 4| 5 4| 5
+--R \| 256a \| 256a
+--R +
+--R +-------+ +-------+3
+--R | c 4 | c
+--R a x |- ----- log(- 64a |- ----- + c x)
+--R 4| 5 4| 5
+--R \| 256a \| 256a
+--R +
+--R +-------+3
+--R 4 | c
+--R 64a |- -----
+--R +-------+ 4| 5
+--R | c \| 256a
+--R - 2a x |- ----- atan(--------------- - 1
+--R 4| 5 c x
+--R \| 256a
+--R /
+--R a x
+--R Type: Union(Expression(Integer),...)
+--E 1039
+
+--S 1040 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - \|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-------+ +-------+3
+--R +-+ | c 4+-+ 4 | c
+--R - 4a\|2 |- ----- \|a log(64a |- ----- + c x)
+--R 4| 5 4| 5
+--R \| 256a \| 256a
+--R +
+--R +-------+ +-------+3
+--R +-+ | c 4+-+ 4 | c
+--R 4a\|2 |- ----- \|a log(- 64a |- ----- + c x)
+--R 4| 5 4| 5
+--R \| 256a \| 256a
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a
+--R \|c log(- x\|2 \|a \|c + x \|c + \|a ) + 2\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-------+3
+--R 4 | c
+--R 64a |- -----
+--R +-+4+-+ 4+-+ +-------+ 4| 5
+--R 4+-+ x\|2 \|c - \|a +-+ | c 4+-+ \| 256a
+--R 2\|c atan(----------------) - 8a\|2 |- ----- \|a atan(---------------)
+--R 4+-+ 4| 5 c x
+--R \|a \| 256a
+--R /
+--R +-+4+-+
+--R 4a\|2 \|a
+--R Type: Expression(Integer)
+--E 1040
+
+--S 1041 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1041
+
+)clear all
+
+--S 1042 of 1309
+t0:=1/(x^3*(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 7 3
+--R c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1042
+
+--S 1043 of 1309
+r0:=(-1/2)/(a*x^2)-1/2*atan(x^2*sqrt(c)/sqrt(a))*sqrt(c)/a^(3/2)
+--R
+--R
+--R 2 +-+
+--R 2 +-+ x \|c +-+
+--R - x \|c atan(------) - \|a
+--R +-+
+--R \|a
+--R (2) ---------------------------
+--R 2 +-+
+--R 2a x \|a
+--R Type: Expression(Integer)
+--E 1043
+
+--S 1044 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+ +-+
+--R 2 | c 4 |c
+--R +---+ - 2a x |- - + c x - a +-+ a |-
+--R 2 | c \| a 2 |c \|a
+--R x |- - log(------------------------) - 2 x |- atan(-----) - 1
+--R \| a 4 \|a 2
+--R c x + a c x
+--R (3) [-----------------------------------------,---------------------]
+--R 2 2
+--R 4a x 2a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1044
+
+--S 1045 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R 2 | c 4
+--R +---+ - 2a x |- - + c x - a 2 +-+
+--R | c +-+ \| a +-+ x \|c
+--R |- - \|a log(------------------------) + 2\|c atan(------)
+--R \| a 4 +-+
+--R c x + a \|a
+--R (4) -----------------------------------------------------------
+--R +-+
+--R 4a\|a
+--R Type: Expression(Integer)
+--E 1045
+
+--S 1046 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1046
+
+--S 1047 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |c
+--R 2 +-+ +-+ a |-
+--R +-+ x \|c +-+ |c \|a
+--R \|c atan(------) + \|a |- atan(-----)
+--R +-+ \|a 2
+--R \|a c x
+--R (6) --------------------------------------
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 1047
+
+--S 1048 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1048
+
+)clear all
+
+--S 1049 of 1309
+t0:=1/(x^4*(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 8 4
+--R c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1049
+
+--S 1050 of 1309
+r0:=(-1/3)/(a*x^3)+1/2*c^(3/4)*atan(1-c^(1/4)*x*_
+ sqrt(2)/a^(1/4))/(a^(7/4)*sqrt(2))-1/2*c^(3/4)*atan(1+c^(1/4)*x*_
+ sqrt(2)/a^(1/4))/(a^(7/4)*sqrt(2))+1/4*c^(3/4)*_
+ log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*_
+ sqrt(c))/(a^(7/4)*sqrt(2))-1/4*c^(3/4)*log(a^(1/4)*c^(1/4)*x*_
+ sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - 3x \|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R 3x \|c log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 3 4+-+3 x\|2 \|c + \|a 3 4+-+3 x\|2 \|c - \|a
+--R - 6x \|c atan(---------------- - 6x \|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+4+-+3
+--R - 4\|2 \|a
+--R /
+--R 3 +-+4+-+3
+--R 12a x \|2 \|a
+--R Type: Expression(Integer)
+--E 1050
+
+--S 1051 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R | 3 | 3
+--R 3 | c 2 | c
+--R - 3a x |- ----- log(4a |- ----- + c x)
+--R 4| 7 4| 7
+--R \| 256a \| 256a
+--R +
+--R +-------+ +-------+
+--R | 3 | 3
+--R 3 | c 2 | c
+--R 3a x |- ----- log(- 4a |- ----- + c x)
+--R 4| 7 4| 7
+--R \| 256a \| 256a
+--R +
+--R +-------+
+--R | 3
+--R 2 | c
+--R +-------+ 4a |- -----
+--R | 3 4| 7
+--R 3 | c \| 256a
+--R 6a x |- ----- atan(------------- - 1
+--R 4| 7 c x
+--R \| 256a
+--R /
+--R 3
+--R 3a x
+--R Type: Union(Expression(Integer),...)
+--E 1051
+
+--S 1052 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R \|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-------+ +-------+
+--R | 3 | 3
+--R +-+ | c 4+-+3 2 | c
+--R - 4a\|2 |- ----- \|a log(4a |- ----- + c x)
+--R 4| 7 4| 7
+--R \| 256a \| 256a
+--R +
+--R +-------+ +-------+
+--R | 3 | 3
+--R +-+ | c 4+-+3 2 | c
+--R 4a\|2 |- ----- \|a log(- 4a |- ----- + c x)
+--R 4| 7 4| 7
+--R \| 256a \| 256a
+--R +
+--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - \|c log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 x\|2 \|c + \|a 4+-+3 x\|2 \|c - \|a
+--R 2\|c atan(----------------) + 2\|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-------+
+--R | 3
+--R 2 | c
+--R +-------+ 4a |- -----
+--R | 3 4| 7
+--R +-+ | c 4+-+3 \| 256a
+--R 8a\|2 |- ----- \|a atan(-------------)
+--R 4| 7 c x
+--R \| 256a
+--R /
+--R +-+4+-+3
+--R 4a\|2 \|a
+--R Type: Expression(Integer)
+--E 1052
+
+--S 1053 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1053
+
+)clear all
+
+--S 1054 of 1309
+t0:=1/(x^5*(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 9 5
+--R c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1054
+
+--S 1055 of 1309
+r0:=(-1/4)/(a*x^4)-c*log(x)/a^2+1/4*c*log(a+c*x^4)/a^2
+--R
+--R
+--R 4 4 4
+--R c x log(c x + a) - 4c x log(x) - a
+--R (2) -----------------------------------
+--R 2 4
+--R 4a x
+--R Type: Expression(Integer)
+--E 1055
+
+--S 1056 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4 4
+--R c x log(c x + a) - 4c x log(x) - a
+--R (3) -----------------------------------
+--R 2 4
+--R 4a x
+--R Type: Union(Expression(Integer),...)
+--E 1056
+
+--S 1057 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1057
+
+--S 1058 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1058
+
+)clear all
+
+--S 1059 of 1309
+t0:=x^7/(a+c*x^4)^2
+--R
+--R
+--R 7
+--R x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1059
+
+--S 1060 of 1309
+r0:=1/4*a/(c^2*(a+c*x^4))+1/4*log(a+c*x^4)/c^2
+--R
+--R
+--R 4 4
+--R (c x + a)log(c x + a) + a
+--R (2) ---------------------------
+--R 3 4 2
+--R 4c x + 4a c
+--R Type: Expression(Integer)
+--E 1060
+
+--S 1061 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4
+--R (c x + a)log(c x + a) + a
+--R (3) ---------------------------
+--R 3 4 2
+--R 4c x + 4a c
+--R Type: Union(Expression(Integer),...)
+--E 1061
+
+--S 1062 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1062
+
+--S 1063 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1063
+
+)clear all
+
+--S 1064 of 1309
+t0:=x^6/(a+c*x^4)^2
+--R
+--R
+--R 6
+--R x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1064
+
+--S 1065 of 1309
+r0:=-1/4*x^3/(c*(a+c*x^4))-3/8*atan(1-c^(1/4)*x*_
+ sqrt(2)/a^(1/4))/(a^(1/4)*c^(7/4)*sqrt(2))+_
+ 3/8*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(7/4)*sqrt(2))+_
+ 3/16*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(1/4)*c^(7/4)*sqrt(2))-_
+ 3/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(1/4)*c^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 3c x - 3a)log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 4 +-+4+-+4+-+ 2 +-+ +-+
+--R (3c x + 3a)log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a
+--R (6c x + 6a)atan(----------------) + (6c x + 6a)atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R 3 +-+4+-+4+-+3
+--R - 4x \|2 \|a \|c
+--R /
+--R 2 4 +-+4+-+4+-+3
+--R (16c x + 16a c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1065
+
+--S 1066 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------+ +-----------+3
+--R 2 4 | 1 5 | 1
+--R (12c x + 12a c) |- --------- log(4096a c |- --------- + x)
+--R 4| 7 4| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+3
+--R 2 4 | 1 5 | 1
+--R (- 12c x - 12a c) |- --------- log(- 4096a c |- --------- + x)
+--R 4| 7 4| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+3
+--R 5 | 1
+--R 4096a c |- ---------
+--R +-----------+ 4| 7
+--R 2 4 | 1 \| 65536a c 3
+--R (24c x + 24a c) |- --------- atan(----------------------- - x
+--R 4| 7 x
+--R \| 65536a c
+--R /
+--R 2 4
+--R 4c x + 4a c
+--R Type: Union(Expression(Integer),...)
+--E 1066
+
+--S 1067 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R 3log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-----------+ +-----------+3
+--R +-+ | 1 4+-+4+-+3 5 | 1
+--R 48c\|2 |- --------- \|a \|c log(4096a c |- --------- + x)
+--R 4| 7 4| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+3
+--R +-+ | 1 4+-+4+-+3 5 | 1
+--R - 48c\|2 |- --------- \|a \|c log(- 4096a c |- --------- + x)
+--R 4| 7 4| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R - 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 6atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-----------+3
+--R 5 | 1
+--R 4096a c |- ---------
+--R +-----------+ 4| 7
+--R +-+ | 1 4+-+4+-+3 \| 65536a c
+--R 96c\|2 |- --------- \|a \|c atan(-----------------------)
+--R 4| 7 x
+--R \| 65536a c
+--R /
+--R +-+4+-+4+-+3
+--R 16c\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1067
+
+--S 1068 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1068
+
+)clear all
+
+--S 1069 of 1309
+t0:=x^5/(a+c*x^4)^2
+--R
+--R
+--R 5
+--R x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1069
+
+--S 1070 of 1309
+r0:=-1/4*x^2/(c*(a+c*x^4))+1/4*atan(x^2*sqrt(c)/sqrt(a))/(c^(3/2)*sqrt(a))
+--R
+--R
+--R 2 +-+
+--R 4 x \|c 2 +-+ +-+
+--R (c x + a)atan(------) - x \|a \|c
+--R +-+
+--R \|a
+--R (2) -----------------------------------
+--R 2 4 +-+ +-+
+--R (4c x + 4a c)\|a \|c
+--R Type: Expression(Integer)
+--E 1070
+
+--S 1071 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 +-----+ 2
+--R 4 (c x - a)\|- a c + 2a c x 2 +-----+
+--R (c x + a)log(----------------------------) - 2x \|- a c
+--R 4
+--R c x + a
+--R [---------------------------------------------------------,
+--R 2 4 +-----+
+--R (8c x + 8a c)\|- a c
+--R 2 +---+
+--R 4 x \|a c 2 +---+
+--R (c x + a)atan(--------) - x \|a c
+--R a
+--R -----------------------------------]
+--R 2 4 +---+
+--R (4c x + 4a c)\|a c
+--R Type: Union(List(Expression(Integer)),...)
+--E 1071
+
+--S 1072 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R 4 +-----+ 2 2 +-+
+--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c
+--R \|a \|c log(----------------------------) - 2\|- a c atan(------)
+--R 4 +-+
+--R c x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 8c\|- a c \|a \|c
+--R Type: Expression(Integer)
+--E 1072
+
+--S 1073 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1073
+
+--S 1074 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R 2 +---+ 2 +-+
+--R +-+ +-+ x \|a c +---+ x \|c
+--R \|a \|c atan(--------) - \|a c atan(------)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 4c\|a \|c \|a c
+--R Type: Expression(Integer)
+--E 1074
+
+--S 1075 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1075
+
+)clear all
+
+--S 1076 of 1309
+t0:=x^4/(a+c*x^4)^2
+--R
+--R
+--R 4
+--R x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1076
+
+--S 1077 of 1309
+r0:=-1/4*x/(c*(a+c*x^4))-1/8*atan(1-c^(1/4)*x*_
+ sqrt(2)/a^(1/4))/(a^(3/4)*c^(5/4)*sqrt(2))+_
+ 1/8*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*_
+ c^(5/4)*sqrt(2))-1/16*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_
+ sqrt(a)+x^2*sqrt(c))/(a^(3/4)*c^(5/4)*sqrt(2))+_
+ 1/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(3/4)*c^(5/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+4+-+4+-+ 2 +-+ +-+
+--R (c x + a)log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 4 +-+4+-+4+-+ 2 +-+ +-+
+--R (- c x - a)log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a
+--R (2c x + 2a)atan(----------------) + (2c x + 2a)atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+4+-+3 4+-+
+--R - 4x\|2 \|a \|c
+--R /
+--R 2 4 +-+4+-+3 4+-+
+--R (16c x + 16a c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1077
+
+--S 1078 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------+ +-----------+
+--R 2 4 | 1 | 1
+--R (4c x + 4a c) |- --------- log(16a c |- --------- + x)
+--R 4| 3 5 4| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+
+--R 2 4 | 1 | 1
+--R (- 4c x - 4a c) |- --------- log(- 16a c |- --------- + x)
+--R 4| 3 5 4| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+
+--R | 1
+--R 16a c |- ---------
+--R +-----------+ 4| 3 5
+--R 2 4 | 1 \| 65536a c
+--R (- 8c x - 8a c) |- --------- atan(------------------- - x
+--R 4| 3 5 x
+--R \| 65536a c
+--R /
+--R 2 4
+--R 4c x + 4a c
+--R Type: Union(Expression(Integer),...)
+--E 1078
+
+--S 1079 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R - log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-----------+ +-----------+
+--R +-+ | 1 4+-+3 4+-+ | 1
+--R 16c\|2 |- --------- \|a \|c log(16a c |- --------- + x)
+--R 4| 3 5 4| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+
+--R +-+ | 1 4+-+3 4+-+ | 1
+--R - 16c\|2 |- --------- \|a \|c log(- 16a c |- --------- + x)
+--R 4| 3 5 4| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 2atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-----------+
+--R | 1
+--R 16a c |- ---------
+--R +-----------+ 4| 3 5
+--R +-+ | 1 4+-+3 4+-+ \| 65536a c
+--R - 32c\|2 |- --------- \|a \|c atan(-------------------)
+--R 4| 3 5 x
+--R \| 65536a c
+--R /
+--R +-+4+-+3 4+-+
+--R 16c\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1079
+
+--S 1080 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1080
+
+)clear all
+
+--S 1081 of 1309
+t0:=x^3/(a+c*x^4)^2
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1081
+
+--S 1082 of 1309
+r0:=(-1/4)/(c*(a+c*x^4))
+--R
+--R
+--R 1
+--R -
+--R 4
+--R (2) - ----------
+--R 2 4
+--R c x + a c
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1082
+
+--S 1083 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ------------
+--R 2 4
+--R 4c x + 4a c
+--R Type: Union(Expression(Integer),...)
+--E 1083
+
+--S 1084 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1084
+
+--S 1085 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1085
+
+)clear all
+
+--S 1086 of 1309
+t0:=x^2/(a+c*x^4)^2
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1086
+
+--S 1087 of 1309
+r0:=1/4*x^3/(a*(a+c*x^4))-1/8*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/_
+ (a^(5/4)*c^(3/4)*sqrt(2))+1/8*atan(1+c^(1/4)*x*sqrt(2)/_
+ a^(1/4))/(a^(5/4)*c^(3/4)*sqrt(2))+1/16*log(-a^(1/4)*_
+ c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(5/4)*c^(3/4)*_
+ sqrt(2))-1/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(5/4)*c^(3/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+4+-+4+-+ 2 +-+ +-+
+--R (- c x - a)log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 4 +-+4+-+4+-+ 2 +-+ +-+
+--R (c x + a)log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a
+--R (2c x + 2a)atan(----------------) + (2c x + 2a)atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R 3 +-+4+-+4+-+3
+--R 4x \|2 \|a \|c
+--R /
+--R 4 2 +-+4+-+4+-+3
+--R (16a c x + 16a )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1087
+
+--S 1088 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------+ +-----------+3
+--R 4 2 | 1 4 2 | 1
+--R (4a c x + 4a ) |- --------- log(4096a c |- --------- + x)
+--R 4| 5 3 4| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+3
+--R 4 2 | 1 4 2 | 1
+--R (- 4a c x - 4a ) |- --------- log(- 4096a c |- --------- + x)
+--R 4| 5 3 4| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+3
+--R 4 2 | 1
+--R 4096a c |- ---------
+--R +-----------+ 4| 5 3
+--R 4 2 | 1 \| 65536a c 3
+--R (8a c x + 8a ) |- --------- atan(----------------------- + x
+--R 4| 5 3 x
+--R \| 65536a c
+--R /
+--R 4 2
+--R 4a c x + 4a
+--R Type: Union(Expression(Integer),...)
+--E 1088
+
+--S 1089 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-----------+ +-----------+3
+--R +-+ | 1 4+-+4+-+3 4 2 | 1
+--R 16a\|2 |- --------- \|a \|c log(4096a c |- --------- + x)
+--R 4| 5 3 4| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+3
+--R +-+ | 1 4+-+4+-+3 4 2 | 1
+--R - 16a\|2 |- --------- \|a \|c log(- 4096a c |- --------- + x)
+--R 4| 5 3 4| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R - log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 2atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-----------+3
+--R 4 2 | 1
+--R 4096a c |- ---------
+--R +-----------+ 4| 5 3
+--R +-+ | 1 4+-+4+-+3 \| 65536a c
+--R 32a\|2 |- --------- \|a \|c atan(-----------------------)
+--R 4| 5 3 x
+--R \| 65536a c
+--R /
+--R +-+4+-+4+-+3
+--R 16a\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1089
+
+--S 1090 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1090
+
+)clear all
+
+--S 1091 of 1309
+t0:=x/(a+c*x^4)^2
+--R
+--R
+--R x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1091
+
+--S 1092 of 1309
+r0:=1/4*x^2/(a*(a+c*x^4))+1/4*atan(x^2*sqrt(c)/sqrt(a))/(a^(3/2)*sqrt(c))
+--R
+--R
+--R 2 +-+
+--R 4 x \|c 2 +-+ +-+
+--R (c x + a)atan(------) + x \|a \|c
+--R +-+
+--R \|a
+--R (2) -----------------------------------
+--R 4 2 +-+ +-+
+--R (4a c x + 4a )\|a \|c
+--R Type: Expression(Integer)
+--E 1092
+
+--S 1093 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 +-----+ 2
+--R 4 (c x - a)\|- a c + 2a c x 2 +-----+
+--R (c x + a)log(----------------------------) + 2x \|- a c
+--R 4
+--R c x + a
+--R [---------------------------------------------------------,
+--R 4 2 +-----+
+--R (8a c x + 8a )\|- a c
+--R 2 +---+
+--R 4 x \|a c 2 +---+
+--R (c x + a)atan(--------) + x \|a c
+--R a
+--R -----------------------------------]
+--R 4 2 +---+
+--R (4a c x + 4a )\|a c
+--R Type: Union(List(Expression(Integer)),...)
+--E 1093
+
+--S 1094 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R 4 +-----+ 2 2 +-+
+--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c
+--R \|a \|c log(----------------------------) - 2\|- a c atan(------)
+--R 4 +-+
+--R c x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 8a\|- a c \|a \|c
+--R Type: Expression(Integer)
+--E 1094
+
+--S 1095 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1095
+
+--S 1096 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R 2 +---+ 2 +-+
+--R +-+ +-+ x \|a c +---+ x \|c
+--R \|a \|c atan(--------) - \|a c atan(------)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 4a\|a \|c \|a c
+--R Type: Expression(Integer)
+--E 1096
+
+--S 1097 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1097
+
+)clear all
+
+--S 1098 of 1309
+t0:=1/(a+c*x^4)^2
+--R
+--R
+--R 1
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1098
+
+--S 1099 of 1309
+r0:=1/4*x/(a*(a+c*x^4))-3/8*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/_
+ (a^(7/4)*c^(1/4)*sqrt(2))+3/8*atan(1+c^(1/4)*x*_
+ sqrt(2)/a^(1/4))/(a^(7/4)*c^(1/4)*sqrt(2))-_
+ 3/16*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(7/4)*c^(1/4)*sqrt(2))+_
+ 3/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/_
+ (a^(7/4)*c^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+4+-+4+-+ 2 +-+ +-+
+--R (3c x + 3a)log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 4 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 3c x - 3a)log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a
+--R (6c x + 6a)atan(----------------) + (6c x + 6a)atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+4+-+3 4+-+
+--R 4x\|2 \|a \|c
+--R /
+--R 4 2 +-+4+-+3 4+-+
+--R (16a c x + 16a )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1099
+
+--S 1100 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+
+--R 4 2 | 1 2 | 1
+--R (12a c x + 12a ) |- -------- log(16a |- -------- + x)
+--R 4| 7 4| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +----------+ +----------+
+--R 4 2 | 1 2 | 1
+--R (- 12a c x - 12a ) |- -------- log(- 16a |- -------- + x)
+--R 4| 7 4| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +----------+
+--R 2 | 1
+--R 16a |- --------
+--R +----------+ 4| 7
+--R 4 2 | 1 \| 65536a c
+--R (- 24a c x - 24a ) |- -------- atan(----------------- + x
+--R 4| 7 x
+--R \| 65536a c
+--R /
+--R 4 2
+--R 4a c x + 4a
+--R Type: Union(Expression(Integer),...)
+--E 1100
+
+--S 1101 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R - 3log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +----------+ +----------+
+--R +-+ | 1 4+-+3 4+-+ 2 | 1
+--R 48a\|2 |- -------- \|a \|c log(16a |- -------- + x)
+--R 4| 7 4| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +----------+ +----------+
+--R +-+ | 1 4+-+3 4+-+ 2 | 1
+--R - 48a\|2 |- -------- \|a \|c log(- 16a |- -------- + x)
+--R 4| 7 4| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 6atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +----------+
+--R 2 | 1
+--R 16a |- --------
+--R +----------+ 4| 7
+--R +-+ | 1 4+-+3 4+-+ \| 65536a c
+--R - 96a\|2 |- -------- \|a \|c atan(-----------------)
+--R 4| 7 x
+--R \| 65536a c
+--R /
+--R +-+4+-+3 4+-+
+--R 16a\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1101
+
+--S 1102 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1102
+
+)clear all
+
+--S 1103 of 1309
+t0:=1/(x*(a+c*x^4)^2)
+--R
+--R
+--R 1
+--R (1) --------------------
+--R 2 9 5 2
+--R c x + 2a c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1103
+
+--S 1104 of 1309
+r0:=1/4/(a*(a+c*x^4))+log(x)/a^2-1/4*log(a+c*x^4)/a^2
+--R
+--R
+--R 4 4 4
+--R (- c x - a)log(c x + a) + (4c x + 4a)log(x) + a
+--R (2) --------------------------------------------------
+--R 2 4 3
+--R 4a c x + 4a
+--R Type: Expression(Integer)
+--E 1104
+
+--S 1105 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4 4
+--R (- c x - a)log(c x + a) + (4c x + 4a)log(x) + a
+--R (3) --------------------------------------------------
+--R 2 4 3
+--R 4a c x + 4a
+--R Type: Union(Expression(Integer),...)
+--E 1105
+
+--S 1106 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1106
+
+--S 1107 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1107
+
+)clear all
+
+--S 1108 of 1309
+t0:=1/(x^2*(a+c*x^4)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 2 10 6 2 2
+--R c x + 2a c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1108
+
+--S 1109 of 1309
+r0:=(-5/4)/(a^2*x)+1/4/(a*x*(a+c*x^4))+5/8*c^(1/4)*atan(1-c^(1/4)*x*_
+ sqrt(2)/a^(1/4))/(a^(9/4)*sqrt(2))-5/8*c^(1/4)*_
+ atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*sqrt(2))-_
+ 5/16*c^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_
+ sqrt(a)+x^2*sqrt(c))/(a^(9/4)*sqrt(2))+5/16*c^(1/4)*_
+ log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(9/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 5 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R (5c x + 5a x)\|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 5 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R (- 5c x - 5a x)\|c log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 5 4+-+ x\|2 \|c + \|a
+--R (- 10c x - 10a x)\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 5 4+-+ x\|2 \|c - \|a 4 +-+4+-+
+--R (- 10c x - 10a x)\|c atan(----------------) + (- 20c x - 16a)\|2 \|a
+--R 4+-+
+--R \|a
+--R /
+--R 2 5 3 +-+4+-+
+--R (16a c x + 16a x)\|2 \|a
+--R Type: Expression(Integer)
+--E 1109
+
+--S 1110 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+3
+--R 2 5 3 | 625c 7 | 625c
+--R (- 4a c x - 4a x) |- ------- log(4096a |- ------- + 125c x)
+--R 4| 9 4| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+ +---------+3
+--R 2 5 3 | 625c 7 | 625c
+--R (4a c x + 4a x) |- ------- log(- 4096a |- ------- + 125c x)
+--R 4| 9 4| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+3
+--R 7 | 625c
+--R 4096a |- -------
+--R +---------+ 4| 9
+--R 2 5 3 | 625c \| 65536a 4
+--R (- 8a c x - 8a x) |- ------- atan(------------------- - 5c x - 4a
+--R 4| 9 125c x
+--R \| 65536a
+--R /
+--R 2 5 3
+--R 4a c x + 4a x
+--R Type: Union(Expression(Integer),...)
+--E 1110
+
+--S 1111 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - 5\|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +---------+ +---------+3
+--R 2 +-+ | 625c 4+-+ 7 | 625c
+--R - 16a \|2 |- ------- \|a log(4096a |- ------- + 125c x)
+--R 4| 9 4| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+ +---------+3
+--R 2 +-+ | 625c 4+-+ 7 | 625c
+--R 16a \|2 |- ------- \|a log(- 4096a |- ------- + 125c x)
+--R 4| 9 4| 9
+--R \| 65536a \| 65536a
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a
+--R 5\|c log(- x\|2 \|a \|c + x \|c + \|a ) + 10\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+ x\|2 \|c - \|a
+--R 10\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +---------+3
+--R 7 | 625c
+--R 4096a |- -------
+--R +---------+ 4| 9
+--R 2 +-+ | 625c 4+-+ \| 65536a
+--R - 32a \|2 |- ------- \|a atan(-------------------)
+--R 4| 9 125c x
+--R \| 65536a
+--R /
+--R 2 +-+4+-+
+--R 16a \|2 \|a
+--R Type: Expression(Integer)
+--E 1111
+
+--S 1112 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1112
+
+)clear all
+
+--S 1113 of 1309
+t0:=1/(x^3*(a+c*x^4)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 2 11 7 2 3
+--R c x + 2a c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1113
+
+--S 1114 of 1309
+r0:=(-3/4)/(a^2*x^2)+1/4/(a*x^2*(a+c*x^4))-_
+ 3/4*atan(x^2*sqrt(c)/sqrt(a))*sqrt(c)/a^(5/2)
+--R
+--R
+--R 2 +-+
+--R 6 2 +-+ x \|c 4 +-+
+--R (- 3c x - 3a x )\|c atan(------) + (- 3c x - 2a)\|a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------
+--R 2 6 3 2 +-+
+--R (4a c x + 4a x )\|a
+--R Type: Expression(Integer)
+--E 1114
+
+--S 1115 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R 2 | c 4
+--R +---+ - 2a x |- - + c x - a
+--R 6 2 | c \| a 4
+--R (3c x + 3a x ) |- - log(------------------------) - 6c x - 4a
+--R \| a 4
+--R c x + a
+--R [---------------------------------------------------------------,
+--R 2 6 3 2
+--R 8a c x + 8a x
+--R +-+
+--R |c
+--R +-+ a |-
+--R 6 2 |c \|a 4
+--R (3c x + 3a x ) |- atan(-----) - 3c x - 2a
+--R \|a 2
+--R c x
+--R -------------------------------------------]
+--R 2 6 3 2
+--R 4a c x + 4a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1115
+
+--S 1116 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R 2 | c 4
+--R +---+ - 2a x |- - + c x - a 2 +-+
+--R | c +-+ \| a +-+ x \|c
+--R 3 |- - \|a log(------------------------ + 6\|c atan(------)
+--R \| a 4 +-+
+--R c x + a \|a
+--R (4) ------------------------------------------------------------
+--R 2 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1116
+
+--S 1117 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1117
+
+--S 1118 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |c
+--R 2 +-+ +-+ a |-
+--R +-+ x \|c +-+ |c \|a
+--R 3\|c atan(------) + 3\|a |- atan(-----)
+--R +-+ \|a 2
+--R \|a c x
+--R (6) ----------------------------------------
+--R 2 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 1118
+
+--S 1119 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1119
+
+)clear all
+
+--S 1120 of 1309
+t0:=1/(x^4*(a+c*x^4)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 2 12 8 2 4
+--R c x + 2a c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1120
+
+--S 1121 of 1309
+r0:=(-7/12)/(a^2*x^3)+1/4/(a*x^3*(a+c*x^4))+7/8*c^(3/4)*_
+ atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*sqrt(2))-_
+ 7/8*c^(3/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*_
+ sqrt(2))+7/16*c^(3/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_
+ sqrt(a)+x^2*sqrt(c))/(a^(11/4)*sqrt(2))-7/16*c^(3/4)*_
+ log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 7 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 21c x - 21a x )\|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 7 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R (21c x + 21a x )\|c log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 7 3 4+-+3 x\|2 \|c + \|a
+--R (- 42c x - 42a x )\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 7 3 4+-+3 x\|2 \|c - \|a 4 +-+4+-+3
+--R (- 42c x - 42a x )\|c atan(----------------) + (- 28c x - 16a)\|2 \|a
+--R 4+-+
+--R \|a
+--R /
+--R 2 7 3 3 +-+4+-+3
+--R (48a c x + 48a x )\|2 \|a
+--R Type: Expression(Integer)
+--E 1121
+
+--S 1122 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+
+--R | 3 | 3
+--R 2 7 3 3 | 2401c 3 | 2401c
+--R (- 12a c x - 12a x ) |- -------- log(16a |- -------- + 7c x)
+--R 4| 11 4| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+
+--R | 3 | 3
+--R 2 7 3 3 | 2401c 3 | 2401c
+--R (12a c x + 12a x ) |- -------- log(- 16a |- -------- + 7c x)
+--R 4| 11 4| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+
+--R | 3
+--R 3 | 2401c
+--R +----------+ 16a |- --------
+--R | 3 4| 11
+--R 2 7 3 3 | 2401c \| 65536a 4
+--R (24a c x + 24a x ) |- -------- atan(----------------- - 7c x - 4a
+--R 4| 11 7c x
+--R \| 65536a
+--R /
+--R 2 7 3 3
+--R 12a c x + 12a x
+--R Type: Union(Expression(Integer),...)
+--E 1122
+
+--S 1123 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R 7\|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +----------+ +----------+
+--R | 3 | 3
+--R 2 +-+ | 2401c 4+-+3 3 | 2401c
+--R - 16a \|2 |- -------- \|a log(16a |- -------- + 7c x)
+--R 4| 11 4| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+
+--R | 3 | 3
+--R 2 +-+ | 2401c 4+-+3 3 | 2401c
+--R 16a \|2 |- -------- \|a log(- 16a |- -------- + 7c x)
+--R 4| 11 4| 11
+--R \| 65536a \| 65536a
+--R +
+--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - 7\|c log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 x\|2 \|c + \|a 4+-+3 x\|2 \|c - \|a
+--R 14\|c atan(----------------) + 14\|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +----------+
+--R | 3
+--R 3 | 2401c
+--R +----------+ 16a |- --------
+--R | 3 4| 11
+--R 2 +-+ | 2401c 4+-+3 \| 65536a
+--R 32a \|2 |- -------- \|a atan(-----------------)
+--R 4| 11 7c x
+--R \| 65536a
+--R /
+--R 2 +-+4+-+3
+--R 16a \|2 \|a
+--R Type: Expression(Integer)
+--E 1123
+
+--S 1124 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1124
+
+)clear all
+
+--S 1125 of 1309
+t0:=x^11/(a+c*x^4)^3
+--R
+--R
+--R 11
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1125
+
+--S 1126 of 1309
+r0:=-1/8*a^2/(c^3*(a+c*x^4)^2)+1/2*a/(c^3*(a+c*x^4))+1/4*log(a+c*x^4)/c^3
+--R
+--R
+--R 2 8 4 2 4 4 2
+--R (2c x + 4a c x + 2a )log(c x + a) + 4a c x + 3a
+--R (2) ----------------------------------------------------
+--R 5 8 4 4 2 3
+--R 8c x + 16a c x + 8a c
+--R Type: Expression(Integer)
+--E 1126
+
+--S 1127 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 4 2 4 4 2
+--R (2c x + 4a c x + 2a )log(c x + a) + 4a c x + 3a
+--R (3) ----------------------------------------------------
+--R 5 8 4 4 2 3
+--R 8c x + 16a c x + 8a c
+--R Type: Union(Expression(Integer),...)
+--E 1127
+
+--S 1128 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1128
+
+--S 1129 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1129
+
+)clear all
+
+--S 1130 of 1309
+t0:=x^10/(a+c*x^4)^3
+--R
+--R
+--R 10
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1130
+
+--S 1131 of 1309
+r0:=-1/8*x^7/(c*(a+c*x^4)^2)-7/32*x^3/(c^2*(a+c*x^4))-_
+ 21/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(11/4)*_
+ sqrt(2))+21/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*_
+ c^(11/4)*sqrt(2))+21/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_
+ sqrt(a)+x^2*sqrt(c))/(a^(1/4)*c^(11/4)*sqrt(2))-21/128*_
+ log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(1/4)*c^(11/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 21c x - 42a c x - 21a )log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (21c x + 42a c x + 21a )log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c + \|a
+--R (42c x + 84a c x + 42a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c - \|a
+--R (42c x + 84a c x + 42a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 7 3 +-+4+-+4+-+3
+--R (- 44c x - 28a x )\|2 \|a \|c
+--R /
+--R 4 8 3 4 2 2 +-+4+-+4+-+3
+--R (128c x + 256a c x + 128a c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1131
+
+--S 1132 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------------+
+--R 4 8 3 4 2 2 | 1
+--R (672c x + 1344a c x + 672a c ) |- --------------
+--R 4| 11
+--R \| 268435456a c
+--R *
+--R +----------------+3
+--R 8 | 1
+--R log(2097152a c |- -------------- + x)
+--R 4| 11
+--R \| 268435456a c
+--R +
+--R +----------------+
+--R 4 8 3 4 2 2 | 1
+--R (- 672c x - 1344a c x - 672a c ) |- --------------
+--R 4| 11
+--R \| 268435456a c
+--R *
+--R +----------------+3
+--R 8 | 1
+--R log(- 2097152a c |- -------------- + x)
+--R 4| 11
+--R \| 268435456a c
+--R +
+--R +----------------+
+--R 4 8 3 4 2 2 | 1
+--R (1344c x + 2688a c x + 1344a c ) |- --------------
+--R 4| 11
+--R \| 268435456a c
+--R *
+--R +----------------+3
+--R 8 | 1
+--R 2097152a c |- --------------
+--R 4| 11
+--R \| 268435456a c
+--R atan(-------------------------------)
+--R x
+--R +
+--R 7 3
+--R - 11c x - 7a x
+--R /
+--R 4 8 3 4 2 2
+--R 32c x + 64a c x + 32a c
+--R Type: Union(Expression(Integer),...)
+--E 1132
+
+--S 1133 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R 21log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +----------------+
+--R 2 +-+ | 1 4+-+4+-+3
+--R 2688c \|2 |- -------------- \|a \|c
+--R 4| 11
+--R \| 268435456a c
+--R *
+--R +----------------+3
+--R 8 | 1
+--R log(2097152a c |- -------------- + x)
+--R 4| 11
+--R \| 268435456a c
+--R +
+--R -
+--R +----------------+
+--R 2 +-+ | 1 4+-+4+-+3
+--R 2688c \|2 |- -------------- \|a \|c
+--R 4| 11
+--R \| 268435456a c
+--R *
+--R +----------------+3
+--R 8 | 1
+--R log(- 2097152a c |- -------------- + x)
+--R 4| 11
+--R \| 268435456a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R - 21log(- x\|2 \|a \|c + x \|c + \|a ) - 42atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 42atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +----------------+3
+--R 8 | 1
+--R 2097152a c |- --------------
+--R +----------------+ 4| 11
+--R 2 +-+ | 1 4+-+4+-+3 \| 268435456a c
+--R 5376c \|2 |- -------------- \|a \|c atan(-------------------------------)
+--R 4| 11 x
+--R \| 268435456a c
+--R /
+--R 2 +-+4+-+4+-+3
+--R 128c \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1133
+
+--S 1134 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1134
+
+)clear all
+
+--S 1135 of 1309
+t0:=x^9/(a+c*x^4)^3
+--R
+--R
+--R 9
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1135
+
+--S 1136 of 1309
+r0:=-1/8*x^6/(c*(a+c*x^4)^2)-3/16*x^2/(c^2*(a+c*x^4))+_
+ 3/16*atan(x^2*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a))
+--R
+--R
+--R 2 +-+
+--R 2 8 4 2 x \|c 6 2 +-+ +-+
+--R (3c x + 6a c x + 3a )atan(------) + (- 5c x - 3a x )\|a \|c
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------------------
+--R 4 8 3 4 2 2 +-+ +-+
+--R (16c x + 32a c x + 16a c )\|a \|c
+--R Type: Expression(Integer)
+--E 1136
+
+--S 1137 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 +-----+ 2
+--R 2 8 4 2 (c x - a)\|- a c + 2a c x
+--R (3c x + 6a c x + 3a )log(----------------------------)
+--R 4
+--R c x + a
+--R +
+--R 6 2 +-----+
+--R (- 10c x - 6a x )\|- a c
+--R /
+--R 4 8 3 4 2 2 +-----+
+--R (32c x + 64a c x + 32a c )\|- a c
+--R ,
+--R 2 +---+
+--R 2 8 4 2 x \|a c 6 2 +---+
+--R (3c x + 6a c x + 3a )atan(--------) + (- 5c x - 3a x )\|a c
+--R a
+--R ---------------------------------------------------------------]
+--R 4 8 3 4 2 2 +---+
+--R (16c x + 32a c x + 16a c )\|a c
+--R Type: Union(List(Expression(Integer)),...)
+--E 1137
+
+--S 1138 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R 4 +-----+ 2 2 +-+
+--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c
+--R 3\|a \|c log(----------------------------) - 6\|- a c atan(------)
+--R 4 +-+
+--R c x + a \|a
+--R (4) ------------------------------------------------------------------
+--R 2 +-----+ +-+ +-+
+--R 32c \|- a c \|a \|c
+--R Type: Expression(Integer)
+--E 1138
+
+--S 1139 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1139
+
+--S 1140 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R 2 +---+ 2 +-+
+--R +-+ +-+ x \|a c +---+ x \|c
+--R 3\|a \|c atan(--------) - 3\|a c atan(------)
+--R a +-+
+--R \|a
+--R (6) ---------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 16c \|a \|c \|a c
+--R Type: Expression(Integer)
+--E 1140
+
+--S 1141 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1141
+
+)clear all
+
+--S 1142 of 1309
+t0:=x^8/(a+c*x^4)^3
+--R
+--R
+--R 8
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1142
+
+--S 1143 of 1309
+r0:=-1/8*x^5/(c*(a+c*x^4)^2)-5/32*x/(c^2*(a+c*x^4))-_
+ 5/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(9/4)*sqrt(2))+_
+ 5/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(9/4)*sqrt(2))-_
+ 5/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(3/4)*c^(9/4)*sqrt(2))+_
+ 5/128*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(3/4)*c^(9/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (5c x + 10a c x + 5a )log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 5c x - 10a c x - 5a )log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c + \|a
+--R (10c x + 20a c x + 10a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c - \|a
+--R (10c x + 20a c x + 10a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 5 +-+4+-+3 4+-+
+--R (- 36c x - 20a x)\|2 \|a \|c
+--R /
+--R 4 8 3 4 2 2 +-+4+-+3 4+-+
+--R (128c x + 256a c x + 128a c )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1143
+
+--S 1144 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------------+
+--R 4 8 3 4 2 2 | 1
+--R (160c x + 320a c x + 160a c ) |- -------------
+--R 4| 3 9
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 2 | 1
+--R log(128a c |- ------------- + x)
+--R 4| 3 9
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 4 8 3 4 2 2 | 1
+--R (- 160c x - 320a c x - 160a c ) |- -------------
+--R 4| 3 9
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 2 | 1
+--R log(- 128a c |- ------------- + x)
+--R 4| 3 9
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 4 8 3 4 2 2 | 1
+--R (- 320c x - 640a c x - 320a c ) |- -------------
+--R 4| 3 9
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 2 | 1
+--R 128a c |- -------------
+--R 4| 3 9
+--R \| 268435456a c
+--R atan(-------------------------)
+--R x
+--R +
+--R 5
+--R - 9c x - 5a x
+--R /
+--R 4 8 3 4 2 2
+--R 32c x + 64a c x + 32a c
+--R Type: Union(Expression(Integer),...)
+--E 1144
+
+--S 1145 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R - 5log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +---------------+ +---------------+
+--R 2 +-+ | 1 4+-+3 4+-+ 2 | 1
+--R 640c \|2 |- ------------- \|a \|c log(128a c |- ------------- + x)
+--R 4| 3 9 4| 3 9
+--R \| 268435456a c \| 268435456a c
+--R +
+--R -
+--R +---------------+
+--R 2 +-+ | 1 4+-+3 4+-+
+--R 640c \|2 |- ------------- \|a \|c
+--R 4| 3 9
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 2 | 1
+--R log(- 128a c |- ------------- + x)
+--R 4| 3 9
+--R \| 268435456a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R 5log(- x\|2 \|a \|c + x \|c + \|a ) - 10atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 10atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +---------------+
+--R 2 | 1
+--R 128a c |- -------------
+--R +---------------+ 4| 3 9
+--R 2 +-+ | 1 4+-+3 4+-+ \| 268435456a c
+--R - 1280c \|2 |- ------------- \|a \|c atan(-------------------------)
+--R 4| 3 9 x
+--R \| 268435456a c
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 128c \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1145
+
+--S 1146 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1146
+
+)clear all
+
+--S 1147 of 1309
+t0:=x^7/(a+c*x^4)^3
+--R
+--R
+--R 7
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1147
+
+--S 1148 of 1309
+r0:=1/8*x^8/(a*(a+c*x^4)^2)
+--R
+--R
+--R 1 8
+--R - x
+--R 8
+--R (2) ---------------------
+--R 2 8 2 4 3
+--R a c x + 2a c x + a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1148
+
+--S 1149 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R - 2c x - a
+--R (3) ------------------------
+--R 4 8 3 4 2 2
+--R 8c x + 16a c x + 8a c
+--R Type: Union(Expression(Integer),...)
+--E 1149
+
+--S 1150 of 1309
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - -----
+--R 2
+--R 8a c
+--R Type: Expression(Integer)
+--E 1150
+
+--S 1151 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1151
+
+)clear all
+
+--S 1152 of 1309
+t0:=x^6/(a+c*x^4)^3
+--R
+--R
+--R 6
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1152
+
+--S 1153 of 1309
+r0:=-1/8*x^3/(c*(a+c*x^4)^2)+3/32*x^3/(a*c*(a+c*x^4))-_
+ 3/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*c^(7/4)*sqrt(2))+_
+ 3/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*c^(7/4)*sqrt(2))+_
+ 3/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(5/4)*c^(7/4)*sqrt(2))-3/128*log(a^(1/4)*c^(1/4)*_
+ x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(5/4)*c^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 3c x - 6a c x - 3a )log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (3c x + 6a c x + 3a )log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c + \|a
+--R (6c x + 12a c x + 6a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c - \|a
+--R (6c x + 12a c x + 6a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 7 3 +-+4+-+4+-+3
+--R (12c x - 4a x )\|2 \|a \|c
+--R /
+--R 3 8 2 2 4 3 +-+4+-+4+-+3
+--R (128a c x + 256a c x + 128a c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1153
+
+--S 1154 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------------+
+--R 3 8 2 2 4 3 | 1
+--R (96a c x + 192a c x + 96a c) |- -------------
+--R 4| 5 7
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 4 5 | 1
+--R log(2097152a c |- ------------- + x)
+--R 4| 5 7
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 96a c x - 192a c x - 96a c) |- -------------
+--R 4| 5 7
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 4 5 | 1
+--R log(- 2097152a c |- ------------- + x)
+--R 4| 5 7
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 3 8 2 2 4 3 | 1
+--R (192a c x + 384a c x + 192a c) |- -------------
+--R 4| 5 7
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 4 5 | 1
+--R 2097152a c |- -------------
+--R 4| 5 7
+--R \| 268435456a c
+--R atan(------------------------------)
+--R x
+--R +
+--R 7 3
+--R 3c x - a x
+--R /
+--R 3 8 2 2 4 3
+--R 32a c x + 64a c x + 32a c
+--R Type: Union(Expression(Integer),...)
+--E 1154
+
+--S 1155 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R 3log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +---------------+
+--R +-+ | 1 4+-+4+-+3
+--R 384a c\|2 |- ------------- \|a \|c
+--R 4| 5 7
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 4 5 | 1
+--R log(2097152a c |- ------------- + x)
+--R 4| 5 7
+--R \| 268435456a c
+--R +
+--R -
+--R +---------------+
+--R +-+ | 1 4+-+4+-+3
+--R 384a c\|2 |- ------------- \|a \|c
+--R 4| 5 7
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 4 5 | 1
+--R log(- 2097152a c |- ------------- + x)
+--R 4| 5 7
+--R \| 268435456a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R - 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 6atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +---------------+3
+--R 4 5 | 1
+--R 2097152a c |- -------------
+--R +---------------+ 4| 5 7
+--R +-+ | 1 4+-+4+-+3 \| 268435456a c
+--R 768a c\|2 |- ------------- \|a \|c atan(------------------------------)
+--R 4| 5 7 x
+--R \| 268435456a c
+--R /
+--R +-+4+-+4+-+3
+--R 128a c\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1155
+
+--S 1156 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1156
+
+)clear all
+
+--S 1157 of 1309
+t0:=x^5/(a+c*x^4)^3
+--R
+--R
+--R 5
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1157
+
+--S 1158 of 1309
+r0:=-1/8*x^2/(c*(a+c*x^4)^2)+1/16*x^2/(a*c*(a+c*x^4))+_
+ 1/16*atan(x^2*sqrt(c)/sqrt(a))/(a^(3/2)*c^(3/2))
+--R
+--R
+--R 2 +-+
+--R 2 8 4 2 x \|c 6 2 +-+ +-+
+--R (c x + 2a c x + a )atan(------) + (c x - a x )\|a \|c
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------------
+--R 3 8 2 2 4 3 +-+ +-+
+--R (16a c x + 32a c x + 16a c)\|a \|c
+--R Type: Expression(Integer)
+--E 1158
+
+--S 1159 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 +-----+ 2
+--R 2 8 4 2 (c x - a)\|- a c + 2a c x
+--R (c x + 2a c x + a )log(----------------------------)
+--R 4
+--R c x + a
+--R +
+--R 6 2 +-----+
+--R (2c x - 2a x )\|- a c
+--R /
+--R 3 8 2 2 4 3 +-----+
+--R (32a c x + 64a c x + 32a c)\|- a c
+--R ,
+--R 2 +---+
+--R 2 8 4 2 x \|a c 6 2 +---+
+--R (c x + 2a c x + a )atan(--------) + (c x - a x )\|a c
+--R a
+--R ---------------------------------------------------------]
+--R 3 8 2 2 4 3 +---+
+--R (16a c x + 32a c x + 16a c)\|a c
+--R Type: Union(List(Expression(Integer)),...)
+--E 1159
+
+--S 1160 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R 4 +-----+ 2 2 +-+
+--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c
+--R \|a \|c log(----------------------------) - 2\|- a c atan(------)
+--R 4 +-+
+--R c x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 32a c\|- a c \|a \|c
+--R Type: Expression(Integer)
+--E 1160
+
+--S 1161 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1161
+
+--S 1162 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R 2 +---+ 2 +-+
+--R +-+ +-+ x \|a c +---+ x \|c
+--R \|a \|c atan(--------) - \|a c atan(------)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 16a c\|a \|c \|a c
+--R Type: Expression(Integer)
+--E 1162
+
+--S 1163 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1163
+
+)clear all
+
+--S 1164 of 1309
+t0:=x^4/(a+c*x^4)^3
+--R
+--R
+--R 4
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1164
+
+--S 1165 of 1309
+r0:=-1/8*x/(c*(a+c*x^4)^2)+1/32*x/(a*c*(a+c*x^4))-_
+ 3/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(7/4)*c^(5/4)*sqrt(2))+_
+ 3/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(7/4)*c^(5/4)*sqrt(2))-_
+ 3/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(7/4)*c^(5/4)*sqrt(2))+3/128*log(a^(1/4)*_
+ c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(7/4)*c^(5/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (3c x + 6a c x + 3a )log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 3c x - 6a c x - 3a )log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c + \|a
+--R (6c x + 12a c x + 6a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c - \|a
+--R (6c x + 12a c x + 6a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 5 +-+4+-+3 4+-+
+--R (4c x - 12a x)\|2 \|a \|c
+--R /
+--R 3 8 2 2 4 3 +-+4+-+3 4+-+
+--R (128a c x + 256a c x + 128a c)\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1165
+
+--S 1166 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------------+
+--R 3 8 2 2 4 3 | 1
+--R (96a c x + 192a c x + 96a c) |- -------------
+--R 4| 7 5
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 2 | 1
+--R log(128a c |- ------------- + x)
+--R 4| 7 5
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 96a c x - 192a c x - 96a c) |- -------------
+--R 4| 7 5
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 2 | 1
+--R log(- 128a c |- ------------- + x)
+--R 4| 7 5
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 192a c x - 384a c x - 192a c) |- -------------
+--R 4| 7 5
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 2 | 1
+--R 128a c |- -------------
+--R 4| 7 5
+--R \| 268435456a c
+--R atan(------------------------)
+--R x
+--R +
+--R 5
+--R c x - 3a x
+--R /
+--R 3 8 2 2 4 3
+--R 32a c x + 64a c x + 32a c
+--R Type: Union(Expression(Integer),...)
+--E 1166
+
+--S 1167 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R - 3log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +---------------+ +---------------+
+--R +-+ | 1 4+-+3 4+-+ 2 | 1
+--R 384a c\|2 |- ------------- \|a \|c log(128a c |- ------------- + x)
+--R 4| 7 5 4| 7 5
+--R \| 268435456a c \| 268435456a c
+--R +
+--R -
+--R +---------------+
+--R +-+ | 1 4+-+3 4+-+
+--R 384a c\|2 |- ------------- \|a \|c
+--R 4| 7 5
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 2 | 1
+--R log(- 128a c |- ------------- + x)
+--R 4| 7 5
+--R \| 268435456a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 6atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +---------------+
+--R 2 | 1
+--R 128a c |- -------------
+--R +---------------+ 4| 7 5
+--R +-+ | 1 4+-+3 4+-+ \| 268435456a c
+--R - 768a c\|2 |- ------------- \|a \|c atan(------------------------)
+--R 4| 7 5 x
+--R \| 268435456a c
+--R /
+--R +-+4+-+3 4+-+
+--R 128a c\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1167
+
+--S 1168 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1168
+
+)clear all
+
+--S 1169 of 1309
+t0:=x^3/(a+c*x^4)^3
+--R
+--R
+--R 3
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1169
+
+--S 1170 of 1309
+r0:=(-1/8)/(c*(a+c*x^4)^2)
+--R
+--R
+--R 1
+--R -
+--R 8
+--R (2) - --------------------
+--R 3 8 2 4 2
+--R c x + 2a c x + a c
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1170
+
+--S 1171 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - -----------------------
+--R 3 8 2 4 2
+--R 8c x + 16a c x + 8a c
+--R Type: Union(Expression(Integer),...)
+--E 1171
+
+--S 1172 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1172
+
+--S 1173 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1173
+
+)clear all
+
+--S 1174 of 1309
+t0:=x^2/(a+c*x^4)^3
+--R
+--R
+--R 2
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1174
+
+--S 1175 of 1309
+r0:=1/8*x^3/(a*(a+c*x^4)^2)+5/32*x^3/(a^2*(a+c*x^4))-_
+ 5/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*c^(3/4)*sqrt(2))+_
+ 5/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*c^(3/4)*sqrt(2))+_
+ 5/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(9/4)*c^(3/4)*sqrt(2))-5/128*log(a^(1/4)*_
+ c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(9/4)*c^(3/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 5c x - 10a c x - 5a )log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (5c x + 10a c x + 5a )log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c + \|a
+--R (10c x + 20a c x + 10a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c - \|a
+--R (10c x + 20a c x + 10a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 7 3 +-+4+-+4+-+3
+--R (20c x + 36a x )\|2 \|a \|c
+--R /
+--R 2 2 8 3 4 4 +-+4+-+4+-+3
+--R (128a c x + 256a c x + 128a )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1175
+
+--S 1176 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------------+
+--R 2 2 8 3 4 4 | 1
+--R (160a c x + 320a c x + 160a ) |- -------------
+--R 4| 9 3
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 7 2 | 1
+--R log(2097152a c |- ------------- + x)
+--R 4| 9 3
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 160a c x - 320a c x - 160a ) |- -------------
+--R 4| 9 3
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 7 2 | 1
+--R log(- 2097152a c |- ------------- + x)
+--R 4| 9 3
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 2 2 8 3 4 4 | 1
+--R (320a c x + 640a c x + 320a ) |- -------------
+--R 4| 9 3
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 7 2 | 1
+--R 2097152a c |- -------------
+--R 4| 9 3
+--R \| 268435456a c
+--R atan(------------------------------)
+--R x
+--R +
+--R 7 3
+--R 5c x + 9a x
+--R /
+--R 2 2 8 3 4 4
+--R 32a c x + 64a c x + 32a
+--R Type: Union(Expression(Integer),...)
+--E 1176
+
+--S 1177 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R 5log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +---------------+
+--R 2 +-+ | 1 4+-+4+-+3
+--R 640a \|2 |- ------------- \|a \|c
+--R 4| 9 3
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 7 2 | 1
+--R log(2097152a c |- ------------- + x)
+--R 4| 9 3
+--R \| 268435456a c
+--R +
+--R -
+--R +---------------+
+--R 2 +-+ | 1 4+-+4+-+3
+--R 640a \|2 |- ------------- \|a \|c
+--R 4| 9 3
+--R \| 268435456a c
+--R *
+--R +---------------+3
+--R 7 2 | 1
+--R log(- 2097152a c |- ------------- + x)
+--R 4| 9 3
+--R \| 268435456a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R - 5log(- x\|2 \|a \|c + x \|c + \|a ) - 10atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 10atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +---------------+3
+--R 7 2 | 1
+--R 2097152a c |- -------------
+--R +---------------+ 4| 9 3
+--R 2 +-+ | 1 4+-+4+-+3 \| 268435456a c
+--R 1280a \|2 |- ------------- \|a \|c atan(------------------------------)
+--R 4| 9 3 x
+--R \| 268435456a c
+--R /
+--R 2 +-+4+-+4+-+3
+--R 128a \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1177
+
+--S 1178 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1178
+
+)clear all
+
+--S 1179 of 1309
+t0:=x/(a+c*x^4)^3
+--R
+--R
+--R x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1179
+
+--S 1180 of 1309
+r0:=1/8*x^2/(a*(a+c*x^4)^2)+3/16*x^2/(a^2*(a+c*x^4))+_
+ 3/16*atan(x^2*sqrt(c)/sqrt(a))/(a^(5/2)*sqrt(c))
+--R
+--R
+--R 2 +-+
+--R 2 8 4 2 x \|c 6 2 +-+ +-+
+--R (3c x + 6a c x + 3a )atan(------) + (3c x + 5a x )\|a \|c
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------
+--R 2 2 8 3 4 4 +-+ +-+
+--R (16a c x + 32a c x + 16a )\|a \|c
+--R Type: Expression(Integer)
+--E 1180
+
+--S 1181 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 +-----+ 2
+--R 2 8 4 2 (c x - a)\|- a c + 2a c x
+--R (3c x + 6a c x + 3a )log(----------------------------)
+--R 4
+--R c x + a
+--R +
+--R 6 2 +-----+
+--R (6c x + 10a x )\|- a c
+--R /
+--R 2 2 8 3 4 4 +-----+
+--R (32a c x + 64a c x + 32a )\|- a c
+--R ,
+--R 2 +---+
+--R 2 8 4 2 x \|a c 6 2 +---+
+--R (3c x + 6a c x + 3a )atan(--------) + (3c x + 5a x )\|a c
+--R a
+--R -------------------------------------------------------------]
+--R 2 2 8 3 4 4 +---+
+--R (16a c x + 32a c x + 16a )\|a c
+--R Type: Union(List(Expression(Integer)),...)
+--E 1181
+
+--S 1182 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R 4 +-----+ 2 2 +-+
+--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c
+--R 3\|a \|c log(----------------------------) - 6\|- a c atan(------)
+--R 4 +-+
+--R c x + a \|a
+--R (4) ------------------------------------------------------------------
+--R 2 +-----+ +-+ +-+
+--R 32a \|- a c \|a \|c
+--R Type: Expression(Integer)
+--E 1182
+
+--S 1183 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1183
+
+--S 1184 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R 2 +---+ 2 +-+
+--R +-+ +-+ x \|a c +---+ x \|c
+--R 3\|a \|c atan(--------) - 3\|a c atan(------)
+--R a +-+
+--R \|a
+--R (6) ---------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 16a \|a \|c \|a c
+--R Type: Expression(Integer)
+--E 1184
+
+--S 1185 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1185
+
+)clear all
+
+--S 1186 of 1309
+t0:=1/(a+c*x^4)^3
+--R
+--R
+--R 1
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1186
+
+--S 1187 of 1309
+r0:=1/8*x/(a*(a+c*x^4)^2)+7/32*x/(a^2*(a+c*x^4))-_
+ 21/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*c^(1/4)*sqrt(2))+_
+ 21/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*c^(1/4)*sqrt(2))-_
+ 21/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(11/4)*c^(1/4)*sqrt(2))+_
+ 21/128*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(11/4)*c^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (21c x + 42a c x + 21a )log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 21c x - 42a c x - 21a )log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c + \|a
+--R (42c x + 84a c x + 42a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 8 4 2 x\|2 \|c - \|a
+--R (42c x + 84a c x + 42a )atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 5 +-+4+-+3 4+-+
+--R (28c x + 44a x)\|2 \|a \|c
+--R /
+--R 2 2 8 3 4 4 +-+4+-+3 4+-+
+--R (128a c x + 256a c x + 128a )\|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1187
+
+--S 1188 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------------+
+--R 2 2 8 3 4 4 | 1
+--R (672a c x + 1344a c x + 672a ) |- -------------
+--R 4| 11
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 3 | 1
+--R log(128a |- ------------- + x)
+--R 4| 11
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 672a c x - 1344a c x - 672a ) |- -------------
+--R 4| 11
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 3 | 1
+--R log(- 128a |- ------------- + x)
+--R 4| 11
+--R \| 268435456a c
+--R +
+--R +---------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 1344a c x - 2688a c x - 1344a ) |- -------------
+--R 4| 11
+--R \| 268435456a c
+--R *
+--R +---------------+
+--R 3 | 1
+--R 128a |- -------------
+--R 4| 11
+--R \| 268435456a c
+--R atan(-----------------------)
+--R x
+--R +
+--R 5
+--R 7c x + 11a x
+--R /
+--R 2 2 8 3 4 4
+--R 32a c x + 64a c x + 32a
+--R Type: Union(Expression(Integer),...)
+--E 1188
+
+--S 1189 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+-+ 2 +-+ +-+
+--R - 21log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +---------------+ +---------------+
+--R 2 +-+ | 1 4+-+3 4+-+ 3 | 1
+--R 2688a \|2 |- ------------- \|a \|c log(128a |- ------------- + x)
+--R 4| 11 4| 11
+--R \| 268435456a c \| 268435456a c
+--R +
+--R +---------------+ +---------------+
+--R 2 +-+ | 1 4+-+3 4+-+ 3 | 1
+--R - 2688a \|2 |- ------------- \|a \|c log(- 128a |- ------------- + x)
+--R 4| 11 4| 11
+--R \| 268435456a c \| 268435456a c
+--R +
+--R +-+4+-+ 4+-+
+--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a
+--R 21log(- x\|2 \|a \|c + x \|c + \|a ) - 42atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R x\|2 \|c - \|a
+--R - 42atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +---------------+
+--R 3 | 1
+--R 128a |- -------------
+--R +---------------+ 4| 11
+--R 2 +-+ | 1 4+-+3 4+-+ \| 268435456a c
+--R - 5376a \|2 |- ------------- \|a \|c atan(-----------------------)
+--R 4| 11 x
+--R \| 268435456a c
+--R /
+--R 2 +-+4+-+3 4+-+
+--R 128a \|2 \|a \|c
+--R Type: Expression(Integer)
+--E 1189
+
+--S 1190 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1190
+
+)clear all
+
+--S 1191 of 1309
+t0:=1/(x*(a+c*x^4)^3)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 13 2 9 2 5 3
+--R c x + 3a c x + 3a c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1191
+
+--S 1192 of 1309
+r0:=1/8/(a*(a+c*x^4)^2)+1/4/(a^2*(a+c*x^4))+log(x)/a^3-1/4*log(a+c*x^4)/a^3
+--R
+--R
+--R (2)
+--R 2 8 4 2 4 2 8 4 2
+--R (- 2c x - 4a c x - 2a )log(c x + a) + (8c x + 16a c x + 8a )log(x)
+--R +
+--R 4 2
+--R 2a c x + 3a
+--R /
+--R 3 2 8 4 4 5
+--R 8a c x + 16a c x + 8a
+--R Type: Expression(Integer)
+--E 1192
+
+--S 1193 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 4 2 4 2 8 4 2
+--R (- 2c x - 4a c x - 2a )log(c x + a) + (8c x + 16a c x + 8a )log(x)
+--R +
+--R 4 2
+--R 2a c x + 3a
+--R /
+--R 3 2 8 4 4 5
+--R 8a c x + 16a c x + 8a
+--R Type: Union(Expression(Integer),...)
+--E 1193
+
+--S 1194 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1194
+
+--S 1195 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1195
+
+)clear all
+
+--S 1196 of 1309
+t0:=1/(x^2*(a+c*x^4)^3)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 3 14 2 10 2 6 3 2
+--R c x + 3a c x + 3a c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1196
+
+--S 1197 of 1309
+r0:=(-45/32)/(a^3*x)+1/8/(a*x*(a+c*x^4)^2)+9/32/(a^2*x*(a+c*x^4))+_
+ 45/64*c^(1/4)*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(13/4)*sqrt(2))-_
+ 45/64*c^(1/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(13/4)*sqrt(2))-_
+ 45/128*c^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(13/4)*sqrt(2))+_
+ 45/128*c^(1/4)*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(13/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 9 5 2 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R (45c x + 90a c x + 45a x)\|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 2 9 5 2 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R (- 45c x - 90a c x - 45a x)\|c log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 9 5 2 4+-+ x\|2 \|c + \|a
+--R (- 90c x - 180a c x - 90a x)\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 9 5 2 4+-+ x\|2 \|c - \|a
+--R (- 90c x - 180a c x - 90a x)\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 8 4 2 +-+4+-+
+--R (- 180c x - 324a c x - 128a )\|2 \|a
+--R /
+--R 3 2 9 4 5 5 +-+4+-+
+--R (128a c x + 256a c x + 128a x)\|2 \|a
+--R Type: Expression(Integer)
+--E 1197
+
+--S 1198 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R 3 2 9 4 5 5 | 4100625c
+--R (- 32a c x - 64a c x - 32a x) |- ------------
+--R 4| 13
+--R \| 268435456a
+--R *
+--R +--------------+3
+--R 10 | 4100625c
+--R log(2097152a |- ------------ + 91125c x)
+--R 4| 13
+--R \| 268435456a
+--R +
+--R +--------------+
+--R 3 2 9 4 5 5 | 4100625c
+--R (32a c x + 64a c x + 32a x) |- ------------
+--R 4| 13
+--R \| 268435456a
+--R *
+--R +--------------+3
+--R 10 | 4100625c
+--R log(- 2097152a |- ------------ + 91125c x)
+--R 4| 13
+--R \| 268435456a
+--R +
+--R +--------------+
+--R 3 2 9 4 5 5 | 4100625c
+--R (- 64a c x - 128a c x - 64a x) |- ------------
+--R 4| 13
+--R \| 268435456a
+--R *
+--R +--------------+3
+--R 10 | 4100625c
+--R 2097152a |- ------------
+--R 4| 13
+--R \| 268435456a
+--R atan(----------------------------)
+--R 91125c x
+--R +
+--R 2 8 4 2
+--R - 45c x - 81a c x - 32a
+--R /
+--R 3 2 9 4 5 5
+--R 32a c x + 64a c x + 32a x
+--R Type: Union(Expression(Integer),...)
+--E 1198
+
+--S 1199 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+
+--R - 45\|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R -
+--R +--------------+
+--R 3 +-+ | 4100625c 4+-+
+--R 128a \|2 |- ------------ \|a
+--R 4| 13
+--R \| 268435456a
+--R *
+--R +--------------+3
+--R 10 | 4100625c
+--R log(2097152a |- ------------ + 91125c x)
+--R 4| 13
+--R \| 268435456a
+--R +
+--R +--------------+
+--R 3 +-+ | 4100625c 4+-+
+--R 128a \|2 |- ------------ \|a
+--R 4| 13
+--R \| 268435456a
+--R *
+--R +--------------+3
+--R 10 | 4100625c
+--R log(- 2097152a |- ------------ + 91125c x)
+--R 4| 13
+--R \| 268435456a
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a
+--R 45\|c log(- x\|2 \|a \|c + x \|c + \|a ) + 90\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 4+-+ x\|2 \|c - \|a
+--R 90\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------------+3
+--R 10 | 4100625c
+--R 2097152a |- ------------
+--R +--------------+ 4| 13
+--R 3 +-+ | 4100625c 4+-+ \| 268435456a
+--R - 256a \|2 |- ------------ \|a atan(----------------------------)
+--R 4| 13 91125c x
+--R \| 268435456a
+--R /
+--R 3 +-+4+-+
+--R 128a \|2 \|a
+--R Type: Expression(Integer)
+--E 1199
+
+--S 1200 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1200
+
+)clear all
+
+--S 1201 of 1309
+t0:=1/(x^3*(a+c*x^4)^3)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 3 15 2 11 2 7 3 3
+--R c x + 3a c x + 3a c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1201
+
+--S 1202 of 1309
+r0:=(-15/16)/(a^3*x^2)+1/8/(a*x^2*(a+c*x^4)^2)+_
+ 5/16/(a^2*x^2*(a+c*x^4))-15/16*atan(x^2*sqrt(c)/sqrt(a))*sqrt(c)/a^(7/2)
+--R
+--R
+--R (2)
+--R 2 +-+
+--R 2 10 6 2 2 +-+ x \|c
+--R (- 15c x - 30a c x - 15a x )\|c atan(------)
+--R +-+
+--R \|a
+--R +
+--R 2 8 4 2 +-+
+--R (- 15c x - 25a c x - 8a )\|a
+--R /
+--R 3 2 10 4 6 5 2 +-+
+--R (16a c x + 32a c x + 16a x )\|a
+--R Type: Expression(Integer)
+--E 1202
+
+--S 1203 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 | c 4
+--R +---+ - 2a x |- - + c x - a
+--R 2 10 6 2 2 | c \| a
+--R (15c x + 30a c x + 15a x ) |- - log(------------------------)
+--R \| a 4
+--R c x + a
+--R +
+--R 2 8 4 2
+--R - 30c x - 50a c x - 16a
+--R /
+--R 3 2 10 4 6 5 2
+--R 32a c x + 64a c x + 32a x
+--R ,
+--R +-+
+--R |c
+--R +-+ a |-
+--R 2 10 6 2 2 |c \|a 2 8 4 2
+--R (15c x + 30a c x + 15a x ) |- atan(-----) - 15c x - 25a c x - 8a
+--R \|a 2
+--R c x
+--R ----------------------------------------------------------------------]
+--R 3 2 10 4 6 5 2
+--R 16a c x + 32a c x + 16a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1203
+
+--S 1204 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R 2 | c 4
+--R +---+ - 2a x |- - + c x - a 2 +-+
+--R | c +-+ \| a +-+ x \|c
+--R 15 |- - \|a log(------------------------ + 30\|c atan(------)
+--R \| a 4 +-+
+--R c x + a \|a
+--R (4) --------------------------------------------------------------
+--R 3 +-+
+--R 32a \|a
+--R Type: Expression(Integer)
+--E 1204
+
+--S 1205 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1205
+
+--S 1206 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |c
+--R 2 +-+ +-+ a |-
+--R +-+ x \|c +-+ |c \|a
+--R 15\|c atan(------) + 15\|a |- atan(-----)
+--R +-+ \|a 2
+--R \|a c x
+--R (6) ------------------------------------------
+--R 3 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 1206
+
+--S 1207 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1207
+
+)clear all
+
+--S 1208 of 1309
+t0:=1/(x^4*(a+c*x^4)^3)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R 3 16 2 12 2 8 3 4
+--R c x + 3a c x + 3a c x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1208
+
+--S 1209 of 1309
+r0:=(-77/96)/(a^3*x^3)+1/8/(a*x^3*(a+c*x^4)^2)+_
+ 11/32/(a^2*x^3*(a+c*x^4))+77/64*c^(3/4)*atan(1-c^(1/4)*_
+ x*sqrt(2)/a^(1/4))/(a^(15/4)*sqrt(2))-77/64*c^(3/4)*_
+ atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(15/4)*sqrt(2))+_
+ 77/128*c^(3/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_
+ x^2*sqrt(c))/(a^(15/4)*sqrt(2))-77/128*c^(3/4)*_
+ log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(15/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 11 7 2 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R (- 231c x - 462a c x - 231a x )\|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R 2 11 7 2 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R (231c x + 462a c x + 231a x )\|c log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+
+--R 2 11 7 2 3 4+-+3 x\|2 \|c + \|a
+--R (- 462c x - 924a c x - 462a x )\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +-+4+-+ 4+-+
+--R 2 11 7 2 3 4+-+3 x\|2 \|c - \|a
+--R (- 462c x - 924a c x - 462a x )\|c atan(----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 8 4 2 +-+4+-+3
+--R (- 308c x - 484a c x - 128a )\|2 \|a
+--R /
+--R 3 2 11 4 7 5 3 +-+4+-+3
+--R (384a c x + 768a c x + 384a x )\|2 \|a
+--R Type: Expression(Integer)
+--E 1209
+
+--S 1210 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R | 3
+--R 3 2 11 4 7 5 3 | 35153041c
+--R (- 96a c x - 192a c x - 96a x ) |- ------------
+--R 4| 15
+--R \| 268435456a
+--R *
+--R +--------------+
+--R | 3
+--R 4 | 35153041c
+--R log(128a |- ------------ + 77c x)
+--R 4| 15
+--R \| 268435456a
+--R +
+--R +--------------+
+--R | 3
+--R 3 2 11 4 7 5 3 | 35153041c
+--R (96a c x + 192a c x + 96a x ) |- ------------
+--R 4| 15
+--R \| 268435456a
+--R *
+--R +--------------+
+--R | 3
+--R 4 | 35153041c
+--R log(- 128a |- ------------ + 77c x)
+--R 4| 15
+--R \| 268435456a
+--R +
+--R +--------------+
+--R | 3
+--R 3 2 11 4 7 5 3 | 35153041c
+--R (192a c x + 384a c x + 192a x ) |- ------------
+--R 4| 15
+--R \| 268435456a
+--R *
+--R +--------------+
+--R | 3
+--R 4 | 35153041c
+--R 128a |- ------------
+--R 4| 15
+--R \| 268435456a
+--R atan(----------------------)
+--R 77c x
+--R +
+--R 2 8 4 2
+--R - 77c x - 121a c x - 32a
+--R /
+--R 3 2 11 4 7 5 3
+--R 96a c x + 192a c x + 96a x
+--R Type: Union(Expression(Integer),...)
+--E 1210
+
+--S 1211 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R 77\|c log(x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +--------------+ +--------------+
+--R | 3 | 3
+--R 3 +-+ | 35153041c 4+-+3 4 | 35153041c
+--R - 128a \|2 |- ------------ \|a log(128a |- ------------ + 77c x)
+--R 4| 15 4| 15
+--R \| 268435456a \| 268435456a
+--R +
+--R +--------------+ +--------------+
+--R | 3 | 3
+--R 3 +-+ | 35153041c 4+-+3 4 | 35153041c
+--R 128a \|2 |- ------------ \|a log(- 128a |- ------------ + 77c x)
+--R 4| 15 4| 15
+--R \| 268435456a \| 268435456a
+--R +
+--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+
+--R - 77\|c log(- x\|2 \|a \|c + x \|c + \|a )
+--R +
+--R +-+4+-+ 4+-+ +-+4+-+ 4+-+
+--R 4+-+3 x\|2 \|c + \|a 4+-+3 x\|2 \|c - \|a
+--R 154\|c atan(----------------) + 154\|c atan(----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +--------------+
+--R | 3
+--R 4 | 35153041c
+--R +--------------+ 128a |- ------------
+--R | 3 4| 15
+--R 3 +-+ | 35153041c 4+-+3 \| 268435456a
+--R 256a \|2 |- ------------ \|a atan(----------------------)
+--R 4| 15 77c x
+--R \| 268435456a
+--R /
+--R 3 +-+4+-+3
+--R 128a \|2 \|a
+--R Type: Expression(Integer)
+--E 1211
+
+--S 1212 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1212
+
+)clear all
+
+--S 1213 of 1309
+t0:=x^4/(2+3*x^4)
+--R
+--R
+--R 4
+--R x
+--R (1) -------
+--R 4
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 1213
+
+--S 1214 of 1309
+r0:=1/3*x+1/6*atan(1-6^(1/4)*x)/6^(1/4)-1/6*atan(1+6^(1/4)*x)/6^(1/4)+_
+ 1/12*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4)-_
+ 1/12*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4)
+--R
+--R
+--R (2)
+--R 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 2 +-+ +-+
+--R - log(x \|2 \|3 + x \|3 + \|2 ) + log(- x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+-+ 4+-+ 4+-+
+--R - 2atan(x\|6 + 1) - 2atan(x\|6 - 1) + 4x\|6
+--R /
+--R 4+-+
+--R 12\|6
+--R Type: Expression(Integer)
+--E 1214
+
+--S 1215 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 4+--+2 +-+4+--+
+--R - \|2 log(x \|24 + 2x\|2 \|24 + 4)
+--R +
+--R +-+ 2 4+--+2 +-+4+--+ +-+ 2
+--R \|2 log(x \|24 - 2x\|2 \|24 + 4) + 2\|2 atan(--------------)
+--R +-+4+--+
+--R x\|2 \|24 - 2
+--R +
+--R +-+ 2 4+--+
+--R 2\|2 atan(--------------) + 4x\|24
+--R +-+4+--+
+--R x\|2 \|24 + 2
+--R /
+--R 4+--+
+--R 12\|24
+--R Type: Union(Expression(Integer),...)
+--E 1215
+
+--S 1216 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+ 2 4+--+2 +-+4+--+
+--R - \|2 \|6 log(x \|24 + 2x\|2 \|24 + 4)
+--R +
+--R +-+4+-+ 2 4+--+2 +-+4+--+
+--R \|2 \|6 log(x \|24 - 2x\|2 \|24 + 4)
+--R +
+--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+
+--R \|24 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ 4+--+ 4+-+
+--R - \|24 log(- x \|2 \|3 + x \|3 + \|2 ) + 2\|24 atan(x\|6 + 1)
+--R +
+--R 4+--+ 4+-+ +-+4+-+ 2
+--R 2\|24 atan(x\|6 - 1) + 2\|2 \|6 atan(--------------)
+--R +-+4+--+
+--R x\|2 \|24 - 2
+--R +
+--R +-+4+-+ 2
+--R 2\|2 \|6 atan(--------------)
+--R +-+4+--+
+--R x\|2 \|24 + 2
+--R /
+--R 4+-+4+--+
+--R 12\|6 \|24
+--R Type: Expression(Integer)
+--E 1216
+
+--S 1217 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 4+-+2 4+-+2 2 +-+ +-+ 4 4+-+2
+--R (- 4x \|2 \|3 + 4x \|2 \|3 + 6x + 4)\|6
+--R +
+--R 6 2 4+-+3 +-+ 4 +-+4+-+3 4+-+4+-+ 4 4+-+2 4+-+2
+--R ((3x + 2x )\|2 \|3 + (- 3x - 2)\|2 \|2 )\|3 \|6 + 12x \|2 \|3
+--R +
+--R 4 +-+ +-+ 6 2
+--R - 12x \|2 \|3 - 18x - 12x
+--R /
+--R 6 2 4+-+2 4+-+2 6 2 +-+ +-+ 8 4 4+-+2
+--R ((36x + 24x )\|2 \|3 + (- 36x - 24x )\|2 \|3 - 54x - 72x - 24)\|6
+--R Type: Expression(Integer)
+--E 1217
+
+)clear all
+
+--S 1218 of 1309
+t0:=x^3/(2+3*x^4)
+--R
+--R
+--R 3
+--R x
+--R (1) -------
+--R 4
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 1218
+
+--S 1219 of 1309
+r0:=1/12*log(2+3*x^4)
+--R
+--R
+--R 4
+--R log(3x + 2)
+--R (2) ------------
+--R 12
+--R Type: Expression(Integer)
+--E 1219
+
+--S 1220 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R log(3x + 2)
+--R (3) ------------
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 1220
+
+--S 1221 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1221
+
+--S 1222 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1222
+
+)clear all
+
+--S 1223 of 1309
+t0:=x^2/(2+3*x^4)
+--R
+--R
+--R 2
+--R x
+--R (1) -------
+--R 4
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 1223
+
+--S 1224 of 1309
+r0:=-1/2*atan(1-6^(1/4)*x)/6^(3/4)+1/2*atan(1+6^(1/4)*x)/6^(3/4)+_
+ 1/4*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4)-_
+ 1/4*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4)
+--R
+--R
+--R (2)
+--R 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 2 +-+ +-+
+--R - log(x \|2 \|3 + x \|3 + \|2 ) + log(- x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+-+ 4+-+
+--R 2atan(x\|6 + 1) + 2atan(x\|6 - 1)
+--R /
+--R 4+-+3
+--R 4\|6
+--R Type: Expression(Integer)
+--E 1224
+
+--S 1225 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+4+--+3 2 4+--+2
+--R - \|2 log(x\|2 \|54 + 3x \|54 + 18)
+--R +
+--R +-+ +-+4+--+3 2 4+--+2 +-+ 18
+--R \|2 log(- x\|2 \|54 + 3x \|54 + 18) - 2\|2 atan(----------------)
+--R +-+4+--+3
+--R x\|2 \|54 - 18
+--R +
+--R +-+ 18
+--R - 2\|2 atan(----------------)
+--R +-+4+--+3
+--R x\|2 \|54 + 18
+--R /
+--R 4+--+
+--R 8\|54
+--R Type: Union(Expression(Integer),...)
+--E 1225
+
+--S 1226 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+3 +-+4+--+3 2 4+--+2
+--R - \|2 \|6 log(x\|2 \|54 + 3x \|54 + 18)
+--R +
+--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+
+--R 2\|54 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+
+--R - 2\|54 log(- x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R +-+4+-+3 +-+4+--+3 2 4+--+2 4+--+ 4+-+
+--R \|2 \|6 log(- x\|2 \|54 + 3x \|54 + 18) - 4\|54 atan(x\|6 + 1)
+--R +
+--R 4+--+ 4+-+ +-+4+-+3 18
+--R - 4\|54 atan(x\|6 - 1) - 2\|2 \|6 atan(----------------)
+--R +-+4+--+3
+--R x\|2 \|54 - 18
+--R +
+--R +-+4+-+3 18
+--R - 2\|2 \|6 atan(----------------)
+--R +-+4+--+3
+--R x\|2 \|54 + 18
+--R /
+--R 4+-+3 4+--+
+--R 8\|6 \|54
+--R Type: Expression(Integer)
+--E 1226
+
+--S 1227 of 1309
+d0:=D(normalize(m0),x)
+--R
+--R
+--R 2 4+-+3 4+-+3 4+-+4+-+ 4+-+3 2 4+-+2
+--R (- x \|2 \|3 + 2\|2 \|3 )\|6 + 6x \|6 - 12
+--R (5) -------------------------------------------------
+--R 4 4+-+2
+--R (36x + 24)\|6
+--R Type: Expression(Integer)
+--E 1227
+
+)clear all
+
+--S 1228 of 1309
+t0:=x/(2+3*x^4)
+--R
+--R
+--R x
+--R (1) -------
+--R 4
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 1228
+
+--S 1229 of 1309
+r0:=1/2*atan(x^2*sqrt(3/2))/sqrt(6)
+--R
+--R
+--R 2 +-+
+--R x \|3
+--R atan(------)
+--R +-+
+--R \|2
+--R (2) ------------
+--R +-+
+--R 2\|6
+--R Type: Expression(Integer)
+--E 1229
+
+--S 1230 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R x \|6
+--R atan(------)
+--R 2
+--R (3) ------------
+--R +-+
+--R 2\|6
+--R Type: Union(Expression(Integer),...)
+--E 1230
+
+--S 1231 of 1309
+m0:=a0-r0
+--R
+--R
+--R 2 +-+ 2 +-+
+--R x \|6 x \|3
+--R atan(------) - atan(------)
+--R 2 +-+
+--R \|2
+--R (4) ---------------------------
+--R +-+
+--R 2\|6
+--R Type: Expression(Integer)
+--E 1231
+
+--S 1232 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R +-+ +-+ +-+
+--R - x\|2 \|3 \|6 + 6x
+--R (5) --------------------
+--R 4
+--R 18x + 12
+--R Type: Expression(Integer)
+--E 1232
+
+)clear all
+
+--S 1233 of 1309
+t0:=1/(2+3*x^4)
+--R
+--R
+--R 1
+--R (1) -------
+--R 4
+--R 3x + 2
+--R Type: Fraction(Polynomial(Integer))
+--E 1233
+
+--S 1234 of 1309
+r0:=-1/4*atan(1-6^(1/4)*x)/6^(1/4)+1/4*atan(1+6^(1/4)*x)/6^(1/4)-_
+ 1/8*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4)+_
+ 1/8*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4)
+--R
+--R
+--R (2)
+--R 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 2 +-+ +-+
+--R log(x \|2 \|3 + x \|3 + \|2 ) - log(- x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+-+ 4+-+
+--R 2atan(x\|6 + 1) + 2atan(x\|6 - 1)
+--R /
+--R 4+-+
+--R 8\|6
+--R Type: Expression(Integer)
+--E 1234
+
+--S 1235 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 4+--+2 +-+4+--+ +-+ 2 4+--+2 +-+4+--+
+--R \|2 log(x \|24 + 2x\|2 \|24 + 4) - \|2 log(x \|24 - 2x\|2 \|24 + 4)
+--R +
+--R +-+ 2 +-+ 2
+--R - 2\|2 atan(--------------) - 2\|2 atan(--------------)
+--R +-+4+--+ +-+4+--+
+--R x\|2 \|24 - 2 x\|2 \|24 + 2
+--R /
+--R 4+--+
+--R 8\|24
+--R Type: Union(Expression(Integer),...)
+--E 1235
+
+--S 1236 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+ 2 4+--+2 +-+4+--+
+--R \|2 \|6 log(x \|24 + 2x\|2 \|24 + 4)
+--R +
+--R +-+4+-+ 2 4+--+2 +-+4+--+
+--R - \|2 \|6 log(x \|24 - 2x\|2 \|24 + 4)
+--R +
+--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+
+--R - \|24 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ 4+--+ 4+-+
+--R \|24 log(- x \|2 \|3 + x \|3 + \|2 ) - 2\|24 atan(x\|6 + 1)
+--R +
+--R 4+--+ 4+-+ +-+4+-+ 2
+--R - 2\|24 atan(x\|6 - 1) - 2\|2 \|6 atan(--------------)
+--R +-+4+--+
+--R x\|2 \|24 - 2
+--R +
+--R +-+4+-+ 2
+--R - 2\|2 \|6 atan(--------------)
+--R +-+4+--+
+--R x\|2 \|24 + 2
+--R /
+--R 4+-+4+--+
+--R 8\|6 \|24
+--R Type: Expression(Integer)
+--E 1236
+
+--S 1237 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 4+-+2 4+-+2 2 +-+ +-+ 4 4+-+2
+--R (4x \|2 \|3 - 4x \|2 \|3 - 6x - 4)\|6
+--R +
+--R 6 2 4+-+3 +-+ 4 +-+4+-+3 4+-+4+-+ 4 4+-+2 4+-+2
+--R ((- 3x - 2x )\|2 \|3 + (3x + 2)\|2 \|2 )\|3 \|6 - 12x \|2 \|3
+--R +
+--R 4 +-+ +-+ 6 2
+--R 12x \|2 \|3 + 18x + 12x
+--R /
+--R 6 2 4+-+2 4+-+2 6 2 +-+ +-+ 8 4 4+-+2
+--R ((24x + 16x )\|2 \|3 + (- 24x - 16x )\|2 \|3 - 36x - 48x - 16)\|6
+--R Type: Expression(Integer)
+--E 1237
+
+)clear all
+
+--S 1238 of 1309
+t0:=1/(x*(2+3*x^4))
+--R
+--R
+--R 1
+--R (1) --------
+--R 5
+--R 3x + 2x
+--R Type: Fraction(Polynomial(Integer))
+--E 1238
+
+--S 1239 of 1309
+r0:=-1/4*atanh(1+3*x^4)
+--R
+--R
+--R 4
+--R atanh(3x + 1)
+--R (2) - --------------
+--R 4
+--R Type: Expression(Integer)
+--E 1239
+
+--S 1240 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R - log(3x + 2) + 4log(x)
+--R (3) ------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 1240
+
+--S 1241 of 1309
+m0:=a0-r0
+--R
+--R
+--R 4 4
+--R - log(3x + 2) + 4log(x) + 2atanh(3x + 1)
+--R (4) ------------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 1241
+
+--S 1242 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1242
+
+)clear all
+
+--S 1243 of 1309
+t0:=1/(x^2*(2+3*x^4))
+--R
+--R
+--R 1
+--R (1) ---------
+--R 6 2
+--R 3x + 2x
+--R Type: Fraction(Polynomial(Integer))
+--E 1243
+
+--S 1244 of 1309
+r0:=(-1/2)/x+1/4*3^(1/4)*atan(1-6^(1/4)*x)/2^(3/4)-_
+ 1/4*3^(1/4)*atan(1+6^(1/4)*x)/2^(3/4)-1/8*3^(1/4)*_
+ log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4)+_
+ 1/8*3^(1/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4)
+--R
+--R
+--R (2)
+--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+
+--R x\|3 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ 4+-+ 4+-+
+--R - x\|3 log(- x \|2 \|3 + x \|3 + \|2 ) - 2x\|3 atan(x\|6 + 1)
+--R +
+--R 4+-+ 4+-+ 4+-+3
+--R - 2x\|3 atan(x\|6 - 1) - 4\|2
+--R /
+--R 4+-+3
+--R 8x \|2
+--R Type: Expression(Integer)
+--E 1244
+
+--S 1245 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2
+--R x\|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 )
+--R +
+--R +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2
+--R - x\|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 )
+--R +
+--R 4+-+3
+--R +-+4+-+ 2\|3
+--R - 2x\|2 \|3 atan(--------------------)
+--R 4+-+3 +-+4+-+3
+--R 2\|3 - 3x\|2 \|2
+--R +
+--R 4+-+3
+--R +-+4+-+ 2\|3 4+-+
+--R 2x\|2 \|3 atan(--------------------) - 8\|2
+--R 4+-+3 +-+4+-+3
+--R 2\|3 + 3x\|2 \|2
+--R /
+--R 4+-+
+--R 16x\|2
+--R Type: Union(Expression(Integer),...)
+--E 1245
+
+--S 1246 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2
+--R \|2 \|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 )
+--R +
+--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+
+--R - 2\|3 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+
+--R 2\|3 log(- x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2
+--R - \|2 \|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 )
+--R +
+--R 4+-+ 4+-+ 4+-+ 4+-+
+--R 4\|3 atan(x\|6 + 1) + 4\|3 atan(x\|6 - 1)
+--R +
+--R 4+-+3
+--R +-+4+-+2 4+-+ 2\|3
+--R - 2\|2 \|2 \|3 atan(--------------------)
+--R 4+-+3 +-+4+-+3
+--R 2\|3 - 3x\|2 \|2
+--R +
+--R 4+-+3
+--R +-+4+-+2 4+-+ 2\|3
+--R 2\|2 \|2 \|3 atan(--------------------)
+--R 4+-+3 +-+4+-+3
+--R 2\|3 + 3x\|2 \|2
+--R /
+--R 4+-+3
+--R 16\|2
+--R Type: Expression(Integer)
+--E 1246
+
+--S 1247 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 4 4+-+4+-+3 4 +-+4+-+3 +-+ 6 2 4+-+3 4+-+ 4+-+3
+--R (4x \|2 \|3 + (- 2x \|2 \|2 \|3 + (- 3x - 2x )\|2 )\|3 )\|6
+--R +
+--R 2 4+-+4+-+3 2 +-+4+-+3 +-+ 4 4+-+3 4+-+ 4+-+
+--R (8x \|2 \|3 + (- 4x \|2 \|2 \|3 + (- 6x - 4)\|2 )\|3 )\|6
+--R +
+--R 6 2 4+-+2 +-+ 4 +-+4+-+2 4 4+-+2
+--R ((- 6x - 4x )\|2 \|3 + (6x + 4)\|2 \|2 - 48x )\|3
+--R +
+--R 4 +-+4+-+2 +-+ 6 2 4+-+2
+--R 24x \|2 \|2 \|3 + (36x + 24x )\|2
+--R /
+--R 6 2 4+-+2 6 2 +-+4+-+2 +-+
+--R (96x + 64x )\|3 + (- 48x - 32x )\|2 \|2 \|3
+--R +
+--R 8 4 4+-+2
+--R (- 72x - 96x - 32)\|2
+--R Type: Expression(Integer)
+--E 1247
+
+)clear all
+
+--S 1248 of 1309
+t0:=1/(x^3*(2+3*x^4))
+--R
+--R
+--R 1
+--R (1) ---------
+--R 7 3
+--R 3x + 2x
+--R Type: Fraction(Polynomial(Integer))
+--E 1248
+
+--S 1249 of 1309
+r0:=(-1/4)/x^2-1/4*atan(x^2*sqrt(3/2))*sqrt(3/2)
+--R
+--R
+--R 2 +-+
+--R 2 +-+ x \|3 +-+
+--R - x \|3 atan(------) - \|2
+--R +-+
+--R \|2
+--R (2) ---------------------------
+--R 2 +-+
+--R 4x \|2
+--R Type: Expression(Integer)
+--E 1249
+
+--S 1250 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R 2 +-+ 2\|3 +-+
+--R x \|3 atan(-------) - \|2
+--R 2 +-+
+--R 3x \|2
+--R (3) --------------------------
+--R 2 +-+
+--R 4x \|2
+--R Type: Union(Expression(Integer),...)
+--E 1250
+
+--S 1251 of 1309
+m0:=a0-r0
+--R
+--R
+--R 2 +-+ +-+
+--R +-+ x \|3 +-+ 2\|3
+--R \|3 atan(------) + \|3 atan(-------)
+--R +-+ 2 +-+
+--R \|2 3x \|2
+--R (4) ------------------------------------
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 1251
+
+--S 1252 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1252
+
+)clear all
+
+--S 1253 of 1309
+t0:=1/(x^4*(2+3*x^4))
+--R
+--R
+--R 1
+--R (1) ---------
+--R 8 4
+--R 3x + 2x
+--R Type: Fraction(Polynomial(Integer))
+--E 1253
+
+--S 1254 of 1309
+r0:=(-1/6)/x^3+1/8*3^(3/4)*atan(1-6^(1/4)*x)/2^(1/4)-_
+ 1/8*3^(3/4)*atan(1+6^(1/4)*x)/2^(1/4)+1/16*3^(3/4)*_
+ log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4)-_
+ 1/16*3^(3/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4)
+--R
+--R
+--R (2)
+--R 3 4+-+3 4+-+3 4+-+ 2 +-+ +-+
+--R - 3x \|3 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 3 4+-+3 4+-+3 4+-+ 2 +-+ +-+ 3 4+-+3 4+-+
+--R 3x \|3 log(- x \|2 \|3 + x \|3 + \|2 - 6x \|3 atan(x\|6 + 1)
+--R +
+--R 3 4+-+3 4+-+ 4+-+
+--R - 6x \|3 atan(x\|6 - 1 - 8\|2
+--R /
+--R 3 4+-+
+--R 48x \|2
+--R Type: Expression(Integer)
+--E 1254
+
+--S 1255 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2
+--R - 3x \|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 )
+--R +
+--R 3 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2
+--R 3x \|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 )
+--R +
+--R 4+--+
+--R 3 +-+4+--+ 2\|27
+--R - 6x \|2 \|27 atan(-------------------)
+--R 4+--+ +-+4+-+
+--R 2\|27 - 3x\|2 \|8
+--R +
+--R 4+--+
+--R 3 +-+4+--+ 2\|27 4+-+
+--R 6x \|2 \|27 atan(-------------------) - 8\|8
+--R 4+--+ +-+4+-+
+--R 2\|27 + 3x\|2 \|8
+--R /
+--R 3 4+-+
+--R 48x \|8
+--R Type: Union(Expression(Integer),...)
+--E 1255
+
+--S 1256 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2
+--R - \|2 \|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 )
+--R +
+--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2
+--R \|2 \|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 )
+--R +
+--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+
+--R \|3 \|8 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 4+-+
+--R - \|3 \|8 log(- x \|2 \|3 + x \|3 + \|2 + 2\|3 \|8 atan(x\|6 + 1)
+--R +
+--R 4+--+
+--R 4+-+3 4+-+ 4+-+ +-+4+-+4+--+ 2\|27
+--R 2\|3 \|8 atan(x\|6 - 1 - 2\|2 \|2 \|27 atan(-------------------)
+--R 4+--+ +-+4+-+
+--R 2\|27 - 3x\|2 \|8
+--R +
+--R 4+--+
+--R +-+4+-+4+--+ 2\|27
+--R 2\|2 \|2 \|27 atan(-------------------)
+--R 4+--+ +-+4+-+
+--R 2\|27 + 3x\|2 \|8
+--R /
+--R 4+-+4+-+
+--R 16\|2 \|8
+--R Type: Expression(Integer)
+--E 1256
+
+--S 1257 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 4 +-+4+-+ +-+ 6 2 4+-+ 4+-+3 4 4+-+3 4+-4+-+3
+--R ((- 2x \|2 \|2 \|3 + (- 3x - 2x )\|2 )\|3 + 6x \|2 \|)\|6
+--R +
+--R 2 +-+4+-+ +-+ 4 4+-+ 4+-+3 2 4+-+3 4+-4+-+
+--R ((- 4x \|2 \|2 \|3 + (- 6x - 4)\|2 )\|3 + 12x \|2 \|)\|6
+--R +
+--R 2 4+-+2 2 +-+4+-+2 6 2 +-+ 4 4+-+2
+--R - 48x \|3 + (24x \|2 \|2 + 18x + 12x )\|3 + (36x + 24)\|2
+--R +
+--R 4 +-+
+--R (- 18x - 12)\|2
+--R /
+--R 6 2 4+-+2 6 2 +-+4+-+2 +-+
+--R (96x + 64x )\|3 + (- 48x - 32x )\|2 \|2 \|3
+--R +
+--R 8 4 4+-+2
+--R (- 72x - 96x - 32)\|2
+--R Type: Expression(Integer)
+--E 1257
+
+)clear all
+
+--S 1258 of 1309
+t0:=x^3/(2+3*x^4)^2
+--R
+--R
+--R 3
+--R x
+--R (1) --------------
+--R 8 4
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 1258
+
+--S 1259 of 1309
+r0:=(-1/12)/(2+3*x^4)
+--R
+--R
+--R 1
+--R --
+--R 36
+--R (2) - ------
+--R 4 2
+--R x + -
+--R 3
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1259
+
+--S 1260 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ---------
+--R 4
+--R 36x + 24
+--R Type: Union(Expression(Integer),...)
+--E 1260
+
+--S 1261 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1261
+
+--S 1262 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1262
+
+)clear all
+
+--S 1263 of 1309
+t0:=x^2/(2+3*x^4)^2
+--R
+--R
+--R 2
+--R x
+--R (1) --------------
+--R 8 4
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 1263
+
+--S 1264 of 1309
+r0:=1/8*x^3/(2+3*x^4)-1/16*atan(1-6^(1/4)*x)/6^(3/4)+_
+ 1/16*atan(1+6^(1/4)*x)/6^(3/4)+_
+ 1/32*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4)-_
+ 1/32*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4)
+--R
+--R
+--R (2)
+--R 4 4+-+3 4+-+ 2 +-+ +-+
+--R (- 3x - 2)log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4 4+-+3 4+-+ 2 +-+ +-+ 4 4+-+
+--R (3x + 2)log(- x \|2 \|3 + x \|3 + \|2 ) + (6x + 4)atan(x\|6 + 1)
+--R +
+--R 4 4+-+ 3 4+-+3
+--R (6x + 4)atan(x\|6 - 1) + 4x \|6
+--R /
+--R 4 4+-+3
+--R (96x + 64)\|6
+--R Type: Expression(Integer)
+--E 1264
+
+--S 1265 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 +-+ +-+4+--+3 2 4+--+2
+--R (- 3x - 2)\|2 log(x\|2 \|54 + 3x \|54 + 18)
+--R +
+--R 4 +-+ +-+4+--+3 2 4+--+2
+--R (3x + 2)\|2 log(- x\|2 \|54 + 3x \|54 + 18)
+--R +
+--R 4 +-+ 18
+--R (- 6x - 4)\|2 atan(----------------)
+--R +-+4+--+3
+--R x\|2 \|54 - 18
+--R +
+--R 4 +-+ 18 3 4+--+
+--R (- 6x - 4)\|2 atan(----------------) + 8x \|54
+--R +-+4+--+3
+--R x\|2 \|54 + 18
+--R /
+--R 4 4+--+
+--R (192x + 128)\|54
+--R Type: Union(Expression(Integer),...)
+--E 1265
+
+--S 1266 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+3 +-+4+--+3 2 4+--+2
+--R - \|2 \|6 log(x\|2 \|54 + 3x \|54 + 18)
+--R +
+--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+
+--R 2\|54 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+
+--R - 2\|54 log(- x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R +-+4+-+3 +-+4+--+3 2 4+--+2 4+--+ 4+-+
+--R \|2 \|6 log(- x\|2 \|54 + 3x \|54 + 18) - 4\|54 atan(x\|6 + 1)
+--R +
+--R 4+--+ 4+-+ +-+4+-+3 18
+--R - 4\|54 atan(x\|6 - 1) - 2\|2 \|6 atan(----------------)
+--R +-+4+--+3
+--R x\|2 \|54 - 18
+--R +
+--R +-+4+-+3 18
+--R - 2\|2 \|6 atan(----------------)
+--R +-+4+--+3
+--R x\|2 \|54 + 18
+--R /
+--R 4+-+3 4+--+
+--R 64\|6 \|54
+--R Type: Expression(Integer)
+--E 1266
+
+--S 1267 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 6 2 4+-+3 +-+ 4 +-+4+-+3 4+-+4+-+3
+--R ((3x + 2x )\|2 \|3 + (- 3x - 2)\|2 \|2 )\|3 \|6
+--R +
+--R 4 4+-+2 4+-+2 4 +-+ +-+ 6 2 4+-+2 2 4+-+2 4+-+2
+--R (12x \|2 \|3 - 12x \|2 \|3 - 18x - 12x )\|6 - 24x \|2 \|3
+--R +
+--R 2 +-+ +-+ 4
+--R 24x \|2 \|3 + 36x + 24
+--R /
+--R 6 2 4+-+2 4+-+2 6 2 +-+ +-+ 8 4
+--R (576x + 384x )\|2 \|3 + (- 576x - 384x )\|2 \|3 - 864x - 1152x
+--R +
+--R - 384
+--R *
+--R 4+-+2
+--R \|6
+--R Type: Expression(Integer)
+--E 1267
+
+)clear all
+
+--S 1268 of 1309
+t0:=x/(2+3*x^4)^2
+--R
+--R
+--R x
+--R (1) --------------
+--R 8 4
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 1268
+
+--S 1269 of 1309
+r0:=1/8*x^2/(2+3*x^4)+1/8*atan(x^2*sqrt(3/2))/sqrt(6)
+--R
+--R
+--R 2 +-+
+--R 4 x \|3 2 +-+
+--R (3x + 2)atan(------) + x \|6
+--R +-+
+--R \|2
+--R (2) ------------------------------
+--R 4 +-+
+--R (24x + 16)\|6
+--R Type: Expression(Integer)
+--E 1269
+
+--S 1270 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R 4 x \|6 2 +-+
+--R (3x + 2)atan(------) + x \|6
+--R 2
+--R (3) ------------------------------
+--R 4 +-+
+--R (24x + 16)\|6
+--R Type: Union(Expression(Integer),...)
+--E 1270
+
+--S 1271 of 1309
+m0:=a0-r0
+--R
+--R
+--R 2 +-+ 2 +-+
+--R x \|6 x \|3
+--R atan(------) - atan(------)
+--R 2 +-+
+--R \|2
+--R (4) ---------------------------
+--R +-+
+--R 8\|6
+--R Type: Expression(Integer)
+--E 1271
+
+--S 1272 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R +-+ +-+ +-+
+--R - x\|2 \|3 \|6 + 6x
+--R (5) --------------------
+--R 4
+--R 72x + 48
+--R Type: Expression(Integer)
+--E 1272
+
+)clear all
+
+--S 1273 of 1309
+t0:=1/(2+3*x^4)^2
+--R
+--R
+--R 1
+--R (1) --------------
+--R 8 4
+--R 9x + 12x + 4
+--R Type: Fraction(Polynomial(Integer))
+--E 1273
+
+--S 1274 of 1309
+r0:=1/8*x/(2+3*x^4)-1/32*3^(3/4)*atan(1-6^(1/4)*x)/2^(1/4)+_
+ 1/32*3^(3/4)*atan(1+6^(1/4)*x)/2^(1/4)-_
+ 1/64*3^(3/4)*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4)+_
+ 1/64*3^(3/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4)
+--R
+--R
+--R (2)
+--R 4 4+-+3 4+-+3 4+-+ 2 +-+ +-+
+--R (3x + 2)\|3 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4 4+-+3 4+-+3 4+-+ 2 +-+ +-+
+--R (- 3x - 2)\|3 log(- x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4 4+-+3 4+-+ 4 4+-+3 4+-+ 4+-+
+--R (6x + 4)\|3 atan(x\|6 + 1) + (6x + 4)\|3 atan(x\|6 - 1) + 8x\|2
+--R /
+--R 4 4+-+
+--R (192x + 128)\|2
+--R Type: Expression(Integer)
+--E 1274
+
+--S 1275 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2
+--R (3x + 2)\|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 )
+--R +
+--R 4 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2
+--R (- 3x - 2)\|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 )
+--R +
+--R 4+--+
+--R 4 +-+4+--+ 2\|27
+--R (6x + 4)\|2 \|27 atan(-------------------)
+--R 4+--+ +-+4+-+
+--R 2\|27 - 3x\|2 \|8
+--R +
+--R 4+--+
+--R 4 +-+4+--+ 2\|27 4+-+
+--R (- 6x - 4)\|2 \|27 atan(-------------------) + 8x\|8
+--R 4+--+ +-+4+-+
+--R 2\|27 + 3x\|2 \|8
+--R /
+--R 4 4+-+
+--R (192x + 128)\|8
+--R Type: Union(Expression(Integer),...)
+--E 1275
+
+--S 1276 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2
+--R \|2 \|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 )
+--R +
+--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2
+--R - \|2 \|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 )
+--R +
+--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+
+--R - \|3 \|8 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 4+-+
+--R \|3 \|8 log(- x \|2 \|3 + x \|3 + \|2 - 2\|3 \|8 atan(x\|6 + 1)
+--R +
+--R 4+--+
+--R 4+-+3 4+-+ 4+-+ +-+4+-+4+--+ 2\|27
+--R - 2\|3 \|8 atan(x\|6 - 1 + 2\|2 \|2 \|27 atan(-------------------)
+--R 4+--+ +-+4+-+
+--R 2\|27 - 3x\|2 \|8
+--R +
+--R 4+--+
+--R +-+4+-+4+--+ 2\|27
+--R - 2\|2 \|2 \|27 atan(-------------------)
+--R 4+--+ +-+4+-+
+--R 2\|27 + 3x\|2 \|8
+--R /
+--R 4+-+4+-+
+--R 64\|2 \|8
+--R Type: Expression(Integer)
+--E 1276
+
+--S 1277 of 1309
+d0:=normalize(D(m0,x))
+--R
+--R
+--R 2 4+-+4+-+3 4+-+3 4+-+4+-+3 4+-+ 2 4+-+2 4+-+2
+--R - x \|2 \|3 \|6 - 2\|2 \|3 \|6 + 6x \|3 + 6\|2
+--R (5) -------------------------------------------------------
+--R 4 4+-+2
+--R (96x + 64)\|2
+--R Type: Expression(Integer)
+--E 1277
+
+)clear all
+
+--S 1278 of 1309
+t0:=1/(x*(2+3*x^4)^2)
+--R
+--R
+--R 1
+--R (1) ---------------
+--R 9 5
+--R 9x + 12x + 4x
+--R Type: Fraction(Polynomial(Integer))
+--E 1278
+
+--S 1279 of 1309
+r0:=1/8/(2+3*x^4)-1/8*atanh(1+3*x^4)
+--R
+--R
+--R 4 4
+--R (- 3x - 2)atanh(3x + 1) + 1
+--R (2) -----------------------------
+--R 4
+--R 24x + 16
+--R Type: Expression(Integer)
+--E 1279
+
+--S 1280 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4 4
+--R (- 3x - 2)log(3x + 2) + (12x + 8)log(x) + 2
+--R (3) ----------------------------------------------
+--R 4
+--R 48x + 32
+--R Type: Union(Expression(Integer),...)
+--E 1280
+
+--S 1281 of 1309
+m0:=a0-r0
+--R
+--R
+--R 4 4
+--R - log(3x + 2) + 4log(x) + 2atanh(3x + 1)
+--R (4) ------------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 1281
+
+--S 1282 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1282
+
+)clear all
+
+--S 1283 of 1309
+t0:=1/(x^2*(2+3*x^4)^2)
+--R
+--R
+--R 1
+--R (1) -----------------
+--R 10 6 2
+--R 9x + 12x + 4x
+--R Type: Fraction(Polynomial(Integer))
+--E 1283
+
+--S 1284 of 1309
+r0:=(-5/16)/x+1/8/(x*(2+3*x^4))+5/32*3^(1/4)*atan(1-6^(1/4)*x)/2^(3/4)-_
+ 5/32*3^(1/4)*atan(1+6^(1/4)*x)/2^(3/4)-_
+ 5/64*3^(1/4)*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4)+_
+ 5/64*3^(1/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4)
+--R
+--R
+--R (2)
+--R 5 4+-+ 4+-+3 4+-+ 2 +-+ +-+
+--R (15x + 10x)\|3 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 5 4+-+ 4+-+3 4+-+ 2 +-+ +-+
+--R (- 15x - 10x)\|3 log(- x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 5 4+-+ 4+-+ 5 4+-+ 4+-+
+--R (- 30x - 20x)\|3 atan(x\|6 + 1) + (- 30x - 20x)\|3 atan(x\|6 - 1)
+--R +
+--R 4 4+-+3
+--R (- 60x - 32)\|2
+--R /
+--R 5 4+-+3
+--R (192x + 128x)\|2
+--R Type: Expression(Integer)
+--E 1284
+
+--S 1285 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2
+--R (15x + 10x)\|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 )
+--R +
+--R 5 +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2
+--R (- 15x - 10x)\|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 )
+--R +
+--R 4+-+3
+--R 5 +-+4+-+ 2\|3
+--R (- 30x - 20x)\|2 \|3 atan(--------------------)
+--R 4+-+3 +-+4+-+3
+--R 2\|3 - 3x\|2 \|2
+--R +
+--R 4+-+3
+--R 5 +-+4+-+ 2\|3 4 4+-+
+--R (30x + 20x)\|2 \|3 atan(--------------------) + (- 120x - 64)\|2
+--R 4+-+3 +-+4+-+3
+--R 2\|3 + 3x\|2 \|2
+--R /
+--R 5 4+-+
+--R (384x + 256x)\|2
+--R Type: Union(Expression(Integer),...)
+--E 1285
+
+--S 1286 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2
+--R 5\|2 \|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 )
+--R +
+--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+
+--R - 10\|3 log(x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+
+--R 10\|3 log(- x \|2 \|3 + x \|3 + \|2 )
+--R +
+--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2
+--R - 5\|2 \|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 )
+--R +
+--R 4+-+ 4+-+ 4+-+ 4+-+
+--R 20\|3 atan(x\|6 + 1) + 20\|3 atan(x\|6 - 1)
+--R +
+--R 4+-+3
+--R +-+4+-+2 4+-+ 2\|3
+--R - 10\|2 \|2 \|3 atan(--------------------)
+--R 4+-+3 +-+4+-+3
+--R 2\|3 - 3x\|2 \|2
+--R +
+--R 4+-+3
+--R +-+4+-+2 4+-+ 2\|3
+--R 10\|2 \|2 \|3 atan(--------------------)
+--R 4+-+3 +-+4+-+3
+--R 2\|3 + 3x\|2 \|2
+--R /
+--R 4+-+3
+--R 128\|2
+--R Type: Expression(Integer)
+--E 1286
+
+--S 1287 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 4 4+-+4+-+3 4 +-+4+-+3 +-+ 6 2 4+-+3 4+-+ 4+-+3
+--R (20x \|2 \|3 + (- 10x \|2 \|2 \|3 + (- 15x - 10x )\|2 )\|3 )\|6
+--R +
+--R 2 4+-+4+-+3 2 +-+4+-+3 +-+ 4 4+-+3 4+-+ 4+-+
+--R (40x \|2 \|3 + (- 20x \|2 \|2 \|3 + (- 30x - 20)\|2 )\|3 )\|6
+--R +
+--R 6 2 4+-+2 +-+ 4 +-+4+-+2 4 4+-+2
+--R ((- 30x - 20x )\|2 \|3 + (30x + 20)\|2 \|2 - 240x )\|3
+--R +
+--R 4 +-+4+-+2 +-+ 6 2 4+-+2
+--R 120x \|2 \|2 \|3 + (180x + 120x )\|2
+--R /
+--R 6 2 4+-+2 6 2 +-+4+-+2 +-+
+--R (768x + 512x )\|3 + (- 384x - 256x )\|2 \|2 \|3
+--R +
+--R 8 4 4+-+2
+--R (- 576x - 768x - 256)\|2
+--R Type: Expression(Integer)
+--E 1287
+
+)clear all
+
+--S 1288 of 1309
+t0:=1/(x^3*(2+3*x^4)^2)
+--R
+--R
+--R 1
+--R (1) -----------------
+--R 11 7 3
+--R 9x + 12x + 4x
+--R Type: Fraction(Polynomial(Integer))
+--E 1288
+
+--S 1289 of 1309
+r0:=(-3/16)/x^2+1/8/(x^2*(2+3*x^4))-3/16*atan(x^2*sqrt(3/2))*sqrt(3/2)
+--R
+--R
+--R 2 +-+
+--R 6 2 +-+ x \|3 4 +-+
+--R (- 9x - 6x )\|3 atan(------) + (- 9x - 4)\|2
+--R +-+
+--R \|2
+--R (2) -----------------------------------------------
+--R 6 2 +-+
+--R (48x + 32x )\|2
+--R Type: Expression(Integer)
+--E 1289
+
+--S 1290 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R 6 2 +-+ 2\|3 4 +-+
+--R (9x + 6x )\|3 atan(-------) + (- 9x - 4)\|2
+--R 2 +-+
+--R 3x \|2
+--R (3) ----------------------------------------------
+--R 6 2 +-+
+--R (48x + 32x )\|2
+--R Type: Union(Expression(Integer),...)
+--E 1290
+
+--S 1291 of 1309
+m0:=a0-r0
+--R
+--R
+--R 2 +-+ +-+
+--R +-+ x \|3 +-+ 2\|3
+--R 3\|3 atan(------) + 3\|3 atan(-------)
+--R +-+ 2 +-+
+--R \|2 3x \|2
+--R (4) --------------------------------------
+--R +-+
+--R 16\|2
+--R Type: Expression(Integer)
+--E 1291
+
+--S 1292 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1292
+
+)clear all
+
+--S 1293 of 1309
+t0:=1/(1+a+(-1+a)*x^4)
+--R
+--R
+--R 1
+--R (1) -----------------
+--R 4
+--R (a - 1)x + a + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1293
+
+--S 1294 of 1309
+r0:=-1/2*atan((-1+a)^(1/4)*x/(-1-a)^(1/4))/((-1-a)^(3/4)*(-1+a)^(1/4))-_
+ 1/2*atanh((-1+a)^(1/4)*x/(-1-a)^(1/4))/((-1-a)^(3/4)*(-1+a)^(1/4))
+--R
+--R
+--R 4+-----+ 4+-----+
+--R x\|a - 1 x\|a - 1
+--R - atanh(----------) - atan(----------)
+--R 4+-------+ 4+-------+
+--R \|- a - 1 \|- a - 1
+--R (2) --------------------------------------
+--R 4+-------+3 4+-----+
+--R 2\|- a - 1 \|a - 1
+--R Type: Expression(Integer)
+--E 1294
+
+--S 1295 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------------------------+
+--R | 1
+--R |- --------------------------
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R *
+--R +----------------------------+
+--R | 1
+--R log((4a + 4) |- -------------------------- + x)
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R +
+--R -
+--R +----------------------------+
+--R | 1
+--R |- --------------------------
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R *
+--R +----------------------------+
+--R | 1
+--R log((- 4a - 4) |- -------------------------- + x)
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R +
+--R -
+--R +----------------------------+
+--R | 1
+--R 2 |- --------------------------
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R *
+--R +----------------------------+
+--R | 1
+--R (4a + 4) |- --------------------------
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R atan(---------------------------------------)
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 1295
+
+--S 1296 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----------------------------+
+--R 4+-------+3 | 1 4+-----+
+--R 2\|- a - 1 |- -------------------------- \|a - 1
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R *
+--R +----------------------------+
+--R | 1
+--R log((4a + 4) |- -------------------------- + x)
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R +
+--R -
+--R +----------------------------+
+--R 4+-------+3 | 1 4+-----+
+--R 2\|- a - 1 |- -------------------------- \|a - 1
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R *
+--R +----------------------------+
+--R | 1
+--R log((- 4a - 4) |- -------------------------- + x)
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R +
+--R 4+-----+ 4+-----+
+--R x\|a - 1 x\|a - 1
+--R atanh(----------) + atan(----------)
+--R 4+-------+ 4+-------+
+--R \|- a - 1 \|- a - 1
+--R +
+--R -
+--R +----------------------------+
+--R 4+-------+3 | 1 4+-----+
+--R 4\|- a - 1 |- -------------------------- \|a - 1
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R *
+--R +----------------------------+
+--R | 1
+--R (4a + 4) |- --------------------------
+--R 4| 4 3
+--R \| 256a + 512a - 512a - 256
+--R atan(---------------------------------------)
+--R x
+--R /
+--R 4+-------+3 4+-----+
+--R 2\|- a - 1 \|a - 1
+--R Type: Expression(Integer)
+--E 1296
+
+--S 1297 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1297
+
+)clear all
+
+--S 1298 of 1309
+t0:=x^7*sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R 7 | 4
+--R (1) x \|c x + a
+--R Type: Expression(Integer)
+--E 1298
+
+--S 1299 of 1309
+r0:=-1/6*a*(a+c*x^4)^(3/2)/c^2+1/10*(a+c*x^4)^(5/2)/c^2
+--R
+--R
+--R +--------+
+--R 2 8 4 2 | 4
+--R (3c x + a c x - 2a )\|c x + a
+--R (2) ---------------------------------
+--R 2
+--R 30c
+--R Type: Expression(Integer)
+--E 1299
+
+--S 1300 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 8 4 2 | 4
+--R (3c x + a c x - 2a )\|c x + a
+--R (3) ---------------------------------
+--R 2
+--R 30c
+--R Type: Union(Expression(Integer),...)
+--E 1300
+
+--S 1301 of 1309
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1301
+
+--S 1302 of 1309
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1302
+
+)clear all
+
+--S 1303 of 1309
+t0:=x^5*sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R 5 | 4
+--R (1) x \|c x + a
+--R Type: Expression(Integer)
+--E 1303
+
+--S 1304 of 1309
+r0:=-1/16*a^2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(3/2)+_
+ 1/16*a*x^2*sqrt(a+c*x^4)/c+1/8*x^6*sqrt(a+c*x^4)
+--R
+--R
+--R 2 +-+ +--------+
+--R 2 x \|c 6 2 +-+ | 4
+--R - a atanh(-----------) + (2c x + a x )\|c \|c x + a
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) ------------------------------------------------------
+--R +-+
+--R 16c\|c
+--R Type: Expression(Integer)
+--E 1304
+
+--S 1305 of 1309
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 4 3 +-+ | 4 2 2 8 3 4 4
+--R ((4a c x + 8a )\|a \|c x + a - a c x - 8a c x - 8a )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R +--------+
+--R 3 14 2 10 2 6 3 2 +-+ | 4
+--R (- 2c x - 17a c x - 24a c x - 8a x )\|c \|c x + a
+--R +
+--R 3 14 2 10 2 6 3 2 +-+ +-+
+--R (8c x + 28a c x + 28a c x + 8a x )\|a \|c
+--R /
+--R +--------+
+--R 2 4 +-+ +-+ | 4
+--R (64c x + 128a c)\|a \|c \|c x + a
+--R +
+--R 3 8 2 4 2 +-+
+--R (- 16c x - 128a c x - 128a c)\|c
+--R ,
+--R
+--R +--------+
+--R 2 4 3 +-+ | 4 2 2 8 3 4 4
+--R ((- 8a c x - 16a )\|a \|c x + a + 2a c x + 16a c x + 16a )
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- c \|c x + a - \|- c \|a
+--R atan(------------------------------)
+--R 2
+--R c x
+--R +
+--R +--------+
+--R 3 14 2 10 2 6 3 2 +---+ | 4
+--R (- 2c x - 17a c x - 24a c x - 8a x )\|- c \|c x + a
+--R +
+--R 3 14 2 10 2 6 3 2 +---+ +-+
+--R (8c x + 28a c x + 28a c x + 8a x )\|- c \|a
+--R /
+--R +--------+
+--R 2 4 +---+ +-+ | 4
+--R (64c x + 128a c)\|- c \|a \|c x + a
+--R +
+--R 3 8 2 4 2 +---+
+--R (- 16c x - 128a c x - 128a c)\|- c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1305
+
+--S 1306 of 1309
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R 2 (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a
+--R a log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R 2 x \|c
+--R a atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R +-+
+--R 16c\|c
+--R Type: Expression(Integer)
+--E 1306
+
+--S 1307 of 1309
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1307
+
+--S 1308 of 1309
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 +-+ +---+ | 4 +---+ +-+
+--R 2 +---+ x \|c 2 +-+ \|- c \|c x + a - \|- c \|a
+--R a \|- c atanh(-----------) - 2a \|c atan(------------------------------)
+--R +--------+ 2
+--R | 4 c x
+--R \|c x + a
+--R ------------------------------------------------------------------------
+--R +---+ +-+
+--R 16c\|- c \|c
+--R Type: Expression(Integer)
+--E 1308
+
+--S 1309 of 1309
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1309
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich4d.input.pdf b/src/axiom-website/CATS/rich4d.input.pdf
new file mode 100644
index 0000000..2b154f1
Binary files /dev/null and b/src/axiom-website/CATS/rich4d.input.pdf differ
diff --git a/src/axiom-website/CATS/rich4e.input.pamphlet b/src/axiom-website/CATS/rich4e.input.pamphlet
new file mode 100644
index 0000000..3df315e
--- /dev/null
+++ b/src/axiom-website/CATS/rich4e.input.pamphlet
@@ -0,0 +1,28917 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich4e.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 261 supplied "optimal results".
+\item 193 matching answers.
+\item 39 cases where Axiom differs from Rubi
+\item 27 cases where Axiom supplied 2 results.
+\item 3 cases that Axiom failed to integrate.
+\item 40 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich4e.output
+)spool rich4e.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1347
+t0:=x^3*sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R 3 | 4
+--R (1) x \|c x + a
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1347
+r0:=1/6*(a+c*x^4)^(3/2)/c
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (2) ---------------------
+--R 6c
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (3) ---------------------
+--R 6c
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1347
+t0:=x*sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R (1) x\|c x + a
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 1347
+r0:=1/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/sqrt(c)+1/4*x^2*sqrt(a+c*x^4)
+--R
+--R
+--R 2 +-+ +--------+
+--R x \|c 2 +-+ | 4
+--R a atanh(-----------) + x \|c \|c x + a
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) ----------------------------------------
+--R +-+
+--R 4\|c
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 4 4 2
+--R (2a\|a \|c x + a - a c x - 2a )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R +--------+
+--R 6 2 +-+ | 4 6 2 +-+ +-+
+--R (- c x - 2a x )\|c \|c x + a + (2c x + 2a x )\|a \|c
+--R /
+--R +--------+
+--R +-+ +-+ | 4 4 +-+
+--R 8\|a \|c \|c x + a + (- 4c x - 8a)\|c
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 4 +---+ +-+
+--R +-+ | 4 4 2 \|- c \|c x + a - \|- c \|a
+--R (4a\|a \|c x + a - 2a c x - 4a )atan(------------------------------)
+--R 2
+--R c x
+--R +
+--R +--------+
+--R 6 2 +---+ | 4 6 2 +---+ +-+
+--R (- c x - 2a x )\|- c \|c x + a + (2c x + 2a x )\|- c \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 4 4 +---+
+--R 8\|- c \|a \|c x + a + (- 4c x - 8a)\|- c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 8
+
+--S 9 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a
+--R a log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R x \|c
+--R - a atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R +-+
+--R 4\|c
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+--S 11 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 +-+ +---+ | 4 +---+ +-+
+--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a
+--R - a\|- c atanh(-----------) + 2a\|c atan(------------------------------)
+--R +--------+ 2
+--R | 4 c x
+--R \|c x + a
+--R ------------------------------------------------------------------------
+--R +---+ +-+
+--R 4\|- c \|c
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 12
+
+)clear all
+
+--S 13 of 1347
+t0:=sqrt(a+c*x^4)/x
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (1) -----------
+--R x
+--R Type: Expression(Integer)
+--E 13
+
+--S 14 of 1347
+r0:=-1/2*atanh(sqrt(a+c*x^4)/sqrt(a))*sqrt(a)+1/2*sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R | 4 +--------+
+--R +-+ \|c x + a | 4
+--R - \|a atanh(-----------) + \|c x + a
+--R +-+
+--R \|a
+--R (2) --------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ | 4 4 +--------+
+--R +-+ - 2\|a \|c x + a + c x + 2a | 4
+--R \|a log(------------------------------) + 2\|c x + a
+--R 4
+--R x
+--R [------------------------------------------------------,
+--R 4
+--R +--------+
+--R | 4 +--------+
+--R +---+ \|c x + a | 4
+--R - \|- a atan(-----------) + \|c x + a
+--R +---+
+--R \|- a
+--R ---------------------------------------]
+--R 2
+--R Type: Union(List(Expression(Integer)),...)
+--E 15
+
+--S 16 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R +-+ | 4 4 | 4
+--R +-+ - 2\|a \|c x + a + c x + 2a +-+ \|c x + a
+--R \|a log(------------------------------) + 2\|a atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) -----------------------------------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 | 4
+--R +-+ \|c x + a +---+ \|c x + a
+--R \|a atanh(-----------) - \|- a atan(-----------)
+--R +-+ +---+
+--R \|a \|- a
+--R (6) ------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 18
+
+--S 19 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 19
+
+)clear all
+
+--S 20 of 1347
+t0:=sqrt(a+c*x^4)/x^3
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (1) -----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 20
+
+--S 21 of 1347
+r0:=1/2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))*sqrt(c)-1/2*sqrt(a+c*x^4)/x^2
+--R
+--R
+--R 2 +-+ +--------+
+--R 2 +-+ x \|c | 4
+--R x \|c atanh(-----------) - \|c x + a
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) --------------------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 +-+ | 4 2 +-+ +-+
+--R (x \|c \|c x + a - x \|a \|c )
+--R *
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a
+--R log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R +--------+
+--R +-+ | 4 4
+--R \|a \|c x + a - c x - a
+--R /
+--R +--------+
+--R 2 | 4 2 +-+
+--R 2x \|c x + a - 2x \|a
+--R ,
+--R
+--R +--------+
+--R +--------+ | 4 +-+
+--R 2 +---+ | 4 2 +---+ +-+ \|c x + a - \|a
+--R (2x \|- c \|c x + a - 2x \|- c \|a )atan(------------------)
+--R 2 +---+
+--R x \|- c
+--R +
+--R +--------+
+--R +-+ | 4 4
+--R \|a \|c x + a - c x - a
+--R /
+--R +--------+
+--R 2 | 4 2 +-+
+--R 2x \|c x + a - 2x \|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 22
+
+--S 23 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R +-+ (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a
+--R \|c log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R +-+ x \|c
+--R - \|c atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 23
+
+--S 24 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R 2 +-+ | 4 +-+
+--R +-+ x \|c +---+ \|c x + a - \|a
+--R - \|c atanh(-----------) + 2\|- c atan(------------------)
+--R +--------+ 2 +---+
+--R | 4 x \|- c
+--R \|c x + a
+--R (6) ----------------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 25
+
+--S 26 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 26
+
+)clear all
+
+--S 27 of 1347
+t0:=sqrt(a+c*x^4)/x^5
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (1) -----------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 1347
+r0:=-1/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))/sqrt(a)-1/4*sqrt(a+c*x^4)/x^4
+--R
+--R
+--R +--------+
+--R | 4 +--------+
+--R 4 \|c x + a +-+ | 4
+--R - c x atanh(-----------) - \|a \|c x + a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------
+--R 4 +-+
+--R 4x \|a
+--R Type: Expression(Integer)
+--E 28
+
+--S 29 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 4 4 +-+ +--------+
+--R 4 - 2a\|c x + a + (c x + 2a)\|a +-+ | 4
+--R c x log(---------------------------------) - 2\|a \|c x + a
+--R 4
+--R x
+--R [-------------------------------------------------------------,
+--R 4 +-+
+--R 8x \|a
+--R +--------+
+--R +---+ | 4 +--------+
+--R 4 \|- a \|c x + a +---+ | 4
+--R - c x atan(-----------------) - \|- a \|c x + a
+--R a
+--R -------------------------------------------------]
+--R 4 +---+
+--R 4x \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 29
+
+--S 30 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 4 +-+ | 4
+--R - 2a\|c x + a + (c x + 2a)\|a \|c x + a
+--R c log(---------------------------------) + 2c atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) ----------------------------------------------------------------
+--R +-+
+--R 8\|a
+--R Type: Expression(Integer)
+--E 30
+
+--S 31 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 +---+ | 4
+--R +---+ \|c x + a +-+ \|- a \|c x + a
+--R c\|- a atanh(-----------) - c\|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R 4\|- a \|a
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 33
+
+)clear all
+
+--S 34 of 1347
+t0:=sqrt(a+c*x^4)/x^7
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (1) -----------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 1347
+r0:=-1/6*(a+c*x^4)^(3/2)/(a*x^6)
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (- c x - a)\|c x + a
+--R (2) -----------------------
+--R 6
+--R 6a x
+--R Type: Expression(Integer)
+--E 35
+
+--S 36 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 3
+--R (3c x + 7a c x + 4a )\|a \|c x + a - c x - 6a c x - 9a c x - 4a
+--R ------------------------------------------------------------------------
+--R +--------+
+--R 10 2 6 | 4 10 2 6 +-+
+--R (6a c x + 24a x )\|c x + a + (- 18a c x - 24a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 36
+
+--S 37 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 38
+
+)clear all
+
+--S 39 of 1347
+t0:=sqrt(a+c*x^4)/x^9
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (1) -----------
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 1347
+r0:=1/16*c^2*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(3/2)-_
+ 1/8*sqrt(a+c*x^4)/x^8-1/16*c*sqrt(a+c*x^4)/(a*x^4)
+--R
+--R
+--R +--------+
+--R | 4 +--------+
+--R 2 8 \|c x + a 4 +-+ | 4
+--R c x atanh(-----------) + (- c x - 2a)\|a \|c x + a
+--R +-+
+--R \|a
+--R (2) -----------------------------------------------------
+--R 8 +-+
+--R 16a x \|a
+--R Type: Expression(Integer)
+--E 40
+
+--S 41 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 4 4 +-+ +--------+
+--R 2 8 2a\|c x + a + (c x + 2a)\|a 4 +-+ | 4
+--R c x log(-------------------------------) + (- 2c x - 4a)\|a \|c x + a
+--R 4
+--R x
+--R [------------------------------------------------------------------------,
+--R 8 +-+
+--R 32a x \|a
+--R +--------+
+--R +---+ | 4 +--------+
+--R 2 8 \|- a \|c x + a 4 +---+ | 4
+--R c x atan(-----------------) + (- c x - 2a)\|- a \|c x + a
+--R a
+--R ------------------------------------------------------------]
+--R 8 +---+
+--R 16a x \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 41
+
+--S 42 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 4 +-+ | 4
+--R 2 2a\|c x + a + (c x + 2a)\|a 2 \|c x + a
+--R c log(-------------------------------) - 2c atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) --------------------------------------------------------------
+--R +-+
+--R 32a\|a
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 43
+
+--S 44 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 +---+ | 4
+--R 2 +---+ \|c x + a 2 +-+ \|- a \|c x + a
+--R - c \|- a atanh(-----------) + c \|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R +---+ +-+
+--R 16a\|- a \|a
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 1347
+t0:=sqrt(a+c*x^4)/x^11
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (1) -----------
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 1347
+r0:=-1/10*(a+c*x^4)^(3/2)/(a*x^10)+1/15*c*(a+c*x^4)^(3/2)/(a^2*x^6)
+--R
+--R
+--R +--------+
+--R 2 8 4 2 | 4
+--R (2c x - a c x - 3a )\|c x + a
+--R (2) ---------------------------------
+--R 2 10
+--R 30a x
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4
+--R (- 10c x - 35a c x + 3a c x + 76a c x + 48a )\|a \|c x + a
+--R +
+--R 5 20 4 16 2 3 12 3 2 8 4 4 5
+--R 2c x + 25a c x + 40a c x - 35a c x - 100a c x - 48a
+--R /
+--R +--------+
+--R 2 2 18 3 14 4 10 | 4
+--R (30a c x + 360a c x + 480a x )\|c x + a
+--R +
+--R 2 2 18 3 14 4 10 +-+
+--R (- 150a c x - 600a c x - 480a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 1347
+t0:=x^4*sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (1) x \|c x + a
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 1347
+--r0:=2/21*a*x*sqrt(a+c*x^4)/c+1/7*x^5*sqrt(a+c*x^4)+2/21*a^(9/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4))
+--E 52
+
+--S 53 of 1347
+--a0:=integrate(t0,x)
+--E 53
+
+--S 54 of 1347
+--m0:=a0-r0
+--E 54
+
+--S 55 of 1347
+--d0:=D(m0,x)
+--E 55
+
+)clear all
+
+--S 56 of 1347
+t0:=x^2*sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R 2 | 4
+--R (1) x \|c x + a
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1347
+--r0:=1/5*x^3*sqrt(a+c*x^4)+2/5*a^(7/4)*_
+-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_
+-- ((-c)^(3/4)*sqrt(a+c*x^4))-2/5*a^(7/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4))
+--E 57
+
+--S 58 of 1347
+--a0:=integrate(t0,x)
+--E 58
+
+--S 59 of 1347
+--m0:=a0-r0
+--E 59
+
+--S 60 of 1347
+--d0:=D(m0,x)
+--E 60
+
+)clear all
+
+--S 61 of 1347
+t0:=sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R (1) \|c x + a
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1347
+--r0:=1/3*x*sqrt(a+c*x^4)+2/3*a^(5/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(1/4)*sqrt(a+c*x^4))
+--E 62
+
+--S 63 of 1347
+--a0:=integrate(t0,x)
+--E 63
+
+--S 64 of 1347
+--m0:=a0-r0
+--E 64
+
+--S 65 of 1347
+--d0:=D(m0,x)
+--E 65
+
+)clear all
+
+--S 66 of 1347
+t0:=sqrt(a+c*x^4)/x^2
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (1) -----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 1347
+--r0:=-sqrt(a+c*x^4)/x-2*a^(3/4)*(-c)^(1/4)*_
+-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)+2*a^(3/4)*(-c)^(1/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)
+--E 67
+
+--S 68 of 1347
+--a0:=integrate(t0,x)
+--E 68
+
+--S 69 of 1347
+--m0:=a0-r0
+--E 69
+
+--S 70 of 1347
+--d0:=D(m0,x)
+--E 70
+
+)clear all
+
+--S 71 of 1347
+t0:=sqrt(a+c*x^4)/x^4
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (1) -----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 1347
+--r0:=-1/3*sqrt(a+c*x^4)/x^3-2/3*a^(1/4)*(-c)^(3/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)
+--E 72
+
+--S 73 of 1347
+--a0:=integrate(t0,x)
+--E 73
+
+--S 74 of 1347
+--m0:=a0-r0
+--E 74
+
+--S 75 of 1347
+--d0:=D(m0,x)
+--E 75
+
+)clear all
+
+--S 76 of 1347
+t0:=sqrt(a+c*x^4)/x^6
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (1) -----------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 1347
+--r0:=-1/5*sqrt(a+c*x^4)/x^5-2/5*c*sqrt(a+c*x^4)/(a*x)+_
+-- 2/5*(-c)^(5/4)*elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/(a^(1/4)*sqrt(a+c*x^4))-2/5*(-c)^(5/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/(a^(1/4)*sqrt(a+c*x^4))
+--E 77
+
+--S 78 of 1347
+--a0:=integrate(t0,x)
+--E 78
+
+--S 79 of 1347
+--m0:=a0-r0
+--E 79
+
+--S 80 of 1347
+--d0:=D(m0,x)
+--E 80
+
+)clear all
+
+--S 81 of 1347
+t0:=x^7*(a+c*x^4)^(3/2)
+--R
+--R
+--R +--------+
+--R 11 7 | 4
+--R (1) (c x + a x )\|c x + a
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 1347
+r0:=-1/10*a*(a+c*x^4)^(5/2)/c^2+1/14*(a+c*x^4)^(7/2)/c^2
+--R
+--R
+--R +--------+
+--R 3 12 2 8 2 4 3 | 4
+--R (5c x + 8a c x + a c x - 2a )\|c x + a
+--R (2) --------------------------------------------
+--R 2
+--R 70c
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 3 12 2 8 2 4 3 | 4
+--R (5c x + 8a c x + a c x - 2a )\|c x + a
+--R (3) --------------------------------------------
+--R 2
+--R 70c
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 1347
+t0:=x^5*(a+c*x^4)^(3/2)
+--R
+--R
+--R +--------+
+--R 9 5 | 4
+--R (1) (c x + a x )\|c x + a
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 1347
+r0:=1/12*x^6*(a+c*x^4)^(3/2)-1/32*a^3*atanh(x^2*sqrt(c)/_
+ sqrt(a+c*x^4))/c^(3/2)+1/32*a^2*x^2*sqrt(a+c*x^4)/c+_
+ 1/16*a*x^6*sqrt(a+c*x^4)
+--R
+--R
+--R 2 +-+ +--------+
+--R 3 x \|c 2 10 6 2 2 +-+ | 4
+--R - 3a atanh(-----------) + (8c x + 14a c x + 3a x )\|c \|c x + a
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) --------------------------------------------------------------------
+--R +-+
+--R 96c\|c
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 2 8 4 4 5 +-+ | 4 3 3 12 4 2 8
+--R (18a c x + 96a c x + 96a )\|a \|c x + a - 3a c x - 54a c x
+--R +
+--R 5 4 6
+--R - 144a c x - 96a
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 5 22 4 18 2 3 14 3 2 10 4 6
+--R - 8c x - 158a c x - 639a c x - 982a c x - 592a c x
+--R +
+--R 5 2
+--R - 96a x
+--R *
+--R +--------+
+--R +-+ | 4
+--R \|c \|c x + a
+--R +
+--R 5 22 4 18 2 3 14 3 2 10 4 6
+--R 48c x + 388a c x + 1062a c x + 1266a c x + 640a c x
+--R +
+--R 5 2
+--R 96a x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R +--------+
+--R 3 8 2 4 2 +-+ +-+ | 4
+--R (576c x + 3072a c x + 3072a c)\|a \|c \|c x + a
+--R +
+--R 4 12 3 8 2 2 4 3 +-+
+--R (- 96c x - 1728a c x - 4608a c x - 3072a c)\|c
+--R ,
+--R
+--R +--------+
+--R 3 2 8 4 4 5 +-+ | 4 3 3 12
+--R (- 36a c x - 192a c x - 192a )\|a \|c x + a + 6a c x
+--R +
+--R 4 2 8 5 4 6
+--R 108a c x + 288a c x + 192a
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- c \|c x + a - \|- c \|a
+--R atan(------------------------------)
+--R 2
+--R c x
+--R +
+--R 5 22 4 18 2 3 14 3 2 10 4 6
+--R - 8c x - 158a c x - 639a c x - 982a c x - 592a c x
+--R +
+--R 5 2
+--R - 96a x
+--R *
+--R +--------+
+--R +---+ | 4
+--R \|- c \|c x + a
+--R +
+--R 5 22 4 18 2 3 14 3 2 10 4 6
+--R 48c x + 388a c x + 1062a c x + 1266a c x + 640a c x
+--R +
+--R 5 2
+--R 96a x
+--R *
+--R +---+ +-+
+--R \|- c \|a
+--R /
+--R +--------+
+--R 3 8 2 4 2 +---+ +-+ | 4
+--R (576c x + 3072a c x + 3072a c)\|- c \|a \|c x + a
+--R +
+--R 4 12 3 8 2 2 4 3 +---+
+--R (- 96c x - 1728a c x - 4608a c x - 3072a c)\|- c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 88
+
+--S 89 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R 3 (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a
+--R a log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R 3 x \|c
+--R a atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R +-+
+--R 32c\|c
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+--S 91 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 +-+ +---+ | 4 +---+ +-+
+--R 3 +---+ x \|c 3 +-+ \|- c \|c x + a - \|- c \|a
+--R a \|- c atanh(-----------) - 2a \|c atan(------------------------------)
+--R +--------+ 2
+--R | 4 c x
+--R \|c x + a
+--R ------------------------------------------------------------------------
+--R +---+ +-+
+--R 32c\|- c \|c
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 92
+
+)clear all
+
+--S 93 of 1347
+t0:=x^3*(a+c*x^4)^(3/2)
+--R
+--R
+--R +--------+
+--R 7 3 | 4
+--R (1) (c x + a x )\|c x + a
+--R Type: Expression(Integer)
+--E 93
+
+--S 94 of 1347
+r0:=1/10*(a+c*x^4)^(5/2)/c
+--R
+--R
+--R +--------+
+--R 2 8 4 2 | 4
+--R (c x + 2a c x + a )\|c x + a
+--R (2) --------------------------------
+--R 10c
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 8 4 2 | 4
+--R (c x + 2a c x + a )\|c x + a
+--R (3) --------------------------------
+--R 10c
+--R Type: Union(Expression(Integer),...)
+--E 95
+
+--S 96 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 97
+
+)clear all
+
+--S 98 of 1347
+t0:=x*(a+c*x^4)^(3/2)
+--R
+--R
+--R +--------+
+--R 5 | 4
+--R (1) (c x + a x)\|c x + a
+--R Type: Expression(Integer)
+--E 98
+
+--S 99 of 1347
+r0:=1/8*x^2*(a+c*x^4)^(3/2)+3/16*a^2*atanh(x^2*sqrt(c)/_
+ sqrt(a+c*x^4))/sqrt(c)+3/16*a*x^2*sqrt(a+c*x^4)
+--R
+--R
+--R 2 +-+ +--------+
+--R 2 x \|c 6 2 +-+ | 4
+--R 3a atanh(-----------) + (2c x + 5a x )\|c \|c x + a
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) ------------------------------------------------------
+--R +-+
+--R 16\|c
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 4 3 +-+ | 4 2 2 8 3 4 4
+--R ((12a c x + 24a )\|a \|c x + a - 3a c x - 24a c x - 24a )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R +--------+
+--R 3 14 2 10 2 6 3 2 +-+ | 4
+--R (- 2c x - 21a c x - 56a c x - 40a x )\|c \|c x + a
+--R +
+--R 3 14 2 10 2 6 3 2 +-+ +-+
+--R (8c x + 44a c x + 76a c x + 40a x )\|a \|c
+--R /
+--R +--------+
+--R 4 +-+ +-+ | 4 2 8 4 2 +-+
+--R (64c x + 128a)\|a \|c \|c x + a + (- 16c x - 128a c x - 128a )\|c
+--R ,
+--R
+--R +--------+
+--R 2 4 3 +-+ | 4 2 2 8 3 4 4
+--R ((24a c x + 48a )\|a \|c x + a - 6a c x - 48a c x - 48a )
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- c \|c x + a - \|- c \|a
+--R atan(------------------------------)
+--R 2
+--R c x
+--R +
+--R +--------+
+--R 3 14 2 10 2 6 3 2 +---+ | 4
+--R (- 2c x - 21a c x - 56a c x - 40a x )\|- c \|c x + a
+--R +
+--R 3 14 2 10 2 6 3 2 +---+ +-+
+--R (8c x + 44a c x + 76a c x + 40a x )\|- c \|a
+--R /
+--R +--------+
+--R 4 +---+ +-+ | 4
+--R (64c x + 128a)\|- c \|a \|c x + a
+--R +
+--R 2 8 4 2 +---+
+--R (- 16c x - 128a c x - 128a )\|- c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 100
+
+--S 101 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R 2 (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a
+--R 3a log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R 2 x \|c
+--R - 3a atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R +-+
+--R 16\|c
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 +-+ +---+ | 4 +---+ +-+
+--R 2 +---+ x \|c 2 +-+ \|- c \|c x + a - \|- c \|a
+--R - 3a \|- c atanh(-----------) + 6a \|c atan(------------------------------)
+--R +--------+ 2
+--R | 4 c x
+--R \|c x + a
+--R ---------------------------------------------------------------------------
+--R +---+ +-+
+--R 16\|- c \|c
+--R Type: Expression(Integer)
+--E 103
+
+--S 104 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 104
+
+)clear all
+
+--S 105 of 1347
+t0:=(a+c*x^4)^(3/2)/x
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R x
+--R Type: Expression(Integer)
+--E 105
+
+--S 106 of 1347
+r0:=1/6*(a+c*x^4)^(3/2)-1/2*a^(3/2)*atanh(sqrt(a+c*x^4)/sqrt(a))+_
+ 1/2*a*sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R | 4 +--------+
+--R +-+ \|c x + a 4 | 4
+--R - 3a\|a atanh(-----------) + (c x + 4a)\|c x + a
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ | 4 4 +--------+
+--R +-+ - 2\|a \|c x + a + c x + 2a 4 | 4
+--R 3a\|a log(------------------------------) + (2c x + 8a)\|c x + a
+--R 4
+--R x
+--R [-------------------------------------------------------------------,
+--R 12
+--R +--------+
+--R | 4 +--------+
+--R +---+ \|c x + a 4 | 4
+--R - 3a\|- a atan(-----------) + (c x + 4a)\|c x + a
+--R +---+
+--R \|- a
+--R ----------------------------------------------------]
+--R 6
+--R Type: Union(List(Expression(Integer)),...)
+--E 107
+
+--S 108 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R +-+ | 4 4 | 4
+--R +-+ - 2\|a \|c x + a + c x + 2a +-+ \|c x + a
+--R a\|a log(------------------------------) + 2a\|a atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) -------------------------------------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 108
+
+--S 109 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 | 4
+--R +-+ \|c x + a +---+ \|c x + a
+--R a\|a atanh(-----------) - a\|- a atan(-----------)
+--R +-+ +---+
+--R \|a \|- a
+--R (6) --------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 110
+
+--S 111 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 111
+
+)clear all
+
+--S 112 of 1347
+t0:=(a+c*x^4)^(3/2)/x^3
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 1347
+r0:=-1/2*(a+c*x^4)^(3/2)/x^2+3/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))*_
+ sqrt(c)+3/4*c*x^2*sqrt(a+c*x^4)
+--R
+--R
+--R 2 +-+ +--------+
+--R 2 +-+ x \|c 4 | 4
+--R 3a x \|c atanh(-----------) + (c x - 2a)\|c x + a
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) ----------------------------------------------------
+--R 2
+--R 4x
+--R Type: Expression(Integer)
+--E 113
+
+--S 114 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+
+--R ((3a c x + 12a x )\|c \|c x + a + (- 9a c x - 12a x )\|a \|c )
+--R *
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a
+--R log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4
+--R (- 3c x + 2a c x + 8a )\|a \|c x + a + c x + 3a c x - 6a c x
+--R +
+--R 3
+--R - 8a
+--R /
+--R +--------+
+--R 6 2 | 4 6 2 +-+
+--R (4c x + 16a x )\|c x + a + (- 12c x - 16a x )\|a
+--R ,
+--R
+--R +--------+
+--R 6 2 2 +---+ | 4
+--R (6a c x + 24a x )\|- c \|c x + a
+--R +
+--R 6 2 2 +---+ +-+
+--R (- 18a c x - 24a x )\|- c \|a
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|c x + a - \|a
+--R atan(------------------)
+--R 2 +---+
+--R x \|- c
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4
+--R (- 3c x + 2a c x + 8a )\|a \|c x + a + c x + 3a c x - 6a c x
+--R +
+--R 3
+--R - 8a
+--R /
+--R +--------+
+--R 6 2 | 4 6 2 +-+
+--R (4c x + 16a x )\|c x + a + (- 12c x - 16a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 114
+
+--S 115 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R +-+ (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a
+--R 3a\|c log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R +-+ x \|c
+--R - 3a\|c atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R 4
+--R Type: Expression(Integer)
+--E 115
+
+--S 116 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R 2 +-+ | 4 +-+
+--R +-+ x \|c +---+ \|c x + a - \|a
+--R - 3a\|c atanh(-----------) + 6a\|- c atan(------------------)
+--R +--------+ 2 +---+
+--R | 4 x \|- c
+--R \|c x + a
+--R (6) -------------------------------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 118
+
+)clear all
+
+--S 119 of 1347
+t0:=(a+c*x^4)^(3/2)/x^5
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 1347
+r0:=-1/4*(a+c*x^4)^(3/2)/x^4-3/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))*_
+ sqrt(a)+3/4*c*sqrt(a+c*x^4)
+--R
+--R
+--R +--------+
+--R | 4 +--------+
+--R 4 +-+ \|c x + a 4 | 4
+--R - 3c x \|a atanh(-----------) + (2c x - a)\|c x + a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 120
+
+--S 121 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ | 4 4 +--------+
+--R 4 +-+ - 2\|a \|c x + a + c x + 2a 4 | 4
+--R 3c x \|a log(------------------------------) + (4c x - 2a)\|c x + a
+--R 4
+--R x
+--R [----------------------------------------------------------------------,
+--R 4
+--R 8x
+--R +--------+
+--R | 4 +--------+
+--R 4 +---+ \|c x + a 4 | 4
+--R - 3c x \|- a atan(-----------) + (2c x - a)\|c x + a
+--R +---+
+--R \|- a
+--R -------------------------------------------------------]
+--R 4
+--R 4x
+--R Type: Union(List(Expression(Integer)),...)
+--E 121
+
+--S 122 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R +-+ | 4 4 | 4
+--R +-+ - 2\|a \|c x + a + c x + 2a +-+ \|c x + a
+--R 3c\|a log(------------------------------) + 6c\|a atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) --------------------------------------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 123
+
+--S 124 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 | 4
+--R +-+ \|c x + a +---+ \|c x + a
+--R 3c\|a atanh(-----------) - 3c\|- a atan(-----------)
+--R +-+ +---+
+--R \|a \|- a
+--R (6) ----------------------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 1347
+t0:=(a+c*x^4)^(3/2)/x^7
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 1347
+r0:=-1/6*(a+c*x^4)^(3/2)/x^6+1/2*c^(3/2)*atanh(x^2*sqrt(c)/_
+ sqrt(a+c*x^4))-1/2*c*sqrt(a+c*x^4)/x^2
+--R
+--R
+--R 2 +-+ +--------+
+--R 6 +-+ x \|c 4 | 4
+--R 3c x \|c atanh(-----------) + (- 4c x - a)\|c x + a
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) ------------------------------------------------------
+--R 6
+--R 6x
+--R Type: Expression(Integer)
+--E 127
+
+--S 128 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+
+--R ((3c x + 12a c x )\|c \|c x + a + (- 9c x - 12a c x )\|a \|c )
+--R *
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a
+--R log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4
+--R (12c x + 19a c x + 4a )\|a \|c x + a - 4c x - 21a c x - 21a c x
+--R +
+--R 3
+--R - 4a
+--R /
+--R +--------+
+--R 10 6 | 4 10 6 +-+
+--R (6c x + 24a x )\|c x + a + (- 18c x - 24a x )\|a
+--R ,
+--R
+--R +--------+
+--R 2 10 6 +---+ | 4
+--R (6c x + 24a c x )\|- c \|c x + a
+--R +
+--R 2 10 6 +---+ +-+
+--R (- 18c x - 24a c x )\|- c \|a
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|c x + a - \|a
+--R atan(------------------)
+--R 2 +---+
+--R x \|- c
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4
+--R (12c x + 19a c x + 4a )\|a \|c x + a - 4c x - 21a c x - 21a c x
+--R +
+--R 3
+--R - 4a
+--R /
+--R +--------+
+--R 10 6 | 4 10 6 +-+
+--R (6c x + 24a x )\|c x + a + (- 18c x - 24a x )\|a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 128
+
+--S 129 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 +-+ +-+ | 4 2 +-+ +-+ 4
+--R +-+ (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a
+--R c\|c log(----------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R +-+ x \|c
+--R - c\|c atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 130
+
+--S 131 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R 2 +-+ | 4 +-+
+--R +-+ x \|c +---+ \|c x + a - \|a
+--R - c\|c atanh(-----------) + 2c\|- c atan(------------------)
+--R +--------+ 2 +---+
+--R | 4 x \|- c
+--R \|c x + a
+--R (6) ------------------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 132
+
+)clear all
+
+--S 133 of 1347
+t0:=(a+c*x^4)^(3/2)/x^9
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 133
+
+--S 134 of 1347
+r0:=-1/8*(a+c*x^4)^(3/2)/x^8-3/16*c^2*atanh(sqrt(a+c*x^4)/sqrt(a))/_
+ sqrt(a)-3/16*c*sqrt(a+c*x^4)/x^4
+--R
+--R
+--R +--------+
+--R | 4 +--------+
+--R 2 8 \|c x + a 4 +-+ | 4
+--R - 3c x atanh(-----------) + (- 5c x - 2a)\|a \|c x + a
+--R +-+
+--R \|a
+--R (2) ---------------------------------------------------------
+--R 8 +-+
+--R 16x \|a
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 4 4 +-+ +--------+
+--R 2 8 - 2a\|c x + a + (c x + 2a)\|a 4 +-+ | 4
+--R 3c x log(---------------------------------) + (- 10c x - 4a)\|a \|c x + a
+--R 4
+--R x
+--R [----------------------------------------------------------------------------
+--R 8 +-+
+--R 32x \|a
+--R ,
+--R +--------+
+--R +---+ | 4 +--------+
+--R 2 8 \|- a \|c x + a 4 +---+ | 4
+--R - 3c x atan(-----------------) + (- 5c x - 2a)\|- a \|c x + a
+--R a
+--R ----------------------------------------------------------------]
+--R 8 +---+
+--R 16x \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 135
+
+--S 136 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 4 +-+ | 4
+--R 2 - 2a\|c x + a + (c x + 2a)\|a 2 \|c x + a
+--R 3c log(---------------------------------) + 6c atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) -----------------------------------------------------------------
+--R +-+
+--R 32\|a
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 137
+
+--S 138 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 +---+ | 4
+--R 2 +---+ \|c x + a 2 +-+ \|- a \|c x + a
+--R 3c \|- a atanh(-----------) - 3c \|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R +---+ +-+
+--R 16\|- a \|a
+--R Type: Expression(Integer)
+--E 138
+
+--S 139 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 139
+
+)clear all
+
+--S 140 of 1347
+t0:=(a+c*x^4)^(3/2)/x^11
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 140
+
+--S 141 of 1347
+r0:=-1/10*(a+c*x^4)^(5/2)/(a*x^10)
+--R
+--R
+--R +--------+
+--R 2 8 4 2 | 4
+--R (- c x - 2a c x - a )\|c x + a
+--R (2) ----------------------------------
+--R 10
+--R 10a x
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 5 20
+--R (5c x + 30a c x + 61a c x + 52a c x + 16a )\|a \|c x + a - c x
+--R +
+--R 4 16 2 3 12 3 2 8 4 4 5
+--R - 15a c x - 55a c x - 85a c x - 60a c x - 16a
+--R /
+--R +--------+
+--R 2 18 2 14 3 10 | 4
+--R (10a c x + 120a c x + 160a x )\|c x + a
+--R +
+--R 2 18 2 14 3 10 +-+
+--R (- 50a c x - 200a c x - 160a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 142
+
+--S 143 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 143
+
+--S 144 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 144
+
+)clear all
+
+--S 145 of 1347
+t0:=(a+c*x^4)^(3/2)/x^13
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 13
+--R x
+--R Type: Expression(Integer)
+--E 145
+
+--S 146 of 1347
+r0:=-1/12*(a+c*x^4)^(3/2)/x^12+1/32*c^3*atanh(sqrt(a+c*x^4)/sqrt(a))/_
+ a^(3/2)-1/16*c*sqrt(a+c*x^4)/x^8-1/32*c^2*sqrt(a+c*x^4)/(a*x^4)
+--R
+--R
+--R +--------+
+--R | 4 +--------+
+--R 3 12 \|c x + a 2 8 4 2 +-+ | 4
+--R 3c x atanh(-----------) + (- 3c x - 14a c x - 8a )\|a \|c x + a
+--R +-+
+--R \|a
+--R (2) --------------------------------------------------------------------
+--R 12 +-+
+--R 96a x \|a
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R | 4 4 +-+
+--R 3 12 2a\|c x + a + (c x + 2a)\|a
+--R 3c x log(-------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4
+--R (- 6c x - 28a c x - 16a )\|a \|c x + a
+--R /
+--R 12 +-+
+--R 192a x \|a
+--R ,
+--R +--------+
+--R +---+ | 4 +--------+
+--R 3 12 \|- a \|c x + a 2 8 4 2 +---+ | 4
+--R 3c x atan(-----------------) + (- 3c x - 14a c x - 8a )\|- a \|c x + a
+--R a
+--R ---------------------------------------------------------------------------]
+--R 12 +---+
+--R 96a x \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 147
+
+--S 148 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 4 +-+ | 4
+--R 3 2a\|c x + a + (c x + 2a)\|a 3 \|c x + a
+--R c log(-------------------------------) - 2c atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) --------------------------------------------------------------
+--R +-+
+--R 64a\|a
+--R Type: Expression(Integer)
+--E 148
+
+--S 149 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 +---+ | 4
+--R 3 +---+ \|c x + a 3 +-+ \|- a \|c x + a
+--R - c \|- a atanh(-----------) + c \|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R +---+ +-+
+--R 32a\|- a \|a
+--R Type: Expression(Integer)
+--E 150
+
+--S 151 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 151
+
+)clear all
+
+--S 152 of 1347
+t0:=(a+c*x^4)^(3/2)/x^15
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 15
+--R x
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 1347
+r0:=-1/14*(a+c*x^4)^(5/2)/(a*x^14)+1/35*c*(a+c*x^4)^(5/2)/(a^2*x^10)
+--R
+--R
+--R +--------+
+--R 3 12 2 8 2 4 3 | 4
+--R (2c x - a c x - 8a c x - 5a )\|c x + a
+--R (2) --------------------------------------------
+--R 2 14
+--R 70a x
+--R Type: Expression(Integer)
+--E 153
+
+--S 154 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 24 5 20 2 4 16 3 3 12 4 2 8
+--R - 14c x - 105a c x - 112a c x + 467a c x + 1240a c x
+--R +
+--R 5 4 6
+--R 1072a c x + 320a
+--R *
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a
+--R +
+--R 7 28 6 24 2 5 20 3 4 16 4 3 12 5 2 8
+--R 2c x + 49a c x + 175a c x - 21a c x - 973a c x - 1736a c x
+--R +
+--R 6 4 7
+--R - 1232a c x - 320a
+--R /
+--R +--------+
+--R 2 3 26 3 2 22 4 18 5 14 | 4
+--R (70a c x + 1680a c x + 5600a c x + 4480a x )\|c x + a
+--R +
+--R 2 3 26 3 2 22 4 18 5 14 +-+
+--R (- 490a c x - 3920a c x - 7840a c x - 4480a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 154
+
+--S 155 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 155
+
+--S 156 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 156
+
+)clear all
+
+--S 157 of 1347
+t0:=x^4*(a+c*x^4)^(3/2)
+--R
+--R
+--R +--------+
+--R 8 4 | 4
+--R (1) (c x + a x )\|c x + a
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 1347
+--r0:=1/11*x^5*(a+c*x^4)^(3/2)+4/77*a^2*x*sqrt(a+c*x^4)/c+_
+-- 6/77*a*x^5*sqrt(a+c*x^4)+4/77*a^(13/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4))
+--E 158
+
+--S 159 of 1347
+--a0:=integrate(t0,x)
+--E 159
+
+--S 160 of 1347
+--m0:=a0-r0
+--E 160
+
+--S 161 of 1347
+--d0:=D(m0,x)
+--E 161
+
+)clear all
+
+--S 162 of 1347
+t0:=x^2*(a+c*x^4)^(3/2)
+--R
+--R
+--R +--------+
+--R 6 2 | 4
+--R (1) (c x + a x )\|c x + a
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 1347
+--r0:=1/9*x^3*(a+c*x^4)^(3/2)+2/15*a*x^3*sqrt(a+c*x^4)+_
+-- 4/15*a^(11/4)*elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4))-4/15*a^(11/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4))
+--E 163
+
+--S 164 of 1347
+--a0:=integrate(t0,x)
+--E 164
+
+--S 165 of 1347
+--m0:=a0-r0
+--E 165
+
+--S 166 of 1347
+--d0:=D(m0,x)
+--E 166
+
+)clear all
+
+--S 167 of 1347
+t0:=(a+c*x^4)^(3/2)
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (1) (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 1347
+--r0:=1/7*x*(a+c*x^4)^(3/2)+2/7*a*x*sqrt(a+c*x^4)+4/7*a^(9/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(1/4)*sqrt(a+c*x^4))
+--E 168
+
+--S 169 of 1347
+--a0:=integrate(t0,x)
+--E 169
+
+--S 170 of 1347
+--m0:=a0-r0
+--E 170
+
+--S 171 of 1347
+--d0:=D(m0,x)
+--E 171
+
+)clear all
+
+--S 172 of 1347
+t0:=(a+c*x^4)^(3/2)/x^2
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 172
+
+--S 173 of 1347
+--r0:=-(a+c*x^4)^(3/2)/x+6/5*c*x^3*sqrt(a+c*x^4)-12/5*a^(7/4)*(-c)^(1/4)*_
+-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_
+-- sqrt(a+c*x^4)+12/5*a^(7/4)*(-c)^(1/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)
+--E 173
+
+--S 174 of 1347
+--a0:=integrate(t0,x)
+--E 174
+
+--S 175 of 1347
+--m0:=a0-r0
+--E 175
+
+--S 176 of 1347
+--d0:=D(m0,x)
+--E 176
+
+)clear all
+
+--S 177 of 1347
+t0:=(a+c*x^4)^(3/2)/x^4
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 1347
+--r0:=-1/3*(a+c*x^4)^(3/2)/x^3+2/3*c*x*sqrt(a+c*x^4)-_
+-- 4/3*a^(5/4)*(-c)^(3/4)*elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)
+--E 178
+
+--S 179 of 1347
+--a0:=integrate(t0,x)
+--E 179
+
+--S 180 of 1347
+--m0:=a0-r0
+--E 180
+
+--S 181 of 1347
+--d0:=D(m0,x)
+--E 181
+
+)clear all
+
+--S 182 of 1347
+t0:=(a+c*x^4)^(3/2)/x^6
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 1347
+--r0:=-1/5*(a+c*x^4)^(3/2)/x^5-6/5*c*sqrt(a+c*x^4)/x+_
+-- 12/5*a^(3/4)*(-c)^(5/4)*elliptic_e(asin((-c)^(1/4)*_
+-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)-_
+-- 12/5*a^(3/4)*(-c)^(5/4)*elliptic_f(asin((-c)^(1/4)*x/_
+-- a^(1/4)),-1)*sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)
+--E 183
+
+--S 184 of 1347
+--a0:=integrate(t0,x)
+--E 184
+
+--S 185 of 1347
+--m0:=a0-r0
+--E 185
+
+--S 186 of 1347
+--d0:=D(m0,x)
+--E 186
+
+)clear all
+
+--S 187 of 1347
+t0:=(a+c*x^4)^(3/2)/x^8
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R (1) ---------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 1347
+--r0:=-1/7*(a+c*x^4)^(3/2)/x^7-2/7*c*sqrt(a+c*x^4)/x^3+_
+-- 4/7*a^(1/4)*(-c)^(7/4)*elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)
+--E 188
+
+--S 189 of 1347
+--a0:=integrate(t0,x)
+--E 189
+
+--S 190 of 1347
+--m0:=a0-r0
+--E 190
+
+--S 191 of 1347
+--d0:=D(m0,x)
+--E 191
+
+)clear all
+
+--S 192 of 1347
+t0:=(1+x^4)^(3/2)
+--R
+--R
+--R +------+
+--R 4 | 4
+--R (1) (x + 1)\|x + 1
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 1347
+--r0:=1/7*x*(1+x^4)^(3/2)-4/7*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x),-1)+_
+-- 2/7*x*sqrt(1+x^4)
+--E 193
+
+--S 194 of 1347
+--a0:=integrate(t0,x)
+--E 194
+
+--S 195 of 1347
+--m0:=a0-r0
+--E 195
+
+--S 196 of 1347
+--d0:=D(m0,x)
+--E 196
+
+)clear all
+
+--S 197 of 1347
+t0:=(1-x^4)^(3/2)
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (1) (- x + 1)\|- x + 1
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 1347
+--r0:=1/7*x*(1-x^4)^(3/2)+4/7*elliptic_f(asin(x),-1)+2/7*x*sqrt(1-x^4)
+--E 198
+
+--S 199 of 1347
+--a0:=integrate(t0,x)
+--E 199
+
+--S 200 of 1347
+--m0:=a0-r0
+--E 200
+
+--S 201 of 1347
+--d0:=D(m0,x)
+--E 201
+
+)clear all
+
+--S 202 of 1347
+t0:=x^7*sqrt(5+3*x^4)
+--R
+--R
+--R +-------+
+--R 7 | 4
+--R (1) x \|3x + 5
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 1347
+r0:=-5/54*(5+3*x^4)^(3/2)+1/90*(5+3*x^4)^(5/2)
+--R
+--R
+--R +-------+
+--R 8 4 | 4
+--R (27x + 15x - 50)\|3x + 5
+--R (2) ----------------------------
+--R 270
+--R Type: Expression(Integer)
+--E 203
+
+--S 204 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 8 4 | 4
+--R (27x + 15x - 50)\|3x + 5
+--R (3) ----------------------------
+--R 270
+--R Type: Union(Expression(Integer),...)
+--E 204
+
+--S 205 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 205
+
+--S 206 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 206
+
+)clear all
+
+--S 207 of 1347
+t0:=x^3*sqrt(5+x^4)
+--R
+--R
+--R +------+
+--R 3 | 4
+--R (1) x \|x + 5
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 1347
+r0:=1/6*(5+x^4)^(3/2)
+--R
+--R
+--R +------+
+--R 4 | 4
+--R (x + 5)\|x + 5
+--R (2) -----------------
+--R 6
+--R Type: Expression(Integer)
+--E 208
+
+--S 209 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R 4 | 4
+--R (x + 5)\|x + 5
+--R (3) -----------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 209
+
+--S 210 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 210
+
+--S 211 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 211
+
+)clear all
+
+--S 212 of 1347
+t0:=x*sqrt(3+2*x^4)
+--R
+--R
+--R +-------+
+--R | 4
+--R (1) x\|2x + 3
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 1347
+r0:=3/4*asinh(x^2*sqrt(2/3))/sqrt(2)+1/4*x^2*sqrt(3+2*x^4)
+--R
+--R
+--R +-------+ 2 +-+
+--R 2 +-+ | 4 x \|2
+--R x \|2 \|2x + 3 + 3asinh(------)
+--R +-+
+--R \|3
+--R (2) ---------------------------------
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 213
+
+--S 214 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R +-+ | 4 4
+--R (3\|3 \|2x + 3 - 3x - 9)
+--R *
+--R +-------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|2 \|3 - 2x )\|2x + 3 + 2x \|3 + (- 2x - 3)\|2
+--R log(------------------------------------------------------)
+--R +-------+
+--R +-+ | 4
+--R \|3 \|2x + 3 - 3
+--R +
+--R +-------+
+--R 6 2 +-+ | 4 6 2 +-+ +-+
+--R (- x - 3x )\|2 \|2x + 3 + (2x + 3x )\|2 \|3
+--R /
+--R +-------+
+--R +-+ +-+ | 4 4 +-+
+--R 4\|2 \|3 \|2x + 3 + (- 4x - 12)\|2
+--R Type: Union(Expression(Integer),...)
+--E 214
+
+--S 215 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ 2 +-+
+--R (\|2 \|3 - 2x )\|2x + 3 + 2x \|3 + (- 2x - 3)\|2 x \|2
+--R 3log(------------------------------------------------------) - 3asinh(------)
+--R +-------+ +-+
+--R +-+ | 4 \|3
+--R \|3 \|2x + 3 - 3
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 215
+
+--S 216 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 216
+
+)clear all
+
+--S 217 of 1347
+t0:=x*sqrt(-2+x^4)
+--R
+--R
+--R +------+
+--R | 4
+--R (1) x\|x - 2
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 1347
+r0:=-1/2*atanh(x^2/sqrt(-2+x^4))+1/4*x^2*sqrt(-2+x^4)
+--R
+--R
+--R 2 +------+
+--R x 2 | 4
+--R - 2atanh(---------) + x \|x - 2
+--R +------+
+--R | 4
+--R \|x - 2
+--R (2) ---------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 218
+
+--S 219 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+ +------+
+--R 2 | 4 4 | 4 2 6 2 | 4 8 4
+--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x - 2x
+--R -----------------------------------------------------------------------------
+--R +------+
+--R 2 | 4 4
+--R 4x \|x - 2 - 4x + 4
+--R Type: Union(Expression(Integer),...)
+--E 219
+
+--S 220 of 1347
+m0:=a0-r0
+--R
+--R
+--R +------+ 2
+--R | 4 2 x
+--R log(\|x - 2 - x ) + atanh(---------)
+--R +------+
+--R | 4
+--R \|x - 2
+--R (4) --------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 220
+
+--S 221 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 221
+
+)clear all
+
+--S 222 of 1347
+t0:=(1+x^4)^(1/2)
+--R
+--R
+--R +------+
+--R | 4
+--R (1) \|x + 1
+--R Type: Expression(Integer)
+--E 222
+
+--S 223 of 1347
+--r0:=-2/3*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x),-1)+1/3*x*sqrt(1+x^4)
+--E 223
+
+--S 224 of 1347
+--a0:=integrate(t0,x)
+--E 224
+
+--S 225 of 1347
+--m0:=a0-r0
+--E 225
+
+--S 226 of 1347
+--d0:=D(m0,x)
+--E 226
+
+)clear all
+
+--S 227 of 1347
+t0:=(1-x^4)^(1/2)
+--R
+--R
+--R +--------+
+--R | 4
+--R (1) \|- x + 1
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 1347
+--r0:=2/3*elliptic_f(asin(x),-1)+1/3*x*sqrt(1-x^4)
+--E 228
+
+--S 229 of 1347
+--a0:=integrate(t0,x)
+--E 229
+
+--S 230 of 1347
+--m0:=a0-r0
+--E 230
+
+--S 231 of 1347
+--d0:=D(m0,x)
+--E 231
+
+)clear all
+
+--S 232 of 1347
+t0:=x^7/sqrt(a+c*x^4)
+--R
+--R
+--R 7
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R \|c x + a
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 1347
+r0:=-1/3*a*sqrt(a+c*x^4)/c^2+1/6*x^4*sqrt(a+c*x^4)/c
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x - 2a)\|c x + a
+--R (2) ----------------------
+--R 2
+--R 6c
+--R Type: Expression(Integer)
+--E 233
+
+--S 234 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (c x - 2a)\|c x + a
+--R (3) ----------------------
+--R 2
+--R 6c
+--R Type: Union(Expression(Integer),...)
+--E 234
+
+--S 235 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 235
+
+--S 236 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 236
+
+)clear all
+
+--S 237 of 1347
+t0:=x^5/sqrt(a+c*x^4)
+--R
+--R
+--R 5
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R \|c x + a
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 1347
+r0:=-1/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(3/2)+1/4*x^2*sqrt(a+c*x^4)/c
+--R
+--R
+--R 2 +-+ +--------+
+--R x \|c 2 +-+ | 4
+--R - a atanh(-----------) + x \|c \|c x + a
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) ------------------------------------------
+--R +-+
+--R 4c\|c
+--R Type: Expression(Integer)
+--E 238
+
+--S 239 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 4 4 2
+--R (2a\|a \|c x + a - a c x - 2a )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R +--------+
+--R 6 2 +-+ | 4 6 2 +-+ +-+
+--R (- c x - 2a x )\|c \|c x + a + (2c x + 2a x )\|a \|c
+--R /
+--R +--------+
+--R +-+ +-+ | 4 2 4 +-+
+--R 8c\|a \|c \|c x + a + (- 4c x - 8a c)\|c
+--R ,
+--R
+--R +--------+
+--R +-+ | 4 4 2
+--R (- 4a\|a \|c x + a + 2a c x + 4a )
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- c \|c x + a - \|- c \|a
+--R atan(------------------------------)
+--R 2
+--R c x
+--R +
+--R +--------+
+--R 6 2 +---+ | 4 6 2 +---+ +-+
+--R (- c x - 2a x )\|- c \|c x + a + (2c x + 2a x )\|- c \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 4 2 4 +---+
+--R 8c\|- c \|a \|c x + a + (- 4c x - 8a c)\|- c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 239
+
+--S 240 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a
+--R a log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R x \|c
+--R a atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R +-+
+--R 4c\|c
+--R Type: Expression(Integer)
+--E 240
+
+--S 241 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R 2 +-+ +---+ | 4 +---+ +-+
+--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a
+--R a\|- c atanh(-----------) - 2a\|c atan(------------------------------)
+--R +--------+ 2
+--R | 4 c x
+--R \|c x + a
+--R (6) ----------------------------------------------------------------------
+--R +---+ +-+
+--R 4c\|- c \|c
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 243
+
+)clear all
+
+--S 244 of 1347
+t0:=x^3/sqrt(a+c*x^4)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R \|c x + a
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 1347
+r0:=1/2*sqrt(a+c*x^4)/c
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) -----------
+--R 2c
+--R Type: Expression(Integer)
+--E 245
+
+--S 246 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (3) -----------
+--R 2c
+--R Type: Union(Expression(Integer),...)
+--E 246
+
+--S 247 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 248
+
+)clear all
+
+--S 249 of 1347
+t0:=x/sqrt(a+c*x^4)
+--R
+--R
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R \|c x + a
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 1347
+r0:=1/2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/sqrt(c)
+--R
+--R
+--R 2 +-+
+--R x \|c
+--R atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) ------------------
+--R +-+
+--R 2\|c
+--R Type: Expression(Integer)
+--E 250
+
+--S 251 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R [---------------------------------------------------------------,
+--R +-+
+--R 2\|c
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- c \|c x + a - \|- c \|a
+--R atan(------------------------------)
+--R 2
+--R c x
+--R ------------------------------------]
+--R +---+
+--R \|- c
+--R Type: Union(List(Expression(Integer)),...)
+--E 251
+
+--S 252 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R x \|c
+--R - atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R +-+
+--R 2\|c
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 253
+
+--S 254 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R 2 +-+ +---+ | 4 +---+ +-+
+--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a
+--R - \|- c atanh(-----------) + 2\|c atan(------------------------------)
+--R +--------+ 2
+--R | 4 c x
+--R \|c x + a
+--R (6) ----------------------------------------------------------------------
+--R +---+ +-+
+--R 2\|- c \|c
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 1347
+t0:=1/(x*sqrt(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +--------+
+--R | 4
+--R x\|c x + a
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 1347
+r0:=-1/2*atanh(sqrt(a+c*x^4)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R (2) - ------------------
+--R +-+
+--R 2\|a
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 4 4 +-+ +--------+
+--R - 2a\|c x + a + (c x + 2a)\|a +---+ | 4
+--R log(---------------------------------) \|- a \|c x + a
+--R 4 atan(-----------------)
+--R x a
+--R (3) [--------------------------------------,- -----------------------]
+--R +-+ +---+
+--R 4\|a 2\|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 258
+
+--S 259 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 4 +-+ | 4
+--R - 2a\|c x + a + (c x + 2a)\|a \|c x + a
+--R log(---------------------------------) + 2atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) ------------------------------------------------------------
+--R +-+
+--R 4\|a
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+--S 261 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 +---+ | 4
+--R +---+ \|c x + a +-+ \|- a \|c x + a
+--R \|- a atanh(-----------) - \|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------
+--R +---+ +-+
+--R 2\|- a \|a
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 262
+
+)clear all
+
+--S 263 of 1347
+t0:=1/(x^3*sqrt(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 3 | 4
+--R x \|c x + a
+--R Type: Expression(Integer)
+--E 263
+
+--S 264 of 1347
+r0:=-1/2*sqrt(a+c*x^4)/(a*x^2)
+--R
+--R
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) - -----------
+--R 2
+--R 2a x
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +-+ | 4 4
+--R \|a \|c x + a - c x - a
+--R (3) ----------------------------
+--R +--------+
+--R 2 | 4 2 +-+
+--R 2a x \|c x + a - 2a x \|a
+--R Type: Union(Expression(Integer),...)
+--E 265
+
+--S 266 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 267
+
+)clear all
+
+--S 268 of 1347
+t0:=1/(x^5*sqrt(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 5 | 4
+--R x \|c x + a
+--R Type: Expression(Integer)
+--E 268
+
+--S 269 of 1347
+r0:=1/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(3/2)-1/4*sqrt(a+c*x^4)/(a*x^4)
+--R
+--R
+--R +--------+
+--R | 4 +--------+
+--R 4 \|c x + a +-+ | 4
+--R c x atanh(-----------) - \|a \|c x + a
+--R +-+
+--R \|a
+--R (2) ----------------------------------------
+--R 4 +-+
+--R 4a x \|a
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 4 4 +-+ +--------+
+--R 4 2a\|c x + a + (c x + 2a)\|a +-+ | 4
+--R c x log(-------------------------------) - 2\|a \|c x + a
+--R 4
+--R x
+--R [-----------------------------------------------------------,
+--R 4 +-+
+--R 8a x \|a
+--R +--------+
+--R +---+ | 4 +--------+
+--R 4 \|- a \|c x + a +---+ | 4
+--R c x atan(-----------------) - \|- a \|c x + a
+--R a
+--R -----------------------------------------------]
+--R 4 +---+
+--R 4a x \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 270
+
+--S 271 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 4 +-+ | 4
+--R 2a\|c x + a + (c x + 2a)\|a \|c x + a
+--R c log(-------------------------------) - 2c atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) --------------------------------------------------------------
+--R +-+
+--R 8a\|a
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 +---+ | 4
+--R +---+ \|c x + a +-+ \|- a \|c x + a
+--R - c\|- a atanh(-----------) + c\|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------------
+--R +---+ +-+
+--R 4a\|- a \|a
+--R Type: Expression(Integer)
+--E 273
+
+--S 274 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 274
+
+)clear all
+
+--S 275 of 1347
+t0:=1/(x^7*sqrt(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 7 | 4
+--R x \|c x + a
+--R Type: Expression(Integer)
+--E 275
+
+--S 276 of 1347
+r0:=-1/6*sqrt(a+c*x^4)/(a*x^6)+1/3*c*sqrt(a+c*x^4)/(a^2*x^2)
+--R
+--R
+--R +--------+
+--R 4 | 4
+--R (2c x - a)\|c x + a
+--R (2) ----------------------
+--R 2 6
+--R 6a x
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 3
+--R (- 6c x - 5a c x + 4a )\|a \|c x + a + 2c x + 9a c x + 3a c x - 4a
+--R ---------------------------------------------------------------------------
+--R +--------+
+--R 2 10 3 6 | 4 2 10 3 6 +-+
+--R (6a c x + 24a x )\|c x + a + (- 18a c x - 24a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 277
+
+--S 278 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 278
+
+--S 279 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 279
+
+)clear all
+
+--S 280 of 1347
+t0:=x^6/sqrt(a+b*x^4)
+--R
+--R
+--R 6
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 280
+
+--S 281 of 1347
+--r0:=1/5*x^3*sqrt(a+b*x^4)/b+3/5*a^(7/4)*_
+-- elliptic_e(asin((-b)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+b*x^4)/a)/((-b)^(7/4)*sqrt(a+b*x^4))-_
+-- 3/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+b*x^4)/a)/((-b)^(7/4)*sqrt(a+b*x^4))
+--E 281
+
+--S 282 of 1347
+--a0:=integrate(t0,x)
+--E 282
+
+--S 283 of 1347
+--m0:=a0-r0
+--E 283
+
+--S 284 of 1347
+--d0:=D(m0,x)
+--E 284
+
+)clear all
+
+--S 285 of 1347
+t0:=x^4/sqrt(a+c*x^4)
+--R
+--R
+--R 4
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R \|c x + a
+--R Type: Expression(Integer)
+--E 285
+
+--S 286 of 1347
+--r0:=1/3*x*sqrt(a+c*x^4)/c+1/3*a^(5/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4))
+--E 286
+
+--S 287 of 1347
+--a0:=integrate(t0,x)
+--E 287
+
+--S 288 of 1347
+--m0:=a0-r0
+--E 288
+
+--S 289 of 1347
+--d0:=D(m0,x)
+--E 289
+
+)clear all
+
+--S 290 of 1347
+t0:=x^2/sqrt(a+c*x^4)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R \|c x + a
+--R Type: Expression(Integer)
+--E 290
+
+--S 291 of 1347
+--r0:=a^(3/4)*elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4))-a^(3/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4))
+--E 291
+
+--S 292 of 1347
+--a0:=integrate(t0,x)
+--E 292
+
+--S 293 of 1347
+--m0:=a0-r0
+--E 293
+
+--S 294 of 1347
+--d0:=D(m0,x)
+--E 294
+
+)clear all
+
+--S 295 of 1347
+t0:=1/sqrt(a+c*x^4)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 4
+--R \|c x + a
+--R Type: Expression(Integer)
+--E 295
+
+--S 296 of 1347
+--r0:=a^(1/4)*elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/((-c)^(1/4)*sqrt(a+c*x^4))
+--E 296
+
+--S 297 of 1347
+--a0:=integrate(t0,x)
+--E 297
+
+--S 298 of 1347
+--m0:=a0-r0
+--E 298
+
+--S 299 of 1347
+--d0:=D(m0,x)
+--E 299
+
+)clear all
+
+--S 300 of 1347
+t0:=1/(x^2*sqrt(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 2 | 4
+--R x \|c x + a
+--R Type: Expression(Integer)
+--E 300
+
+--S 301 of 1347
+--r0:=-sqrt(a+c*x^4)/(a*x)-(-c)^(1/4)*elliptic_e(asin((-c)^(1/4)*_
+-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/(a^(1/4)*_
+-- sqrt(a+c*x^4))+(-c)^(1/4)*elliptic_f(asin((-c)^(1/4)*_
+-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/(a^(1/4)*sqrt(a+c*x^4))
+--E 301
+
+--S 302 of 1347
+--a0:=integrate(t0,x)
+--E 302
+
+--S 303 of 1347
+--m0:=a0-r0
+--E 303
+
+--S 304 of 1347
+--d0:=D(m0,x)
+--E 304
+
+)clear all
+
+--S 305 of 1347
+t0:=1/(x^4*sqrt(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R 4 | 4
+--R x \|c x + a
+--R Type: Expression(Integer)
+--E 305
+
+--S 306 of 1347
+--r0:=-1/3*sqrt(a+c*x^4)/(a*x^3)+1/3*(-c)^(3/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/(a^(3/4)*sqrt(a+c*x^4))
+--E 306
+
+--S 307 of 1347
+--a0:=integrate(t0,x)
+--E 307
+
+--S 308 of 1347
+--m0:=a0-r0
+--E 308
+
+--S 309 of 1347
+--d0:=D(m0,x)
+--E 309
+
+)clear all
+
+--S 310 of 1347
+t0:=x^9/(a+c*x^4)^(3/2)
+--R
+--R
+--R 9
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 310
+
+--S 311 of 1347
+r0:=-3/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(5/2)-_
+ 1/2*x^6/(c*sqrt(a+c*x^4))+3/4*x^2*sqrt(a+c*x^4)/c^2
+--R
+--R
+--R +--------+ 2 +-+
+--R | 4 x \|c 6 2 +-+
+--R - 3a\|c x + a atanh(-----------) + (c x + 3a x )\|c
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) ------------------------------------------------------
+--R +--------+
+--R 2 +-+ | 4
+--R 4c \|c \|c x + a
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 4 2 +-+ | 4 2 8 2 4 3
+--R ((9a c x + 12a )\|a \|c x + a - 3a c x - 15a c x - 12a )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R +--------+
+--R 2 10 6 2 2 +-+ | 4
+--R (- c x - 7a c x - 12a x )\|c \|c x + a
+--R +
+--R 2 10 6 2 2 +-+ +-+
+--R (3c x + 13a c x + 12a x )\|a \|c
+--R /
+--R +--------+
+--R 3 4 2 +-+ +-+ | 4 4 8 3 4 2 2 +-+
+--R (12c x + 16a c )\|a \|c \|c x + a + (- 4c x - 20a c x - 16a c )\|c
+--R ,
+--R
+--R +--------+
+--R 4 2 +-+ | 4 2 8 2 4 3
+--R ((- 18a c x - 24a )\|a \|c x + a + 6a c x + 30a c x + 24a )
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- c \|c x + a - \|- c \|a
+--R atan(------------------------------)
+--R 2
+--R c x
+--R +
+--R +--------+
+--R 2 10 6 2 2 +---+ | 4
+--R (- c x - 7a c x - 12a x )\|- c \|c x + a
+--R +
+--R 2 10 6 2 2 +---+ +-+
+--R (3c x + 13a c x + 12a x )\|- c \|a
+--R /
+--R +--------+
+--R 3 4 2 +---+ +-+ | 4
+--R (12c x + 16a c )\|- c \|a \|c x + a
+--R +
+--R 4 8 3 4 2 2 +---+
+--R (- 4c x - 20a c x - 16a c )\|- c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 312
+
+--S 313 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a
+--R 3a log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R x \|c
+--R 3a atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R 2 +-+
+--R 4c \|c
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 +-+ +---+ | 4 +---+ +-+
+--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a
+--R 3a\|- c atanh(-----------) - 6a\|c atan(------------------------------)
+--R +--------+ 2
+--R | 4 c x
+--R \|c x + a
+--R -----------------------------------------------------------------------
+--R 2 +---+ +-+
+--R 4c \|- c \|c
+--R Type: Expression(Integer)
+--E 315
+
+--S 316 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 316
+
+)clear all
+
+--S 317 of 1347
+t0:=x^7/(a+c*x^4)^(3/2)
+--R
+--R
+--R 7
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 1347
+r0:=1/2*a/(c^2*sqrt(a+c*x^4))+1/2*sqrt(a+c*x^4)/c^2
+--R
+--R
+--R 4
+--R c x + 2a
+--R (2) --------------
+--R +--------+
+--R 2 | 4
+--R 2c \|c x + a
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R c x + 2a
+--R (3) --------------
+--R +--------+
+--R 2 | 4
+--R 2c \|c x + a
+--R Type: Union(Expression(Integer),...)
+--E 319
+
+--S 320 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 320
+
+--S 321 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 321
+
+)clear all
+
+--S 322 of 1347
+t0:=x^5/(a+c*x^4)^(3/2)
+--R
+--R
+--R 5
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 1347
+r0:=1/2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(3/2)-1/2*x^2/(c*sqrt(a+c*x^4))
+--R
+--R
+--R +--------+ 2 +-+
+--R | 4 x \|c 2 +-+
+--R \|c x + a atanh(-----------) - x \|c
+--R +--------+
+--R | 4
+--R \|c x + a
+--R (2) --------------------------------------
+--R +--------+
+--R +-+ | 4
+--R 2c\|c \|c x + a
+--R Type: Expression(Integer)
+--E 323
+
+--S 324 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 4 4
+--R (\|a \|c x + a - c x - a)
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R +--------+
+--R 2 +-+ | 4 2 +-+ +-+
+--R x \|c \|c x + a - x \|a \|c
+--R /
+--R +--------+
+--R +-+ +-+ | 4 2 4 +-+
+--R 2c\|a \|c \|c x + a + (- 2c x - 2a c)\|c
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 4 +---+ +-+
+--R +-+ | 4 4 \|- c \|c x + a - \|- c \|a
+--R (2\|a \|c x + a - 2c x - 2a)atan(------------------------------)
+--R 2
+--R c x
+--R +
+--R +--------+
+--R 2 +---+ | 4 2 +---+ +-+
+--R x \|- c \|c x + a - x \|- c \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 4 2 4 +---+
+--R 2c\|- c \|a \|c x + a + (- 2c x - 2a c)\|- c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 324
+
+--S 325 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ 2 | 4 4 +-+ 2 +-+
+--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|a \|c x + a - a
+--R +
+--R 2 +-+
+--R x \|c
+--R - atanh(-----------)
+--R +--------+
+--R | 4
+--R \|c x + a
+--R /
+--R +-+
+--R 2c\|c
+--R Type: Expression(Integer)
+--E 325
+
+--S 326 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R 2 +-+ +---+ | 4 +---+ +-+
+--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a
+--R - \|- c atanh(-----------) + 2\|c atan(------------------------------)
+--R +--------+ 2
+--R | 4 c x
+--R \|c x + a
+--R (6) ----------------------------------------------------------------------
+--R +---+ +-+
+--R 2c\|- c \|c
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 328
+
+)clear all
+
+--S 329 of 1347
+t0:=x^3/(a+c*x^4)^(3/2)
+--R
+--R
+--R 3
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 1347
+r0:=(-1/2)/(c*sqrt(a+c*x^4))
+--R
+--R
+--R 1
+--R (2) - -------------
+--R +--------+
+--R | 4
+--R 2c\|c x + a
+--R Type: Expression(Integer)
+--E 330
+
+--S 331 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - -------------
+--R +--------+
+--R | 4
+--R 2c\|c x + a
+--R Type: Union(Expression(Integer),...)
+--E 331
+
+--S 332 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 333
+
+)clear all
+
+--S 334 of 1347
+t0:=x/(a+c*x^4)^(3/2)
+--R
+--R
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 1347
+r0:=1/2*x^2/(a*sqrt(a+c*x^4))
+--R
+--R
+--R 2
+--R x
+--R (2) -------------
+--R +--------+
+--R | 4
+--R 2a\|c x + a
+--R Type: Expression(Integer)
+--E 335
+
+--S 336 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 | 4 2 +-+
+--R - x \|c x + a + x \|a
+--R (3) ---------------------------------
+--R +--------+
+--R +-+ | 4 4 2
+--R 2a\|a \|c x + a - 2a c x - 2a
+--R Type: Union(Expression(Integer),...)
+--E 336
+
+--S 337 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 338
+
+)clear all
+
+--S 339 of 1347
+t0:=1/(x*(a+c*x^4)^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +--------+
+--R 5 | 4
+--R (c x + a x)\|c x + a
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1347
+r0:=-1/2*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(3/2)+1/2/(a*sqrt(a+c*x^4))
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R | 4 \|c x + a +-+
+--R - \|c x + a atanh(-----------) + \|a
+--R +-+
+--R \|a
+--R (2) --------------------------------------
+--R +--------+
+--R +-+ | 4
+--R 2a\|a \|c x + a
+--R Type: Expression(Integer)
+--E 340
+
+--S 341 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +--------+ | 4 4 +-+
+--R | 4 - 2a\|c x + a + (c x + 2a)\|a +-+
+--R \|c x + a log(---------------------------------) + 2\|a
+--R 4
+--R x
+--R [---------------------------------------------------------,
+--R +--------+
+--R +-+ | 4
+--R 4a\|a \|c x + a
+--R +--------+
+--R +--------+ +---+ | 4
+--R | 4 \|- a \|c x + a +---+
+--R - \|c x + a atan(-----------------) + \|- a
+--R a
+--R ---------------------------------------------]
+--R +--------+
+--R +---+ | 4
+--R 2a\|- a \|c x + a
+--R Type: Union(List(Expression(Integer)),...)
+--E 341
+
+--S 342 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 4 +-+ | 4
+--R - 2a\|c x + a + (c x + 2a)\|a \|c x + a
+--R log(---------------------------------) + 2atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) ------------------------------------------------------------
+--R +-+
+--R 4a\|a
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 343
+
+--S 344 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 +---+ | 4
+--R +---+ \|c x + a +-+ \|- a \|c x + a
+--R \|- a atanh(-----------) - \|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------
+--R +---+ +-+
+--R 2a\|- a \|a
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 1347
+t0:=1/(x^3*(a+c*x^4)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 7 3 | 4
+--R (c x + a x )\|c x + a
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 1347
+r0:=1/2/(a*x^2*sqrt(a+c*x^4))-sqrt(a+c*x^4)/(a^2*x^2)
+--R
+--R
+--R 4
+--R - 2c x - a
+--R (2) ----------------
+--R +--------+
+--R 2 2 | 4
+--R 2a x \|c x + a
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 4 +-+ | 4 2 8 4 2
+--R (4c x + 2a)\|a \|c x + a - 2c x - 5a c x - 2a
+--R (3) ------------------------------------------------------
+--R +--------+
+--R 2 6 3 2 | 4 2 6 3 2 +-+
+--R (2a c x + 4a x )\|c x + a + (- 4a c x - 4a x )\|a
+--R Type: Union(Expression(Integer),...)
+--E 348
+
+--S 349 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+)clear all
+
+--S 351 of 1347
+t0:=1/(x^5*(a+c*x^4)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 9 5 | 4
+--R (c x + a x )\|c x + a
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1347
+r0:=3/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(5/2)+1/2/(a*x^4*sqrt(a+c*x^4))-_
+ 3/4*sqrt(a+c*x^4)/(a^2*x^4)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R 4 | 4 \|c x + a 4 +-+
+--R 3c x \|c x + a atanh(-----------) + (- 3c x - a)\|a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------
+--R +--------+
+--R 2 4 +-+ | 4
+--R 4a x \|a \|c x + a
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +--------+ | 4 4 +-+
+--R 4 | 4 2a\|c x + a + (c x + 2a)\|a 4 +-+
+--R 3c x \|c x + a log(-------------------------------) + (- 6c x - 2a)\|a
+--R 4
+--R x
+--R [-------------------------------------------------------------------------,
+--R +--------+
+--R 2 4 +-+ | 4
+--R 8a x \|a \|c x + a
+--R +--------+
+--R +--------+ +---+ | 4
+--R 4 | 4 \|- a \|c x + a 4 +---+
+--R 3c x \|c x + a atan(-----------------) + (- 3c x - a)\|- a
+--R a
+--R -------------------------------------------------------------]
+--R +--------+
+--R 2 4 +---+ | 4
+--R 4a x \|- a \|c x + a
+--R Type: Union(List(Expression(Integer)),...)
+--E 353
+
+--S 354 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 4 +-+ | 4
+--R 2a\|c x + a + (c x + 2a)\|a \|c x + a
+--R 3c log(-------------------------------) - 6c atanh(-----------)
+--R 4 +-+
+--R x \|a
+--R (4) ---------------------------------------------------------------
+--R 2 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 355
+
+--S 356 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 4 +---+ | 4
+--R +---+ \|c x + a +-+ \|- a \|c x + a
+--R - 3c\|- a atanh(-----------) + 3c\|a atan(-----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R 2 +---+ +-+
+--R 4a \|- a \|a
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 357
+
+)clear all
+
+--S 358 of 1347
+t0:=x^6/(a+c*x^4)^(3/2)
+--R
+--R
+--R 6
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 358
+
+--S 359 of 1347
+--r0:=-1/2*x^3/(c*sqrt(a+c*x^4))-3/2*a^(3/4)*_
+-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_
+-- ((-c)^(7/4)*sqrt(a+c*x^4))+3/2*a^(3/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_
+-- ((-c)^(7/4)*sqrt(a+c*x^4))
+--E 359
+
+--S 360 of 1347
+--a0:=integrate(t0,x)
+--E 360
+
+--S 361 of 1347
+--m0:=a0-r0
+--E 361
+
+--S 362 of 1347
+--d0:=D(m0,x)
+--E 362
+
+)clear all
+
+--S 363 of 1347
+t0:=x^4/(a+c*x^4)^(3/2)
+--R
+--R
+--R 4
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 1347
+--r0:=-1/2*x/(c*sqrt(a+c*x^4))-1/2*a^(1/4)*elliptic_f(asin((-c)^(1/4)*_
+-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4))
+--E 364
+
+--S 365 of 1347
+--a0:=integrate(t0,x)
+--E 365
+
+--S 366 of 1347
+--m0:=a0-r0
+--E 366
+
+--S 367 of 1347
+--d0:=D(m0,x)
+--E 367
+
+)clear all
+
+--S 368 of 1347
+t0:=x^2/(a+c*x^4)^(3/2)
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1347
+--r0:=1/2*x^3/(a*sqrt(a+c*x^4))-1/2*_
+-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_
+-- (a^(1/4)*(-c)^(3/4)*sqrt(a+c*x^4))+1/2*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/(a^(1/4)*(-c)^(3/4)*sqrt(a+c*x^4))
+--E 369
+
+--S 370 of 1347
+--a0:=integrate(t0,x)
+--E 370
+
+--S 371 of 1347
+--m0:=a0-r0
+--E 371
+
+--S 372 of 1347
+--d0:=D(m0,x)
+--E 372
+
+)clear all
+
+--S 373 of 1347
+t0:=1/(a+c*x^4)^(3/2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R 4 | 4
+--R (c x + a)\|c x + a
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 1347
+--r0:=1/2*x/(a*sqrt(a+c*x^4))+1/2*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/(a^(3/4)*(-c)^(1/4)*sqrt(a+c*x^4))
+--E 374
+
+--S 375 of 1347
+--a0:=integrate(t0,x)
+--E 375
+
+--S 376 of 1347
+--m0:=a0-r0
+--E 376
+
+--S 377 of 1347
+--d0:=D(m0,x)
+--E 377
+
+)clear all
+
+--S 378 of 1347
+t0:=1/(x^2*(a+c*x^4)^(3/2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R 6 2 | 4
+--R (c x + a x )\|c x + a
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 1347
+--r0:=1/2/(a*x*sqrt(a+c*x^4))-3/2*sqrt(a+c*x^4)/(a^2*x)-3/2*(-c)^(1/4)*_
+-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_
+-- (a^(5/4)*sqrt(a+c*x^4))+3/2*(-c)^(1/4)*_
+-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+c*x^4)/a)/(a^(5/4)*sqrt(a+c*x^4))
+--E 379
+
+--S 380 of 1347
+--a0:=integrate(t0,x)
+--E 380
+
+--S 381 of 1347
+--m0:=a0-r0
+--E 381
+
+--S 382 of 1347
+--d0:=D(m0,x)
+--E 382
+
+)clear all
+
+--S 383 of 1347
+t0:=1/(a+b*x^4)^(5/2)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+
+--R 2 8 4 2 | 4
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 383
+
+--S 384 of 1347
+--r0:=1/6*x/(a*(a+b*x^4)^(3/2))+5/12*x/(a^2*sqrt(a+b*x^4))+_
+-- 5/12*elliptic_f(asin((-b)^(1/4)*x/a^(1/4)),-1)*_
+-- sqrt((a+b*x^4)/a)/(a^(7/4)*(-b)^(1/4)*sqrt(a+b*x^4))
+--E 384
+
+--S 385 of 1347
+--a0:=integrate(t0,x)
+--E 385
+
+--S 386 of 1347
+--m0:=a0-r0
+--E 386
+
+--S 387 of 1347
+--d0:=D(m0,x)
+--E 387
+
+)clear all
+
+--S 388 of 1347
+t0:=x^7/sqrt(16-x^4)
+--R
+--R
+--R 7
+--R x
+--R (1) ------------
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R Type: Expression(Integer)
+--E 388
+
+--S 389 of 1347
+r0:=-16/3*sqrt(16-x^4)-1/6*x^4*sqrt(16-x^4)
+--R
+--R
+--R +---------+
+--R 4 | 4
+--R (- x - 32)\|- x + 16
+--R (2) -----------------------
+--R 6
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 4 | 4
+--R (- x - 32)\|- x + 16
+--R (3) -----------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 390
+
+--S 391 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 392
+
+)clear all
+
+--S 393 of 1347
+t0:=x^6/sqrt(16-x^4)
+--R
+--R
+--R 6
+--R x
+--R (1) ------------
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R Type: Expression(Integer)
+--E 393
+
+--S 394 of 1347
+--r0:=96/5*elliptic_e(asin(1/2*x),-1)-96/5*elliptic_f(asin(1/2*x),-1)-_
+-- 1/5*x^3*sqrt(16-x^4)
+--E 394
+
+--S 395 of 1347
+--a0:=integrate(t0,x)
+--E 395
+
+--S 396 of 1347
+--m0:=a0-r0
+--E 396
+
+--S 397 of 1347
+--d0:=D(m0,x)
+--E 397
+
+)clear all
+
+--S 398 of 1347
+t0:=x^5/sqrt(16-x^4)
+--R
+--R
+--R 5
+--R x
+--R (1) ------------
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 1347
+r0:=4*asin(1/4*x^2)-1/4*x^2*sqrt(16-x^4)
+--R
+--R
+--R +---------+ 2
+--R 2 | 4 x
+--R - x \|- x + 16 + 16asin(--)
+--R 4
+--R (2) -----------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+
+--R +---------+ | 4
+--R | 4 4 \|- x + 16 - 4
+--R (- 256\|- x + 16 - 32x + 1024)atan(----------------)
+--R 2
+--R x
+--R +
+--R +---------+
+--R 6 2 | 4 6 2
+--R (- x + 32x )\|- x + 16 + 8x - 128x
+--R /
+--R +---------+
+--R | 4 4
+--R 32\|- x + 16 + 4x - 128
+--R Type: Union(Expression(Integer),...)
+--E 400
+
+--S 401 of 1347
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 4 2
+--R \|- x + 16 - 4 x
+--R (4) - 8atan(----------------) - 4asin(--)
+--R 2 4
+--R x
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 402
+
+)clear all
+
+--S 403 of 1347
+t0:=x^4/sqrt(16-x^4)
+--R
+--R
+--R 4
+--R x
+--R (1) ------------
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R Type: Expression(Integer)
+--E 403
+
+--S 404 of 1347
+--r0:=8/3*elliptic_f(asin(1/2*x),-1)-1/3*x*sqrt(16-x^4)
+--E 404
+
+--S 405 of 1347
+--a0:=integrate(t0,x)
+--E 405
+
+--S 406 of 1347
+--m0:=a0-r0
+--E 406
+
+--S 407 of 1347
+--d0:=D(m0,x)
+--E 407
+
+)clear all
+
+--S 408 of 1347
+t0:=x^3/sqrt(16-x^4)
+--R
+--R
+--R 3
+--R x
+--R (1) ------------
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R Type: Expression(Integer)
+--E 408
+
+--S 409 of 1347
+r0:=-1/2*sqrt(16-x^4)
+--R
+--R
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R (2) - ------------
+--R 2
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R (3) - ------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 410
+
+--S 411 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 412
+
+)clear all
+
+--S 413 of 1347
+t0:=x^2/sqrt(16-x^4)
+--R
+--R
+--R 2
+--R x
+--R (1) ------------
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R Type: Expression(Integer)
+--E 413
+
+--S 414 of 1347
+--r0:=2*elliptic_e(asin(1/2*x),-1)-2*elliptic_f(asin(1/2*x),-1)
+--E 414
+
+--S 415 of 1347
+--a0:=integrate(t0,x)
+--E 415
+
+--S 416 of 1347
+--m0:=a0-r0
+--E 416
+
+--S 417 of 1347
+--d0:=D(m0,x)
+--E 417
+
+)clear all
+
+--S 418 of 1347
+t0:=x/sqrt(16-x^4)
+--R
+--R
+--R x
+--R (1) ------------
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R Type: Expression(Integer)
+--E 418
+
+--S 419 of 1347
+r0:=1/2*asin(1/4*x^2)
+--R
+--R
+--R 2
+--R x
+--R asin(--)
+--R 4
+--R (2) --------
+--R 2
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R | 4
+--R \|- x + 16 - 4
+--R (3) - atan(----------------)
+--R 2
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 420
+
+--S 421 of 1347
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 4 2
+--R \|- x + 16 - 4 x
+--R - 2atan(----------------) - asin(--)
+--R 2 4
+--R x
+--R (4) ------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 422
+
+)clear all
+
+--S 423 of 1347
+t0:=1/sqrt(16-x^4)
+--R
+--R
+--R 1
+--R (1) ------------
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R Type: Expression(Integer)
+--E 423
+
+--S 424 of 1347
+--r0:=1/2*elliptic_f(asin(1/2*x),-1)
+--E 424
+
+--S 425 of 1347
+--a0:=integrate(t0,x)
+--E 425
+
+--S 426 of 1347
+--m0:=a0-r0
+--E 426
+
+--S 427 of 1347
+--d0:=D(m0,x)
+--E 427
+
+)clear all
+
+--S 428 of 1347
+t0:=1/(x*sqrt(16-x^4))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +---------+
+--R | 4
+--R x\|- x + 16
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 1347
+r0:=-1/8*atanh(1/4*sqrt(16-x^4))
+--R
+--R
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R atanh(------------)
+--R 4
+--R (2) - -------------------
+--R 8
+--R Type: Expression(Integer)
+--E 429
+
+--S 430 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+ +---------+
+--R | 4 | 4
+--R - log(\|- x + 16 + 4) + log(\|- x + 16 - 4)
+--R (3) -----------------------------------------------
+--R 16
+--R Type: Union(Expression(Integer),...)
+--E 430
+
+--S 431 of 1347
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R +---------+ +---------+ | 4
+--R | 4 | 4 \|- x + 16
+--R - log(\|- x + 16 + 4) + log(\|- x + 16 - 4) + 2atanh(------------)
+--R 4
+--R (4) ----------------------------------------------------------------------
+--R 16
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 432
+
+)clear all
+
+--S 433 of 1347
+t0:=1/(x^2*sqrt(16-x^4))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 2 | 4
+--R x \|- x + 16
+--R Type: Expression(Integer)
+--E 433
+
+--S 434 of 1347
+--r0:=-1/8*elliptic_e(asin(1/2*x),-1)+1/8*elliptic_f(asin(1/2*x),-1)-_
+-- 1/16*sqrt(16-x^4)/x
+--E 434
+
+--S 435 of 1347
+--a0:=integrate(t0,x)
+--E 435
+
+--S 436 of 1347
+--m0:=a0-r0
+--E 436
+
+--S 437 of 1347
+--d0:=D(m0,x)
+--E 437
+
+)clear all
+
+--S 438 of 1347
+t0:=1/(x^3*sqrt(16-x^4))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 3 | 4
+--R x \|- x + 16
+--R Type: Expression(Integer)
+--E 438
+
+--S 439 of 1347
+r0:=-1/32*sqrt(16-x^4)/x^2
+--R
+--R
+--R +---------+
+--R | 4
+--R \|- x + 16
+--R (2) - ------------
+--R 2
+--R 32x
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R | 4 4
+--R 4\|- x + 16 + x - 16
+--R (3) ------------------------
+--R +---------+
+--R 2 | 4 2
+--R 32x \|- x + 16 - 128x
+--R Type: Union(Expression(Integer),...)
+--E 440
+
+--S 441 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 442
+
+)clear all
+
+--S 443 of 1347
+t0:=1/(x^4*sqrt(16-x^4))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +---------+
+--R 4 | 4
+--R x \|- x + 16
+--R Type: Expression(Integer)
+--E 443
+
+--S 444 of 1347
+--r0:=1/96*elliptic_f(asin(1/2*x),-1)-1/48*sqrt(16-x^4)/x^3
+--E 444
+
+--S 445 of 1347
+--a0:=integrate(t0,x)
+--E 445
+
+--S 446 of 1347
+--m0:=a0-r0
+--E 446
+
+--S 447 of 1347
+--d0:=D(m0,x)
+--E 447
+
+)clear all
+
+--S 448 of 1347
+t0:=x^7/(1+x^4)^(3/2)
+--R
+--R
+--R 7
+--R x
+--R (1) -----------------
+--R +------+
+--R 4 | 4
+--R (x + 1)\|x + 1
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 1347
+r0:=1/2/sqrt(1+x^4)+1/2*sqrt(1+x^4)
+--R
+--R
+--R 4
+--R x + 2
+--R (2) ----------
+--R +------+
+--R | 4
+--R 2\|x + 1
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R x + 2
+--R (3) ----------
+--R +------+
+--R | 4
+--R 2\|x + 1
+--R Type: Union(Expression(Integer),...)
+--E 450
+
+--S 451 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 452
+
+)clear all
+
+--S 453 of 1347
+t0:=1/(1+x^4)^(3/2)
+--R
+--R
+--R 1
+--R (1) -----------------
+--R +------+
+--R 4 | 4
+--R (x + 1)\|x + 1
+--R Type: Expression(Integer)
+--E 453
+
+--S 454 of 1347
+--r0:=-1/2*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x),-1)+1/2*x/sqrt(1+x^4)
+--E 454
+
+--S 455 of 1347
+--a0:=integrate(t0,x)
+--E 455
+
+--S 456 of 1347
+--m0:=a0-r0
+--E 456
+
+--S 457 of 1347
+--d0:=D(m0,x)
+--E 457
+
+)clear all
+
+--S 458 of 1347
+t0:=1/(1+x^4)^(5/2)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +------+
+--R 8 4 | 4
+--R (x + 2x + 1)\|x + 1
+--R Type: Expression(Integer)
+--E 458
+
+--S 459 of 1347
+--r0:=1/6*x/(1+x^4)^(3/2)-5/12*(-1)^(3/4)*_
+-- elliptic_f(asin((-1)^(1/4)*x),-1)+5/12*x/sqrt(1+x^4)
+--E 459
+
+--S 460 of 1347
+--a0:=integrate(t0,x)
+--E 460
+
+--S 461 of 1347
+--m0:=a0-r0
+--E 461
+
+--S 462 of 1347
+--d0:=D(m0,x)
+--E 462
+
+)clear all
+
+--S 463 of 1347
+t0:=1/(1-x^4)^(3/2)
+--R
+--R
+--R 1
+--R (1) - -------------------
+--R +--------+
+--R 4 | 4
+--R (x - 1)\|- x + 1
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 1347
+--r0:=1/2*elliptic_f(asin(x),-1)+1/2*x/sqrt(1-x^4)
+--E 464
+
+--S 465 of 1347
+--a0:=integrate(t0,x)
+--E 465
+
+--S 466 of 1347
+--m0:=a0-r0
+--E 466
+
+--S 467 of 1347
+--d0:=D(m0,x)
+--E 467
+
+)clear all
+
+--S 468 of 1347
+t0:=1/(1-x^4)^(5/2)
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R +--------+
+--R 8 4 | 4
+--R (x - 2x + 1)\|- x + 1
+--R Type: Expression(Integer)
+--E 468
+
+--S 469 of 1347
+--r0:=1/6*x/(1-x^4)^(3/2)+5/12*elliptic_f(asin(x),-1)+5/12*x/sqrt(1-x^4)
+--E 469
+
+--S 470 of 1347
+--a0:=integrate(t0,x)
+--E 470
+
+--S 471 of 1347
+--m0:=a0-r0
+--E 471
+
+--S 472 of 1347
+--d0:=D(m0,x)
+--E 472
+
+)clear all
+
+--S 473 of 1347
+t0:=x/sqrt(-4+x^4)
+--R
+--R
+--R x
+--R (1) ---------
+--R +------+
+--R | 4
+--R \|x - 4
+--R Type: Expression(Integer)
+--E 473
+
+--S 474 of 1347
+r0:=1/2*atanh(x^2/sqrt(-4+x^4))
+--R
+--R
+--R 2
+--R x
+--R atanh(---------)
+--R +------+
+--R | 4
+--R \|x - 4
+--R (2) ----------------
+--R 2
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R | 4 2
+--R log(\|x - 4 - x )
+--R (3) - -------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 475
+
+--S 476 of 1347
+m0:=a0-r0
+--R
+--R
+--R +------+ 2
+--R | 4 2 x
+--R - log(\|x - 4 - x ) - atanh(---------)
+--R +------+
+--R | 4
+--R \|x - 4
+--R (4) ----------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 477
+
+)clear all
+
+--S 478 of 1347
+t0:=x/sqrt(4+x^4)
+--R
+--R
+--R x
+--R (1) ---------
+--R +------+
+--R | 4
+--R \|x + 4
+--R Type: Expression(Integer)
+--E 478
+
+--S 479 of 1347
+r0:=1/2*asinh(1/2*x^2)
+--R
+--R
+--R 2
+--R x
+--R asinh(--)
+--R 2
+--R (2) ---------
+--R 2
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R | 4 2
+--R log(\|x + 4 - x )
+--R (3) - -------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 480
+
+--S 481 of 1347
+m0:=a0-r0
+--R
+--R
+--R +------+ 2
+--R | 4 2 x
+--R - log(\|x + 4 - x ) - asinh(--)
+--R 2
+--R (4) ---------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 482
+
+)clear all
+
+--S 483 of 1347
+t0:=1/(x*sqrt(-1+x^4))
+--R
+--R
+--R 1
+--R (1) ----------
+--R +------+
+--R | 4
+--R x\|x - 1
+--R Type: Expression(Integer)
+--E 483
+
+--S 484 of 1347
+r0:=1/2*atan(sqrt(-1+x^4))
+--R
+--R
+--R +------+
+--R | 4
+--R atan(\|x - 1 )
+--R (2) ---------------
+--R 2
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R | 4
+--R atan(\|x - 1 )
+--R (3) ---------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 485
+
+--S 486 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 487
+
+)clear all
+
+--S 488 of 1347
+t0:=x^(7/2)*(a+c*x^4)
+--R
+--R
+--R 7 3 +-+
+--R (1) (c x + a x )\|x
+--R Type: Expression(Integer)
+--E 488
+
+--S 489 of 1347
+r0:=2/9*a*x^(9/2)+2/17*c*x^(17/2)
+--R
+--R
+--R 8 4 +-+
+--R (18c x + 34a x )\|x
+--R (2) ---------------------
+--R 153
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 4 +-+
+--R (18c x + 34a x )\|x
+--R (3) ---------------------
+--R 153
+--R Type: Union(Expression(Integer),...)
+--E 490
+
+--S 491 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 492
+
+)clear all
+
+--S 493 of 1347
+t0:=x^(5/2)*(a+c*x^4)
+--R
+--R
+--R 6 2 +-+
+--R (1) (c x + a x )\|x
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 1347
+r0:=2/7*a*x^(7/2)+2/15*c*x^(15/2)
+--R
+--R
+--R 7 3 +-+
+--R (14c x + 30a x )\|x
+--R (2) ---------------------
+--R 105
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 7 3 +-+
+--R (14c x + 30a x )\|x
+--R (3) ---------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 495
+
+--S 496 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 497
+
+)clear all
+
+--S 498 of 1347
+t0:=x^(3/2)*(a+c*x^4)
+--R
+--R
+--R 5 +-+
+--R (1) (c x + a x)\|x
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 1347
+r0:=2/5*a*x^(5/2)+2/13*c*x^(13/2)
+--R
+--R
+--R 6 2 +-+
+--R (10c x + 26a x )\|x
+--R (2) ---------------------
+--R 65
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 2 +-+
+--R (10c x + 26a x )\|x
+--R (3) ---------------------
+--R 65
+--R Type: Union(Expression(Integer),...)
+--E 500
+
+--S 501 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 502
+
+)clear all
+
+--S 503 of 1347
+t0:=(a+c*x^4)*sqrt(x)
+--R
+--R
+--R 4 +-+
+--R (1) (c x + a)\|x
+--R Type: Expression(Integer)
+--E 503
+
+--S 504 of 1347
+r0:=2/3*a*x^(3/2)+2/11*c*x^(11/2)
+--R
+--R
+--R 5 +-+
+--R (6c x + 22a x)\|x
+--R (2) -------------------
+--R 33
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 +-+
+--R (6c x + 22a x)\|x
+--R (3) -------------------
+--R 33
+--R Type: Union(Expression(Integer),...)
+--E 505
+
+--S 506 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 506
+
+--S 507 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 507
+
+)clear all
+
+--S 508 of 1347
+t0:=(a+c*x^4)/sqrt(x)
+--R
+--R
+--R 4
+--R c x + a
+--R (1) --------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 508
+
+--S 509 of 1347
+r0:=2/9*c*x^(9/2)+2*a*sqrt(x)
+--R
+--R
+--R 4 +-+
+--R (2c x + 18a)\|x
+--R (2) -----------------
+--R 9
+--R Type: Expression(Integer)
+--E 509
+
+--S 510 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 +-+
+--R (2c x + 18a)\|x
+--R (3) -----------------
+--R 9
+--R Type: Union(Expression(Integer),...)
+--E 510
+
+--S 511 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 511
+
+--S 512 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 512
+
+)clear all
+
+--S 513 of 1347
+t0:=(a+c*x^4)/x^(3/2)
+--R
+--R
+--R 4
+--R c x + a
+--R (1) --------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 513
+
+--S 514 of 1347
+r0:=2/7*c*x^(7/2)-2*a/sqrt(x)
+--R
+--R
+--R 4
+--R 2c x - 14a
+--R (2) -----------
+--R +-+
+--R 7\|x
+--R Type: Expression(Integer)
+--E 514
+
+--S 515 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R 2c x - 14a
+--R (3) -----------
+--R +-+
+--R 7\|x
+--R Type: Union(Expression(Integer),...)
+--E 515
+
+--S 516 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 516
+
+--S 517 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 517
+
+)clear all
+
+--S 518 of 1347
+t0:=(a+c*x^4)/x^(5/2)
+--R
+--R
+--R 4
+--R c x + a
+--R (1) --------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 518
+
+--S 519 of 1347
+r0:=-2/3*a/x^(3/2)+2/5*c*x^(5/2)
+--R
+--R
+--R 4
+--R 6c x - 10a
+--R (2) -----------
+--R +-+
+--R 15x\|x
+--R Type: Expression(Integer)
+--E 519
+
+--S 520 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R 6c x - 10a
+--R (3) -----------
+--R +-+
+--R 15x\|x
+--R Type: Union(Expression(Integer),...)
+--E 520
+
+--S 521 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 521
+
+--S 522 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 522
+
+)clear all
+
+--S 523 of 1347
+t0:=(a+c*x^4)/x^(7/2)
+--R
+--R
+--R 4
+--R c x + a
+--R (1) --------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 523
+
+--S 524 of 1347
+r0:=-2/5*a/x^(5/2)+2/3*c*x^(3/2)
+--R
+--R
+--R 4
+--R 10c x - 6a
+--R (2) -----------
+--R 2 +-+
+--R 15x \|x
+--R Type: Expression(Integer)
+--E 524
+
+--S 525 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R 10c x - 6a
+--R (3) -----------
+--R 2 +-+
+--R 15x \|x
+--R Type: Union(Expression(Integer),...)
+--E 525
+
+--S 526 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 526
+
+--S 527 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 527
+
+)clear all
+
+--S 528 of 1347
+t0:=x^(7/2)*(a+c*x^4)^2
+--R
+--R
+--R 2 11 7 2 3 +-+
+--R (1) (c x + 2a c x + a x )\|x
+--R Type: Expression(Integer)
+--E 528
+
+--S 529 of 1347
+r0:=2/9*a^2*x^(9/2)+4/17*a*c*x^(17/2)+2/25*c^2*x^(25/2)
+--R
+--R
+--R 2 12 8 2 4 +-+
+--R (306c x + 900a c x + 850a x )\|x
+--R (2) ------------------------------------
+--R 3825
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 12 8 2 4 +-+
+--R (306c x + 900a c x + 850a x )\|x
+--R (3) ------------------------------------
+--R 3825
+--R Type: Union(Expression(Integer),...)
+--E 530
+
+--S 531 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 531
+
+--S 532 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 532
+
+)clear all
+
+--S 533 of 1347
+t0:=x^(5/2)*(a+c*x^4)^2
+--R
+--R
+--R 2 10 6 2 2 +-+
+--R (1) (c x + 2a c x + a x )\|x
+--R Type: Expression(Integer)
+--E 533
+
+--S 534 of 1347
+r0:=2/7*a^2*x^(7/2)+4/15*a*c*x^(15/2)+2/23*c^2*x^(23/2)
+--R
+--R
+--R 2 11 7 2 3 +-+
+--R (210c x + 644a c x + 690a x )\|x
+--R (2) ------------------------------------
+--R 2415
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 11 7 2 3 +-+
+--R (210c x + 644a c x + 690a x )\|x
+--R (3) ------------------------------------
+--R 2415
+--R Type: Union(Expression(Integer),...)
+--E 535
+
+--S 536 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 536
+
+--S 537 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 537
+
+)clear all
+
+--S 538 of 1347
+t0:=x^(3/2)*(a+c*x^4)^2
+--R
+--R
+--R 2 9 5 2 +-+
+--R (1) (c x + 2a c x + a x)\|x
+--R Type: Expression(Integer)
+--E 538
+
+--S 539 of 1347
+r0:=2/5*a^2*x^(5/2)+4/13*a*c*x^(13/2)+2/21*c^2*x^(21/2)
+--R
+--R
+--R 2 10 6 2 2 +-+
+--R (130c x + 420a c x + 546a x )\|x
+--R (2) ------------------------------------
+--R 1365
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 10 6 2 2 +-+
+--R (130c x + 420a c x + 546a x )\|x
+--R (3) ------------------------------------
+--R 1365
+--R Type: Union(Expression(Integer),...)
+--E 540
+
+--S 541 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 542
+
+)clear all
+
+--S 543 of 1347
+t0:=(a+c*x^4)^2*sqrt(x)
+--R
+--R
+--R 2 8 4 2 +-+
+--R (1) (c x + 2a c x + a )\|x
+--R Type: Expression(Integer)
+--E 543
+
+--S 544 of 1347
+r0:=2/3*a^2*x^(3/2)+4/11*a*c*x^(11/2)+2/19*c^2*x^(19/2)
+--R
+--R
+--R 2 9 5 2 +-+
+--R (66c x + 228a c x + 418a x)\|x
+--R (2) ---------------------------------
+--R 627
+--R Type: Expression(Integer)
+--E 544
+
+--S 545 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 9 5 2 +-+
+--R (66c x + 228a c x + 418a x)\|x
+--R (3) ---------------------------------
+--R 627
+--R Type: Union(Expression(Integer),...)
+--E 545
+
+--S 546 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 546
+
+--S 547 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 547
+
+)clear all
+
+--S 548 of 1347
+t0:=(a+c*x^4)^2/sqrt(x)
+--R
+--R
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R (1) -------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 548
+
+--S 549 of 1347
+r0:=4/9*a*c*x^(9/2)+2/17*c^2*x^(17/2)+2*a^2*sqrt(x)
+--R
+--R
+--R 2 8 4 2 +-+
+--R (18c x + 68a c x + 306a )\|x
+--R (2) -------------------------------
+--R 153
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 4 2 +-+
+--R (18c x + 68a c x + 306a )\|x
+--R (3) -------------------------------
+--R 153
+--R Type: Union(Expression(Integer),...)
+--E 550
+
+--S 551 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 551
+
+--S 552 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 552
+
+)clear all
+
+--S 553 of 1347
+t0:=(a+c*x^4)^2/x^(3/2)
+--R
+--R
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R (1) -------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 553
+
+--S 554 of 1347
+r0:=4/7*a*c*x^(7/2)+2/15*c^2*x^(15/2)-2*a^2/sqrt(x)
+--R
+--R
+--R 2 8 4 2
+--R 14c x + 60a c x - 210a
+--R (2) -------------------------
+--R +-+
+--R 105\|x
+--R Type: Expression(Integer)
+--E 554
+
+--S 555 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 4 2
+--R 14c x + 60a c x - 210a
+--R (3) -------------------------
+--R +-+
+--R 105\|x
+--R Type: Union(Expression(Integer),...)
+--E 555
+
+--S 556 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 557
+
+)clear all
+
+--S 558 of 1347
+t0:=(a+c*x^4)^2/x^(5/2)
+--R
+--R
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R (1) -------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 558
+
+--S 559 of 1347
+r0:=-2/3*a^2/x^(3/2)+4/5*a*c*x^(5/2)+2/13*c^2*x^(13/2)
+--R
+--R
+--R 2 8 4 2
+--R 30c x + 156a c x - 130a
+--R (2) --------------------------
+--R +-+
+--R 195x\|x
+--R Type: Expression(Integer)
+--E 559
+
+--S 560 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 4 2
+--R 30c x + 156a c x - 130a
+--R (3) --------------------------
+--R +-+
+--R 195x\|x
+--R Type: Union(Expression(Integer),...)
+--E 560
+
+--S 561 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 561
+
+--S 562 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 562
+
+)clear all
+
+--S 563 of 1347
+t0:=(a+c*x^4)^2/x^(7/2)
+--R
+--R
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R (1) -------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 1347
+r0:=-2/5*a^2/x^(5/2)+4/3*a*c*x^(3/2)+2/11*c^2*x^(11/2)
+--R
+--R
+--R 2 8 4 2
+--R 30c x + 220a c x - 66a
+--R (2) -------------------------
+--R 2 +-+
+--R 165x \|x
+--R Type: Expression(Integer)
+--E 564
+
+--S 565 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 4 2
+--R 30c x + 220a c x - 66a
+--R (3) -------------------------
+--R 2 +-+
+--R 165x \|x
+--R Type: Union(Expression(Integer),...)
+--E 565
+
+--S 566 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 566
+
+--S 567 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 567
+
+)clear all
+
+--S 568 of 1347
+t0:=x^(7/2)*(a+c*x^4)^3
+--R
+--R
+--R 3 15 2 11 2 7 3 3 +-+
+--R (1) (c x + 3a c x + 3a c x + a x )\|x
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 1347
+r0:=2/9*a^3*x^(9/2)+6/17*a^2*c*x^(17/2)+6/25*a*c^2*x^(25/2)+2/33*c^3*x^(33/2)
+--R
+--R
+--R 3 16 2 12 2 8 3 4 +-+
+--R (2550c x + 10098a c x + 14850a c x + 9350a x )\|x
+--R (2) -------------------------------------------------------
+--R 42075
+--R Type: Expression(Integer)
+--E 569
+
+--S 570 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 16 2 12 2 8 3 4 +-+
+--R (2550c x + 10098a c x + 14850a c x + 9350a x )\|x
+--R (3) -------------------------------------------------------
+--R 42075
+--R Type: Union(Expression(Integer),...)
+--E 570
+
+--S 571 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 572
+
+)clear all
+
+--S 573 of 1347
+t0:=x^(5/2)*(a+c*x^4)^3
+--R
+--R
+--R 3 14 2 10 2 6 3 2 +-+
+--R (1) (c x + 3a c x + 3a c x + a x )\|x
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 1347
+r0:=2/7*a^3*x^(7/2)+2/5*a^2*c*x^(15/2)+6/23*a*c^2*x^(23/2)+2/31*c^3*x^(31/2)
+--R
+--R
+--R 3 15 2 11 2 7 3 3 +-+
+--R (1610c x + 6510a c x + 9982a c x + 7130a x )\|x
+--R (2) -----------------------------------------------------
+--R 24955
+--R Type: Expression(Integer)
+--E 574
+
+--S 575 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 15 2 11 2 7 3 3 +-+
+--R (1610c x + 6510a c x + 9982a c x + 7130a x )\|x
+--R (3) -----------------------------------------------------
+--R 24955
+--R Type: Union(Expression(Integer),...)
+--E 575
+
+--S 576 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 576
+
+--S 577 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 577
+
+)clear all
+
+--S 578 of 1347
+t0:=x^(3/2)*(a+c*x^4)^3
+--R
+--R
+--R 3 13 2 9 2 5 3 +-+
+--R (1) (c x + 3a c x + 3a c x + a x)\|x
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 1347
+r0:=2/5*a^3*x^(5/2)+6/13*a^2*c*x^(13/2)+2/7*a*c^2*x^(21/2)+2/29*c^3*x^(29/2)
+--R
+--R
+--R 3 14 2 10 2 6 3 2 +-+
+--R (910c x + 3770a c x + 6090a c x + 5278a x )\|x
+--R (2) ----------------------------------------------------
+--R 13195
+--R Type: Expression(Integer)
+--E 579
+
+--S 580 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 14 2 10 2 6 3 2 +-+
+--R (910c x + 3770a c x + 6090a c x + 5278a x )\|x
+--R (3) ----------------------------------------------------
+--R 13195
+--R Type: Union(Expression(Integer),...)
+--E 580
+
+--S 581 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 581
+
+--S 582 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 582
+
+)clear all
+
+--S 583 of 1347
+t0:=(a+c*x^4)^3*sqrt(x)
+--R
+--R
+--R 3 12 2 8 2 4 3 +-+
+--R (1) (c x + 3a c x + 3a c x + a )\|x
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 1347
+r0:=2/3*a^3*x^(3/2)+6/11*a^2*c*x^(11/2)+6/19*a*c^2*x^(19/2)+2/27*c^3*x^(27/2)
+--R
+--R
+--R 3 13 2 9 2 5 3 +-+
+--R (418c x + 1782a c x + 3078a c x + 3762a x)\|x
+--R (2) --------------------------------------------------
+--R 5643
+--R Type: Expression(Integer)
+--E 584
+
+--S 585 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 13 2 9 2 5 3 +-+
+--R (418c x + 1782a c x + 3078a c x + 3762a x)\|x
+--R (3) --------------------------------------------------
+--R 5643
+--R Type: Union(Expression(Integer),...)
+--E 585
+
+--S 586 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 586
+
+--S 587 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 587
+
+)clear all
+
+--S 588 of 1347
+t0:=(a+c*x^4)^3/sqrt(x)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R (1) ------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 1347
+r0:=2/3*a^2*c*x^(9/2)+6/17*a*c^2*x^(17/2)+2/25*c^3*x^(25/2)+2*a^3*sqrt(x)
+--R
+--R
+--R 3 12 2 8 2 4 3 +-+
+--R (102c x + 450a c x + 850a c x + 2550a )\|x
+--R (2) -----------------------------------------------
+--R 1275
+--R Type: Expression(Integer)
+--E 589
+
+--S 590 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 12 2 8 2 4 3 +-+
+--R (102c x + 450a c x + 850a c x + 2550a )\|x
+--R (3) -----------------------------------------------
+--R 1275
+--R Type: Union(Expression(Integer),...)
+--E 590
+
+--S 591 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 591
+
+--S 592 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 592
+
+)clear all
+
+--S 593 of 1347
+t0:=(a+c*x^4)^3/x^(3/2)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R (1) ------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 593
+
+--S 594 of 1347
+r0:=6/7*a^2*c*x^(7/2)+2/5*a*c^2*x^(15/2)+2/23*c^3*x^(23/2)-2*a^3/sqrt(x)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R 70c x + 322a c x + 690a c x - 1610a
+--R (2) ----------------------------------------
+--R +-+
+--R 805\|x
+--R Type: Expression(Integer)
+--E 594
+
+--S 595 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R 70c x + 322a c x + 690a c x - 1610a
+--R (3) ----------------------------------------
+--R +-+
+--R 805\|x
+--R Type: Union(Expression(Integer),...)
+--E 595
+
+--S 596 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 596
+
+--S 597 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 597
+
+)clear all
+
+--S 598 of 1347
+t0:=(a+c*x^4)^3/x^(5/2)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R (1) ------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 598
+
+--S 599 of 1347
+r0:=-2/3*a^3/x^(3/2)+6/5*a^2*c*x^(5/2)+6/13*a*c^2*x^(13/2)+2/21*c^3*x^(21/2)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R 130c x + 630a c x + 1638a c x - 910a
+--R (2) -----------------------------------------
+--R +-+
+--R 1365x\|x
+--R Type: Expression(Integer)
+--E 599
+
+--S 600 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R 130c x + 630a c x + 1638a c x - 910a
+--R (3) -----------------------------------------
+--R +-+
+--R 1365x\|x
+--R Type: Union(Expression(Integer),...)
+--E 600
+
+--S 601 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 601
+
+--S 602 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 602
+
+)clear all
+
+--S 603 of 1347
+t0:=(a+c*x^4)^3/x^(7/2)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R (1) ------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 603
+
+--S 604 of 1347
+r0:=-2/5*a^3/x^(5/2)+2*a^2*c*x^(3/2)+6/11*a*c^2*x^(11/2)+2/19*c^3*x^(19/2)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R 110c x + 570a c x + 2090a c x - 418a
+--R (2) -----------------------------------------
+--R 2 +-+
+--R 1045x \|x
+--R Type: Expression(Integer)
+--E 604
+
+--S 605 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 12 2 8 2 4 3
+--R 110c x + 570a c x + 2090a c x - 418a
+--R (3) -----------------------------------------
+--R 2 +-+
+--R 1045x \|x
+--R Type: Union(Expression(Integer),...)
+--E 605
+
+--S 606 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 606
+
+--S 607 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 607
+
+)clear all
+
+--S 608 of 1347
+t0:=x^(9/2)/(a+c*x^4)
+--R
+--R
+--R 4 +-+
+--R x \|x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 1347
+r0:=2/3*x^(3/2)/c+1/2*(-a)^(3/8)*atan(c^(1/8)*sqrt(x)/_
+ (-a)^(1/8))/c^(11/8)-1/2*(-a)^(3/8)*atanh(c^(1/8)*_
+ sqrt(x)/(-a)^(1/8))/c^(11/8)+1/2*(-a)^(3/8)*_
+ atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/(c^(11/8)*_
+ sqrt(2))-1/2*(-a)^(3/8)*atan(1+c^(1/8)*sqrt(2)*_
+ sqrt(x)/(-a)^(1/8))/(c^(11/8)*sqrt(2))-1/4*(-a)^(3/8)*_
+ log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/(c^(11/8)*sqrt(2))+1/4*(-a)^(3/8)*_
+ log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/(c^(11/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 3\|- a log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 3\|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+-+ +-+ 8+---+
+--R +-+8+---+3 \|c \|x 8+---+3 \|2 \|c \|x + \|- a
+--R - 6\|2 \|- a atanh(--------) - 6\|- a atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 8+---+3 \|2 \|c \|x - \|- a +-+8+---+3 \|c \|x
+--R - 6\|- a atan(---------------------) + 6\|2 \|- a atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+3 +-+
+--R 8x\|2 \|c \|x
+--R /
+--R +-+8+-+3
+--R 12c\|2 \|c
+--R Type: Expression(Integer)
+--E 609
+
+--S 610 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +----------+
+--R | 3
+--R | a
+--R 3c |- --------
+--R 8| 11
+--R \| 65536c
+--R *
+--R +----------+3 +----------+6
+--R | 3 | 3
+--R 4 +-+ | a +-+ 8 | a 2
+--R log(64a c \|2 |- -------- \|x + 4096c |- -------- + a x)
+--R 8| 11 8| 11
+--R \| 65536c \| 65536c
+--R +
+--R +----------+ +----------+3
+--R | 3 | 3
+--R +-+ | a +-+ 4 | a
+--R 3c\|2 |- -------- log(a\|x + 64c |- -------- )
+--R 8| 11 8| 11
+--R \| 65536c \| 65536c
+--R +
+--R +----------+ +----------+3
+--R | 3 | 3
+--R +-+ | a +-+ 4 | a
+--R - 3c\|2 |- -------- log(a\|x - 64c |- -------- )
+--R 8| 11 8| 11
+--R \| 65536c \| 65536c
+--R +
+--R +----------+
+--R | 3
+--R | a
+--R 3c |- --------
+--R 8| 11
+--R \| 65536c
+--R *
+--R +----------+3 +----------+6
+--R | 3 | 3
+--R 4 +-+ | a +-+ 8 | a 2
+--R log(- 64a c \|2 |- -------- \|x + 4096c |- -------- + a x)
+--R 8| 11 8| 11
+--R \| 65536c \| 65536c
+--R +
+--R +----------+3
+--R | 3
+--R 4 | a
+--R +----------+ 64c |- --------
+--R | 3 8| 11
+--R +-+ | a \| 65536c
+--R 6c\|2 |- -------- atan(------------------)
+--R 8| 11 +-+
+--R \| 65536c a\|x
+--R +
+--R +----------+3
+--R | 3
+--R 4 | a
+--R +----------+ 64c |- --------
+--R | 3 8| 11
+--R | a \| 65536c
+--R - 6c |- -------- atan(------------------------------)
+--R 8| 11 +----------+3
+--R \| 65536c | 3
+--R +-+ +-+ 4 | a
+--R a\|2 \|x - 64c |- --------
+--R 8| 11
+--R \| 65536c
+--R +
+--R +----------+3
+--R | 3
+--R 4 | a
+--R +----------+ 64c |- --------
+--R | 3 8| 11
+--R | a \| 65536c +-+ +-+
+--R - 6c |- -------- atan(------------------------------ + 2x\|2 \|x
+--R 8| 11 +----------+3
+--R \| 65536c | 3
+--R +-+ +-+ 4 | a
+--R a\|2 \|x + 64c |- --------
+--R 8| 11
+--R \| 65536c
+--R /
+--R +-+
+--R 3c\|2
+--R Type: Union(Expression(Integer),...)
+--E 610
+
+--S 611 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - \|- a log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R -
+--R +----------+
+--R | 3
+--R | a 8+-+3
+--R 4c |- -------- \|c
+--R 8| 11
+--R \| 65536c
+--R *
+--R +----------+3 +----------+6
+--R | 3 | 3
+--R 4 +-+ | a +-+ 8 | a 2
+--R log(64a c \|2 |- -------- \|x + 4096c |- -------- + a x)
+--R 8| 11 8| 11
+--R \| 65536c \| 65536c
+--R +
+--R +----------+ +----------+3
+--R | 3 | 3
+--R +-+ | a 8+-+3 +-+ 4 | a
+--R 4c\|2 |- -------- \|c log(a\|x + 64c |- -------- )
+--R 8| 11 8| 11
+--R \| 65536c \| 65536c
+--R +
+--R +----------+ +----------+3
+--R | 3 | 3
+--R +-+ | a 8+-+3 +-+ 4 | a
+--R - 4c\|2 |- -------- \|c log(a\|x - 64c |- -------- )
+--R 8| 11 8| 11
+--R \| 65536c \| 65536c
+--R +
+--R +----------+
+--R | 3
+--R | a 8+-+3
+--R 4c |- -------- \|c
+--R 8| 11
+--R \| 65536c
+--R *
+--R +----------+3 +----------+6
+--R | 3 | 3
+--R 4 +-+ | a +-+ 8 | a 2
+--R log(- 64a c \|2 |- -------- \|x + 4096c |- -------- + a x)
+--R 8| 11 8| 11
+--R \| 65536c \| 65536c
+--R +
+--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R \|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+-+ +-+ 8+---+
+--R +-+8+---+3 \|c \|x 8+---+3 \|2 \|c \|x + \|- a
+--R 2\|2 \|- a atanh(--------) + 2\|- a atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 8+---+3 \|2 \|c \|x - \|- a +-+8+---+3 \|c \|x
+--R 2\|- a atan(---------------------) - 2\|2 \|- a atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +----------+3
+--R | 3
+--R 4 | a
+--R +----------+ 64c |- --------
+--R | 3 8| 11
+--R +-+ | a 8+-+3 \| 65536c
+--R 8c\|2 |- -------- \|c atan(------------------)
+--R 8| 11 +-+
+--R \| 65536c a\|x
+--R +
+--R +----------+3
+--R | 3
+--R 4 | a
+--R +----------+ 64c |- --------
+--R | 3 8| 11
+--R | a 8+-+3 \| 65536c
+--R - 8c |- -------- \|c atan(------------------------------)
+--R 8| 11 +----------+3
+--R \| 65536c | 3
+--R +-+ +-+ 4 | a
+--R a\|2 \|x - 64c |- --------
+--R 8| 11
+--R \| 65536c
+--R +
+--R +----------+3
+--R | 3
+--R 4 | a
+--R +----------+ 64c |- --------
+--R | 3 8| 11
+--R | a 8+-+3 \| 65536c
+--R - 8c |- -------- \|c atan(------------------------------)
+--R 8| 11 +----------+3
+--R \| 65536c | 3
+--R +-+ +-+ 4 | a
+--R a\|2 \|x + 64c |- --------
+--R 8| 11
+--R \| 65536c
+--R /
+--R +-+8+-+3
+--R 4c\|2 \|c
+--R Type: Expression(Integer)
+--E 611
+
+--S 612 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 612
+
+)clear all
+
+--S 613 of 1347
+t0:=x^(7/2)/(a+c*x^4)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Expression(Integer)
+--E 613
+
+--S 614 of 1347
+r0:=-1/2*(-a)^(1/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/c^(9/8)-_
+ 1/2*(-a)^(1/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/c^(9/8)+_
+ 1/2*(-a)^(1/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ (c^(9/8)*sqrt(2))-1/2*(-a)^(1/8)*atan(1+c^(1/8)*sqrt(2)*_
+ sqrt(x)/(-a)^(1/8))/(c^(9/8)*sqrt(2))+1/4*(-a)^(1/8)*_
+ log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/(c^(9/8)*sqrt(2))-1/4*(-a)^(1/8)*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/(c^(9/8)*_
+ sqrt(2))+2*sqrt(x)/c
+--R
+--R
+--R (2)
+--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - \|- a log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R \|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+-+ +-+ 8+---+
+--R +-+8+---+ \|c \|x 8+---+ \|2 \|c \|x + \|- a
+--R - 2\|2 \|- a atanh(--------) - 2\|- a atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 8+---+ \|2 \|c \|x - \|- a +-+8+---+ \|c \|x
+--R - 2\|- a atan(---------------------) - 2\|2 \|- a atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+
+--R 8\|2 \|c \|x
+--R /
+--R +-+8+-+
+--R 4c\|2 \|c
+--R Type: Expression(Integer)
+--E 614
+
+--S 615 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+ +---------+2
+--R | a +-+ | a +-+ 2 | a
+--R - c |- ------- log(4c\|2 |- ------- \|x + 16c |- ------- + x)
+--R 8| 9 8| 9 8| 9
+--R \| 65536c \| 65536c \| 65536c
+--R +
+--R +---------+ +---------+
+--R +-+ | a +-+ | a
+--R - c\|2 |- ------- log(\|x + 4c |- -------)
+--R 8| 9 8| 9
+--R \| 65536c \| 65536c
+--R +
+--R +---------+ +---------+
+--R +-+ | a +-+ | a
+--R c\|2 |- ------- log(\|x - 4c |- -------)
+--R 8| 9 8| 9
+--R \| 65536c \| 65536c
+--R +
+--R +---------+ +---------+ +---------+2
+--R | a +-+ | a +-+ 2 | a
+--R c |- ------- log(- 4c\|2 |- ------- \|x + 16c |- ------- + x)
+--R 8| 9 8| 9 8| 9
+--R \| 65536c \| 65536c \| 65536c
+--R +
+--R +---------+
+--R | a
+--R 4c |- -------
+--R +---------+ 8| 9
+--R +-+ | a \| 65536c
+--R 2c\|2 |- ------- atan(--------------)
+--R 8| 9 +-+
+--R \| 65536c \|x
+--R +
+--R +---------+
+--R | a
+--R 4c |- -------
+--R +---------+ 8| 9
+--R | a \| 65536c
+--R 2c |- ------- atan(-------------------------)
+--R 8| 9 +---------+
+--R \| 65536c +-+ +-+ | a
+--R \|2 \|x - 4c |- -------
+--R 8| 9
+--R \| 65536c
+--R +
+--R +---------+
+--R | a
+--R 4c |- -------
+--R +---------+ 8| 9
+--R | a \| 65536c +-+ +-+
+--R 2c |- ------- atan(------------------------- + 2\|2 \|x
+--R 8| 9 +---------+
+--R \| 65536c +-+ +-+ | a
+--R \|2 \|x + 4c |- -------
+--R 8| 9
+--R \| 65536c
+--R /
+--R +-+
+--R c\|2
+--R Type: Union(Expression(Integer),...)
+--E 615
+
+--S 616 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R \|- a log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +---------+ +---------+ +---------+2
+--R | a 8+-+ +-+ | a +-+ 2 | a
+--R - 4c |- ------- \|c log(4c\|2 |- ------- \|x + 16c |- ------- + x)
+--R 8| 9 8| 9 8| 9
+--R \| 65536c \| 65536c \| 65536c
+--R +
+--R +---------+ +---------+
+--R +-+ | a 8+-+ +-+ | a
+--R - 4c\|2 |- ------- \|c log(\|x + 4c |- -------)
+--R 8| 9 8| 9
+--R \| 65536c \| 65536c
+--R +
+--R +---------+ +---------+
+--R +-+ | a 8+-+ +-+ | a
+--R 4c\|2 |- ------- \|c log(\|x - 4c |- -------)
+--R 8| 9 8| 9
+--R \| 65536c \| 65536c
+--R +
+--R +---------+ +---------+ +---------+2
+--R | a 8+-+ +-+ | a +-+ 2 | a
+--R 4c |- ------- \|c log(- 4c\|2 |- ------- \|x + 16c |- ------- + x)
+--R 8| 9 8| 9 8| 9
+--R \| 65536c \| 65536c \| 65536c
+--R +
+--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - \|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+-+ +-+ 8+---+
+--R +-+8+---+ \|c \|x 8+---+ \|2 \|c \|x + \|- a
+--R 2\|2 \|- a atanh(--------) + 2\|- a atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 8+---+ \|2 \|c \|x - \|- a +-+8+---+ \|c \|x
+--R 2\|- a atan(---------------------) + 2\|2 \|- a atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +---------+
+--R | a
+--R 4c |- -------
+--R +---------+ 8| 9
+--R +-+ | a 8+-+ \| 65536c
+--R 8c\|2 |- ------- \|c atan(--------------)
+--R 8| 9 +-+
+--R \| 65536c \|x
+--R +
+--R +---------+
+--R | a
+--R 4c |- -------
+--R +---------+ 8| 9
+--R | a 8+-+ \| 65536c
+--R 8c |- ------- \|c atan(-------------------------)
+--R 8| 9 +---------+
+--R \| 65536c +-+ +-+ | a
+--R \|2 \|x - 4c |- -------
+--R 8| 9
+--R \| 65536c
+--R +
+--R +---------+
+--R | a
+--R 4c |- -------
+--R +---------+ 8| 9
+--R | a 8+-+ \| 65536c
+--R 8c |- ------- \|c atan(-------------------------)
+--R 8| 9 +---------+
+--R \| 65536c +-+ +-+ | a
+--R \|2 \|x + 4c |- -------
+--R 8| 9
+--R \| 65536c
+--R /
+--R +-+8+-+
+--R 4c\|2 \|c
+--R Type: Expression(Integer)
+--E 616
+
+--S 617 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 617
+
+)clear all
+
+--S 618 of 1347
+t0:=x^(5/2)/(a+c*x^4)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Expression(Integer)
+--E 618
+
+--S 619 of 1347
+r0:=1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(7/8))-_
+ 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(7/8))-_
+ 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*_
+ c^(7/8)*sqrt(2))+1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(1/8)*c^(7/8)*sqrt(2))+1/4*log((-a)^(1/4)+c^(1/4)*x-_
+ (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(1/8)*c^(7/8)*_
+ sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(1/8)*c^(7/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 2atan(---------------------) + 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R /
+--R +-+8+---+8+-+7
+--R 4\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 619
+
+--S 620 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------+
+--R | 1
+--R |- ---------
+--R 8| 7
+--R \| 65536a c
+--R *
+--R +-----------+7 +-----------+6
+--R 6 +-+ | 1 +-+ 5 | 1
+--R log(16384a c \|2 |- --------- \|x - 4096a c |- --------- + x)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+7
+--R +-+ | 1 +-+ 6 | 1
+--R \|2 |- --------- log(\|x + 16384a c |- --------- )
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+7
+--R +-+ | 1 +-+ 6 | 1
+--R - \|2 |- --------- log(\|x - 16384a c |- --------- )
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R -
+--R +-----------+
+--R | 1
+--R |- ---------
+--R 8| 7
+--R \| 65536a c
+--R *
+--R +-----------+7 +-----------+6
+--R 6 +-+ | 1 +-+ 5 | 1
+--R log(- 16384a c \|2 |- --------- \|x - 4096a c |- --------- + x)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+7
+--R 6 | 1
+--R 16384a c |- ---------
+--R +-----------+ 8| 7
+--R | 1 \| 65536a c
+--R 2 |- --------- atan(-----------------------------------)
+--R 8| 7 +-----------+7
+--R \| 65536a c +-+ +-+ 6 | 1
+--R \|2 \|x - 16384a c |- ---------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +-----------+7
+--R 6 | 1
+--R 16384a c |- ---------
+--R +-----------+ 8| 7
+--R | 1 \| 65536a c
+--R 2 |- --------- atan(-----------------------------------)
+--R 8| 7 +-----------+7
+--R \| 65536a c +-+ +-+ 6 | 1
+--R \|2 \|x + 16384a c |- ---------
+--R 8| 7
+--R \| 65536a c
+--R /
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 620
+
+--S 621 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-----------+
+--R 8+---+ | 1 8+-+7
+--R 4\|- a |- --------- \|c
+--R 8| 7
+--R \| 65536a c
+--R *
+--R +-----------+7 +-----------+6
+--R 6 +-+ | 1 +-+ 5 | 1
+--R log(16384a c \|2 |- --------- \|x - 4096a c |- --------- + x)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+7
+--R +-+8+---+ | 1 8+-+7 +-+ 6 | 1
+--R 4\|2 \|- a |- --------- \|c log(\|x + 16384a c |- --------- )
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+7
+--R +-+8+---+ | 1 8+-+7 +-+ 6 | 1
+--R - 4\|2 \|- a |- --------- \|c log(\|x - 16384a c |- --------- )
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R -
+--R +-----------+
+--R 8+---+ | 1 8+-+7
+--R 4\|- a |- --------- \|c
+--R 8| 7
+--R \| 65536a c
+--R *
+--R +-----------+7 +-----------+6
+--R 6 +-+ | 1 +-+ 5 | 1
+--R log(- 16384a c \|2 |- --------- \|x - 4096a c |- --------- + x)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 2atan(---------------------) - 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-----------+7
+--R 6 | 1
+--R 16384a c |- ---------
+--R +-----------+ 8| 7
+--R 8+---+ | 1 8+-+7 \| 65536a c
+--R 8\|- a |- --------- \|c atan(-----------------------------------)
+--R 8| 7 +-----------+7
+--R \| 65536a c +-+ +-+ 6 | 1
+--R \|2 \|x - 16384a c |- ---------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +-----------+7
+--R 6 | 1
+--R 16384a c |- ---------
+--R +-----------+ 8| 7
+--R 8+---+ | 1 8+-+7 \| 65536a c
+--R 8\|- a |- --------- \|c atan(-----------------------------------)
+--R 8| 7 +-----------+7
+--R \| 65536a c +-+ +-+ 6 | 1
+--R \|2 \|x + 16384a c |- ---------
+--R 8| 7
+--R \| 65536a c
+--R /
+--R +-+8+---+8+-+7
+--R 4\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 621
+
+--S 622 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R +-----------+6
+--R 7 9 2 6 5 3 5 | 1
+--R (- 12288a c x + 55296a c x - 6144a c x) |- ---------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +-----------+4
+--R 5 8 2 4 4 3 3 | 1
+--R (1600a c x - 2944a c x + 64a c ) |- ---------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +-----------+2
+--R 3 7 2 2 3 | 1 2 10 6 2 2
+--R (- 168a c x + 120a c x ) |- --------- - c x + 13a c x - 4a x
+--R 8| 7
+--R \| 65536a c
+--R /
+--R +-----------+6
+--R 8 10 2 7 6 3 6 2 | 1
+--R (32768a c x - 8192a c x - 40960a c x ) |- ---------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +-----------+4
+--R 6 9 2 5 5 3 4 | 1
+--R (- 3328a c x - 2048a c x + 1280a c x) |- ---------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +-----------+2
+--R 4 8 2 3 4 3 2 | 1 3 11 2 7
+--R (272a c x + 256a c x - 16a c ) |- --------- + 4c x - 10a c x
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 3
+--R - 14a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 622
+
+)clear all
+
+--S 623 of 1347
+t0:=x^(3/2)/(a+c*x^4)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 1347
+r0:=-1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*c^(5/8))-_
+ 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*c^(5/8))-_
+ 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*_
+ c^(5/8)*sqrt(2))+1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(3/8)*c^(5/8)*sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x-_
+ (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(5/8)*_
+ sqrt(2))+1/4*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(5/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 2atan(---------------------) + 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R /
+--R +-+8+---+3 8+-+5
+--R 4\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 624
+
+--S 625 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------+
+--R | 1
+--R |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R *
+--R +-----------+5 +-----------+2
+--R 2 3 +-+ | 1 +-+ | 1
+--R log(1024a c \|2 |- --------- \|x - 16a c |- --------- + x)
+--R 8| 3 5 8| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+5
+--R +-+ | 1 +-+ 2 3 | 1
+--R - \|2 |- --------- log(\|x + 1024a c |- --------- )
+--R 8| 3 5 8| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+5
+--R +-+ | 1 +-+ 2 3 | 1
+--R \|2 |- --------- log(\|x - 1024a c |- --------- )
+--R 8| 3 5 8| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R -
+--R +-----------+
+--R | 1
+--R |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R *
+--R +-----------+5 +-----------+2
+--R 2 3 +-+ | 1 +-+ | 1
+--R log(- 1024a c \|2 |- --------- \|x - 16a c |- --------- + x)
+--R 8| 3 5 8| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+5
+--R 2 3 | 1
+--R 1024a c |- ---------
+--R +-----------+ 8| 3 5
+--R | 1 \| 65536a c
+--R - 2 |- --------- atan(----------------------------------)
+--R 8| 3 5 +-----------+5
+--R \| 65536a c +-+ +-+ 2 3 | 1
+--R \|2 \|x - 1024a c |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R +
+--R +-----------+5
+--R 2 3 | 1
+--R 1024a c |- ---------
+--R +-----------+ 8| 3 5
+--R | 1 \| 65536a c
+--R - 2 |- --------- atan(----------------------------------)
+--R 8| 3 5 +-----------+5
+--R \| 65536a c +-+ +-+ 2 3 | 1
+--R \|2 \|x + 1024a c |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R /
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 625
+
+--S 626 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-----------+
+--R 8+---+3 | 1 8+-+5
+--R 4\|- a |- --------- \|c
+--R 8| 3 5
+--R \| 65536a c
+--R *
+--R +-----------+5 +-----------+2
+--R 2 3 +-+ | 1 +-+ | 1
+--R log(1024a c \|2 |- --------- \|x - 16a c |- --------- + x)
+--R 8| 3 5 8| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+5
+--R +-+8+---+3 | 1 8+-+5 +-+ 2 3 | 1
+--R - 4\|2 \|- a |- --------- \|c log(\|x + 1024a c |- --------- )
+--R 8| 3 5 8| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+5
+--R +-+8+---+3 | 1 8+-+5 +-+ 2 3 | 1
+--R 4\|2 \|- a |- --------- \|c log(\|x - 1024a c |- --------- )
+--R 8| 3 5 8| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R -
+--R +-----------+
+--R 8+---+3 | 1 8+-+5
+--R 4\|- a |- --------- \|c
+--R 8| 3 5
+--R \| 65536a c
+--R *
+--R +-----------+5 +-----------+2
+--R 2 3 +-+ | 1 +-+ | 1
+--R log(- 1024a c \|2 |- --------- \|x - 16a c |- --------- + x)
+--R 8| 3 5 8| 3 5
+--R \| 65536a c \| 65536a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 2atan(---------------------) - 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-----------+5
+--R 2 3 | 1
+--R 1024a c |- ---------
+--R +-----------+ 8| 3 5
+--R 8+---+3 | 1 8+-+5 \| 65536a c
+--R - 8\|- a |- --------- \|c atan(----------------------------------)
+--R 8| 3 5 +-----------+5
+--R \| 65536a c +-+ +-+ 2 3 | 1
+--R \|2 \|x - 1024a c |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R +
+--R +-----------+5
+--R 2 3 | 1
+--R 1024a c |- ---------
+--R +-----------+ 8| 3 5
+--R 8+---+3 | 1 8+-+5 \| 65536a c
+--R - 8\|- a |- --------- \|c atan(----------------------------------)
+--R 8| 3 5 +-----------+5
+--R \| 65536a c +-+ +-+ 2 3 | 1
+--R \|2 \|x + 1024a c |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R /
+--R +-+8+---+3 8+-+5
+--R 4\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R +-----------+6
+--R 2 6 10 3 5 6 4 4 2 | 1
+--R (8192a c x - 106496a c x + 32768a c x ) |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R +
+--R +-----------+4
+--R 2 4 7 3 3 3 | 1
+--R (- 5376a c x + 3840a c x ) |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R +
+--R +-----------+2
+--R 3 8 2 2 4 3 | 1 2 9 5 2
+--R (- 200a c x + 368a c x - 8a c) |- --------- - 6c x + 27a c x - 3a x
+--R 8| 3 5
+--R \| 65536a c
+--R /
+--R +-----------+6
+--R 3 6 8 4 5 4 5 4 | 1
+--R (139264a c x + 131072a c x - 8192a c ) |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R +
+--R +-----------+4
+--R 2 5 9 3 4 5 4 3 | 1
+--R (6656a c x + 4096a c x - 2560a c x) |- ---------
+--R 8| 3 5
+--R \| 65536a c
+--R +
+--R +-----------+2
+--R 4 10 2 3 6 3 2 2 | 1 3 11 2 7
+--R (256a c x - 64a c x - 320a c x ) |- --------- + 8c x - 20a c x
+--R 8| 3 5
+--R \| 65536a c
+--R +
+--R 2 3
+--R - 28a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 627
+
+)clear all
+
+--S 628 of 1347
+t0:=sqrt(x)/(a+c*x^4)
+--R
+--R
+--R +-+
+--R \|x
+--R (1) --------
+--R 4
+--R c x + a
+--R Type: Expression(Integer)
+--E 628
+
+--S 629 of 1347
+r0:=1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(3/8))-_
+ 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(3/8))+_
+ 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(3/8)*_
+ sqrt(2))-1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*_
+ c^(3/8)*sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(5/8)*c^(3/8)*sqrt(2))+1/4*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/_
+ ((-a)^(5/8)*c^(3/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 2atan(---------------------) - 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R /
+--R +-+8+---+5 8+-+3
+--R 4\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 629
+
+--S 630 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------+
+--R | 1
+--R |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R *
+--R +-----------+3 +-----------+6
+--R 2 +-+ | 1 +-+ 4 2 | 1
+--R log(64a c\|2 |- --------- \|x + 4096a c |- --------- + x)
+--R 8| 5 3 8| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+3
+--R +-+ | 1 +-+ 2 | 1
+--R - \|2 |- --------- log(\|x + 64a c |- --------- )
+--R 8| 5 3 8| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+3
+--R +-+ | 1 +-+ 2 | 1
+--R \|2 |- --------- log(\|x - 64a c |- --------- )
+--R 8| 5 3 8| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R -
+--R +-----------+
+--R | 1
+--R |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R *
+--R +-----------+3 +-----------+6
+--R 2 +-+ | 1 +-+ 4 2 | 1
+--R log(- 64a c\|2 |- --------- \|x + 4096a c |- --------- + x)
+--R 8| 5 3 8| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+3
+--R 2 | 1
+--R 64a c |- ---------
+--R +-----------+ 8| 5 3
+--R | 1 \| 65536a c
+--R 2 |- --------- atan(--------------------------------)
+--R 8| 5 3 +-----------+3
+--R \| 65536a c +-+ +-+ 2 | 1
+--R \|2 \|x - 64a c |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R +
+--R +-----------+3
+--R 2 | 1
+--R 64a c |- ---------
+--R +-----------+ 8| 5 3
+--R | 1 \| 65536a c
+--R 2 |- --------- atan(--------------------------------)
+--R 8| 5 3 +-----------+3
+--R \| 65536a c +-+ +-+ 2 | 1
+--R \|2 \|x + 64a c |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R /
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 630
+
+--S 631 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-----------+
+--R 8+---+5 | 1 8+-+3
+--R 4\|- a |- --------- \|c
+--R 8| 5 3
+--R \| 65536a c
+--R *
+--R +-----------+3 +-----------+6
+--R 2 +-+ | 1 +-+ 4 2 | 1
+--R log(64a c\|2 |- --------- \|x + 4096a c |- --------- + x)
+--R 8| 5 3 8| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+3
+--R +-+8+---+5 | 1 8+-+3 +-+ 2 | 1
+--R - 4\|2 \|- a |- --------- \|c log(\|x + 64a c |- --------- )
+--R 8| 5 3 8| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R +-----------+ +-----------+3
+--R +-+8+---+5 | 1 8+-+3 +-+ 2 | 1
+--R 4\|2 \|- a |- --------- \|c log(\|x - 64a c |- --------- )
+--R 8| 5 3 8| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R -
+--R +-----------+
+--R 8+---+5 | 1 8+-+3
+--R 4\|- a |- --------- \|c
+--R 8| 5 3
+--R \| 65536a c
+--R *
+--R +-----------+3 +-----------+6
+--R 2 +-+ | 1 +-+ 4 2 | 1
+--R log(- 64a c\|2 |- --------- \|x + 4096a c |- --------- + x)
+--R 8| 5 3 8| 5 3
+--R \| 65536a c \| 65536a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 2atan(---------------------) + 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-----------+3
+--R 2 | 1
+--R 64a c |- ---------
+--R +-----------+ 8| 5 3
+--R 8+---+5 | 1 8+-+3 \| 65536a c
+--R 8\|- a |- --------- \|c atan(--------------------------------)
+--R 8| 5 3 +-----------+3
+--R \| 65536a c +-+ +-+ 2 | 1
+--R \|2 \|x - 64a c |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R +
+--R +-----------+3
+--R 2 | 1
+--R 64a c |- ---------
+--R +-----------+ 8| 5 3
+--R 8+---+5 | 1 8+-+3 \| 65536a c
+--R 8\|- a |- --------- \|c atan(--------------------------------)
+--R 8| 5 3 +-----------+3
+--R \| 65536a c +-+ +-+ 2 | 1
+--R \|2 \|x + 64a c |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R /
+--R +-+8+---+5 8+-+3
+--R 4\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 631
+
+--S 632 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R +-----------+6
+--R 4 4 7 5 3 3 | 1
+--R (- 172032a c x + 122880a c x ) |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R +
+--R +-----------+4
+--R 2 4 10 3 3 6 4 2 2 | 1
+--R (1024a c x - 13312a c x + 4096a c x ) |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R +
+--R +-----------+2
+--R 3 9 2 2 5 3 | 1 2 8 4 2
+--R (192a c x - 864a c x + 96a c x) |- --------- + 25c x - 46a c x + a
+--R 8| 5 3
+--R \| 65536a c
+--R /
+--R +-----------+6
+--R 4 5 10 5 4 6 6 3 2 | 1
+--R (131072a c x - 32768a c x - 163840a c x ) |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R +
+--R +-----------+4
+--R 3 4 9 4 3 5 5 2 | 1
+--R (13312a c x + 8192a c x - 5120a c x) |- ---------
+--R 8| 5 3
+--R \| 65536a c
+--R +
+--R +-----------+2
+--R 2 3 8 3 2 4 4 | 1 3 11 2 7
+--R (1088a c x + 1024a c x - 64a c) |- --------- - 16c x + 40a c x
+--R 8| 5 3
+--R \| 65536a c
+--R +
+--R 2 3
+--R 56a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 632
+
+)clear all
+
+--S 633 of 1347
+t0:=1/((a+c*x^4)*sqrt(x))
+--R
+--R
+--R 1
+--R (1) --------------
+--R 4 +-+
+--R (c x + a)\|x
+--R Type: Expression(Integer)
+--E 633
+
+--S 634 of 1347
+r0:=-1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(1/8))-_
+ 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(1/8))+_
+ 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*_
+ c^(1/8)*sqrt(2))-1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(7/8)*c^(1/8)*sqrt(2))+1/4*log((-a)^(1/4)+_
+ c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(7/8)*_
+ c^(1/8)*sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_
+ c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(1/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 2atan(---------------------) - 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R /
+--R +-+8+---+7 8+-+
+--R 4\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 634
+
+--S 635 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+ +----------+2
+--R | 1 +-+ | 1 +-+ 2 | 1
+--R |- -------- log(4a\|2 |- -------- \|x + 16a |- -------- + x)
+--R 8| 7 8| 7 8| 7
+--R \| 65536a c \| 65536a c \| 65536a c
+--R +
+--R +----------+ +----------+
+--R +-+ | 1 +-+ | 1
+--R \|2 |- -------- log(\|x + 4a |- --------)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +----------+ +----------+
+--R +-+ | 1 +-+ | 1
+--R - \|2 |- -------- log(\|x - 4a |- --------)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +----------+ +----------+ +----------+2
+--R | 1 +-+ | 1 +-+ 2 | 1
+--R - |- -------- log(- 4a\|2 |- -------- \|x + 16a |- -------- + x)
+--R 8| 7 8| 7 8| 7
+--R \| 65536a c \| 65536a c \| 65536a c
+--R +
+--R +----------+
+--R | 1
+--R 4a |- --------
+--R +----------+ 8| 7
+--R | 1 \| 65536a c
+--R - 2 |- -------- atan(--------------------------)
+--R 8| 7 +----------+
+--R \| 65536a c +-+ +-+ | 1
+--R \|2 \|x - 4a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+
+--R | 1
+--R 4a |- --------
+--R +----------+ 8| 7
+--R | 1 \| 65536a c
+--R - 2 |- -------- atan(--------------------------)
+--R 8| 7 +----------+
+--R \| 65536a c +-+ +-+ | 1
+--R \|2 \|x + 4a |- --------
+--R 8| 7
+--R \| 65536a c
+--R /
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 635
+
+--S 636 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +----------+
+--R 8+---+7 | 1 8+-+
+--R 4\|- a |- -------- \|c
+--R 8| 7
+--R \| 65536a c
+--R *
+--R +----------+ +----------+2
+--R +-+ | 1 +-+ 2 | 1
+--R log(4a\|2 |- -------- \|x + 16a |- -------- + x)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +----------+ +----------+
+--R +-+8+---+7 | 1 8+-+ +-+ | 1
+--R 4\|2 \|- a |- -------- \|c log(\|x + 4a |- --------)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R +----------+ +----------+
+--R +-+8+---+7 | 1 8+-+ +-+ | 1
+--R - 4\|2 \|- a |- -------- \|c log(\|x - 4a |- --------)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R -
+--R +----------+
+--R 8+---+7 | 1 8+-+
+--R 4\|- a |- -------- \|c
+--R 8| 7
+--R \| 65536a c
+--R *
+--R +----------+ +----------+2
+--R +-+ | 1 +-+ 2 | 1
+--R log(- 4a\|2 |- -------- \|x + 16a |- -------- + x)
+--R 8| 7 8| 7
+--R \| 65536a c \| 65536a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 2atan(---------------------) + 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +----------+
+--R | 1
+--R 4a |- --------
+--R +----------+ 8| 7
+--R 8+---+7 | 1 8+-+ \| 65536a c
+--R - 8\|- a |- -------- \|c atan(--------------------------)
+--R 8| 7 +----------+
+--R \| 65536a c +-+ +-+ | 1
+--R \|2 \|x - 4a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+
+--R | 1
+--R 4a |- --------
+--R +----------+ 8| 7
+--R 8+---+7 | 1 8+-+ \| 65536a c
+--R - 8\|- a |- -------- \|c atan(--------------------------)
+--R 8| 7 +----------+
+--R \| 65536a c +-+ +-+ | 1
+--R \|2 \|x + 4a |- --------
+--R 8| 7
+--R \| 65536a c
+--R /
+--R +-+8+---+7 8+-+
+--R 4\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 636
+
+--S 637 of 1347 sometimes Axiom computes a zero
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +----------+6
+--R 6 8 7 4 8+---+2 | 1
+--R (- 34816a c x + 2048a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 4 9 5 5 8+---+2 | 1
+--R (1664a c x - 640a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 10 3 6 8+---+2 | 1
+--R (- 64a c x + 80a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 11 7 8+---+2
+--R (2c x - 7a x )\|- a
+--R *
+--R 4+-+2
+--R \|c
+--R +
+--R +----------+6
+--R 6 7 7 3 4+---+8+---+2 | 1
+--R (- 69632a c x + 4096a x )\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 4 8 5 4 4+---+8+---+2 | 1
+--R (3328a c x - 1280a x )\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 9 3 5 4+---+8+---+2 | 1
+--R (- 128a c x + 160a x )\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 10 6 4+---+8+---+2
+--R (4c x - 14a x )\|- a \|- a
+--R *
+--R 4+-+
+--R \|c
+--R +
+--R 6 6 7 2 8+---+6
+--R (69632a c x - 4096a x )\|- a
+--R +
+--R 6 6 7 2 4+---+2 8+---+2
+--R (- 34816a c x + 2048a x )\|- a \|- a
+--R *
+--R +----------+6
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 4 7 5 3 8+---+6
+--R (- 3328a c x + 1280a x )\|- a
+--R +
+--R 4 7 5 3 4+---+2 8+---+2
+--R (1664a c x - 640a x )\|- a \|- a
+--R *
+--R +----------+4
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 8 3 4 8+---+6
+--R (128a c x - 160a x )\|- a
+--R +
+--R 2 8 3 4 4+---+2 8+---+2
+--R (- 64a c x + 80a x )\|- a \|- a
+--R *
+--R +----------+2
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 9 5 8+---+6 9 5 4+---+2 8+---+2
+--R (- 4c x + 14a x )\|- a + (2c x - 7a x )\|- a \|- a
+--R *
+--R 8+-+6
+--R \|c
+--R +
+--R +----------+6
+--R 6 7 7 3 8+---+4 | 1
+--R (- 34816a c x + 2048a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 4 8 5 4 8+---+4 | 1
+--R (1664a c x - 640a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 9 3 5 8+---+4 | 1
+--R (- 64a c x + 80a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 10 6 8+---+4
+--R (2c x - 7a x )\|- a
+--R *
+--R 4+-+2
+--R \|c
+--R +
+--R +----------+6
+--R 6 6 7 2 4+---+8+---+4 | 1
+--R (- 69632a c x + 4096a x )\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 4 7 5 3 4+---+8+---+4 | 1
+--R (3328a c x - 1280a x )\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 8 3 4 4+---+8+---+4 | 1
+--R (- 128a c x + 160a x )\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 9 5 4+---+8+---+4
+--R (4c x - 14a x )\|- a \|- a
+--R *
+--R 4+-+
+--R \|c
+--R +
+--R 6 5 7 4+---+2 8+---+4 6 2 9
+--R (- 34816a c x + 2048a x)\|- a \|- a + 102400a c x
+--R +
+--R 7 5
+--R - 118784a c x
+--R *
+--R +----------+6
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 4 6 5 2 4+---+2 8+---+4 4 2 10 5 6
+--R (1664a c x - 640a x )\|- a \|- a - 3072a c x + 10496a c x
+--R +
+--R 6 2
+--R - 256a x
+--R *
+--R +----------+4
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 7 3 3 4+---+2 8+---+4 2 2 11 3 7
+--R (- 64a c x + 80a x )\|- a \|- a + 64a c x - 704a c x
+--R +
+--R 4 3
+--R 96a x
+--R *
+--R +----------+2
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 8 4 4+---+2 8+---+4 8 2 4
+--R (2c x - 7a x )\|- a \|- a + 38a c x - 16a x
+--R *
+--R 8+-+4
+--R \|c
+--R +
+--R +----------+6
+--R 5 2 10 6 6 8+---+6 | 1
+--R (51200a c x - 59392a c x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 3 2 11 4 7 5 3 8+---+6 | 1
+--R (- 1536a c x + 5248a c x - 128a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 12 2 8 3 4 8+---+6 | 1
+--R (32a c x - 352a c x + 48a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 9 5 8+---+6
+--R (19c x - 8a x )\|- a
+--R *
+--R 4+-+2
+--R \|c
+--R +
+--R 5 2 9 6 5 4+---+8+---+6 6 2 9
+--R (102400a c x - 118784a c x )\|- a \|- a - 34816a c x
+--R +
+--R 7 5 8
+--R - 32768a c x + 2048a x
+--R *
+--R +----------+6
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 3 2 10 4 6 5 2 4+---+8+---+6
+--R (- 3072a c x + 10496a c x - 256a x )\|- a \|- a
+--R +
+--R 4 2 10 5 6 6 2
+--R 1664a c x + 1024a c x - 640a x
+--R *
+--R +----------+4
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 11 2 7 3 3 4+---+8+---+6 2 2 11
+--R (64a c x - 704a c x + 96a x )\|- a \|- a - 64a c x
+--R +
+--R 3 7 4 3
+--R 16a c x + 80a x
+--R *
+--R +----------+2
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 8 4 4+---+8+---+6 2 12 8 2 4
+--R (38c x - 16a x )\|- a \|- a + 2c x - 5a c x - 7a x
+--R *
+--R 4+-+
+--R \|c
+--R +
+--R 5 2 8 6 4 4+---+2 8+---+6
+--R (51200a c x - 59392a c x )\|- a \|- a
+--R +
+--R 6 2 8 7 4 8+---+2
+--R (- 69632a c x + 4096a c x )\|- a
+--R +
+--R 6 2 8 7 4 8 4+---+
+--R (34816a c x + 32768a c x - 2048a )\|- a
+--R *
+--R +----------+6
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 3 2 9 4 5 5 4+---+2 8+---+6
+--R (- 1536a c x + 5248a c x - 128a x)\|- a \|- a
+--R +
+--R 4 2 9 5 5 8+---+2
+--R (3328a c x - 1280a c x )\|- a
+--R +
+--R 4 2 9 5 5 6 4+---+
+--R (- 1664a c x - 1024a c x + 640a x)\|- a
+--R *
+--R +----------+4
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 10 2 6 3 2 4+---+2 8+---+6
+--R (32a c x - 352a c x + 48a x )\|- a \|- a
+--R +
+--R 2 2 10 3 6 8+---+2
+--R (- 128a c x + 160a c x )\|- a
+--R +
+--R 2 2 10 3 6 4 2 4+---+
+--R (64a c x - 16a c x - 80a x )\|- a
+--R *
+--R +----------+2
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 7 3 4+---+2 8+---+6 2 11 7 8+---+2
+--R (19c x - 8a x )\|- a \|- a + (4c x - 14a c x )\|- a
+--R +
+--R 2 11 7 2 3 4+---+
+--R (- 2c x + 5a c x + 7a x )\|- a
+--R *
+--R 8+-+2
+--R \|c
+--R +
+--R +----------+6
+--R 6 2 9 7 5 | 1
+--R (34816a c x - 2048a c x ) |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 4 2 10 5 6 | 1
+--R (- 1664a c x + 640a c x ) |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 2 11 3 7 | 1 2 12 8
+--R (64a c x - 80a c x ) |- -------- - 2c x + 7a c x
+--R 8| 7
+--R \| 65536a c
+--R *
+--R 4+-+2
+--R \|c
+--R +
+--R +----------+6
+--R 6 2 8 7 4 4+---+ | 1
+--R (69632a c x - 4096a c x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 4 2 9 5 5 4+---+ | 1
+--R (- 3328a c x + 1280a c x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 2 10 3 6 4+---+ | 1
+--R (128a c x - 160a c x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 11 7 4+---+
+--R (- 4c x + 14a c x )\|- a
+--R *
+--R 4+-+
+--R \|c
+--R +
+--R 6 2 7 7 3 8+---+4 6 2 7 7 3 4+---+2
+--R ((69632a c x - 4096a c x )\|- a + (34816a c x - 2048a c x )\|- a )
+--R *
+--R +----------+6
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 4 2 8 5 4 8+---+4
+--R (- 3328a c x + 1280a c x )\|- a
+--R +
+--R 4 2 8 5 4 4+---+2
+--R (- 1664a c x + 640a c x )\|- a
+--R *
+--R +----------+4
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 2 9 3 5 8+---+4 2 2 9 3 5 4+---+2
+--R ((128a c x - 160a c x )\|- a + (64a c x - 80a c x )\|- a )
+--R *
+--R +----------+2
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 10 6 8+---+4 2 10 6 4+---+2
+--R (- 4c x + 14a c x )\|- a + (- 2c x + 7a c x )\|- a
+--R /
+--R +----------+6
+--R 7 2 9 8 5 9 | 1
+--R (278528a c x + 262144a c x - 16384a x) |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 5 2 10 6 6 7 2 | 1
+--R (- 13312a c x - 8192a c x + 5120a x ) |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 3 2 11 4 7 5 3 | 1 2 12
+--R (512a c x - 128a c x - 640a x ) |- -------- - 16a c x
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 8 3 4
+--R 40a c x + 56a x
+--R *
+--R 8+-+4
+--R \|c
+--R +
+--R +----------+6
+--R 6 2 10 7 6 8 2 8+---+6 | 1
+--R (139264a c x + 131072a c x - 8192a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 4 2 11 5 7 6 3 8+---+6 | 1
+--R (- 6656a c x - 4096a c x + 2560a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 2 12 3 8 4 4 8+---+6 | 1
+--R (256a c x - 64a c x - 320a x )\|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 13 9 2 5 8+---+6
+--R (- 8c x + 20a c x + 28a x )\|- a
+--R *
+--R 4+-+2
+--R \|c
+--R +
+--R 6 2 9 7 5 8 4+---+8+---+6
+--R (278528a c x + 262144a c x - 16384a x)\|- a \|- a
+--R *
+--R +----------+6
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 4 2 10 5 6 6 2 4+---+8+---+6
+--R (- 13312a c x - 8192a c x + 5120a x )\|- a \|- a
+--R *
+--R +----------+4
+--R | 1
+--R |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 2 11 3 7 4 3 4+---+8+---+6 | 1
+--R (512a c x - 128a c x - 640a x )\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 12 8 2 4 4+---+8+---+6
+--R (- 16c x + 40a c x + 56a x )\|- a \|- a
+--R *
+--R 4+-+
+--R \|c
+--R +
+--R +----------+6
+--R 6 2 8 7 4 8 4+---+2 8+---+6 | 1
+--R (139264a c x + 131072a c x - 8192a )\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+4
+--R 4 2 9 5 5 6 4+---+2 8+---+6 | 1
+--R (- 6656a c x - 4096a c x + 2560a x)\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R +----------+2
+--R 2 2 10 3 6 4 2 4+---+2 8+---+6 | 1
+--R (256a c x - 64a c x - 320a x )\|- a \|- a |- --------
+--R 8| 7
+--R \| 65536a c
+--R +
+--R 2 11 7 2 3 4+---+2 8+---+6
+--R (- 8c x + 20a c x + 28a x )\|- a \|- a
+--R *
+--R 8+-+2
+--R \|c
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 637
+
+)clear all
+
+--S 638 of 1347
+t0:=1/(x^(3/2)*(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) ----------------
+--R 5 +-+
+--R (c x + a x)\|x
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 1347
+r0:=1/2*c^(1/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(9/8)-_
+ 1/2*c^(1/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(9/8)-_
+ 1/2*c^(1/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(9/8)*sqrt(2))+1/2*c^(1/8)*atan(1+c^(1/8)*sqrt(2)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*sqrt(2))+1/4*c^(1/8)*_
+ log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(9/8)*sqrt(2))-1/4*c^(1/8)*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(9/8)*_
+ sqrt(2))+(-2)/(a*sqrt(x))
+--R
+--R
+--R (2)
+--R 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R \|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - \|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+-+ +-+ 8+---+
+--R +-+8+-+ +-+ \|c \|x 8+-+ +-+ \|2 \|c \|x + \|- a
+--R 2\|2 \|c \|x atanh(--------) - 2\|c \|x atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 8+-+ +-+ \|2 \|c \|x - \|- a +-+8+-+ +-+ \|c \|x
+--R - 2\|c \|x atan(---------------------) - 2\|2 \|c \|x atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+---+
+--R - 8\|2 \|- a
+--R /
+--R +-+8+---+ +-+
+--R 4a\|2 \|- a \|x
+--R Type: Expression(Integer)
+--E 639
+
+--S 640 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +---------+
+--R | c +-+
+--R a |- ------- \|x
+--R 8| 9
+--R \| 65536a
+--R *
+--R +---------+7 +---------+6
+--R 8 +-+ | c +-+ 7 | c
+--R log(16384a \|2 |- ------- \|x - 4096a |- ------- + c x)
+--R 8| 9 8| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+ +---------+7
+--R +-+ | c +-+ +-+ 8 | c
+--R - a\|2 |- ------- \|x log(c\|x + 16384a |- ------- )
+--R 8| 9 8| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+ +---------+7
+--R +-+ | c +-+ +-+ 8 | c
+--R a\|2 |- ------- \|x log(c\|x - 16384a |- ------- )
+--R 8| 9 8| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+
+--R | c +-+
+--R a |- ------- \|x
+--R 8| 9
+--R \| 65536a
+--R *
+--R +---------+7 +---------+6
+--R 8 +-+ | c +-+ 7 | c
+--R log(- 16384a \|2 |- ------- \|x - 4096a |- ------- + c x)
+--R 8| 9 8| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+7
+--R 8 | c
+--R 16384a |- -------
+--R +---------+ 8| 9
+--R | c +-+ \| 65536a
+--R - 2a |- ------- \|x atan(--------------------------------)
+--R 8| 9 +---------+7
+--R \| 65536a +-+ +-+ 8 | c
+--R c\|2 \|x - 16384a |- -------
+--R 8| 9
+--R \| 65536a
+--R +
+--R +---------+7
+--R 8 | c
+--R 16384a |- -------
+--R +---------+ 8| 9
+--R | c +-+ \| 65536a +-+
+--R - 2a |- ------- \|x atan(-------------------------------- - 2\|2
+--R 8| 9 +---------+7
+--R \| 65536a +-+ +-+ 8 | c
+--R c\|2 \|x + 16384a |- -------
+--R 8| 9
+--R \| 65536a
+--R /
+--R +-+ +-+
+--R a\|2 \|x
+--R Type: Union(Expression(Integer),...)
+--E 640
+
+--S 641 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - \|c log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R -
+--R +---------+
+--R | c 8+---+
+--R 4a |- ------- \|- a
+--R 8| 9
+--R \| 65536a
+--R *
+--R +---------+7 +---------+6
+--R 8 +-+ | c +-+ 7 | c
+--R log(16384a \|2 |- ------- \|x - 4096a |- ------- + c x)
+--R 8| 9 8| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+ +---------+7
+--R +-+ | c 8+---+ +-+ 8 | c
+--R - 4a\|2 |- ------- \|- a log(c\|x + 16384a |- ------- )
+--R 8| 9 8| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+ +---------+7
+--R +-+ | c 8+---+ +-+ 8 | c
+--R 4a\|2 |- ------- \|- a log(c\|x - 16384a |- ------- )
+--R 8| 9 8| 9
+--R \| 65536a \| 65536a
+--R +
+--R +---------+
+--R | c 8+---+
+--R 4a |- ------- \|- a
+--R 8| 9
+--R \| 65536a
+--R *
+--R +---------+7 +---------+6
+--R 8 +-+ | c +-+ 7 | c
+--R log(- 16384a \|2 |- ------- \|x - 4096a |- ------- + c x)
+--R 8| 9 8| 9
+--R \| 65536a \| 65536a
+--R +
+--R 8+-+ +-+
+--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+8+-+ \|c \|x
+--R \|c log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 \|c atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R 8+-+ \|2 \|c \|x + \|- a 8+-+ \|2 \|c \|x - \|- a
+--R 2\|c atan(---------------------) + 2\|c atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+8+-+ \|c \|x
+--R 2\|2 \|c atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +---------+7
+--R 8 | c
+--R 16384a |- -------
+--R +---------+ 8| 9
+--R | c 8+---+ \| 65536a
+--R - 8a |- ------- \|- a atan(--------------------------------)
+--R 8| 9 +---------+7
+--R \| 65536a +-+ +-+ 8 | c
+--R c\|2 \|x - 16384a |- -------
+--R 8| 9
+--R \| 65536a
+--R +
+--R +---------+7
+--R 8 | c
+--R 16384a |- -------
+--R +---------+ 8| 9
+--R | c 8+---+ \| 65536a
+--R - 8a |- ------- \|- a atan(--------------------------------)
+--R 8| 9 +---------+7
+--R \| 65536a +-+ +-+ 8 | c
+--R c\|2 \|x + 16384a |- -------
+--R 8| 9
+--R \| 65536a
+--R /
+--R +-+8+---+
+--R 4a\|2 \|- a
+--R Type: Expression(Integer)
+--E 641
+
+--S 642 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R +---------+6
+--R 7 2 9 8 5 9 | c
+--R (12288a c x - 55296a c x + 6144a x) |- -------
+--R 8| 9
+--R \| 65536a
+--R +
+--R +---------+4
+--R 5 2 8 6 4 7 | c
+--R (- 1600a c x + 2944a c x - 64a ) |- -------
+--R 8| 9
+--R \| 65536a
+--R +
+--R +---------+2
+--R 3 2 7 4 3 | c 3 10 2 6 2 2
+--R (168a c x - 120a c x ) |- ------- + c x - 13a c x + 4a c x
+--R 8| 9
+--R \| 65536a
+--R /
+--R +---------+6
+--R 8 2 10 9 6 10 2 | c
+--R (32768a c x - 8192a c x - 40960a x ) |- -------
+--R 8| 9
+--R \| 65536a
+--R +
+--R +---------+4
+--R 6 2 9 7 5 8 | c
+--R (- 3328a c x - 2048a c x + 1280a x) |- -------
+--R 8| 9
+--R \| 65536a
+--R +
+--R +---------+2
+--R 4 2 8 5 4 6 | c 3 11 2 2 7
+--R (272a c x + 256a c x - 16a ) |- ------- + 4a c x - 10a c x
+--R 8| 9
+--R \| 65536a
+--R +
+--R 3 3
+--R - 14a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 642
+
+)clear all
+
+--S 643 of 1347
+t0:=1/(x^(5/2)*(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R 6 2 +-+
+--R (c x + a x )\|x
+--R Type: Expression(Integer)
+--E 643
+
+--S 644 of 1347
+r0:=(-2/3)/(a*x^(3/2))-1/2*c^(3/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ (-a)^(11/8)-1/2*c^(3/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ (-a)^(11/8)-1/2*c^(3/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(11/8)*sqrt(2))+1/2*c^(3/8)*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(11/8)*sqrt(2))-1/4*c^(3/8)*log((-a)^(1/4)+_
+ c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(11/8)*_
+ sqrt(2))+1/4*c^(3/8)*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_
+ c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(11/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 8+-+3 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 3x \|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+3 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 3x \|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+-+ +-+ 8+---+
+--R +-+8+-+3 +-+ \|c \|x 8+-+3 +-+ \|2 \|c \|x + \|- a
+--R 6x\|2 \|c \|x atanh(--------) - 6x \|c \|x atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 8+-+3 +-+ \|2 \|c \|x - \|- a +-+8+-+3 +-+ \|c \|x
+--R - 6x \|c \|x atan(---------------------) + 6x\|2 \|c \|x atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+---+3
+--R - 8\|2 \|- a
+--R /
+--R +-+8+---+3 +-+
+--R 12a x\|2 \|- a \|x
+--R Type: Expression(Integer)
+--E 644
+
+--S 645 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +----------+
+--R | 3
+--R | c +-+
+--R 3a x |- -------- \|x
+--R 8| 11
+--R \| 65536a
+--R *
+--R +----------+5 +----------+2
+--R | 3 | 3
+--R 7 +-+ | c +-+ 3 | c 2
+--R log(1024a \|2 |- -------- \|x - 16a c |- -------- + c x)
+--R 8| 11 8| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+5
+--R | 3 | 3
+--R +-+ | c +-+ 2 +-+ 7 | c
+--R 3a x\|2 |- -------- \|x log(c \|x + 1024a |- -------- )
+--R 8| 11 8| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+5
+--R | 3 | 3
+--R +-+ | c +-+ 2 +-+ 7 | c
+--R - 3a x\|2 |- -------- \|x log(c \|x - 1024a |- -------- )
+--R 8| 11 8| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+
+--R | 3
+--R | c +-+
+--R 3a x |- -------- \|x
+--R 8| 11
+--R \| 65536a
+--R *
+--R +----------+5 +----------+2
+--R | 3 | 3
+--R 7 +-+ | c +-+ 3 | c 2
+--R log(- 1024a \|2 |- -------- \|x - 16a c |- -------- + c x)
+--R 8| 11 8| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+5
+--R | 3
+--R 7 | c
+--R +----------+ 1024a |- --------
+--R | 3 8| 11
+--R | c +-+ \| 65536a
+--R 6a x |- -------- \|x atan(---------------------------------)
+--R 8| 11 +----------+5
+--R \| 65536a | 3
+--R 2 +-+ +-+ 7 | c
+--R c \|2 \|x - 1024a |- --------
+--R 8| 11
+--R \| 65536a
+--R +
+--R +----------+5
+--R | 3
+--R 7 | c
+--R +----------+ 1024a |- --------
+--R | 3 8| 11
+--R | c +-+ \| 65536a +-+
+--R 6a x |- -------- \|x atan(--------------------------------- - 2\|2
+--R 8| 11 +----------+5
+--R \| 65536a | 3
+--R 2 +-+ +-+ 7 | c
+--R c \|2 \|x + 1024a |- --------
+--R 8| 11
+--R \| 65536a
+--R /
+--R +-+ +-+
+--R 3a x\|2 \|x
+--R Type: Union(Expression(Integer),...)
+--E 645
+
+--S 646 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+-+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R \|c log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R -
+--R +----------+
+--R | 3
+--R | c 8+---+3
+--R 4a |- -------- \|- a
+--R 8| 11
+--R \| 65536a
+--R *
+--R +----------+5 +----------+2
+--R | 3 | 3
+--R 7 +-+ | c +-+ 3 | c 2
+--R log(1024a \|2 |- -------- \|x - 16a c |- -------- + c x)
+--R 8| 11 8| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+5
+--R | 3 | 3
+--R +-+ | c 8+---+3 2 +-+ 7 | c
+--R 4a\|2 |- -------- \|- a log(c \|x + 1024a |- -------- )
+--R 8| 11 8| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+5
+--R | 3 | 3
+--R +-+ | c 8+---+3 2 +-+ 7 | c
+--R - 4a\|2 |- -------- \|- a log(c \|x - 1024a |- -------- )
+--R 8| 11 8| 11
+--R \| 65536a \| 65536a
+--R +
+--R +----------+
+--R | 3
+--R | c 8+---+3
+--R 4a |- -------- \|- a
+--R 8| 11
+--R \| 65536a
+--R *
+--R +----------+5 +----------+2
+--R | 3 | 3
+--R 7 +-+ | c +-+ 3 | c 2
+--R log(- 1024a \|2 |- -------- \|x - 16a c |- -------- + c x)
+--R 8| 11 8| 11
+--R \| 65536a \| 65536a
+--R +
+--R 8+-+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - \|c log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+-+ +-+ 8+---+
+--R +-+8+-+3 \|c \|x 8+-+3 \|2 \|c \|x + \|- a
+--R - 2\|2 \|c atanh(--------) + 2\|c atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 8+-+3 \|2 \|c \|x - \|- a +-+8+-+3 \|c \|x
+--R 2\|c atan(---------------------) - 2\|2 \|c atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +----------+5
+--R | 3
+--R 7 | c
+--R +----------+ 1024a |- --------
+--R | 3 8| 11
+--R | c 8+---+3 \| 65536a
+--R 8a |- -------- \|- a atan(---------------------------------)
+--R 8| 11 +----------+5
+--R \| 65536a | 3
+--R 2 +-+ +-+ 7 | c
+--R c \|2 \|x - 1024a |- --------
+--R 8| 11
+--R \| 65536a
+--R +
+--R +----------+5
+--R | 3
+--R 7 | c
+--R +----------+ 1024a |- --------
+--R | 3 8| 11
+--R | c 8+---+3 \| 65536a
+--R 8a |- -------- \|- a atan(---------------------------------)
+--R 8| 11 +----------+5
+--R \| 65536a | 3
+--R 2 +-+ +-+ 7 | c
+--R c \|2 \|x + 1024a |- --------
+--R 8| 11
+--R \| 65536a
+--R /
+--R +-+8+---+3
+--R 4a\|2 \|- a
+--R Type: Expression(Integer)
+--E 646
+
+--S 647 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R +----------+6
+--R | 3
+--R 8 3 10 9 2 6 10 2 | c
+--R (- 8192a c x + 106496a c x - 32768a c x ) |- --------
+--R 8| 11
+--R \| 65536a
+--R +
+--R +----------+4
+--R | 3
+--R 6 3 7 7 2 3 | c
+--R (5376a c x - 3840a c x ) |- --------
+--R 8| 11
+--R \| 65536a
+--R +
+--R +----------+2
+--R | 3
+--R 3 4 8 4 3 4 5 2 | c 5 9 4 5 2 3
+--R (200a c x - 368a c x + 8a c ) |- -------- + 6c x - 27a c x + 3a c x
+--R 8| 11
+--R \| 65536a
+--R /
+--R +----------+6
+--R | 3
+--R 10 2 8 11 4 12 | c
+--R (139264a c x + 131072a c x - 8192a ) |- --------
+--R 8| 11
+--R \| 65536a
+--R +
+--R +----------+4
+--R | 3
+--R 7 3 9 8 2 5 9 | c
+--R (6656a c x + 4096a c x - 2560a c x) |- --------
+--R 8| 11
+--R \| 65536a
+--R +
+--R +----------+2
+--R | 3
+--R 4 4 10 5 3 6 6 2 2 | c 5 11 2 4 7
+--R (256a c x - 64a c x - 320a c x ) |- -------- + 8a c x - 20a c x
+--R 8| 11
+--R \| 65536a
+--R +
+--R 3 3 3
+--R - 28a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 647
+
+)clear all
+
+--S 648 of 1347
+t0:=1/(x^(7/2)*(a+c*x^4))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R 7 3 +-+
+--R (c x + a x )\|x
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 1347
+r0:=(-2/5)/(a*x^(5/2))+1/2*c^(5/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ (-a)^(13/8)-1/2*c^(5/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ (-a)^(13/8)+1/2*c^(5/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(13/8)*sqrt(2))-1/2*c^(5/8)*atan(1+c^(1/8)*_
+ sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*sqrt(2))-_
+ 1/4*c^(5/8)*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(13/8)*sqrt(2))+1/4*c^(5/8)*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(13/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8+-+5 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 5x \|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8+-+5 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 5x \|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 +-+8+-+5 +-+ \|c \|x
+--R 10x \|2 \|c \|x atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8+-+5 +-+ \|2 \|c \|x + \|- a
+--R 10x \|c \|x atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8+-+5 +-+ \|2 \|c \|x - \|- a
+--R 10x \|c \|x atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 +-+8+-+5 +-+ \|c \|x +-+8+---+5
+--R - 10x \|2 \|c \|x atan(--------) - 8\|2 \|- a
+--R 8+---+
+--R \|- a
+--R /
+--R 2 +-+8+---+5 +-+
+--R 20a x \|2 \|- a \|x
+--R Type: Expression(Integer)
+--E 649
+
+--S 650 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +----------+
+--R | 5
+--R 2 | c +-+
+--R 5a x |- -------- \|x
+--R 8| 13
+--R \| 65536a
+--R *
+--R +----------+3 +----------+6
+--R | 5 | 5
+--R 5 2 +-+ | c +-+ 10 | c 4
+--R log(64a c \|2 |- -------- \|x + 4096a |- -------- + c x)
+--R 8| 13 8| 13
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+3
+--R | 5 | 5
+--R 2 +-+ | c +-+ 2 +-+ 5 | c
+--R 5a x \|2 |- -------- \|x log(c \|x + 64a |- -------- )
+--R 8| 13 8| 13
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+3
+--R | 5 | 5
+--R 2 +-+ | c +-+ 2 +-+ 5 | c
+--R - 5a x \|2 |- -------- \|x log(c \|x - 64a |- -------- )
+--R 8| 13 8| 13
+--R \| 65536a \| 65536a
+--R +
+--R +----------+
+--R | 5
+--R 2 | c +-+
+--R 5a x |- -------- \|x
+--R 8| 13
+--R \| 65536a
+--R *
+--R +----------+3 +----------+6
+--R | 5 | 5
+--R 5 2 +-+ | c +-+ 10 | c 4
+--R log(- 64a c \|2 |- -------- \|x + 4096a |- -------- + c x)
+--R 8| 13 8| 13
+--R \| 65536a \| 65536a
+--R +
+--R +----------+3
+--R | 5
+--R 5 | c
+--R +----------+ 64a |- --------
+--R | 5 8| 13
+--R 2 | c +-+ \| 65536a
+--R - 10a x |- -------- \|x atan(-------------------------------)
+--R 8| 13 +----------+3
+--R \| 65536a | 5
+--R 2 +-+ +-+ 5 | c
+--R c \|2 \|x - 64a |- --------
+--R 8| 13
+--R \| 65536a
+--R +
+--R +----------+3
+--R | 5
+--R 5 | c
+--R +----------+ 64a |- --------
+--R | 5 8| 13
+--R 2 | c +-+ \| 65536a +-+
+--R - 10a x |- -------- \|x atan(------------------------------- - 2\|2
+--R 8| 13 +----------+3
+--R \| 65536a | 5
+--R 2 +-+ +-+ 5 | c
+--R c \|2 \|x + 64a |- --------
+--R 8| 13
+--R \| 65536a
+--R /
+--R 2 +-+ +-+
+--R 5a x \|2 \|x
+--R Type: Union(Expression(Integer),...)
+--E 650
+
+--S 651 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+-+5 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R \|c log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R -
+--R +----------+
+--R | 5
+--R | c 8+---+5
+--R 4a |- -------- \|- a
+--R 8| 13
+--R \| 65536a
+--R *
+--R +----------+3 +----------+6
+--R | 5 | 5
+--R 5 2 +-+ | c +-+ 10 | c 4
+--R log(64a c \|2 |- -------- \|x + 4096a |- -------- + c x)
+--R 8| 13 8| 13
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+3
+--R | 5 | 5
+--R +-+ | c 8+---+5 2 +-+ 5 | c
+--R 4a\|2 |- -------- \|- a log(c \|x + 64a |- -------- )
+--R 8| 13 8| 13
+--R \| 65536a \| 65536a
+--R +
+--R +----------+ +----------+3
+--R | 5 | 5
+--R +-+ | c 8+---+5 2 +-+ 5 | c
+--R - 4a\|2 |- -------- \|- a log(c \|x - 64a |- -------- )
+--R 8| 13 8| 13
+--R \| 65536a \| 65536a
+--R +
+--R +----------+
+--R | 5
+--R | c 8+---+5
+--R 4a |- -------- \|- a
+--R 8| 13
+--R \| 65536a
+--R *
+--R +----------+3 +----------+6
+--R | 5 | 5
+--R 5 2 +-+ | c +-+ 10 | c 4
+--R log(- 64a c \|2 |- -------- \|x + 4096a |- -------- + c x)
+--R 8| 13 8| 13
+--R \| 65536a \| 65536a
+--R +
+--R 8+-+5 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - \|c log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+-+ +-+ 8+---+
+--R +-+8+-+5 \|c \|x 8+-+5 \|2 \|c \|x + \|- a
+--R - 2\|2 \|c atanh(--------) - 2\|c atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 8+-+5 \|2 \|c \|x - \|- a +-+8+-+5 \|c \|x
+--R - 2\|c atan(---------------------) + 2\|2 \|c atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +----------+3
+--R | 5
+--R 5 | c
+--R +----------+ 64a |- --------
+--R | 5 8| 13
+--R | c 8+---+5 \| 65536a
+--R - 8a |- -------- \|- a atan(-------------------------------)
+--R 8| 13 +----------+3
+--R \| 65536a | 5
+--R 2 +-+ +-+ 5 | c
+--R c \|2 \|x - 64a |- --------
+--R 8| 13
+--R \| 65536a
+--R +
+--R +----------+3
+--R | 5
+--R 5 | c
+--R +----------+ 64a |- --------
+--R | 5 8| 13
+--R | c 8+---+5 \| 65536a
+--R - 8a |- -------- \|- a atan(-------------------------------)
+--R 8| 13 +----------+3
+--R \| 65536a | 5
+--R 2 +-+ +-+ 5 | c
+--R c \|2 \|x + 64a |- --------
+--R 8| 13
+--R \| 65536a
+--R /
+--R +-+8+---+5
+--R 4a\|2 \|- a
+--R Type: Expression(Integer)
+--E 651
+
+--S 652 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R +----------+6
+--R | 5
+--R 10 2 7 11 3 | c
+--R (172032a c x - 122880a c x ) |- --------
+--R 8| 13
+--R \| 65536a
+--R +
+--R +----------+4
+--R | 5
+--R 6 4 10 7 3 6 8 2 2 | c
+--R (- 1024a c x + 13312a c x - 4096a c x ) |- --------
+--R 8| 13
+--R \| 65536a
+--R +
+--R +----------+2
+--R | 5
+--R 3 5 9 4 4 5 5 3 | c 6 8 5 4
+--R (- 192a c x + 864a c x - 96a c x) |- -------- - 25c x + 46a c x
+--R 8| 13
+--R \| 65536a
+--R +
+--R 2 4
+--R - a c
+--R /
+--R +----------+6
+--R | 5
+--R 11 2 10 12 6 13 2 | c
+--R (131072a c x - 32768a c x - 163840a x ) |- --------
+--R 8| 13
+--R \| 65536a
+--R +
+--R +----------+4
+--R | 5
+--R 8 3 9 9 2 5 10 | c
+--R (13312a c x + 8192a c x - 5120a c x) |- --------
+--R 8| 13
+--R \| 65536a
+--R +
+--R +----------+2
+--R | 5
+--R 5 4 8 6 3 4 7 2 | c 6 11 2 5 7
+--R (1088a c x + 1024a c x - 64a c ) |- -------- - 16a c x + 40a c x
+--R 8| 13
+--R \| 65536a
+--R +
+--R 3 4 3
+--R 56a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 652
+
+)clear all
+
+--S 653 of 1347
+t0:=x^(13/2)/(a+c*x^4)^2
+--R
+--R
+--R 6 +-+
+--R x \|x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Expression(Integer)
+--E 653
+
+--S 654 of 1347
+r0:=-1/4*x^(7/2)/(c*(a+c*x^4))+7/16*atan(c^(1/8)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(1/8)*c^(15/8))-7/16*atanh(c^(1/8)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(15/8))-7/16*atan(1-c^(1/8)*_
+ sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(15/8)*sqrt(2))+_
+ 7/16*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(1/8)*c^(15/8)*sqrt(2))+7/32*log((-a)^(1/4)+c^(1/4)*x-_
+ (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(1/8)*_
+ c^(15/8)*sqrt(2))-7/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_
+ c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(1/8)*c^(15/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 7c x - 7a)log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (7c x + 7a)log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x
+--R (- 14c x - 14a)\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x + \|- a
+--R (14c x + 14a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x - \|- a
+--R (14c x + 14a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x 3 +-+8+---+8+-+7 +-+
+--R (14c x + 14a)\|2 atan(--------) - 8x \|2 \|- a \|c \|x
+--R 8+---+
+--R \|- a
+--R /
+--R 2 4 +-+8+---+8+-+7
+--R (32c x + 32a c)\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 654
+
+--S 655 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------+
+--R 2 4 | 1
+--R (28c x + 28a c) |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+7
+--R 13 +-+ | 1 +-+
+--R 34359738368a c \|2 |- ------------------ \|x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 11 | 1
+--R - 1073741824a c |- ------------------ + x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 +-+ | 1
+--R (28c x + 28a c)\|2 |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +--------------------+7
+--R +-+ 13 | 1
+--R log(\|x + 34359738368a c |- ------------------ )
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 +-+ | 1
+--R (- 28c x - 28a c)\|2 |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +--------------------+7
+--R +-+ 13 | 1
+--R log(\|x - 34359738368a c |- ------------------ )
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 | 1
+--R (- 28c x - 28a c) |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+7
+--R 13 +-+ | 1 +-+
+--R - 34359738368a c \|2 |- ------------------ \|x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 11 | 1
+--R - 1073741824a c |- ------------------ + x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 | 1
+--R (56c x + 56a c) |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +--------------------+7
+--R 13 | 1
+--R 34359738368a c |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R atan(---------------------------------------------------)
+--R +--------------------+7
+--R +-+ +-+ 13 | 1
+--R \|2 \|x - 34359738368a c |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 | 1
+--R (56c x + 56a c) |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +--------------------+7
+--R 13 | 1
+--R 34359738368a c |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R atan(---------------------------------------------------)
+--R +--------------------+7
+--R +-+ +-+ 13 | 1
+--R \|2 \|x + 34359738368a c |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R 3 +-+ +-+
+--R - x \|2 \|x
+--R /
+--R 2 4 +-+
+--R (4c x + 4a c)\|2
+--R Type: Union(Expression(Integer),...)
+--E 655
+
+--S 656 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +--------------------+
+--R 8+---+ | 1 8+-+7
+--R 224c\|- a |- ------------------ \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+7
+--R 13 +-+ | 1 +-+
+--R 34359738368a c \|2 |- ------------------ \|x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 11 | 1
+--R - 1073741824a c |- ------------------ + x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R +-+8+---+ | 1 8+-+7
+--R 224c\|2 \|- a |- ------------------ \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +--------------------+7
+--R +-+ 13 | 1
+--R log(\|x + 34359738368a c |- ------------------ )
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R +-+8+---+ | 1 8+-+7
+--R 224c\|2 \|- a |- ------------------ \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +--------------------+7
+--R +-+ 13 | 1
+--R log(\|x - 34359738368a c |- ------------------ )
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R 8+---+ | 1 8+-+7
+--R 224c\|- a |- ------------------ \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+7
+--R 13 +-+ | 1 +-+
+--R - 34359738368a c \|2 |- ------------------ \|x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 11 | 1
+--R - 1073741824a c |- ------------------ + x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 14atan(---------------------) - 14atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 14\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +--------------------+
+--R 8+---+ | 1 8+-+7
+--R 448c\|- a |- ------------------ \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +--------------------+7
+--R 13 | 1
+--R 34359738368a c |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R atan(---------------------------------------------------)
+--R +--------------------+7
+--R +-+ +-+ 13 | 1
+--R \|2 \|x - 34359738368a c |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 8+---+ | 1 8+-+7
+--R 448c\|- a |- ------------------ \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +--------------------+7
+--R 13 | 1
+--R 34359738368a c |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R atan(---------------------------------------------------)
+--R +--------------------+7
+--R +-+ +-+ 13 | 1
+--R \|2 \|x + 34359738368a c |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R /
+--R +-+8+---+8+-+7
+--R 32c\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 656
+
+--S 657 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 13 9 2 12 5 3 11
+--R (- 22548578304a c x + 101468602368a c x - 11274289152a c x)
+--R *
+--R +--------------------+6
+--R | 1
+--R |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+4
+--R 9 8 2 8 4 3 7 | 1
+--R (45875200a c x - 84410368a c x + 1835008a c ) |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 5 7 2 4 3 | 1 2 10 6
+--R (- 75264a c x + 53760a c x ) |- ------------------ - 7c x + 91a c x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R 2 2
+--R - 28a x
+--R /
+--R 15 10 2 14 6 3 13 2
+--R (68719476736a c x - 17179869184a c x - 85899345920a c x )
+--R *
+--R +--------------------+6
+--R | 1
+--R |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R 11 9 2 10 5 3 9
+--R (- 109051904a c x - 67108864a c x + 41943040a c x)
+--R *
+--R +--------------------+4
+--R | 1
+--R |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 7 8 2 6 4 3 5 | 1
+--R (139264a c x + 131072a c x - 8192a c ) |- ------------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R 4 11 3 7 2 2 3
+--R 32c x - 80a c x - 112a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 657
+
+)clear all
+
+--S 658 of 1347
+t0:=x^(11/2)/(a+c*x^4)^2
+--R
+--R
+--R 5 +-+
+--R x \|x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 1347
+r0:=-1/4*x^(5/2)/(c*(a+c*x^4))-5/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(3/8)*c^(13/8))-5/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(3/8)*c^(13/8))-5/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(3/8)*c^(13/8)*sqrt(2))+5/16*_
+ atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*_
+ c^(13/8)*sqrt(2))-5/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*_
+ c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(13/8)*sqrt(2))+_
+ 5/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(13/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (5c x + 5a)log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 5c x - 5a)log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x
+--R (- 10c x - 10a)\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x + \|- a
+--R (10c x + 10a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x - \|- a
+--R (10c x + 10a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x 2 +-+8+---+3 8+-+5 +-+
+--R (- 10c x - 10a)\|2 atan(--------) - 8x \|2 \|- a \|c \|x
+--R 8+---+
+--R \|- a
+--R /
+--R 2 4 +-+8+---+3 8+-+5
+--R (32c x + 32a c)\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 659
+
+--S 660 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------+
+--R 2 4 | 1
+--R (20c x + 20a c) |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+5
+--R 2 8 +-+ | 1 +-+
+--R 33554432a c \|2 |- ------------------ \|x
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 | 1
+--R - 1024a c |- ------------------ + x
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 +-+ | 1
+--R (- 20c x - 20a c)\|2 |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R +-+ 2 8 | 1
+--R log(\|x + 33554432a c |- ------------------ )
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 +-+ | 1
+--R (20c x + 20a c)\|2 |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R +-+ 2 8 | 1
+--R log(\|x - 33554432a c |- ------------------ )
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 | 1
+--R (- 20c x - 20a c) |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+5
+--R 2 8 +-+ | 1 +-+
+--R - 33554432a c \|2 |- ------------------ \|x
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 | 1
+--R - 1024a c |- ------------------ + x
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 | 1
+--R (- 40c x - 40a c) |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R 2 8 | 1
+--R 33554432a c |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R atan(-----------------------------------------------)
+--R +--------------------+5
+--R +-+ +-+ 2 8 | 1
+--R \|2 \|x - 33554432a c |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 | 1
+--R (- 40c x - 40a c) |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R 2 8 | 1
+--R 33554432a c |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R atan(-----------------------------------------------)
+--R +--------------------+5
+--R +-+ +-+ 2 8 | 1
+--R \|2 \|x + 33554432a c |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R 2 +-+ +-+
+--R - x \|2 \|x
+--R /
+--R 2 4 +-+
+--R (4c x + 4a c)\|2
+--R Type: Union(Expression(Integer),...)
+--E 660
+
+--S 661 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 5log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +--------------------+
+--R 8+---+3 | 1 8+-+5
+--R 160c \|- a |- ------------------ \|c
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+5
+--R 2 8 +-+ | 1 +-+
+--R 33554432a c \|2 |- ------------------ \|x
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 | 1
+--R - 1024a c |- ------------------ + x
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R +-+8+---+3 | 1 8+-+5
+--R 160c\|2 \|- a |- ------------------ \|c
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R +-+ 2 8 | 1
+--R log(\|x + 33554432a c |- ------------------ )
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R +-+8+---+3 | 1 8+-+5
+--R 160c\|2 \|- a |- ------------------ \|c
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R +-+ 2 8 | 1
+--R log(\|x - 33554432a c |- ------------------ )
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R 8+---+3 | 1 8+-+5
+--R 160c \|- a |- ------------------ \|c
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+5
+--R 2 8 +-+ | 1 +-+
+--R - 33554432a c \|2 |- ------------------ \|x
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 | 1
+--R - 1024a c |- ------------------ + x
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R 5log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 10\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 10atan(---------------------) - 10atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 10\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R -
+--R +--------------------+
+--R 8+---+3 | 1 8+-+5
+--R 320c \|- a |- ------------------ \|c
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R 2 8 | 1
+--R 33554432a c |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R atan(-----------------------------------------------)
+--R +--------------------+5
+--R +-+ +-+ 2 8 | 1
+--R \|2 \|x - 33554432a c |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R 8+---+3 | 1 8+-+5
+--R 320c \|- a |- ------------------ \|c
+--R 8| 3 13
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R 2 8 | 1
+--R 33554432a c |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R atan(-----------------------------------------------)
+--R +--------------------+5
+--R +-+ +-+ 2 8 | 1
+--R \|2 \|x + 33554432a c |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R /
+--R +-+8+---+3 8+-+5
+--R 32c\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 2 12 10 3 11 6 4 10 2
+--R (10737418240a c x - 139586437120a c x + 42949672960a c x )
+--R *
+--R +--------------------+6
+--R | 1
+--R |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+4
+--R 2 8 7 3 7 3 | 1
+--R (- 110100480a c x + 78643200a c x ) |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 5 8 2 4 4 3 3 | 1
+--R (- 64000a c x + 117760a c x - 2560a c ) |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R 2 9 5 2
+--R - 30c x + 135a c x - 15a x
+--R /
+--R 3 13 8 4 12 4 5 11
+--R (292057776128a c x + 274877906944a c x - 17179869184a c )
+--R *
+--R +--------------------+6
+--R | 1
+--R |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R 2 10 9 3 9 5 4 8
+--R (218103808a c x + 134217728a c x - 83886080a c x)
+--R *
+--R +--------------------+4
+--R | 1
+--R |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 7 10 2 6 6 3 5 2 | 1
+--R (131072a c x - 32768a c x - 163840a c x ) |- ------------------
+--R 8| 3 13
+--R \| 1099511627776a c
+--R +
+--R 4 11 3 7 2 2 3
+--R 64c x - 160a c x - 224a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 662
+
+)clear all
+
+--S 663 of 1347
+t0:=x^(9/2)/(a+c*x^4)^2
+--R
+--R
+--R 4 +-+
+--R x \|x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 1347
+r0:=-1/4*x^(3/2)/(c*(a+c*x^4))+3/16*atan(c^(1/8)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(5/8)*c^(11/8))-3/16*atanh(c^(1/8)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(11/8))+3/16*atan(1-c^(1/8)*_
+ sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(11/8)*sqrt(2))-3/16*_
+ atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*_
+ c^(11/8)*sqrt(2))-3/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*_
+ c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(5/8)*c^(11/8)*sqrt(2))+_
+ 3/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(5/8)*c^(11/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (3c x + 3a)log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 3c x - 3a)log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x
+--R (- 6c x - 6a)\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x + \|- a
+--R (- 6c x - 6a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x - \|- a
+--R (- 6c x - 6a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x +-+8+---+5 8+-+3 +-+
+--R (6c x + 6a)\|2 atan(--------) - 8x\|2 \|- a \|c \|x
+--R 8+---+
+--R \|- a
+--R /
+--R 2 4 +-+8+---+5 8+-+3
+--R (32c x + 32a c)\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 664
+
+--S 665 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------+
+--R 2 4 | 1
+--R (12c x + 12a c) |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+3
+--R 2 4 +-+ | 1 +-+
+--R 32768a c \|2 |- ------------------ \|x
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 4 8 | 1
+--R 1073741824a c |- ------------------ + x
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 +-+ | 1
+--R (- 12c x - 12a c)\|2 |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R +-+ 2 4 | 1
+--R log(\|x + 32768a c |- ------------------ )
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 +-+ | 1
+--R (12c x + 12a c)\|2 |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R +-+ 2 4 | 1
+--R log(\|x - 32768a c |- ------------------ )
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 | 1
+--R (- 12c x - 12a c) |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+3
+--R 2 4 +-+ | 1 +-+
+--R - 32768a c \|2 |- ------------------ \|x
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 4 8 | 1
+--R 1073741824a c |- ------------------ + x
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 | 1
+--R (24c x + 24a c) |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R 2 4 | 1
+--R 32768a c |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R atan(--------------------------------------------)
+--R +--------------------+3
+--R +-+ +-+ 2 4 | 1
+--R \|2 \|x - 32768a c |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 2 4 | 1
+--R (24c x + 24a c) |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R 2 4 | 1
+--R 32768a c |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R atan(--------------------------------------------)
+--R +--------------------+3
+--R +-+ +-+ 2 4 | 1
+--R \|2 \|x + 32768a c |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +-+ +-+
+--R - x\|2 \|x
+--R /
+--R 2 4 +-+
+--R (4c x + 4a c)\|2
+--R Type: Union(Expression(Integer),...)
+--E 665
+
+--S 666 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 3log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +--------------------+
+--R 8+---+5 | 1 8+-+3
+--R 96c \|- a |- ------------------ \|c
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+3
+--R 2 4 +-+ | 1 +-+
+--R 32768a c \|2 |- ------------------ \|x
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 4 8 | 1
+--R 1073741824a c |- ------------------ + x
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R +-+8+---+5 | 1 8+-+3
+--R 96c\|2 \|- a |- ------------------ \|c
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R +-+ 2 4 | 1
+--R log(\|x + 32768a c |- ------------------ )
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R +-+8+---+5 | 1 8+-+3
+--R 96c\|2 \|- a |- ------------------ \|c
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R +-+ 2 4 | 1
+--R log(\|x - 32768a c |- ------------------ )
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R 8+---+5 | 1 8+-+3
+--R 96c \|- a |- ------------------ \|c
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+3
+--R 2 4 +-+ | 1 +-+
+--R - 32768a c \|2 |- ------------------ \|x
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 4 8 | 1
+--R 1073741824a c |- ------------------ + x
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R 3log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 6\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 6atan(---------------------) + 6atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 6\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +--------------------+
+--R 8+---+5 | 1 8+-+3
+--R 192c \|- a |- ------------------ \|c
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R 2 4 | 1
+--R 32768a c |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R atan(--------------------------------------------)
+--R +--------------------+3
+--R +-+ +-+ 2 4 | 1
+--R \|2 \|x - 32768a c |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 8+---+5 | 1 8+-+3
+--R 192c \|- a |- ------------------ \|c
+--R 8| 5 11
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R 2 4 | 1
+--R 32768a c |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R atan(--------------------------------------------)
+--R +--------------------+3
+--R +-+ +-+ 2 4 | 1
+--R \|2 \|x + 32768a c |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R /
+--R +-+8+---+5 8+-+3
+--R 32c\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 666
+
+--S 667 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R +--------------------+6
+--R 4 10 7 5 9 3 | 1
+--R (- 135291469824a c x + 96636764160a c x ) |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R 2 8 10 3 7 6 4 6 2
+--R (12582912a c x - 163577856a c x + 50331648a c x )
+--R *
+--R +--------------------+4
+--R | 1
+--R |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 5 9 2 4 5 3 3 | 1
+--R (36864a c x - 165888a c x + 18432a c x) |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R 2 8 4 2
+--R 75c x - 138a c x + 3a
+--R /
+--R 4 12 10 5 11 6 6 10 2
+--R (274877906944a c x - 68719476736a c x - 343597383680a c x )
+--R *
+--R +--------------------+6
+--R | 1
+--R |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R 3 9 9 4 8 5 5 7
+--R (436207616a c x + 268435456a c x - 167772160a c x)
+--R *
+--R +--------------------+4
+--R | 1
+--R |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 2 6 8 3 5 4 4 4 | 1
+--R (557056a c x + 524288a c x - 32768a c ) |- ------------------
+--R 8| 5 11
+--R \| 1099511627776a c
+--R +
+--R 4 11 3 7 2 2 3
+--R - 128c x + 320a c x + 448a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 667
+
+)clear all
+
+--S 668 of 1347
+t0:=x^(7/2)/(a+c*x^4)^2
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 1347
+r0:=-1/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(9/8))-_
+ 1/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(9/8))+_
+ 1/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(9/8)*_
+ sqrt(2))-1/16*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*_
+ c^(9/8)*sqrt(2))+1/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(9/8)*sqrt(2))-1/32*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(9/8)*_
+ sqrt(2))-1/4*sqrt(x)/(c*(a+c*x^4))
+--R
+--R
+--R (2)
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- c x - a)log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (c x + a)log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x
+--R (- 2c x - 2a)\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x + \|- a
+--R (- 2c x - 2a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x - \|- a
+--R (- 2c x - 2a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x +-+8+---+7 8+-+ +-+
+--R (- 2c x - 2a)\|2 atan(--------) - 8\|2 \|- a \|c \|x
+--R 8+---+
+--R \|- a
+--R /
+--R 2 4 +-+8+---+7 8+-+
+--R (32c x + 32a c)\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 669
+
+--S 670 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------------------+
+--R 2 4 | 1
+--R (4c x + 4a c) |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+
+--R +-+ | 1 +-+
+--R 32a c\|2 |- ----------------- \|x
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 2 2 | 1
+--R 1024a c |- ----------------- + x
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 2 4 +-+ | 1
+--R (4c x + 4a c)\|2 |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R +-+ | 1
+--R log(\|x + 32a c |- -----------------)
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 2 4 +-+ | 1
+--R (- 4c x - 4a c)\|2 |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R +-+ | 1
+--R log(\|x - 32a c |- -----------------)
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 2 4 | 1
+--R (- 4c x - 4a c) |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+
+--R +-+ | 1 +-+
+--R - 32a c\|2 |- ----------------- \|x
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 2 2 | 1
+--R 1024a c |- ----------------- + x
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 2 4 | 1
+--R (- 8c x - 8a c) |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R | 1
+--R 32a c |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R atan(--------------------------------------)
+--R +-------------------+
+--R +-+ +-+ | 1
+--R \|2 \|x - 32a c |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 2 4 | 1
+--R (- 8c x - 8a c) |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R | 1
+--R 32a c |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R atan(--------------------------------------)
+--R +-------------------+
+--R +-+ +-+ | 1
+--R \|2 \|x + 32a c |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-+ +-+
+--R - \|2 \|x
+--R /
+--R 2 4 +-+
+--R (4c x + 4a c)\|2
+--R Type: Union(Expression(Integer),...)
+--E 670
+
+--S 671 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-------------------+
+--R 8+---+7 | 1 8+-+
+--R 32c \|- a |- ----------------- \|c
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+
+--R +-+ | 1 +-+
+--R 32a c\|2 |- ----------------- \|x
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 2 2 | 1
+--R 1024a c |- ----------------- + x
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R +-+8+---+7 | 1 8+-+
+--R 32c\|2 \|- a |- ----------------- \|c
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R +-+ | 1
+--R log(\|x + 32a c |- -----------------)
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R -
+--R +-------------------+
+--R +-+8+---+7 | 1 8+-+
+--R 32c\|2 \|- a |- ----------------- \|c
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R +-+ | 1
+--R log(\|x - 32a c |- -----------------)
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R -
+--R +-------------------+
+--R 8+---+7 | 1 8+-+
+--R 32c \|- a |- ----------------- \|c
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+
+--R +-+ | 1 +-+
+--R - 32a c\|2 |- ----------------- \|x
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 2 2 | 1
+--R 1024a c |- ----------------- + x
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 2atan(---------------------) + 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R -
+--R +-------------------+
+--R 8+---+7 | 1 8+-+
+--R 64c \|- a |- ----------------- \|c
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R | 1
+--R 32a c |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R atan(--------------------------------------)
+--R +-------------------+
+--R +-+ +-+ | 1
+--R \|2 \|x - 32a c |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R -
+--R +-------------------+
+--R 8+---+7 | 1 8+-+
+--R 64c \|- a |- ----------------- \|c
+--R 8| 7 9
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R | 1
+--R 32a c |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R atan(--------------------------------------)
+--R +-------------------+
+--R +-+ +-+ | 1
+--R \|2 \|x + 32a c |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R /
+--R +-+8+---+7 8+-+
+--R 32c\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 671
+
+--S 672 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 5 8 8 6 7 4 7 6
+--R (13421772800a c x - 24696061952a c x + 536870912a c )
+--R *
+--R +-------------------+6
+--R | 1
+--R |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+4
+--R 3 6 9 4 5 5 5 4 | 1
+--R (- 6291456a c x + 28311552a c x - 3145728a c x) |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 4 10 2 3 6 3 2 2 | 1 7
+--R (2048a c x - 26624a c x + 8192a c x ) |- ----------------- + 21c x
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R 3
+--R - 15a x
+--R /
+--R 6 9 8 7 8 4 8 7
+--R (292057776128a c x + 274877906944a c x - 17179869184a c )
+--R *
+--R +-------------------+6
+--R | 1
+--R |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R 4 7 9 5 6 5 6 5
+--R (- 218103808a c x - 134217728a c x + 83886080a c x)
+--R *
+--R +-------------------+4
+--R | 1
+--R |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 2 5 10 3 4 6 4 3 2 | 1
+--R (131072a c x - 32768a c x - 163840a c x ) |- -----------------
+--R 8| 7 9
+--R \| 1099511627776a c
+--R +
+--R 3 11 2 7 2 3
+--R - 64c x + 160a c x + 224a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 672
+
+)clear all
+
+--S 673 of 1347
+t0:=x^(5/2)/(a+c*x^4)^2
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 1347
+r0:=1/4*x^(7/2)/(a*(a+c*x^4))-1/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(9/8)*c^(7/8))+1/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(9/8)*c^(7/8))+1/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(9/8)*c^(7/8)*sqrt(2))-1/16*atan(1+c^(1/8)*_
+ sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(7/8)*sqrt(2))-_
+ 1/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/_
+ ((-a)^(9/8)*c^(7/8)*sqrt(2))+1/32*log((-a)^(1/4)+c^(1/4)*x+_
+ (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(9/8)*c^(7/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- c x - a)log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (c x + a)log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x
+--R (- 2c x - 2a)\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x + \|- a
+--R (2c x + 2a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 4 \|2 \|c \|x - \|- a 4 +-+ \|c \|x
+--R (2c x + 2a)atan(---------------------) + (2c x + 2a)\|2 atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 3 +-+8+---+8+-+7 +-+
+--R 8x \|2 \|- a \|c \|x
+--R /
+--R 4 2 +-+8+---+8+-+7
+--R (32a c x + 32a )\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 674
+
+--S 675 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------------------+
+--R 4 2 | 1
+--R (4a c x + 4a ) |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+7
+--R 8 6 +-+ | 1 +-+
+--R 34359738368a c \|2 |- ----------------- \|x
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+6
+--R 7 5 | 1
+--R - 1073741824a c |- ----------------- + x
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 4 2 +-+ | 1
+--R (4a c x + 4a )\|2 |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R +-------------------+7
+--R +-+ 8 6 | 1
+--R log(\|x + 34359738368a c |- ----------------- )
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 4 2 +-+ | 1
+--R (- 4a c x - 4a )\|2 |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R +-------------------+7
+--R +-+ 8 6 | 1
+--R log(\|x - 34359738368a c |- ----------------- )
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 4 2 | 1
+--R (- 4a c x - 4a ) |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+7
+--R 8 6 +-+ | 1 +-+
+--R - 34359738368a c \|2 |- ----------------- \|x
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+6
+--R 7 5 | 1
+--R - 1073741824a c |- ----------------- + x
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 4 2 | 1
+--R (8a c x + 8a ) |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R +-------------------+7
+--R 8 6 | 1
+--R 34359738368a c |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R atan(-------------------------------------------------)
+--R +-------------------+7
+--R +-+ +-+ 8 6 | 1
+--R \|2 \|x - 34359738368a c |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 4 2 | 1
+--R (8a c x + 8a ) |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R +-------------------+7
+--R 8 6 | 1
+--R 34359738368a c |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R atan(-------------------------------------------------)
+--R +-------------------+7
+--R +-+ +-+ 8 6 | 1
+--R \|2 \|x + 34359738368a c |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R 3 +-+ +-+
+--R x \|2 \|x
+--R /
+--R 4 2 +-+
+--R (4a c x + 4a )\|2
+--R Type: Union(Expression(Integer),...)
+--E 675
+
+--S 676 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-------------------+
+--R 8+---+ | 1 8+-+7
+--R 32a\|- a |- ----------------- \|c
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+7
+--R 8 6 +-+ | 1 +-+
+--R 34359738368a c \|2 |- ----------------- \|x
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+6
+--R 7 5 | 1
+--R - 1073741824a c |- ----------------- + x
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R +-+8+---+ | 1 8+-+7
+--R 32a\|2 \|- a |- ----------------- \|c
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R +-------------------+7
+--R +-+ 8 6 | 1
+--R log(\|x + 34359738368a c |- ----------------- )
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R -
+--R +-------------------+
+--R +-+8+---+ | 1 8+-+7
+--R 32a\|2 \|- a |- ----------------- \|c
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R +-------------------+7
+--R +-+ 8 6 | 1
+--R log(\|x - 34359738368a c |- ----------------- )
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R -
+--R +-------------------+
+--R 8+---+ | 1 8+-+7
+--R 32a\|- a |- ----------------- \|c
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+7
+--R 8 6 +-+ | 1 +-+
+--R - 34359738368a c \|2 |- ----------------- \|x
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+6
+--R 7 5 | 1
+--R - 1073741824a c |- ----------------- + x
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 2atan(---------------------) - 2atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 2\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-------------------+
+--R 8+---+ | 1 8+-+7
+--R 64a\|- a |- ----------------- \|c
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R +-------------------+7
+--R 8 6 | 1
+--R 34359738368a c |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R atan(-------------------------------------------------)
+--R +-------------------+7
+--R +-+ +-+ 8 6 | 1
+--R \|2 \|x - 34359738368a c |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 8+---+ | 1 8+-+7
+--R 64a\|- a |- ----------------- \|c
+--R 8| 9 7
+--R \| 1099511627776a c
+--R *
+--R +-------------------+7
+--R 8 6 | 1
+--R 34359738368a c |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R atan(-------------------------------------------------)
+--R +-------------------+7
+--R +-+ +-+ 8 6 | 1
+--R \|2 \|x + 34359738368a c |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R /
+--R +-+8+---+8+-+7
+--R 32a\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 676
+
+--S 677 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 7 7 9 8 6 5 9 5
+--R (- 3221225472a c x + 14495514624a c x - 1610612736a c x)
+--R *
+--R +-------------------+6
+--R | 1
+--R |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+4
+--R 5 5 8 6 4 4 7 3 | 1
+--R (6553600a c x - 12058624a c x + 262144a c ) |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 3 3 7 4 2 3 | 1 2 10 6
+--R (- 10752a c x + 7680a c x ) |- ----------------- - c x + 13a c x
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R 2 2
+--R - 4a x
+--R /
+--R 8 8 10 9 7 6 10 6 2
+--R (68719476736a c x - 17179869184a c x - 85899345920a c x )
+--R *
+--R +-------------------+6
+--R | 1
+--R |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R 6 6 9 7 5 5 8 4
+--R (- 109051904a c x - 67108864a c x + 41943040a c x)
+--R *
+--R +-------------------+4
+--R | 1
+--R |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 4 4 8 5 3 4 6 2 | 1
+--R (139264a c x + 131072a c x - 8192a c ) |- -----------------
+--R 8| 9 7
+--R \| 1099511627776a c
+--R +
+--R 3 11 2 2 7 3 3
+--R 32a c x - 80a c x - 112a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 677
+
+)clear all
+
+--S 678 of 1347
+t0:=x^(3/2)/(a+c*x^4)^2
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 1347
+r0:=1/4*x^(5/2)/(a*(a+c*x^4))+3/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(11/8)*c^(5/8))+3/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(11/8)*c^(5/8))+3/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(11/8)*c^(5/8)*sqrt(2))-3/16*atan(1+c^(1/8)*_
+ sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*c^(5/8)*sqrt(2))+_
+ 3/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(11/8)*c^(5/8)*sqrt(2))-3/32*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(11/8)*_
+ c^(5/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (3c x + 3a)log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 3c x - 3a)log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x
+--R (- 6c x - 6a)\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x + \|- a
+--R (6c x + 6a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x - \|- a
+--R (6c x + 6a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x 2 +-+8+---+3 8+-+5 +-+
+--R (- 6c x - 6a)\|2 atan(--------) + 8x \|2 \|- a \|c \|x
+--R 8+---+
+--R \|- a
+--R /
+--R 4 2 +-+8+---+3 8+-+5
+--R (32a c x + 32a )\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 679
+
+--S 680 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------+
+--R 4 2 | 1
+--R (12a c x + 12a ) |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+5
+--R 7 3 +-+ | 1 +-+
+--R 33554432a c \|2 |- ------------------ \|x
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 | 1
+--R - 1024a c |- ------------------ + x
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 +-+ | 1
+--R (- 12a c x - 12a )\|2 |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R +-+ 7 3 | 1
+--R log(\|x + 33554432a c |- ------------------ )
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 +-+ | 1
+--R (12a c x + 12a )\|2 |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R +-+ 7 3 | 1
+--R log(\|x - 33554432a c |- ------------------ )
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 | 1
+--R (- 12a c x - 12a ) |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+5
+--R 7 3 +-+ | 1 +-+
+--R - 33554432a c \|2 |- ------------------ \|x
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 | 1
+--R - 1024a c |- ------------------ + x
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 | 1
+--R (- 24a c x - 24a ) |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R 7 3 | 1
+--R 33554432a c |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R atan(-----------------------------------------------)
+--R +--------------------+5
+--R +-+ +-+ 7 3 | 1
+--R \|2 \|x - 33554432a c |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 | 1
+--R (- 24a c x - 24a ) |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R 7 3 | 1
+--R 33554432a c |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R atan(-----------------------------------------------)
+--R +--------------------+5
+--R +-+ +-+ 7 3 | 1
+--R \|2 \|x + 33554432a c |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R 2 +-+ +-+
+--R x \|2 \|x
+--R /
+--R 4 2 +-+
+--R (4a c x + 4a )\|2
+--R Type: Union(Expression(Integer),...)
+--E 680
+
+--S 681 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 3log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +--------------------+
+--R 8+---+3 | 1 8+-+5
+--R 96a \|- a |- ------------------ \|c
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+5
+--R 7 3 +-+ | 1 +-+
+--R 33554432a c \|2 |- ------------------ \|x
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 | 1
+--R - 1024a c |- ------------------ + x
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R +-+8+---+3 | 1 8+-+5
+--R 96a\|2 \|- a |- ------------------ \|c
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R +-+ 7 3 | 1
+--R log(\|x + 33554432a c |- ------------------ )
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R +-+8+---+3 | 1 8+-+5
+--R 96a\|2 \|- a |- ------------------ \|c
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R +-+ 7 3 | 1
+--R log(\|x - 33554432a c |- ------------------ )
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R 8+---+3 | 1 8+-+5
+--R 96a \|- a |- ------------------ \|c
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+5
+--R 7 3 +-+ | 1 +-+
+--R - 33554432a c \|2 |- ------------------ \|x
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 | 1
+--R - 1024a c |- ------------------ + x
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R 3log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 6\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 6atan(---------------------) - 6atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 6\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R -
+--R +--------------------+
+--R 8+---+3 | 1 8+-+5
+--R 192a \|- a |- ------------------ \|c
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R 7 3 | 1
+--R 33554432a c |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R atan(-----------------------------------------------)
+--R +--------------------+5
+--R +-+ +-+ 7 3 | 1
+--R \|2 \|x - 33554432a c |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R 8+---+3 | 1 8+-+5
+--R 192a \|- a |- ------------------ \|c
+--R 8| 11 5
+--R \| 1099511627776a c
+--R *
+--R +--------------------+5
+--R 7 3 | 1
+--R 33554432a c |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R atan(-----------------------------------------------)
+--R +--------------------+5
+--R +-+ +-+ 7 3 | 1
+--R \|2 \|x + 33554432a c |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R /
+--R +-+8+---+3 8+-+5
+--R 32a\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 681
+
+--S 682 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 8 6 10 9 5 6 10 4 2
+--R (6442450944a c x - 83751862272a c x + 25769803776a c x )
+--R *
+--R +--------------------+6
+--R | 1
+--R |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+4
+--R 6 4 7 7 3 3 | 1
+--R (- 66060288a c x + 47185920a c x ) |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 3 8 4 2 4 5 | 1 2 9
+--R (- 38400a c x + 70656a c x - 1536a c) |- ------------------ - 18c x
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R 5 2
+--R 81a c x - 9a x
+--R /
+--R 10 6 8 11 5 4 12 4
+--R (292057776128a c x + 274877906944a c x - 17179869184a c )
+--R *
+--R +--------------------+6
+--R | 1
+--R |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R 7 5 9 8 4 5 9 3
+--R (218103808a c x + 134217728a c x - 83886080a c x)
+--R *
+--R +--------------------+4
+--R | 1
+--R |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 4 4 10 5 3 6 6 2 2 | 1
+--R (131072a c x - 32768a c x - 163840a c x ) |- ------------------
+--R 8| 11 5
+--R \| 1099511627776a c
+--R +
+--R 3 11 2 2 7 3 3
+--R 64a c x - 160a c x - 224a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 682
+
+)clear all
+
+--S 683 of 1347
+t0:=sqrt(x)/(a+c*x^4)^2
+--R
+--R
+--R +-+
+--R \|x
+--R (1) -------------------
+--R 2 8 4 2
+--R c x + 2a c x + a
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 1347
+r0:=1/4*x^(3/2)/(a*(a+c*x^4))-5/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(13/8)*c^(3/8))+5/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(13/8)*c^(3/8))-5/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(13/8)*c^(3/8)*sqrt(2))+5/16*atan(1+c^(1/8)*_
+ sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*c^(3/8)*sqrt(2))+_
+ 5/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(13/8)*c^(3/8)*sqrt(2))-5/32*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(13/8)*_
+ c^(3/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (5c x + 5a)log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 5c x - 5a)log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x
+--R (- 10c x - 10a)\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x + \|- a
+--R (- 10c x - 10a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x - \|- a
+--R (- 10c x - 10a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x +-+8+---+5 8+-+3 +-+
+--R (10c x + 10a)\|2 atan(--------) + 8x\|2 \|- a \|c \|x
+--R 8+---+
+--R \|- a
+--R /
+--R 4 2 +-+8+---+5 8+-+3
+--R (32a c x + 32a )\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 684
+
+--S 685 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------+
+--R 4 2 | 1
+--R (20a c x + 20a ) |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+3
+--R 5 +-+ | 1 +-+
+--R 32768a c\|2 |- ------------------ \|x
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 10 2 | 1
+--R 1073741824a c |- ------------------ + x
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 +-+ | 1
+--R (- 20a c x - 20a )\|2 |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R +-+ 5 | 1
+--R log(\|x + 32768a c |- ------------------ )
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 +-+ | 1
+--R (20a c x + 20a )\|2 |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R +-+ 5 | 1
+--R log(\|x - 32768a c |- ------------------ )
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 | 1
+--R (- 20a c x - 20a ) |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+3
+--R 5 +-+ | 1 +-+
+--R - 32768a c\|2 |- ------------------ \|x
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 10 2 | 1
+--R 1073741824a c |- ------------------ + x
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 | 1
+--R (40a c x + 40a ) |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R 5 | 1
+--R 32768a c |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R atan(--------------------------------------------)
+--R +--------------------+3
+--R +-+ +-+ 5 | 1
+--R \|2 \|x - 32768a c |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 4 2 | 1
+--R (40a c x + 40a ) |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R 5 | 1
+--R 32768a c |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R atan(--------------------------------------------)
+--R +--------------------+3
+--R +-+ +-+ 5 | 1
+--R \|2 \|x + 32768a c |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +-+ +-+
+--R x\|2 \|x
+--R /
+--R 4 2 +-+
+--R (4a c x + 4a )\|2
+--R Type: Union(Expression(Integer),...)
+--E 685
+
+--S 686 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 5log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +--------------------+
+--R 8+---+5 | 1 8+-+3
+--R 160a \|- a |- ------------------ \|c
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+3
+--R 5 +-+ | 1 +-+
+--R 32768a c\|2 |- ------------------ \|x
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 10 2 | 1
+--R 1073741824a c |- ------------------ + x
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R +-+8+---+5 | 1 8+-+3
+--R 160a\|2 \|- a |- ------------------ \|c
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R +-+ 5 | 1
+--R log(\|x + 32768a c |- ------------------ )
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R +-+8+---+5 | 1 8+-+3
+--R 160a\|2 \|- a |- ------------------ \|c
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R +-+ 5 | 1
+--R log(\|x - 32768a c |- ------------------ )
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R -
+--R +--------------------+
+--R 8+---+5 | 1 8+-+3
+--R 160a \|- a |- ------------------ \|c
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R log
+--R +--------------------+3
+--R 5 +-+ | 1 +-+
+--R - 32768a c\|2 |- ------------------ \|x
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+6
+--R 10 2 | 1
+--R 1073741824a c |- ------------------ + x
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R 5log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 10\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 10atan(---------------------) + 10atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 10\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +--------------------+
+--R 8+---+5 | 1 8+-+3
+--R 320a \|- a |- ------------------ \|c
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R 5 | 1
+--R 32768a c |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R atan(--------------------------------------------)
+--R +--------------------+3
+--R +-+ +-+ 5 | 1
+--R \|2 \|x - 32768a c |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+
+--R 8+---+5 | 1 8+-+3
+--R 320a \|- a |- ------------------ \|c
+--R 8| 13 3
+--R \| 1099511627776a c
+--R *
+--R +--------------------+3
+--R 5 | 1
+--R 32768a c |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R atan(--------------------------------------------)
+--R +--------------------+3
+--R +-+ +-+ 5 | 1
+--R \|2 \|x + 32768a c |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R /
+--R +-+8+---+5 8+-+3
+--R 32a\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 686
+
+--S 687 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R +--------------------+6
+--R 10 4 7 11 3 3 | 1
+--R (- 225485783040a c x + 161061273600a c x ) |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R 6 4 10 7 3 6 8 2 2
+--R (20971520a c x - 272629760a c x + 83886080a c x )
+--R *
+--R +--------------------+4
+--R | 1
+--R |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 3 3 9 4 2 5 5 | 1
+--R (61440a c x - 276480a c x + 30720a c x) |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R 2 8 4 2
+--R 125c x - 230a c x + 5a
+--R /
+--R 11 5 10 12 4 6 13 3 2
+--R (274877906944a c x - 68719476736a c x - 343597383680a c x )
+--R *
+--R +--------------------+6
+--R | 1
+--R |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R 8 4 9 9 3 5 10 2
+--R (436207616a c x + 268435456a c x - 167772160a c x)
+--R *
+--R +--------------------+4
+--R | 1
+--R |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R +--------------------+2
+--R 5 3 8 6 2 4 7 | 1
+--R (557056a c x + 524288a c x - 32768a c) |- ------------------
+--R 8| 13 3
+--R \| 1099511627776a c
+--R +
+--R 3 11 2 2 7 3 3
+--R - 128a c x + 320a c x + 448a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 687
+
+)clear all
+
+--S 688 of 1347
+t0:=1/((a+c*x^4)^2*sqrt(x))
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R 2 8 4 2 +-+
+--R (c x + 2a c x + a )\|x
+--R Type: Expression(Integer)
+--E 688
+
+--S 689 of 1347
+r0:=7/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(1/8))+_
+ 7/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(1/8))-_
+ 7/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*_
+ c^(1/8)*sqrt(2))+7/16*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(15/8)*c^(1/8)*sqrt(2))-7/32*log((-a)^(1/4)+c^(1/4)*x-_
+ (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(15/8)*c^(1/8)*_
+ sqrt(2))+7/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(15/8)*c^(1/8)*sqrt(2))+1/4*_
+ sqrt(x)/(a*(a+c*x^4))
+--R
+--R
+--R (2)
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 7c x - 7a)log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (7c x + 7a)log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x
+--R (- 14c x - 14a)\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x + \|- a
+--R (- 14c x - 14a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 \|2 \|c \|x - \|- a
+--R (- 14c x - 14a)atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 4 +-+ \|c \|x +-+8+---+7 8+-+ +-+
+--R (- 14c x - 14a)\|2 atan(--------) + 8\|2 \|- a \|c \|x
+--R 8+---+
+--R \|- a
+--R /
+--R 4 2 +-+8+---+7 8+-+
+--R (32a c x + 32a )\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 689
+
+--S 690 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------------------+
+--R 4 2 | 1
+--R (28a c x + 28a ) |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+ +-------------------+2
+--R 2 +-+ | 1 +-+ 4 | 1
+--R 32a \|2 |- ----------------- \|x + 1024a |- -----------------
+--R 8| 15 8| 15
+--R \| 1099511627776a c \| 1099511627776a c
+--R +
+--R x
+--R +
+--R +-------------------+
+--R 4 2 +-+ | 1
+--R (28a c x + 28a )\|2 |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R +-+ 2 | 1
+--R log(\|x + 32a |- -----------------)
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 4 2 +-+ | 1
+--R (- 28a c x - 28a )\|2 |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R +-+ 2 | 1
+--R log(\|x - 32a |- -----------------)
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 4 2 | 1
+--R (- 28a c x - 28a ) |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+
+--R 2 +-+ | 1 +-+
+--R - 32a \|2 |- ----------------- \|x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 4 | 1
+--R 1024a |- ----------------- + x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 4 2 | 1
+--R (- 56a c x - 56a ) |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R 2 | 1
+--R 32a |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R atan(-------------------------------------)
+--R +-------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x - 32a |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-------------------+
+--R 4 2 | 1
+--R (- 56a c x - 56a ) |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R 2 | 1
+--R 32a |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R atan(-------------------------------------)
+--R +-------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x + 32a |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-+ +-+
+--R \|2 \|x
+--R /
+--R 4 2 +-+
+--R (4a c x + 4a )\|2
+--R Type: Union(Expression(Integer),...)
+--E 690
+
+--S 691 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-------------------+
+--R 8+---+7 | 1 8+-+
+--R 224a \|- a |- ----------------- \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+ +-------------------+2
+--R 2 +-+ | 1 +-+ 4 | 1
+--R 32a \|2 |- ----------------- \|x + 1024a |- -----------------
+--R 8| 15 8| 15
+--R \| 1099511627776a c \| 1099511627776a c
+--R +
+--R x
+--R +
+--R +-------------------+
+--R +-+8+---+7 | 1 8+-+
+--R 224a\|2 \|- a |- ----------------- \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R +-+ 2 | 1
+--R log(\|x + 32a |- -----------------)
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R -
+--R +-------------------+
+--R +-+8+---+7 | 1 8+-+
+--R 224a\|2 \|- a |- ----------------- \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R +-+ 2 | 1
+--R log(\|x - 32a |- -----------------)
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R -
+--R +-------------------+
+--R 8+---+7 | 1 8+-+
+--R 224a \|- a |- ----------------- \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R log
+--R +-------------------+
+--R 2 +-+ | 1 +-+
+--R - 32a \|2 |- ----------------- \|x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 4 | 1
+--R 1024a |- ----------------- + x
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 14atan(---------------------) + 14atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 14\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R -
+--R +-------------------+
+--R 8+---+7 | 1 8+-+
+--R 448a \|- a |- ----------------- \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R 2 | 1
+--R 32a |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R atan(-------------------------------------)
+--R +-------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x - 32a |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R -
+--R +-------------------+
+--R 8+---+7 | 1 8+-+
+--R 448a \|- a |- ----------------- \|c
+--R 8| 15
+--R \| 1099511627776a c
+--R *
+--R +-------------------+
+--R 2 | 1
+--R 32a |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R atan(-------------------------------------)
+--R +-------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x + 32a |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R /
+--R +-+8+---+7 8+-+
+--R 32a\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 691
+
+--S 692 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 11 2 8 12 4 13
+--R (93952409600a c x - 172872433664a c x + 3758096384a )
+--R *
+--R +-------------------+6
+--R | 1
+--R |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-------------------+4
+--R 7 2 9 8 5 9 | 1
+--R (- 44040192a c x + 198180864a c x - 22020096a x) |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 3 2 10 4 6 5 2 | 1
+--R (14336a c x - 186368a c x + 57344a x ) |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R 7 3
+--R 147c x - 105a x
+--R /
+--R 13 2 8 14 4 15
+--R (292057776128a c x + 274877906944a c x - 17179869184a )
+--R *
+--R +-------------------+6
+--R | 1
+--R |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R 9 2 9 10 5 11
+--R (- 218103808a c x - 134217728a c x + 83886080a x)
+--R *
+--R +-------------------+4
+--R | 1
+--R |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R +-------------------+2
+--R 5 2 10 6 6 7 2 | 1
+--R (131072a c x - 32768a c x - 163840a x ) |- -----------------
+--R 8| 15
+--R \| 1099511627776a c
+--R +
+--R 2 11 2 7 3 3
+--R - 64a c x + 160a c x + 224a x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 692
+
+)clear all
+
+--S 693 of 1347
+t0:=1/(x^(3/2)*(a+c*x^4)^2)
+--R
+--R
+--R 1
+--R (1) --------------------------
+--R 2 9 5 2 +-+
+--R (c x + 2a c x + a x)\|x
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 1347
+r0:=-9/16*c^(1/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(17/8)+_
+ 9/16*c^(1/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(17/8)+_
+ 9/16*c^(1/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(17/8)*sqrt(2))-9/16*c^(1/8)*atan(1+c^(1/8)*sqrt(2)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*sqrt(2))-9/32*c^(1/8)*_
+ log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(17/8)*sqrt(2))+9/32*c^(1/8)*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(17/8)*_
+ sqrt(2))+(-9/4)/(a^2*sqrt(x))+1/4/(a*(a+c*x^4)*sqrt(x))
+--R
+--R
+--R (2)
+--R 4 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (9c x + 9a)\|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 4 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 9c x - 9a)\|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 4 +-+8+-+ +-+ \|c \|x
+--R (18c x + 18a)\|2 \|c \|x atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 8+-+ +-+ \|2 \|c \|x + \|- a
+--R (- 18c x - 18a)\|c \|x atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 4 8+-+ +-+ \|2 \|c \|x - \|- a
+--R (- 18c x - 18a)\|c \|x atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 4 +-+8+-+ +-+ \|c \|x 4 +-+8+---+
+--R (- 18c x - 18a)\|2 \|c \|x atan(--------) + (- 72c x - 64a)\|2 \|- a
+--R 8+---+
+--R \|- a
+--R /
+--R 2 4 3 +-+8+---+ +-+
+--R (32a c x + 32a )\|2 \|- a \|x
+--R Type: Expression(Integer)
+--E 694
+
+--S 695 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------------------+
+--R 2 4 3 | 43046721c +-+
+--R (- 4a c x - 4a ) |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R log
+--R +------------------+7
+--R 15 +-+ | 43046721c +-+
+--R 34359738368a \|2 |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+6
+--R 13 | 43046721c
+--R - 9663676416a |- ---------------- + 4782969c x
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+
+--R 2 4 3 +-+ | 43046721c +-+
+--R (- 4a c x - 4a )\|2 |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R +------------------+7
+--R +-+ 15 | 43046721c
+--R log(4782969c\|x + 34359738368a |- ---------------- )
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+
+--R 2 4 3 +-+ | 43046721c +-+
+--R (4a c x + 4a )\|2 |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R +------------------+7
+--R +-+ 15 | 43046721c
+--R log(4782969c\|x - 34359738368a |- ---------------- )
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+
+--R 2 4 3 | 43046721c +-+
+--R (4a c x + 4a ) |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R log
+--R +------------------+7
+--R 15 +-+ | 43046721c +-+
+--R - 34359738368a \|2 |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+6
+--R 13 | 43046721c
+--R - 9663676416a |- ---------------- + 4782969c x
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+
+--R 2 4 3 | 43046721c +-+
+--R (- 8a c x - 8a ) |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R +------------------+7
+--R 15 | 43046721c
+--R 34359738368a |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R atan(-------------------------------------------------------)
+--R +------------------+7
+--R +-+ +-+ 15 | 43046721c
+--R 4782969c\|2 \|x - 34359738368a |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+
+--R 2 4 3 | 43046721c +-+
+--R (- 8a c x - 8a ) |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R +------------------+7
+--R 15 | 43046721c
+--R 34359738368a |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R atan(-------------------------------------------------------)
+--R +------------------+7
+--R +-+ +-+ 15 | 43046721c
+--R 4782969c\|2 \|x + 34359738368a |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R 4 +-+
+--R (- 9c x - 8a)\|2
+--R /
+--R 2 4 3 +-+ +-+
+--R (4a c x + 4a )\|2 \|x
+--R Type: Union(Expression(Integer),...)
+--E 695
+
+--S 696 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 9\|c log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R -
+--R +------------------+
+--R 2 | 43046721c 8+---+
+--R 32a |- ---------------- \|- a
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R log
+--R +------------------+7
+--R 15 +-+ | 43046721c +-+
+--R 34359738368a \|2 |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+6
+--R 13 | 43046721c
+--R - 9663676416a |- ---------------- + 4782969c x
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R -
+--R +------------------+
+--R 2 +-+ | 43046721c 8+---+
+--R 32a \|2 |- ---------------- \|- a
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R +------------------+7
+--R +-+ 15 | 43046721c
+--R log(4782969c\|x + 34359738368a |- ---------------- )
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+
+--R 2 +-+ | 43046721c 8+---+
+--R 32a \|2 |- ---------------- \|- a
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R +------------------+7
+--R +-+ 15 | 43046721c
+--R log(4782969c\|x - 34359738368a |- ---------------- )
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+
+--R 2 | 43046721c 8+---+
+--R 32a |- ---------------- \|- a
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R log
+--R +------------------+7
+--R 15 +-+ | 43046721c +-+
+--R - 34359738368a \|2 |- ---------------- \|x
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+6
+--R 13 | 43046721c
+--R - 9663676416a |- ---------------- + 4782969c x
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 9\|c log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+ +-+8+-+ +-+ 8+---+
+--R +-+8+-+ \|c \|x 8+-+ \|2 \|c \|x + \|- a
+--R - 18\|2 \|c atanh(--------) + 18\|c atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ 8+-+ +-+
+--R 8+-+ \|2 \|c \|x - \|- a +-+8+-+ \|c \|x
+--R 18\|c atan(---------------------) + 18\|2 \|c atan(--------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R -
+--R +------------------+
+--R 2 | 43046721c 8+---+
+--R 64a |- ---------------- \|- a
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R +------------------+7
+--R 15 | 43046721c
+--R 34359738368a |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R atan(-------------------------------------------------------)
+--R +------------------+7
+--R +-+ +-+ 15 | 43046721c
+--R 4782969c\|2 \|x - 34359738368a |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R -
+--R +------------------+
+--R 2 | 43046721c 8+---+
+--R 64a |- ---------------- \|- a
+--R 8| 17
+--R \| 1099511627776a
+--R *
+--R +------------------+7
+--R 15 | 43046721c
+--R 34359738368a |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R atan(-------------------------------------------------------)
+--R +------------------+7
+--R +-+ +-+ 15 | 43046721c
+--R 4782969c\|2 \|x + 34359738368a |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R /
+--R 2 +-+8+---+
+--R 32a \|2 \|- a
+--R Type: Expression(Integer)
+--E 696
+
+--S 697 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 13 2 9 14 5 15
+--R (28991029248a c x - 130459631616a c x + 14495514624a x)
+--R *
+--R +------------------+6
+--R | 43046721c
+--R |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R 9 2 8 10 4 11
+--R (- 4777574400a c x + 8790736896a c x - 191102976a )
+--R *
+--R +------------------+4
+--R | 43046721c
+--R |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+2
+--R 5 2 7 6 3 | 43046721c 3 10
+--R (634894848a c x - 453496320a c x ) |- ---------------- + 4782969c x
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R 2 6 2 2
+--R - 62178597a c x + 19131876a c x
+--R /
+--R 15 2 10 16 6 17 2
+--R (68719476736a c x - 17179869184a c x - 85899345920a x )
+--R *
+--R +------------------+6
+--R | 43046721c
+--R |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R 11 2 9 12 5 13
+--R (- 8833204224a c x - 5435817984a c x + 3397386240a x)
+--R *
+--R +------------------+4
+--R | 43046721c
+--R |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R +------------------+2
+--R 7 2 8 8 4 9 | 43046721c
+--R (913711104a c x + 859963392a c x - 53747712a ) |- ----------------
+--R 8| 17
+--R \| 1099511627776a
+--R +
+--R 2 3 11 3 2 7 4 3
+--R 17006112a c x - 42515280a c x - 59521392a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 697
+
+)clear all
+
+--S 698 of 1347
+t0:=x^(15/2)/(a+c*x^4)^3
+--R
+--R
+--R 7 +-+
+--R x \|x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 1347
+r0:=-1/8*x^(9/2)/(c*(a+c*x^4)^2)-9/256*atan(c^(1/8)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(17/8))-9/256*_
+ atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(17/8))+_
+ 9/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*_
+ c^(17/8)*sqrt(2))-9/256*atan(1+c^(1/8)*sqrt(2)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(17/8)*sqrt(2))+_
+ 9/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(17/8)*sqrt(2))-_
+ 9/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(17/8)*sqrt(2))-_
+ 9/64*sqrt(x)/(c^2*(a+c*x^4))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 9c x - 18a c x - 9a )log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (9c x + 18a c x + 9a )log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 18c x - 36a c x - 18a )\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x + \|- a
+--R (- 18c x - 36a c x - 18a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x - \|- a
+--R (- 18c x - 36a c x - 18a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 18c x - 36a c x - 18a )\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R 4 +-+8+---+7 8+-+ +-+
+--R (- 136c x - 72a)\|2 \|- a \|c \|x
+--R /
+--R 4 8 3 4 2 2 +-+8+---+7 8+-+
+--R (512c x + 1024a c x + 512a c )\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 699
+
+--S 700 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------+
+--R 4 8 3 4 2 2 | 1
+--R (576c x + 1152a c x + 576a c ) |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+
+--R 2 +-+ | 1 +-+
+--R 512a c \|2 |- --------------------------- \|x
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 2 4 | 1
+--R 262144a c |- --------------------------- + x
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 4 8 3 4 2 2 +-+ | 1
+--R (576c x + 1152a c x + 576a c )\|2 |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R +-+ 2 | 1
+--R log(\|x + 512a c |- ---------------------------)
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 4 8 3 4 2 2 +-+ | 1
+--R (- 576c x - 1152a c x - 576a c )\|2 |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R +-+ 2 | 1
+--R log(\|x - 512a c |- ---------------------------)
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 4 8 3 4 2 2 | 1
+--R (- 576c x - 1152a c x - 576a c ) |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+
+--R 2 +-+ | 1 +-+
+--R - 512a c \|2 |- --------------------------- \|x
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 2 4 | 1
+--R 262144a c |- --------------------------- + x
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 4 8 3 4 2 2 | 1
+--R (- 1152c x - 2304a c x - 1152a c ) |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R 2 | 1
+--R 512a c |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R atan(--------------------------------------------------)
+--R +-----------------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x - 512a c |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 4 8 3 4 2 2 | 1
+--R (- 1152c x - 2304a c x - 1152a c ) |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R 2 | 1
+--R 512a c |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R atan(--------------------------------------------------)
+--R +-----------------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x + 512a c |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R 4 +-+ +-+
+--R (- 17c x - 9a)\|2 \|x
+--R /
+--R 4 8 3 4 2 2 +-+
+--R (64c x + 128a c x + 64a c )\|2
+--R Type: Union(Expression(Integer),...)
+--E 700
+
+--S 701 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 9log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-----------------------------+
+--R 2 8+---+7 | 1 8+-+
+--R 4608c \|- a |- --------------------------- \|c
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+
+--R 2 +-+ | 1 +-+
+--R 512a c \|2 |- --------------------------- \|x
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 2 4 | 1
+--R 262144a c |- --------------------------- + x
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 +-+8+---+7 | 1 8+-+
+--R 4608c \|2 \|- a |- --------------------------- \|c
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R +-+ 2 | 1
+--R log(\|x + 512a c |- ---------------------------)
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 +-+8+---+7 | 1 8+-+
+--R 4608c \|2 \|- a |- --------------------------- \|c
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R +-+ 2 | 1
+--R log(\|x - 512a c |- ---------------------------)
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 8+---+7 | 1 8+-+
+--R 4608c \|- a |- --------------------------- \|c
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+
+--R 2 +-+ | 1 +-+
+--R - 512a c \|2 |- --------------------------- \|x
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 2 4 | 1
+--R 262144a c |- --------------------------- + x
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - 9log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 18\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 18atan(---------------------) + 18atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 18\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R -
+--R +-----------------------------+
+--R 2 8+---+7 | 1 8+-+
+--R 9216c \|- a |- --------------------------- \|c
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R 2 | 1
+--R 512a c |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R atan(--------------------------------------------------)
+--R +-----------------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x - 512a c |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 8+---+7 | 1 8+-+
+--R 9216c \|- a |- --------------------------- \|c
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R 2 | 1
+--R 512a c |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R atan(--------------------------------------------------)
+--R +-----------------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x + 512a c |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R /
+--R 2 +-+8+---+7 8+-+
+--R 512c \|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 701
+
+--S 702 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 5 14 8 6 13 4
+--R 2026619832316723200a c x - 3728980491462770688a c x
+--R +
+--R 7 12
+--R 81064793292668928a c
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R 3 10 9 4 9 5 5 8
+--R (- 3710851743744a c x + 16698832846848a c x - 1855425871872a c x)
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R 6 10 2 5 6 3 4 2
+--R (4718592a c x - 61341696a c x + 18874368a c x )
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R 7 3
+--R 189c x - 135a x
+--R /
+--R 6 16 8 7 15 4
+--R 78398662313265594368a c x + 73786976294838206464a c x
+--R +
+--R 8 14
+--R - 4611686018427387904a c
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R 4 12 9 5 11 5
+--R - 228698418577408a c x - 140737488355328a c x
+--R +
+--R 6 10
+--R 87960930222080a c x
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R 2 8 10 3 7 6 4 6 2
+--R (536870912a c x - 134217728a c x - 671088640a c x )
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 7 17
+--R \| 4722366482869645213696a c
+--R +
+--R 4 11 3 7 2 2 3
+--R - 1024c x + 2560a c x + 3584a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 702
+
+)clear all
+
+--S 703 of 1347
+t0:=x^(13/2)/(a+c*x^4)^3
+--R
+--R
+--R 6 +-+
+--R x \|x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 1347
+r0:=-1/8*x^(7/2)/(c*(a+c*x^4)^2)+7/64*x^(7/2)/(a*c*(a+c*x^4))-_
+ 7/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(15/8))+_
+ 7/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(15/8))+_
+ 7/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*_
+ c^(15/8)*sqrt(2))-7/256*atan(1+c^(1/8)*sqrt(2)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(15/8)*sqrt(2))-_
+ 7/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(9/8)*c^(15/8)*sqrt(2))+7/512*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(9/8)*_
+ c^(15/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 7c x - 14a c x - 7a )log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (7c x + 14a c x + 7a )log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 14c x - 28a c x - 14a )\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x + \|- a
+--R (14c x + 28a c x + 14a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x - \|- a
+--R (14c x + 28a c x + 14a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (14c x + 28a c x + 14a )\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R 7 3 +-+8+---+8+-+7 +-+
+--R (56c x - 8a x )\|2 \|- a \|c \|x
+--R /
+--R 3 8 2 2 4 3 +-+8+---+8+-+7
+--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 704
+
+--S 705 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (448a c x + 896a c x + 448a c) |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+7
+--R 8 13 +-+ | 1 +-+
+--R 9223372036854775808a c \|2 |- --------------------------- \|x
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 7 11 | 1
+--R - 18014398509481984a c |- --------------------------- + x
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 +-+ | 1
+--R (448a c x + 896a c x + 448a c)\|2 |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+7
+--R +-+ 8 13 | 1
+--R log(\|x + 9223372036854775808a c |- --------------------------- )
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 +-+ | 1
+--R (- 448a c x - 896a c x - 448a c)\|2 |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+7
+--R +-+ 8 13 | 1
+--R log(\|x - 9223372036854775808a c |- --------------------------- )
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 448a c x - 896a c x - 448a c) |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R -
+--R +-----------------------------+7
+--R 8 13 +-+ | 1
+--R 9223372036854775808a c \|2 |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R +-+
+--R \|x
+--R +
+--R +-----------------------------+6
+--R 7 11 | 1
+--R - 18014398509481984a c |- --------------------------- + x
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (896a c x + 1792a c x + 896a c) |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R atan
+--R +-----------------------------+7
+--R 8 13 | 1
+--R 9223372036854775808a c |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R --------------------------------------------------------------------
+--R +-----------------------------+7
+--R +-+ +-+ 8 13 | 1
+--R \|2 \|x - 9223372036854775808a c |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (896a c x + 1792a c x + 896a c) |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R atan
+--R +-----------------------------+7
+--R 8 13 | 1
+--R 9223372036854775808a c |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R --------------------------------------------------------------------
+--R +-----------------------------+7
+--R +-+ +-+ 8 13 | 1
+--R \|2 \|x + 9223372036854775808a c |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R 7 3 +-+ +-+
+--R (7c x - a x )\|2 \|x
+--R /
+--R 3 8 2 2 4 3 +-+
+--R (64a c x + 128a c x + 64a c)\|2
+--R Type: Union(Expression(Integer),...)
+--E 705
+
+--S 706 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-----------------------------+
+--R 8+---+ | 1 8+-+7
+--R 3584a c\|- a |- --------------------------- \|c
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+7
+--R 8 13 +-+ | 1 +-+
+--R 9223372036854775808a c \|2 |- --------------------------- \|x
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 7 11 | 1
+--R - 18014398509481984a c |- --------------------------- + x
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R +-+8+---+ | 1 8+-+7
+--R 3584a c\|2 \|- a |- --------------------------- \|c
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+7
+--R +-+ 8 13 | 1
+--R log(\|x + 9223372036854775808a c |- --------------------------- )
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R +-+8+---+ | 1 8+-+7
+--R 3584a c\|2 \|- a |- --------------------------- \|c
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+7
+--R +-+ 8 13 | 1
+--R log(\|x - 9223372036854775808a c |- --------------------------- )
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 8+---+ | 1 8+-+7
+--R 3584a c\|- a |- --------------------------- \|c
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R -
+--R 8 13 +-+
+--R 9223372036854775808a c \|2
+--R *
+--R +-----------------------------+7
+--R | 1 +-+
+--R |- --------------------------- \|x
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 7 11 | 1
+--R - 18014398509481984a c |- --------------------------- + x
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 14atan(---------------------) - 14atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 14\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-----------------------------+
+--R 8+---+ | 1 8+-+7
+--R 7168a c\|- a |- --------------------------- \|c
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R atan
+--R +-----------------------------+7
+--R 8 13 | 1
+--R 9223372036854775808a c |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R --------------------------------------------------------------------
+--R +-----------------------------+7
+--R +-+ +-+ 8 13 | 1
+--R \|2 \|x - 9223372036854775808a c |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 8+---+ | 1 8+-+7
+--R 7168a c\|- a |- --------------------------- \|c
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R *
+--R atan
+--R +-----------------------------+7
+--R 8 13 | 1
+--R 9223372036854775808a c |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R --------------------------------------------------------------------
+--R +-----------------------------+7
+--R +-+ +-+ 8 13 | 1
+--R \|2 \|x + 9223372036854775808a c |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R /
+--R +-+8+---+8+-+7
+--R 512a c\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 706
+
+--S 707 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 7 13 9 8 12 5
+--R - 378302368699121664a c x + 1702360659146047488a c x
+--R +
+--R 9 11
+--R - 189151184349560832a c x
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R 5 9 8 6 8 4 7 7
+--R (3006477107200a c x - 5531917877248a c x + 120259084288a c )
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 3 5 7 4 4 3 | 1
+--R (- 19267584a c x + 13762560a c x ) |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R 2 10 6 2 2
+--R - 7c x + 91a c x - 28a x
+--R /
+--R 8 15 10 9 14 6
+--R 18446744073709551616a c x - 4611686018427387904a c x
+--R +
+--R 10 13 2
+--R - 23058430092136939520a c x
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R 6 11 9 7 10 5
+--R - 114349209288704a c x - 70368744177664a c x
+--R +
+--R 8 9
+--R 43980465111040a c x
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R 4 7 8 5 6 4 6 5
+--R (570425344a c x + 536870912a c x - 33554432a c )
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 9 15
+--R \| 4722366482869645213696a c
+--R +
+--R 4 11 2 3 7 3 2 3
+--R 512a c x - 1280a c x - 1792a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 707
+
+)clear all
+
+--S 708 of 1347
+t0:=x^(11/2)/(a+c*x^4)^3
+--R
+--R
+--R 5 +-+
+--R x \|x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 1347
+r0:=-1/8*x^(5/2)/(c*(a+c*x^4)^2)+5/64*x^(5/2)/(a*c*(a+c*x^4))+_
+ 15/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*c^(13/8))+_
+ 15/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*_
+ c^(13/8))+15/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(11/8)*c^(13/8)*sqrt(2))-15/256*atan(1+c^(1/8)*_
+ sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*c^(13/8)*sqrt(2))+_
+ 15/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(11/8)*c^(13/8)*sqrt(2))-_
+ 15/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(11/8)*c^(13/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (15c x + 30a c x + 15a )log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 15c x - 30a c x - 15a )log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 30c x - 60a c x - 30a )\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x + \|- a
+--R (30c x + 60a c x + 30a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x - \|- a
+--R (30c x + 60a c x + 30a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 30c x - 60a c x - 30a )\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R 6 2 +-+8+---+3 8+-+5 +-+
+--R (40c x - 24a x )\|2 \|- a \|c \|x
+--R /
+--R 3 8 2 2 4 3 +-+8+---+3 8+-+5
+--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 709
+
+--S 710 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (960a c x + 1920a c x + 960a c) |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +------------------------------+5
+--R 7 8 +-+ | 1 +-+
+--R 35184372088832a c \|2 |- ---------------------------- \|x
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+2
+--R 3 3 | 1
+--R - 262144a c |- ---------------------------- + x
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R 3 8 2 2 4 3 +-+
+--R (- 960a c x - 1920a c x - 960a c)\|2
+--R *
+--R +------------------------------+
+--R | 1
+--R |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+5
+--R +-+ 7 8 | 1
+--R log(\|x + 35184372088832a c |- ---------------------------- )
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R 3 8 2 2 4 3 +-+ | 1
+--R (960a c x + 1920a c x + 960a c)\|2 |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+5
+--R +-+ 7 8 | 1
+--R log(\|x - 35184372088832a c |- ---------------------------- )
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 960a c x - 1920a c x - 960a c) |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +------------------------------+5
+--R 7 8 +-+ | 1 +-+
+--R - 35184372088832a c \|2 |- ---------------------------- \|x
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+2
+--R 3 3 | 1
+--R - 262144a c |- ---------------------------- + x
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 1920a c x - 3840a c x - 1920a c) |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+5
+--R 7 8 | 1
+--R 35184372088832a c |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------------)
+--R +------------------------------+5
+--R +-+ +-+ 7 8 | 1
+--R \|2 \|x - 35184372088832a c |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 1920a c x - 3840a c x - 1920a c) |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+5
+--R 7 8 | 1
+--R 35184372088832a c |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------------)
+--R +------------------------------+5
+--R +-+ +-+ 7 8 | 1
+--R \|2 \|x + 35184372088832a c |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R 6 2 +-+ +-+
+--R (5c x - 3a x )\|2 \|x
+--R /
+--R 3 8 2 2 4 3 +-+
+--R (64a c x + 128a c x + 64a c)\|2
+--R Type: Union(Expression(Integer),...)
+--E 710
+
+--S 711 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 15log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +------------------------------+
+--R 8+---+3 | 1 8+-+5
+--R 7680a c \|- a |- ---------------------------- \|c
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +------------------------------+5
+--R 7 8 +-+ | 1 +-+
+--R 35184372088832a c \|2 |- ---------------------------- \|x
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+2
+--R 3 3 | 1
+--R - 262144a c |- ---------------------------- + x
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +------------------------------+
+--R +-+8+---+3 | 1 8+-+5
+--R 7680a c\|2 \|- a |- ---------------------------- \|c
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+5
+--R +-+ 7 8 | 1
+--R log(\|x + 35184372088832a c |- ---------------------------- )
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R +-+8+---+3 | 1 8+-+5
+--R 7680a c\|2 \|- a |- ---------------------------- \|c
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+5
+--R +-+ 7 8 | 1
+--R log(\|x - 35184372088832a c |- ---------------------------- )
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +------------------------------+
+--R 8+---+3 | 1 8+-+5
+--R 7680a c \|- a |- ---------------------------- \|c
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +------------------------------+5
+--R 7 8 +-+ | 1 +-+
+--R - 35184372088832a c \|2 |- ---------------------------- \|x
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+2
+--R 3 3 | 1
+--R - 262144a c |- ---------------------------- + x
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R 15log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 30\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 30atan(---------------------) - 30atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 30\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R -
+--R +------------------------------+
+--R 8+---+3 | 1 8+-+5
+--R 15360a c \|- a |- ---------------------------- \|c
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+5
+--R 7 8 | 1
+--R 35184372088832a c |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------------)
+--R +------------------------------+5
+--R +-+ +-+ 7 8 | 1
+--R \|2 \|x - 35184372088832a c |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +------------------------------+
+--R 8+---+3 | 1 8+-+5
+--R 15360a c \|- a |- ---------------------------- \|c
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+5
+--R 7 8 | 1
+--R 35184372088832a c |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------------)
+--R +------------------------------+5
+--R +-+ +-+ 7 8 | 1
+--R \|2 \|x + 35184372088832a c |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R /
+--R +-+8+---+3 8+-+5
+--R 512a c\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 8 12 10 9 11 6
+--R 540431955284459520a c x - 7025615418697973760a c x
+--R +
+--R 10 10 2
+--R 2161727821137838080a c x
+--R *
+--R +------------------------------+6
+--R | 1
+--R |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R 6 8 7 7 7 3
+--R (- 21646635171840a c x + 15461882265600a c x )
+--R *
+--R +------------------------------+4
+--R | 1
+--R |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R 3 5 8 4 4 4 5 3
+--R (- 49152000a c x + 90439680a c x - 1966080a c )
+--R *
+--R +------------------------------+2
+--R | 1
+--R |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R 2 9 5 2
+--R - 90c x + 405a c x - 45a x
+--R /
+--R 10 13 8 11 12 4
+--R 78398662313265594368a c x + 73786976294838206464a c x
+--R +
+--R 12 11
+--R - 4611686018427387904a c
+--R *
+--R +------------------------------+6
+--R | 1
+--R |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R 7 10 9 8 9 5
+--R 228698418577408a c x + 140737488355328a c x
+--R +
+--R 9 8
+--R - 87960930222080a c x
+--R *
+--R +------------------------------+4
+--R | 1
+--R |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R 4 7 10 5 6 6 6 5 2
+--R (536870912a c x - 134217728a c x - 671088640a c x )
+--R *
+--R +------------------------------+2
+--R | 1
+--R |- ----------------------------
+--R 8| 11 13
+--R \| 4722366482869645213696a c
+--R +
+--R 4 11 2 3 7 3 2 3
+--R 1024a c x - 2560a c x - 3584a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 712
+
+)clear all
+
+--S 713 of 1347
+t0:=x^(9/2)/(a+c*x^4)^3
+--R
+--R
+--R 4 +-+
+--R x \|x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Expression(Integer)
+--E 713
+
+--S 714 of 1347
+r0:=-1/8*x^(3/2)/(c*(a+c*x^4)^2)+3/64*x^(3/2)/(a*c*(a+c*x^4))-_
+ 15/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*c^(11/8))+_
+ 15/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*c^(11/8))-_
+ 15/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*_
+ c^(11/8)*sqrt(2))+15/256*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(13/8)*c^(11/8)*sqrt(2))+15/512*_
+ log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(13/8)*c^(11/8)*sqrt(2))-15/512*_
+ log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(13/8)*c^(11/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (15c x + 30a c x + 15a )log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 15c x - 30a c x - 15a )log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 30c x - 60a c x - 30a )\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x + \|- a
+--R (- 30c x - 60a c x - 30a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x - \|- a
+--R (- 30c x - 60a c x - 30a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (30c x + 60a c x + 30a )\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R 5 +-+8+---+5 8+-+3 +-+
+--R (24c x - 40a x)\|2 \|- a \|c \|x
+--R /
+--R 3 8 2 2 4 3 +-+8+---+5 8+-+3
+--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 714
+
+--S 715 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (960a c x + 1920a c x + 960a c) |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +------------------------------+3
+--R 5 4 +-+ | 1 +-+
+--R 134217728a c \|2 |- ---------------------------- \|x
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+6
+--R 10 8 | 1
+--R 18014398509481984a c |- ---------------------------- + x
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R 3 8 2 2 4 3 +-+
+--R (- 960a c x - 1920a c x - 960a c)\|2
+--R *
+--R +------------------------------+
+--R | 1
+--R |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+3
+--R +-+ 5 4 | 1
+--R log(\|x + 134217728a c |- ---------------------------- )
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R 3 8 2 2 4 3 +-+ | 1
+--R (960a c x + 1920a c x + 960a c)\|2 |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+3
+--R +-+ 5 4 | 1
+--R log(\|x - 134217728a c |- ---------------------------- )
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 960a c x - 1920a c x - 960a c) |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +------------------------------+3
+--R 5 4 +-+ | 1 +-+
+--R - 134217728a c \|2 |- ---------------------------- \|x
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+6
+--R 10 8 | 1
+--R 18014398509481984a c |- ---------------------------- + x
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (1920a c x + 3840a c x + 1920a c) |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+3
+--R 5 4 | 1
+--R 134217728a c |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R atan(----------------------------------------------------------)
+--R +------------------------------+3
+--R +-+ +-+ 5 4 | 1
+--R \|2 \|x - 134217728a c |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (1920a c x + 3840a c x + 1920a c) |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+3
+--R 5 4 | 1
+--R 134217728a c |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R atan(----------------------------------------------------------)
+--R +------------------------------+3
+--R +-+ +-+ 5 4 | 1
+--R \|2 \|x + 134217728a c |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R 5 +-+ +-+
+--R (3c x - 5a x)\|2 \|x
+--R /
+--R 3 8 2 2 4 3 +-+
+--R (64a c x + 128a c x + 64a c)\|2
+--R Type: Union(Expression(Integer),...)
+--E 715
+
+--S 716 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 15log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +------------------------------+
+--R 8+---+5 | 1 8+-+3
+--R 7680a c \|- a |- ---------------------------- \|c
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +------------------------------+3
+--R 5 4 +-+ | 1 +-+
+--R 134217728a c \|2 |- ---------------------------- \|x
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+6
+--R 10 8 | 1
+--R 18014398509481984a c |- ---------------------------- + x
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +------------------------------+
+--R +-+8+---+5 | 1 8+-+3
+--R 7680a c\|2 \|- a |- ---------------------------- \|c
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+3
+--R +-+ 5 4 | 1
+--R log(\|x + 134217728a c |- ---------------------------- )
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R +-+8+---+5 | 1 8+-+3
+--R 7680a c\|2 \|- a |- ---------------------------- \|c
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+3
+--R +-+ 5 4 | 1
+--R log(\|x - 134217728a c |- ---------------------------- )
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +------------------------------+
+--R 8+---+5 | 1 8+-+3
+--R 7680a c \|- a |- ---------------------------- \|c
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +------------------------------+3
+--R 5 4 +-+ | 1 +-+
+--R - 134217728a c \|2 |- ---------------------------- \|x
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+6
+--R 10 8 | 1
+--R 18014398509481984a c |- ---------------------------- + x
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R 15log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 30\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 30atan(---------------------) + 30atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 30\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +------------------------------+
+--R 8+---+5 | 1 8+-+3
+--R 15360a c \|- a |- ---------------------------- \|c
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+3
+--R 5 4 | 1
+--R 134217728a c |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R atan(----------------------------------------------------------)
+--R +------------------------------+3
+--R +-+ +-+ 5 4 | 1
+--R \|2 \|x - 134217728a c |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R +------------------------------+
+--R 8+---+5 | 1 8+-+3
+--R 15360a c \|- a |- ---------------------------- \|c
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R *
+--R +------------------------------+3
+--R 5 4 | 1
+--R 134217728a c |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R atan(----------------------------------------------------------)
+--R +------------------------------+3
+--R +-+ +-+ 5 4 | 1
+--R \|2 \|x + 134217728a c |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R /
+--R +-+8+---+5 8+-+3
+--R 512a c\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 10 10 7 11 9 3
+--R (- 11349071060973649920a c x + 8106479329266892800a c x )
+--R *
+--R +------------------------------+6
+--R | 1
+--R |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R 6 8 10 7 7 6 8 6 2
+--R (4123168604160a c x - 53601191854080a c x + 16492674416640a c x )
+--R *
+--R +------------------------------+4
+--R | 1
+--R |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R 3 5 9 4 4 5 5 3
+--R (47185920a c x - 212336640a c x + 23592960a c x)
+--R *
+--R +------------------------------+2
+--R | 1
+--R |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R 2 8 4 2
+--R 375c x - 690a c x + 15a
+--R /
+--R 11 12 10 12 11 6
+--R 73786976294838206464a c x - 18446744073709551616a c x
+--R +
+--R 13 10 2
+--R - 92233720368547758080a c x
+--R *
+--R +------------------------------+6
+--R | 1
+--R |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R 8 9 9 9 8 5
+--R 457396837154816a c x + 281474976710656a c x
+--R +
+--R 10 7
+--R - 175921860444160a c x
+--R *
+--R +------------------------------+4
+--R | 1
+--R |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R 5 6 8 6 5 4 7 4
+--R (2281701376a c x + 2147483648a c x - 134217728a c )
+--R *
+--R +------------------------------+2
+--R | 1
+--R |- ----------------------------
+--R 8| 13 11
+--R \| 4722366482869645213696a c
+--R +
+--R 4 11 2 3 7 3 2 3
+--R - 2048a c x + 5120a c x + 7168a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 717
+
+)clear all
+
+--S 718 of 1347
+t0:=x^(7/2)/(a+c*x^4)^3
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 1347
+r0:=7/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(9/8))+_
+ 7/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(9/8))-_
+ 7/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*_
+ c^(9/8)*sqrt(2))+7/256*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(15/8)*c^(9/8)*sqrt(2))-7/512*_
+ log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(15/8)*c^(9/8)*sqrt(2))+7/512*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(15/8)*_
+ c^(9/8)*sqrt(2))-1/8*sqrt(x)/(c*(a+c*x^4)^2)+1/64*_
+ sqrt(x)/(a*c*(a+c*x^4))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 7c x - 14a c x - 7a )log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (7c x + 14a c x + 7a )log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 14c x - 28a c x - 14a )\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x + \|- a
+--R (- 14c x - 28a c x - 14a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x - \|- a
+--R (- 14c x - 28a c x - 14a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 14c x - 28a c x - 14a )\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R 4 +-+8+---+7 8+-+ +-+
+--R (8c x - 56a)\|2 \|- a \|c \|x
+--R /
+--R 3 8 2 2 4 3 +-+8+---+7 8+-+
+--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 719
+
+--S 720 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (448a c x + 896a c x + 448a c) |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+
+--R 2 +-+ | 1 +-+
+--R 512a c\|2 |- --------------------------- \|x
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 4 2 | 1
+--R 262144a c |- --------------------------- + x
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 +-+ | 1
+--R (448a c x + 896a c x + 448a c)\|2 |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R +-+ 2 | 1
+--R log(\|x + 512a c |- ---------------------------)
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 +-+ | 1
+--R (- 448a c x - 896a c x - 448a c)\|2 |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R +-+ 2 | 1
+--R log(\|x - 512a c |- ---------------------------)
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 448a c x - 896a c x - 448a c) |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+
+--R 2 +-+ | 1 +-+
+--R - 512a c\|2 |- --------------------------- \|x
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 4 2 | 1
+--R 262144a c |- --------------------------- + x
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 896a c x - 1792a c x - 896a c) |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R 2 | 1
+--R 512a c |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R atan(-------------------------------------------------)
+--R +-----------------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x - 512a c |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 3 8 2 2 4 3 | 1
+--R (- 896a c x - 1792a c x - 896a c) |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R 2 | 1
+--R 512a c |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R atan(-------------------------------------------------)
+--R +-----------------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x + 512a c |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R 4 +-+ +-+
+--R (c x - 7a)\|2 \|x
+--R /
+--R 3 8 2 2 4 3 +-+
+--R (64a c x + 128a c x + 64a c)\|2
+--R Type: Union(Expression(Integer),...)
+--E 720
+
+--S 721 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-----------------------------+
+--R 8+---+7 | 1 8+-+
+--R 3584a c \|- a |- --------------------------- \|c
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+
+--R 2 +-+ | 1 +-+
+--R 512a c\|2 |- --------------------------- \|x
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 4 2 | 1
+--R 262144a c |- --------------------------- + x
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R +-+8+---+7 | 1 8+-+
+--R 3584a c\|2 \|- a |- --------------------------- \|c
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R +-+ 2 | 1
+--R log(\|x + 512a c |- ---------------------------)
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R +-+8+---+7 | 1 8+-+
+--R 3584a c\|2 \|- a |- --------------------------- \|c
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R +-+ 2 | 1
+--R log(\|x - 512a c |- ---------------------------)
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 8+---+7 | 1 8+-+
+--R 3584a c \|- a |- --------------------------- \|c
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+
+--R 2 +-+ | 1 +-+
+--R - 512a c\|2 |- --------------------------- \|x
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 4 2 | 1
+--R 262144a c |- --------------------------- + x
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 14atan(---------------------) + 14atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 14\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R -
+--R +-----------------------------+
+--R 8+---+7 | 1 8+-+
+--R 7168a c \|- a |- --------------------------- \|c
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R 2 | 1
+--R 512a c |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R atan(-------------------------------------------------)
+--R +-----------------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x - 512a c |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 8+---+7 | 1 8+-+
+--R 7168a c \|- a |- --------------------------- \|c
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+
+--R 2 | 1
+--R 512a c |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R atan(-------------------------------------------------)
+--R +-----------------------------+
+--R +-+ +-+ 2 | 1
+--R \|2 \|x + 512a c |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R /
+--R +-+8+---+7 8+-+
+--R 512a c\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 721
+
+--S 722 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 11 8 8 12 7 4
+--R 1576259869579673600a c x - 2900318160026599424a c x
+--R +
+--R 13 6
+--R 63050394783186944a c
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R 7 6 9 8 5 5 9 4
+--R (- 2886218022912a c x + 12987981103104a c x - 1443109011456a c x)
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R 3 4 10 4 3 6 5 2 2
+--R (3670016a c x - 47710208a c x + 14680064a c x )
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R 7 3
+--R 147c x - 105a x
+--R /
+--R 13 9 8 14 8 4
+--R 78398662313265594368a c x + 73786976294838206464a c x
+--R +
+--R 15 7
+--R - 4611686018427387904a c
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R 9 7 9 10 6 5
+--R - 228698418577408a c x - 140737488355328a c x
+--R +
+--R 11 5
+--R 87960930222080a c x
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R 5 5 10 6 4 6 7 3 2
+--R (536870912a c x - 134217728a c x - 671088640a c x )
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 15 9
+--R \| 4722366482869645213696a c
+--R +
+--R 3 11 2 2 7 3 3
+--R - 1024a c x + 2560a c x + 3584a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 722
+
+)clear all
+
+--S 723 of 1347
+t0:=x^(5/2)/(a+c*x^4)^3
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 1347
+r0:=1/8*x^(7/2)/(a*(a+c*x^4)^2)+9/64*x^(7/2)/(a^2*(a+c*x^4))+_
+ 9/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*c^(7/8))-_
+ 9/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*c^(7/8))-_
+ 9/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_
+ ((-a)^(17/8)*c^(7/8)*sqrt(2))+9/256*atan(1+c^(1/8)*sqrt(2)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*c^(7/8)*sqrt(2))+_
+ 9/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(17/8)*c^(7/8)*sqrt(2))-9/512*log((-a)^(1/4)+_
+ c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/_
+ ((-a)^(17/8)*c^(7/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 9c x - 18a c x - 9a )log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (9c x + 18a c x + 9a )log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 18c x - 36a c x - 18a )\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x + \|- a
+--R (18c x + 36a c x + 18a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x - \|- a
+--R (18c x + 36a c x + 18a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (18c x + 36a c x + 18a )\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R 7 3 +-+8+---+8+-+7 +-+
+--R (72c x + 136a x )\|2 \|- a \|c \|x
+--R /
+--R 2 2 8 3 4 4 +-+8+---+8+-+7
+--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 724
+
+--S 725 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (576a c x + 1152a c x + 576a ) |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+7
+--R 15 6 +-+ | 1 +-+
+--R 9223372036854775808a c \|2 |- --------------------------- \|x
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 13 5 | 1
+--R - 18014398509481984a c |- --------------------------- + x
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 +-+ | 1
+--R (576a c x + 1152a c x + 576a )\|2 |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+7
+--R +-+ 15 6 | 1
+--R log(\|x + 9223372036854775808a c |- --------------------------- )
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 +-+ | 1
+--R (- 576a c x - 1152a c x - 576a )\|2 |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+7
+--R +-+ 15 6 | 1
+--R log(\|x - 9223372036854775808a c |- --------------------------- )
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 576a c x - 1152a c x - 576a ) |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R -
+--R +-----------------------------+7
+--R 15 6 +-+ | 1
+--R 9223372036854775808a c \|2 |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R +-+
+--R \|x
+--R +
+--R +-----------------------------+6
+--R 13 5 | 1
+--R - 18014398509481984a c |- --------------------------- + x
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (1152a c x + 2304a c x + 1152a ) |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R atan
+--R +-----------------------------+7
+--R 15 6 | 1
+--R 9223372036854775808a c |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R --------------------------------------------------------------------
+--R +-----------------------------+7
+--R +-+ +-+ 15 6 | 1
+--R \|2 \|x - 9223372036854775808a c |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (1152a c x + 2304a c x + 1152a ) |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R atan
+--R +-----------------------------+7
+--R 15 6 | 1
+--R 9223372036854775808a c |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R --------------------------------------------------------------------
+--R +-----------------------------+7
+--R +-+ +-+ 15 6 | 1
+--R \|2 \|x + 9223372036854775808a c |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R 7 3 +-+ +-+
+--R (9c x + 17a x )\|2 \|x
+--R /
+--R 2 2 8 3 4 4 +-+
+--R (64a c x + 128a c x + 64a )\|2
+--R Type: Union(Expression(Integer),...)
+--E 725
+
+--S 726 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 9log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-----------------------------+
+--R 2 8+---+ | 1 8+-+7
+--R 4608a \|- a |- --------------------------- \|c
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+7
+--R 15 6 +-+ | 1 +-+
+--R 9223372036854775808a c \|2 |- --------------------------- \|x
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 13 5 | 1
+--R - 18014398509481984a c |- --------------------------- + x
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 +-+8+---+ | 1 8+-+7
+--R 4608a \|2 \|- a |- --------------------------- \|c
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+7
+--R +-+ 15 6 | 1
+--R log(\|x + 9223372036854775808a c |- --------------------------- )
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 +-+8+---+ | 1 8+-+7
+--R 4608a \|2 \|- a |- --------------------------- \|c
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+7
+--R +-+ 15 6 | 1
+--R log(\|x - 9223372036854775808a c |- --------------------------- )
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 8+---+ | 1 8+-+7
+--R 4608a \|- a |- --------------------------- \|c
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R -
+--R 15 6 +-+
+--R 9223372036854775808a c \|2
+--R *
+--R +-----------------------------+7
+--R | 1 +-+
+--R |- --------------------------- \|x
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 13 5 | 1
+--R - 18014398509481984a c |- --------------------------- + x
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - 9log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 18\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 18atan(---------------------) - 18atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 18\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-----------------------------+
+--R 2 8+---+ | 1 8+-+7
+--R 9216a \|- a |- --------------------------- \|c
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R atan
+--R +-----------------------------+7
+--R 15 6 | 1
+--R 9223372036854775808a c |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R --------------------------------------------------------------------
+--R +-----------------------------+7
+--R +-+ +-+ 15 6 | 1
+--R \|2 \|x - 9223372036854775808a c |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 8+---+ | 1 8+-+7
+--R 9216a \|- a |- --------------------------- \|c
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R *
+--R atan
+--R +-----------------------------+7
+--R 15 6 | 1
+--R 9223372036854775808a c |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R --------------------------------------------------------------------
+--R +-----------------------------+7
+--R +-+ +-+ 15 6 | 1
+--R \|2 \|x + 9223372036854775808a c |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R /
+--R 2 +-+8+---+8+-+7
+--R 512a \|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 13 7 9 14 6 5
+--R - 486388759756013568a c x + 2188749418902061056a c x
+--R +
+--R 15 5
+--R - 243194379878006784a c x
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R 9 5 8 10 4 4 11 3
+--R (3865470566400a c x - 7112465842176a c x + 154618822656a c )
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 5 3 7 6 2 3 | 1
+--R (- 24772608a c x + 17694720a c x ) |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R 2 10 6 2 2
+--R - 9c x + 117a c x - 36a x
+--R /
+--R 15 8 10 16 7 6
+--R 18446744073709551616a c x - 4611686018427387904a c x
+--R +
+--R 17 6 2
+--R - 23058430092136939520a c x
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R 11 6 9 12 5 5
+--R - 114349209288704a c x - 70368744177664a c x
+--R +
+--R 13 4
+--R 43980465111040a c x
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R 7 4 8 8 3 4 9 2
+--R (570425344a c x + 536870912a c x - 33554432a c )
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 17 7
+--R \| 4722366482869645213696a c
+--R +
+--R 2 3 11 3 2 7 4 3
+--R 512a c x - 1280a c x - 1792a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 727
+
+)clear all
+
+--S 728 of 1347
+t0:=x^(3/2)/(a+c*x^4)^3
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 1347
+r0:=1/8*x^(5/2)/(a*(a+c*x^4)^2)+11/64*x^(5/2)/(a^2*(a+c*x^4))-_
+ 33/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*c^(5/8))-_
+ 33/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*c^(5/8))-_
+ 33/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*_
+ c^(5/8)*sqrt(2))+33/256*atan(1+c^(1/8)*sqrt(2)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*c^(5/8)*sqrt(2))-_
+ 33/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(19/8)*c^(5/8)*sqrt(2))+_
+ 33/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(19/8)*c^(5/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (33c x + 66a c x + 33a )log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 33c x - 66a c x - 33a )log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 66c x - 132a c x - 66a )\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x + \|- a
+--R (66c x + 132a c x + 66a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x - \|- a
+--R (66c x + 132a c x + 66a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 66c x - 132a c x - 66a )\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R 6 2 +-+8+---+3 8+-+5 +-+
+--R (88c x + 152a x )\|2 \|- a \|c \|x
+--R /
+--R 2 2 8 3 4 4 +-+8+---+3 8+-+5
+--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 729
+
+--S 730 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (2112a c x + 4224a c x + 2112a ) |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+5
+--R 12 3 +-+ | 1 +-+
+--R 35184372088832a c \|2 |- --------------------------- \|x
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 5 | 1
+--R - 262144a c |- --------------------------- + x
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R 2 2 8 3 4 4 +-+
+--R (- 2112a c x - 4224a c x - 2112a )\|2
+--R *
+--R +-----------------------------+
+--R | 1
+--R |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+5
+--R +-+ 12 3 | 1
+--R log(\|x + 35184372088832a c |- --------------------------- )
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 +-+ | 1
+--R (2112a c x + 4224a c x + 2112a )\|2 |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+5
+--R +-+ 12 3 | 1
+--R log(\|x - 35184372088832a c |- --------------------------- )
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 2112a c x - 4224a c x - 2112a ) |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+5
+--R 12 3 +-+ | 1 +-+
+--R - 35184372088832a c \|2 |- --------------------------- \|x
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 5 | 1
+--R - 262144a c |- --------------------------- + x
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 4224a c x - 8448a c x - 4224a ) |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+5
+--R 12 3 | 1
+--R 35184372088832a c |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------------)
+--R +-----------------------------+5
+--R +-+ +-+ 12 3 | 1
+--R \|2 \|x - 35184372088832a c |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 4224a c x - 8448a c x - 4224a ) |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+5
+--R 12 3 | 1
+--R 35184372088832a c |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------------)
+--R +-----------------------------+5
+--R +-+ +-+ 12 3 | 1
+--R \|2 \|x + 35184372088832a c |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R 6 2 +-+ +-+
+--R (11c x + 19a x )\|2 \|x
+--R /
+--R 2 2 8 3 4 4 +-+
+--R (64a c x + 128a c x + 64a )\|2
+--R Type: Union(Expression(Integer),...)
+--E 730
+
+--S 731 of 1347 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 33log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-----------------------------+
+--R 2 8+---+3 | 1 8+-+5
+--R 16896a \|- a |- --------------------------- \|c
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+5
+--R 12 3 +-+ | 1 +-+
+--R 35184372088832a c \|2 |- --------------------------- \|x
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 5 | 1
+--R - 262144a c |- --------------------------- + x
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 +-+8+---+3 | 1 8+-+5
+--R 16896a \|2 \|- a |- --------------------------- \|c
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+5
+--R +-+ 12 3 | 1
+--R log(\|x + 35184372088832a c |- --------------------------- )
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 +-+8+---+3 | 1 8+-+5
+--R 16896a \|2 \|- a |- --------------------------- \|c
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+5
+--R +-+ 12 3 | 1
+--R log(\|x - 35184372088832a c |- --------------------------- )
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 8+---+3 | 1 8+-+5
+--R 16896a \|- a |- --------------------------- \|c
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+5
+--R 12 3 +-+ | 1 +-+
+--R - 35184372088832a c \|2 |- --------------------------- \|x
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+2
+--R 5 | 1
+--R - 262144a c |- --------------------------- + x
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R 33log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 66\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R - 66atan(---------------------) - 66atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 66\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R -
+--R +-----------------------------+
+--R 2 8+---+3 | 1 8+-+5
+--R 33792a \|- a |- --------------------------- \|c
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+5
+--R 12 3 | 1
+--R 35184372088832a c |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------------)
+--R +-----------------------------+5
+--R +-+ +-+ 12 3 | 1
+--R \|2 \|x - 35184372088832a c |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 8+---+3 | 1 8+-+5
+--R 33792a \|- a |- --------------------------- \|c
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+5
+--R 12 3 | 1
+--R 35184372088832a c |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------------)
+--R +-----------------------------+5
+--R +-+ +-+ 12 3 | 1
+--R \|2 \|x + 35184372088832a c |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R /
+--R 2 +-+8+---+3 8+-+5
+--R 512a \|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 14 6 10 15 5 6
+--R 1188950301625810944a c x - 15456353921135542272a c x
+--R +
+--R 16 4 2
+--R 4755801206503243776a c x
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R 10 4 7 11 3 3
+--R (- 47622597378048a c x + 34016140984320a c x )
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R 5 3 8 6 2 4 7
+--R (- 108134400a c x + 198967296a c x - 4325376a c)
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R 2 9 5 2
+--R - 198c x + 891a c x - 99a x
+--R /
+--R 17 6 8 18 5 4
+--R 78398662313265594368a c x + 73786976294838206464a c x
+--R +
+--R 19 4
+--R - 4611686018427387904a c
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R 12 5 9 13 4 5
+--R 228698418577408a c x + 140737488355328a c x
+--R +
+--R 14 3
+--R - 87960930222080a c x
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R 7 4 10 8 3 6 9 2 2
+--R (536870912a c x - 134217728a c x - 671088640a c x )
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 19 5
+--R \| 4722366482869645213696a c
+--R +
+--R 2 3 11 3 2 7 4 3
+--R 1024a c x - 2560a c x - 3584a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 732
+
+)clear all
+
+--S 733 of 1347
+t0:=sqrt(x)/(a+c*x^4)^3
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ------------------------------
+--R 3 12 2 8 2 4 3
+--R c x + 3a c x + 3a c x + a
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 1347
+r0:=1/8*x^(3/2)/(a*(a+c*x^4)^2)+13/64*x^(3/2)/(a^2*(a+c*x^4))+_
+ 65/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*c^(3/8))-_
+ 65/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*c^(3/8))+_
+ 65/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*_
+ c^(3/8)*sqrt(2))-65/256*atan(1+c^(1/8)*sqrt(2)*_
+ sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*c^(3/8)*sqrt(2))-_
+ 65/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_
+ sqrt(2)*sqrt(x))/((-a)^(21/8)*c^(3/8)*sqrt(2))+65/512*_
+ log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_
+ sqrt(x))/((-a)^(21/8)*c^(3/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (65c x + 130a c x + 65a )log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 65c x - 130a c x - 65a )log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 130c x - 260a c x - 130a )\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x + \|- a
+--R (- 130c x - 260a c x - 130a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x - \|- a
+--R (- 130c x - 260a c x - 130a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (130c x + 260a c x + 130a )\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R 5 +-+8+---+5 8+-+3 +-+
+--R (104c x + 168a x)\|2 \|- a \|c \|x
+--R /
+--R 2 2 8 3 4 4 +-+8+---+5 8+-+3
+--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 734
+
+--S 735 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (4160a c x + 8320a c x + 4160a ) |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+3
+--R 8 +-+ | 1 +-+
+--R 134217728a c\|2 |- --------------------------- \|x
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 16 2 | 1
+--R 18014398509481984a c |- --------------------------- + x
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R 2 2 8 3 4 4 +-+
+--R (- 4160a c x - 8320a c x - 4160a )\|2
+--R *
+--R +-----------------------------+
+--R | 1
+--R |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+3
+--R +-+ 8 | 1
+--R log(\|x + 134217728a c |- --------------------------- )
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 +-+ | 1
+--R (4160a c x + 8320a c x + 4160a )\|2 |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+3
+--R +-+ 8 | 1
+--R log(\|x - 134217728a c |- --------------------------- )
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 4160a c x - 8320a c x - 4160a ) |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+3
+--R 8 +-+ | 1 +-+
+--R - 134217728a c\|2 |- --------------------------- \|x
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 16 2 | 1
+--R 18014398509481984a c |- --------------------------- + x
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (8320a c x + 16640a c x + 8320a ) |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+3
+--R 8 | 1
+--R 134217728a c |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------)
+--R +-----------------------------+3
+--R +-+ +-+ 8 | 1
+--R \|2 \|x - 134217728a c |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (8320a c x + 16640a c x + 8320a ) |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+3
+--R 8 | 1
+--R 134217728a c |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------)
+--R +-----------------------------+3
+--R +-+ +-+ 8 | 1
+--R \|2 \|x + 134217728a c |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R 5 +-+ +-+
+--R (13c x + 21a x)\|2 \|x
+--R /
+--R 2 2 8 3 4 4 +-+
+--R (64a c x + 128a c x + 64a )\|2
+--R Type: Union(Expression(Integer),...)
+--E 735
+
+--S 736 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R - 65log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +-----------------------------+
+--R 2 8+---+5 | 1 8+-+3
+--R 33280a \|- a |- --------------------------- \|c
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+3
+--R 8 +-+ | 1 +-+
+--R 134217728a c\|2 |- --------------------------- \|x
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 16 2 | 1
+--R 18014398509481984a c |- --------------------------- + x
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 +-+8+---+5 | 1 8+-+3
+--R 33280a \|2 \|- a |- --------------------------- \|c
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+3
+--R +-+ 8 | 1
+--R log(\|x + 134217728a c |- --------------------------- )
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 +-+8+---+5 | 1 8+-+3
+--R 33280a \|2 \|- a |- --------------------------- \|c
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+3
+--R +-+ 8 | 1
+--R log(\|x - 134217728a c |- --------------------------- )
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +-----------------------------+
+--R 2 8+---+5 | 1 8+-+3
+--R 33280a \|- a |- --------------------------- \|c
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +-----------------------------+3
+--R 8 +-+ | 1 +-+
+--R - 134217728a c\|2 |- --------------------------- \|x
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+6
+--R 16 2 | 1
+--R 18014398509481984a c |- --------------------------- + x
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R 65log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 130\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 130atan(---------------------) + 130atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R - 130\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-----------------------------+
+--R 2 8+---+5 | 1 8+-+3
+--R 66560a \|- a |- --------------------------- \|c
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+3
+--R 8 | 1
+--R 134217728a c |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------)
+--R +-----------------------------+3
+--R +-+ +-+ 8 | 1
+--R \|2 \|x - 134217728a c |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R +-----------------------------+
+--R 2 8+---+5 | 1 8+-+3
+--R 66560a \|- a |- --------------------------- \|c
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R *
+--R +-----------------------------+3
+--R 8 | 1
+--R 134217728a c |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R atan(---------------------------------------------------------)
+--R +-----------------------------+3
+--R +-+ +-+ 8 | 1
+--R \|2 \|x + 134217728a c |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R /
+--R 2 +-+8+---+5 8+-+3
+--R 512a \|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 736
+
+--S 737 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 16 4 7 17 3 3
+--R (- 49179307930885816320a c x + 35128077093489868800a c x )
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R 10 4 10 11 3 6
+--R 17867063951360a c x - 232271831367680a c x
+--R +
+--R 12 2 2
+--R 71468255805440a c x
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R 5 3 9 6 2 5 7
+--R (204472320a c x - 920125440a c x + 102236160a c x)
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R 2 8 4 2
+--R 1625c x - 2990a c x + 65a
+--R /
+--R 18 5 10 19 4 6
+--R 73786976294838206464a c x - 18446744073709551616a c x
+--R +
+--R 20 3 2
+--R - 92233720368547758080a c x
+--R *
+--R +-----------------------------+6
+--R | 1
+--R |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R 13 4 9 14 3 5
+--R 457396837154816a c x + 281474976710656a c x
+--R +
+--R 15 2
+--R - 175921860444160a c x
+--R *
+--R +-----------------------------+4
+--R | 1
+--R |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R 8 3 8 9 2 4 10
+--R (2281701376a c x + 2147483648a c x - 134217728a c)
+--R *
+--R +-----------------------------+2
+--R | 1
+--R |- ---------------------------
+--R 8| 21 3
+--R \| 4722366482869645213696a c
+--R +
+--R 2 3 11 3 2 7 4 3
+--R - 2048a c x + 5120a c x + 7168a c x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 737
+
+)clear all
+
+--S 738 of 1347
+t0:=1/((a+c*x^4)^3*sqrt(x))
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R 3 12 2 8 2 4 3 +-+
+--R (c x + 3a c x + 3a c x + a )\|x
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 1347
+r0:=-105/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(23/8)*c^(1/8))-_
+ 105/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(23/8)*c^(1/8))+_
+ 105/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(23/8)*_
+ c^(1/8)*sqrt(2))-105/256*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_
+ (-a)^(1/8))/((-a)^(23/8)*c^(1/8)*sqrt(2))+105/512*log((-a)^(1/4)+_
+ c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(23/8)*_
+ c^(1/8)*sqrt(2))-105/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_
+ c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(23/8)*c^(1/8)*sqrt(2))+_
+ 1/8*sqrt(x)/(a*(a+c*x^4)^2)+15/64*sqrt(x)/(a^2*(a+c*x^4))
+--R
+--R
+--R (2)
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (- 105c x - 210a c x - 105a )log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R (105c x + 210a c x + 105a )log(- \|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 210c x - 420a c x - 210a )\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x + \|- a
+--R (- 210c x - 420a c x - 210a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+
+--R 2 8 4 2 \|2 \|c \|x - \|- a
+--R (- 210c x - 420a c x - 210a )atan(---------------------)
+--R 8+---+
+--R \|- a
+--R +
+--R 8+-+ +-+
+--R 2 8 4 2 +-+ \|c \|x
+--R (- 210c x - 420a c x - 210a )\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R 4 +-+8+---+7 8+-+ +-+
+--R (120c x + 184a)\|2 \|- a \|c \|x
+--R /
+--R 2 2 8 3 4 4 +-+8+---+7 8+-+
+--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 739
+
+--S 740 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (6720a c x + 13440a c x + 6720a ) |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +----------------------------+
+--R 3 +-+ | 1 +-+
+--R 512a \|2 |- -------------------------- \|x
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R +----------------------------+2
+--R 6 | 1
+--R 262144a |- -------------------------- + x
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R +----------------------------+
+--R 2 2 8 3 4 4 +-+ | 1
+--R (6720a c x + 13440a c x + 6720a )\|2 |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R +----------------------------+
+--R +-+ 3 | 1
+--R log(\|x + 512a |- --------------------------)
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R 2 2 8 3 4 4 +-+
+--R (- 6720a c x - 13440a c x - 6720a )\|2
+--R *
+--R +----------------------------+
+--R | 1
+--R |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R +----------------------------+
+--R +-+ 3 | 1
+--R log(\|x - 512a |- --------------------------)
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R +----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 6720a c x - 13440a c x - 6720a ) |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +----------------------------+
+--R 3 +-+ | 1 +-+
+--R - 512a \|2 |- -------------------------- \|x
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R +----------------------------+2
+--R 6 | 1
+--R 262144a |- -------------------------- + x
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R +----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 13440a c x - 26880a c x - 13440a ) |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R +----------------------------+
+--R 3 | 1
+--R 512a |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R atan(-----------------------------------------------)
+--R +----------------------------+
+--R +-+ +-+ 3 | 1
+--R \|2 \|x - 512a |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R +----------------------------+
+--R 2 2 8 3 4 4 | 1
+--R (- 13440a c x - 26880a c x - 13440a ) |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R +----------------------------+
+--R 3 | 1
+--R 512a |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R atan(-----------------------------------------------)
+--R +----------------------------+
+--R +-+ +-+ 3 | 1
+--R \|2 \|x + 512a |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R 4 +-+ +-+
+--R (15c x + 23a)\|2 \|x
+--R /
+--R 2 2 8 3 4 4 +-+
+--R (64a c x + 128a c x + 64a )\|2
+--R Type: Union(Expression(Integer),...)
+--E 740
+
+--S 741 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+
+--R 105log(\|2 \|- a \|c \|x + x\|c + \|- a )
+--R +
+--R +----------------------------+
+--R 2 8+---+7 | 1 8+-+
+--R 53760a \|- a |- -------------------------- \|c
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +----------------------------+
+--R 3 +-+ | 1 +-+
+--R 512a \|2 |- -------------------------- \|x
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R +----------------------------+2
+--R 6 | 1
+--R 262144a |- -------------------------- + x
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R +----------------------------+
+--R 2 +-+8+---+7 | 1 8+-+
+--R 53760a \|2 \|- a |- -------------------------- \|c
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R +----------------------------+
+--R +-+ 3 | 1
+--R log(\|x + 512a |- --------------------------)
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +----------------------------+
+--R 2 +-+8+---+7 | 1 8+-+
+--R 53760a \|2 \|- a |- -------------------------- \|c
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R +----------------------------+
+--R +-+ 3 | 1
+--R log(\|x - 512a |- --------------------------)
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +----------------------------+
+--R 2 8+---+7 | 1 8+-+
+--R 53760a \|- a |- -------------------------- \|c
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R log
+--R +----------------------------+
+--R 3 +-+ | 1 +-+
+--R - 512a \|2 |- -------------------------- \|x
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R +----------------------------+2
+--R 6 | 1
+--R 262144a |- -------------------------- + x
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R 8+-+ +-+
+--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x
+--R - 105log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 210\|2 atanh(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+
+--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a
+--R 210atan(---------------------) + 210atan(---------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+ +-+
+--R +-+ \|c \|x
+--R 210\|2 atan(--------)
+--R 8+---+
+--R \|- a
+--R +
+--R -
+--R +----------------------------+
+--R 2 8+---+7 | 1 8+-+
+--R 107520a \|- a |- -------------------------- \|c
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R +----------------------------+
+--R 3 | 1
+--R 512a |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R atan(-----------------------------------------------)
+--R +----------------------------+
+--R +-+ +-+ 3 | 1
+--R \|2 \|x - 512a |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R -
+--R +----------------------------+
+--R 2 8+---+7 | 1 8+-+
+--R 107520a \|- a |- -------------------------- \|c
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R *
+--R +----------------------------+
+--R 3 | 1
+--R 512a |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R atan(-----------------------------------------------)
+--R +----------------------------+
+--R +-+ +-+ 3 | 1
+--R \|2 \|x + 512a |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R /
+--R 2 +-+8+---+7 8+-+
+--R 512a \|2 \|- a \|c
+--R Type: Expression(Integer)
+--E 741
+
+--S 742 of 1347 sometimes Axiom computes a zero
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5)
+--R 17 2 8 18 4
+--R 23643898043695104000a c x - 43504772400398991360a c x
+--R +
+--R 19
+--R 945755921747804160a
+--R *
+--R +----------------------------+6
+--R | 1
+--R |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R 11 2 9 12 5 13
+--R (- 43293270343680a c x + 194819716546560a c x - 21646635171840a x)
+--R *
+--R +----------------------------+4
+--R | 1
+--R |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R 5 2 10 6 6 7 2
+--R (55050240a c x - 715653120a c x + 220200960a x )
+--R *
+--R +----------------------------+2
+--R | 1
+--R |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R 7 3
+--R 2205c x - 1575a x
+--R /
+--R 20 2 8 21 4
+--R 78398662313265594368a c x + 73786976294838206464a c x
+--R +
+--R 22
+--R - 4611686018427387904a
+--R *
+--R +----------------------------+6
+--R | 1
+--R |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R 14 2 9 15 5
+--R - 228698418577408a c x - 140737488355328a c x
+--R +
+--R 16
+--R 87960930222080a x
+--R *
+--R +----------------------------+4
+--R | 1
+--R |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R 8 2 10 9 6 10 2
+--R (536870912a c x - 134217728a c x - 671088640a x )
+--R *
+--R +----------------------------+2
+--R | 1
+--R |- --------------------------
+--R 8| 23
+--R \| 4722366482869645213696a c
+--R +
+--R 2 2 11 3 7 4 3
+--R - 1024a c x + 2560a c x + 3584a x
+--R *
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 742
+
+)clear all
+
+--S 743 of 1347
+t0:=x^7*(a+b*x^4)^p
+--R
+--R
+--R 7 4 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1347
+r0:=-1/4*a*(a+b*x^4)^(1+p)/(b^2*(1+p))+1/4*(a+b*x^4)^(2+p)/(b^2*(2+p))
+--R
+--R
+--R 4 p + 2 4 p + 1
+--R (p + 1)(b x + a) + (- a p - 2a)(b x + a)
+--R (2) ----------------------------------------------------
+--R 2 2 2 2
+--R 4b p + 12b p + 8b
+--R Type: Expression(Integer)
+--E 744
+
+--S 745 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R 2 2 8 4 2 p log(b x + a)
+--R ((b p + b )x + a b p x - a )%e
+--R (3) -----------------------------------------------
+--R 2 2 2 2
+--R 4b p + 12b p + 8b
+--R Type: Union(Expression(Integer),...)
+--E 745
+
+--S 746 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4
+--R 2 2 8 4 2 p log(b x + a)
+--R ((b p + b )x + a b p x - a )%e
+--R +
+--R 4 p + 2 4 p + 1
+--R (- p - 1)(b x + a) + (a p + 2a)(b x + a)
+--R /
+--R 2 2 2 2
+--R 4b p + 12b p + 8b
+--R Type: Expression(Integer)
+--E 746
+
+--S 747 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 747
+
+)clear all
+
+--S 748 of 1347
+t0:=x^3*(a+b*x^4)^p
+--R
+--R
+--R 3 4 p
+--R (1) x (b x + a)
+--R Type: Expression(Integer)
+--E 748
+
+--S 749 of 1347
+r0:=1/4*(a+b*x^4)^(1+p)/(b*(1+p))
+--R
+--R
+--R 4 p + 1
+--R (b x + a)
+--R (2) ---------------
+--R 4b p + 4b
+--R Type: Expression(Integer)
+--E 749
+
+--S 750 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R 4 p log(b x + a)
+--R (b x + a)%e
+--R (3) ---------------------------
+--R 4b p + 4b
+--R Type: Union(Expression(Integer),...)
+--E 750
+
+--S 751 of 1347
+m0:=a0-r0
+--R
+--R
+--R 4
+--R 4 p log(b x + a) 4 p + 1
+--R (b x + a)%e - (b x + a)
+--R (4) ---------------------------------------------
+--R 4b p + 4b
+--R Type: Expression(Integer)
+--E 751
+
+--S 752 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 752
+
+)clear all
+
+--S 753 of 1347
+t0:=(a+b*x^4)^p/x
+--R
+--R
+--R 4 p
+--R (b x + a)
+--R (1) -----------
+--R x
+--R Type: Expression(Integer)
+--E 753
+
+--S 754 of 1347
+--r0:=1/4*(a+b*x^4)^p*hypergeometric(-p,-p,1-p,-a/(b*x^4))/_
+-- (p*((a+b*x^4)/(b*x^4))^p)
+--E 754
+
+--S 755 of 1347
+--a0:=integrate(t0,x)
+--E 755
+
+--S 756 of 1347
+--m0:=a0-r0
+--E 756
+
+--S 757 of 1347
+--d0:=D(m0,x)
+--E 757
+
+)clear all
+
+--S 758 of 1347
+t0:=x^7*(1+x^4)^(1/3)
+--R
+--R
+--R +------+
+--R 7 3| 4
+--R (1) x \|x + 1
+--R Type: Expression(Integer)
+--E 758
+
+--S 759 of 1347
+r0:=-3/16*(1+x^4)^(4/3)+3/28*(1+x^4)^(7/3)
+--R
+--R
+--R +------+
+--R 8 4 3| 4
+--R (12x + 3x - 9)\|x + 1
+--R (2) -------------------------
+--R 112
+--R Type: Expression(Integer)
+--E 759
+
+--S 760 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R 8 4 3| 4
+--R (12x + 3x - 9)\|x + 1
+--R (3) -------------------------
+--R 112
+--R Type: Union(Expression(Integer),...)
+--E 760
+
+--S 761 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 761
+
+--S 762 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 762
+
+)clear all
+
+--S 763 of 1347
+t0:=x^3/(1+x^4)^(4/3)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------------
+--R +------+
+--R 4 3| 4
+--R (x + 1)\|x + 1
+--R Type: Expression(Integer)
+--E 763
+
+--S 764 of 1347
+r0:=(-3/4)/(1+x^4)^(1/3)
+--R
+--R
+--R 3
+--R (2) - ----------
+--R +------+
+--R 3| 4
+--R 4\|x + 1
+--R Type: Expression(Integer)
+--E 764
+
+--S 765 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R (3) - ----------
+--R +------+
+--R 3| 4
+--R 4\|x + 1
+--R Type: Union(Expression(Integer),...)
+--E 765
+
+--S 766 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 766
+
+--S 767 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 767
+
+)clear all
+
+--S 768 of 1347
+t0:=x^3/(1+x^4)^(1/3)
+--R
+--R
+--R 3
+--R x
+--R (1) ---------
+--R +------+
+--R 3| 4
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 768
+
+--S 769 of 1347
+r0:=3/8*(1+x^4)^(2/3)
+--R
+--R
+--R +------+2
+--R 3| 4
+--R 3\|x + 1
+--R (2) -----------
+--R 8
+--R Type: Expression(Integer)
+--E 769
+
+--S 770 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+2
+--R 3| 4
+--R 3\|x + 1
+--R (3) -----------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 770
+
+--S 771 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 771
+
+--S 772 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 772
+
+)clear all
+
+--S 773 of 1347
+t0:=x^3/(1+x^4)^(1/4)
+--R
+--R
+--R 3
+--R x
+--R (1) ---------
+--R +------+
+--R 4| 4
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 773
+
+--S 774 of 1347
+r0:=1/3*(1+x^4)^(3/4)
+--R
+--R
+--R +------+3
+--R 4| 4
+--R \|x + 1
+--R (2) ----------
+--R 3
+--R Type: Expression(Integer)
+--E 774
+
+--S 775 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+3
+--R 4| 4
+--R \|x + 1
+--R (3) ----------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 775
+
+--S 776 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 776
+
+--S 777 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 777
+
+)clear all
+
+--S 778 of 1347
+t0:=x^24/(a+b*x^5)
+--R
+--R
+--R 24
+--R x
+--R (1) --------
+--R 5
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 778
+
+--S 779 of 1347
+r0:=-1/5*a^3*x^5/b^4+1/10*a^2*x^10/b^3-1/15*a*x^15/b^2+1/20*x^20/b+_
+ 1/5*a^4*log(a+b*x^5)/b^5
+--R
+--R
+--R 4 5 4 20 3 15 2 2 10 3 5
+--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x
+--R (2) -----------------------------------------------------------
+--R 5
+--R 60b
+--R Type: Expression(Integer)
+--E 779
+
+--S 780 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 5 4 20 3 15 2 2 10 3 5
+--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x
+--R (3) -----------------------------------------------------------
+--R 5
+--R 60b
+--R Type: Union(Expression(Integer),...)
+--E 780
+
+--S 781 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 781
+
+--S 782 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 782
+
+)clear all
+
+--S 783 of 1347
+t0:=x^19/(a+b*x^5)
+--R
+--R
+--R 19
+--R x
+--R (1) --------
+--R 5
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 783
+
+--S 784 of 1347
+r0:=1/5*a^2*x^5/b^3-1/10*a*x^10/b^2+1/15*x^15/b-1/5*a^3*log(a+b*x^5)/b^4
+--R
+--R
+--R 3 5 3 15 2 10 2 5
+--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x
+--R (2) ------------------------------------------------
+--R 4
+--R 30b
+--R Type: Expression(Integer)
+--E 784
+
+--S 785 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 5 3 15 2 10 2 5
+--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x
+--R (3) ------------------------------------------------
+--R 4
+--R 30b
+--R Type: Union(Expression(Integer),...)
+--E 785
+
+--S 786 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 786
+
+--S 787 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 787
+
+)clear all
+
+--S 788 of 1347
+t0:=x^14/(a+b*x^5)
+--R
+--R
+--R 14
+--R x
+--R (1) --------
+--R 5
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 788
+
+--S 789 of 1347
+r0:=-1/5*a*x^5/b^2+1/10*x^10/b+1/5*a^2*log(a+b*x^5)/b^3
+--R
+--R
+--R 2 5 2 10 5
+--R 2a log(b x + a) + b x - 2a b x
+--R (2) ----------------------------------
+--R 3
+--R 10b
+--R Type: Expression(Integer)
+--E 789
+
+--S 790 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 5 2 10 5
+--R 2a log(b x + a) + b x - 2a b x
+--R (3) ----------------------------------
+--R 3
+--R 10b
+--R Type: Union(Expression(Integer),...)
+--E 790
+
+--S 791 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 791
+
+--S 792 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 792
+
+)clear all
+
+--S 793 of 1347
+t0:=x^9/(a+b*x^5)
+--R
+--R
+--R 9
+--R x
+--R (1) --------
+--R 5
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 793
+
+--S 794 of 1347
+r0:=1/5*x^5/b-1/5*a*log(a+b*x^5)/b^2
+--R
+--R
+--R 5 5
+--R - a log(b x + a) + b x
+--R (2) ------------------------
+--R 2
+--R 5b
+--R Type: Expression(Integer)
+--E 794
+
+--S 795 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5
+--R - a log(b x + a) + b x
+--R (3) ------------------------
+--R 2
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 795
+
+--S 796 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 796
+
+--S 797 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 797
+
+)clear all
+
+--S 798 of 1347
+t0:=x^4/(a+b*x^5)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 5
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 798
+
+--S 799 of 1347
+r0:=1/5*log(a+b*x^5)/b
+--R
+--R
+--R 5
+--R log(b x + a)
+--R (2) -------------
+--R 5b
+--R Type: Expression(Integer)
+--E 799
+
+--S 800 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5
+--R log(b x + a)
+--R (3) -------------
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 800
+
+--S 801 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 801
+
+--S 802 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 802
+
+)clear all
+
+--S 803 of 1347
+t0:=1/(x*(a+b*x^5))
+--R
+--R
+--R 1
+--R (1) ----------
+--R 6
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 803
+
+--S 804 of 1347
+r0:=log(x)/a-1/5*log(a+b*x^5)/a
+--R
+--R
+--R 5
+--R - log(b x + a) + 5log(x)
+--R (2) -------------------------
+--R 5a
+--R Type: Expression(Integer)
+--E 804
+
+--S 805 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5
+--R - log(b x + a) + 5log(x)
+--R (3) -------------------------
+--R 5a
+--R Type: Union(Expression(Integer),...)
+--E 805
+
+--S 806 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 806
+
+--S 807 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 807
+
+)clear all
+
+--S 808 of 1347
+t0:=1/(x^6*(a+b*x^5))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 11 6
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 808
+
+--S 809 of 1347
+r0:=(-1/5)/(a*x^5)-b*log(x)/a^2+1/5*b*log(a+b*x^5)/a^2
+--R
+--R
+--R 5 5 5
+--R b x log(b x + a) - 5b x log(x) - a
+--R (2) -----------------------------------
+--R 2 5
+--R 5a x
+--R Type: Expression(Integer)
+--E 809
+
+--S 810 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5 5
+--R b x log(b x + a) - 5b x log(x) - a
+--R (3) -----------------------------------
+--R 2 5
+--R 5a x
+--R Type: Union(Expression(Integer),...)
+--E 810
+
+--S 811 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 811
+
+--S 812 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 812
+
+)clear all
+
+--S 813 of 1347
+t0:=1/(x^11*(a+b*x^5))
+--R
+--R
+--R 1
+--R (1) -------------
+--R 16 11
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 813
+
+--S 814 of 1347
+r0:=(-1/10)/(a*x^10)+1/5*b/(a^2*x^5)+b^2*log(x)/a^3-1/5*b^2*log(a+b*x^5)/a^3
+--R
+--R
+--R 2 10 5 2 10 5 2
+--R - 2b x log(b x + a) + 10b x log(x) + 2a b x - a
+--R (2) ----------------------------------------------------
+--R 3 10
+--R 10a x
+--R Type: Expression(Integer)
+--E 814
+
+--S 815 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 10 5 2 10 5 2
+--R - 2b x log(b x + a) + 10b x log(x) + 2a b x - a
+--R (3) ----------------------------------------------------
+--R 3 10
+--R 10a x
+--R Type: Union(Expression(Integer),...)
+--E 815
+
+--S 816 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 816
+
+--S 817 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 817
+
+)clear all
+
+--S 818 of 1347
+t0:=x^24/(a+b*x^5)^2
+--R
+--R
+--R 24
+--R x
+--R (1) --------------------
+--R 2 10 5 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 818
+
+--S 819 of 1347
+r0:=3/5*a^2*x^5/b^4-1/5*a*x^10/b^3+1/15*x^15/b^2-_
+ 1/5*a^4/(b^5*(a+b*x^5))-4/5*a^3*log(a+b*x^5)/b^5
+--R
+--R
+--R (2)
+--R 3 5 4 5 4 20 3 15 2 2 10 3 5
+--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x
+--R +
+--R 4
+--R - 3a
+--R /
+--R 6 5 5
+--R 15b x + 15a b
+--R Type: Expression(Integer)
+--E 819
+
+--S 820 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 5 4 5 4 20 3 15 2 2 10 3 5
+--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x
+--R +
+--R 4
+--R - 3a
+--R /
+--R 6 5 5
+--R 15b x + 15a b
+--R Type: Union(Expression(Integer),...)
+--E 820
+
+--S 821 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 821
+
+--S 822 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 822
+
+)clear all
+
+--S 823 of 1347
+t0:=x^19/(a+b*x^5)^2
+--R
+--R
+--R 19
+--R x
+--R (1) --------------------
+--R 2 10 5 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 823
+
+--S 824 of 1347
+r0:=-2/5*a*x^5/b^3+1/10*x^10/b^2+1/5*a^3/(b^4*(a+b*x^5))+_
+ 3/5*a^2*log(a+b*x^5)/b^4
+--R
+--R
+--R 2 5 3 5 3 15 2 10 2 5 3
+--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a
+--R (2) ---------------------------------------------------------------
+--R 5 5 4
+--R 10b x + 10a b
+--R Type: Expression(Integer)
+--E 824
+
+--S 825 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 5 3 5 3 15 2 10 2 5 3
+--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a
+--R (3) ---------------------------------------------------------------
+--R 5 5 4
+--R 10b x + 10a b
+--R Type: Union(Expression(Integer),...)
+--E 825
+
+--S 826 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 826
+
+--S 827 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 827
+
+)clear all
+
+--S 828 of 1347
+t0:=x^14/(a+b*x^5)^2
+--R
+--R
+--R 14
+--R x
+--R (1) --------------------
+--R 2 10 5 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 828
+
+--S 829 of 1347
+r0:=1/5*x^5/b^2-1/5*a^2/(b^3*(a+b*x^5))-2/5*a*log(a+b*x^5)/b^3
+--R
+--R
+--R 5 2 5 2 10 5 2
+--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a
+--R (2) ----------------------------------------------------
+--R 4 5 3
+--R 5b x + 5a b
+--R Type: Expression(Integer)
+--E 829
+
+--S 830 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 2 5 2 10 5 2
+--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a
+--R (3) ----------------------------------------------------
+--R 4 5 3
+--R 5b x + 5a b
+--R Type: Union(Expression(Integer),...)
+--E 830
+
+--S 831 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 831
+
+--S 832 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 832
+
+)clear all
+
+--S 833 of 1347
+t0:=x^9/(a+b*x^5)^2
+--R
+--R
+--R 9
+--R x
+--R (1) --------------------
+--R 2 10 5 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 833
+
+--S 834 of 1347
+r0:=1/5*a/(b^2*(a+b*x^5))+1/5*log(a+b*x^5)/b^2
+--R
+--R
+--R 5 5
+--R (b x + a)log(b x + a) + a
+--R (2) ---------------------------
+--R 3 5 2
+--R 5b x + 5a b
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5
+--R (b x + a)log(b x + a) + a
+--R (3) ---------------------------
+--R 3 5 2
+--R 5b x + 5a b
+--R Type: Union(Expression(Integer),...)
+--E 835
+
+--S 836 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 836
+
+--S 837 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 837
+
+)clear all
+
+--S 838 of 1347
+t0:=x^4/(a+b*x^5)^2
+--R
+--R
+--R 4
+--R x
+--R (1) --------------------
+--R 2 10 5 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 838
+
+--S 839 of 1347
+r0:=(-1/5)/(b*(a+b*x^5))
+--R
+--R
+--R 1
+--R -
+--R 5
+--R (2) - ----------
+--R 2 5
+--R b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 839
+
+--S 840 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ------------
+--R 2 5
+--R 5b x + 5a b
+--R Type: Union(Expression(Integer),...)
+--E 840
+
+--S 841 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 842
+
+)clear all
+
+--S 843 of 1347
+t0:=1/(x*(a+b*x^5)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 11 6 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 843
+
+--S 844 of 1347
+r0:=1/5/(a*(a+b*x^5))+log(x)/a^2-1/5*log(a+b*x^5)/a^2
+--R
+--R
+--R 5 5 5
+--R (- b x - a)log(b x + a) + (5b x + 5a)log(x) + a
+--R (2) --------------------------------------------------
+--R 2 5 3
+--R 5a b x + 5a
+--R Type: Expression(Integer)
+--E 844
+
+--S 845 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5 5
+--R (- b x - a)log(b x + a) + (5b x + 5a)log(x) + a
+--R (3) --------------------------------------------------
+--R 2 5 3
+--R 5a b x + 5a
+--R Type: Union(Expression(Integer),...)
+--E 845
+
+--S 846 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 847
+
+)clear all
+
+--S 848 of 1347
+t0:=1/(x^6*(a+b*x^5)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 2 16 11 2 6
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 848
+
+--S 849 of 1347
+r0:=(-2/5)/(a^2*x^5)+1/5/(a*x^5*(a+b*x^5))-_
+ 2*b*log(x)/a^3+2/5*b*log(a+b*x^5)/a^3
+--R
+--R
+--R (2)
+--R 2 10 5 5 2 10 5 5 2
+--R (2b x + 2a b x )log(b x + a) + (- 10b x - 10a b x )log(x) - 2a b x - a
+--R -----------------------------------------------------------------------------
+--R 3 10 4 5
+--R 5a b x + 5a x
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 10 5 5 2 10 5 5 2
+--R (2b x + 2a b x )log(b x + a) + (- 10b x - 10a b x )log(x) - 2a b x - a
+--R -----------------------------------------------------------------------------
+--R 3 10 4 5
+--R 5a b x + 5a x
+--R Type: Union(Expression(Integer),...)
+--E 850
+
+--S 851 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 851
+
+--S 852 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 852
+
+)clear all
+
+--S 853 of 1347
+t0:=1/(x^11*(a+b*x^5)^2)
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R 2 21 16 2 11
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 853
+
+--S 854 of 1347
+r0:=(-3/10)/(a^2*x^10)+3/5*b/(a^3*x^5)+1/5/(a*x^10*(a+b*x^5))+_
+ 3*b^2*log(x)/a^4-3/5*b^2*log(a+b*x^5)/a^4
+--R
+--R
+--R (2)
+--R 3 15 2 10 5 3 15 2 10
+--R (- 6b x - 6a b x )log(b x + a) + (30b x + 30a b x )log(x)
+--R +
+--R 2 10 2 5 3
+--R 6a b x + 3a b x - a
+--R /
+--R 4 15 5 10
+--R 10a b x + 10a x
+--R Type: Expression(Integer)
+--E 854
+
+--S 855 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 15 2 10 5 3 15 2 10
+--R (- 6b x - 6a b x )log(b x + a) + (30b x + 30a b x )log(x)
+--R +
+--R 2 10 2 5 3
+--R 6a b x + 3a b x - a
+--R /
+--R 4 15 5 10
+--R 10a b x + 10a x
+--R Type: Union(Expression(Integer),...)
+--E 855
+
+--S 856 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 856
+
+--S 857 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 857
+
+)clear all
+
+--S 858 of 1347
+t0:=x^9/(2*b+b*x^5)
+--R
+--R
+--R 9
+--R x
+--R (1) ---------
+--R 5
+--R b x + 2b
+--R Type: Fraction(Polynomial(Integer))
+--E 858
+
+--S 859 of 1347
+r0:=1/5*x^5/b-2/5*log(2+x^5)/b
+--R
+--R
+--R 5 5
+--R - 2log(x + 2) + x
+--R (2) -------------------
+--R 5b
+--R Type: Expression(Integer)
+--E 859
+
+--S 860 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5
+--R - 2log(x + 2) + x
+--R (3) -------------------
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 860
+
+--S 861 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 861
+
+--S 862 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 862
+
+)clear all
+
+--S 863 of 1347
+t0:=x^4/(2*b+b*x^5)
+--R
+--R
+--R 4
+--R x
+--R (1) ---------
+--R 5
+--R b x + 2b
+--R Type: Fraction(Polynomial(Integer))
+--E 863
+
+--S 864 of 1347
+r0:=1/5*log(2+x^5)/b
+--R
+--R
+--R 5
+--R log(x + 2)
+--R (2) -----------
+--R 5b
+--R Type: Expression(Integer)
+--E 864
+
+--S 865 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5
+--R log(x + 2)
+--R (3) -----------
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 865
+
+--S 866 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 866
+
+--S 867 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 867
+
+)clear all
+
+--S 868 of 1347
+t0:=1/(x*(2*b+b*x^5))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 6
+--R b x + 2b x
+--R Type: Fraction(Polynomial(Integer))
+--E 868
+
+--S 869 of 1347
+r0:=-1/5*atanh(1+x^5)/b
+--R
+--R
+--R 5
+--R atanh(x + 1)
+--R (2) - -------------
+--R 5b
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5
+--R - log(x + 2) + 5log(x)
+--R (3) -----------------------
+--R 10b
+--R Type: Union(Expression(Integer),...)
+--E 870
+
+--S 871 of 1347
+m0:=a0-r0
+--R
+--R
+--R 5 5
+--R - log(x + 2) + 5log(x) + 2atanh(x + 1)
+--R (4) ----------------------------------------
+--R 10b
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 872
+
+)clear all
+
+--S 873 of 1347
+t0:=1/(x^6*(2*b+b*x^5))
+--R
+--R
+--R 1
+--R (1) -------------
+--R 11 6
+--R b x + 2b x
+--R Type: Fraction(Polynomial(Integer))
+--E 873
+
+--S 874 of 1347
+r0:=(-1/10)/(b*x^5)+1/10*atanh(1+x^5)/b
+--R
+--R
+--R 5 5
+--R x atanh(x + 1) - 1
+--R (2) -------------------
+--R 5
+--R 10b x
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5 5
+--R x log(x + 2) - 5x log(x) - 2
+--R (3) -----------------------------
+--R 5
+--R 20b x
+--R Type: Union(Expression(Integer),...)
+--E 875
+
+--S 876 of 1347
+m0:=a0-r0
+--R
+--R
+--R 5 5
+--R log(x + 2) - 5log(x) - 2atanh(x + 1)
+--R (4) --------------------------------------
+--R 20b
+--R Type: Expression(Integer)
+--E 876
+
+--S 877 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 877
+
+)clear all
+
+--S 878 of 1347
+t0:=x^9/(3+b*x^5)
+--R
+--R
+--R 9
+--R x
+--R (1) --------
+--R 5
+--R b x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 878
+
+--S 879 of 1347
+r0:=1/5*x^5/b-3/5*log(3+b*x^5)/b^2
+--R
+--R
+--R 5 5
+--R - 3log(b x + 3) + b x
+--R (2) -----------------------
+--R 2
+--R 5b
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5
+--R - 3log(b x + 3) + b x
+--R (3) -----------------------
+--R 2
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 880
+
+--S 881 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 882
+
+)clear all
+
+--S 883 of 1347
+t0:=x^4/(3+b*x^5)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 5
+--R b x + 3
+--R Type: Fraction(Polynomial(Integer))
+--E 883
+
+--S 884 of 1347
+r0:=1/5*log(3+b*x^5)/b
+--R
+--R
+--R 5
+--R log(b x + 3)
+--R (2) -------------
+--R 5b
+--R Type: Expression(Integer)
+--E 884
+
+--S 885 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5
+--R log(b x + 3)
+--R (3) -------------
+--R 5b
+--R Type: Union(Expression(Integer),...)
+--E 885
+
+--S 886 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 886
+
+--S 887 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 887
+
+)clear all
+
+--S 888 of 1347
+t0:=1/(x*(3+b*x^5))
+--R
+--R
+--R 1
+--R (1) ---------
+--R 6
+--R b x + 3x
+--R Type: Fraction(Polynomial(Integer))
+--E 888
+
+--S 889 of 1347
+r0:=-2/15*atanh(1+2/3*b*x^5)
+--R
+--R
+--R 5
+--R 2b x + 3
+--R 2atanh(---------)
+--R 3
+--R (2) - -----------------
+--R 15
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5
+--R - log(b x + 3) + 5log(x)
+--R (3) -------------------------
+--R 15
+--R Type: Union(Expression(Integer),...)
+--E 890
+
+--S 891 of 1347
+m0:=a0-r0
+--R
+--R
+--R 5
+--R 5 2b x + 3
+--R - log(b x + 3) + 5log(x) + 2atanh(---------)
+--R 3
+--R (4) ---------------------------------------------
+--R 15
+--R Type: Expression(Integer)
+--E 891
+
+--S 892 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 892
+
+)clear all
+
+--S 893 of 1347
+t0:=1/(x^6*(3+b*x^5))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 11 6
+--R b x + 3x
+--R Type: Fraction(Polynomial(Integer))
+--E 893
+
+--S 894 of 1347
+r0:=(-1/15)/x^5+2/45*b*atanh(1+2/3*b*x^5)
+--R
+--R
+--R 5
+--R 5 2b x + 3
+--R 2b x atanh(---------) - 3
+--R 3
+--R (2) -------------------------
+--R 5
+--R 45x
+--R Type: Expression(Integer)
+--E 894
+
+--S 895 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5 5
+--R b x log(b x + 3) - 5b x log(x) - 3
+--R (3) -----------------------------------
+--R 5
+--R 45x
+--R Type: Union(Expression(Integer),...)
+--E 895
+
+--S 896 of 1347
+m0:=a0-r0
+--R
+--R
+--R 5
+--R 5 2b x + 3
+--R b log(b x + 3) - 5b log(x) - 2b atanh(---------)
+--R 3
+--R (4) -------------------------------------------------
+--R 45
+--R Type: Expression(Integer)
+--E 896
+
+--S 897 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 897
+
+)clear all
+
+--S 898 of 1347
+t0:=x^5/(1+x^5)
+--R
+--R
+--R 5
+--R x
+--R (1) ------
+--R 5
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 898
+
+--S 899 of 1347
+r0:=x-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1-sqrt(5)))*_
+ (1-sqrt(5))+1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))+_
+ 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_
+ sqrt(1/2*(5-sqrt(5)))+1/5*atan((1-4*x-sqrt(5))/_
+ sqrt(2*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))
+--R
+--R
+--R (2)
+--R +----------+
+--R +--------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R 4\|\|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +----------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R 4\|- \|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2 +-+
+--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) - 4\|2 log(x + 1)
+--R +
+--R +-+ +-+ +-+ +-+ 2 +-+
+--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) + 20x\|2
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 899
+
+--S 900 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3
+--R +
+--I - 5%%ID1 - 5%%ID0 + 1
+--R *
+--R log
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3
+--R +
+--I 5%%ID1 + 5%%ID0 + 2x - 1
+--R +
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3
+--R +
+--I - 5%%ID1 - 5%%ID0 + 1
+--R *
+--R log
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3
+--R +
+--I 5%%ID1 + 5%%ID0 + 2x - 1
+--R +
+--I 10%%ID1 log(- 5%%ID1 + x) + 10%%ID0 log(- 5%%ID0 + x) - 2log(x + 1) + 10x
+--R /
+--R 10
+--R Type: Union(Expression(Integer),...)
+--E 900
+
+--S 901 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I - 2\|2 \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%ID1 - 10\|2 %%ID0 + 2\|2
+--R *
+--R log
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3
+--R +
+--I 5%%ID1 + 5%%ID0 + 2x - 1
+--R +
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I 2\|2 \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%ID1 - 10\|2 %%ID0 + 2\|2
+--R *
+--R log
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3
+--R +
+--I 5%%ID1 + 5%%ID0 + 2x - 1
+--R +
+--R +-+ +-+
+--I 20\|2 %%ID1 log(- 5%%ID1 + x) + 20\|2 %%ID0 log(- 5%%ID0 + x)
+--R +
+--R +----------+
+--R +--------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R - 4\|\|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +----------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R - 4\|- \|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 - \|2 )log(x\|5 + 2x - x + 2)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 901
+
+--S 902 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +----------+
+--R +-+ +-+ 2 +-+ | +-+ | +-+
+--R (- 5x\|2 \|5 + (10x - 5x + 10)\|2 )\|\|5 + 5 \|2\|5 + 10
+--R +
+--R +----------+
+--R 2 +-+ +-+ 2 +-+ +--+ | +-+
+--R ((- x + 3x - 1)\|2 \|5 + (5x - 5x + 5)\|2 )\|10 \|- \|5 + 5
+--R *
+--R +--------+
+--R | +-+
+--R \|\|5 + 5
+--R +
+--R 2
+--R - 200x + 200x - 200
+--R /
+--R 4 3 2
+--R 400x - 400x + 400x - 400x + 400
+--R Type: Expression(Integer)
+--E 902
+
+)clear all
+
+--S 903 of 1347
+t0:=x^4/(1+x^5)
+--R
+--R
+--R 4
+--R x
+--R (1) ------
+--R 5
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 903
+
+--S 904 of 1347
+r0:=1/5*log(1+x^5)
+--R
+--R
+--R 5
+--R log(x + 1)
+--R (2) -----------
+--R 5
+--R Type: Expression(Integer)
+--E 904
+
+--S 905 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5
+--R log(x + 1)
+--R (3) -----------
+--R 5
+--R Type: Union(Expression(Integer),...)
+--E 905
+
+--S 906 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 907
+
+)clear all
+
+--S 908 of 1347
+t0:=x^3/(1+x^5)
+--R
+--R
+--R 3
+--R x
+--R (1) ------
+--R 5
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 908
+
+--S 909 of 1347
+r0:=-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1-sqrt(5))+_
+ 1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))-_
+ 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_
+ sqrt(1/2*(5-sqrt(5)))-1/5*atan((1-4*x-sqrt(5))/sqrt(2*_
+ (5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))
+--R
+--R
+--R (2)
+--R +----------+
+--R +--------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R - 4\|\|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +----------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R - 4\|- \|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2 +-+
+--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) - 4\|2 log(x + 1)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 909
+
+--S 910 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3
+--R +
+--I - 5%%IE1 - 5%%IE0 + 1
+--R *
+--R log
+--I 25%%IE0 %%IE1
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3
+--R +
+--R 2 2
+--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x
+--R +
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3
+--R +
+--I - 5%%IE1 - 5%%IE0 + 1
+--R *
+--R log
+--R -
+--I 25%%IE0 %%IE1
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3
+--R +
+--R 2 2
+--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x
+--R +
+--I 10%%IE1
+--R *
+--R log
+--R 2 2 3
+--I - 125%%IE0 %%IE1 + (- 125%%IE0 + 25%%IE0)%%IE1 - 125%%IE0
+--R +
+--R 2
+--I 25%%IE0 - 5%%IE0 + x
+--R +
+--R 3 2
+--I 10%%IE0 log(125%%IE0 - 25%%IE0 + 5%%IE0 + x - 1) - 2log(x + 1)
+--R /
+--R 10
+--R Type: Union(Expression(Integer),...)
+--E 910
+
+--S 911 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I 2\|2 \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IE1 - 10\|2 %%IE0 + 2\|2
+--R *
+--R log
+--I 25%%IE0 %%IE1
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3
+--R +
+--R 2 2
+--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x
+--R +
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I - 2\|2 \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IE1 - 10\|2 %%IE0 + 2\|2
+--R *
+--R log
+--R -
+--I 25%%IE0 %%IE1
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3
+--R +
+--R 2 2
+--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x
+--R +
+--R +-+
+--I 20\|2 %%IE1
+--R *
+--R log
+--R 2 2 3
+--I - 125%%IE0 %%IE1 + (- 125%%IE0 + 25%%IE0)%%IE1 - 125%%IE0
+--R +
+--R 2
+--I 25%%IE0 - 5%%IE0 + x
+--R +
+--R +-+ 3 2
+--I 20\|2 %%IE0 log(125%%IE0 - 25%%IE0 + 5%%IE0 + x - 1)
+--R +
+--R +----------+
+--R +--------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R 4\|\|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +----------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R 4\|- \|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 - \|2 )log(x\|5 + 2x - x + 2)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 911
+
+--S 912 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +----------+
+--R +-+ +-+ 2 +-+ | +-+ | +-+
+--R (5x\|2 \|5 + (- 10x + 5x - 10)\|2 )\|\|5 + 5 \|2\|5 + 10
+--R +
+--R +----------+
+--R 2 +-+ +-+ 2 +-+ +--+ | +-+
+--R ((x - 3x + 1)\|2 \|5 + (- 5x + 5x - 5)\|2 )\|10 \|- \|5 + 5
+--R *
+--R +--------+
+--R | +-+
+--R \|\|5 + 5
+--R +
+--R 2
+--R 200x - 200x + 200
+--R /
+--R 4 3 2
+--R 400x - 400x + 400x - 400x + 400
+--R Type: Expression(Integer)
+--E 912
+
+)clear all
+
+--S 913 of 1347
+t0:=x^2/(1+x^5)
+--R
+--R
+--R 2
+--R x
+--R (1) ------
+--R 5
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 913
+
+--S 914 of 1347
+r0:=1/5*log(1+x)-1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1-sqrt(5))-_
+ 1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))+_
+ atan((1-4*x-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/(5+sqrt(5)))-_
+ 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_
+ sqrt(1/2*(5+sqrt(5)))
+--R
+--R
+--R (2)
+--R +----------+
+--R +----------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R 4\|- \|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +--------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R - 4\|\|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2 +-+
+--R (- \|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) + 4\|2 log(x + 1)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3
+--R +
+--I - 5%%IF1 - 5%%IF0 - 1
+--R *
+--R log
+--I (5%%IF1 + 5%%IF0 + 1)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3
+--R +
+--R 2 2
+--I - 25%%IF1 - 25%%IF0 + 2x - 1
+--R +
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3
+--R +
+--I - 5%%IF1 - 5%%IF0 - 1
+--R *
+--R log
+--I (- 5%%IF1 - 5%%IF0 - 1)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3
+--R +
+--R 2 2
+--I - 25%%IF1 - 25%%IF0 + 2x - 1
+--R +
+--R 2 2
+--I 10%%IF1 log(25%%IF1 + x) + 10%%IF0 log(25%%IF0 + x) + 2log(x + 1)
+--R /
+--R 10
+--R Type: Union(Expression(Integer),...)
+--E 915
+
+--S 916 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I - 2\|2 \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IF1 - 10\|2 %%IF0 - 2\|2
+--R *
+--R log
+--I (5%%IF1 + 5%%IF0 + 1)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3
+--R +
+--R 2 2
+--I - 25%%IF1 - 25%%IF0 + 2x - 1
+--R +
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I 2\|2 \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IF1 - 10\|2 %%IF0 - 2\|2
+--R *
+--R log
+--I (- 5%%IF1 - 5%%IF0 - 1)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3
+--R +
+--R 2 2
+--I - 25%%IF1 - 25%%IF0 + 2x - 1
+--R +
+--R +-+ 2 +-+ 2
+--I 20\|2 %%IF1 log(25%%IF1 + x) + 20\|2 %%IF0 log(25%%IF0 + x)
+--R +
+--R +----------+
+--R +----------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R - 4\|- \|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +--------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R 4\|\|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 + \|2 )log(x\|5 + 2x - x + 2)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 916
+
+--S 917 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +----------+ +----------+
+--R +-+ +-+ 2 +-+ | +-+ | +-+
+--R (- x\|2 \|5 + (2x - x + 2)\|2 )\|- \|5 + 5 \|2\|5 + 10
+--R +
+--R +-+ +-+ 2 +-+ +--+
+--R (- 2x\|2 \|5 + (- 4x + 2x - 4)\|2 )\|10 + 40x
+--R /
+--R 4 3 2
+--R 80x - 80x + 80x - 80x + 80
+--R Type: Expression(Integer)
+--E 917
+
+)clear all
+
+--S 918 of 1347
+t0:=x/(1+x^5)
+--R
+--R
+--R x
+--R (1) ------
+--R 5
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 918
+
+--S 919 of 1347
+r0:=-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1-sqrt(5))+_
+ 1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))+atan((1-4*x-sqrt(5))/_
+ sqrt(2*(5+sqrt(5))))*sqrt(2/5/(5+sqrt(5)))-_
+ 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_
+ sqrt(1/2*(5+sqrt(5)))
+--R
+--R
+--R (2)
+--R +----------+
+--R +----------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R 4\|- \|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +--------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R - 4\|\|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2 +-+
+--R (\|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) - 4\|2 log(x + 1)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 919
+
+--S 920 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3
+--R +
+--I - 5%%IG1 - 5%%IG0 + 1
+--R *
+--R log
+--I ((25%%IG0 - 5)%%IG1 - 5%%IG0)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3
+--R +
+--R 2 2
+--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1
+--R +
+--R 2
+--I 25%%IG0 - 5%%IG0 + 2x
+--R +
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3
+--R +
+--I - 5%%IG1 - 5%%IG0 + 1
+--R *
+--R log
+--I ((- 25%%IG0 + 5)%%IG1 + 5%%IG0)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3
+--R +
+--R 2 2
+--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1
+--R +
+--R 2
+--I 25%%IG0 - 5%%IG0 + 2x
+--R +
+--I 10%%IG1
+--R *
+--R log
+--R 2 2 3
+--I (125%%IG0 - 25)%%IG1 + (125%%IG0 - 25%%IG0 + 5)%%IG1 + 125%%IG0
+--R +
+--R 2
+--I - 25%%IG0 + 5%%IG0 + x - 1
+--R +
+--R 3
+--I 10%%IG0 log(- 125%%IG0 + x) - 2log(x + 1)
+--R /
+--R 10
+--R Type: Union(Expression(Integer),...)
+--E 920
+
+--S 921 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I - 2\|2 \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IG1 - 10\|2 %%IG0 + 2\|2
+--R *
+--R log
+--I ((25%%IG0 - 5)%%IG1 - 5%%IG0)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3
+--R +
+--R 2 2
+--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1
+--R +
+--R 2
+--I 25%%IG0 - 5%%IG0 + 2x
+--R +
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I 2\|2 \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IG1 - 10\|2 %%IG0 + 2\|2
+--R *
+--R log
+--I ((- 25%%IG0 + 5)%%IG1 + 5%%IG0)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3
+--R +
+--R 2 2
+--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1
+--R +
+--R 2
+--I 25%%IG0 - 5%%IG0 + 2x
+--R +
+--R +-+
+--I 20\|2 %%IG1
+--R *
+--R log
+--R 2 2 3
+--I (125%%IG0 - 25)%%IG1 + (125%%IG0 - 25%%IG0 + 5)%%IG1 + 125%%IG0
+--R +
+--R 2
+--I - 25%%IG0 + 5%%IG0 + x - 1
+--R +
+--R +-+ 3
+--I 20\|2 %%IG0 log(- 125%%IG0 + x)
+--R +
+--R +----------+
+--R +----------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R - 4\|- \|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +--------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R 4\|\|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 - \|2 )log(x\|5 + 2x - x + 2)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 921
+
+--S 922 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +----------+ +----------+
+--R +-+ +-+ 2 +-+ | +-+ | +-+
+--R (- x\|2 \|5 + (2x - x + 2)\|2 )\|- \|5 + 5 \|2\|5 + 10
+--R +
+--R +-+ +-+ 2 +-+ +--+
+--R (- 2x\|2 \|5 + (- 4x + 2x - 4)\|2 )\|10 + 40x
+--R /
+--R 4 3 2
+--R 80x - 80x + 80x - 80x + 80
+--R Type: Expression(Integer)
+--E 922
+
+)clear all
+
+--S 923 of 1347
+t0:=1/(1+x^5)
+--R
+--R
+--R 1
+--R (1) ------
+--R 5
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 923
+
+--S 924 of 1347
+r0:=1/5*log(1+x)-1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1-sqrt(5))-_
+ 1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))-_
+ 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_
+ sqrt(1/2*(5-sqrt(5)))-1/5*atan((1-4*x-sqrt(5))/_
+ sqrt(2*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))
+--R
+--R
+--R (2)
+--R +----------+
+--R +--------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R - 4\|\|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +----------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R - 4\|- \|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2 +-+
+--R (\|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) + 4\|2 log(x + 1)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 924
+
+--S 925 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3
+--R +
+--I - 5%%IH1 - 5%%IH0 - 1
+--R *
+--R log
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3
+--R +
+--I - 5%%IH1 - 5%%IH0 + 2x - 1
+--R +
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3
+--R +
+--I - 5%%IH1 - 5%%IH0 - 1
+--R *
+--R log
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3
+--R +
+--I - 5%%IH1 - 5%%IH0 + 2x - 1
+--R +
+--I 10%%IH1 log(5%%IH1 + x) + 10%%IH0 log(5%%IH0 + x) + 2log(x + 1)
+--R /
+--R 10
+--R Type: Union(Expression(Integer),...)
+--E 925
+
+--S 926 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I 2\|2 \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IH1 - 10\|2 %%IH0 - 2\|2
+--R *
+--R log
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3
+--R +
+--I - 5%%IH1 - 5%%IH0 + 2x - 1
+--R +
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I - 2\|2 \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IH1 - 10\|2 %%IH0 - 2\|2
+--R *
+--R log
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3
+--R +
+--I - 5%%IH1 - 5%%IH0 + 2x - 1
+--R +
+--R +-+ +-+
+--I 20\|2 %%IH1 log(5%%IH1 + x) + 20\|2 %%IH0 log(5%%IH0 + x)
+--R +
+--R +----------+
+--R +--------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R 4\|\|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +----------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R 4\|- \|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +----------+
+--R +-+ +-+ 2 +-+ | +-+ | +-+
+--R (5x\|2 \|5 + (- 10x + 5x - 10)\|2 )\|\|5 + 5 \|2\|5 + 10
+--R +
+--R +----------+
+--R 2 +-+ +-+ 2 +-+ +--+ | +-+
+--R ((x - 3x + 1)\|2 \|5 + (- 5x + 5x - 5)\|2 )\|10 \|- \|5 + 5
+--R *
+--R +--------+
+--R | +-+
+--R \|\|5 + 5
+--R +
+--R 2
+--R 200x - 200x + 200
+--R /
+--R 4 3 2
+--R 400x - 400x + 400x - 400x + 400
+--R Type: Expression(Integer)
+--E 927
+
+)clear all
+
+--S 928 of 1347
+t0:=1/(x*(1+x^5))
+--R
+--R
+--R 1
+--R (1) ------
+--R 6
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 928
+
+--S 929 of 1347
+r0:=-2/5*atanh(1+2*x^5)
+--R
+--R
+--R 5
+--R 2atanh(2x + 1)
+--R (2) - ---------------
+--R 5
+--R Type: Expression(Integer)
+--E 929
+
+--S 930 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 5
+--R - log(x + 1) + 5log(x)
+--R (3) -----------------------
+--R 5
+--R Type: Union(Expression(Integer),...)
+--E 930
+
+--S 931 of 1347
+m0:=a0-r0
+--R
+--R
+--R 5 5
+--R - log(x + 1) + 5log(x) + 2atanh(2x + 1)
+--R (4) -----------------------------------------
+--R 5
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 932
+
+)clear all
+
+--S 933 of 1347
+t0:=1/(x^2*(1+x^5))
+--R
+--R
+--R 1
+--R (1) -------
+--R 7 2
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 933
+
+--S 934 of 1347
+r0:=(-1)/x+1/5*log(1+x)-1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1-sqrt(5))-_
+ 1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))+_
+ 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_
+ sqrt(1/2*(5-sqrt(5)))+1/5*atan((1-4*x-sqrt(5))/_
+ sqrt(2*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))
+--R
+--R
+--R (2)
+--R +----------+
+--R +--------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R 4x\|\|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +----------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R 4x\|- \|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2 +-+
+--R (x\|2 \|5 - x\|2 )log(x\|5 + 2x - x + 2) + 4x\|2 log(x + 1)
+--R +
+--R +-+ +-+ +-+ +-+ 2 +-+
+--R (- x\|2 \|5 - x\|2 )log(- x\|5 + 2x - x + 2) - 20\|2
+--R /
+--R +-+
+--R 20x\|2
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I - x\|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3
+--R +
+--I - 5x %%II1 - 5x %%II0 - x
+--R *
+--R log
+--I 25%%II0 %%II1
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3
+--R +
+--R 2 2
+--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x
+--R +
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I x\|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3
+--R +
+--I - 5x %%II1 - 5x %%II0 - x
+--R *
+--R log
+--R -
+--I 25%%II0 %%II1
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3
+--R +
+--R 2 2
+--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x
+--R +
+--I 10x %%II1
+--R *
+--R log
+--R 2 2 3
+--I 125%%II0 %%II1 + (125%%II0 + 25%%II0)%%II1 + 125%%II0
+--R +
+--R 2
+--I 25%%II0 + 5%%II0 + x
+--R +
+--R 3 2
+--I 10x %%II0 log(- 125%%II0 - 25%%II0 - 5%%II0 + x - 1) + 2x log(x + 1) - 10
+--R /
+--R 10x
+--R Type: Union(Expression(Integer),...)
+--E 935
+
+--S 936 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I - 2\|2 \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%II1 - 10\|2 %%II0 - 2\|2
+--R *
+--R log
+--I 25%%II0 %%II1
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3
+--R +
+--R 2 2
+--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x
+--R +
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I 2\|2 \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%II1 - 10\|2 %%II0 - 2\|2
+--R *
+--R log
+--R -
+--I 25%%II0 %%II1
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3
+--R +
+--R 2 2
+--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x
+--R +
+--R +-+
+--I 20\|2 %%II1
+--R *
+--R log
+--R 2 2 3
+--I 125%%II0 %%II1 + (125%%II0 + 25%%II0)%%II1 + 125%%II0
+--R +
+--R 2
+--I 25%%II0 + 5%%II0 + x
+--R +
+--R +-+ 3 2
+--I 20\|2 %%II0 log(- 125%%II0 - 25%%II0 - 5%%II0 + x - 1)
+--R +
+--R +----------+
+--R +--------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R - 4\|\|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +----------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R - 4\|- \|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 936
+
+--S 937 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +----------+
+--R +-+ +-+ 2 +-+ | +-+ | +-+
+--R (- 5x\|2 \|5 + (10x - 5x + 10)\|2 )\|\|5 + 5 \|2\|5 + 10
+--R +
+--R +----------+
+--R 2 +-+ +-+ 2 +-+ +--+ | +-+
+--R ((- x + 3x - 1)\|2 \|5 + (5x - 5x + 5)\|2 )\|10 \|- \|5 + 5
+--R *
+--R +--------+
+--R | +-+
+--R \|\|5 + 5
+--R +
+--R 2
+--R - 200x + 200x - 200
+--R /
+--R 4 3 2
+--R 400x - 400x + 400x - 400x + 400
+--R Type: Expression(Integer)
+--E 937
+
+)clear all
+
+--S 938 of 1347
+t0:=1/(x^3*(1+x^5))
+--R
+--R
+--R 1
+--R (1) -------
+--R 8 3
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 938
+
+--S 939 of 1347
+r0:=(-1/2)/x^2-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1+sqrt(5)))*_
+ (1-sqrt(5))+1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))-_
+ atan((1-4*x-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/_
+ (5+sqrt(5)))+1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*_
+ (5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))
+--R
+--R
+--R (2)
+--R +----------+
+--R +----------+ +-+ | +-+
+--R 2 | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R - 4x \|- \|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +--------+ +-+ | +-+
+--R 2 | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R 4x \|\|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R 2 +-+ +-+ 2 +-+ +-+ 2 2 +-+
+--R (x \|2 \|5 + x \|2 )log(x\|5 + 2x - x + 2) - 4x \|2 log(x + 1)
+--R +
+--R 2 +-+ +-+ 2 +-+ +-+ 2 +-+
+--R (- x \|2 \|5 + x \|2 )log(- x\|5 + 2x - x + 2) - 10\|2
+--R /
+--R 2 +-+
+--R 20x \|2
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------------------------------------+
+--R 2 | 2 2
+--I - x \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3
+--R +
+--R 2 2 2
+--I - 5x %%IJ1 - 5x %%IJ0 + x
+--R *
+--R log
+--I (5%%IJ1 + 5%%IJ0 - 1)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3
+--R +
+--R 2 2
+--I - 25%%IJ1 - 25%%IJ0 + 2x - 1
+--R +
+--R +-----------------------------------------------------------+
+--R 2 | 2 2
+--I x \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3
+--R +
+--R 2 2 2
+--I - 5x %%IJ1 - 5x %%IJ0 + x
+--R *
+--R log
+--I (- 5%%IJ1 - 5%%IJ0 + 1)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3
+--R +
+--R 2 2
+--I - 25%%IJ1 - 25%%IJ0 + 2x - 1
+--R +
+--R 2 2 2 2 2
+--I 10x %%IJ1 log(25%%IJ1 + x) + 10x %%IJ0 log(25%%IJ0 + x) - 2x log(x + 1)
+--R +
+--R - 5
+--R /
+--R 2
+--R 10x
+--R Type: Union(Expression(Integer),...)
+--E 940
+
+--S 941 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I - 2\|2 \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IJ1 - 10\|2 %%IJ0 + 2\|2
+--R *
+--R log
+--I (5%%IJ1 + 5%%IJ0 - 1)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3
+--R +
+--R 2 2
+--I - 25%%IJ1 - 25%%IJ0 + 2x - 1
+--R +
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I 2\|2 \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IJ1 - 10\|2 %%IJ0 + 2\|2
+--R *
+--R log
+--I (- 5%%IJ1 - 5%%IJ0 + 1)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3
+--R +
+--R 2 2
+--I - 25%%IJ1 - 25%%IJ0 + 2x - 1
+--R +
+--R +-+ 2 +-+ 2
+--I 20\|2 %%IJ1 log(25%%IJ1 + x) + 20\|2 %%IJ0 log(25%%IJ0 + x)
+--R +
+--R +----------+
+--R +----------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R 4\|- \|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +--------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R - 4\|\|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 - \|2 )log(x\|5 + 2x - x + 2)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +----------+ +----------+
+--R +-+ +-+ 2 +-+ | +-+ | +-+
+--R (x\|2 \|5 + (- 2x + x - 2)\|2 )\|- \|5 + 5 \|2\|5 + 10
+--R +
+--R +-+ +-+ 2 +-+ +--+
+--R (2x\|2 \|5 + (4x - 2x + 4)\|2 )\|10 - 40x
+--R /
+--R 4 3 2
+--R 80x - 80x + 80x - 80x + 80
+--R Type: Expression(Integer)
+--E 942
+
+)clear all
+
+--S 943 of 1347
+t0:=1/(x^4*(1+x^5))
+--R
+--R
+--R 1
+--R (1) -------
+--R 9 4
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 943
+
+--S 944 of 1347
+r0:=(-1/3)/x^3+1/5*log(1+x)-1/20*log(2+2*x^2-x*(1+sqrt(5)))*_
+ (1-sqrt(5))-1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))-_
+ atan((1-4*x-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/_
+ (5+sqrt(5)))+1/5*atan(1/2*(1-4*x+sqrt(5))*_
+ sqrt(1/10*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))
+--R
+--R
+--R (2)
+--R +----------+
+--R +----------+ +-+ | +-+
+--R 3 | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R - 12x \|- \|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +--------+ +-+ | +-+
+--R 3 | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R 12x \|\|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R 3 +-+ +-+ 3 +-+ +-+ 2 3 +-+
+--R (- 3x \|2 \|5 - 3x \|2 )log(x\|5 + 2x - x + 2) + 12x \|2 log(x + 1)
+--R +
+--R 3 +-+ +-+ 3 +-+ +-+ 2 +-+
+--R (3x \|2 \|5 - 3x \|2 )log(- x\|5 + 2x - x + 2) - 20\|2
+--R /
+--R 3 +-+
+--R 60x \|2
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------------------------------------------------------+
+--R 3 | 2 2
+--I 3x \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3
+--R +
+--R 3 3 3
+--I - 15x %%IK1 - 15x %%IK0 - 3x
+--R *
+--R log
+--I ((25%%IK0 + 5)%%IK1 + 5%%IK0)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3
+--R +
+--R 2 2 2
+--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0
+--R +
+--I 5%%IK0 + 2x
+--R +
+--R +-----------------------------------------------------------+
+--R 3 | 2 2
+--I - 3x \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3
+--R +
+--R 3 3 3
+--I - 15x %%IK1 - 15x %%IK0 - 3x
+--R *
+--R log
+--I ((- 25%%IK0 - 5)%%IK1 - 5%%IK0)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3
+--R +
+--R 2 2 2
+--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0
+--R +
+--I 5%%IK0 + 2x
+--R +
+--R 3
+--I 30x %%IK1
+--R *
+--R log
+--R 2 2
+--I (- 125%%IK0 - 25)%%IK1 + (- 125%%IK0 - 25%%IK0 - 5)%%IK1
+--R +
+--R 3 2
+--I - 125%%IK0 - 25%%IK0 - 5%%IK0 + x - 1
+--R +
+--R 3 3 3
+--I 30x %%IK0 log(125%%IK0 + x) + 6x log(x + 1) - 10
+--R /
+--R 3
+--R 30x
+--R Type: Union(Expression(Integer),...)
+--E 945
+
+--S 946 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I 2\|2 \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IK1 - 10\|2 %%IK0 - 2\|2
+--R *
+--R log
+--I ((25%%IK0 + 5)%%IK1 + 5%%IK0)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3
+--R +
+--R 2 2 2
+--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0
+--R +
+--I 5%%IK0 + 2x
+--R +
+--R +-----------------------------------------------------------+
+--R +-+ | 2 2
+--I - 2\|2 \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3
+--R +
+--R +-+ +-+ +-+
+--I - 10\|2 %%IK1 - 10\|2 %%IK0 - 2\|2
+--R *
+--R log
+--I ((- 25%%IK0 - 5)%%IK1 - 5%%IK0)
+--R *
+--R +-----------------------------------------------------------+
+--R | 2 2
+--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3
+--R +
+--R 2 2 2
+--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0
+--R +
+--I 5%%IK0 + 2x
+--R +
+--R +-+
+--I 20\|2 %%IK1
+--R *
+--R log
+--R 2 2
+--I (- 125%%IK0 - 25)%%IK1 + (- 125%%IK0 - 25%%IK0 - 5)%%IK1
+--R +
+--R 3 2
+--I - 125%%IK0 - 25%%IK0 - 5%%IK0 + x - 1
+--R +
+--R +-+ 3
+--I 20\|2 %%IK0 log(125%%IK0 + x)
+--R +
+--R +----------+
+--R +----------+ +-+ | +-+
+--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10
+--R 4\|- \|5 + 5 atan(-------------------------------------)
+--R 20
+--R +
+--R +--------+
+--R +--------+ +-+ | +-+
+--R | +-+ (\|5 - 4x + 1)\|\|5 + 5
+--R - 4\|\|5 + 5 atan(--------------------------)
+--R +--+
+--R 2\|10
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (\|2 \|5 + \|2 )log(x\|5 + 2x - x + 2)
+--R +
+--R +-+ +-+ +-+ +-+ 2
+--R (- \|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2)
+--R /
+--R +-+
+--R 20\|2
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +----------+ +----------+
+--R +-+ +-+ 2 +-+ | +-+ | +-+
+--R (x\|2 \|5 + (- 2x + x - 2)\|2 )\|- \|5 + 5 \|2\|5 + 10
+--R +
+--R +-+ +-+ 2 +-+ +--+
+--R (2x\|2 \|5 + (4x - 2x + 4)\|2 )\|10 - 40x
+--R /
+--R 4 3 2
+--R 80x - 80x + 80x - 80x + 80
+--R Type: Expression(Integer)
+--E 947
+
+)clear all
+
+--S 948 of 1347
+t0:=1/(a+b*x^5)
+--R
+--R
+--R 1
+--R (1) --------
+--R 5
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 948
+
+--S 949 of 1347
+r0a:=1/5*log(a^(1/5)+b^(1/5)*x)/(a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+_
+ 2*b^(2/5)*x^2-a^(1/5)*b^(1/5)*x*(1-sqrt(5)))*(1-sqrt(5))/_
+ (a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+2*b^(2/5)*x^2-a^(1/5)*_
+ b^(1/5)*x*(1+sqrt(5)))*(1+sqrt(5))/(a^(4/5)*b^(1/5))-_
+ 1/5*atan((-4*b^(1/5)*x+a^(1/5)*(1+sqrt(5)))/(a^(1/5)*_
+ sqrt(2*(5-sqrt(5)))))*sqrt(1/2*(5-sqrt(5)))/(a^(4/5)*b^(1/5))-_
+ 1/5*atan((-4*b^(1/5)*x+a^(1/5)*(1-sqrt(5)))/(a^(1/5)*_
+ sqrt(2*(5+sqrt(5)))))*sqrt(1/2*(5+sqrt(5)))/(a^(4/5)*b^(1/5))
+--R
+--R
+--R (2)
+--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2
+--R (\|2 \|5 - \|2 )log(2x \|b + (x\|5 - x)\|a \|b + 2\|a )
+--R +
+--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2
+--R (- \|2 \|5 - \|2 )log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a )
+--R +
+--R +----------+ 5+-+ +-+ 5+-+
+--R +-+ 5+-+ 5+-+ | +-+ 4x\|b + (- \|5 - 1)\|a
+--R 4\|2 log(x\|b + \|a ) + 4\|- \|5 + 5 atan(-------------------------)
+--R +------------+
+--R | +-+ 5+-+
+--R \|- 2\|5 + 10 \|a
+--R +
+--R +--------+ 5+-+ +-+ 5+-+
+--R | +-+ 4x\|b + (\|5 - 1)\|a
+--R 4\|\|5 + 5 atan(-----------------------)
+--R +----------+
+--R 5+-+ | +-+
+--R \|a \|2\|5 + 10
+--R /
+--R +-+5+-+4 5+-+
+--R 20\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 1347
+r0b:=1/5*log(a^(1/5)+b^(1/5)*x)/(a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+_
+ 2*b^(2/5)*x^2-a^(1/5)*b^(1/5)*x*(1-sqrt(5)))*(1-sqrt(5))/_
+ (a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+2*b^(2/5)*x^2-a^(1/5)*_
+ b^(1/5)*x*(1+sqrt(5)))*(1+sqrt(5))/(a^(4/5)*b^(1/5))-_
+ 1/5*atan(1/2*(-4*b^(1/5)*x+a^(1/5)*(1+sqrt(5)))*sqrt(5+sqrt(5))/_
+ (a^(1/5)*sqrt(10)))*sqrt(1/2*(5-sqrt(5)))/(a^(4/5)*b^(1/5))-_
+ 1/5*atan((-4*b^(1/5)*x+a^(1/5)*(1-sqrt(5)))/(a^(1/5)*_
+ sqrt(2*(5+sqrt(5)))))*sqrt(1/2*(5+sqrt(5)))/(a^(4/5)*b^(1/5))
+--R
+--R
+--R (3)
+--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2
+--R (\|2 \|5 - \|2 )log(2x \|b + (x\|5 - x)\|a \|b + 2\|a )
+--R +
+--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2
+--R (- \|2 \|5 - \|2 )log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a )
+--R +
+--R +-+ 5+-+ 5+-+
+--R 4\|2 log(x\|b + \|a )
+--R +
+--R +--------+
+--R +----------+ 5+-+ +-+ 5+-+ | +-+
+--R | +-+ (4x\|b + (- \|5 - 1)\|a )\|\|5 + 5
+--R 4\|- \|5 + 5 atan(--------------------------------------)
+--R +--+5+-+
+--R 2\|10 \|a
+--R +
+--R +--------+ 5+-+ +-+ 5+-+
+--R | +-+ 4x\|b + (\|5 - 1)\|a
+--R 4\|\|5 + 5 atan(-----------------------)
+--R +----------+
+--R 5+-+ | +-+
+--R \|a \|2\|5 + 10
+--R /
+--R +-+5+-+4 5+-+
+--R 20\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 950
+
+--S 951 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R +---+
+--R 5| 4
+--R 5\|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+
+--R 5| 4 5| 4
+--I - 5\|a b %%IM1 - 5\|a b %%IM0 - 1
+--R *
+--R log
+--R +---+
+--R 5| 4
+--R 5a\|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+ +---+
+--R 5| 4 5| 4 5| 4
+--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a
+--R +
+--R -
+--R +---+
+--R 5| 4
+--R 5\|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+
+--R 5| 4 5| 4
+--I - 5\|a b %%IM1 - 5\|a b %%IM0 - 1
+--R *
+--R log
+--R -
+--R +---+
+--R 5| 4
+--R 5a\|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+ +---+
+--R 5| 4 5| 4 5| 4
+--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a
+--R +
+--R +---+ +---+
+--R 5| 4 5| 4
+--I 10\|a b %%IM1 log(5a %%IM1 + x) + 10\|a b %%IM0 log(5a %%IM0 + x)
+--R +
+--R +---+
+--R 5| 4
+--R 2log(x\|a b + a)
+--R /
+--R +---+
+--R 5| 4
+--R 10\|a b
+--R Type: Union(Expression(Integer),...)
+--E 951
+
+--S 952 of 1347
+m0a:=a0-r0a
+--R
+--R
+--R (5)
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--R 10\|2 \|a \|b \|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+
+--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4
+--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0
+--R +
+--R +-+5+-+4 5+-+
+--R - 2\|2 \|a \|b
+--R *
+--R log
+--R +---+
+--R 5| 4
+--R 5a\|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+ +---+
+--R 5| 4 5| 4 5| 4
+--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a
+--R +
+--R -
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--R 10\|2 \|a \|b \|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+
+--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4
+--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0
+--R +
+--R +-+5+-+4 5+-+
+--R - 2\|2 \|a \|b
+--R *
+--R log
+--R -
+--R +---+
+--R 5| 4
+--R 5a\|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+ +---+
+--R 5| 4 5| 4 5| 4
+--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a
+--R +
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--I 20\|2 \|a \|b \|a b %%IM1 log(5a %%IM1 + x)
+--R +
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--I 20\|2 \|a \|b \|a b %%IM0 log(5a %%IM0 + x)
+--R +
+--R +---+
+--R +-+5+-+4 5+-+ 5| 4
+--R 4\|2 \|a \|b log(x\|a b + a)
+--R +
+--R +---+
+--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2
+--R (- \|2 \|5 + \|2 )\|a b log(2x \|b + (x\|5 - x)\|a \|b + 2\|a )
+--R +
+--R +---+
+--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2
+--R (\|2 \|5 + \|2 )\|a b log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a )
+--R +
+--R +---+
+--R +-+5| 4 5+-+ 5+-+
+--R - 4\|2 \|a b log(x\|b + \|a )
+--R +
+--R +----------+ +---+ 5+-+ +-+ 5+-+
+--R | +-+ 5| 4 4x\|b + (- \|5 - 1)\|a
+--R - 4\|- \|5 + 5 \|a b atan(-------------------------)
+--R +------------+
+--R | +-+ 5+-+
+--R \|- 2\|5 + 10 \|a
+--R +
+--R +---+ +--------+ 5+-+ +-+ 5+-+
+--R 5| 4 | +-+ 4x\|b + (\|5 - 1)\|a
+--R - 4\|a b \|\|5 + 5 atan(-----------------------)
+--R +----------+
+--R 5+-+ | +-+
+--R \|a \|2\|5 + 10
+--R /
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--R 20\|2 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 952
+
+--S 953 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 +-+5+-+2 +-+ +-+ +-+ 5+-+5+-+ +-+5+-+2 | +-+
+--R (- 2x \|2 \|b + (x\|2 \|5 + x\|2 )\|a \|b - 2\|2 \|a )\|\|5 + 5
+--R *
+--R +----------+
+--R | +-+
+--R \|2\|5 + 10
+--R +
+--R +------------+ +----------+
+--R 2 +-+ | +-+ | +-+ 2 5+-+2
+--R (- 2x \|2 \|- 2\|5 + 10 \|- \|5 + 5 + 40x )\|b
+--R +
+--R +------------+ +----------+
+--R +-+ +-+ +-+ | +-+ | +-+ 5+-+5+-+
+--R ((- x\|2 \|5 + x\|2 )\|- 2\|5 + 10 \|- \|5 + 5 - 40x)\|a \|b
+--R +
+--R +------------+ +----------+
+--R +-+ | +-+ | +-+ 5+-+2
+--R (- 2\|2 \|- 2\|5 + 10 \|- \|5 + 5 + 40)\|a
+--R /
+--R 4 5+-+3 5+-+4 3 5+-+4 5+-+3 2 5+-+2 5+-+5+-+ 5+-+2
+--R 80x \|a \|b - 80x \|a \|b + 80a x \|b - 80a x\|a \|b + 80a \|a
+--R Type: Expression(Integer)
+--E 953
+
+--S 954 of 1347
+m0a:=a0-r0b
+--R
+--R
+--R (7)
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--R 10\|2 \|a \|b \|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+
+--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4
+--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0
+--R +
+--R +-+5+-+4 5+-+
+--R - 2\|2 \|a \|b
+--R *
+--R log
+--R +---+
+--R 5| 4
+--R 5a\|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+ +---+
+--R 5| 4 5| 4 5| 4
+--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a
+--R +
+--R -
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--R 10\|2 \|a \|b \|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+
+--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4
+--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0
+--R +
+--R +-+5+-+4 5+-+
+--R - 2\|2 \|a \|b
+--R *
+--R log
+--R -
+--R +---+
+--R 5| 4
+--R 5a\|a b
+--R *
+--R ROOT
+--R +---+2 +---+2 +---+
+--R 5| 4 2 5| 4 5| 4
+--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1
+--R +
+--R +---+2 +---+
+--R 5| 4 2 5| 4
+--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3
+--R /
+--R +---+2
+--R 5| 4
+--R 25\|a b
+--R +
+--R +---+ +---+ +---+
+--R 5| 4 5| 4 5| 4
+--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a
+--R +
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--I 20\|2 \|a \|b \|a b %%IM1 log(5a %%IM1 + x)
+--R +
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--I 20\|2 \|a \|b \|a b %%IM0 log(5a %%IM0 + x)
+--R +
+--R +---+
+--R +-+5+-+4 5+-+ 5| 4
+--R 4\|2 \|a \|b log(x\|a b + a)
+--R +
+--R +---+
+--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2
+--R (- \|2 \|5 + \|2 )\|a b log(2x \|b + (x\|5 - x)\|a \|b + 2\|a )
+--R +
+--R +---+
+--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2
+--R (\|2 \|5 + \|2 )\|a b log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a )
+--R +
+--R +---+
+--R +-+5| 4 5+-+ 5+-+
+--R - 4\|2 \|a b log(x\|b + \|a )
+--R +
+--R +--------+
+--R +----------+ +---+ 5+-+ +-+ 5+-+ | +-+
+--R | +-+ 5| 4 (4x\|b + (- \|5 - 1)\|a )\|\|5 + 5
+--R - 4\|- \|5 + 5 \|a b atan(--------------------------------------)
+--R +--+5+-+
+--R 2\|10 \|a
+--R +
+--R +---+ +--------+ 5+-+ +-+ 5+-+
+--R 5| 4 | +-+ 4x\|b + (\|5 - 1)\|a
+--R - 4\|a b \|\|5 + 5 atan(-----------------------)
+--R +----------+
+--R 5+-+ | +-+
+--R \|a \|2\|5 + 10
+--R /
+--R +---+
+--R +-+5+-+4 5+-+5| 4
+--R 20\|2 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 954
+
+--S 955 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Polynomial(Integer)
+--E 955
+
+)clear all
+
+--S 956 of 1347
+t0:=x^(23/2)/sqrt(a+b*x^5)
+--R
+--R
+--R 11 +-+
+--R x \|x
+--R (1) -----------
+--R +--------+
+--R | 5
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 956
+
+--S 957 of 1347
+r0:=3/20*a^2*atanh(x^(5/2)*sqrt(b)/sqrt(a+b*x^5))/b^(5/2)-_
+ 3/20*a*x^(5/2)*sqrt(a+b*x^5)/b^2+1/10*x^(15/2)*sqrt(a+b*x^5)/b
+--R
+--R
+--R 2 +-+ +-+ +--------+
+--R 2 x \|b \|x 7 2 +-+ +-+ | 5
+--R 3a atanh(-----------) + (2b x - 3a x )\|b \|x \|b x + a
+--R +--------+
+--R | 5
+--R \|b x + a
+--R (2) ----------------------------------------------------------
+--R 2 +-+
+--R 20b \|b
+--R Type: Expression(Integer)
+--E 957
+
+--S 958 of 1347
+--a0:=integrate(t0,x)
+--E 958
+
+--S 959 of 1347
+--m0:=a0-r0
+--E 959
+
+--S 960 of 1347
+--d0:=D(m0,x)
+--E 960
+
+)clear all
+
+--S 961 of 1347
+t0:=x^(13/2)/sqrt(a+b*x^5)
+--R
+--R
+--R 6 +-+
+--R x \|x
+--R (1) -----------
+--R +--------+
+--R | 5
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 961
+
+--S 962 of 1347
+r0:=-1/5*a*atanh(x^(5/2)*sqrt(b)/sqrt(a+b*x^5))/b^(3/2)+_
+ 1/5*x^(5/2)*sqrt(a+b*x^5)/b
+--R
+--R
+--R 2 +-+ +-+ +--------+
+--R x \|b \|x 2 +-+ +-+ | 5
+--R - a atanh(-----------) + x \|b \|x \|b x + a
+--R +--------+
+--R | 5
+--R \|b x + a
+--R (2) ----------------------------------------------
+--R +-+
+--R 5b\|b
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 1347
+--a0:=integrate(t0,x)
+--E 963
+
+--S 964 of 1347
+--m0:=a0-r0
+--E 964
+
+--S 965 of 1347
+--d0:=D(m0,x)
+--E 965
+
+)clear all
+
+--S 966 of 1347
+t0:=x^(3/2)/sqrt(a+b*x^5)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) -----------
+--R +--------+
+--R | 5
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 1347
+r0:=2/5*atanh(x^(5/2)*sqrt(b)/sqrt(a+b*x^5))/sqrt(b)
+--R
+--R
+--R 2 +-+ +-+
+--R x \|b \|x
+--R 2atanh(-----------)
+--R +--------+
+--R | 5
+--R \|b x + a
+--R (2) -------------------
+--R +-+
+--R 5\|b
+--R Type: Expression(Integer)
+--E 967
+
+--S 968 of 1347
+--a0:=integrate(t0,x)
+--E 968
+
+--S 969 of 1347
+--m0:=a0-r0
+--E 969
+
+--S 970 of 1347
+--d0:=D(m0,x)
+--E 970
+
+)clear all
+
+--S 971 of 1347
+t0:=1/(x^(7/2)*sqrt(a+b*x^5))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R +--------+
+--R 3 +-+ | 5
+--R x \|x \|b x + a
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 1347
+r0:=-2/5*sqrt(a+b*x^5)/(a*x^(5/2))
+--R
+--R
+--R +--------+
+--R | 5
+--R 2\|b x + a
+--R (2) - ------------
+--R 2 +-+
+--R 5a x \|x
+--R Type: Expression(Integer)
+--E 972
+
+--S 973 of 1347 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +-+ | 5 3
+--R - 2\|x \|b x + a + (- b - a - 1)x
+--R (3) ------------------------------------
+--R 3
+--R 5a x
+--R Type: Union(Expression(Integer),...)
+--E 973
+
+--S 974 of 1347 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R - b - a - 1
+--R (4) -----------
+--R 5a
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 975
+
+)clear all
+
+--S 976 of 1347
+t0:=1/(x^(17/2)*sqrt(a+b*x^5))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R +--------+
+--R 8 +-+ | 5
+--R x \|x \|b x + a
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1347
+r0:=-2/15*sqrt(a+b*x^5)/(a*x^(15/2))+4/15*b*sqrt(a+b*x^5)/(a^2*x^(5/2))
+--R
+--R
+--R +--------+
+--R 5 | 5
+--R (4b x - 2a)\|b x + a
+--R (2) -----------------------
+--R 2 7 +-+
+--R 15a x \|x
+--R Type: Expression(Integer)
+--E 977
+
+--S 978 of 1347 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 5 +-+ | 5 2 2 8
+--R (12b x - 6a)\|x \|b x + a + (- 2b + (- a - 18)b + a + 9a)x
+--R (3) ----------------------------------------------------------------
+--R 2 8
+--R 45a x
+--R Type: Union(Expression(Integer),...)
+--E 978
+
+--S 979 of 1347 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - 2b + (- a - 18)b + a + 9a
+--R (4) -----------------------------
+--R 2
+--R 45a
+--R Type: Expression(Integer)
+--E 979
+
+--S 980 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 980
+
+)clear all
+
+--S 981 of 1347
+t0:=x^(23/2)/sqrt(1+x^5)
+--R
+--R
+--R 11 +-+
+--R x \|x
+--R (1) ---------
+--R +------+
+--R | 5
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1347
+r0:=3/20*asinh(x^(5/2))-3/20*x^(5/2)*sqrt(1+x^5)+1/10*x^(15/2)*sqrt(1+x^5)
+--R
+--R
+--R +------+
+--R 2 +-+ 7 2 +-+ | 5
+--R 3asinh(x \|x ) + (2x - 3x )\|x \|x + 1
+--R (2) -----------------------------------------
+--R 20
+--R Type: Expression(Integer)
+--E 982
+
+--S 983 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+ +------+
+--R 2 +-+ | 5 5 7 2 +-+ | 5
+--R - 3log(- 2x \|x \|x + 1 + 2x + 1) + (4x - 6x )\|x \|x + 1
+--R (3) ---------------------------------------------------------------
+--R 40
+--R Type: Union(Expression(Integer),...)
+--E 983
+
+--S 984 of 1347
+m0:=a0-r0
+--R
+--R
+--R +------+
+--R 2 +-+ | 5 5 2 +-+
+--R - 3log(- 2x \|x \|x + 1 + 2x + 1) - 6asinh(x \|x )
+--R (4) -----------------------------------------------------
+--R 40
+--R Type: Expression(Integer)
+--E 984
+
+--S 985 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 985
+
+)clear all
+
+--S 986 of 1347
+t0:=x^(13/2)/sqrt(1+x^5)
+--R
+--R
+--R 6 +-+
+--R x \|x
+--R (1) ---------
+--R +------+
+--R | 5
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1347
+r0:=-1/5*asinh(x^(5/2))+1/5*x^(5/2)*sqrt(1+x^5)
+--R
+--R
+--R +------+
+--R 2 +-+ 2 +-+ | 5
+--R - asinh(x \|x ) + x \|x \|x + 1
+--R (2) ---------------------------------
+--R 5
+--R Type: Expression(Integer)
+--E 987
+
+-- (1 . failed) cannot be coerced to mode
+-- (Matrix (Fraction (SparseUnivariatePolynomial (InnerPrimeField 3))))
+--S 988 of 1347
+--a0:=integrate(t0,x)
+--E 988
+
+--S 989 of 1347
+--m0:=a0-r0
+--E 989
+
+--S 990 of 1347
+--d0:=normalize(D(m0,x))
+--E 990
+
+)clear all
+
+--S 991 of 1347
+t0:=x^(3/2)/sqrt(1+x^5)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ---------
+--R +------+
+--R | 5
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1347
+r0:=2/5*asinh(x^(5/2))
+--R
+--R
+--R 2 +-+
+--R 2asinh(x \|x )
+--R (2) --------------
+--R 5
+--R Type: Expression(Integer)
+--E 992
+
+-- (1 . failed) cannot be coerced to mode
+-- (Matrix (Fraction (SparseUnivariatePolynomial (InnerPrimeField 3))))
+--S 993 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R 2 +-+ | 5 5
+--R log(- 2x \|x \|x + 1 + 2x + 1)
+--R (3) - ---------------------------------
+--R 5
+--R Type: Union(Expression(Integer),...)
+--E 993
+
+--S 994 of 1347
+m0:=a0-r0
+--R
+--R
+--R +------+
+--R 2 +-+ | 5 5 2 +-+
+--R - log(- 2x \|x \|x + 1 + 2x + 1) - 2asinh(x \|x )
+--R (4) ----------------------------------------------------
+--R 5
+--R Type: Expression(Integer)
+--E 994
+
+--S 995 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 995
+
+)clear all
+
+--S 996 of 1347
+t0:=1/(x^(7/2)*sqrt(1+x^5))
+--R
+--R
+--R 1
+--R (1) ---------------
+--R +------+
+--R 3 +-+ | 5
+--R x \|x \|x + 1
+--R Type: Expression(Integer)
+--E 996
+
+--S 997 of 1347
+r0:=-2/5*sqrt(1+x^5)/x^(5/2)
+--R
+--R
+--R +------+
+--R | 5
+--R 2\|x + 1
+--R (2) - ----------
+--R 2 +-+
+--R 5x \|x
+--R Type: Expression(Integer)
+--E 997
+
+--S 998 of 1347 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R +-+ | 5 3
+--R - 2\|x \|x + 1 + 3x
+--R (3) ----------------------
+--R 3
+--R 5x
+--R Type: Union(Expression(Integer),...)
+--E 998
+
+--S 999 of 1347 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 3
+--R (4) -
+--R 5
+--R Type: Expression(Integer)
+--E 999
+
+--S 1000 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1000
+
+)clear all
+
+--S 1001 of 1347
+t0:=1/(x^(17/2)*sqrt(1+x^5))
+--R
+--R
+--R 1
+--R (1) ---------------
+--R +------+
+--R 8 +-+ | 5
+--R x \|x \|x + 1
+--R Type: Expression(Integer)
+--E 1001
+
+--S 1002 of 1347
+r0:=-2/15*sqrt(1+x^5)/x^(15/2)+4/15*sqrt(1+x^5)/x^(5/2)
+--R
+--R
+--R +------+
+--R 5 | 5
+--R (4x - 2)\|x + 1
+--R (2) ------------------
+--R 7 +-+
+--R 15x \|x
+--R Type: Expression(Integer)
+--E 1002
+
+--S 1003 of 1347 ok to fail, differs by a constant
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R 5 +-+ | 5 8
+--R (8x - 4)\|x \|x + 1 + 9x
+--R (3) ----------------------------
+--R 8
+--R 30x
+--R Type: Union(Expression(Integer),...)
+--E 1003
+
+--S 1004 of 1347 ok to fail, differs by a constant
+m0:=a0-r0
+--R
+--R
+--R 3
+--R (4) --
+--R 10
+--R Type: Expression(Integer)
+--E 1004
+
+--S 1005 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1005
+
+)clear all
+
+--S 1006 of 1347
+t0:=x^8/(a+b*x^6)
+--R
+--R
+--R 8
+--R x
+--R (1) --------
+--R 6
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1006
+
+--S 1007 of 1347
+r0:=1/3*x^3/b-1/3*atan(x^3*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2)
+--R
+--R
+--R 3 +-+
+--R +-+ x \|b 3 +-+
+--R - \|a atan(------) + x \|b
+--R +-+
+--R \|a
+--R (2) ---------------------------
+--R +-+
+--R 3b\|b
+--R Type: Expression(Integer)
+--E 1007
+
+--S 1008 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+ +-+
+--R 3 | a 6 |a
+--R +---+ - 2b x |- - + b x - a +-+ |-
+--R | a \| b 3 |a \|b 3
+--R |- - log(------------------------) + 2x |- atan(----) + x
+--R \| b 6 \|b 3
+--R b x + a x
+--R (3) [-----------------------------------------,-------------------]
+--R 6b 3b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1008
+
+--S 1009 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R 3 | a 6
+--R +---+ - 2b x |- - + b x - a 3 +-+
+--R | a +-+ \| b +-+ x \|b
+--R |- - \|b log(------------------------) + 2\|a atan(------)
+--R \| b 6 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R +-+
+--R 6b\|b
+--R Type: Expression(Integer)
+--E 1009
+
+--S 1010 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1010
+
+--S 1011 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R 3 +-+ +-+ |-
+--R +-+ x \|b |a +-+ \|b
+--R \|a atan(------) + |- \|b atan(----)
+--R +-+ \|b 3
+--R \|a x
+--R (6) -------------------------------------
+--R +-+
+--R 3b\|b
+--R Type: Expression(Integer)
+--E 1011
+
+--S 1012 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1012
+
+)clear all
+
+--S 1013 of 1347
+t0:=x^7/(a+b*x^6)
+--R
+--R
+--R 7
+--R x
+--R (1) --------
+--R 6
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1013
+
+--S 1014 of 1347
+r0:=1/2*x^2/b-1/6*a^(1/3)*log(a^(1/3)+b^(1/3)*x^2)/b^(4/3)+_
+ 1/12*a^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/b^(4/3)+_
+ 1/2*a^(1/3)*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*_
+ sqrt(3)))/(b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+
+--R \|3 \|a log(x \|b - x \|a \|b + \|a ) - 2\|3 \|a log(x \|b + \|a )
+--R +
+--R 2 3+-+ 3+-+
+--R 3+-+ 2x \|b - \|a 2 +-+3+-+
+--R - 6\|a atan(--------------) + 6x \|3 \|b
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+
+--R 12b\|3 \|b
+--R Type: Expression(Integer)
+--E 1014
+
+--S 1015 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+2 +---+ +---+ +---+
+--R +-+ | a | a 2 | a 4 +-+ | a | a 2
+--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x )
+--R \| b \| b \| b \| b \| b
+--R +
+--R +---+
+--R +-+ | a 2 +-+
+--R +---+ \|3 3|- - + 2x \|3
+--R | a \| b 2 +-+
+--R - 6 3|- - atan(-------------------- + 6x \|3
+--R \| b +---+
+--R | a
+--R 3 3|- -
+--R \| b
+--R /
+--R +-+
+--R 12b\|3
+--R Type: Union(Expression(Integer),...)
+--E 1015
+
+--S 1016 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+
+--R - \|3 \|a log(x \|b - x \|a \|b + \|a ) + 2\|3 \|a log(x \|b + \|a )
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | a 3+-+ | a 2 | a 4
+--R - \|3 3|- - \|b log(3|- - + x 3|- - + x )
+--R \| b \| b \| b
+--R +
+--R +---+ +---+ 2 3+-+ 3+-+
+--R +-+ | a 3+-+ | a 2 3+-+ 2x \|b - \|a
+--R 2\|3 3|- - \|b log(- 3|- - + x + 6\|a atan(--------------)
+--R \| b \| b +-+3+-+
+--R \|3 \|a
+--R +
+--R +---+
+--R +-+ | a 2 +-+
+--R +---+ \|3 3|- - + 2x \|3
+--R | a 3+-+ \| b
+--R - 6 3|- - \|b atan(--------------------)
+--R \| b +---+
+--R | a
+--R 3 3|- -
+--R \| b
+--R /
+--R +-+3+-+
+--R 12b\|3 \|b
+--R Type: Expression(Integer)
+--E 1016
+
+--S 1017 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1017
+
+)clear all
+
+--S 1018 of 1347
+t0:=x^6/(a+b*x^6)
+--R
+--R
+--R 6
+--R x
+--R (1) --------
+--R 6
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1018
+
+--S 1019 of 1347
+r0:=x/b-1/3*a^(1/6)*atan(b^(1/6)*x/a^(1/6))/b^(7/6)-_
+ 1/3*a^(1/6)*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3)))))*sqrt(-b^(1/3)+sqrt(3)*_
+ sqrt(-b^(2/3)))/(b^(4/3)*sqrt(2))-1/3*a^(1/6)*_
+ atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+sqrt(3)*_
+ sqrt(-b^(2/3)))))*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(b^(4/3)*sqrt(2))
+--R
+--R
+--R (2)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - \|a \|b \|\|3 \|- \|b + \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - \|a \|b \|\|3 \|- \|b - \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R 6+-+
+--R +-+6+-+3+-+ x\|b +-+3+-+6+-+
+--R - \|2 \|a \|b atan(-----) + 3x\|2 \|b \|b
+--R 6+-+
+--R \|a
+--R /
+--R +-+3+-+6+-+
+--R 3b\|2 \|b \|b
+--R Type: Expression(Integer)
+--E 1019
+
+--S 1020 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+2 +---------+
+--R | a 2 | a | a 2
+--R - b |- ------- log(36b |- ------- + 6b x |- ------- + x )
+--R 6| 7 6| 7 6| 7
+--R \| 46656b \| 46656b \| 46656b
+--R +
+--R +---------+ +---------+2 +---------+
+--R | a 2 | a | a 2
+--R b |- ------- log(36b |- ------- - 6b x |- ------- + x )
+--R 6| 7 6| 7 6| 7
+--R \| 46656b \| 46656b \| 46656b
+--R +
+--R +---------+ +---------+
+--R | a | a
+--R - 2b |- ------- log(6b |- ------- + x)
+--R 6| 7 6| 7
+--R \| 46656b \| 46656b
+--R +
+--R +---------+ +---------+
+--R | a | a
+--R 2b |- ------- log(- 6b |- ------- + x)
+--R 6| 7 6| 7
+--R \| 46656b \| 46656b
+--R +
+--R +---------+
+--R +-+ | a
+--R 3b\|3 |- -------
+--R +---------+ 6| 7
+--R +-+ | a \| 46656b
+--R - 2b\|3 |- ------- atan(------------------)
+--R 6| 7 +---------+
+--R \| 46656b | a
+--R 3b |- ------- - x
+--R 6| 7
+--R \| 46656b
+--R +
+--R +---------+
+--R +-+ | a
+--R 3b\|3 |- -------
+--R +---------+ 6| 7
+--R +-+ | a \| 46656b
+--R 2b\|3 |- ------- atan(------------------ + 2x
+--R 6| 7 +---------+
+--R \| 46656b | a
+--R 3b |- ------- + x
+--R 6| 7
+--R \| 46656b
+--R /
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 1020
+
+--S 1021 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R 2\|a \|b \|\|3 \|- \|b + \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R 2\|a \|b \|\|3 \|- \|b - \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R -
+--R +---------+
+--R +-+ | a 3+-+6+-+
+--R 3b\|2 |- ------- \|b \|b
+--R 6| 7
+--R \| 46656b
+--R *
+--R +---------+2 +---------+
+--R 2 | a | a 2
+--R log(36b |- ------- + 6b x |- ------- + x )
+--R 6| 7 6| 7
+--R \| 46656b \| 46656b
+--R +
+--R +---------+ +---------+2 +---------+
+--R +-+ | a 3+-+6+-+ 2 | a | a 2
+--R 3b\|2 |- ------- \|b \|b log(36b |- ------- - 6b x |- ------- + x )
+--R 6| 7 6| 7 6| 7
+--R \| 46656b \| 46656b \| 46656b
+--R +
+--R +---------+ +---------+
+--R +-+ | a 3+-+6+-+ | a
+--R - 6b\|2 |- ------- \|b \|b log(6b |- ------- + x)
+--R 6| 7 6| 7
+--R \| 46656b \| 46656b
+--R +
+--R +---------+ +---------+
+--R +-+ | a 3+-+6+-+ | a
+--R 6b\|2 |- ------- \|b \|b log(- 6b |- ------- + x)
+--R 6| 7 6| 7
+--R \| 46656b \| 46656b
+--R +
+--R 6+-+
+--R +-+6+-+3+-+ x\|b
+--R 2\|2 \|a \|b atan(-----)
+--R 6+-+
+--R \|a
+--R +
+--R +---------+
+--R +-+ | a
+--R 3b\|3 |- -------
+--R +---------+ 6| 7
+--R +-+ +-+ | a 3+-+6+-+ \| 46656b
+--R - 6b\|2 \|3 |- ------- \|b \|b atan(------------------)
+--R 6| 7 +---------+
+--R \| 46656b | a
+--R 3b |- ------- - x
+--R 6| 7
+--R \| 46656b
+--R +
+--R +---------+
+--R +-+ | a
+--R 3b\|3 |- -------
+--R +---------+ 6| 7
+--R +-+ +-+ | a 3+-+6+-+ \| 46656b
+--R 6b\|2 \|3 |- ------- \|b \|b atan(------------------)
+--R 6| 7 +---------+
+--R \| 46656b | a
+--R 3b |- ------- + x
+--R 6| 7
+--R \| 46656b
+--R /
+--R +-+3+-+6+-+
+--R 6b\|2 \|b \|b
+--R Type: Expression(Integer)
+--E 1021
+
+--S 1022 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1022
+
+)clear all
+
+--S 1023 of 1347
+t0:=x^5/(a+b*x^6)
+--R
+--R
+--R 5
+--R x
+--R (1) --------
+--R 6
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1023
+
+--S 1024 of 1347
+r0:=1/6*log(a+b*x^6)/b
+--R
+--R
+--R 6
+--R log(b x + a)
+--R (2) -------------
+--R 6b
+--R Type: Expression(Integer)
+--E 1024
+
+--S 1025 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6
+--R log(b x + a)
+--R (3) -------------
+--R 6b
+--R Type: Union(Expression(Integer),...)
+--E 1025
+
+--S 1026 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1026
+
+--S 1027 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1027
+
+)clear all
+
+--S 1028 of 1347
+t0:=x^4/(a+b*x^6)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 6
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1028
+
+--S 1029 of 1347
+r0:=1/3*atan(b^(1/6)*x/a^(1/6))/(a^(1/6)*b^(5/6))+_
+ 1/3*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*_
+ sqrt(-b^(2/3)))))*sqrt(2)/(a^(1/6)*b^(2/3)*sqrt(-b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3))))-1/3*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*_
+ sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*sqrt(2)/(a^(1/6)*b^(2/3)*_
+ sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))
+--R
+--R
+--R (2)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - \|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R \|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R +---------------------+ +---------------------+
+--R 6+-+ | +-------+ | +-------+
+--R 3+-+2 x\|b | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R \|b atan(-----)\|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R 6+-+
+--R \|a
+--R /
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R 6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R 3\|a \|b \|b \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R Type: Expression(Integer)
+--E 1029
+
+--S 1030 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------+
+--R | 1
+--R |- ---------
+--R 6| 5
+--R \| 46656a b
+--R *
+--R +-----------+5 +-----------+4
+--R 4 | 1 3 | 1 2
+--R log(7776a b x |- --------- - 1296a b |- --------- + x )
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R +-----------+ +-----------+5
+--R | 1 4 | 1
+--R 2 |- --------- log(7776a b |- --------- + x)
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R +-----------+ +-----------+5
+--R | 1 4 | 1
+--R - 2 |- --------- log(- 7776a b |- --------- + x)
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R -
+--R +-----------+
+--R | 1
+--R |- ---------
+--R 6| 5
+--R \| 46656a b
+--R *
+--R +-----------+5 +-----------+4
+--R 4 | 1 3 | 1 2
+--R log(- 7776a b x |- --------- - 1296a b |- --------- + x )
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R +-----------+5
+--R 4 +-+ | 1
+--R 3888a b \|3 |- ---------
+--R +-----------+ 6| 5
+--R +-+ | 1 \| 46656a b
+--R - 2\|3 |- --------- atan(---------------------------)
+--R 6| 5 +-----------+5
+--R \| 46656a b 4 | 1
+--R 3888a b |- --------- - x
+--R 6| 5
+--R \| 46656a b
+--R +
+--R +-----------+5
+--R 4 +-+ | 1
+--R 3888a b \|3 |- ---------
+--R +-----------+ 6| 5
+--R +-+ | 1 \| 46656a b
+--R 2\|3 |- --------- atan(---------------------------)
+--R 6| 5 +-----------+5
+--R \| 46656a b 4 | 1
+--R 3888a b |- --------- + x
+--R 6| 5
+--R \| 46656a b
+--R /
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 1030
+
+--S 1031 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R 2\|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - 2\|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R +-----------+
+--R | 1 6+-+3+-+2 6+-+5
+--R 3 |- --------- \|a \|b \|b
+--R 6| 5
+--R \| 46656a b
+--R *
+--R +-----------+5 +-----------+4
+--R 4 | 1 3 | 1 2
+--R log(7776a b x |- --------- - 1296a b |- --------- + x )
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R +-----------+ +-----------+5
+--R | 1 6+-+3+-+2 6+-+5 4 | 1
+--R 6 |- --------- \|a \|b \|b log(7776a b |- --------- + x)
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R +-----------+ +-----------+5
+--R | 1 6+-+3+-+2 6+-+5 4 | 1
+--R - 6 |- --------- \|a \|b \|b log(- 7776a b |- --------- + x)
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R -
+--R +-----------+
+--R | 1 6+-+3+-+2 6+-+5
+--R 3 |- --------- \|a \|b \|b
+--R 6| 5
+--R \| 46656a b
+--R *
+--R +-----------+5 +-----------+4
+--R 4 | 1 3 | 1 2
+--R log(- 7776a b x |- --------- - 1296a b |- --------- + x )
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R 6+-+
+--R 3+-+2 x\|b
+--R - 2\|b atan(-----)
+--R 6+-+
+--R \|a
+--R +
+--R +-----------+5
+--R 4 +-+ | 1
+--R 3888a b \|3 |- ---------
+--R +-----------+ 6| 5
+--R +-+ | 1 6+-+3+-+2 6+-+5 \| 46656a b
+--R - 6\|3 |- --------- \|a \|b \|b atan(---------------------------)
+--R 6| 5 +-----------+5
+--R \| 46656a b 4 | 1
+--R 3888a b |- --------- - x
+--R 6| 5
+--R \| 46656a b
+--R +
+--R +-----------+5
+--R 4 +-+ | 1
+--R 3888a b \|3 |- ---------
+--R +-----------+ 6| 5
+--R +-+ | 1 6+-+3+-+2 6+-+5 \| 46656a b
+--R 6\|3 |- --------- \|a \|b \|b atan(---------------------------)
+--R 6| 5 +-----------+5
+--R \| 46656a b 4 | 1
+--R 3888a b |- --------- + x
+--R 6| 5
+--R \| 46656a b
+--R *
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R /
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R 6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R 6\|a \|b \|b \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R Type: Expression(Integer)
+--E 1031
+
+--S 1032 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1032
+
+)clear all
+
+--S 1033 of 1347
+t0:=x^3/(a+b*x^6)
+--R
+--R
+--R 3
+--R x
+--R (1) --------
+--R 6
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1033
+
+--S 1034 of 1347
+r0:=-1/6*log(a^(1/3)+b^(1/3)*x^2)/(a^(1/3)*b^(2/3))+1/12*log(a^(2/3)-_
+ a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/(a^(1/3)*b^(2/3))-_
+ 1/2*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/_
+ (a^(1/3)*b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+ 2 3+-+ 3+-+
+--R \|3 log(x \|b - x \|a \|b + \|a ) - 2\|3 log(x \|b + \|a )
+--R +
+--R 2 3+-+ 3+-+
+--R 2x \|b - \|a
+--R 6atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+3+-+2
+--R 12\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1034
+
+--S 1035 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R +-+ 2 3| 2 4 3| 2
+--R - \|3 log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2
+--R +------+2 2 +-+3| 2 +-+
+--R +-+ 2 3| 2 2x \|3 \|- a b - a b\|3
+--R 2\|3 log(x \|- a b + a b) - 6atan(---------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2
+--R 12\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 1035
+
+--S 1036 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R - \|3 \|- a b log(x \|b - x \|a \|b + \|a )
+--R +
+--R +------+
+--R +-+3| 2 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(x \|b + \|a )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 2 3| 2 4 3| 2
+--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2 +------+ 2 3+-+ 3+-+
+--R +-+3+-+3+-+2 2 3| 2 3| 2 2x \|b - \|a
+--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +------+2
+--R 2 +-+3| 2 +-+
+--R 3+-+3+-+2 2x \|3 \|- a b - a b\|3
+--R - 6\|a \|b atan(---------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2 3+-+3+-+2
+--R 12\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1036
+
+--S 1037 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1037
+
+)clear all
+
+--S 1038 of 1347
+t0:=x^2/(a+b*x^6)
+--R
+--R
+--R 2
+--R x
+--R (1) --------
+--R 6
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1038
+
+--S 1039 of 1347
+r0:=1/3*atan(x^3*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b))
+--R
+--R
+--R 3 +-+
+--R x \|b
+--R atan(------)
+--R +-+
+--R \|a
+--R (2) ------------
+--R +-+ +-+
+--R 3\|a \|b
+--R Type: Expression(Integer)
+--E 1039
+
+--S 1040 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 +-----+ 3
+--R (b x - a)\|- a b + 2a b x 3 +---+
+--R log(----------------------------) x \|a b
+--R 6 atan(--------)
+--R b x + a a
+--R (3) [---------------------------------,--------------]
+--R +-----+ +---+
+--R 6\|- a b 3\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1040
+
+--S 1041 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R 6 +-----+ 3 3 +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b
+--R \|a \|b log(----------------------------) - 2\|- a b atan(------)
+--R 6 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 6\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1041
+
+--S 1042 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1042
+
+--S 1043 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R 3 +---+ 3 +-+
+--R +-+ +-+ x \|a b +---+ x \|b
+--R \|a \|b atan(--------) - \|a b atan(------)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 3\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1043
+
+--S 1044 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1044
+
+)clear all
+
+--S 1045 of 1347
+t0:=x/(a+b*x^6)
+--R
+--R
+--R x
+--R (1) --------
+--R 6
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1045
+
+--S 1046 of 1347
+r0:=1/6*log(a^(1/3)+b^(1/3)*x^2)/(a^(2/3)*b^(1/3))-1/12*log(a^(2/3)-_
+ a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/(a^(2/3)*b^(1/3))-_
+ 1/2*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/_
+ (a^(2/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+ 2 3+-+ 3+-+
+--R - \|3 log(x \|b - x \|a \|b + \|a ) + 2\|3 log(x \|b + \|a )
+--R +
+--R 2 3+-+ 3+-+
+--R 2x \|b - \|a
+--R 6atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2 3+-+
+--R 12\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1046
+
+--S 1047 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+ +---+
+--R +-+ 4 3| 2 2 3| 2 2 +-+ 2 3| 2
+--R - \|3 log(x \|a b - a x \|a b + a ) + 2\|3 log(x \|a b + a)
+--R +
+--R +---+
+--R 2 +-+3| 2 +-+
+--R 2x \|3 \|a b - a\|3
+--R 6atan(---------------------)
+--R 3a
+--R /
+--R +---+
+--R +-+3| 2
+--R 12\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 1047
+
+--S 1048 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 4 3| 2 2 3| 2 2
+--R - \|3 \|a \|b log(x \|a b - a x \|a b + a )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 2 3| 2
+--R 2\|3 \|a \|b log(x \|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R \|3 \|a b log(x \|b - x \|a \|b + \|a )
+--R +
+--R +---+
+--R +---+ 2 +-+3| 2 +-+
+--R +-+3| 2 2 3+-+ 3+-+ 3+-+2 3+-+ 2x \|3 \|a b - a\|3
+--R - 2\|3 \|a b log(x \|b + \|a ) + 6\|a \|b atan(---------------------)
+--R 3a
+--R +
+--R +---+ 2 3+-+ 3+-+
+--R 3| 2 2x \|b - \|a
+--R - 6\|a b atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 12\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1048
+
+--S 1049 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1049
+
+)clear all
+
+--S 1050 of 1347
+t0:=1/(a+b*x^6)
+--R
+--R
+--R 1
+--R (1) --------
+--R 6
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1050
+
+--S 1051 of 1347
+r0:=1/3*atan(b^(1/6)*x/a^(1/6))/(a^(5/6)*b^(1/6))+1/3*atan(b^(1/3)*_
+ x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_
+ sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(a^(5/6)*b^(1/3)*_
+ sqrt(2))+1/3*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3)))))*sqrt(b^(1/3)+sqrt(3)*_
+ sqrt(-b^(2/3)))/(a^(5/6)*b^(1/3)*sqrt(2))
+--R
+--R
+--R (2)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R \|b \|\|3 \|- \|b + \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R \|b \|\|3 \|- \|b - \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R 6+-+
+--R +-+3+-+ x\|b
+--R \|2 \|b atan(-----)
+--R 6+-+
+--R \|a
+--R /
+--R +-+6+-+5 3+-+6+-+
+--R 3\|2 \|a \|b \|b
+--R Type: Expression(Integer)
+--E 1051
+
+--S 1052 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+2 +----------+
+--R | 1 2 | 1 | 1 2
+--R |- -------- log(36a |- -------- + 6a x |- -------- + x )
+--R 6| 5 6| 5 6| 5
+--R \| 46656a b \| 46656a b \| 46656a b
+--R +
+--R +----------+ +----------+2 +----------+
+--R | 1 2 | 1 | 1 2
+--R - |- -------- log(36a |- -------- - 6a x |- -------- + x )
+--R 6| 5 6| 5 6| 5
+--R \| 46656a b \| 46656a b \| 46656a b
+--R +
+--R +----------+ +----------+
+--R | 1 | 1
+--R 2 |- -------- log(6a |- -------- + x)
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R +----------+ +----------+
+--R | 1 | 1
+--R - 2 |- -------- log(- 6a |- -------- + x)
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R +----------+
+--R +-+ | 1
+--R 3a\|3 |- --------
+--R +----------+ 6| 5
+--R +-+ | 1 \| 46656a b
+--R 2\|3 |- -------- atan(-------------------)
+--R 6| 5 +----------+
+--R \| 46656a b | 1
+--R 3a |- -------- - x
+--R 6| 5
+--R \| 46656a b
+--R +
+--R +----------+
+--R +-+ | 1
+--R 3a\|3 |- --------
+--R +----------+ 6| 5
+--R +-+ | 1 \| 46656a b
+--R - 2\|3 |- -------- atan(-------------------)
+--R 6| 5 +----------+
+--R \| 46656a b | 1
+--R 3a |- -------- + x
+--R 6| 5
+--R \| 46656a b
+--R /
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 1052
+
+--S 1053 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - 2\|b \|\|3 \|- \|b + \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - 2\|b \|\|3 \|- \|b - \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R +----------+
+--R +-+ | 1 6+-+5 3+-+6+-+
+--R 3\|2 |- -------- \|a \|b \|b
+--R 6| 5
+--R \| 46656a b
+--R *
+--R +----------+2 +----------+
+--R 2 | 1 | 1 2
+--R log(36a |- -------- + 6a x |- -------- + x )
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R -
+--R +----------+
+--R +-+ | 1 6+-+5 3+-+6+-+
+--R 3\|2 |- -------- \|a \|b \|b
+--R 6| 5
+--R \| 46656a b
+--R *
+--R +----------+2 +----------+
+--R 2 | 1 | 1 2
+--R log(36a |- -------- - 6a x |- -------- + x )
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R +----------+ +----------+
+--R +-+ | 1 6+-+5 3+-+6+-+ | 1
+--R 6\|2 |- -------- \|a \|b \|b log(6a |- -------- + x)
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R +----------+ +----------+
+--R +-+ | 1 6+-+5 3+-+6+-+ | 1
+--R - 6\|2 |- -------- \|a \|b \|b log(- 6a |- -------- + x)
+--R 6| 5 6| 5
+--R \| 46656a b \| 46656a b
+--R +
+--R 6+-+
+--R +-+3+-+ x\|b
+--R - 2\|2 \|b atan(-----)
+--R 6+-+
+--R \|a
+--R +
+--R +----------+
+--R +-+ | 1
+--R 3a\|3 |- --------
+--R +----------+ 6| 5
+--R +-+ +-+ | 1 6+-+5 3+-+6+-+ \| 46656a b
+--R 6\|2 \|3 |- -------- \|a \|b \|b atan(-------------------)
+--R 6| 5 +----------+
+--R \| 46656a b | 1
+--R 3a |- -------- - x
+--R 6| 5
+--R \| 46656a b
+--R +
+--R +----------+
+--R +-+ | 1
+--R 3a\|3 |- --------
+--R +----------+ 6| 5
+--R +-+ +-+ | 1 6+-+5 3+-+6+-+ \| 46656a b
+--R - 6\|2 \|3 |- -------- \|a \|b \|b atan(-------------------)
+--R 6| 5 +----------+
+--R \| 46656a b | 1
+--R 3a |- -------- + x
+--R 6| 5
+--R \| 46656a b
+--R /
+--R +-+6+-+5 3+-+6+-+
+--R 6\|2 \|a \|b \|b
+--R Type: Expression(Integer)
+--E 1053
+
+--S 1054 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1054
+
+)clear all
+
+--S 1055 of 1347
+t0:=1/(x*(a+b*x^6))
+--R
+--R
+--R 1
+--R (1) ----------
+--R 7
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1055
+
+--S 1056 of 1347
+r0:=log(x)/a-1/6*log(a+b*x^6)/a
+--R
+--R
+--R 6
+--R - log(b x + a) + 6log(x)
+--R (2) -------------------------
+--R 6a
+--R Type: Expression(Integer)
+--E 1056
+
+--S 1057 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6
+--R - log(b x + a) + 6log(x)
+--R (3) -------------------------
+--R 6a
+--R Type: Union(Expression(Integer),...)
+--E 1057
+
+--S 1058 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1058
+
+--S 1059 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1059
+
+)clear all
+
+--S 1060 of 1347
+t0:=1/(x^2*(a+b*x^6))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 8 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1060
+
+--S 1061 of 1347
+r0:=(-1)/(a*x)-1/3*b^(1/6)*atan(b^(1/6)*x/a^(1/6))/a^(7/6)-_
+ 1/3*b^(1/3)*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3)))))*sqrt(2)/(a^(7/6)*sqrt(-b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3))))+1/3*b^(1/3)*atanh(b^(1/3)*x*_
+ sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_
+ sqrt(2)/(a^(7/6)*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))
+--R
+--R
+--R (2)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R x\|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - x\|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R +---------------------+
+--R 6+-+ | +-------+
+--R 6+-+ x\|b 6+-+ | +-+ | 3+-+2 3+-+
+--R (- x\|b atan(-----) - 3\|a )\|\|3 \|- \|b - \|b
+--R 6+-+
+--R \|a
+--R *
+--R +---------------------+
+--R | +-------+
+--R | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b + \|b
+--R /
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R 3a x\|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R Type: Expression(Integer)
+--E 1061
+
+--S 1062 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+5 +---------+4
+--R | b 6 | b 5 | b 2
+--R - a x |- ------- log(7776a x |- ------- - 1296a |- ------- + b x )
+--R 6| 7 6| 7 6| 7
+--R \| 46656a \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+5
+--R | b 6 | b
+--R - 2a x |- ------- log(7776a |- ------- + b x)
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+5
+--R | b 6 | b
+--R 2a x |- ------- log(- 7776a |- ------- + b x)
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+5 +---------+4
+--R | b 6 | b 5 | b 2
+--R a x |- ------- log(- 7776a x |- ------- - 1296a |- ------- + b x )
+--R 6| 7 6| 7 6| 7
+--R \| 46656a \| 46656a \| 46656a
+--R +
+--R +---------+5
+--R 6 +-+ | b
+--R 3888a \|3 |- -------
+--R +---------+ 6| 7
+--R +-+ | b \| 46656a
+--R 2a x\|3 |- ------- atan(-------------------------)
+--R 6| 7 +---------+5
+--R \| 46656a 6 | b
+--R 3888a |- ------- - b x
+--R 6| 7
+--R \| 46656a
+--R +
+--R +---------+5
+--R 6 +-+ | b
+--R 3888a \|3 |- -------
+--R +---------+ 6| 7
+--R +-+ | b \| 46656a
+--R - 2a x\|3 |- ------- atan(------------------------- - 2
+--R 6| 7 +---------+5
+--R \| 46656a 6 | b
+--R 3888a |- ------- + b x
+--R 6| 7
+--R \| 46656a
+--R /
+--R 2a x
+--R Type: Union(Expression(Integer),...)
+--E 1062
+
+--S 1063 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - 2\|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R 2\|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R -
+--R +---------+
+--R | b 6+-+
+--R 3a |- ------- \|a
+--R 6| 7
+--R \| 46656a
+--R *
+--R +---------+5 +---------+4
+--R 6 | b 5 | b 2
+--R log(7776a x |- ------- - 1296a |- ------- + b x )
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+5
+--R | b 6+-+ 6 | b
+--R - 6a |- ------- \|a log(7776a |- ------- + b x)
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+5
+--R | b 6+-+ 6 | b
+--R 6a |- ------- \|a log(- 7776a |- ------- + b x)
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R +---------+
+--R | b 6+-+
+--R 3a |- ------- \|a
+--R 6| 7
+--R \| 46656a
+--R *
+--R +---------+5 +---------+4
+--R 6 | b 5 | b 2
+--R log(- 7776a x |- ------- - 1296a |- ------- + b x )
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R 6+-+
+--R 6+-+ x\|b
+--R 2\|b atan(-----)
+--R 6+-+
+--R \|a
+--R +
+--R +---------+5
+--R 6 +-+ | b
+--R 3888a \|3 |- -------
+--R +---------+ 6| 7
+--R +-+ | b 6+-+ \| 46656a
+--R 6a\|3 |- ------- \|a atan(-------------------------)
+--R 6| 7 +---------+5
+--R \| 46656a 6 | b
+--R 3888a |- ------- - b x
+--R 6| 7
+--R \| 46656a
+--R +
+--R +---------+5
+--R 6 +-+ | b
+--R 3888a \|3 |- -------
+--R +---------+ 6| 7
+--R +-+ | b 6+-+ \| 46656a
+--R - 6a\|3 |- ------- \|a atan(-------------------------)
+--R 6| 7 +---------+5
+--R \| 46656a 6 | b
+--R 3888a |- ------- + b x
+--R 6| 7
+--R \| 46656a
+--R *
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R /
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R 6a\|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R Type: Expression(Integer)
+--E 1063
+
+--S 1064 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1064
+
+)clear all
+
+--S 1065 of 1347
+t0:=1/(x^3*(a+b*x^6))
+--R
+--R
+--R 1
+--R (1) -----------
+--R 9 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1065
+
+--S 1066 of 1347
+r0:=(-1/2)/(a*x^2)+1/6*b^(1/3)*log(a^(1/3)+b^(1/3)*x^2)/a^(4/3)-_
+ 1/12*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/a^(4/3)+_
+ 1/2*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*_
+ sqrt(3)))/(a^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R - x \|3 \|b log(x \|b - x \|a \|b + \|a )
+--R +
+--R 2 3+-+ 3+-+
+--R 2 +-+3+-+ 2 3+-+ 3+-+ 2 3+-+ 2x \|b - \|a +-+3+-+
+--R 2x \|3 \|b log(x \|b + \|a ) - 6x \|b atan(-------------- - 6\|3 \|a
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 2 +-+3+-+
+--R 12a x \|3 \|a
+--R Type: Expression(Integer)
+--E 1066
+
+--S 1067 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2
+--R 2 +-+ |b |b 2
+--R 2x \|3 3|- log(a 3|- + b x )
+--R \|a \|a
+--R +
+--R +-+ +-+2 +-+
+--R 2 +-+ |b 2 |b |b 4
+--R - x \|3 3|- log(- a x 3|- + a 3|- + b x )
+--R \|a \|a \|a
+--R +
+--R +-+2
+--R +-+ |b 2 +-+
+--R +-+ a\|3 3|- - 2b x \|3
+--R 2 |b \|a +-+
+--R 6x 3|- atan(---------------------- - 6\|3
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R /
+--R 2 +-+
+--R 12a x \|3
+--R Type: Union(Expression(Integer),...)
+--E 1067
+
+--S 1068 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+
+--R \|3 \|b log(x \|b - x \|a \|b + \|a ) - 2\|3 \|b log(x \|b + \|a )
+--R +
+--R +-+ +-+2
+--R +-+3+-+ |b |b 2
+--R 2\|3 \|a 3|- log(a 3|- + b x )
+--R \|a \|a
+--R +
+--R +-+ +-+2 +-+ 2 3+-+ 3+-+
+--R +-+3+-+ |b 2 |b |b 4 3+-+ 2x \|b - \|a
+--R - \|3 \|a 3|- log(- a x 3|- + a 3|- + b x + 6\|b atan(--------------)
+--R \|a \|a \|a +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+2
+--R +-+ |b 2 +-+
+--R +-+ a\|3 3|- - 2b x \|3
+--R 3+-+ |b \|a
+--R 6\|a 3|- atan(----------------------)
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R /
+--R +-+3+-+
+--R 12a\|3 \|a
+--R Type: Expression(Integer)
+--E 1068
+
+--S 1069 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1069
+
+)clear all
+
+--S 1070 of 1347
+t0:=1/(x^4*(a+b*x^6))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 10 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1070
+
+--S 1071 of 1347
+r0:=(-1/3)/(a*x^3)-1/3*atan(x^3*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2)
+--R
+--R
+--R 3 +-+
+--R 3 +-+ x \|b +-+
+--R - x \|b atan(------) - \|a
+--R +-+
+--R \|a
+--R (2) ---------------------------
+--R 3 +-+
+--R 3a x \|a
+--R Type: Expression(Integer)
+--E 1071
+
+--S 1072 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+ +-+
+--R 3 | b 6 |b
+--R +---+ - 2a x |- - + b x - a +-+ a |-
+--R 3 | b \| a 3 |b \|a
+--R x |- - log(------------------------) - 2 x |- atan(-----) - 1
+--R \| a 6 \|a 3
+--R b x + a b x
+--R (3) [-----------------------------------------,---------------------]
+--R 3 3
+--R 6a x 3a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1072
+
+--S 1073 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R 3 | b 6
+--R +---+ - 2a x |- - + b x - a 3 +-+
+--R | b +-+ \| a +-+ x \|b
+--R |- - \|a log(------------------------) + 2\|b atan(------)
+--R \| a 6 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R +-+
+--R 6a\|a
+--R Type: Expression(Integer)
+--E 1073
+
+--S 1074 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1074
+
+--S 1075 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R 3 +-+ +-+ a |-
+--R +-+ x \|b +-+ |b \|a
+--R \|b atan(------) + \|a |- atan(-----)
+--R +-+ \|a 3
+--R \|a b x
+--R (6) --------------------------------------
+--R +-+
+--R 3a\|a
+--R Type: Expression(Integer)
+--E 1075
+
+--S 1076 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1076
+
+)clear all
+
+--S 1077 of 1347
+t0:=x^8/(a+b*x^6)^2
+--R
+--R
+--R 8
+--R x
+--R (1) --------------------
+--R 2 12 6 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1077
+
+--S 1078 of 1347
+r0:=-1/6*x^3/(b*(a+b*x^6))+1/6*atan(x^3*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R 3 +-+
+--R 6 x \|b 3 +-+ +-+
+--R (b x + a)atan(------) - x \|a \|b
+--R +-+
+--R \|a
+--R (2) -----------------------------------
+--R 2 6 +-+ +-+
+--R (6b x + 6a b)\|a \|b
+--R Type: Expression(Integer)
+--E 1078
+
+--S 1079 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 +-----+ 3
+--R 6 (b x - a)\|- a b + 2a b x 3 +-----+
+--R (b x + a)log(----------------------------) - 2x \|- a b
+--R 6
+--R b x + a
+--R [---------------------------------------------------------,
+--R 2 6 +-----+
+--R (12b x + 12a b)\|- a b
+--R 3 +---+
+--R 6 x \|a b 3 +---+
+--R (b x + a)atan(--------) - x \|a b
+--R a
+--R -----------------------------------]
+--R 2 6 +---+
+--R (6b x + 6a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1079
+
+--S 1080 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R 6 +-----+ 3 3 +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b
+--R \|a \|b log(----------------------------) - 2\|- a b atan(------)
+--R 6 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 12b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1080
+
+--S 1081 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1081
+
+--S 1082 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R 3 +---+ 3 +-+
+--R +-+ +-+ x \|a b +---+ x \|b
+--R \|a \|b atan(--------) - \|a b atan(------)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 6b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1082
+
+--S 1083 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1083
+
+)clear all
+
+--S 1084 of 1347
+t0:=x^7/(a+b*x^6)^2
+--R
+--R
+--R 7
+--R x
+--R (1) --------------------
+--R 2 12 6 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1084
+
+--S 1085 of 1347
+r0:=-1/6*x^2/(b*(a+b*x^6))+1/18*log(a^(1/3)+b^(1/3)*x^2)/_
+ (a^(2/3)*b^(4/3))-1/36*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+_
+ b^(2/3)*x^4)/(a^(2/3)*b^(4/3))-1/6*atan((a^(1/3)-_
+ 2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 6 +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R (- b x - a)\|3 log(x \|b - x \|a \|b + \|a )
+--R +
+--R 2 3+-+ 3+-+
+--R 6 +-+ 2 3+-+ 3+-+ 6 2x \|b - \|a
+--R (2b x + 2a)\|3 log(x \|b + \|a ) + (6b x + 6a)atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 +-+3+-+2 3+-+
+--R - 6x \|3 \|a \|b
+--R /
+--R 2 6 +-+3+-+2 3+-+
+--R (36b x + 36a b)\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1085
+
+--S 1086 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 6 +-+ 4 3| 2 2 3| 2 2
+--R (- b x - a)\|3 log(x \|a b - a x \|a b + a )
+--R +
+--R +---+
+--R 6 +-+ 2 3| 2
+--R (2b x + 2a)\|3 log(x \|a b + a)
+--R +
+--R +---+
+--R 2 +-+3| 2 +-+ +---+
+--R 6 2x \|3 \|a b - a\|3 2 +-+3| 2
+--R (6b x + 6a)atan(---------------------) - 6x \|3 \|a b
+--R 3a
+--R /
+--R +---+
+--R 2 6 +-+3| 2
+--R (36b x + 36a b)\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 1086
+
+--S 1087 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 4 3| 2 2 3| 2 2
+--R - \|3 \|a \|b log(x \|a b - a x \|a b + a )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 2 3| 2
+--R 2\|3 \|a \|b log(x \|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R \|3 \|a b log(x \|b - x \|a \|b + \|a )
+--R +
+--R +---+
+--R +---+ 2 +-+3| 2 +-+
+--R +-+3| 2 2 3+-+ 3+-+ 3+-+2 3+-+ 2x \|3 \|a b - a\|3
+--R - 2\|3 \|a b log(x \|b + \|a ) + 6\|a \|b atan(---------------------)
+--R 3a
+--R +
+--R +---+ 2 3+-+ 3+-+
+--R 3| 2 2x \|b - \|a
+--R - 6\|a b atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 36b\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1087
+
+--S 1088 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1088
+
+)clear all
+
+--S 1089 of 1347
+t0:=x^6/(a+b*x^6)^2
+--R
+--R
+--R 6
+--R x
+--R (1) --------------------
+--R 2 12 6 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1089
+
+--S 1090 of 1347
+r0:=-1/6*x/(b*(a+b*x^6))+1/18*atan(b^(1/6)*x/a^(1/6))/(a^(5/6)*_
+ b^(7/6))+1/18*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3)))))*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/_
+ (a^(5/6)*b^(4/3)*sqrt(2))+1/18*atanh(b^(1/3)*x*sqrt(2)/_
+ (a^(1/6)*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_
+ sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(a^(5/6)*b^(4/3)*sqrt(2))
+--R
+--R
+--R (2)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R (b x + a)\|b \|\|3 \|- \|b + \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R (b x + a)\|b \|\|3 \|- \|b - \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R 6+-+
+--R 6 +-+3+-+ x\|b +-+6+-+5 3+-+6+-+
+--R (b x + a)\|2 \|b atan(-----) - 3x\|2 \|a \|b \|b
+--R 6+-+
+--R \|a
+--R /
+--R 2 6 +-+6+-+5 3+-+6+-+
+--R (18b x + 18a b)\|2 \|a \|b \|b
+--R Type: Expression(Integer)
+--E 1090
+
+--S 1091 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------------+
+--R 2 6 | 1
+--R (3b x + 3a b) |- --------------
+--R 6| 5 7
+--R \| 2176782336a b
+--R *
+--R +----------------+2 +----------------+
+--R 2 2 | 1 | 1 2
+--R log(1296a b |- -------------- + 36a b x |- -------------- + x )
+--R 6| 5 7 6| 5 7
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+
+--R 2 6 | 1
+--R (- 3b x - 3a b) |- --------------
+--R 6| 5 7
+--R \| 2176782336a b
+--R *
+--R +----------------+2 +----------------+
+--R 2 2 | 1 | 1 2
+--R log(1296a b |- -------------- - 36a b x |- -------------- + x )
+--R 6| 5 7 6| 5 7
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+ +----------------+
+--R 2 6 | 1 | 1
+--R (6b x + 6a b) |- -------------- log(36a b |- -------------- + x)
+--R 6| 5 7 6| 5 7
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+ +----------------+
+--R 2 6 | 1 | 1
+--R (- 6b x - 6a b) |- -------------- log(- 36a b |- -------------- + x)
+--R 6| 5 7 6| 5 7
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+
+--R +-+ | 1
+--R 18a b\|3 |- --------------
+--R +----------------+ 6| 5 7
+--R 2 6 +-+ | 1 \| 2176782336a b
+--R (6b x + 6a b)\|3 |- -------------- atan(----------------------------)
+--R 6| 5 7 +----------------+
+--R \| 2176782336a b | 1
+--R 18a b |- -------------- - x
+--R 6| 5 7
+--R \| 2176782336a b
+--R +
+--R +----------------+
+--R +-+ | 1
+--R 18a b\|3 |- --------------
+--R +----------------+ 6| 5 7
+--R 2 6 +-+ | 1 \| 2176782336a b
+--R (- 6b x - 6a b)\|3 |- -------------- atan(----------------------------)
+--R 6| 5 7 +----------------+
+--R \| 2176782336a b | 1
+--R 18a b |- -------------- + x
+--R 6| 5 7
+--R \| 2176782336a b
+--R +
+--R - x
+--R /
+--R 2 6
+--R 6b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 1091
+
+--S 1092 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - \|b \|\|3 \|- \|b + \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - \|b \|\|3 \|- \|b - \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R +----------------+
+--R +-+ | 1 6+-+5 3+-+6+-+
+--R 9b\|2 |- -------------- \|a \|b \|b
+--R 6| 5 7
+--R \| 2176782336a b
+--R *
+--R +----------------+2 +----------------+
+--R 2 2 | 1 | 1 2
+--R log(1296a b |- -------------- + 36a b x |- -------------- + x )
+--R 6| 5 7 6| 5 7
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R -
+--R +----------------+
+--R +-+ | 1 6+-+5 3+-+6+-+
+--R 9b\|2 |- -------------- \|a \|b \|b
+--R 6| 5 7
+--R \| 2176782336a b
+--R *
+--R +----------------+2 +----------------+
+--R 2 2 | 1 | 1 2
+--R log(1296a b |- -------------- - 36a b x |- -------------- + x )
+--R 6| 5 7 6| 5 7
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+ +----------------+
+--R +-+ | 1 6+-+5 3+-+6+-+ | 1
+--R 18b\|2 |- -------------- \|a \|b \|b log(36a b |- -------------- + x)
+--R 6| 5 7 6| 5 7
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R -
+--R +----------------+
+--R +-+ | 1 6+-+5 3+-+6+-+
+--R 18b\|2 |- -------------- \|a \|b \|b
+--R 6| 5 7
+--R \| 2176782336a b
+--R *
+--R +----------------+
+--R | 1
+--R log(- 36a b |- -------------- + x)
+--R 6| 5 7
+--R \| 2176782336a b
+--R +
+--R 6+-+
+--R +-+3+-+ x\|b
+--R - \|2 \|b atan(-----)
+--R 6+-+
+--R \|a
+--R +
+--R +----------------+
+--R +-+ +-+ | 1 6+-+5 3+-+6+-+
+--R 18b\|2 \|3 |- -------------- \|a \|b \|b
+--R 6| 5 7
+--R \| 2176782336a b
+--R *
+--R +----------------+
+--R +-+ | 1
+--R 18a b\|3 |- --------------
+--R 6| 5 7
+--R \| 2176782336a b
+--R atan(----------------------------)
+--R +----------------+
+--R | 1
+--R 18a b |- -------------- - x
+--R 6| 5 7
+--R \| 2176782336a b
+--R +
+--R -
+--R +----------------+
+--R +-+ +-+ | 1 6+-+5 3+-+6+-+
+--R 18b\|2 \|3 |- -------------- \|a \|b \|b
+--R 6| 5 7
+--R \| 2176782336a b
+--R *
+--R +----------------+
+--R +-+ | 1
+--R 18a b\|3 |- --------------
+--R 6| 5 7
+--R \| 2176782336a b
+--R atan(----------------------------)
+--R +----------------+
+--R | 1
+--R 18a b |- -------------- + x
+--R 6| 5 7
+--R \| 2176782336a b
+--R /
+--R +-+6+-+5 3+-+6+-+
+--R 18b\|2 \|a \|b \|b
+--R Type: Expression(Integer)
+--E 1092
+
+--S 1093 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1093
+
+)clear all
+
+--S 1094 of 1347
+t0:=x^5/(a+b*x^6)^2
+--R
+--R
+--R 5
+--R x
+--R (1) --------------------
+--R 2 12 6 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1094
+
+--S 1095 of 1347
+r0:=(-1/6)/(b*(a+b*x^6))
+--R
+--R
+--R 1
+--R -
+--R 6
+--R (2) - ----------
+--R 2 6
+--R b x + a b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 1095
+
+--S 1096 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ------------
+--R 2 6
+--R 6b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 1096
+
+--S 1097 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1097
+
+--S 1098 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1098
+
+)clear all
+
+--S 1099 of 1347
+t0:=x^4/(a+b*x^6)^2
+--R
+--R
+--R 4
+--R x
+--R (1) --------------------
+--R 2 12 6 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1099
+
+--S 1100 of 1347
+r0:=1/6*x^5/(a*(a+b*x^6))+1/18*atan(b^(1/6)*x/a^(1/6))/_
+ (a^(7/6)*b^(5/6))+1/9*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*_
+ sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))/(a^(7/6)*b^(2/3)*_
+ sqrt(2)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))-1/9*_
+ atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+sqrt(3)*_
+ sqrt(-b^(2/3)))))/(a^(7/6)*b^(2/3)*sqrt(2)*_
+ sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))
+--R
+--R
+--R (2)
+--R +---------------------+
+--R | +-------+
+--R 6 6+-+5 | +-+ | 3+-+2 3+-+
+--R (- 2b x - 2a)\|b \|\|3 \|- \|b - \|b
+--R *
+--R +-+3+-+
+--R x\|2 \|b
+--R atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+
+--R 6 6+-+5 | +-+ | 3+-+2 3+-+
+--R (2b x + 2a)\|b \|\|3 \|- \|b + \|b
+--R *
+--R +-+3+-+
+--R x\|2 \|b
+--R atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R 6+-+
+--R 6 +-+3+-+2 x\|b 5 +-+6+-+3+-+2 6+-+5
+--R ((b x + a)\|2 \|b atan(-----) + 3x \|2 \|a \|b \|b )
+--R 6+-+
+--R \|a
+--R *
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R /
+--R +---------------------+
+--R | +-------+
+--R 6 2 +-+6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+
+--R (18a b x + 18a )\|2 \|a \|b \|b \|\|3 \|- \|b - \|b
+--R *
+--R +---------------------+
+--R | +-------+
+--R | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b + \|b
+--R Type: Expression(Integer)
+--E 1100
+
+--S 1101 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------------+
+--R 6 2 | 1
+--R (3a b x + 3a ) |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R log
+--R +----------------+5
+--R 6 4 | 1
+--R 60466176a b x |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+4
+--R 5 3 | 1 2
+--R - 1679616a b |- -------------- + x
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+
+--R 6 2 | 1
+--R (6a b x + 6a ) |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R +----------------+5
+--R 6 4 | 1
+--R log(60466176a b |- -------------- + x)
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+
+--R 6 2 | 1
+--R (- 6a b x - 6a ) |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R +----------------+5
+--R 6 4 | 1
+--R log(- 60466176a b |- -------------- + x)
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+
+--R 6 2 | 1
+--R (- 3a b x - 3a ) |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R log
+--R +----------------+5
+--R 6 4 | 1
+--R - 60466176a b x |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+4
+--R 5 3 | 1 2
+--R - 1679616a b |- -------------- + x
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+
+--R 6 2 +-+ | 1
+--R (- 6a b x - 6a )\|3 |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R +----------------+5
+--R 6 4 +-+ | 1
+--R 30233088a b \|3 |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R atan(------------------------------------)
+--R +----------------+5
+--R 6 4 | 1
+--R 30233088a b |- -------------- - x
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+
+--R 6 2 +-+ | 1
+--R (6a b x + 6a )\|3 |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R +----------------+5
+--R 6 4 +-+ | 1
+--R 30233088a b \|3 |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R atan(------------------------------------)
+--R +----------------+5
+--R 6 4 | 1
+--R 30233088a b |- -------------- + x
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R 5
+--R x
+--R /
+--R 6 2
+--R 6a b x + 6a
+--R Type: Union(Expression(Integer),...)
+--E 1101
+
+--S 1102 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R 2\|b \|\|3 \|- \|b - \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - 2\|b \|\|3 \|- \|b + \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R +----------------+
+--R +-+ | 1 6+-+3+-+2 6+-+5
+--R 9a\|2 |- -------------- \|a \|b \|b
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R log
+--R +----------------+5
+--R 6 4 | 1
+--R 60466176a b x |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+4
+--R 5 3 | 1 2
+--R - 1679616a b |- -------------- + x
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+
+--R +-+ | 1 6+-+3+-+2 6+-+5
+--R 18a\|2 |- -------------- \|a \|b \|b
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R +----------------+5
+--R 6 4 | 1
+--R log(60466176a b |- -------------- + x)
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R -
+--R +----------------+
+--R +-+ | 1 6+-+3+-+2 6+-+5
+--R 18a\|2 |- -------------- \|a \|b \|b
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R +----------------+5
+--R 6 4 | 1
+--R log(- 60466176a b |- -------------- + x)
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R -
+--R +----------------+
+--R +-+ | 1 6+-+3+-+2 6+-+5
+--R 9a\|2 |- -------------- \|a \|b \|b
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R log
+--R +----------------+5
+--R 6 4 | 1
+--R - 60466176a b x |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+4
+--R 5 3 | 1 2
+--R - 1679616a b |- -------------- + x
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R 6+-+
+--R +-+3+-+2 x\|b
+--R - \|2 \|b atan(-----)
+--R 6+-+
+--R \|a
+--R +
+--R -
+--R +----------------+
+--R +-+ +-+ | 1 6+-+3+-+2 6+-+5
+--R 18a\|2 \|3 |- -------------- \|a \|b \|b
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R +----------------+5
+--R 6 4 +-+ | 1
+--R 30233088a b \|3 |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R atan(------------------------------------)
+--R +----------------+5
+--R 6 4 | 1
+--R 30233088a b |- -------------- - x
+--R 6| 7 5
+--R \| 2176782336a b
+--R +
+--R +----------------+
+--R +-+ +-+ | 1 6+-+3+-+2 6+-+5
+--R 18a\|2 \|3 |- -------------- \|a \|b \|b
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R +----------------+5
+--R 6 4 +-+ | 1
+--R 30233088a b \|3 |- --------------
+--R 6| 7 5
+--R \| 2176782336a b
+--R atan(------------------------------------)
+--R +----------------+5
+--R 6 4 | 1
+--R 30233088a b |- -------------- + x
+--R 6| 7 5
+--R \| 2176782336a b
+--R *
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R /
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R +-+6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R 18a\|2 \|a \|b \|b \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R Type: Expression(Integer)
+--E 1102
+
+--S 1103 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1103
+
+)clear all
+
+--S 1104 of 1347
+t0:=x^3/(a+b*x^6)^2
+--R
+--R
+--R 3
+--R x
+--R (1) --------------------
+--R 2 12 6 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1104
+
+--S 1105 of 1347
+r0:=1/6*x^4/(a*(a+b*x^6))-1/18*log(a^(1/3)+b^(1/3)*x^2)/_
+ (a^(4/3)*b^(2/3))+1/36*log(a^(2/3)-a^(1/3)*b^(1/3)*_
+ x^2+b^(2/3)*x^4)/(a^(4/3)*b^(2/3))-1/6*atan((a^(1/3)-_
+ 2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(4/3)*b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 6 +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R (b x + a)\|3 log(x \|b - x \|a \|b + \|a )
+--R +
+--R 2 3+-+ 3+-+
+--R 6 +-+ 2 3+-+ 3+-+ 6 2x \|b - \|a
+--R (- 2b x - 2a)\|3 log(x \|b + \|a ) + (6b x + 6a)atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 4 +-+3+-+3+-+2
+--R 6x \|3 \|a \|b
+--R /
+--R 6 2 +-+3+-+3+-+2
+--R (36a b x + 36a )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1105
+
+--S 1106 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R 6 +-+ 2 3| 2 4 3| 2
+--R (- b x - a)\|3 log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2
+--R 6 +-+ 2 3| 2
+--R (2b x + 2a)\|3 log(x \|- a b + a b)
+--R +
+--R +------+2
+--R 2 +-+3| 2 +-+ +------+
+--R 6 2x \|3 \|- a b - a b\|3 4 +-+3| 2
+--R (- 6b x - 6a)atan(---------------------------) + 6x \|3 \|- a b
+--R 3a b
+--R /
+--R +------+
+--R 6 2 +-+3| 2
+--R (36a b x + 36a )\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 1106
+
+--S 1107 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R - \|3 \|- a b log(x \|b - x \|a \|b + \|a )
+--R +
+--R +------+
+--R +-+3| 2 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(x \|b + \|a )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 2 3| 2 4 3| 2
+--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b)
+--R +
+--R +------+2 +------+ 2 3+-+ 3+-+
+--R +-+3+-+3+-+2 2 3| 2 3| 2 2x \|b - \|a
+--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +------+2
+--R 2 +-+3| 2 +-+
+--R 3+-+3+-+2 2x \|3 \|- a b - a b\|3
+--R - 6\|a \|b atan(---------------------------)
+--R 3a b
+--R /
+--R +------+
+--R +-+3| 2 3+-+3+-+2
+--R 36a\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1107
+
+--S 1108 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1108
+
+)clear all
+
+--S 1109 of 1347
+t0:=x^2/(a+b*x^6)^2
+--R
+--R
+--R 2
+--R x
+--R (1) --------------------
+--R 2 12 6 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1109
+
+--S 1110 of 1347
+r0:=1/6*x^3/(a*(a+b*x^6))+1/6*atan(x^3*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))
+--R
+--R
+--R 3 +-+
+--R 6 x \|b 3 +-+ +-+
+--R (b x + a)atan(------) + x \|a \|b
+--R +-+
+--R \|a
+--R (2) -----------------------------------
+--R 6 2 +-+ +-+
+--R (6a b x + 6a )\|a \|b
+--R Type: Expression(Integer)
+--E 1110
+
+--S 1111 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 +-----+ 3
+--R 6 (b x - a)\|- a b + 2a b x 3 +-----+
+--R (b x + a)log(----------------------------) + 2x \|- a b
+--R 6
+--R b x + a
+--R [---------------------------------------------------------,
+--R 6 2 +-----+
+--R (12a b x + 12a )\|- a b
+--R 3 +---+
+--R 6 x \|a b 3 +---+
+--R (b x + a)atan(--------) + x \|a b
+--R a
+--R -----------------------------------]
+--R 6 2 +---+
+--R (6a b x + 6a )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1111
+
+--S 1112 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R 6 +-----+ 3 3 +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b
+--R \|a \|b log(----------------------------) - 2\|- a b atan(------)
+--R 6 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 12a\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1112
+
+--S 1113 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1113
+
+--S 1114 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R 3 +---+ 3 +-+
+--R +-+ +-+ x \|a b +---+ x \|b
+--R \|a \|b atan(--------) - \|a b atan(------)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 6a\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1114
+
+--S 1115 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1115
+
+)clear all
+
+--S 1116 of 1347
+t0:=x/(a+b*x^6)^2
+--R
+--R
+--R x
+--R (1) --------------------
+--R 2 12 6 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1116
+
+--S 1117 of 1347
+r0:=1/6*x^2/(a*(a+b*x^6))+1/9*log(a^(1/3)+b^(1/3)*x^2)/_
+ (a^(5/3)*b^(1/3))-1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+_
+ b^(2/3)*x^4)/(a^(5/3)*b^(1/3))-1/3*atan((a^(1/3)-_
+ 2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 6 +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R (- b x - a)\|3 log(x \|b - x \|a \|b + \|a )
+--R +
+--R 2 3+-+ 3+-+
+--R 6 +-+ 2 3+-+ 3+-+ 6 2x \|b - \|a
+--R (2b x + 2a)\|3 log(x \|b + \|a ) + (6b x + 6a)atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 +-+3+-+2 3+-+
+--R 3x \|3 \|a \|b
+--R /
+--R 6 2 +-+3+-+2 3+-+
+--R (18a b x + 18a )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1117
+
+--S 1118 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 6 +-+ 4 3| 2 2 3| 2 2
+--R (- b x - a)\|3 log(x \|a b - a x \|a b + a )
+--R +
+--R +---+
+--R 6 +-+ 2 3| 2
+--R (2b x + 2a)\|3 log(x \|a b + a)
+--R +
+--R +---+
+--R 2 +-+3| 2 +-+ +---+
+--R 6 2x \|3 \|a b - a\|3 2 +-+3| 2
+--R (6b x + 6a)atan(---------------------) + 3x \|3 \|a b
+--R 3a
+--R /
+--R +---+
+--R 6 2 +-+3| 2
+--R (18a b x + 18a )\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 1118
+
+--S 1119 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 4 3| 2 2 3| 2 2
+--R - \|3 \|a \|b log(x \|a b - a x \|a b + a )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 2 3| 2
+--R 2\|3 \|a \|b log(x \|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R \|3 \|a b log(x \|b - x \|a \|b + \|a )
+--R +
+--R +---+
+--R +---+ 2 +-+3| 2 +-+
+--R +-+3| 2 2 3+-+ 3+-+ 3+-+2 3+-+ 2x \|3 \|a b - a\|3
+--R - 2\|3 \|a b log(x \|b + \|a ) + 6\|a \|b atan(---------------------)
+--R 3a
+--R +
+--R +---+ 2 3+-+ 3+-+
+--R 3| 2 2x \|b - \|a
+--R - 6\|a b atan(--------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 18a\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1119
+
+--S 1120 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1120
+
+)clear all
+
+--S 1121 of 1347
+t0:=1/(a+b*x^6)^2
+--R
+--R
+--R 1
+--R (1) --------------------
+--R 2 12 6 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 1121
+
+--S 1122 of 1347
+r0:=1/6*x/(a*(a+b*x^6))+5/18*atan(b^(1/6)*x/a^(1/6))/_
+ (a^(11/6)*b^(1/6))+5/18*atan(b^(1/3)*x*sqrt(2)/_
+ (a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_
+ sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(a^(11/6)*_
+ b^(1/3)*sqrt(2))+5/18*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*_
+ sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*sqrt(b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3)))/(a^(11/6)*b^(1/3)*sqrt(2))
+--R
+--R
+--R (2)
+--R +---------------------+
+--R | +-------+
+--R 6 6+-+ | +-+ | 3+-+2 3+-+
+--R (5b x + 5a)\|b \|\|3 \|- \|b + \|b
+--R *
+--R +-+3+-+
+--R x\|2 \|b
+--R atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+
+--R 6 6+-+ | +-+ | 3+-+2 3+-+
+--R (5b x + 5a)\|b \|\|3 \|- \|b - \|b
+--R *
+--R +-+3+-+
+--R x\|2 \|b
+--R atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R 6+-+
+--R 6 +-+3+-+ x\|b +-+6+-+5 3+-+6+-+
+--R (5b x + 5a)\|2 \|b atan(-----) + 3x\|2 \|a \|b \|b
+--R 6+-+
+--R \|a
+--R /
+--R 6 2 +-+6+-+5 3+-+6+-+
+--R (18a b x + 18a )\|2 \|a \|b \|b
+--R Type: Expression(Integer)
+--E 1122
+
+--S 1123 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------------+
+--R 6 2 | 1
+--R (15a b x + 15a ) |- --------------
+--R 6| 11
+--R \| 2176782336a b
+--R *
+--R +----------------+2 +----------------+
+--R 4 | 1 2 | 1 2
+--R log(1296a |- -------------- + 36a x |- -------------- + x )
+--R 6| 11 6| 11
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+
+--R 6 2 | 1
+--R (- 15a b x - 15a ) |- --------------
+--R 6| 11
+--R \| 2176782336a b
+--R *
+--R +----------------+2 +----------------+
+--R 4 | 1 2 | 1 2
+--R log(1296a |- -------------- - 36a x |- -------------- + x )
+--R 6| 11 6| 11
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+ +----------------+
+--R 6 2 | 1 2 | 1
+--R (30a b x + 30a ) |- -------------- log(36a |- -------------- + x)
+--R 6| 11 6| 11
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+ +----------------+
+--R 6 2 | 1 2 | 1
+--R (- 30a b x - 30a ) |- -------------- log(- 36a |- -------------- + x)
+--R 6| 11 6| 11
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+
+--R 2 +-+ | 1
+--R 18a \|3 |- --------------
+--R +----------------+ 6| 11
+--R 6 2 +-+ | 1 \| 2176782336a b
+--R (30a b x + 30a )\|3 |- -------------- atan(---------------------------)
+--R 6| 11 +----------------+
+--R \| 2176782336a b 2 | 1
+--R 18a |- -------------- - x
+--R 6| 11
+--R \| 2176782336a b
+--R +
+--R +----------------+
+--R 6 2 +-+ | 1
+--R (- 30a b x - 30a )\|3 |- --------------
+--R 6| 11
+--R \| 2176782336a b
+--R *
+--R +----------------+
+--R 2 +-+ | 1
+--R 18a \|3 |- --------------
+--R 6| 11
+--R \| 2176782336a b
+--R atan(---------------------------)
+--R +----------------+
+--R 2 | 1
+--R 18a |- -------------- + x
+--R 6| 11
+--R \| 2176782336a b
+--R +
+--R x
+--R /
+--R 6 2
+--R 6a b x + 6a
+--R Type: Union(Expression(Integer),...)
+--E 1123
+
+--S 1124 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - 5\|b \|\|3 \|- \|b + \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - 5\|b \|\|3 \|- \|b - \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R +----------------+
+--R +-+ | 1 6+-+5 3+-+6+-+
+--R 45a\|2 |- -------------- \|a \|b \|b
+--R 6| 11
+--R \| 2176782336a b
+--R *
+--R +----------------+2 +----------------+
+--R 4 | 1 2 | 1 2
+--R log(1296a |- -------------- + 36a x |- -------------- + x )
+--R 6| 11 6| 11
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R -
+--R +----------------+
+--R +-+ | 1 6+-+5 3+-+6+-+
+--R 45a\|2 |- -------------- \|a \|b \|b
+--R 6| 11
+--R \| 2176782336a b
+--R *
+--R +----------------+2 +----------------+
+--R 4 | 1 2 | 1 2
+--R log(1296a |- -------------- - 36a x |- -------------- + x )
+--R 6| 11 6| 11
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R +----------------+ +----------------+
+--R +-+ | 1 6+-+5 3+-+6+-+ 2 | 1
+--R 90a\|2 |- -------------- \|a \|b \|b log(36a |- -------------- + x)
+--R 6| 11 6| 11
+--R \| 2176782336a b \| 2176782336a b
+--R +
+--R -
+--R +----------------+
+--R +-+ | 1 6+-+5 3+-+6+-+
+--R 90a\|2 |- -------------- \|a \|b \|b
+--R 6| 11
+--R \| 2176782336a b
+--R *
+--R +----------------+
+--R 2 | 1
+--R log(- 36a |- -------------- + x)
+--R 6| 11
+--R \| 2176782336a b
+--R +
+--R 6+-+
+--R +-+3+-+ x\|b
+--R - 5\|2 \|b atan(-----)
+--R 6+-+
+--R \|a
+--R +
+--R +----------------+
+--R +-+ +-+ | 1 6+-+5 3+-+6+-+
+--R 90a\|2 \|3 |- -------------- \|a \|b \|b
+--R 6| 11
+--R \| 2176782336a b
+--R *
+--R +----------------+
+--R 2 +-+ | 1
+--R 18a \|3 |- --------------
+--R 6| 11
+--R \| 2176782336a b
+--R atan(---------------------------)
+--R +----------------+
+--R 2 | 1
+--R 18a |- -------------- - x
+--R 6| 11
+--R \| 2176782336a b
+--R +
+--R -
+--R +----------------+
+--R +-+ +-+ | 1 6+-+5 3+-+6+-+
+--R 90a\|2 \|3 |- -------------- \|a \|b \|b
+--R 6| 11
+--R \| 2176782336a b
+--R *
+--R +----------------+
+--R 2 +-+ | 1
+--R 18a \|3 |- --------------
+--R 6| 11
+--R \| 2176782336a b
+--R atan(---------------------------)
+--R +----------------+
+--R 2 | 1
+--R 18a |- -------------- + x
+--R 6| 11
+--R \| 2176782336a b
+--R /
+--R +-+6+-+5 3+-+6+-+
+--R 18a\|2 \|a \|b \|b
+--R Type: Expression(Integer)
+--E 1124
+
+--S 1125 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1125
+
+)clear all
+
+--S 1126 of 1347
+t0:=1/(x*(a+b*x^6)^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 13 7 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1126
+
+--S 1127 of 1347
+r0:=1/6/(a*(a+b*x^6))+log(x)/a^2-1/6*log(a+b*x^6)/a^2
+--R
+--R
+--R 6 6 6
+--R (- b x - a)log(b x + a) + (6b x + 6a)log(x) + a
+--R (2) --------------------------------------------------
+--R 2 6 3
+--R 6a b x + 6a
+--R Type: Expression(Integer)
+--E 1127
+
+--S 1128 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 6 6
+--R (- b x - a)log(b x + a) + (6b x + 6a)log(x) + a
+--R (3) --------------------------------------------------
+--R 2 6 3
+--R 6a b x + 6a
+--R Type: Union(Expression(Integer),...)
+--E 1128
+
+--S 1129 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1129
+
+--S 1130 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1130
+
+)clear all
+
+--S 1131 of 1347
+t0:=1/(x^2*(a+b*x^6)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 2 14 8 2 2
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1131
+
+--S 1132 of 1347
+r0:=(-7/6)/(a^2*x)+1/6/(a*x*(a+b*x^6))-7/18*b^(1/6)*atan(b^(1/6)*_
+ x/a^(1/6))/a^(13/6)-7/9*b^(1/3)*atan(b^(1/3)*x*sqrt(2)/_
+ (a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))/(a^(13/6)*_
+ sqrt(2)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))+7/9*_
+ b^(1/3)*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3)))))/(a^(13/6)*sqrt(2)*sqrt(b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3))))
+--R
+--R
+--R (2)
+--R +---------------------+
+--R | +-------+
+--R 7 3+-+ | +-+ | 3+-+2 3+-+
+--R (14b x + 14a x)\|b \|\|3 \|- \|b - \|b
+--R *
+--R +-+3+-+
+--R x\|2 \|b
+--R atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+
+--R 7 3+-+ | +-+ | 3+-+2 3+-+
+--R (- 14b x - 14a x)\|b \|\|3 \|- \|b + \|b
+--R *
+--R +-+3+-+
+--R x\|2 \|b
+--R atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R 6+-+
+--R 7 +-+6+-+ x\|b 6 +-+6+-+
+--R ((- 7b x - 7a x)\|2 \|b atan(-----) + (- 21b x - 18a)\|2 \|a )
+--R 6+-+
+--R \|a
+--R *
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R /
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R 2 7 3 +-+6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R (18a b x + 18a x)\|2 \|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R Type: Expression(Integer)
+--E 1132
+
+--S 1133 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------------+
+--R 2 7 3 | 117649b
+--R (- 3a b x - 3a x) |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R log
+--R +---------------+5 +---------------+4
+--R 11 | 117649b 9 | 117649b
+--R 60466176a x |- ------------- - 11757312a |- -------------
+--R 6| 13 6| 13
+--R \| 2176782336a \| 2176782336a
+--R +
+--R 2
+--R 16807b x
+--R +
+--R +---------------+
+--R 2 7 3 | 117649b
+--R (- 6a b x - 6a x) |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R +---------------+5
+--R 11 | 117649b
+--R log(60466176a |- ------------- + 16807b x)
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R +---------------+
+--R 2 7 3 | 117649b
+--R (6a b x + 6a x) |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R +---------------+5
+--R 11 | 117649b
+--R log(- 60466176a |- ------------- + 16807b x)
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R +---------------+
+--R 2 7 3 | 117649b
+--R (3a b x + 3a x) |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R log
+--R +---------------+5 +---------------+4
+--R 11 | 117649b 9 | 117649b
+--R - 60466176a x |- ------------- - 11757312a |- -------------
+--R 6| 13 6| 13
+--R \| 2176782336a \| 2176782336a
+--R +
+--R 2
+--R 16807b x
+--R +
+--R +---------------+
+--R 2 7 3 +-+ | 117649b
+--R (6a b x + 6a x)\|3 |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R +---------------+5
+--R 11 +-+ | 117649b
+--R 30233088a \|3 |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R atan(-----------------------------------------)
+--R +---------------+5
+--R 11 | 117649b
+--R 30233088a |- ------------- - 16807b x
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R +---------------+
+--R 2 7 3 +-+ | 117649b
+--R (- 6a b x - 6a x)\|3 |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R +---------------+5
+--R 11 +-+ | 117649b
+--R 30233088a \|3 |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R atan(-----------------------------------------)
+--R +---------------+5
+--R 11 | 117649b
+--R 30233088a |- ------------- + 16807b x
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R 6
+--R - 7b x - 6a
+--R /
+--R 2 7 3
+--R 6a b x + 6a x
+--R Type: Union(Expression(Integer),...)
+--E 1133
+
+--S 1134 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R - 14\|b \|\|3 \|- \|b - \|b atanh(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+3+-+
+--R 3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b
+--R 14\|b \|\|3 \|- \|b + \|b atan(----------------------------)
+--R +---------------------+
+--R | +-------+
+--R 6+-+ | +-+ | 3+-+2 3+-+
+--R \|a \|\|3 \|- \|b - \|b
+--R +
+--R -
+--R +---------------+
+--R 2 +-+ | 117649b 6+-+
+--R 9a \|2 |- ------------- \|a
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R log
+--R +---------------+5
+--R 11 | 117649b
+--R 60466176a x |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R +---------------+4
+--R 9 | 117649b 2
+--R - 11757312a |- ------------- + 16807b x
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R -
+--R +---------------+
+--R 2 +-+ | 117649b 6+-+
+--R 18a \|2 |- ------------- \|a
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R +---------------+5
+--R 11 | 117649b
+--R log(60466176a |- ------------- + 16807b x)
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R +---------------+
+--R 2 +-+ | 117649b 6+-+
+--R 18a \|2 |- ------------- \|a
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R +---------------+5
+--R 11 | 117649b
+--R log(- 60466176a |- ------------- + 16807b x)
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R +---------------+
+--R 2 +-+ | 117649b 6+-+
+--R 9a \|2 |- ------------- \|a
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R log
+--R +---------------+5
+--R 11 | 117649b
+--R - 60466176a x |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R +---------------+4
+--R 9 | 117649b 2
+--R - 11757312a |- ------------- + 16807b x
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R 6+-+
+--R +-+6+-+ x\|b
+--R 7\|2 \|b atan(-----)
+--R 6+-+
+--R \|a
+--R +
+--R +---------------+
+--R 2 +-+ +-+ | 117649b 6+-+
+--R 18a \|2 \|3 |- ------------- \|a
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R +---------------+5
+--R 11 +-+ | 117649b
+--R 30233088a \|3 |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R atan(-----------------------------------------)
+--R +---------------+5
+--R 11 | 117649b
+--R 30233088a |- ------------- - 16807b x
+--R 6| 13
+--R \| 2176782336a
+--R +
+--R -
+--R +---------------+
+--R 2 +-+ +-+ | 117649b 6+-+
+--R 18a \|2 \|3 |- ------------- \|a
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R +---------------+5
+--R 11 +-+ | 117649b
+--R 30233088a \|3 |- -------------
+--R 6| 13
+--R \| 2176782336a
+--R atan(-----------------------------------------)
+--R +---------------+5
+--R 11 | 117649b
+--R 30233088a |- ------------- + 16807b x
+--R 6| 13
+--R \| 2176782336a
+--R *
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R /
+--R +---------------------+ +---------------------+
+--R | +-------+ | +-------+
+--R 2 +-+6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+
+--R 18a \|2 \|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b
+--R Type: Expression(Integer)
+--E 1134
+
+--S 1135 of 1347
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1135
+
+)clear all
+
+--S 1136 of 1347
+t0:=1/(x^3*(a+b*x^6)^2)
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R 2 15 9 2 3
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1136
+
+--S 1137 of 1347
+r0:=(-2/3)/(a^2*x^2)+1/6/(a*x^2*(a+b*x^6))+2/9*b^(1/3)*_
+ log(a^(1/3)+b^(1/3)*x^2)/a^(7/3)-1/9*b^(1/3)*log(a^(2/3)-_
+ a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/a^(7/3)+2/3*b^(1/3)*_
+ atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 8 2 +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2
+--R (- 2b x - 2a x )\|3 \|b log(x \|b - x \|a \|b + \|a )
+--R +
+--R 8 2 +-+3+-+ 2 3+-+ 3+-+
+--R (4b x + 4a x )\|3 \|b log(x \|b + \|a )
+--R +
+--R 2 3+-+ 3+-+
+--R 8 2 3+-+ 2x \|b - \|a 6 +-+3+-+
+--R (- 12b x - 12a x )\|b atan(--------------) + (- 12b x - 9a)\|3 \|a
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R 2 8 3 2 +-+3+-+
+--R (18a b x + 18a x )\|3 \|a
+--R Type: Expression(Integer)
+--E 1137
+
+--S 1138 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2
+--R 8 2 +-+ |b |b 2
+--R (4b x + 4a x )\|3 3|- log(a 3|- + b x )
+--R \|a \|a
+--R +
+--R +-+ +-+2 +-+
+--R 8 2 +-+ |b 2 |b |b 4
+--R (- 2b x - 2a x )\|3 3|- log(- a x 3|- + a 3|- + b x )
+--R \|a \|a \|a
+--R +
+--R +-+2
+--R +-+ |b 2 +-+
+--R +-+ a\|3 3|- - 2b x \|3
+--R 8 2 |b \|a 6 +-+
+--R (12b x + 12a x ) 3|- atan(---------------------- + (- 12b x - 9a)\|3
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R /
+--R 2 8 3 2 +-+
+--R (18a b x + 18a x )\|3
+--R Type: Union(Expression(Integer),...)
+--E 1138
+
+--S 1139 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+
+--R \|3 \|b log(x \|b - x \|a \|b + \|a ) - 2\|3 \|b log(x \|b + \|a )
+--R +
+--R +-+ +-+2
+--R +-+3+-+ |b |b 2
+--R 2\|3 \|a 3|- log(a 3|- + b x )
+--R \|a \|a
+--R +
+--R +-+ +-+2 +-+ 2 3+-+ 3+-+
+--R +-+3+-+ |b 2 |b |b 4 3+-+ 2x \|b - \|a
+--R - \|3 \|a 3|- log(- a x 3|- + a 3|- + b x + 6\|b atan(--------------)
+--R \|a \|a \|a +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+2
+--R +-+ |b 2 +-+
+--R +-+ a\|3 3|- - 2b x \|3
+--R 3+-+ |b \|a
+--R 6\|a 3|- atan(----------------------)
+--R \|a +-+2
+--R |b
+--R 3a 3|-
+--R \|a
+--R /
+--R 2 +-+3+-+
+--R 9a \|3 \|a
+--R Type: Expression(Integer)
+--E 1139
+
+--S 1140 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1140
+
+)clear all
+
+--S 1141 of 1347
+t0:=1/(x^4*(a+b*x^6)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R 2 16 10 2 4
+--R b x + 2a b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 1141
+
+--S 1142 of 1347
+r0:=(-1/2)/(a^2*x^3)+1/6/(a*x^3*(a+b*x^6))-1/2*atan(x^3*_
+ sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2)
+--R
+--R
+--R 3 +-+
+--R 9 3 +-+ x \|b 6 +-+
+--R (- 3b x - 3a x )\|b atan(------) + (- 3b x - 2a)\|a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------
+--R 2 9 3 3 +-+
+--R (6a b x + 6a x )\|a
+--R Type: Expression(Integer)
+--E 1142
+
+--S 1143 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R 3 | b 6
+--R +---+ - 2a x |- - + b x - a
+--R 9 3 | b \| a 6
+--R (3b x + 3a x ) |- - log(------------------------) - 6b x - 4a
+--R \| a 6
+--R b x + a
+--R [---------------------------------------------------------------,
+--R 2 9 3 3
+--R 12a b x + 12a x
+--R +-+
+--R |b
+--R +-+ a |-
+--R 9 3 |b \|a 6
+--R (3b x + 3a x ) |- atan(-----) - 3b x - 2a
+--R \|a 3
+--R b x
+--R -------------------------------------------]
+--R 2 9 3 3
+--R 6a b x + 6a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1143
+
+--S 1144 of 1347
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R 3 | b 6
+--R +---+ - 2a x |- - + b x - a 3 +-+
+--R | b +-+ \| a +-+ x \|b
+--R |- - \|a log(------------------------) + 2\|b atan(------)
+--R \| a 6 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R 2 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 1144
+
+--S 1145 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1145
+
+--S 1146 of 1347
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R 3 +-+ +-+ a |-
+--R +-+ x \|b +-+ |b \|a
+--R \|b atan(------) + \|a |- atan(-----)
+--R +-+ \|a 3
+--R \|a b x
+--R (6) --------------------------------------
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 1146
+
+--S 1147 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1147
+
+)clear all
+
+--S 1148 of 1347
+t0:=x^8/(1-x^6)
+--R
+--R
+--R 8
+--R x
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1148
+
+--S 1149 of 1347
+r0:=-1/3*x^3+1/3*atanh(x^3)
+--R
+--R
+--R 3 3
+--R atanh(x ) - x
+--R (2) --------------
+--R 3
+--R Type: Expression(Integer)
+--E 1149
+
+--S 1150 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3
+--R log(x + 1) - log(x - 1) - 2x
+--R (3) -------------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1150
+
+--S 1151 of 1347
+m0:=a0-r0
+--R
+--R
+--R 3 3 3
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1151
+
+--S 1152 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1152
+
+)clear all
+
+--S 1153 of 1347
+t0:=x^7/(1-x^6)
+--R
+--R
+--R 7
+--R x
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1153
+
+--S 1154 of 1347
+r0:=-1/2*x^2-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)+1/2*atan((1+2*x^2)/_
+ sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x + 1)\|3 2 +-+
+--R \|3 log(x + x + 1) - 2\|3 log(- x + 1) + 6atan(-------------) - 6x \|3
+--R 3
+--R --------------------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1154
+
+--S 1155 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x + 1)\|3 2 +-+
+--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) - 6x \|3
+--R 3
+--R ------------------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 1155
+
+--S 1156 of 1347
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(x - 1) + log(- x + 1)
+--R (4) -----------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1156
+
+--S 1157 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1157
+
+)clear all
+
+--S 1158 of 1347
+t0:=x^6/(1-x^6)
+--R
+--R
+--R 6
+--R x
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1158
+
+--S 1159 of 1347
+r0a:=-x+1/3*atanh(x)+1/6*atanh(x/(1+x^2))+1/2*atan(x*sqrt(3)/(1-x^2))/sqrt(3)
+--R
+--R
+--R +-+
+--R +-+ +-+ x x\|3 +-+
+--R 2\|3 atanh(x) + \|3 atanh(------) - 3atan(------) - 6x\|3
+--R 2 2
+--R x + 1 x - 1
+--R (2) ----------------------------------------------------------
+--R +-+
+--R 6\|3
+--R Type: Expression(Integer)
+--E 1159
+
+--S 1160 of 1347
+r0b:=-x+1/3*atanh(x)-1/12*log(1-x+x^2)+_
+ 1/12*log(1+x+x^2)-1/2*atan((1-2*x)/sqrt(3))/sqrt(3)+_
+ 1/2*atan((1+2*x)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 4\|3 atanh(x)
+--R +
+--R +-+ +-+
+--R (2x + 1)\|3 (2x - 1)\|3 +-+
+--R 6atan(------------) + 6atan(------------) - 12x\|3
+--R 3 3
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1160
+
+--S 1161 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1)
+--R +
+--R +-+ +-+
+--R +-+ (2x + 1)\|3 (2x - 1)\|3 +-+
+--R - 2\|3 log(x - 1) + 6atan(------------) + 6atan(------------) - 12x\|3
+--R 3 3
+--R /
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 1161
+
+--S 1162 of 1347
+m0a:=a0-r0a
+--R
+--R
+--R (5)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1)
+--R +
+--R +-+ +-+ +-+ x
+--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------)
+--R 2
+--R x + 1
+--R +
+--R +-+ +-+ +-+
+--R (2x + 1)\|3 (2x - 1)\|3 x\|3
+--R 6atan(------------) + 6atan(------------) + 6atan(------)
+--R 3 3 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1162
+
+--S 1163 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 1163
+
+--S 1164 of 1347
+m0b:=a0-r0b
+--R
+--R
+--R log(x + 1) - log(x - 1) - 2atanh(x)
+--R (7) -----------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1164
+
+--S 1165 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 1165
+
+)clear all
+
+--S 1166 of 1347
+t0:=x^5/(1-x^6)
+--R
+--R
+--R 5
+--R x
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1166
+
+--S 1167 of 1347
+r0:=-1/6*log(1-x^6)
+--R
+--R
+--R 6
+--R log(- x + 1)
+--R (2) - -------------
+--R 6
+--R Type: Expression(Integer)
+--E 1167
+
+--S 1168 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6
+--R log(x - 1)
+--R (3) - -----------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1168
+
+--S 1169 of 1347
+m0:=a0-r0
+--R
+--R
+--R 6 6
+--R - log(x - 1) + log(- x + 1)
+--R (4) -----------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1169
+
+--S 1170 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1170
+
+)clear all
+
+--S 1171 of 1347
+t0:=x^4/(1-x^6)
+--R
+--R
+--R 4
+--R x
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1171
+
+--S 1172 of 1347
+r0a:=1/3*atanh(x)+1/6*atanh(x/(1+x^2))-1/2*atan(x*sqrt(3)/(1-x^2))/sqrt(3)
+--R
+--R
+--R +-+
+--R +-+ +-+ x x\|3
+--R 2\|3 atanh(x) + \|3 atanh(------) + 3atan(------)
+--R 2 2
+--R x + 1 x - 1
+--R (2) -------------------------------------------------
+--R +-+
+--R 6\|3
+--R Type: Expression(Integer)
+--E 1172
+
+--S 1173 of 1347
+r0b:=1/3*atanh(x)-1/12*log(1-x+x^2)+1/12*log(1+x+x^2)+_
+ 1/2*atan((1-2*x)/sqrt(3))/sqrt(3)-1/2*atan((1+2*x)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 4\|3 atanh(x)
+--R +
+--R +-+ +-+
+--R (2x + 1)\|3 (2x - 1)\|3
+--R - 6atan(------------) - 6atan(------------)
+--R 3 3
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1173
+
+--S 1174 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1)
+--R +
+--R +-+ +-+
+--R +-+ (2x + 1)\|3 (2x - 1)\|3
+--R - 2\|3 log(x - 1) - 6atan(------------) - 6atan(------------)
+--R 3 3
+--R /
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 1174
+
+--S 1175 of 1347
+m0a:=a0-r0a
+--R
+--R
+--R (5)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1)
+--R +
+--R +-+ +-+ +-+ x
+--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------)
+--R 2
+--R x + 1
+--R +
+--R +-+ +-+ +-+
+--R (2x + 1)\|3 (2x - 1)\|3 x\|3
+--R - 6atan(------------) - 6atan(------------) - 6atan(------)
+--R 3 3 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1175
+
+--S 1176 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 1176
+
+--S 1177 of 1347
+m0b:=a0-r0b
+--R
+--R
+--R log(x + 1) - log(x - 1) - 2atanh(x)
+--R (7) -----------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1177
+
+--S 1178 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 1178
+
+)clear all
+
+--S 1179 of 1347
+t0:=x^3/(1-x^6)
+--R
+--R
+--R 3
+--R x
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1179
+
+--S 1180 of 1347
+r0:=-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)-1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3)
+--R
+--R
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x + 1)\|3
+--R \|3 log(x + x + 1) - 2\|3 log(- x + 1) - 6atan(-------------)
+--R 3
+--R (2) ----------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1180
+
+--S 1181 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x + 1)\|3
+--R \|3 log(x + x + 1) - 2\|3 log(x - 1) - 6atan(-------------)
+--R 3
+--R (3) --------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 1181
+
+--S 1182 of 1347
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(x - 1) + log(- x + 1)
+--R (4) -----------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1182
+
+--S 1183 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1183
+
+)clear all
+
+--S 1184 of 1347
+t0:=x^2/(1-x^6)
+--R
+--R
+--R 2
+--R x
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1184
+
+--S 1185 of 1347
+r0:=1/3*atanh(x^3)
+--R
+--R
+--R 3
+--R atanh(x )
+--R (2) ---------
+--R 3
+--R Type: Expression(Integer)
+--E 1185
+
+--S 1186 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R log(x + 1) - log(x - 1)
+--R (3) -------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1186
+
+--S 1187 of 1347
+m0:=a0-r0
+--R
+--R
+--R 3 3 3
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1187
+
+--S 1188 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1188
+
+)clear all
+
+--S 1189 of 1347
+t0:=x/(1-x^6)
+--R
+--R
+--R x
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1189
+
+--S 1190 of 1347
+r0:=-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)+1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3)
+--R
+--R
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x + 1)\|3
+--R \|3 log(x + x + 1) - 2\|3 log(- x + 1) + 6atan(-------------)
+--R 3
+--R (2) ----------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1190
+
+--S 1191 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x + 1)\|3
+--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------)
+--R 3
+--R (3) --------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 1191
+
+--S 1192 of 1347
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(x - 1) + log(- x + 1)
+--R (4) -----------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1192
+
+--S 1193 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1193
+
+)clear all
+
+--S 1194 of 1347
+t0:=1/(1-x^6)
+--R
+--R
+--R 1
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1194
+
+--S 1195 of 1347
+r0a:=1/3*atanh(x)+1/6*atanh(x/(1+x^2))+1/2*atan(x*sqrt(3)/(1-x^2))/sqrt(3)
+--R
+--R
+--R +-+
+--R +-+ +-+ x x\|3
+--R 2\|3 atanh(x) + \|3 atanh(------) - 3atan(------)
+--R 2 2
+--R x + 1 x - 1
+--R (2) -------------------------------------------------
+--R +-+
+--R 6\|3
+--R Type: Expression(Integer)
+--E 1195
+
+--S 1196 of 1347
+r0b:=1/3*atanh(x)-1/12*log(1-x+x^2)+1/12*log(1+x+x^2)-_
+ 1/2*atan((1-2*x)/sqrt(3))/sqrt(3)+1/2*atan((1+2*x)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 4\|3 atanh(x)
+--R +
+--R +-+ +-+
+--R (2x + 1)\|3 (2x - 1)\|3
+--R 6atan(------------) + 6atan(------------)
+--R 3 3
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1196
+
+--S 1197 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1)
+--R +
+--R +-+ +-+
+--R +-+ (2x + 1)\|3 (2x - 1)\|3
+--R - 2\|3 log(x - 1) + 6atan(------------) + 6atan(------------)
+--R 3 3
+--R /
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 1197
+
+--S 1198 of 1347
+m0a:=a0-r0a
+--R
+--R
+--R (5)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1)
+--R +
+--R +-+ +-+ +-+ x
+--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------)
+--R 2
+--R x + 1
+--R +
+--R +-+ +-+ +-+
+--R (2x + 1)\|3 (2x - 1)\|3 x\|3
+--R 6atan(------------) + 6atan(------------) + 6atan(------)
+--R 3 3 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1198
+
+--S 1199 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 1199
+
+--S 1200 of 1347
+m0b:=a0-r0b
+--R
+--R
+--R log(x + 1) - log(x - 1) - 2atanh(x)
+--R (7) -----------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1200
+
+--S 1201 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 1201
+
+)clear all
+
+--S 1202 of 1347
+t0:=1/(x*(1-x^6))
+--R
+--R
+--R 1
+--R (1) - ------
+--R 7
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 1202
+
+--S 1203 of 1347
+r0:=-1/3*atanh(1-2*x^6)
+--R
+--R
+--R 6
+--R atanh(2x - 1)
+--R (2) --------------
+--R 3
+--R Type: Expression(Integer)
+--E 1203
+
+--S 1204 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6
+--R - log(x - 1) + 6log(x)
+--R (3) -----------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1204
+
+--S 1205 of 1347
+m0:=a0-r0
+--R
+--R
+--R 6 6
+--R - log(x - 1) + 6log(x) - 2atanh(2x - 1)
+--R (4) -----------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1205
+
+--S 1206 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1206
+
+)clear all
+
+--S 1207 of 1347
+t0:=1/(x^2*(1-x^6))
+--R
+--R
+--R 1
+--R (1) - -------
+--R 8 2
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 1207
+
+--S 1208 of 1347
+r0a:=(-1)/x+1/3*atanh(x)+1/6*atanh(x/(1+x^2))-1/2*atan(x*sqrt(3)/_
+ (1-x^2))/sqrt(3)
+--R
+--R
+--R +-+
+--R +-+ +-+ x x\|3 +-+
+--R 2x\|3 atanh(x) + x\|3 atanh(------) + 3x atan(------) - 6\|3
+--R 2 2
+--R x + 1 x - 1
+--R (2) -------------------------------------------------------------
+--R +-+
+--R 6x\|3
+--R Type: Expression(Integer)
+--E 1208
+
+--S 1209 of 1347
+r0b:=(-1)/x+1/3*atanh(x)-1/12*log(1-x+x^2)+_
+ 1/12*log(1+x+x^2)+1/2*atan((1-2*x)/sqrt(3))/sqrt(3)-_
+ 1/2*atan((1+2*x)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ 2 +-+
+--R x\|3 log(x + x + 1) - x\|3 log(x - x + 1) + 4x\|3 atanh(x)
+--R +
+--R +-+ +-+
+--R (2x + 1)\|3 (2x - 1)\|3 +-+
+--R - 6x atan(------------) - 6x atan(------------) - 12\|3
+--R 3 3
+--R /
+--R +-+
+--R 12x\|3
+--R Type: Expression(Integer)
+--E 1209
+
+--S 1210 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R +-+ 2 +-+ 2 +-+
+--R x\|3 log(x + x + 1) - x\|3 log(x - x + 1) + 2x\|3 log(x + 1)
+--R +
+--R +-+ +-+
+--R +-+ (2x + 1)\|3 (2x - 1)\|3 +-+
+--R - 2x\|3 log(x - 1) - 6x atan(------------) - 6x atan(------------) - 12\|3
+--R 3 3
+--R /
+--R +-+
+--R 12x\|3
+--R Type: Union(Expression(Integer),...)
+--E 1210
+
+--S 1211 of 1347
+m0a:=a0-r0a
+--R
+--R
+--R (5)
+--R +-+ 2 +-+ 2 +-+
+--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1)
+--R +
+--R +-+ +-+ +-+ x
+--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------)
+--R 2
+--R x + 1
+--R +
+--R +-+ +-+ +-+
+--R (2x + 1)\|3 (2x - 1)\|3 x\|3
+--R - 6atan(------------) - 6atan(------------) - 6atan(------)
+--R 3 3 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1211
+
+--S 1212 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 1212
+
+--S 1213 of 1347
+m0b:=a0-r0b
+--R
+--R
+--R log(x + 1) - log(x - 1) - 2atanh(x)
+--R (7) -----------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1213
+
+--S 1214 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 1214
+
+)clear all
+
+--S 1215 of 1347
+t0:=1/(x^3*(1-x^6))
+--R
+--R
+--R 1
+--R (1) - -------
+--R 9 3
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 1215
+
+--S 1216 of 1347
+r0:=(-1/2)/x^2-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)-_
+ 1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 2 +-+
+--R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3
+--R x \|3 log(x + x + 1) - 2x \|3 log(- x + 1) - 6x atan(-------------)
+--R 3
+--R +
+--R +-+
+--R - 6\|3
+--R /
+--R 2 +-+
+--R 12x \|3
+--R Type: Expression(Integer)
+--E 1216
+
+--S 1217 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 +-+
+--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) - 6x atan(-------------) - 6\|3
+--R 3
+--R ----------------------------------------------------------------------------
+--R 2 +-+
+--R 12x \|3
+--R Type: Union(Expression(Integer),...)
+--E 1217
+
+--S 1218 of 1347
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(x - 1) + log(- x + 1)
+--R (4) -----------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1218
+
+--S 1219 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1219
+
+)clear all
+
+--S 1220 of 1347
+t0:=1/(x^4*(1-x^6))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 10 4
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 1220
+
+--S 1221 of 1347
+r0:=(-1/3)/x^3+1/3*atanh(x^3)
+--R
+--R
+--R 3 3
+--R x atanh(x ) - 1
+--R (2) ---------------
+--R 3
+--R 3x
+--R Type: Expression(Integer)
+--E 1221
+
+--S 1222 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3 3
+--R x log(x + 1) - x log(x - 1) - 2
+--R (3) ---------------------------------
+--R 3
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 1222
+
+--S 1223 of 1347
+m0:=a0-r0
+--R
+--R
+--R 3 3 3
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1223
+
+--S 1224 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1224
+
+)clear all
+
+--S 1225 of 1347
+t0:=1/(x^5*(1-x^6))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 11 5
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 1225
+
+--S 1226 of 1347
+r0:=(-1/4)/x^4-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)+_
+ 1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 2 +-+
+--R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3
+--R x \|3 log(x + x + 1) - 2x \|3 log(- x + 1) + 6x atan(-------------)
+--R 3
+--R +
+--R +-+
+--R - 3\|3
+--R /
+--R 4 +-+
+--R 12x \|3
+--R Type: Expression(Integer)
+--E 1226
+
+--S 1227 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 +-+
+--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) + 6x atan(-------------) - 3\|3
+--R 3
+--R ----------------------------------------------------------------------------
+--R 4 +-+
+--R 12x \|3
+--R Type: Union(Expression(Integer),...)
+--E 1227
+
+--S 1228 of 1347
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R - log(x - 1) + log(- x + 1)
+--R (4) -----------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1228
+
+--S 1229 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1229
+
+)clear all
+
+--S 1230 of 1347
+t0:=1/(x^6*(1-x^6))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 12 6
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 1230
+
+--S 1231 of 1347
+r0:=(-1/5)/x^5+1/3*atanh(x)-1/12*log(1-x+x^2)+_
+ 1/12*log(1+x+x^2)-1/2*atan((1-2*x)/sqrt(3))/sqrt(3)+_
+ 1/2*atan((1+2*x)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 5 +-+ 2 5 +-+ 2 5 +-+
+--R 5x \|3 log(x + x + 1) - 5x \|3 log(x - x + 1) + 20x \|3 atanh(x)
+--R +
+--R +-+ +-+
+--R 5 (2x + 1)\|3 5 (2x - 1)\|3 +-+
+--R 30x atan(------------) + 30x atan(------------) - 12\|3
+--R 3 3
+--R /
+--R 5 +-+
+--R 60x \|3
+--R Type: Expression(Integer)
+--E 1231
+
+--S 1232 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 +-+ 2 5 +-+ 2 5 +-+
+--R 5x \|3 log(x + x + 1) - 5x \|3 log(x - x + 1) + 10x \|3 log(x + 1)
+--R +
+--R +-+ +-+
+--R 5 +-+ 5 (2x + 1)\|3 5 (2x - 1)\|3
+--R - 10x \|3 log(x - 1) + 30x atan(------------) + 30x atan(------------)
+--R 3 3
+--R +
+--R +-+
+--R - 12\|3
+--R /
+--R 5 +-+
+--R 60x \|3
+--R Type: Union(Expression(Integer),...)
+--E 1232
+
+--S 1233 of 1347
+m0:=a0-r0
+--R
+--R
+--R log(x + 1) - log(x - 1) - 2atanh(x)
+--R (4) -----------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1233
+
+--S 1234 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1234
+
+)clear all
+
+--S 1235 of 1347
+t0:=1/(x^7*(1-x^6))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 13 7
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 1235
+
+--S 1236 of 1347
+r0:=(-1/6)/x^6-1/3*atanh(1-2*x^6)
+--R
+--R
+--R 6 6
+--R 2x atanh(2x - 1) - 1
+--R (2) ---------------------
+--R 6
+--R 6x
+--R Type: Expression(Integer)
+--E 1236
+
+--S 1237 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 6 6
+--R - x log(x - 1) + 6x log(x) - 1
+--R (3) -------------------------------
+--R 6
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 1237
+
+--S 1238 of 1347
+m0:=a0-r0
+--R
+--R
+--R 6 6
+--R - log(x - 1) + 6log(x) - 2atanh(2x - 1)
+--R (4) -----------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1238
+
+--S 1239 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1239
+
+)clear all
+
+--S 1240 of 1347
+t0:=1/(x^8*(1-x^6))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 14 8
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 1240
+
+--S 1241 of 1347
+r0:=(-1/7)/x^7+(-1)/x+1/3*atanh(x)-1/12*log(1-x+x^2)+_
+ 1/12*log(1+x+x^2)+1/2*atan((1-2*x)/sqrt(3))/sqrt(3)-_
+ 1/2*atan((1+2*x)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 7 +-+ 2 7 +-+ 2 7 +-+
+--R 7x \|3 log(x + x + 1) - 7x \|3 log(x - x + 1) + 28x \|3 atanh(x)
+--R +
+--R +-+ +-+
+--R 7 (2x + 1)\|3 7 (2x - 1)\|3 6 +-+
+--R - 42x atan(------------) - 42x atan(------------) + (- 84x - 12)\|3
+--R 3 3
+--R /
+--R 7 +-+
+--R 84x \|3
+--R Type: Expression(Integer)
+--E 1241
+
+--S 1242 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 +-+ 2 7 +-+ 2 7 +-+
+--R 7x \|3 log(x + x + 1) - 7x \|3 log(x - x + 1) + 14x \|3 log(x + 1)
+--R +
+--R +-+ +-+
+--R 7 +-+ 7 (2x + 1)\|3 7 (2x - 1)\|3
+--R - 14x \|3 log(x - 1) - 42x atan(------------) - 42x atan(------------)
+--R 3 3
+--R +
+--R 6 +-+
+--R (- 84x - 12)\|3
+--R /
+--R 7 +-+
+--R 84x \|3
+--R Type: Union(Expression(Integer),...)
+--E 1242
+
+--S 1243 of 1347
+m0:=a0-r0
+--R
+--R
+--R log(x + 1) - log(x - 1) - 2atanh(x)
+--R (4) -----------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1243
+
+--S 1244 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1244
+
+)clear all
+
+--S 1245 of 1347
+t0:=x^8/(1+x^6)
+--R
+--R
+--R 8
+--R x
+--R (1) ------
+--R 6
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1245
+
+--S 1246 of 1347
+r0:=1/3*x^3-1/3*atan(x^3)
+--R
+--R
+--R 3 3
+--R - atan(x ) + x
+--R (2) ---------------
+--R 3
+--R Type: Expression(Integer)
+--E 1246
+
+--S 1247 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R - atan(x ) + x
+--R (3) ---------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 1247
+
+--S 1248 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1248
+
+--S 1249 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1249
+
+)clear all
+
+--S 1250 of 1347
+t0:=x^7/(1+x^6)
+--R
+--R
+--R 7
+--R x
+--R (1) ------
+--R 6
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1250
+
+--S 1251 of 1347
+r0:=1/2*x^2-1/6*log(1+x^2)+1/12*log(1-x^2+x^4)+_
+ 1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x - 1)\|3 2 +-+
+--R \|3 log(x - x + 1) - 2\|3 log(x + 1) - 6atan(-------------) + 6x \|3
+--R 3
+--R ------------------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1251
+
+--S 1252 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x - 1)\|3 2 +-+
+--R \|3 log(x - x + 1) - 2\|3 log(x + 1) - 6atan(-------------) + 6x \|3
+--R 3
+--R ------------------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 1252
+
+--S 1253 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1253
+
+--S 1254 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1254
+
+)clear all
+
+--S 1255 of 1347
+t0:=x^6/(1+x^6)
+--R
+--R
+--R 6
+--R x
+--R (1) ------
+--R 6
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1255
+
+--S 1256 of 1347
+r0:=x-1/3*atan(x)+1/6*atan(-2*x+sqrt(3))-_
+ 1/6*atan(2*x+sqrt(3))+1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-_
+ 1/4*log(1+x^2+x*sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+ +-+
+--R - 3log(x\|3 + x + 1) + 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x)
+--R +
+--R +-+ +-+ +-+ +-+
+--R 2\|3 atan(\|3 - 2x) - 4\|3 atan(x) + 12x\|3
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1256
+
+--S 1257 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) + 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) - 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R \|3 2
+--R - 2sin(----------)atan(-------------------)
+--R 2 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------) - x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R \|3 2 2x
+--R 2sin(----------)atan(-------------------) + atan(------) + 6x
+--R 2 3 2
+--R atan(----) x - 1
+--R +-+
+--R \|3
+--R cos(----------) + x
+--R 2
+--R /
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1257
+
+--S 1258 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) + 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) - 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R +-+ \|3 2
+--R - 4\|3 sin(----------)atan(-------------------)
+--R 2 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------) - x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R +-+ \|3 2 +-+ 2
+--R 4\|3 sin(----------)atan(-------------------) + 3log(x\|3 + x + 1)
+--R 2 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------) + x
+--R 2
+--R +
+--R +-+ 2 +-+ +-+ +-+ +-+
+--R - 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) - 2\|3 atan(\|3 - 2x)
+--R +
+--R +-+ +-+ 2x
+--R 4\|3 atan(x) + 2\|3 atan(------)
+--R 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1258
+
+--S 1259 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 4
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (- 2x + x )sin(----------)
+--R 2
+--R +
+--R 3 2 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 2 \|3
+--R ((- 4x + 2x )cos(----------) - 2x + 2x )sin(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 2 \|3 6 4
+--R (- 2x + x )cos(----------) + (2x - 2x )cos(----------) - x + 2x
+--R 2 2
+--R /
+--R 3 4
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (3x - 3x + 3)sin(----------)
+--R 2
+--R +
+--R 3 2 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R ((6x - 6x + 6)cos(----------) + 6x - 6x + 6x )sin(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R (3x - 3x + 3)cos(----------) + (- 6x + 6x - 6x )cos(----------)
+--R 2 2
+--R +
+--R 8 6 4
+--R 3x - 3x + 3x
+--R Type: Expression(Integer)
+--E 1259
+
+)clear all
+
+--S 1260 of 1347
+t0:=x^5/(1+x^6)
+--R
+--R
+--R 5
+--R x
+--R (1) ------
+--R 6
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1260
+
+--S 1261 of 1347
+r0:=1/6*log(1+x^6)
+--R
+--R
+--R 6
+--R log(x + 1)
+--R (2) -----------
+--R 6
+--R Type: Expression(Integer)
+--E 1261
+
+--S 1262 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6
+--R log(x + 1)
+--R (3) -----------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1262
+
+--S 1263 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1263
+
+--S 1264 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1264
+
+)clear all
+
+--S 1265 of 1347
+t0:=x^4/(1+x^6)
+--R
+--R
+--R 4
+--R x
+--R (1) ------
+--R 6
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1265
+
+--S 1266 of 1347
+r0:=1/3*atan(x)-1/6*atan(-2*x+sqrt(3))+1/6*atan(2*x+sqrt(3))+_
+ 1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-1/4*log(1+x^2+x*sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+ +-+
+--R - 3log(x\|3 + x + 1) + 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x)
+--R +
+--R +-+ +-+ +-+
+--R - 2\|3 atan(\|3 - 2x) + 4\|3 atan(x)
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1266
+
+--S 1267 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) + x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R x cos(----------) + x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) - x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R - x cos(----------) + x
+--R 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R \|3 2 2
+--R - 2sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) - 2x
+--R 2 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R \|3 2 2
+--R 2sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) + 2x
+--R 2 2
+--R +
+--R 2x
+--R - atan(------)
+--R 2
+--R x - 1
+--R /
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1267
+
+--S 1268 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) + x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R x cos(----------) + x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) - x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R - x cos(----------) + x
+--R 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R +-+ \|3 2 2
+--R - 4\|3 sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) - 2x
+--R 2 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R +-+ \|3 2 2
+--R 4\|3 sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) + 2x
+--R 2 2
+--R +
+--R +-+ 2 +-+ 2 +-+ +-+
+--R 3log(x\|3 + x + 1) - 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x)
+--R +
+--R +-+ +-+ +-+ +-+ 2x
+--R 2\|3 atan(\|3 - 2x) - 4\|3 atan(x) - 2\|3 atan(------)
+--R 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1268
+
+--S 1269 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 8
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (- x - x )sin(----------)
+--R 2
+--R +
+--R 3 2 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3
+--R ((- 4x - 4x )cos(----------) + 4x - 2x )sin(----------)
+--R 2 2
+--R +
+--R 3 3 5
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 +-+ \|3 \|3
+--R (4x + 4x )\|3 cos(----------)sin(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3 6
+--R (- 6x - 6x )cos(----------) + (4x - 2x )cos(----------) - 6x
+--R 2 2
+--R +
+--R 4
+--R 3x
+--R *
+--R 3 4
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 +-+ \|3 6 4 +-+ \|3
+--R ((8x + 8x )\|3 cos(----------) + (- 8x + 4x )\|3 cos(----------))
+--R 2 2
+--R *
+--R 3 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 6 3 4
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3
+--R (- 4x - 4x )cos(----------) + (- 4x + 2x )cos(----------)
+--R 2 2
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 8 6 4 \|3 10 8 6
+--R (- 16x - 12x - 2x )cos(----------) - x + 5x - 3x
+--R 2
+--R *
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 5 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 +-+ \|3 6 4 +-+ \|3
+--R (4x + 4x )\|3 cos(----------) + (8x - 4x )\|3 cos(----------)
+--R 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 10 8 6 +-+ \|3
+--R (2x + 6x - 2x )\|3 cos(----------)
+--R 2
+--R *
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 8 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3
+--R (- x - x )cos(----------) + (- 4x + 2x )cos(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 \|3 10 8 6 \|3 10
+--R (- 6x + 3x )cos(----------) + (x - 5x + 3x )cos(----------) - 2x
+--R 2 2
+--R +
+--R 8
+--R x
+--R /
+--R 3 8
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (3x - 3x + 3)sin(----------)
+--R 2
+--R +
+--R 3 2 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R ((12x - 12x + 12)cos(----------) - 6x + 6x - 6x )sin(----------)
+--R 2 2
+--R +
+--R 3 3 5
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 2 +-+ \|3 \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)sin(----------)
+--R 2 2
+--R +
+--R 3 4
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (18x - 18x + 18)cos(----------)
+--R 2
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 6 4 2 \|3 8 6 4
+--R (- 6x + 6x - 6x )cos(----------) + 9x - 9x + 9x
+--R 2
+--R *
+--R 3 4
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 3
+--R atan(----)
+--R +-+
+--R 6 4 2 +-+ \|3
+--R (- 24x + 24x - 24x )\|3 cos(----------)
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 8 6 4 +-+ \|3
+--R (12x - 12x + 12x )\|3 cos(----------)
+--R 2
+--R *
+--R 3 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 6
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (12x - 12x + 12)cos(----------)
+--R 2
+--R +
+--R 3 4
+--R atan(----)
+--R +-+
+--R 6 4 2 \|3
+--R (6x - 6x + 6x )cos(----------)
+--R 2
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 8 6 4 \|3 10 8 6
+--R (42x - 42x + 42x )cos(----------) - 6x + 6x - 6x
+--R 2
+--R *
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 5
+--R atan(----)
+--R +-+
+--R 6 4 2 +-+ \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)
+--R 2
+--R +
+--R 3 3
+--R atan(----)
+--R +-+
+--R 8 6 4 +-+ \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 10 8 6 +-+ \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)
+--R 2
+--R *
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 8 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R (3x - 3x + 3)cos(----------) + (6x - 6x + 6x )cos(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 8 6 4 \|3 10 8 6 \|3
+--R (9x - 9x + 9x )cos(----------) + (6x - 6x + 6x )cos(----------)
+--R 2 2
+--R +
+--R 12 10 8
+--R 3x - 3x + 3x
+--R Type: Expression(Integer)
+--E 1269
+
+)clear all
+
+--S 1270 of 1347
+t0:=x^3/(1+x^6)
+--R
+--R
+--R 3
+--R x
+--R (1) ------
+--R 6
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1270
+
+--S 1271 of 1347
+r0:=-1/6*log(1+x^2)+1/12*log(1-x^2+x^4)-1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3)
+--R
+--R
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x - 1)\|3
+--R \|3 log(x - x + 1) - 2\|3 log(x + 1) + 6atan(-------------)
+--R 3
+--R (2) --------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1271
+
+--S 1272 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x - 1)\|3
+--R \|3 log(x - x + 1) - 2\|3 log(x + 1) + 6atan(-------------)
+--R 3
+--R (3) --------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 1272
+
+--S 1273 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1273
+
+--S 1274 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1274
+
+)clear all
+
+--S 1275 of 1347
+t0:=x^2/(1+x^6)
+--R
+--R
+--R 2
+--R x
+--R (1) ------
+--R 6
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1275
+
+--S 1276 of 1347
+r0:=1/3*atan(x^3)
+--R
+--R
+--R 3
+--R atan(x )
+--R (2) --------
+--R 3
+--R Type: Expression(Integer)
+--E 1276
+
+--S 1277 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R atan(x )
+--R (3) --------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 1277
+
+--S 1278 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1278
+
+--S 1279 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1279
+
+)clear all
+
+--S 1280 of 1347
+t0:=x/(1+x^6)
+--R
+--R
+--R x
+--R (1) ------
+--R 6
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1280
+
+--S 1281 of 1347
+r0:=1/6*log(1+x^2)-1/12*log(1-x^2+x^4)-1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3)
+--R
+--R
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x - 1)\|3
+--R - \|3 log(x - x + 1) + 2\|3 log(x + 1) + 6atan(-------------)
+--R 3
+--R (2) ----------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1281
+
+--S 1282 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R +-+ 4 2 +-+ 2 (2x - 1)\|3
+--R - \|3 log(x - x + 1) + 2\|3 log(x + 1) + 6atan(-------------)
+--R 3
+--R (3) ----------------------------------------------------------------
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 1282
+
+--S 1283 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1283
+
+--S 1284 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1284
+
+)clear all
+
+--S 1285 of 1347
+t0:=1/(1+x^6)
+--R
+--R
+--R 1
+--R (1) ------
+--R 6
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 1285
+
+--S 1286 of 1347
+r0:=1/3*atan(x)-1/6*atan(-2*x+sqrt(3))+1/6*atan(2*x+sqrt(3))-_
+ 1/4*log(1+x^2-x*sqrt(3))/sqrt(3)+1/4*log(1+x^2+x*sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+ +-+
+--R 3log(x\|3 + x + 1) - 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x)
+--R +
+--R +-+ +-+ +-+
+--R - 2\|3 atan(\|3 - 2x) + 4\|3 atan(x)
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1286
+
+--S 1287 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) + 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) - 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R \|3 2
+--R 2sin(----------)atan(-------------------)
+--R 2 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------) - x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R \|3 2 2x
+--R - 2sin(----------)atan(-------------------) - atan(------)
+--R 2 3 2
+--R atan(----) x - 1
+--R +-+
+--R \|3
+--R cos(----------) + x
+--R 2
+--R /
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1287
+
+--S 1288 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) + 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) - 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R +-+ \|3 2
+--R 4\|3 sin(----------)atan(-------------------)
+--R 2 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------) - x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R +-+ \|3 2 +-+ 2
+--R - 4\|3 sin(----------)atan(-------------------) - 3log(x\|3 + x + 1)
+--R 2 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------) + x
+--R 2
+--R +
+--R +-+ 2 +-+ +-+ +-+ +-+
+--R 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x) + 2\|3 atan(\|3 - 2x)
+--R +
+--R +-+ +-+ 2x
+--R - 4\|3 atan(x) - 2\|3 atan(------)
+--R 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1288
+
+--S 1289 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 4
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (2x - x )sin(----------)
+--R 2
+--R +
+--R 3 2 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 2 \|3
+--R ((4x - 2x )cos(----------) + 2x - 2x )sin(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 2 \|3 6 4
+--R (2x - x )cos(----------) + (- 2x + 2x )cos(----------) + x - 2x
+--R 2 2
+--R /
+--R 3 4
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (3x - 3x + 3)sin(----------)
+--R 2
+--R +
+--R 3 2 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R ((6x - 6x + 6)cos(----------) + 6x - 6x + 6x )sin(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R (3x - 3x + 3)cos(----------) + (- 6x + 6x - 6x )cos(----------)
+--R 2 2
+--R +
+--R 8 6 4
+--R 3x - 3x + 3x
+--R Type: Expression(Integer)
+--E 1289
+
+)clear all
+
+--S 1290 of 1347
+t0:=1/(x*(1+x^6))
+--R
+--R
+--R 1
+--R (1) ------
+--R 7
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 1290
+
+--S 1291 of 1347
+r0:=-1/3*atanh(1+2*x^6)
+--R
+--R
+--R 6
+--R atanh(2x + 1)
+--R (2) - --------------
+--R 3
+--R Type: Expression(Integer)
+--E 1291
+
+--S 1292 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6
+--R - log(x + 1) + 6log(x)
+--R (3) -----------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1292
+
+--S 1293 of 1347
+m0:=a0-r0
+--R
+--R
+--R 6 6
+--R - log(x + 1) + 6log(x) + 2atanh(2x + 1)
+--R (4) -----------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1293
+
+--S 1294 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1294
+
+)clear all
+
+--S 1295 of 1347
+t0:=1/(x^2*(1+x^6))
+--R
+--R
+--R 1
+--R (1) -------
+--R 8 2
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 1295
+
+--S 1296 of 1347
+r0:=(-1)/x-1/3*atan(x)+1/6*atan(-2*x+sqrt(3))-1/6*atan(2*x+sqrt(3))-_
+ 1/4*log(1+x^2-x*sqrt(3))/sqrt(3)+1/4*log(1+x^2+x*sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+ +-+
+--R 3x log(x\|3 + x + 1) - 3x log(- x\|3 + x + 1) - 2x\|3 atan(\|3 + 2x)
+--R +
+--R +-+ +-+ +-+ +-+
+--R 2x\|3 atan(\|3 - 2x) - 4x\|3 atan(x) - 12\|3
+--R /
+--R +-+
+--R 12x\|3
+--R Type: Expression(Integer)
+--E 1296
+
+--S 1297 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R x cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) + x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R x cos(----------) + x
+--R 2
+--R +
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R x cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) - x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R - x cos(----------) + x
+--R 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R \|3 2 2
+--R 2x sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) - 2x
+--R 2 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R \|3 2 2
+--R - 2x sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) + 2x
+--R 2 2
+--R +
+--R 2x
+--R x atan(------) - 6
+--R 2
+--R x - 1
+--R /
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 1297
+
+--S 1298 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) + x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R x cos(----------) + x
+--R 2
+--R +
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) - x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R - x cos(----------) + x
+--R 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R +-+ \|3 2 2
+--R 4\|3 sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) - 2x
+--R 2 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R +-+ \|3 2 2
+--R - 4\|3 sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) + 2x
+--R 2 2
+--R +
+--R +-+ 2 +-+ 2 +-+ +-+
+--R - 3log(x\|3 + x + 1) + 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x)
+--R +
+--R +-+ +-+ +-+ +-+ 2x
+--R - 2\|3 atan(\|3 - 2x) + 4\|3 atan(x) + 2\|3 atan(------)
+--R 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1298
+
+--S 1299 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 8
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (x + x )sin(----------)
+--R 2
+--R +
+--R 3 2 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3
+--R ((4x + 4x )cos(----------) - 4x + 2x )sin(----------)
+--R 2 2
+--R +
+--R 3 3 5
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 +-+ \|3 \|3
+--R (- 4x - 4x )\|3 cos(----------)sin(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3 6
+--R (6x + 6x )cos(----------) + (- 4x + 2x )cos(----------) + 6x
+--R 2 2
+--R +
+--R 4
+--R - 3x
+--R *
+--R 3 4
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 +-+ \|3 6 4 +-+ \|3
+--R ((- 8x - 8x )\|3 cos(----------) + (8x - 4x )\|3 cos(----------))
+--R 2 2
+--R *
+--R 3 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 6 3 4
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3
+--R (4x + 4x )cos(----------) + (4x - 2x )cos(----------)
+--R 2 2
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 8 6 4 \|3 10 8 6
+--R (16x + 12x + 2x )cos(----------) + x - 5x + 3x
+--R 2
+--R *
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 5 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 +-+ \|3 6 4 +-+ \|3
+--R (- 4x - 4x )\|3 cos(----------) + (- 8x + 4x )\|3 cos(----------)
+--R 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 10 8 6 +-+ \|3
+--R (- 2x - 6x + 2x )\|3 cos(----------)
+--R 2
+--R *
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 8 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3
+--R (x + x )cos(----------) + (4x - 2x )cos(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 \|3 10 8 6 \|3 10
+--R (6x - 3x )cos(----------) + (- x + 5x - 3x )cos(----------) + 2x
+--R 2 2
+--R +
+--R 8
+--R - x
+--R /
+--R 3 8
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (3x - 3x + 3)sin(----------)
+--R 2
+--R +
+--R 3 2 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R ((12x - 12x + 12)cos(----------) - 6x + 6x - 6x )sin(----------)
+--R 2 2
+--R +
+--R 3 3 5
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 2 +-+ \|3 \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)sin(----------)
+--R 2 2
+--R +
+--R 3 4
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (18x - 18x + 18)cos(----------)
+--R 2
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 6 4 2 \|3 8 6 4
+--R (- 6x + 6x - 6x )cos(----------) + 9x - 9x + 9x
+--R 2
+--R *
+--R 3 4
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 3
+--R atan(----)
+--R +-+
+--R 6 4 2 +-+ \|3
+--R (- 24x + 24x - 24x )\|3 cos(----------)
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 8 6 4 +-+ \|3
+--R (12x - 12x + 12x )\|3 cos(----------)
+--R 2
+--R *
+--R 3 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 6
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (12x - 12x + 12)cos(----------)
+--R 2
+--R +
+--R 3 4
+--R atan(----)
+--R +-+
+--R 6 4 2 \|3
+--R (6x - 6x + 6x )cos(----------)
+--R 2
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 8 6 4 \|3 10 8 6
+--R (42x - 42x + 42x )cos(----------) - 6x + 6x - 6x
+--R 2
+--R *
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 5
+--R atan(----)
+--R +-+
+--R 6 4 2 +-+ \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)
+--R 2
+--R +
+--R 3 3
+--R atan(----)
+--R +-+
+--R 8 6 4 +-+ \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 10 8 6 +-+ \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)
+--R 2
+--R *
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 8 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R (3x - 3x + 3)cos(----------) + (6x - 6x + 6x )cos(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 8 6 4 \|3 10 8 6 \|3
+--R (9x - 9x + 9x )cos(----------) + (6x - 6x + 6x )cos(----------)
+--R 2 2
+--R +
+--R 12 10 8
+--R 3x - 3x + 3x
+--R Type: Expression(Integer)
+--E 1299
+
+)clear all
+
+--S 1300 of 1347
+t0:=1/(x^3*(1+x^6))
+--R
+--R
+--R 1
+--R (1) -------
+--R 9 3
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 1300
+
+--S 1301 of 1347
+r0:=(-1/2)/x^2+1/6*log(1+x^2)-1/12*log(1-x^2+x^4)+1/2*_
+ atan((1-2*x^2)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 2 +-+
+--R 2 +-+ 4 2 2 +-+ 2 2 (2x - 1)\|3
+--R - x \|3 log(x - x + 1) + 2x \|3 log(x + 1) - 6x atan(-------------)
+--R 3
+--R +
+--R +-+
+--R - 6\|3
+--R /
+--R 2 +-+
+--R 12x \|3
+--R Type: Expression(Integer)
+--E 1301
+
+--S 1302 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R 2 +-+ 4 2 2 +-+ 2 2 (2x - 1)\|3
+--R - x \|3 log(x - x + 1) + 2x \|3 log(x + 1) - 6x atan(-------------)
+--R 3
+--R +
+--R +-+
+--R - 6\|3
+--R /
+--R 2 +-+
+--R 12x \|3
+--R Type: Union(Expression(Integer),...)
+--E 1302
+
+--S 1303 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1303
+
+--S 1304 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1304
+
+)clear all
+
+--S 1305 of 1347
+t0:=1/(x^4*(1+x^6))
+--R
+--R
+--R 1
+--R (1) --------
+--R 10 4
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 1305
+
+--S 1306 of 1347
+r0:=(-1/3)/x^3-1/3*atan(x^3)
+--R
+--R
+--R 3 3
+--R - x atan(x ) - 1
+--R (2) ----------------
+--R 3
+--R 3x
+--R Type: Expression(Integer)
+--E 1306
+
+--S 1307 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R - x atan(x ) - 1
+--R (3) ----------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 1307
+
+--S 1308 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1308
+
+--S 1309 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1309
+
+)clear all
+
+--S 1310 of 1347
+t0:=1/(x^5*(1+x^6))
+--R
+--R
+--R 1
+--R (1) --------
+--R 11 5
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 1310
+
+--S 1311 of 1347
+r0:=(-1/4)/x^4-1/6*log(1+x^2)+1/12*log(1-x^2+x^4)+_
+ 1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 2 +-+
+--R 4 +-+ 4 2 4 +-+ 2 4 (2x - 1)\|3 +-+
+--R x \|3 log(x - x + 1) - 2x \|3 log(x + 1) - 6x atan(-------------) - 3\|3
+--R 3
+--R ----------------------------------------------------------------------------
+--R 4 +-+
+--R 12x \|3
+--R Type: Expression(Integer)
+--E 1311
+
+--S 1312 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+
+--R 4 +-+ 4 2 4 +-+ 2 4 (2x - 1)\|3 +-+
+--R x \|3 log(x - x + 1) - 2x \|3 log(x + 1) - 6x atan(-------------) - 3\|3
+--R 3
+--R ----------------------------------------------------------------------------
+--R 4 +-+
+--R 12x \|3
+--R Type: Union(Expression(Integer),...)
+--E 1312
+
+--S 1313 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1313
+
+--S 1314 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1314
+
+)clear all
+
+--S 1315 of 1347
+t0:=1/(x^6*(1+x^6))
+--R
+--R
+--R 1
+--R (1) --------
+--R 12 6
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 1315
+
+--S 1316 of 1347
+r0:=(-1/5)/x^5-1/3*atan(x)+1/6*atan(-2*x+sqrt(3))-_
+ 1/6*atan(2*x+sqrt(3))+1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-_
+ 1/4*log(1+x^2+x*sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 5 +-+ 2 5 +-+ 2
+--R - 15x log(x\|3 + x + 1) + 15x log(- x\|3 + x + 1)
+--R +
+--R 5 +-+ +-+ 5 +-+ +-+ 5 +-+
+--R - 10x \|3 atan(\|3 + 2x) + 10x \|3 atan(\|3 - 2x) - 20x \|3 atan(x)
+--R +
+--R +-+
+--R - 12\|3
+--R /
+--R 5 +-+
+--R 60x \|3
+--R Type: Expression(Integer)
+--E 1316
+
+--S 1317 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R 5 \|3
+--R 5x cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) + 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 5 \|3
+--R 5x cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) - 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R 5 \|3 2
+--R - 10x sin(----------)atan(-------------------)
+--R 2 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------) - x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R 5 \|3 2 5 2x
+--R 10x sin(----------)atan(-------------------) + 5x atan(------) - 6
+--R 2 3 2
+--R atan(----) x - 1
+--R +-+
+--R \|3
+--R cos(----------) + x
+--R 2
+--R /
+--R 5
+--R 30x
+--R Type: Union(Expression(Integer),...)
+--E 1317
+
+--S 1318 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) + 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R 3 2 3 2 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 \|3 2
+--R log(sin(----------) + cos(----------) - 2x cos(----------) + x )
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R +-+ \|3 2
+--R - 4\|3 sin(----------)atan(-------------------)
+--R 2 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------) - x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R 3 +-+
+--R atan(----) \|3
+--R +-+ sin(----------)
+--R +-+ \|3 2 +-+ 2
+--R 4\|3 sin(----------)atan(-------------------) + 3log(x\|3 + x + 1)
+--R 2 3
+--R atan(----)
+--R +-+
+--R \|3
+--R cos(----------) + x
+--R 2
+--R +
+--R +-+ 2 +-+ +-+ +-+ +-+
+--R - 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) - 2\|3 atan(\|3 - 2x)
+--R +
+--R +-+ +-+ 2x
+--R 4\|3 atan(x) + 2\|3 atan(------)
+--R 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1318
+
+--S 1319 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 4
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (- 2x + x )sin(----------)
+--R 2
+--R +
+--R 3 2 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 2 \|3
+--R ((- 4x + 2x )cos(----------) - 2x + 2x )sin(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 2 \|3 6 4
+--R (- 2x + x )cos(----------) + (2x - 2x )cos(----------) - x + 2x
+--R 2 2
+--R /
+--R 3 4
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (3x - 3x + 3)sin(----------)
+--R 2
+--R +
+--R 3 2 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R ((6x - 6x + 6)cos(----------) + 6x - 6x + 6x )sin(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R (3x - 3x + 3)cos(----------) + (- 6x + 6x - 6x )cos(----------)
+--R 2 2
+--R +
+--R 8 6 4
+--R 3x - 3x + 3x
+--R Type: Expression(Integer)
+--E 1319
+
+)clear all
+
+--S 1320 of 1347
+t0:=1/(x^7*(1+x^6))
+--R
+--R
+--R 1
+--R (1) --------
+--R 13 7
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 1320
+
+--S 1321 of 1347
+r0:=(-1/6)/x^6+1/3*atanh(1+2*x^6)
+--R
+--R
+--R 6 6
+--R 2x atanh(2x + 1) - 1
+--R (2) ---------------------
+--R 6
+--R 6x
+--R Type: Expression(Integer)
+--E 1321
+
+--S 1322 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 6 6
+--R x log(x + 1) - 6x log(x) - 1
+--R (3) -----------------------------
+--R 6
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 1322
+
+--S 1323 of 1347
+m0:=a0-r0
+--R
+--R
+--R 6 6
+--R log(x + 1) - 6log(x) - 2atanh(2x + 1)
+--R (4) ---------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 1323
+
+--S 1324 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1324
+
+)clear all
+
+--S 1325 of 1347
+t0:=1/(x^8*(1+x^6))
+--R
+--R
+--R 1
+--R (1) --------
+--R 14 8
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 1325
+
+--S 1326 of 1347
+r0:=(-1/7)/x^7+1/x+1/3*atan(x)-1/6*atan(-2*x+sqrt(3))+_
+ 1/6*atan(2*x+sqrt(3))+1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-_
+ 1/4*log(1+x^2+x*sqrt(3))/sqrt(3)
+--R
+--R
+--R (2)
+--R 7 +-+ 2 7 +-+ 2
+--R - 21x log(x\|3 + x + 1) + 21x log(- x\|3 + x + 1)
+--R +
+--R 7 +-+ +-+ 7 +-+ +-+ 7 +-+
+--R 14x \|3 atan(\|3 + 2x) - 14x \|3 atan(\|3 - 2x) + 28x \|3 atan(x)
+--R +
+--R 6 +-+
+--R (84x - 12)\|3
+--R /
+--R 7 +-+
+--R 84x \|3
+--R Type: Expression(Integer)
+--E 1326
+
+--S 1327 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R 7 \|3
+--R 7x cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) + x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R x cos(----------) + x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 7 \|3
+--R 7x cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) - x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R - x cos(----------) + x
+--R 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R 7 \|3 2 2
+--R - 14x sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) - 2x
+--R 2 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R 7 \|3 2 2
+--R 14x sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) + 2x
+--R 2 2
+--R +
+--R 7 2x 6
+--R - 7x atan(------) + 42x - 6
+--R 2
+--R x - 1
+--R /
+--R 7
+--R 42x
+--R Type: Union(Expression(Integer),...)
+--E 1327
+
+--S 1328 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) + x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R x cos(----------) + x
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 2
+--R *
+--R log
+--R 3 2 3 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R sin(----------) - x\|3 sin(----------) + cos(----------)
+--R 2 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R \|3 2
+--R - x cos(----------) + x
+--R 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R +-+ \|3 2 2
+--R - 4\|3 sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) - 2x
+--R 2 2
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R 3 +-+ +-+
+--R atan(----) \|3 +-+ \|3
+--R +-+ sin(----------) - \|3 cos(----------)
+--R +-+ \|3 2 2
+--R 4\|3 sin(----------)atan(------------------------------------------)
+--R 2 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R \|3 sin(----------) + cos(----------) + 2x
+--R 2 2
+--R +
+--R +-+ 2 +-+ 2 +-+ +-+
+--R 3log(x\|3 + x + 1) - 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x)
+--R +
+--R +-+ +-+ +-+ +-+ 2x
+--R 2\|3 atan(\|3 - 2x) - 4\|3 atan(x) - 2\|3 atan(------)
+--R 2
+--R x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Expression(Integer)
+--E 1328
+
+--S 1329 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 8
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (- x - x )sin(----------)
+--R 2
+--R +
+--R 3 2 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3
+--R ((- 4x - 4x )cos(----------) + 4x - 2x )sin(----------)
+--R 2 2
+--R +
+--R 3 3 5
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 +-+ \|3 \|3
+--R (4x + 4x )\|3 cos(----------)sin(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3 6
+--R (- 6x - 6x )cos(----------) + (4x - 2x )cos(----------) - 6x
+--R 2 2
+--R +
+--R 4
+--R 3x
+--R *
+--R 3 4
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 +-+ \|3 6 4 +-+ \|3
+--R ((8x + 8x )\|3 cos(----------) + (- 8x + 4x )\|3 cos(----------))
+--R 2 2
+--R *
+--R 3 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 6 3 4
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3
+--R (- 4x - 4x )cos(----------) + (- 4x + 2x )cos(----------)
+--R 2 2
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 8 6 4 \|3 10 8 6
+--R (- 16x - 12x - 2x )cos(----------) - x + 5x - 3x
+--R 2
+--R *
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 5 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 +-+ \|3 6 4 +-+ \|3
+--R (4x + 4x )\|3 cos(----------) + (8x - 4x )\|3 cos(----------)
+--R 2 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 10 8 6 +-+ \|3
+--R (2x + 6x - 2x )\|3 cos(----------)
+--R 2
+--R *
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 8 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 4 2 \|3
+--R (- x - x )cos(----------) + (- 4x + 2x )cos(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 \|3 10 8 6 \|3 10
+--R (- 6x + 3x )cos(----------) + (x - 5x + 3x )cos(----------) - 2x
+--R 2 2
+--R +
+--R 8
+--R x
+--R /
+--R 3 8
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (3x - 3x + 3)sin(----------)
+--R 2
+--R +
+--R 3 2 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R ((12x - 12x + 12)cos(----------) - 6x + 6x - 6x )sin(----------)
+--R 2 2
+--R +
+--R 3 3 5
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 6 4 2 +-+ \|3 \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)sin(----------)
+--R 2 2
+--R +
+--R 3 4
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (18x - 18x + 18)cos(----------)
+--R 2
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 6 4 2 \|3 8 6 4
+--R (- 6x + 6x - 6x )cos(----------) + 9x - 9x + 9x
+--R 2
+--R *
+--R 3 4
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 3
+--R atan(----)
+--R +-+
+--R 6 4 2 +-+ \|3
+--R (- 24x + 24x - 24x )\|3 cos(----------)
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 8 6 4 +-+ \|3
+--R (12x - 12x + 12x )\|3 cos(----------)
+--R 2
+--R *
+--R 3 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 6
+--R atan(----)
+--R +-+
+--R 4 2 \|3
+--R (12x - 12x + 12)cos(----------)
+--R 2
+--R +
+--R 3 4
+--R atan(----)
+--R +-+
+--R 6 4 2 \|3
+--R (6x - 6x + 6x )cos(----------)
+--R 2
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 8 6 4 \|3 10 8 6
+--R (42x - 42x + 42x )cos(----------) - 6x + 6x - 6x
+--R 2
+--R *
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 5
+--R atan(----)
+--R +-+
+--R 6 4 2 +-+ \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)
+--R 2
+--R +
+--R 3 3
+--R atan(----)
+--R +-+
+--R 8 6 4 +-+ \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)
+--R 2
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R 10 8 6 +-+ \|3
+--R (- 12x + 12x - 12x )\|3 cos(----------)
+--R 2
+--R *
+--R 3
+--R atan(----)
+--R +-+
+--R \|3
+--R sin(----------)
+--R 2
+--R +
+--R 3 8 3 6
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 4 2 \|3 6 4 2 \|3
+--R (3x - 3x + 3)cos(----------) + (6x - 6x + 6x )cos(----------)
+--R 2 2
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R 8 6 4 \|3 10 8 6 \|3
+--R (9x - 9x + 9x )cos(----------) + (6x - 6x + 6x )cos(----------)
+--R 2 2
+--R +
+--R 12 10 8
+--R 3x - 3x + 3x
+--R Type: Expression(Integer)
+--E 1329
+
+)clear all
+
+--S 1330 of 1347
+t0:=1/(2-3*x^6)
+--R
+--R
+--R 1
+--R (1) - -------
+--R 6
+--R 3x - 2
+--R Type: Fraction(Polynomial(Integer))
+--E 1330
+
+--S 1331 of 1347
+r0a:=1/2*atan(3*2^(1/6)*3^(1/3)*x/(2^(1/3)*3^(2/3)-3*x^2))/(2^(5/6)*_
+ 3^(2/3))+1/3*atanh((3/2)^(1/6)*x)/(2^(5/6)*3^(1/6))+_
+ 1/6*atanh(2^(1/6)*3^(5/6)*x/(2^(1/3)*3^(2/3)+3*x^2))/_
+ (2^(5/6)*3^(1/6))
+--R
+--R
+--R (2)
+--R 6+-+6+-+5 6+-+ 6+-+3+-+
+--R 3+-+2 x\|2 \|3 3+-+2 x\|3 6+-+ 3x\|2 \|3
+--R \|3 atanh(---------------) + 2\|3 atanh(-----) + 3\|3 atan(---------------)
+--R 3+-+3+-+2 2 6+-+ 3+-+3+-+2 2
+--R \|2 \|3 + 3x \|2 \|2 \|3 - 3x
+--R -----------------------------------------------------------------------------
+--R 6+-+5 3+-+2 6+-+
+--R 6\|2 \|3 \|3
+--R Type: Expression(Integer)
+--E 1331
+
+--S 1332 of 1347
+r0b:=-1/2*atan(1/3*(2^(1/6)*3^(5/6)-6*x)/_
+ (2^(1/6)*3^(1/3)))/(2^(5/6)*3^(2/3))+1/2*atan(1/3*_
+ (2^(1/6)*3^(5/6)+6*x)/(2^(1/6)*3^(1/3)))/(2^(5/6)*3^(2/3))+_
+ 1/3*atanh((3/2)^(1/6)*x)/(2^(5/6)*3^(1/6))-_
+ 1/12*log(2^(1/3)-6^(1/6)*x+3^(1/3)*x^2)/(2^(5/6)*3^(1/6))+_
+ 1/12*log(2^(1/3)+6^(1/6)*x+3^(1/3)*x^2)/(2^(5/6)*3^(1/6))
+--R
+--R
+--R (3)
+--R 3+-+2 6+-+ 2 3+-+ 3+-+ 3+-+2 6+-+ 2 3+-+ 3+-+
+--R \|3 log(x\|6 + x \|3 + \|2 ) - \|3 log(- x\|6 + x \|3 + \|2 )
+--R +
+--R 6+-+ 3+-+2 6+-+5 6+-+5 3+-+2
+--R 3+-+2 x\|3 6+-+ \|3 \|3 + 3x \|2 \|3
+--R 4\|3 atanh(-----) + 6\|3 atan(--------------------------)
+--R 6+-+ 9
+--R \|2
+--R +
+--R 3+-+2 6+-+5 6+-+5 3+-+2
+--R 6+-+ \|3 \|3 - 3x \|2 \|3
+--R - 6\|3 atan(--------------------------)
+--R 9
+--R /
+--R 6+-+5 3+-+2 6+-+
+--R 12\|2 \|3 \|3
+--R Type: Expression(Integer)
+--E 1332
+
+--S 1333 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R 2 6+--+2 6+--+ 2 6+--+2 6+--+
+--R log(x \|96 + 2x\|96 + 4) - log(x \|96 - 2x\|96 + 4)
+--R +
+--R +-+
+--R 6+--+ 6+--+ +-+ \|3
+--R 2log(x\|96 + 2) - 2log(x\|96 - 2) - 2\|3 atan(----------)
+--R 6+--+
+--R x\|96 - 1
+--R +
+--R +-+
+--R +-+ \|3
+--R - 2\|3 atan(----------)
+--R 6+--+
+--R x\|96 + 1
+--R /
+--R 6+--+
+--R 12\|96
+--R Type: Union(Expression(Integer),...)
+--E 1333
+
+--S 1334 of 1347
+m0a:=a0-r0a
+--R
+--R
+--R (5)
+--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+
+--R \|2 \|3 \|3 log(x \|96 + 2x\|96 + 4)
+--R +
+--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+
+--R - \|2 \|3 \|3 log(x \|96 - 2x\|96 + 4)
+--R +
+--R 6+-+5 3+-+2 6+-+ 6+--+ 6+-+5 3+-+2 6+-+ 6+--+
+--R 2\|2 \|3 \|3 log(x\|96 + - 2\|2 \|3 \|3 log(x\|96 - 2)
+--R +
+--R 6+-+6+-+5 6+-+
+--R 3+-+2 6+--+ x\|2 \|3 3+-+2 6+--+ x\|3
+--R - 2\|3 \|96 atanh(--------------- - 4\|3 \|96 atanh(-----)
+--R 3+-+3+-+2 2 6+-+
+--R \|2 \|3 + 3x \|2
+--R +
+--R 6+-+3+-+ +-+
+--R 6+-+6+--+ 3x\|2 \|3 6+-+5 +-+3+-+2 6+-+ \|3
+--R - 6\|3 \|96 atan(---------------) - 2\|2 \|3 \|3 \|3 atan(----------)
+--R 3+-+3+-+2 2 6+--+
+--R \|2 \|3 - 3x x\|96 - 1
+--R +
+--R +-+
+--R 6+-+5 +-+3+-+2 6+-+ \|3
+--R - 2\|2 \|3 \|3 \|3 atan(----------)
+--R 6+--+
+--R x\|96 + 1
+--R /
+--R 6+-+5 3+-+2 6+-+6+--+
+--R 12\|2 \|3 \|3 \|96
+--R Type: Expression(Integer)
+--E 1334
+
+--S 1335 of 1347
+d0a:=D(m0a,x)
+--R
+--R
+--R (6)
+--R 6 3+-+2 6+-+4 12 6 3+-+ 3+-+2
+--R (- 12x \|2 \|2 + (27x + 54x )\|2 )\|3
+--R +
+--R 10 6+-+4 10 4 3+-+2 3+-+ 2 3+-+6+-+4 14
+--R (18x \|2 + (27x + 18x )\|2 )\|3 + 12x \|2 \|2 + 27x
+--R +
+--R 8 2
+--R 108x - 12x
+--R *
+--R 6+-+4
+--R \|3
+--R +
+--R 10 4 3+-+6+-+2 10 4 3+-+2 3+-+2
+--R ((- 63x - 30x )\|2 \|2 + (3x + 10x )\|2 )\|3
+--R +
+--R 8 2 3+-+2 6+-+2 14 8 2 3+-+
+--R ((- 45x - 6x )\|2 \|2 - 27x - 48x - 4x )\|3
+--R +
+--R 12 6 6+-+2 12 6 3+-+
+--R (- 135x - 144x + 12)\|2 + (27x + 42x - 16)\|2
+--R *
+--R 6+-+2
+--R \|3
+--R +
+--R 8 2 3+-+2 6+-+2 3+-+2 12 6 6+-+2 3+-+
+--R (15x + 2x )\|2 \|2 \|3 + (27x + 12x + 4)\|2 \|3
+--R +
+--R 10 4 6+-+4 10 4 3+-+6+-+2
+--R (108x + 36x )\|2 + (- 63x - 30x )\|2 \|2
+--R /
+--R 12 6 3+-+2 6+-+4 12 6 3+-+ 3+-+2
+--R ((36x - 24x )\|2 \|2 + (- 216x + 144x )\|2 )\|3
+--R +
+--R 16 10 6+-+4 10 4 3+-+2 3+-+
+--R ((- 54x + 36x )\|2 + (- 108x + 72x )\|2 )\|3
+--R +
+--R 8 2 3+-+6+-+4 14 8
+--R (- 36x + 24x )\|2 \|2 - 324x + 216x
+--R *
+--R 6+-+4
+--R \|3
+--R +
+--R 10 4 3+-+6+-+2 10 4 3+-+2 3+-+2
+--R ((216x - 144x )\|2 \|2 + (- 36x + 24x )\|2 )\|3
+--R +
+--R 8 2 3+-+2 6+-+2 14 8 3+-+
+--R ((108x - 72x )\|2 \|2 + 216x - 144x )\|3
+--R +
+--R 12 6 6+-+2 12 6 3+-+
+--R (648x - 432x )\|2 + (- 216x + 216x - 48)\|2
+--R *
+--R 6+-+2
+--R \|3
+--R +
+--R 8 2 3+-+2 6+-+2 3+-+2 12 6 6+-+2 3+-+
+--R (- 36x + 24x )\|2 \|2 \|3 + (- 108x + 72x )\|2 \|3
+--R +
+--R 10 4 6+-+4 10 4 3+-+6+-+2
+--R (- 324x + 216x )\|2 + (216x - 144x )\|2 \|2
+--R Type: Expression(Integer)
+--E 1335
+
+--S 1336 of 1347
+m0b:=a0-r0b
+--R
+--R
+--R (7)
+--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+
+--R \|2 \|3 \|3 log(x \|96 + 2x\|96 + 4)
+--R +
+--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+
+--R - \|2 \|3 \|3 log(x \|96 - 2x\|96 + 4)
+--R +
+--R 6+-+5 3+-+2 6+-+ 6+--+ 6+-+5 3+-+2 6+-+ 6+--+
+--R 2\|2 \|3 \|3 log(x\|96 + - 2\|2 \|3 \|3 log(x\|96 - 2)
+--R +
+--R 3+-+2 6+--+ 6+-+ 2 3+-+ 3+-+
+--R - \|3 \|96 log(x\|6 + x \|3 + \|2 )
+--R +
+--R 6+-+
+--R 3+-+2 6+--+ 6+-+ 2 3+-+ 3+-+ 3+-+2 6+--+ x\|3
+--R \|3 \|96 log(- x\|6 + x \|3 + \|2 - 4\|3 \|96 atanh(-----)
+--R 6+-+
+--R \|2
+--R +
+--R 3+-+2 6+-+5 6+-+5 3+-+2
+--R 6+-+6+--+ \|3 \|3 + 3x \|2 \|3
+--R - 6\|3 \|96 atan(--------------------------)
+--R 9
+--R +
+--R 3+-+2 6+-+5 6+-+5 3+-+2
+--R 6+-+6+--+ \|3 \|3 - 3x \|2 \|3
+--R 6\|3 \|96 atan(--------------------------)
+--R 9
+--R +
+--R +-+ +-+
+--R 6+-+5 +-+3+-+2 6+-+ \|3 6+-+5 +-+3+-+2 6+-+ \|3
+--R - 2\|2 \|3 \|3 \|3 atan(---------- - 2\|2 \|3 \|3 \|3 atan(----------)
+--R 6+--+ 6+--+
+--R x\|96 - 1 x\|96 + 1
+--R /
+--R 6+-+5 3+-+2 6+-+6+--+
+--R 12\|2 \|3 \|3 \|96
+--R Type: Expression(Integer)
+--E 1336
+
+--S 1337 of 1347
+d0b:=D(m0b,x)
+--R
+--R
+--R (8)
+--R 12 6 6+-+2 3+-+2 10 4 6+-+4 3+-+ 8
+--R (- 144x - 192x )\|2 \|3 + (- 108x - 36x )\|2 \|3 - 564x
+--R +
+--R 2
+--R 16x
+--R *
+--R 6+-+4
+--R \|3
+--R +
+--R 10 4 6+-+4 3+-+2 8 3+-+ 12 6 6+-+2 6+-+2
+--R ((252x + 48x )\|2 \|3 + 324x \|3 + (288x + 672x )\|2 )\|3
+--R +
+--R 8 2 3+-+2 10 4 6+-+4
+--R (144x + 48x )\|3 + (- 144x - 228x )\|2
+--R *
+--R 6+-+2
+--R \|6
+--R +
+--R 6 3+-+6+-+3+-+2 10 4 6+-+5 3+-+
+--R (- 12x + 8)\|2 \|2 \|3 + (- 27x + 18x )\|2 \|3
+--R +
+--R 8 2 3+-+6+-+5 8 2 6+-+
+--R (27x - 18x )\|2 \|2 + (36x - 24x )\|2
+--R *
+--R 6+-+5
+--R \|3
+--R +
+--R 10 4 6+-+5 10 4 3+-+6+-+3 3+-+2
+--R ((- 27x + 18x )\|2 + (72x - 48x )\|2 \|2 )\|3
+--R +
+--R 8 2 3+-+6+-+5 14 8 2 6+-+ 3+-+
+--R ((27x - 18x )\|2 \|2 + (- 144x + 102x - 4x )\|2 )\|3
+--R +
+--R 12 6 6+-+3 12 6 3+-+6+-+
+--R (- 216x + 144x )\|2 + (144x - 102x + 4)\|2 \|2
+--R *
+--R 6+-+3
+--R \|3
+--R +
+--R 8 2 3+-+6+-+5 8 2 6+-+ 3+-+2
+--R ((- 54x + 36x )\|2 \|2 + (54x - 36x )\|2 )\|3
+--R +
+--R 12 6 6+-+3 6 3+-+6+-+ 3+-+
+--R ((216x - 144x )\|2 + (- 54x + 36)\|2 \|2 )\|3
+--R +
+--R 10 4 6+-+5 10 4 3+-+6+-+3
+--R (162x - 108x )\|2 + (- 216x + 144x )\|2 \|2
+--R *
+--R 6+-+
+--R \|3
+--R *
+--R 6+-+
+--R \|6
+--R +
+--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 10
+--R (216x + 72x )\|2 \|2 + (144x + 192x )\|2 \|2 + 564x
+--R +
+--R 4
+--R - 16x
+--R *
+--R 3+-+2
+--R \|3
+--R +
+--R 8 2 3+-+2 6+-+4 14 8 6+-+2
+--R (108x + 36x )\|2 \|2 + (432x + 576x )\|2
+--R +
+--R 8 2 3+-+
+--R (1128x - 32x )\|2
+--R *
+--R 3+-+
+--R \|3
+--R +
+--R 12 6 6+-+4 12 6 3+-+6+-+2 6 3+-+2
+--R (324x + 108x )\|2 + (864x + 1152x )\|2 \|2 + (564x - 16)\|2
+--R *
+--R 6+-+4
+--R \|3
+--R +
+--R 8 2 3+-+2 6+-+4 14 8 6+-+2 8 3+-+
+--R ((- 252x - 48x )\|2 \|2 + (- 288x - 672x )\|2 - 648x \|2)
+--R *
+--R 3+-+2
+--R \|3
+--R +
+--R 12 6 6+-+4 12 6 3+-+6+-+2
+--R (- 756x - 144x )\|2 + (- 576x - 1344x )\|2 \|2
+--R +
+--R 6 3+-+2
+--R - 324x \|2
+--R *
+--R 3+-+
+--R \|3
+--R +
+--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 10
+--R (- 1512x - 288x )\|2 \|2 + (- 288x - 672x )\|2 \|2 - 972x
+--R *
+--R 6+-+2
+--R \|3
+--R +
+--R 12 6 6+-+4 6 3+-+2 3+-+2
+--R ((144x + 228x )\|2 + (- 144x - 48)\|2 )\|3
+--R +
+--R 10 4 3+-+6+-+4 10 4 3+-+
+--R ((288x + 456x )\|2 \|2 - 432x - 144x )\|3
+--R +
+--R 8 2 3+-+2 6+-+4 8 2 3+-+
+--R (144x + 228x )\|2 \|2 + (- 864x - 288x )\|2
+--R /
+--R 12 6 6+-+2 3+-+2 10 4 6+-+4 3+-+ 14
+--R (864x - 576x )\|2 \|3 + (324x - 216x )\|2 \|3 + 1728x
+--R +
+--R 8 2
+--R - 1224x + 48x
+--R *
+--R 6+-+4
+--R \|3
+--R +
+--R 10 4 6+-+4 3+-+2 8 2 3+-+
+--R (- 648x + 432x )\|2 \|3 + (- 648x + 432x )\|3
+--R +
+--R 12 6 6+-+2
+--R (- 2592x + 1728x )\|2
+--R *
+--R 6+-+2
+--R \|3
+--R +
+--R 8 2 3+-+2 10 4 6+-+4
+--R (- 432x + 288x )\|3 + (972x - 648x )\|2
+--R *
+--R 6+-+2
+--R \|6
+--R +
+--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2
+--R (- 648x + 432x )\|2 \|2 + (- 864x + 576x )\|2 \|2
+--R +
+--R 16 10 4
+--R - 1728x + 1224x - 48x
+--R *
+--R 3+-+2
+--R \|3
+--R +
+--R 8 2 3+-+2 6+-+4 14 8 6+-+2
+--R (- 324x + 216x )\|2 \|2 + (- 2592x + 1728x )\|2
+--R +
+--R 14 8 2 3+-+
+--R (- 3456x + 2448x - 96x )\|2
+--R *
+--R 3+-+
+--R \|3
+--R +
+--R 12 6 6+-+4 12 6 3+-+6+-+2
+--R (- 972x + 648x )\|2 + (- 5184x + 3456x )\|2 \|2
+--R +
+--R 12 6 3+-+2
+--R (- 1728x + 1224x - 48)\|2
+--R *
+--R 6+-+4
+--R \|3
+--R +
+--R 8 2 3+-+2 6+-+4 14 8 6+-+2
+--R (648x - 432x )\|2 \|2 + (2592x - 1728x )\|2
+--R +
+--R 8 2 3+-+
+--R (1296x - 864x )\|2
+--R *
+--R 3+-+2
+--R \|3
+--R +
+--R 12 6 6+-+4 12 6 3+-+6+-+2
+--R (1944x - 1296x )\|2 + (5184x - 3456x )\|2 \|2
+--R +
+--R 6 3+-+2
+--R (648x - 432)\|2
+--R *
+--R 3+-+
+--R \|3
+--R +
+--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 10
+--R (3888x - 2592x )\|2 \|2 + (2592x - 1728x )\|2 \|2 + 1944x
+--R +
+--R 4
+--R - 1296x
+--R *
+--R 6+-+2
+--R \|3
+--R +
+--R 12 6 6+-+4 6 3+-+2 3+-+2
+--R ((- 972x + 648x )\|2 + (432x - 288)\|2 )\|3
+--R +
+--R 10 4 3+-+6+-+4 10 4 3+-+
+--R ((- 1944x + 1296x )\|2 \|2 + 1296x - 864x )\|3
+--R +
+--R 8 2 3+-+2 6+-+4 8 2 3+-+
+--R (- 972x + 648x )\|2 \|2 + (2592x - 1728x )\|2
+--R Type: Expression(Integer)
+--E 1337
+
+)clear all
+
+--S 1338 of 1347
+t0:=x^8*sqrt(-1+4*x^6)
+--R
+--R
+--R +-------+
+--R 8 | 6
+--R (1) x \|4x - 1
+--R Type: Expression(Integer)
+--E 1338
+
+--S 1339 of 1347
+r0:=-1/192*atanh(2*x^3/sqrt(-1+4*x^6))-1/96*x^3*sqrt(-1+4*x^6)+_
+ 1/12*x^9*sqrt(-1+4*x^6)
+--R
+--R
+--R 3 +-------+
+--R 2x 9 3 | 6
+--R - atanh(----------) + (16x - 2x )\|4x - 1
+--R +-------+
+--R | 6
+--R \|4x - 1
+--R (2) --------------------------------------------
+--R 192
+--R Type: Expression(Integer)
+--E 1339
+
+--S 1340 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R 9 3 | 6 12 6 | 6 3
+--R ((64x - 8x )\|4x - 1 - 128x + 32x - 1)log(\|4x - 1 - 2x )
+--R +
+--R +-------+
+--R 21 15 9 3 | 6 24 18 12
+--R (- 2048x + 768x - 80x + 2x )\|4x - 1 + 4096x - 2048x + 320x
+--R +
+--R 6
+--R - 16x
+--R /
+--R +-------+
+--R 9 3 | 6 12 6
+--R (12288x - 1536x )\|4x - 1 - 24576x + 6144x - 192
+--R Type: Union(Expression(Integer),...)
+--E 1340
+
+--S 1341 of 1347
+m0:=a0-r0
+--R
+--R
+--R +-------+ 3
+--R | 6 3 2x
+--R log(\|4x - 1 - 2x ) + atanh(----------)
+--R +-------+
+--R | 6
+--R \|4x - 1
+--R (4) -----------------------------------------
+--R 192
+--R Type: Expression(Integer)
+--E 1341
+
+--S 1342 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1342
+
+)clear all
+
+--S 1343 of 1347
+t0:=x^5*sqrt(a^6-x^6)
+--R
+--R
+--R +---------+
+--R 5 | 6 6
+--R (1) x \|- x + a
+--R Type: Expression(Integer)
+--E 1343
+
+--S 1344 of 1347
+r0:=-1/9*(a^6-x^6)^(3/2)
+--R
+--R
+--R +---------+
+--R 6 6 | 6 6
+--R (x - a )\|- x + a
+--R (2) ---------------------
+--R 9
+--R Type: Expression(Integer)
+--E 1344
+
+--S 1345 of 1347
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R 6 6 | 6 6
+--R (x - a )\|- x + a
+--R (3) ---------------------
+--R 9
+--R Type: Union(Expression(Integer),...)
+--E 1345
+
+--S 1346 of 1347
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1346
+
+--S 1347 of 1347
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1347
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich4e.input.pdf b/src/axiom-website/CATS/rich4e.input.pdf
new file mode 100644
index 0000000..2b54cad
Binary files /dev/null and b/src/axiom-website/CATS/rich4e.input.pdf differ
diff --git a/src/axiom-website/CATS/rich4f.input.pamphlet b/src/axiom-website/CATS/rich4f.input.pamphlet
new file mode 100644
index 0000000..e70485a
--- /dev/null
+++ b/src/axiom-website/CATS/rich4f.input.pamphlet
@@ -0,0 +1,21558 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich4f.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 255 supplied "optimal results".
+\item 311 matching answers.
+\item 59 cases where Axiom supplied 2 results.
+\item 10 cases that Axiom failed to integrate.
+\item 3 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich4f.output
+)spool rich4f.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1369
+t0:=x^2*sqrt(-2+x^6)
+--R
+--R
+--R +------+
+--R 2 | 6
+--R (1) x \|x - 2
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1369
+r0:=-1/3*atanh(x^3/sqrt(-2+x^6))+1/6*x^3*sqrt(-2+x^6)
+--R
+--R
+--R 3 +------+
+--R x 3 | 6
+--R - 2atanh(---------) + x \|x - 2
+--R +------+
+--R | 6
+--R \|x - 2
+--R (2) ---------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+ +------+
+--R 3 | 6 6 | 6 3 9 3 | 6 12
+--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x
+--R +
+--R 6
+--R - 2x
+--R /
+--R +------+
+--R 3 | 6 6
+--R 6x \|x - 2 - 6x + 6
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1369
+m0:=a0-r0
+--R
+--R
+--R +------+ 3
+--R | 6 3 x
+--R log(\|x - 2 - x ) + atanh(---------)
+--R +------+
+--R | 6
+--R \|x - 2
+--R (4) --------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1369
+t0:=x^2/sqrt(1-x^6)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------
+--R +--------+
+--R | 6
+--R \|- x + 1
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 1369
+r0:=1/3*asin(x^3)
+--R
+--R
+--R 3
+--R asin(x )
+--R (2) --------
+--R 3
+--R Type: Expression(Integer)
+--E 7
+
+--S 8 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 6
+--R \|- x + 1 - 1
+--R 2atan(---------------)
+--R 3
+--R x
+--R (3) - ----------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 8
+
+--S 9 of 1369
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R | 6
+--R \|- x + 1 - 1 3
+--R - 2atan(---------------) - asin(x )
+--R 3
+--R x
+--R (4) -----------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 10
+
+)clear all
+
+--S 11 of 1369
+t0:=x^2/sqrt(1+x^6)
+--R
+--R
+--R 2
+--R x
+--R (1) ---------
+--R +------+
+--R | 6
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1369
+r0:=1/3*asinh(x^3)
+--R
+--R
+--R 3
+--R asinh(x )
+--R (2) ---------
+--R 3
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R | 6 3
+--R log(\|x + 1 - x )
+--R (3) - -------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 13
+
+--S 14 of 1369
+m0:=a0-r0
+--R
+--R
+--R +------+
+--R | 6 3 3
+--R - log(\|x + 1 - x ) - asinh(x )
+--R (4) ---------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 14
+
+--S 15 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 15
+
+)clear all
+
+--S 16 of 1369
+t0:=1/(x*sqrt(1+x^6))
+--R
+--R
+--R 1
+--R (1) ----------
+--R +------+
+--R | 6
+--R x\|x + 1
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1369
+r0:=-1/3*atanh(sqrt(1+x^6))
+--R
+--R
+--R +------+
+--R | 6
+--R atanh(\|x + 1 )
+--R (2) - ----------------
+--R 3
+--R Type: Expression(Integer)
+--E 17
+
+--S 18 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+ +------+
+--R | 6 | 6
+--R - log(\|x + 1 + 1) + log(\|x + 1 - 1)
+--R (3) -----------------------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 18
+
+--S 19 of 1369
+m0:=a0-r0
+--R
+--R
+--R +------+ +------+ +------+
+--R | 6 | 6 | 6
+--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 )
+--R (4) -------------------------------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 20
+
+)clear all
+
+--S 21 of 1369
+t0:=1/(x*sqrt(-25+x^6))
+--R
+--R
+--R 1
+--R (1) -----------
+--R +-------+
+--R | 6
+--R x\|x - 25
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 1369
+r0:=1/15*atan(1/5*sqrt(-25+x^6))
+--R
+--R
+--R +-------+
+--R | 6
+--R \|x - 25
+--R atan(----------)
+--R 5
+--R (2) ----------------
+--R 15
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 6
+--R \|x - 25
+--R atan(----------)
+--R 5
+--R (3) ----------------
+--R 15
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 1369
+t0:=x^(1/3)/(1-x^6)
+--R
+--R
+--R 3+-+
+--R \|x
+--R (1) - ------
+--R 6
+--R x - 1
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 1369
+r0:=-1/6*log(1-x^(2/3))+1/12*log(1+x^(2/3)+x^(4/3))-1/6*cos(2/9*%pi)*_
+ log(1+x^(4/3)+2*x^(2/3)*cos(1/9*%pi))+1/6*cos(1/9*%pi)*log(1+_
+ x^(4/3)-2*x^(2/3)*sin(1/18*%pi))-1/6*log(1+x^(4/3)-2*x^(2/3)*_
+ cos(2/9*%pi))*sin(1/18*%pi)-1/2*atan((1+2*x^(2/3))/sqrt(3))/_
+ sqrt(3)-1/3*atan((x^(2/3)+cos(1/9*%pi))/sqrt(1-cos(1/9*%pi)^2))*_
+ cos(1/9*%pi)*(1-cos(2/9*%pi))/sqrt(1-cos(1/9*%pi)^2)+1/3*_
+ atan((x^(2/3)-cos(2/9*%pi))/sqrt(1-cos(2/9*%pi)^2))*cos(2/9*%pi)*_
+ (1-sin(1/18*%pi))/sqrt(1-cos(2/9*%pi)^2)+1/3*atan((x^(2/3)-_
+ sin(1/18*%pi))/sqrt(1-sin(1/18*%pi)^2))*(1+cos(1/9*%pi))*_
+ sin(1/18*%pi)/sqrt(1-sin(1/18*%pi)^2)
+--R
+--R
+--R (2)
+--R +----------------+ +---------------+
+--R +-+ %pi +-+ %pi | 2%pi 2 | %pi 2
+--R (4\|3 cos(---) + 4\|3 )sin(---) |- cos(----) + 1 |- cos(---) + 1
+--R 9 18 \| 9 \| 9
+--R *
+--R 3+-+2 %pi
+--R \|x - sin(---)
+--R 18
+--R atan(------------------)
+--R +---------------+
+--R | %pi 2
+--R |- sin(---) + 1
+--R \| 18
+--R +
+--R +---------------+
+--R +-+ 2%pi %pi +-+ 2%pi | %pi 2
+--R (- 4\|3 cos(----)sin(---) + 4\|3 cos(----)) |- sin(---) + 1
+--R 9 18 9 \| 18
+--R *
+--R 3+-+2 2%pi
+--R +---------------+ \|x - cos(----)
+--R | %pi 2 9
+--R |- cos(---) + 1 atan(-------------------)
+--R \| 9 +----------------+
+--R | 2%pi 2
+--R |- cos(----) + 1
+--R \| 9
+--R +
+--R +---------------+
+--R +-+ %pi 2%pi +-+ %pi | %pi 2
+--R (4\|3 cos(---)cos(----) - 4\|3 cos(---)) |- sin(---) + 1
+--R 9 9 9 \| 18
+--R *
+--R 3+-+2 %pi
+--R +----------------+ \|x + cos(---)
+--R | 2%pi 2 9
+--R |- cos(----) + 1 atan(------------------)
+--R \| 9 +---------------+
+--R | %pi 2
+--R |- cos(---) + 1
+--R \| 9
+--R +
+--R +-+ 2%pi %pi 3+-+2 3+-+
+--R - 2\|3 cos(----)log(2cos(---)\|x + x\|x + 1)
+--R 9 9
+--R +
+--R +-+ 3+-+2 3+-+ +-+ 3+-+2
+--R \|3 log(\|x + x\|x + 1) - 2\|3 log(- \|x + 1)
+--R +
+--R +-+ %pi 2%pi 3+-+2 3+-+
+--R - 2\|3 sin(---)log(- 2cos(----)\|x + x\|x + 1)
+--R 18 9
+--R +
+--R 3+-+2
+--R +-+ %pi %pi 3+-+2 3+-+ 2\|x + 1
+--R 2\|3 cos(---)log(- 2sin(---)\|x + x\|x + 1) - 6atan(----------)
+--R 9 18 +-+
+--R \|3
+--R *
+--R +---------------+ +----------------+ +---------------+
+--R | %pi 2 | 2%pi 2 | %pi 2
+--R |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1
+--R \| 18 \| 9 \| 9
+--R /
+--R +---------------+ +----------------+ +---------------+
+--R +-+ | %pi 2 | 2%pi 2 | %pi 2
+--R 12\|3 |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1
+--R \| 18 \| 9 \| 9
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R \|3 +-+ \|3
+--R (3sin(----------) - \|3 cos(----------))
+--R 3 3
+--R *
+--R log
+--R 3 4 3 2 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 3+-+2 \|3
+--R sin(----------) + (2cos(----------) + 2\|x )sin(----------)
+--R 3 3 3
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R \|3 3+-+2 \|3 3+-+
+--R cos(----------) - 2\|x cos(----------) + x\|x
+--R 3 3
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R \|3 +-+ \|3
+--R (- 3sin(----------) - \|3 cos(----------))
+--R 3 3
+--R *
+--R log
+--R 3 4 3 2 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 3+-+2 \|3
+--R sin(----------) + (2cos(----------) - \|x )sin(----------)
+--R 3 3 3
+--R +
+--R 3 3 3 4
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R +-+3+-+2 \|3 \|3 \|3
+--R 2\|3 \|x cos(----------)sin(----------) + cos(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 3+-+2 \|3 3+-+
+--R \|x cos(----------) + x\|x
+--R 3
+--R +
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 2\|3 cos(----------)
+--R 3
+--R *
+--R log
+--R 3 4 3 2 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 3+-+2 \|3
+--R sin(----------) + (2cos(----------) - \|x )sin(----------)
+--R 3 3 3
+--R +
+--R 3 3 3 4
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R +-+3+-+2 \|3 \|3 \|3
+--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 3+-+2 \|3 3+-+
+--R \|x cos(----------) + x\|x
+--R 3
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R (- 2\|3 sin(----------) + 6cos(----------))
+--R 3 3
+--R *
+--R atan
+--R 3 2 3 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R 3sin(----------) + 2\|3 cos(----------)sin(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R - 3cos(----------)
+--R 3
+--R /
+--R 3 2 3 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R +-+ \|3 \|3 \|3
+--R \|3 sin(----------) - 6cos(----------)sin(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R +-+ \|3 +-+3+-+2
+--R - \|3 cos(----------) - 2\|3 \|x
+--R 3
+--R +
+--R -
+--R 3
+--R atan(----)
+--R +-+
+--R +-+ \|3
+--R 4\|3 sin(----------)
+--R 3
+--R *
+--R atan
+--R 3 2 3 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R 3sin(----------) - 2\|3 cos(----------)sin(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R - 3cos(----------)
+--R 3
+--R /
+--R 3 2 3 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R +-+ \|3 \|3 \|3
+--R \|3 sin(----------) + 6cos(----------)sin(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R +-+ \|3 +-+3+-+2
+--R - \|3 cos(----------) - 2\|3 \|x
+--R 3
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R +-+ \|3 \|3
+--R (- 2\|3 sin(----------) - 6cos(----------))
+--R 3 3
+--R *
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R \|3 \|3
+--R 2cos(----------)sin(----------)
+--R 3 3
+--R atan(-------------------------------------------)
+--R 3 2 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R \|3 \|3 3+-+2
+--R sin(----------) - cos(----------) + \|x
+--R 3 3
+--R +
+--R +-+ 3+-+2 3+-+ +-+ 3+-+2
+--R \|3 log(\|x + x\|x + 1) - 2\|3 log(\|x - 1)
+--R +
+--R +-+3+-+2 +-+
+--R 2\|3 \|x + \|3
+--R 3atan(-------------------)
+--R 3+-+2 3+-+
+--R 2\|x + 2x\|x - 1
+--R /
+--R +-+
+--R 12\|3
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+ +---------------+
+--R \|3 +-+ \|3 | %pi 2
+--R (3sin(----------) - \|3 cos(----------)) |- sin(---) + 1
+--R 3 3 \| 18
+--R *
+--R +----------------+ +---------------+
+--R | 2%pi 2 | %pi 2
+--R |- cos(----) + 1 |- cos(---) + 1
+--R \| 9 \| 9
+--R *
+--R log
+--R 3 4 3 2 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 3+-+2 \|3
+--R sin(----------) + (2cos(----------) + 2\|x )sin(----------)
+--R 3 3 3
+--R +
+--R 3 4 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R \|3 3+-+2 \|3 3+-+
+--R cos(----------) - 2\|x cos(----------) + x\|x
+--R 3 3
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+ +---------------+
+--R \|3 +-+ \|3 | %pi 2
+--R (- 3sin(----------) - \|3 cos(----------)) |- sin(---) + 1
+--R 3 3 \| 18
+--R *
+--R +----------------+ +---------------+
+--R | 2%pi 2 | %pi 2
+--R |- cos(----) + 1 |- cos(---) + 1
+--R \| 9 \| 9
+--R *
+--R log
+--R 3 4 3 2 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 3+-+2 \|3
+--R sin(----------) + (2cos(----------) - \|x )sin(----------)
+--R 3 3 3
+--R +
+--R 3 3 3 4
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R +-+3+-+2 \|3 \|3 \|3
+--R 2\|3 \|x cos(----------)sin(----------) + cos(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 3+-+2 \|3 3+-+
+--R \|x cos(----------) + x\|x
+--R 3
+--R +
+--R 3
+--R atan(----)
+--R +-+ +---------------+ +----------------+
+--R +-+ \|3 | %pi 2 | 2%pi 2
+--R 2\|3 cos(----------) |- sin(---) + 1 |- cos(----) + 1
+--R 3 \| 18 \| 9
+--R *
+--R +---------------+
+--R | %pi 2
+--R |- cos(---) + 1
+--R \| 9
+--R *
+--R log
+--R 3 4 3 2 3 2
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 \|3 3+-+2 \|3
+--R sin(----------) + (2cos(----------) - \|x )sin(----------)
+--R 3 3 3
+--R +
+--R 3 3 3 4
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R +-+3+-+2 \|3 \|3 \|3
+--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R 3+-+2 \|3 3+-+
+--R \|x cos(----------) + x\|x
+--R 3
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+ +---------------+
+--R +-+ \|3 \|3 | %pi 2
+--R (- 2\|3 sin(----------) + 6cos(----------)) |- sin(---) + 1
+--R 3 3 \| 18
+--R *
+--R +----------------+ +---------------+
+--R | 2%pi 2 | %pi 2
+--R |- cos(----) + 1 |- cos(---) + 1
+--R \| 9 \| 9
+--R *
+--R atan
+--R 3 2 3 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R 3sin(----------) + 2\|3 cos(----------)sin(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R - 3cos(----------)
+--R 3
+--R /
+--R 3 2 3 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R +-+ \|3 \|3 \|3
+--R \|3 sin(----------) - 6cos(----------)sin(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R +-+ \|3 +-+3+-+2
+--R - \|3 cos(----------) - 2\|3 \|x
+--R 3
+--R +
+--R -
+--R 3
+--R atan(----)
+--R +-+ +---------------+ +----------------+
+--R +-+ \|3 | %pi 2 | 2%pi 2
+--R 4\|3 sin(----------) |- sin(---) + 1 |- cos(----) + 1
+--R 3 \| 18 \| 9
+--R *
+--R +---------------+
+--R | %pi 2
+--R |- cos(---) + 1
+--R \| 9
+--R *
+--R atan
+--R 3 2 3 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R \|3 +-+ \|3 \|3
+--R 3sin(----------) - 2\|3 cos(----------)sin(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R \|3
+--R - 3cos(----------)
+--R 3
+--R /
+--R 3 2 3 3
+--R atan(----) atan(----) atan(----)
+--R +-+ +-+ +-+
+--R +-+ \|3 \|3 \|3
+--R \|3 sin(----------) + 6cos(----------)sin(----------)
+--R 3 3 3
+--R +
+--R 3 2
+--R atan(----)
+--R +-+
+--R +-+ \|3 +-+3+-+2
+--R - \|3 cos(----------) - 2\|3 \|x
+--R 3
+--R +
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+ +---------------+
+--R +-+ \|3 \|3 | %pi 2
+--R (- 2\|3 sin(----------) - 6cos(----------)) |- sin(---) + 1
+--R 3 3 \| 18
+--R *
+--R +----------------+ +---------------+
+--R | 2%pi 2 | %pi 2
+--R |- cos(----) + 1 |- cos(---) + 1
+--R \| 9 \| 9
+--R *
+--R 3 3
+--R atan(----) atan(----)
+--R +-+ +-+
+--R \|3 \|3
+--R 2cos(----------)sin(----------)
+--R 3 3
+--R atan(-------------------------------------------)
+--R 3 2 3 2
+--R atan(----) atan(----)
+--R +-+ +-+
+--R \|3 \|3 3+-+2
+--R sin(----------) - cos(----------) + \|x
+--R 3 3
+--R +
+--R +----------------+ +---------------+
+--R +-+ %pi +-+ %pi | 2%pi 2 | %pi 2
+--R (- 4\|3 cos(---) - 4\|3 )sin(---) |- cos(----) + 1 |- cos(---) + 1
+--R 9 18 \| 9 \| 9
+--R *
+--R 3+-+2 %pi
+--R \|x - sin(---)
+--R 18
+--R atan(------------------)
+--R +---------------+
+--R | %pi 2
+--R |- sin(---) + 1
+--R \| 18
+--R +
+--R +---------------+
+--R +-+ 2%pi %pi +-+ 2%pi | %pi 2
+--R (4\|3 cos(----)sin(---) - 4\|3 cos(----)) |- sin(---) + 1
+--R 9 18 9 \| 18
+--R *
+--R 3+-+2 2%pi
+--R +---------------+ \|x - cos(----)
+--R | %pi 2 9
+--R |- cos(---) + 1 atan(-------------------)
+--R \| 9 +----------------+
+--R | 2%pi 2
+--R |- cos(----) + 1
+--R \| 9
+--R +
+--R +---------------+
+--R +-+ %pi 2%pi +-+ %pi | %pi 2
+--R (- 4\|3 cos(---)cos(----) + 4\|3 cos(---)) |- sin(---) + 1
+--R 9 9 9 \| 18
+--R *
+--R 3+-+2 %pi
+--R +----------------+ \|x + cos(---)
+--R | 2%pi 2 9
+--R |- cos(----) + 1 atan(------------------)
+--R \| 9 +---------------+
+--R | %pi 2
+--R |- cos(---) + 1
+--R \| 9
+--R +
+--R +-+ 2%pi %pi 3+-+2 3+-+ +-+ 3+-+2
+--R 2\|3 cos(----)log(2cos(---)\|x + x\|x + 1) - 2\|3 log(\|x - 1)
+--R 9 9
+--R +
+--R +-+ 3+-+2
+--R 2\|3 log(- \|x + 1)
+--R +
+--R +-+ %pi 2%pi 3+-+2 3+-+
+--R 2\|3 sin(---)log(- 2cos(----)\|x + x\|x + 1)
+--R 18 9
+--R +
+--R 3+-+2
+--R +-+ %pi %pi 3+-+2 3+-+ 2\|x + 1
+--R - 2\|3 cos(---)log(- 2sin(---)\|x + x\|x + 1) + 6atan(----------)
+--R 9 18 +-+
+--R \|3
+--R +
+--R +-+3+-+2 +-+
+--R 2\|3 \|x + \|3
+--R 3atan(-------------------)
+--R 3+-+2 3+-+
+--R 2\|x + 2x\|x - 1
+--R *
+--R +---------------+ +----------------+ +---------------+
+--R | %pi 2 | 2%pi 2 | %pi 2
+--R |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1
+--R \| 18 \| 9 \| 9
+--R /
+--R +---------------+ +----------------+ +---------------+
+--R +-+ | %pi 2 | 2%pi 2 | %pi 2
+--R 12\|3 |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1
+--R \| 18 \| 9 \| 9
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 1369 Value stack overflow
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 1369
+t0:=x^8*(a+b*x^7)
+--R
+--R
+--R 15 8
+--R (1) b x + a x
+--R Type: Polynomial(Integer)
+--E 31
+
+--S 32 of 1369
+r0:=1/9*a*x^9+1/16*b*x^16
+--R
+--R
+--R 1 16 1 9
+--R (2) -- b x + - a x
+--R 16 9
+--R Type: Polynomial(Fraction(Integer))
+--E 32
+
+--S 33 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 16 1 9
+--R (3) -- b x + - a x
+--R 16 9
+--R Type: Polynomial(Fraction(Integer))
+--E 33
+
+--S 34 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 34
+
+--S 35 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 35
+
+)clear all
+
+--S 36 of 1369
+t0:=x^9/(a+b*x^8)
+--R
+--R
+--R 9
+--R x
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 36
+
+--S 37 of 1369
+r0:=1/2*x^2/b+1/4*a^(1/4)*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/(b^(5/4)*_
+ sqrt(2))-1/4*a^(1/4)*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/(b^(5/4)*_
+ sqrt(2))+1/8*a^(1/4)*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+sqrt(a)+_
+ x^4*sqrt(b))/(b^(5/4)*sqrt(2))-1/8*a^(1/4)*log(a^(1/4)*b^(1/4)*_
+ x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/(b^(5/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+
+--R - \|a log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 +-+4+-+ 4+-+
+--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ 4+-+ x \|2 \|b + \|a
+--R \|a log(- x \|2 \|a \|b + x \|b + \|a ) - 2\|a atan(-----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+ 4+-+
+--R 4+-+ x \|2 \|b - \|a 2 +-+4+-+
+--R - 2\|a atan(-----------------) + 4x \|2 \|b
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+
+--R 8b\|2 \|b
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+
+--R | a | a 2
+--R - 2b |- ------ log(8b |- ------ + x )
+--R 4| 5 4| 5
+--R \| 4096b \| 4096b
+--R +
+--R +--------+
+--R | a
+--R 8b |- ------
+--R +--------+ +--------+ +--------+ 4| 5
+--R | a | a 2 | a \| 4096b
+--R 2b |- ------ log(- 8b |- ------ + x + 4b |- ------ atan(-------------)
+--R 4| 5 4| 5 4| 5 2
+--R \| 4096b \| 4096b \| 4096b x
+--R +
+--R 2
+--R x
+--R /
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+
+--R \|a log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R +--------+ +--------+
+--R +-+ | a 4+-+ | a 2
+--R - 8b\|2 |- ------ \|b log(8b |- ------ + x )
+--R 4| 5 4| 5
+--R \| 4096b \| 4096b
+--R +
+--R +--------+ +--------+
+--R +-+ | a 4+-+ | a 2
+--R 8b\|2 |- ------ \|b log(- 8b |- ------ + x )
+--R 4| 5 4| 5
+--R \| 4096b \| 4096b
+--R +
+--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+
+--R - \|a log(- x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+
+--R 4+-+ x \|2 \|b + \|a 4+-+ x \|2 \|b - \|a
+--R 2\|a atan(-----------------) + 2\|a atan(-----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +--------+
+--R | a
+--R 8b |- ------
+--R +--------+ 4| 5
+--R +-+ | a 4+-+ \| 4096b
+--R 16b\|2 |- ------ \|b atan(-------------)
+--R 4| 5 2
+--R \| 4096b x
+--R /
+--R +-+4+-+
+--R 8b\|2 \|b
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 1369
+t0:=x^7/(a+b*x^8)
+--R
+--R
+--R 7
+--R x
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 41
+
+--S 42 of 1369
+r0:=1/8*log(a+b*x^8)/b
+--R
+--R
+--R 8
+--R log(b x + a)
+--R (2) -------------
+--R 8b
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8
+--R log(b x + a)
+--R (3) -------------
+--R 8b
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 1369
+t0:=x^5/(a+b*x^8)
+--R
+--R
+--R 5
+--R x
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 46
+
+--S 47 of 1369
+r0:=-1/4*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_
+ 1/4*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_
+ 1/8*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/_
+ (a^(1/4)*b^(3/4)*sqrt(2))-1/8*log(a^(1/4)*b^(1/4)*x^2*sqrt(2)+_
+ sqrt(a)+x^4*sqrt(b))/(a^(1/4)*b^(3/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 +-+4+-+4+-+ 4 +-+ +-+
+--R - log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 +-+4+-+ 4+-+
+--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a
+--R log(- x \|2 \|a \|b + x \|b + \|a ) + 2atan(-----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+ 4+-+
+--R x \|2 \|b - \|a
+--R 2atan(-----------------)
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+4+-+3
+--R 8\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+3
+--R | 1 2 | 1 2
+--R |- -------- log(512a b |- -------- + x )
+--R 4| 3 4| 3
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+ +----------+3
+--R | 1 2 | 1 2
+--R - |- -------- log(- 512a b |- -------- + x )
+--R 4| 3 4| 3
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+3
+--R 2 | 1
+--R 512a b |- --------
+--R +----------+ 4| 3
+--R | 1 \| 4096a b
+--R 2 |- -------- atan(---------------------)
+--R 4| 3 2
+--R \| 4096a b x
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 +-+4+-+4+-+ 4 +-+ +-+
+--R log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R +----------+ +----------+3
+--R +-+ | 1 4+-+4+-+3 2 | 1 2
+--R 8\|2 |- -------- \|a \|b log(512a b |- -------- + x )
+--R 4| 3 4| 3
+--R \| 4096a b \| 4096a b
+--R +
+--R +----------+ +----------+3
+--R +-+ | 1 4+-+4+-+3 2 | 1 2
+--R - 8\|2 |- -------- \|a \|b log(- 512a b |- -------- + x )
+--R 4| 3 4| 3
+--R \| 4096a b \| 4096a b
+--R +
+--R 2 +-+4+-+ 4+-+
+--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a
+--R - log(- x \|2 \|a \|b + x \|b + \|a ) - 2atan(-----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+ 4+-+
+--R x \|2 \|b - \|a
+--R - 2atan(-----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +----------+3
+--R 2 | 1
+--R 512a b |- --------
+--R +----------+ 4| 3
+--R +-+ | 1 4+-+4+-+3 \| 4096a b
+--R 16\|2 |- -------- \|a \|b atan(---------------------)
+--R 4| 3 2
+--R \| 4096a b x
+--R /
+--R +-+4+-+4+-+3
+--R 8\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 1369
+t0:=x^3/(a+b*x^8)
+--R
+--R
+--R 3
+--R x
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 1369
+r0:=1/4*atan(x^4*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b))
+--R
+--R
+--R 4 +-+
+--R x \|b
+--R atan(------)
+--R +-+
+--R \|a
+--R (2) ------------
+--R +-+ +-+
+--R 4\|a \|b
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 +-----+ 4
+--R (b x - a)\|- a b + 2a b x 4 +---+
+--R log(----------------------------) x \|a b
+--R 8 atan(--------)
+--R b x + a a
+--R (3) [---------------------------------,--------------]
+--R +-----+ +---+
+--R 8\|- a b 4\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 53
+
+--S 54 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R 8 +-----+ 4 4 +-+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b
+--R \|a \|b log(----------------------------) - 2\|- a b atan(------)
+--R 8 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 8\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+--S 56 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R 4 +---+ 4 +-+
+--R +-+ +-+ x \|a b +---+ x \|b
+--R \|a \|b atan(--------) - \|a b atan(------)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------
+--R +-+ +-+ +---+
+--R 4\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 57
+
+)clear all
+
+--S 58 of 1369
+t0:=x/(a+b*x^8)
+--R
+--R
+--R x
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 58
+
+--S 59 of 1369
+r0:=-1/4*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))+_
+ 1/4*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))-_
+ 1/8*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/_
+ (a^(3/4)*b^(1/4)*sqrt(2))+1/8*log(a^(1/4)*b^(1/4)*x^2*sqrt(2)+_
+ sqrt(a)+x^4*sqrt(b))/(a^(3/4)*b^(1/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 +-+4+-+4+-+ 4 +-+ +-+
+--R log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 +-+4+-+ 4+-+
+--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a
+--R - log(- x \|2 \|a \|b + x \|b + \|a ) + 2atan(-----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+ 4+-+
+--R x \|2 \|b - \|a
+--R 2atan(-----------------)
+--R 4+-+
+--R \|a
+--R /
+--R +-+4+-+3 4+-+
+--R 8\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+
+--R | 1 | 1 2
+--R |- ------- log(8a |- ------- + x )
+--R 4| 3 4| 3
+--R \| 4096a b \| 4096a b
+--R +
+--R +---------+
+--R | 1
+--R 8a |- -------
+--R +---------+ +---------+ +---------+ 4| 3
+--R | 1 | 1 2 | 1 \| 4096a b
+--R - |- ------- log(- 8a |- ------- + x ) - 2 |- ------- atan(--------------)
+--R 4| 3 4| 3 4| 3 2
+--R \| 4096a b \| 4096a b \| 4096a b x
+--R Type: Union(Expression(Integer),...)
+--E 60
+
+--S 61 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 +-+4+-+4+-+ 4 +-+ +-+
+--R - log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R +---------+ +---------+
+--R +-+ | 1 4+-+3 4+-+ | 1 2
+--R 8\|2 |- ------- \|a \|b log(8a |- ------- + x )
+--R 4| 3 4| 3
+--R \| 4096a b \| 4096a b
+--R +
+--R +---------+ +---------+
+--R +-+ | 1 4+-+3 4+-+ | 1 2
+--R - 8\|2 |- ------- \|a \|b log(- 8a |- ------- + x )
+--R 4| 3 4| 3
+--R \| 4096a b \| 4096a b
+--R +
+--R 2 +-+4+-+ 4+-+
+--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a
+--R log(- x \|2 \|a \|b + x \|b + \|a ) - 2atan(-----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+ 4+-+
+--R x \|2 \|b - \|a
+--R - 2atan(-----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +---------+
+--R | 1
+--R 8a |- -------
+--R +---------+ 4| 3
+--R +-+ | 1 4+-+3 4+-+ \| 4096a b
+--R - 16\|2 |- ------- \|a \|b atan(--------------)
+--R 4| 3 2
+--R \| 4096a b x
+--R /
+--R +-+4+-+3 4+-+
+--R 8\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 62
+
+)clear all
+
+--S 63 of 1369
+t0:=1/(x*(a+b*x^8))
+--R
+--R
+--R 1
+--R (1) ----------
+--R 9
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 63
+
+--S 64 of 1369
+r0:=log(x)/a-1/8*log(a+b*x^8)/a
+--R
+--R
+--R 8
+--R - log(b x + a) + 8log(x)
+--R (2) -------------------------
+--R 8a
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8
+--R - log(b x + a) + 8log(x)
+--R (3) -------------------------
+--R 8a
+--R Type: Union(Expression(Integer),...)
+--E 65
+
+--S 66 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 67
+
+)clear all
+
+--S 68 of 1369
+t0:=1/(x^3*(a+b*x^8))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 11 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 68
+
+--S 69 of 1369
+r0:=(-1/2)/(a*x^2)+1/4*b^(1/4)*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/_
+ (a^(5/4)*sqrt(2))-1/4*b^(1/4)*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/_
+ (a^(5/4)*sqrt(2))-1/8*b^(1/4)*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+_
+ sqrt(a)+x^4*sqrt(b))/(a^(5/4)*sqrt(2))+1/8*b^(1/4)*log(a^(1/4)*_
+ b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/(a^(5/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 2 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+
+--R x \|b log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+
+--R - x \|b log(- x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+
+--R 2 4+-+ x \|2 \|b + \|a 2 4+-+ x \|2 \|b - \|a
+--R - 2x \|b atan(----------------- - 2x \|b atan(-----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+4+-+
+--R - 4\|2 \|a
+--R /
+--R 2 +-+4+-+
+--R 8a x \|2 \|a
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+3
+--R 2 | b 4 | b 2
+--R - 2a x |- ------ log(512a |- ------ + b x )
+--R 4| 5 4| 5
+--R \| 4096a \| 4096a
+--R +
+--R +--------+ +--------+3
+--R 2 | b 4 | b 2
+--R 2a x |- ------ log(- 512a |- ------ + b x )
+--R 4| 5 4| 5
+--R \| 4096a \| 4096a
+--R +
+--R +--------+3
+--R 4 | b
+--R 512a |- ------
+--R +--------+ 4| 5
+--R 2 | b \| 4096a
+--R - 4a x |- ------ atan(----------------- - 1
+--R 4| 5 2
+--R \| 4096a b x
+--R /
+--R 2
+--R 2a x
+--R Type: Union(Expression(Integer),...)
+--E 70
+
+--S 71 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+
+--R - \|b log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R +--------+ +--------+3
+--R +-+ | b 4+-+ 4 | b 2
+--R - 8a\|2 |- ------ \|a log(512a |- ------ + b x )
+--R 4| 5 4| 5
+--R \| 4096a \| 4096a
+--R +
+--R +--------+ +--------+3
+--R +-+ | b 4+-+ 4 | b 2
+--R 8a\|2 |- ------ \|a log(- 512a |- ------ + b x )
+--R 4| 5 4| 5
+--R \| 4096a \| 4096a
+--R +
+--R 2 +-+4+-+ 4+-+
+--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ 4+-+ x \|2 \|b + \|a
+--R \|b log(- x \|2 \|a \|b + x \|b + \|a ) + 2\|b atan(-----------------)
+--R 4+-+
+--R \|a
+--R +
+--R 2 +-+4+-+ 4+-+
+--R 4+-+ x \|2 \|b - \|a
+--R 2\|b atan(-----------------)
+--R 4+-+
+--R \|a
+--R +
+--R +--------+3
+--R 4 | b
+--R 512a |- ------
+--R +--------+ 4| 5
+--R +-+ | b 4+-+ \| 4096a
+--R - 16a\|2 |- ------ \|a atan(-----------------)
+--R 4| 5 2
+--R \| 4096a b x
+--R /
+--R +-+4+-+
+--R 8a\|2 \|a
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 72
+
+)clear all
+
+--S 73 of 1369
+t0:=1/(x^5*(a+b*x^8))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 13 5
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 73
+
+--S 74 of 1369
+r0:=(-1/4)/(a*x^4)-1/4*atan(x^4*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2)
+--R
+--R
+--R 4 +-+
+--R 4 +-+ x \|b +-+
+--R - x \|b atan(------) - \|a
+--R +-+
+--R \|a
+--R (2) ---------------------------
+--R 4 +-+
+--R 4a x \|a
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+ +-+
+--R 4 | b 8 |b
+--R +---+ - 2a x |- - + b x - a +-+ a |-
+--R 4 | b \| a 4 |b \|a
+--R x |- - log(------------------------) - 2 x |- atan(-----) - 1
+--R \| a 8 \|a 4
+--R b x + a b x
+--R (3) [-----------------------------------------,---------------------]
+--R 4 4
+--R 8a x 4a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 75
+
+--S 76 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R 4 | b 8
+--R +---+ - 2a x |- - + b x - a 4 +-+
+--R | b +-+ \| a +-+ x \|b
+--R |- - \|a log(------------------------) + 2\|b atan(------)
+--R \| a 8 +-+
+--R b x + a \|a
+--R (4) -----------------------------------------------------------
+--R +-+
+--R 8a\|a
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R 4 +-+ +-+ a |-
+--R +-+ x \|b +-+ |b \|a
+--R \|b atan(------) + \|a |- atan(-----)
+--R +-+ \|a 4
+--R \|a b x
+--R (6) --------------------------------------
+--R +-+
+--R 4a\|a
+--R Type: Expression(Integer)
+--E 78
+
+--S 79 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 79
+
+)clear all
+
+--S 80 of 1369
+t0:=1/(x^7*(a+b*x^8))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 15 7
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 80
+
+--S 81 of 1369
+r0:=(-1/6)/(a*x^6)+1/4*b^(3/4)*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/_
+ (a^(7/4)*sqrt(2))-1/4*b^(3/4)*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/_
+ (a^(7/4)*sqrt(2))+1/8*b^(3/4)*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+_
+ sqrt(a)+x^4*sqrt(b))/(a^(7/4)*sqrt(2))-1/8*b^(3/4)*log(a^(1/4)*_
+ b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/(a^(7/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 6 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+
+--R - 3x \|b log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R 6 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+
+--R 3x \|b log(- x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+
+--R 6 4+-+3 x \|2 \|b + \|a 6 4+-+3 x \|2 \|b - \|a
+--R - 6x \|b atan(----------------- - 6x \|b atan(-----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +-+4+-+3
+--R - 4\|2 \|a
+--R /
+--R 6 +-+4+-+3
+--R 24a x \|2 \|a
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+
+--R | 3 | 3
+--R 6 | b 2 | b 2
+--R - 6a x |- ------ log(8a |- ------ + b x )
+--R 4| 7 4| 7
+--R \| 4096a \| 4096a
+--R +
+--R +--------+ +--------+
+--R | 3 | 3
+--R 6 | b 2 | b 2
+--R 6a x |- ------ log(- 8a |- ------ + b x )
+--R 4| 7 4| 7
+--R \| 4096a \| 4096a
+--R +
+--R +--------+
+--R | 3
+--R 2 | b
+--R +--------+ 8a |- ------
+--R | 3 4| 7
+--R 6 | b \| 4096a
+--R 12a x |- ------ atan(-------------- - 1
+--R 4| 7 2
+--R \| 4096a b x
+--R /
+--R 6
+--R 6a x
+--R Type: Union(Expression(Integer),...)
+--E 82
+
+--S 83 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+
+--R \|b log(x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R +--------+ +--------+
+--R | 3 | 3
+--R +-+ | b 4+-+3 2 | b 2
+--R - 8a\|2 |- ------ \|a log(8a |- ------ + b x )
+--R 4| 7 4| 7
+--R \| 4096a \| 4096a
+--R +
+--R +--------+ +--------+
+--R | 3 | 3
+--R +-+ | b 4+-+3 2 | b 2
+--R 8a\|2 |- ------ \|a log(- 8a |- ------ + b x )
+--R 4| 7 4| 7
+--R \| 4096a \| 4096a
+--R +
+--R 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+
+--R - \|b log(- x \|2 \|a \|b + x \|b + \|a )
+--R +
+--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+
+--R 4+-+3 x \|2 \|b + \|a 4+-+3 x \|2 \|b - \|a
+--R 2\|b atan(-----------------) + 2\|b atan(-----------------)
+--R 4+-+ 4+-+
+--R \|a \|a
+--R +
+--R +--------+
+--R | 3
+--R 2 | b
+--R +--------+ 8a |- ------
+--R | 3 4| 7
+--R +-+ | b 4+-+3 \| 4096a
+--R 16a\|2 |- ------ \|a atan(--------------)
+--R 4| 7 2
+--R \| 4096a b x
+--R /
+--R +-+4+-+3
+--R 8a\|2 \|a
+--R Type: Expression(Integer)
+--E 83
+
+--S 84 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 84
+
+)clear all
+
+--S 85 of 1369
+t0:=1/(x^9*(a+b*x^8))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 17 9
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 85
+
+--S 86 of 1369
+r0:=(-1/8)/(a*x^8)-b*log(x)/a^2+1/8*b*log(a+b*x^8)/a^2
+--R
+--R
+--R 8 8 8
+--R b x log(b x + a) - 8b x log(x) - a
+--R (2) -----------------------------------
+--R 2 8
+--R 8a x
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 8 8
+--R b x log(b x + a) - 8b x log(x) - a
+--R (3) -----------------------------------
+--R 2 8
+--R 8a x
+--R Type: Union(Expression(Integer),...)
+--E 87
+
+--S 88 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 88
+
+--S 89 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 89
+
+)clear all
+
+--S 90 of 1369
+t0:=x^8/(a+b*x^8)
+--R
+--R
+--R 8
+--R x
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 90
+
+--S 91 of 1369
+r0:=x/b-1/4*(-a)^(1/8)*atan(b^(1/8)*x/(-a)^(1/8))/b^(9/8)-1/4*(-a)^(1/8)*_
+ atanh(b^(1/8)*x/(-a)^(1/8))/b^(9/8)+1/4*(-a)^(1/8)*atan(1-b^(1/8)*_
+ x*sqrt(2)/(-a)^(1/8))/(b^(9/8)*sqrt(2))-1/4*(-a)^(1/8)*_
+ atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/(b^(9/8)*sqrt(2))+1/8*_
+ (-a)^(1/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*_
+ sqrt(2))/(b^(9/8)*sqrt(2))-1/8*(-a)^(1/8)*log((-a)^(1/4)+b^(1/4)*_
+ x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/(b^(9/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - \|- a log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+
+--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+---+ x\|b
+--R \|- a log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|- a atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+
+--R 8+---+ x\|2 \|b + \|- a 8+---+ x\|2 \|b - \|- a
+--R - 2\|- a atan(------------------) - 2\|- a atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+
+--R +-+8+---+ x\|b +-+8+-+
+--R - 2\|2 \|- a atan(------) + 8x\|2 \|b
+--R 8+---+
+--R \|- a
+--R /
+--R +-+8+-+
+--R 8b\|2 \|b
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +------------+
+--R | a
+--R b |- ----------
+--R 8| 9
+--R \| 16777216b
+--R *
+--R +------------+2 +------------+
+--R 2 | a +-+ | a 2
+--R log(64b |- ---------- + 8b x\|2 |- ---------- + x )
+--R 8| 9 8| 9
+--R \| 16777216b \| 16777216b
+--R +
+--R +------------+ +------------+2 +------------+
+--R | a 2 | a +-+ | a 2
+--R b |- ---------- log(64b |- ---------- - 8b x\|2 |- ---------- + x )
+--R 8| 9 8| 9 8| 9
+--R \| 16777216b \| 16777216b \| 16777216b
+--R +
+--R +------------+ +------------+
+--R +-+ | a | a
+--R - b\|2 |- ---------- log(8b |- ---------- + x)
+--R 8| 9 8| 9
+--R \| 16777216b \| 16777216b
+--R +
+--R +------------+ +------------+
+--R +-+ | a | a
+--R b\|2 |- ---------- log(- 8b |- ---------- + x)
+--R 8| 9 8| 9
+--R \| 16777216b \| 16777216b
+--R +
+--R +------------+
+--R | a
+--R 8b |- ----------
+--R +------------+ 8| 9
+--R +-+ | a \| 16777216b
+--R 2b\|2 |- ---------- atan(-----------------)
+--R 8| 9 x
+--R \| 16777216b
+--R +
+--R +------------+
+--R | a
+--R 8b |- ----------
+--R +------------+ 8| 9
+--R | a \| 16777216b
+--R - 2b |- ---------- atan(-------------------------)
+--R 8| 9 +------------+
+--R \| 16777216b | a +-+
+--R 8b |- ---------- - x\|2
+--R 8| 9
+--R \| 16777216b
+--R +
+--R +------------+
+--R | a
+--R 8b |- ----------
+--R +------------+ 8| 9
+--R | a \| 16777216b +-+
+--R 2b |- ---------- atan(------------------------- + x\|2
+--R 8| 9 +------------+
+--R \| 16777216b | a +-+
+--R 8b |- ---------- + x\|2
+--R 8| 9
+--R \| 16777216b
+--R /
+--R +-+
+--R b\|2
+--R Type: Union(Expression(Integer),...)
+--E 92
+
+--S 93 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+
+--R \|- a log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R -
+--R +------------+
+--R | a 8+-+
+--R 8b |- ---------- \|b
+--R 8| 9
+--R \| 16777216b
+--R *
+--R +------------+2 +------------+
+--R 2 | a +-+ | a 2
+--R log(64b |- ---------- + 8b x\|2 |- ---------- + x )
+--R 8| 9 8| 9
+--R \| 16777216b \| 16777216b
+--R +
+--R +------------+
+--R | a 8+-+
+--R 8b |- ---------- \|b
+--R 8| 9
+--R \| 16777216b
+--R *
+--R +------------+2 +------------+
+--R 2 | a +-+ | a 2
+--R log(64b |- ---------- - 8b x\|2 |- ---------- + x )
+--R 8| 9 8| 9
+--R \| 16777216b \| 16777216b
+--R +
+--R +------------+ +------------+
+--R +-+ | a 8+-+ | a
+--R - 8b\|2 |- ---------- \|b log(8b |- ---------- + x)
+--R 8| 9 8| 9
+--R \| 16777216b \| 16777216b
+--R +
+--R +------------+ +------------+
+--R +-+ | a 8+-+ | a
+--R 8b\|2 |- ---------- \|b log(- 8b |- ---------- + x)
+--R 8| 9 8| 9
+--R \| 16777216b \| 16777216b
+--R +
+--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - \|- a log(- x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+ +-+8+-+ 8+---+
+--R +-+8+---+ x\|b 8+---+ x\|2 \|b + \|- a
+--R 2\|2 \|- a atanh(------) + 2\|- a atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ 8+---+ 8+-+
+--R 8+---+ x\|2 \|b - \|- a +-+8+---+ x\|b
+--R 2\|- a atan(------------------) + 2\|2 \|- a atan(------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +------------+
+--R | a
+--R 8b |- ----------
+--R +------------+ 8| 9
+--R +-+ | a 8+-+ \| 16777216b
+--R 16b\|2 |- ---------- \|b atan(-----------------)
+--R 8| 9 x
+--R \| 16777216b
+--R +
+--R +------------+
+--R | a
+--R 8b |- ----------
+--R +------------+ 8| 9
+--R | a 8+-+ \| 16777216b
+--R - 16b |- ---------- \|b atan(-------------------------)
+--R 8| 9 +------------+
+--R \| 16777216b | a +-+
+--R 8b |- ---------- - x\|2
+--R 8| 9
+--R \| 16777216b
+--R +
+--R +------------+
+--R | a
+--R 8b |- ----------
+--R +------------+ 8| 9
+--R | a 8+-+ \| 16777216b
+--R 16b |- ---------- \|b atan(-------------------------)
+--R 8| 9 +------------+
+--R \| 16777216b | a +-+
+--R 8b |- ---------- + x\|2
+--R 8| 9
+--R \| 16777216b
+--R /
+--R +-+8+-+
+--R 8b\|2 \|b
+--R Type: Expression(Integer)
+--E 93
+
+--S 94 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 94
+
+)clear all
+
+--S 95 of 1369
+t0:=x^6/(a+b*x^8)
+--R
+--R
+--R 6
+--R x
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 95
+
+--S 96 of 1369
+r0:=1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(1/8)*b^(7/8))-1/4*atanh(b^(1/8)*_
+ x/(-a)^(1/8))/((-a)^(1/8)*b^(7/8))-1/4*atan(1-b^(1/8)*x*sqrt(2)/_
+ (-a)^(1/8))/((-a)^(1/8)*b^(7/8)*sqrt(2))+1/4*atan(1+b^(1/8)*x*_
+ sqrt(2)/(-a)^(1/8))/((-a)^(1/8)*b^(7/8)*sqrt(2))+1/8*log((-a)^(1/4)+_
+ b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(1/8)*b^(7/8)*_
+ sqrt(2))-1/8*log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*_
+ x*sqrt(2))/((-a)^(1/8)*b^(7/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+
+--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b
+--R log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+
+--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b
+--R 2atan(------------------) + 2atan(------------------) + 2\|2 atan(------)
+--R 8+---+ 8+---+ 8+---+
+--R \|- a \|- a \|- a
+--R /
+--R +-+8+---+8+-+7
+--R 8\|2 \|- a \|b
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R | 1
+--R |- ------------
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R log
+--R +--------------+7 +--------------+6
+--R 6 +-+ | 1 5 | 1
+--R 2097152a b x\|2 |- ------------ - 262144a b |- ------------
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R 2
+--R x
+--R +
+--R +--------------+ +--------------+7
+--R +-+ | 1 6 | 1
+--R \|2 |- ------------ log(2097152a b |- ------------ + x)
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+7
+--R +-+ | 1 6 | 1
+--R - \|2 |- ------------ log(- 2097152a b |- ------------ + x)
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R | 1
+--R |- ------------
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R log
+--R +--------------+7
+--R 6 +-+ | 1
+--R - 2097152a b x\|2 |- ------------
+--R 8| 7
+--R \| 16777216a b
+--R +
+--R +--------------+6
+--R 5 | 1 2
+--R - 262144a b |- ------------ + x
+--R 8| 7
+--R \| 16777216a b
+--R +
+--R +--------------+7
+--R 6 | 1
+--R 2097152a b |- ------------
+--R +--------------+ 8| 7
+--R +-+ | 1 \| 16777216a b
+--R 2\|2 |- ------------ atan(-----------------------------)
+--R 8| 7 x
+--R \| 16777216a b
+--R +
+--R +--------------+7
+--R 6 | 1
+--R 2097152a b |- ------------
+--R +--------------+ 8| 7
+--R | 1 \| 16777216a b
+--R - 2 |- ------------ atan(-------------------------------------)
+--R 8| 7 +--------------+7
+--R \| 16777216a b 6 | 1 +-+
+--R 2097152a b |- ------------ - x\|2
+--R 8| 7
+--R \| 16777216a b
+--R +
+--R +--------------+7
+--R 6 | 1
+--R 2097152a b |- ------------
+--R +--------------+ 8| 7
+--R | 1 \| 16777216a b
+--R 2 |- ------------ atan(-------------------------------------)
+--R 8| 7 +--------------+7
+--R \| 16777216a b 6 | 1 +-+
+--R 2097152a b |- ------------ + x\|2
+--R 8| 7
+--R \| 16777216a b
+--R /
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 97
+
+--S 98 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ 2 4+-+ 4+---+
+--R log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R +--------------+
+--R 8+---+ | 1 8+-+7
+--R 8\|- a |- ------------ \|b
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R log
+--R +--------------+7 +--------------+6
+--R 6 +-+ | 1 5 | 1
+--R 2097152a b x\|2 |- ------------ - 262144a b |- ------------
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R 2
+--R x
+--R +
+--R +--------------+ +--------------+7
+--R +-+8+---+ | 1 8+-+7 6 | 1
+--R 8\|2 \|- a |- ------------ \|b log(2097152a b |- ------------ + x)
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R +-+8+---+ | 1 8+-+7
+--R 8\|2 \|- a |- ------------ \|b
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R +--------------+7
+--R 6 | 1
+--R log(- 2097152a b |- ------------ + x)
+--R 8| 7
+--R \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R 8+---+ | 1 8+-+7
+--R 8\|- a |- ------------ \|b
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R log
+--R +--------------+7
+--R 6 +-+ | 1
+--R - 2097152a b x\|2 |- ------------
+--R 8| 7
+--R \| 16777216a b
+--R +
+--R +--------------+6
+--R 5 | 1 2
+--R - 262144a b |- ------------ + x
+--R 8| 7
+--R \| 16777216a b
+--R +
+--R 8+-+
+--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b
+--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+
+--R x\|2 \|b + \|- a x\|2 \|b - \|- a
+--R - 2atan(------------------) - 2atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+
+--R +-+ x\|b
+--R - 2\|2 atan(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +--------------+7
+--R 6 | 1
+--R 2097152a b |- ------------
+--R +--------------+ 8| 7
+--R +-+8+---+ | 1 8+-+7 \| 16777216a b
+--R 16\|2 \|- a |- ------------ \|b atan(-----------------------------)
+--R 8| 7 x
+--R \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R 8+---+ | 1 8+-+7
+--R 16\|- a |- ------------ \|b
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R +--------------+7
+--R 6 | 1
+--R 2097152a b |- ------------
+--R 8| 7
+--R \| 16777216a b
+--R atan(-------------------------------------)
+--R +--------------+7
+--R 6 | 1 +-+
+--R 2097152a b |- ------------ - x\|2
+--R 8| 7
+--R \| 16777216a b
+--R +
+--R +--------------+7
+--R 6 | 1
+--R 2097152a b |- ------------
+--R +--------------+ 8| 7
+--R 8+---+ | 1 8+-+7 \| 16777216a b
+--R 16\|- a |- ------------ \|b atan(-------------------------------------)
+--R 8| 7 +--------------+7
+--R \| 16777216a b 6 | 1 +-+
+--R 2097152a b |- ------------ + x\|2
+--R 8| 7
+--R \| 16777216a b
+--R /
+--R +-+8+---+8+-+7
+--R 8\|2 \|- a \|b
+--R Type: Expression(Integer)
+--E 98
+
+--S 99 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 99
+
+)clear all
+
+--S 100 of 1369
+t0:=x^4/(a+b*x^8)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 100
+
+--S 101 of 1369
+r0:=-1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(3/8)*b^(5/8))-1/4*atanh(b^(1/8)*_
+ x/(-a)^(1/8))/((-a)^(3/8)*b^(5/8))-1/4*atan(1-b^(1/8)*x*sqrt(2)/_
+ (-a)^(1/8))/((-a)^(3/8)*b^(5/8)*sqrt(2))+1/4*atan(1+b^(1/8)*x*_
+ sqrt(2)/(-a)^(1/8))/((-a)^(3/8)*b^(5/8)*sqrt(2))-1/8*log((-a)^(1/4)+_
+ b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(3/8)*b^(5/8)*_
+ sqrt(2))+1/8*log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*_
+ sqrt(2))/((-a)^(3/8)*b^(5/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+8+---+8+-+ 2 4+-+ 4+---+
+--R log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+
+--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b
+--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+
+--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b
+--R 2atan(------------------) + 2atan(------------------) - 2\|2 atan(------)
+--R 8+---+ 8+---+ 8+---+
+--R \|- a \|- a \|- a
+--R /
+--R +-+8+---+3 8+-+5
+--R 8\|2 \|- a \|b
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R | 1
+--R |- ------------
+--R 8| 3 5
+--R \| 16777216a b
+--R *
+--R +--------------+5 +--------------+2
+--R 2 3 +-+ | 1 | 1 2
+--R log(32768a b x\|2 |- ------------ - 64a b |- ------------ + x )
+--R 8| 3 5 8| 3 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+5
+--R +-+ | 1 2 3 | 1
+--R - \|2 |- ------------ log(32768a b |- ------------ + x)
+--R 8| 3 5 8| 3 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+5
+--R +-+ | 1 2 3 | 1
+--R \|2 |- ------------ log(- 32768a b |- ------------ + x)
+--R 8| 3 5 8| 3 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R | 1
+--R |- ------------
+--R 8| 3 5
+--R \| 16777216a b
+--R *
+--R log
+--R +--------------+5 +--------------+2
+--R 2 3 +-+ | 1 | 1
+--R - 32768a b x\|2 |- ------------ - 64a b |- ------------
+--R 8| 3 5 8| 3 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R 2
+--R x
+--R +
+--R +--------------+5
+--R 2 3 | 1
+--R 32768a b |- ------------
+--R +--------------+ 8| 3 5
+--R +-+ | 1 \| 16777216a b
+--R 2\|2 |- ------------ atan(---------------------------)
+--R 8| 3 5 x
+--R \| 16777216a b
+--R +
+--R +--------------+5
+--R 2 3 | 1
+--R 32768a b |- ------------
+--R +--------------+ 8| 3 5
+--R | 1 \| 16777216a b
+--R 2 |- ------------ atan(-----------------------------------)
+--R 8| 3 5 +--------------+5
+--R \| 16777216a b 2 3 | 1 +-+
+--R 32768a b |- ------------ - x\|2
+--R 8| 3 5
+--R \| 16777216a b
+--R +
+--R +--------------+5
+--R 2 3 | 1
+--R 32768a b |- ------------
+--R +--------------+ 8| 3 5
+--R | 1 \| 16777216a b
+--R - 2 |- ------------ atan(-----------------------------------)
+--R 8| 3 5 +--------------+5
+--R \| 16777216a b 2 3 | 1 +-+
+--R 32768a b |- ------------ + x\|2
+--R 8| 3 5
+--R \| 16777216a b
+--R /
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 102
+
+--S 103 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R +--------------+
+--R 8+---+3 | 1 8+-+5
+--R 8\|- a |- ------------ \|b
+--R 8| 3 5
+--R \| 16777216a b
+--R *
+--R +--------------+5 +--------------+2
+--R 2 3 +-+ | 1 | 1 2
+--R log(32768a b x\|2 |- ------------ - 64a b |- ------------ + x )
+--R 8| 3 5 8| 3 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+5
+--R +-+8+---+3 | 1 8+-+5 2 3 | 1
+--R - 8\|2 \|- a |- ------------ \|b log(32768a b |- ------------ + x)
+--R 8| 3 5 8| 3 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+5
+--R +-+8+---+3 | 1 8+-+5 2 3 | 1
+--R 8\|2 \|- a |- ------------ \|b log(- 32768a b |- ------------ + x)
+--R 8| 3 5 8| 3 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R 8+---+3 | 1 8+-+5
+--R 8\|- a |- ------------ \|b
+--R 8| 3 5
+--R \| 16777216a b
+--R *
+--R log
+--R +--------------+5 +--------------+2
+--R 2 3 +-+ | 1 | 1
+--R - 32768a b x\|2 |- ------------ - 64a b |- ------------
+--R 8| 3 5 8| 3 5
+--R \| 16777216a b \| 16777216a b
+--R +
+--R 2
+--R x
+--R +
+--R 8+-+
+--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b
+--R log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+
+--R x\|2 \|b + \|- a x\|2 \|b - \|- a
+--R - 2atan(------------------) - 2atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+
+--R +-+ x\|b
+--R 2\|2 atan(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +--------------+5
+--R 2 3 | 1
+--R 32768a b |- ------------
+--R +--------------+ 8| 3 5
+--R +-+8+---+3 | 1 8+-+5 \| 16777216a b
+--R 16\|2 \|- a |- ------------ \|b atan(---------------------------)
+--R 8| 3 5 x
+--R \| 16777216a b
+--R +
+--R +--------------+5
+--R 2 3 | 1
+--R 32768a b |- ------------
+--R +--------------+ 8| 3 5
+--R 8+---+3 | 1 8+-+5 \| 16777216a b
+--R 16\|- a |- ------------ \|b atan(-----------------------------------)
+--R 8| 3 5 +--------------+5
+--R \| 16777216a b 2 3 | 1 +-+
+--R 32768a b |- ------------ - x\|2
+--R 8| 3 5
+--R \| 16777216a b
+--R +
+--R +--------------+5
+--R 2 3 | 1
+--R 32768a b |- ------------
+--R +--------------+ 8| 3 5
+--R 8+---+3 | 1 8+-+5 \| 16777216a b
+--R - 16\|- a |- ------------ \|b atan(-----------------------------------)
+--R 8| 3 5 +--------------+5
+--R \| 16777216a b 2 3 | 1 +-+
+--R 32768a b |- ------------ + x\|2
+--R 8| 3 5
+--R \| 16777216a b
+--R /
+--R +-+8+---+3 8+-+5
+--R 8\|2 \|- a \|b
+--R Type: Expression(Integer)
+--E 103
+
+--S 104 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 104
+
+)clear all
+
+--S 105 of 1369
+t0:=x^2/(a+b*x^8)
+--R
+--R
+--R 2
+--R x
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 105
+
+--S 106 of 1369
+r0:=1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(5/8)*b^(3/8))-1/4*atanh(b^(1/8)*_
+ x/(-a)^(1/8))/((-a)^(5/8)*b^(3/8))+1/4*atan(1-b^(1/8)*x*sqrt(2)/_
+ (-a)^(1/8))/((-a)^(5/8)*b^(3/8)*sqrt(2))-1/4*atan(1+b^(1/8)*x*_
+ sqrt(2)/(-a)^(1/8))/((-a)^(5/8)*b^(3/8)*sqrt(2))-_
+ 1/8*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/_
+ ((-a)^(5/8)*b^(3/8)*sqrt(2))+1/8*log((-a)^(1/4)+b^(1/4)*x^2+_
+ (-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(5/8)*b^(3/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+8+---+8+-+ 2 4+-+ 4+---+
+--R log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+
+--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b
+--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+
+--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b
+--R - 2atan(------------------) - 2atan(------------------) + 2\|2 atan(------)
+--R 8+---+ 8+---+ 8+---+
+--R \|- a \|- a \|- a
+--R /
+--R +-+8+---+5 8+-+3
+--R 8\|2 \|- a \|b
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------+
+--R | 1
+--R |- ------------
+--R 8| 5 3
+--R \| 16777216a b
+--R *
+--R +--------------+6 +--------------+3
+--R 4 2 | 1 2 +-+ | 1 2
+--R log(262144a b |- ------------ + 512a b x\|2 |- ------------ + x )
+--R 8| 5 3 8| 5 3
+--R \| 16777216a b \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R | 1
+--R |- ------------
+--R 8| 5 3
+--R \| 16777216a b
+--R *
+--R log
+--R +--------------+6 +--------------+3
+--R 4 2 | 1 2 +-+ | 1
+--R 262144a b |- ------------ - 512a b x\|2 |- ------------
+--R 8| 5 3 8| 5 3
+--R \| 16777216a b \| 16777216a b
+--R +
+--R 2
+--R x
+--R +
+--R +--------------+ +--------------+3
+--R +-+ | 1 2 | 1
+--R - \|2 |- ------------ log(512a b |- ------------ + x)
+--R 8| 5 3 8| 5 3
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+3
+--R +-+ | 1 2 | 1
+--R \|2 |- ------------ log(- 512a b |- ------------ + x)
+--R 8| 5 3 8| 5 3
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+3
+--R 2 | 1
+--R 512a b |- ------------
+--R +--------------+ 8| 5 3
+--R +-+ | 1 \| 16777216a b
+--R - 2\|2 |- ------------ atan(-------------------------)
+--R 8| 5 3 x
+--R \| 16777216a b
+--R +
+--R +--------------+3
+--R 2 | 1
+--R 512a b |- ------------
+--R +--------------+ 8| 5 3
+--R | 1 \| 16777216a b
+--R - 2 |- ------------ atan(---------------------------------)
+--R 8| 5 3 +--------------+3
+--R \| 16777216a b 2 | 1 +-+
+--R 512a b |- ------------ - x\|2
+--R 8| 5 3
+--R \| 16777216a b
+--R +
+--R +--------------+3
+--R 2 | 1
+--R 512a b |- ------------
+--R +--------------+ 8| 5 3
+--R | 1 \| 16777216a b
+--R 2 |- ------------ atan(---------------------------------)
+--R 8| 5 3 +--------------+3
+--R \| 16777216a b 2 | 1 +-+
+--R 512a b |- ------------ + x\|2
+--R 8| 5 3
+--R \| 16777216a b
+--R /
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 107
+
+--S 108 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R +--------------+
+--R 8+---+5 | 1 8+-+3
+--R 8\|- a |- ------------ \|b
+--R 8| 5 3
+--R \| 16777216a b
+--R *
+--R +--------------+6 +--------------+3
+--R 4 2 | 1 2 +-+ | 1 2
+--R log(262144a b |- ------------ + 512a b x\|2 |- ------------ + x )
+--R 8| 5 3 8| 5 3
+--R \| 16777216a b \| 16777216a b
+--R +
+--R -
+--R +--------------+
+--R 8+---+5 | 1 8+-+3
+--R 8\|- a |- ------------ \|b
+--R 8| 5 3
+--R \| 16777216a b
+--R *
+--R log
+--R +--------------+6 +--------------+3
+--R 4 2 | 1 2 +-+ | 1
+--R 262144a b |- ------------ - 512a b x\|2 |- ------------
+--R 8| 5 3 8| 5 3
+--R \| 16777216a b \| 16777216a b
+--R +
+--R 2
+--R x
+--R +
+--R +--------------+ +--------------+3
+--R +-+8+---+5 | 1 8+-+3 2 | 1
+--R - 8\|2 \|- a |- ------------ \|b log(512a b |- ------------ + x)
+--R 8| 5 3 8| 5 3
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +--------------+ +--------------+3
+--R +-+8+---+5 | 1 8+-+3 2 | 1
+--R 8\|2 \|- a |- ------------ \|b log(- 512a b |- ------------ + x)
+--R 8| 5 3 8| 5 3
+--R \| 16777216a b \| 16777216a b
+--R +
+--R 8+-+
+--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b
+--R log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+
+--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b
+--R 2atan(------------------) + 2atan(------------------) - 2\|2 atan(------)
+--R 8+---+ 8+---+ 8+---+
+--R \|- a \|- a \|- a
+--R +
+--R +--------------+3
+--R 2 | 1
+--R 512a b |- ------------
+--R +--------------+ 8| 5 3
+--R +-+8+---+5 | 1 8+-+3 \| 16777216a b
+--R - 16\|2 \|- a |- ------------ \|b atan(-------------------------)
+--R 8| 5 3 x
+--R \| 16777216a b
+--R +
+--R +--------------+3
+--R 2 | 1
+--R 512a b |- ------------
+--R +--------------+ 8| 5 3
+--R 8+---+5 | 1 8+-+3 \| 16777216a b
+--R - 16\|- a |- ------------ \|b atan(---------------------------------)
+--R 8| 5 3 +--------------+3
+--R \| 16777216a b 2 | 1 +-+
+--R 512a b |- ------------ - x\|2
+--R 8| 5 3
+--R \| 16777216a b
+--R +
+--R +--------------+3
+--R 2 | 1
+--R 512a b |- ------------
+--R +--------------+ 8| 5 3
+--R 8+---+5 | 1 8+-+3 \| 16777216a b
+--R 16\|- a |- ------------ \|b atan(---------------------------------)
+--R 8| 5 3 +--------------+3
+--R \| 16777216a b 2 | 1 +-+
+--R 512a b |- ------------ + x\|2
+--R 8| 5 3
+--R \| 16777216a b
+--R /
+--R +-+8+---+5 8+-+3
+--R 8\|2 \|- a \|b
+--R Type: Expression(Integer)
+--E 108
+
+--S 109 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 109
+
+)clear all
+
+--S 110 of 1369
+t0:=1/(a+b*x^8)
+--R
+--R
+--R 1
+--R (1) --------
+--R 8
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 110
+
+--S 111 of 1369
+r0:=-1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(7/8)*b^(1/8))-1/4*atanh(b^(1/8)*_
+ x/(-a)^(1/8))/((-a)^(7/8)*b^(1/8))+1/4*atan(1-b^(1/8)*x*sqrt(2)/_
+ (-a)^(1/8))/((-a)^(7/8)*b^(1/8)*sqrt(2))-1/4*atan(1+b^(1/8)*x*_
+ sqrt(2)/(-a)^(1/8))/((-a)^(7/8)*b^(1/8)*sqrt(2))+1/8*log((-a)^(1/4)+_
+ b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(7/8)*b^(1/8)*_
+ sqrt(2))-1/8*log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*_
+ sqrt(2))/((-a)^(7/8)*b^(1/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+
+--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b
+--R log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+
+--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b
+--R - 2atan(------------------) - 2atan(------------------) - 2\|2 atan(------)
+--R 8+---+ 8+---+ 8+---+
+--R \|- a \|- a \|- a
+--R /
+--R +-+8+---+7 8+-+
+--R 8\|2 \|- a \|b
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------------+
+--R | 1
+--R |- -----------
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R +-------------+2 +-------------+
+--R 2 | 1 +-+ | 1 2
+--R log(64a |- ----------- + 8a x\|2 |- ----------- + x )
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R -
+--R +-------------+
+--R | 1
+--R |- -----------
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R +-------------+2 +-------------+
+--R 2 | 1 +-+ | 1 2
+--R log(64a |- ----------- - 8a x\|2 |- ----------- + x )
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +-------------+ +-------------+
+--R +-+ | 1 | 1
+--R \|2 |- ----------- log(8a |- ----------- + x)
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +-------------+ +-------------+
+--R +-+ | 1 | 1
+--R - \|2 |- ----------- log(- 8a |- ----------- + x)
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +-------------+
+--R | 1
+--R 8a |- -----------
+--R +-------------+ 8| 7
+--R +-+ | 1 \| 16777216a b
+--R - 2\|2 |- ----------- atan(------------------)
+--R 8| 7 x
+--R \| 16777216a b
+--R +
+--R +-------------+
+--R | 1
+--R 8a |- -----------
+--R +-------------+ 8| 7
+--R | 1 \| 16777216a b
+--R 2 |- ----------- atan(--------------------------)
+--R 8| 7 +-------------+
+--R \| 16777216a b | 1 +-+
+--R 8a |- ----------- - x\|2
+--R 8| 7
+--R \| 16777216a b
+--R +
+--R +-------------+
+--R | 1
+--R 8a |- -----------
+--R +-------------+ 8| 7
+--R | 1 \| 16777216a b
+--R - 2 |- ----------- atan(--------------------------)
+--R 8| 7 +-------------+
+--R \| 16777216a b | 1 +-+
+--R 8a |- ----------- + x\|2
+--R 8| 7
+--R \| 16777216a b
+--R /
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 112
+
+--S 113 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+---+8+-+ 2 4+-+ 4+---+
+--R log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R +-------------+
+--R 8+---+7 | 1 8+-+
+--R 8\|- a |- ----------- \|b
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R +-------------+2 +-------------+
+--R 2 | 1 +-+ | 1 2
+--R log(64a |- ----------- + 8a x\|2 |- ----------- + x )
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R -
+--R +-------------+
+--R 8+---+7 | 1 8+-+
+--R 8\|- a |- ----------- \|b
+--R 8| 7
+--R \| 16777216a b
+--R *
+--R +-------------+2 +-------------+
+--R 2 | 1 +-+ | 1 2
+--R log(64a |- ----------- - 8a x\|2 |- ----------- + x )
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +-------------+ +-------------+
+--R +-+8+---+7 | 1 8+-+ | 1
+--R 8\|2 \|- a |- ----------- \|b log(8a |- ----------- + x)
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R +-------------+ +-------------+
+--R +-+8+---+7 | 1 8+-+ | 1
+--R - 8\|2 \|- a |- ----------- \|b log(- 8a |- ----------- + x)
+--R 8| 7 8| 7
+--R \| 16777216a b \| 16777216a b
+--R +
+--R 8+-+
+--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b
+--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+
+--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b
+--R 2atan(------------------) + 2atan(------------------) + 2\|2 atan(------)
+--R 8+---+ 8+---+ 8+---+
+--R \|- a \|- a \|- a
+--R +
+--R +-------------+
+--R | 1
+--R 8a |- -----------
+--R +-------------+ 8| 7
+--R +-+8+---+7 | 1 8+-+ \| 16777216a b
+--R - 16\|2 \|- a |- ----------- \|b atan(------------------)
+--R 8| 7 x
+--R \| 16777216a b
+--R +
+--R +-------------+
+--R | 1
+--R 8a |- -----------
+--R +-------------+ 8| 7
+--R 8+---+7 | 1 8+-+ \| 16777216a b
+--R 16\|- a |- ----------- \|b atan(--------------------------)
+--R 8| 7 +-------------+
+--R \| 16777216a b | 1 +-+
+--R 8a |- ----------- - x\|2
+--R 8| 7
+--R \| 16777216a b
+--R +
+--R +-------------+
+--R | 1
+--R 8a |- -----------
+--R +-------------+ 8| 7
+--R 8+---+7 | 1 8+-+ \| 16777216a b
+--R - 16\|- a |- ----------- \|b atan(--------------------------)
+--R 8| 7 +-------------+
+--R \| 16777216a b | 1 +-+
+--R 8a |- ----------- + x\|2
+--R 8| 7
+--R \| 16777216a b
+--R /
+--R +-+8+---+7 8+-+
+--R 8\|2 \|- a \|b
+--R Type: Expression(Integer)
+--E 113
+
+--S 114 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 114
+
+)clear all
+
+--S 115 of 1369
+t0:=1/(x^2*(a+b*x^8))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 10 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 115
+
+--S 116 of 1369
+r0:=(-1)/(a*x)+1/4*b^(1/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(9/8)-_
+ 1/4*b^(1/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(9/8)-1/4*b^(1/8)*_
+ atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(9/8)*sqrt(2))+_
+ 1/4*b^(1/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(9/8)*_
+ sqrt(2))+1/8*b^(1/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*_
+ x*sqrt(2))/((-a)^(9/8)*sqrt(2))-1/8*b^(1/8)*log((-a)^(1/4)+b^(1/4)*_
+ x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(9/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+
+--R x\|b log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+
+--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+ x\|b
+--R - x\|b log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2x\|2 \|b atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+
+--R 8+-+ x\|2 \|b + \|- a 8+-+ x\|2 \|b - \|- a
+--R - 2x\|b atan(------------------) - 2x\|b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+
+--R +-+8+-+ x\|b +-+8+---+
+--R - 2x\|2 \|b atan(------) - 8\|2 \|- a
+--R 8+---+
+--R \|- a
+--R /
+--R +-+8+---+
+--R 8a x\|2 \|- a
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +------------+
+--R | b
+--R a x |- ----------
+--R 8| 9
+--R \| 16777216a
+--R *
+--R +------------+7 +------------+6
+--R 8 +-+ | b 7 | b 2
+--R log(2097152a x\|2 |- ---------- - 262144a |- ---------- + b x )
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+ +------------+7
+--R +-+ | b 8 | b
+--R - a x\|2 |- ---------- log(2097152a |- ---------- + b x)
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+ +------------+7
+--R +-+ | b 8 | b
+--R a x\|2 |- ---------- log(- 2097152a |- ---------- + b x)
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+
+--R | b
+--R a x |- ----------
+--R 8| 9
+--R \| 16777216a
+--R *
+--R +------------+7 +------------+6
+--R 8 +-+ | b 7 | b 2
+--R log(- 2097152a x\|2 |- ---------- - 262144a |- ---------- + b x )
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+7
+--R 8 | b
+--R 2097152a |- ----------
+--R +------------+ 8| 9
+--R +-+ | b \| 16777216a
+--R - 2a x\|2 |- ---------- atan(-------------------------)
+--R 8| 9 b x
+--R \| 16777216a
+--R +
+--R +------------+7
+--R 8 | b
+--R 2097152a |- ----------
+--R +------------+ 8| 9
+--R | b \| 16777216a
+--R 2a x |- ---------- atan(-----------------------------------)
+--R 8| 9 +------------+7
+--R \| 16777216a 8 | b +-+
+--R 2097152a |- ---------- - b x\|2
+--R 8| 9
+--R \| 16777216a
+--R +
+--R +------------+7
+--R 8 | b
+--R 2097152a |- ----------
+--R +------------+ 8| 9
+--R | b \| 16777216a +-+
+--R - 2a x |- ---------- atan(----------------------------------- - \|2
+--R 8| 9 +------------+7
+--R \| 16777216a 8 | b +-+
+--R 2097152a |- ---------- + b x\|2
+--R 8| 9
+--R \| 16777216a
+--R /
+--R +-+
+--R a x\|2
+--R Type: Union(Expression(Integer),...)
+--E 117
+
+--S 118 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - \|b log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R -
+--R +------------+
+--R | b 8+---+
+--R 8a |- ---------- \|- a
+--R 8| 9
+--R \| 16777216a
+--R *
+--R +------------+7 +------------+6
+--R 8 +-+ | b 7 | b 2
+--R log(2097152a x\|2 |- ---------- - 262144a |- ---------- + b x )
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+ +------------+7
+--R +-+ | b 8+---+ 8 | b
+--R - 8a\|2 |- ---------- \|- a log(2097152a |- ---------- + b x)
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+ +------------+7
+--R +-+ | b 8+---+ 8 | b
+--R 8a\|2 |- ---------- \|- a log(- 2097152a |- ---------- + b x)
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+
+--R | b 8+---+
+--R 8a |- ---------- \|- a
+--R 8| 9
+--R \| 16777216a
+--R *
+--R +------------+7 +------------+6
+--R 8 +-+ | b 7 | b 2
+--R log(- 2097152a x\|2 |- ---------- - 262144a |- ---------- + b x )
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R 8+-+
+--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+ x\|b
+--R \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+
+--R 8+-+ x\|2 \|b + \|- a 8+-+ x\|2 \|b - \|- a
+--R 2\|b atan(------------------) + 2\|b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+
+--R +-+8+-+ x\|b
+--R 2\|2 \|b atan(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +------------+7
+--R 8 | b
+--R 2097152a |- ----------
+--R +------------+ 8| 9
+--R +-+ | b 8+---+ \| 16777216a
+--R - 16a\|2 |- ---------- \|- a atan(-------------------------)
+--R 8| 9 b x
+--R \| 16777216a
+--R +
+--R +------------+7
+--R 8 | b
+--R 2097152a |- ----------
+--R +------------+ 8| 9
+--R | b 8+---+ \| 16777216a
+--R 16a |- ---------- \|- a atan(-----------------------------------)
+--R 8| 9 +------------+7
+--R \| 16777216a 8 | b +-+
+--R 2097152a |- ---------- - b x\|2
+--R 8| 9
+--R \| 16777216a
+--R +
+--R +------------+7
+--R 8 | b
+--R 2097152a |- ----------
+--R +------------+ 8| 9
+--R | b 8+---+ \| 16777216a
+--R - 16a |- ---------- \|- a atan(-----------------------------------)
+--R 8| 9 +------------+7
+--R \| 16777216a 8 | b +-+
+--R 2097152a |- ---------- + b x\|2
+--R 8| 9
+--R \| 16777216a
+--R /
+--R +-+8+---+
+--R 8a\|2 \|- a
+--R Type: Expression(Integer)
+--E 118
+
+--S 119 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 119
+
+)clear all
+
+--S 120 of 1369
+t0:=1/(x^4*(a+b*x^8))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 12 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 120
+
+--S 121 of 1369
+r0:=(-1/3)/(a*x^3)-1/4*b^(3/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(11/8)-_
+ 1/4*b^(3/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(11/8)-1/4*b^(3/8)*_
+ atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(11/8)*sqrt(2))+_
+ 1/4*b^(3/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(11/8)*_
+ sqrt(2))-1/8*b^(3/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*_
+ x*sqrt(2))/((-a)^(11/8)*sqrt(2))+1/8*b^(3/8)*log((-a)^(1/4)+_
+ b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(11/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 3 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - 3x \|b log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 3 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+
+--R 3x \|b log(- x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+ +-+8+-+ 8+---+
+--R 3 +-+8+-+3 x\|b 3 8+-+3 x\|2 \|b + \|- a
+--R 6x \|2 \|b atanh(------) - 6x \|b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ 8+---+ 8+-+
+--R 3 8+-+3 x\|2 \|b - \|- a 3 +-+8+-+3 x\|b
+--R - 6x \|b atan(------------------ + 6x \|2 \|b atan(------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+---+3
+--R - 8\|2 \|- a
+--R /
+--R 3 +-+8+---+3
+--R 24a x \|2 \|- a
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-------------+
+--R | 3
+--R 3 | b
+--R 3a x |- -----------
+--R 8| 11
+--R \| 16777216a
+--R *
+--R +-------------+5 +-------------+2
+--R | 3 | 3
+--R 7 +-+ | b 3 | b 2 2
+--R log(32768a x\|2 |- ----------- - 64a b |- ----------- + b x )
+--R 8| 11 8| 11
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+5
+--R | 3 | 3
+--R 3 +-+ | b 7 | b 2
+--R 3a x \|2 |- ----------- log(32768a |- ----------- + b x)
+--R 8| 11 8| 11
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+5
+--R | 3 | 3
+--R 3 +-+ | b 7 | b 2
+--R - 3a x \|2 |- ----------- log(- 32768a |- ----------- + b x)
+--R 8| 11 8| 11
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+
+--R | 3
+--R 3 | b
+--R 3a x |- -----------
+--R 8| 11
+--R \| 16777216a
+--R *
+--R +-------------+5 +-------------+2
+--R | 3 | 3
+--R 7 +-+ | b 3 | b 2 2
+--R log(- 32768a x\|2 |- ----------- - 64a b |- ----------- + b x )
+--R 8| 11 8| 11
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+5
+--R | 3
+--R 7 | b
+--R +-------------+ 32768a |- -----------
+--R | 3 8| 11
+--R 3 +-+ | b \| 16777216a
+--R - 6a x \|2 |- ----------- atan(------------------------)
+--R 8| 11 2
+--R \| 16777216a b x
+--R +
+--R +-------------+5
+--R | 3
+--R 7 | b
+--R +-------------+ 32768a |- -----------
+--R | 3 8| 11
+--R 3 | b \| 16777216a
+--R - 6a x |- ----------- atan(----------------------------------)
+--R 8| 11 +-------------+5
+--R \| 16777216a | 3
+--R 7 | b 2 +-+
+--R 32768a |- ----------- - b x\|2
+--R 8| 11
+--R \| 16777216a
+--R +
+--R +-------------+5
+--R | 3
+--R 7 | b
+--R +-------------+ 32768a |- -----------
+--R | 3 8| 11
+--R 3 | b \| 16777216a +-+
+--R 6a x |- ----------- atan(---------------------------------- - \|2
+--R 8| 11 +-------------+5
+--R \| 16777216a | 3
+--R 7 | b 2 +-+
+--R 32768a |- ----------- + b x\|2
+--R 8| 11
+--R \| 16777216a
+--R /
+--R 3 +-+
+--R 3a x \|2
+--R Type: Union(Expression(Integer),...)
+--E 122
+
+--S 123 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+
+--R \|b log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R -
+--R +-------------+
+--R | 3
+--R | b 8+---+3
+--R 8a |- ----------- \|- a
+--R 8| 11
+--R \| 16777216a
+--R *
+--R +-------------+5 +-------------+2
+--R | 3 | 3
+--R 7 +-+ | b 3 | b 2 2
+--R log(32768a x\|2 |- ----------- - 64a b |- ----------- + b x )
+--R 8| 11 8| 11
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+5
+--R | 3 | 3
+--R +-+ | b 8+---+3 7 | b 2
+--R 8a\|2 |- ----------- \|- a log(32768a |- ----------- + b x)
+--R 8| 11 8| 11
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+5
+--R | 3 | 3
+--R +-+ | b 8+---+3 7 | b 2
+--R - 8a\|2 |- ----------- \|- a log(- 32768a |- ----------- + b x)
+--R 8| 11 8| 11
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+
+--R | 3
+--R | b 8+---+3
+--R 8a |- ----------- \|- a
+--R 8| 11
+--R \| 16777216a
+--R *
+--R +-------------+5 +-------------+2
+--R | 3 | 3
+--R 7 +-+ | b 3 | b 2 2
+--R log(- 32768a x\|2 |- ----------- - 64a b |- ----------- + b x )
+--R 8| 11 8| 11
+--R \| 16777216a \| 16777216a
+--R +
+--R 8+-+
+--R 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+3 x\|b
+--R - \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+
+--R 8+-+3 x\|2 \|b + \|- a 8+-+3 x\|2 \|b - \|- a
+--R 2\|b atan(------------------) + 2\|b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+
+--R +-+8+-+3 x\|b
+--R - 2\|2 \|b atan(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-------------+5
+--R | 3
+--R 7 | b
+--R +-------------+ 32768a |- -----------
+--R | 3 8| 11
+--R +-+ | b 8+---+3 \| 16777216a
+--R - 16a\|2 |- ----------- \|- a atan(------------------------)
+--R 8| 11 2
+--R \| 16777216a b x
+--R +
+--R +-------------+5
+--R | 3
+--R 7 | b
+--R +-------------+ 32768a |- -----------
+--R | 3 8| 11
+--R | b 8+---+3 \| 16777216a
+--R - 16a |- ----------- \|- a atan(----------------------------------)
+--R 8| 11 +-------------+5
+--R \| 16777216a | 3
+--R 7 | b 2 +-+
+--R 32768a |- ----------- - b x\|2
+--R 8| 11
+--R \| 16777216a
+--R +
+--R +-------------+5
+--R | 3
+--R 7 | b
+--R +-------------+ 32768a |- -----------
+--R | 3 8| 11
+--R | b 8+---+3 \| 16777216a
+--R 16a |- ----------- \|- a atan(----------------------------------)
+--R 8| 11 +-------------+5
+--R \| 16777216a | 3
+--R 7 | b 2 +-+
+--R 32768a |- ----------- + b x\|2
+--R 8| 11
+--R \| 16777216a
+--R /
+--R +-+8+---+3
+--R 8a\|2 \|- a
+--R Type: Expression(Integer)
+--E 123
+
+--S 124 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 124
+
+)clear all
+
+--S 125 of 1369
+t0:=1/(x^6*(a+b*x^8))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 14 6
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 125
+
+--S 126 of 1369
+r0:=(-1/5)/(a*x^5)+1/4*b^(5/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(13/8)-_
+ 1/4*b^(5/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(13/8)+1/4*b^(5/8)*_
+ atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(13/8)*sqrt(2))-_
+ 1/4*b^(5/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(13/8)*_
+ sqrt(2))-1/8*b^(5/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*_
+ x*sqrt(2))/((-a)^(13/8)*sqrt(2))+1/8*b^(5/8)*log((-a)^(1/4)+_
+ b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(13/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 5 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - 5x \|b log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 5 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+
+--R 5x \|b log(- x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+ +-+8+-+ 8+---+
+--R 5 +-+8+-+5 x\|b 5 8+-+5 x\|2 \|b + \|- a
+--R 10x \|2 \|b atanh(------) + 10x \|b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ 8+---+ 8+-+
+--R 5 8+-+5 x\|2 \|b - \|- a 5 +-+8+-+5 x\|b
+--R 10x \|b atan(------------------ - 10x \|2 \|b atan(------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+---+5
+--R - 8\|2 \|- a
+--R /
+--R 5 +-+8+---+5
+--R 40a x \|2 \|- a
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-------------+
+--R | 5
+--R 5 | b
+--R 5a x |- -----------
+--R 8| 13
+--R \| 16777216a
+--R *
+--R +-------------+6 +-------------+3
+--R | 5 | 5
+--R 10 | b 5 2 +-+ | b 4 2
+--R log(262144a |- ----------- + 512a b x\|2 |- ----------- + b x )
+--R 8| 13 8| 13
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+
+--R | 5
+--R 5 | b
+--R 5a x |- -----------
+--R 8| 13
+--R \| 16777216a
+--R *
+--R +-------------+6 +-------------+3
+--R | 5 | 5
+--R 10 | b 5 2 +-+ | b 4 2
+--R log(262144a |- ----------- - 512a b x\|2 |- ----------- + b x )
+--R 8| 13 8| 13
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+3
+--R | 5 | 5
+--R 5 +-+ | b 5 | b 2
+--R 5a x \|2 |- ----------- log(512a |- ----------- + b x)
+--R 8| 13 8| 13
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+3
+--R | 5 | 5
+--R 5 +-+ | b 5 | b 2
+--R - 5a x \|2 |- ----------- log(- 512a |- ----------- + b x)
+--R 8| 13 8| 13
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+3
+--R | 5
+--R 5 | b
+--R +-------------+ 512a |- -----------
+--R | 5 8| 13
+--R 5 +-+ | b \| 16777216a
+--R 10a x \|2 |- ----------- atan(----------------------)
+--R 8| 13 2
+--R \| 16777216a b x
+--R +
+--R +-------------+3
+--R | 5
+--R 5 | b
+--R +-------------+ 512a |- -----------
+--R | 5 8| 13
+--R 5 | b \| 16777216a
+--R 10a x |- ----------- atan(--------------------------------)
+--R 8| 13 +-------------+3
+--R \| 16777216a | 5
+--R 5 | b 2 +-+
+--R 512a |- ----------- - b x\|2
+--R 8| 13
+--R \| 16777216a
+--R +
+--R +-------------+3
+--R | 5
+--R 5 | b
+--R +-------------+ 512a |- -----------
+--R | 5 8| 13
+--R 5 | b \| 16777216a +-+
+--R - 10a x |- ----------- atan(-------------------------------- - \|2
+--R 8| 13 +-------------+3
+--R \| 16777216a | 5
+--R 5 | b 2 +-+
+--R 512a |- ----------- + b x\|2
+--R 8| 13
+--R \| 16777216a
+--R /
+--R 5 +-+
+--R 5a x \|2
+--R Type: Union(Expression(Integer),...)
+--E 127
+
+--S 128 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+
+--R \|b log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R -
+--R +-------------+
+--R | 5
+--R | b 8+---+5
+--R 8a |- ----------- \|- a
+--R 8| 13
+--R \| 16777216a
+--R *
+--R +-------------+6 +-------------+3
+--R | 5 | 5
+--R 10 | b 5 2 +-+ | b 4 2
+--R log(262144a |- ----------- + 512a b x\|2 |- ----------- + b x )
+--R 8| 13 8| 13
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+
+--R | 5
+--R | b 8+---+5
+--R 8a |- ----------- \|- a
+--R 8| 13
+--R \| 16777216a
+--R *
+--R +-------------+6 +-------------+3
+--R | 5 | 5
+--R 10 | b 5 2 +-+ | b 4 2
+--R log(262144a |- ----------- - 512a b x\|2 |- ----------- + b x )
+--R 8| 13 8| 13
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+3
+--R | 5 | 5
+--R +-+ | b 8+---+5 5 | b 2
+--R 8a\|2 |- ----------- \|- a log(512a |- ----------- + b x)
+--R 8| 13 8| 13
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+3
+--R | 5 | 5
+--R +-+ | b 8+---+5 5 | b 2
+--R - 8a\|2 |- ----------- \|- a log(- 512a |- ----------- + b x)
+--R 8| 13 8| 13
+--R \| 16777216a \| 16777216a
+--R +
+--R 8+-+
+--R 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+5 x\|b
+--R - \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+
+--R 8+-+5 x\|2 \|b + \|- a 8+-+5 x\|2 \|b - \|- a
+--R - 2\|b atan(------------------) - 2\|b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+
+--R +-+8+-+5 x\|b
+--R 2\|2 \|b atan(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-------------+3
+--R | 5
+--R 5 | b
+--R +-------------+ 512a |- -----------
+--R | 5 8| 13
+--R +-+ | b 8+---+5 \| 16777216a
+--R 16a\|2 |- ----------- \|- a atan(----------------------)
+--R 8| 13 2
+--R \| 16777216a b x
+--R +
+--R +-------------+3
+--R | 5
+--R 5 | b
+--R +-------------+ 512a |- -----------
+--R | 5 8| 13
+--R | b 8+---+5 \| 16777216a
+--R 16a |- ----------- \|- a atan(--------------------------------)
+--R 8| 13 +-------------+3
+--R \| 16777216a | 5
+--R 5 | b 2 +-+
+--R 512a |- ----------- - b x\|2
+--R 8| 13
+--R \| 16777216a
+--R +
+--R +-------------+3
+--R | 5
+--R 5 | b
+--R +-------------+ 512a |- -----------
+--R | 5 8| 13
+--R | b 8+---+5 \| 16777216a
+--R - 16a |- ----------- \|- a atan(--------------------------------)
+--R 8| 13 +-------------+3
+--R \| 16777216a | 5
+--R 5 | b 2 +-+
+--R 512a |- ----------- + b x\|2
+--R 8| 13
+--R \| 16777216a
+--R /
+--R +-+8+---+5
+--R 8a\|2 \|- a
+--R Type: Expression(Integer)
+--E 128
+
+--S 129 of 1369
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 129
+
+)clear all
+
+--S 130 of 1369
+t0:=1/(x^8*(a+b*x^8))
+--R
+--R
+--R 1
+--R (1) ------------
+--R 16 8
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 130
+
+--S 131 of 1369
+r0:=(-1/7)/(a*x^7)-1/4*b^(7/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(15/8)-_
+ 1/4*b^(7/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(15/8)+1/4*b^(7/8)*_
+ atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(15/8)*sqrt(2))-_
+ 1/4*b^(7/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(15/8)*_
+ sqrt(2))+1/8*b^(7/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*_
+ b^(1/8)*x*sqrt(2))/((-a)^(15/8)*sqrt(2))-1/8*b^(7/8)*_
+ log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/_
+ ((-a)^(15/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 7 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+
+--R 7x \|b log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 7 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - 7x \|b log(- x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R 8+-+ +-+8+-+ 8+---+
+--R 7 +-+8+-+7 x\|b 7 8+-+7 x\|2 \|b + \|- a
+--R 14x \|2 \|b atanh(------) + 14x \|b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+-+ 8+---+ 8+-+
+--R 7 8+-+7 x\|2 \|b - \|- a 7 +-+8+-+7 x\|b
+--R 14x \|b atan(------------------ + 14x \|2 \|b atan(------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R +-+8+---+7
+--R - 8\|2 \|- a
+--R /
+--R 7 +-+8+---+7
+--R 56a x \|2 \|- a
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +-------------+
+--R | 7
+--R 7 | b
+--R 7a x |- -----------
+--R 8| 15
+--R \| 16777216a
+--R *
+--R +-------------+2 +-------------+
+--R | 7 | 7
+--R 4 | b 2 +-+ | b 2 2
+--R log(64a |- ----------- + 8a b x\|2 |- ----------- + b x )
+--R 8| 15 8| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+
+--R | 7
+--R 7 | b
+--R 7a x |- -----------
+--R 8| 15
+--R \| 16777216a
+--R *
+--R +-------------+2 +-------------+
+--R | 7 | 7
+--R 4 | b 2 +-+ | b 2 2
+--R log(64a |- ----------- - 8a b x\|2 |- ----------- + b x )
+--R 8| 15 8| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+
+--R | 7 | 7
+--R 7 +-+ | b 2 | b
+--R - 7a x \|2 |- ----------- log(8a |- ----------- + b x)
+--R 8| 15 8| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+
+--R | 7 | 7
+--R 7 +-+ | b 2 | b
+--R 7a x \|2 |- ----------- log(- 8a |- ----------- + b x)
+--R 8| 15 8| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+
+--R | 7
+--R 2 | b
+--R +-------------+ 8a |- -----------
+--R | 7 8| 15
+--R 7 +-+ | b \| 16777216a
+--R 14a x \|2 |- ----------- atan(-------------------)
+--R 8| 15 b x
+--R \| 16777216a
+--R +
+--R +-------------+
+--R | 7
+--R 2 | b
+--R +-------------+ 8a |- -----------
+--R | 7 8| 15
+--R 7 | b \| 16777216a
+--R - 14a x |- ----------- atan(-----------------------------)
+--R 8| 15 +-------------+
+--R \| 16777216a | 7
+--R 2 | b +-+
+--R 8a |- ----------- - b x\|2
+--R 8| 15
+--R \| 16777216a
+--R +
+--R +-------------+
+--R | 7
+--R 2 | b
+--R +-------------+ 8a |- -----------
+--R | 7 8| 15
+--R 7 | b \| 16777216a +-+
+--R 14a x |- ----------- atan(----------------------------- - \|2
+--R 8| 15 +-------------+
+--R \| 16777216a | 7
+--R 2 | b +-+
+--R 8a |- ----------- + b x\|2
+--R 8| 15
+--R \| 16777216a
+--R /
+--R 7 +-+
+--R 7a x \|2
+--R Type: Union(Expression(Integer),...)
+--E 132
+
+--S 133 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - \|b log(x\|2 \|- a \|b + x \|b + \|- a )
+--R +
+--R -
+--R +-------------+
+--R | 7
+--R | b 8+---+7
+--R 8a |- ----------- \|- a
+--R 8| 15
+--R \| 16777216a
+--R *
+--R +-------------+2 +-------------+
+--R | 7 | 7
+--R 4 | b 2 +-+ | b 2 2
+--R log(64a |- ----------- + 8a b x\|2 |- ----------- + b x )
+--R 8| 15 8| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+
+--R | 7
+--R | b 8+---+7
+--R 8a |- ----------- \|- a
+--R 8| 15
+--R \| 16777216a
+--R *
+--R +-------------+2 +-------------+
+--R | 7 | 7
+--R 4 | b 2 +-+ | b 2 2
+--R log(64a |- ----------- - 8a b x\|2 |- ----------- + b x )
+--R 8| 15 8| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+
+--R | 7 | 7
+--R +-+ | b 8+---+7 2 | b
+--R - 8a\|2 |- ----------- \|- a log(8a |- ----------- + b x)
+--R 8| 15 8| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R +-------------+ +-------------+
+--R | 7 | 7
+--R +-+ | b 8+---+7 2 | b
+--R 8a\|2 |- ----------- \|- a log(- 8a |- ----------- + b x)
+--R 8| 15 8| 15
+--R \| 16777216a \| 16777216a
+--R +
+--R 8+-+
+--R 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+7 x\|b
+--R \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+
+--R 8+-+7 x\|2 \|b + \|- a 8+-+7 x\|2 \|b - \|- a
+--R - 2\|b atan(------------------) - 2\|b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- a \|- a
+--R +
+--R 8+-+
+--R +-+8+-+7 x\|b
+--R - 2\|2 \|b atan(------)
+--R 8+---+
+--R \|- a
+--R +
+--R +-------------+
+--R | 7
+--R 2 | b
+--R +-------------+ 8a |- -----------
+--R | 7 8| 15
+--R +-+ | b 8+---+7 \| 16777216a
+--R 16a\|2 |- ----------- \|- a atan(-------------------)
+--R 8| 15 b x
+--R \| 16777216a
+--R +
+--R +-------------+
+--R | 7
+--R 2 | b
+--R +-------------+ 8a |- -----------
+--R | 7 8| 15
+--R | b 8+---+7 \| 16777216a
+--R - 16a |- ----------- \|- a atan(-----------------------------)
+--R 8| 15 +-------------+
+--R \| 16777216a | 7
+--R 2 | b +-+
+--R 8a |- ----------- - b x\|2
+--R 8| 15
+--R \| 16777216a
+--R +
+--R +-------------+
+--R | 7
+--R 2 | b
+--R +-------------+ 8a |- -----------
+--R | 7 8| 15
+--R | b 8+---+7 \| 16777216a
+--R 16a |- ----------- \|- a atan(-----------------------------)
+--R 8| 15 +-------------+
+--R \| 16777216a | 7
+--R 2 | b +-+
+--R 8a |- ----------- + b x\|2
+--R 8| 15
+--R \| 16777216a
+--R /
+--R +-+8+---+7
+--R 8a\|2 \|- a
+--R Type: Expression(Integer)
+--E 133
+
+--S 134 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 10 4+-+2 8 4+---+4+-+ 6 8+---+4 6 4+---+28+-+6
+--R (- b x \|b - 2b x \|- a \|b - 2b x \|- a - b x \|- a )\|b
+--R +
+--R 8 8+---+2 4+-+2 6 4+---+8+---+2 4+-+ 4 8+---+6
+--R b x \|- a \|b + 2b x \|- a \|- a \| - 2b x \|- a
+--R +
+--R 4 4+---+2 8+---+2
+--R b x \|- a \|- a
+--R *
+--R 8+-+4
+--R \|b
+--R +
+--R 6 8+---+4 4+-+2 4 4+---+8+---+4 4+-+ 2 4+---+2 8+---+4
+--R b x \|- a \|b + 2b x \|- a \|- a \| + b x \|- a \|- a
+--R +
+--R 2
+--R - 2a b x
+--R *
+--R 8+-+2
+--R \|b
+--R +
+--R 4 8+---+6 4+-+2 2 4+---+8+---+6 2 10 2 4+-+
+--R - b x \|- a \|b + (- 2b x \|- a \|- a + b x + a b x )\|b
+--R +
+--R 4+---+2 8+---+6 2 8 8+---+2 2 8 4+---+
+--R - b \|- a \|- a + 2b x \|- a + (- b x - a b)\|- a
+--R /
+--R 2 10 3 2 8+-+2 12 2 4 8+---+6 4+-+2
+--R (8a b x + 8a x )\|b + (4a b x + 4a x )\|- a \|b
+--R +
+--R 10 2 2 4+---+8+---+6 4+-+ 8 2 4+---+2 8+---+6
+--R (8a b x + 8a x )\|- a \|- a \|b + (4a b x + 4a )\|- a \|- a
+--R Type: Expression(Integer)
+--E 134
+
+)clear all
+
+--S 135 of 1369
+t0:=1/(a-b*x^8)
+--R
+--R
+--R 1
+--R (1) - --------
+--R 8
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 135
+
+--S 136 of 1369
+r0:=1/4*atan(b^(1/8)*x/a^(1/8))/(a^(7/8)*b^(1/8))+1/4*atanh(b^(1/8)*_
+ x/a^(1/8))/(a^(7/8)*b^(1/8))-1/4*atan(1-b^(1/8)*x*sqrt(2)/_
+ a^(1/8))/(a^(7/8)*b^(1/8)*sqrt(2))+1/4*atan(1+b^(1/8)*x*_
+ sqrt(2)/a^(1/8))/(a^(7/8)*b^(1/8)*sqrt(2))-1/8*log(a^(1/4)+_
+ b^(1/4)*x^2-a^(1/8)*b^(1/8)*x*sqrt(2))/(a^(7/8)*b^(1/8)*sqrt(2))+_
+ 1/8*log(a^(1/4)+b^(1/4)*x^2+a^(1/8)*b^(1/8)*x*sqrt(2))/_
+ (a^(7/8)*b^(1/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R +-+8+-+8+-+ 2 4+-+ 4+-+ +-+8+-+8+-+ 2 4+-+ 4+-+
+--R log(x\|2 \|a \|b + x \|b + \|a ) - log(- x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R 8+-+ +-+8+-+ 8+-+ +-+8+-+ 8+-+
+--R +-+ x\|b x\|2 \|b + \|a x\|2 \|b - \|a
+--R 2\|2 atanh(-----) + 2atan(----------------) + 2atan(----------------)
+--R 8+-+ 8+-+ 8+-+
+--R \|a \|a \|a
+--R +
+--R 8+-+
+--R +-+ x\|b
+--R 2\|2 atan(-----)
+--R 8+-+
+--R \|a
+--R /
+--R +-+8+-+7 8+-+
+--R 8\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----------+ +-----------+2 +-----------+
+--R | 1 2 | 1 +-+ | 1 2
+--R |----------- log(64a |----------- + 8a x\|2 |----------- + x )
+--R 8| 7 8| 7 8| 7
+--R \|16777216a b \|16777216a b \|16777216a b
+--R +
+--R +-----------+ +-----------+2 +-----------+
+--R | 1 2 | 1 +-+ | 1 2
+--R - |----------- log(64a |----------- - 8a x\|2 |----------- + x )
+--R 8| 7 8| 7 8| 7
+--R \|16777216a b \|16777216a b \|16777216a b
+--R +
+--R +-----------+ +-----------+
+--R +-+ | 1 | 1
+--R \|2 |----------- log(8a |----------- + x)
+--R 8| 7 8| 7
+--R \|16777216a b \|16777216a b
+--R +
+--R +-----------+ +-----------+
+--R +-+ | 1 | 1
+--R - \|2 |----------- log(- 8a |----------- + x)
+--R 8| 7 8| 7
+--R \|16777216a b \|16777216a b
+--R +
+--R +-----------+
+--R | 1
+--R 8a |-----------
+--R +-----------+ 8| 7
+--R +-+ | 1 \|16777216a b
+--R - 2\|2 |----------- atan(----------------)
+--R 8| 7 x
+--R \|16777216a b
+--R +
+--R +-----------+
+--R | 1
+--R 8a |-----------
+--R +-----------+ 8| 7
+--R | 1 \|16777216a b
+--R 2 |----------- atan(------------------------)
+--R 8| 7 +-----------+
+--R \|16777216a b | 1 +-+
+--R 8a |----------- - x\|2
+--R 8| 7
+--R \|16777216a b
+--R +
+--R +-----------+
+--R | 1
+--R 8a |-----------
+--R +-----------+ 8| 7
+--R | 1 \|16777216a b
+--R - 2 |----------- atan(------------------------)
+--R 8| 7 +-----------+
+--R \|16777216a b | 1 +-+
+--R 8a |----------- + x\|2
+--R 8| 7
+--R \|16777216a b
+--R /
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 137
+
+--S 138 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+8+-+8+-+ 2 4+-+ 4+-+
+--R - log(x\|2 \|a \|b + x \|b + \|a )
+--R +
+--R +-----------+
+--R | 1 8+-+7 8+-+
+--R 8 |----------- \|a \|b
+--R 8| 7
+--R \|16777216a b
+--R *
+--R +-----------+2 +-----------+
+--R 2 | 1 +-+ | 1 2
+--R log(64a |----------- + 8a x\|2 |----------- + x )
+--R 8| 7 8| 7
+--R \|16777216a b \|16777216a b
+--R +
+--R -
+--R +-----------+
+--R | 1 8+-+7 8+-+
+--R 8 |----------- \|a \|b
+--R 8| 7
+--R \|16777216a b
+--R *
+--R +-----------+2 +-----------+
+--R 2 | 1 +-+ | 1 2
+--R log(64a |----------- - 8a x\|2 |----------- + x )
+--R 8| 7 8| 7
+--R \|16777216a b \|16777216a b
+--R +
+--R +-----------+ +-----------+
+--R +-+ | 1 8+-+7 8+-+ | 1
+--R 8\|2 |----------- \|a \|b log(8a |----------- + x)
+--R 8| 7 8| 7
+--R \|16777216a b \|16777216a b
+--R +
+--R +-----------+ +-----------+
+--R +-+ | 1 8+-+7 8+-+ | 1
+--R - 8\|2 |----------- \|a \|b log(- 8a |----------- + x)
+--R 8| 7 8| 7
+--R \|16777216a b \|16777216a b
+--R +
+--R 8+-+
+--R +-+8+-+8+-+ 2 4+-+ 4+-+ +-+ x\|b
+--R log(- x\|2 \|a \|b + x \|b + \|a ) - 2\|2 atanh(-----)
+--R 8+-+
+--R \|a
+--R +
+--R +-+8+-+ 8+-+ +-+8+-+ 8+-+ 8+-+
+--R x\|2 \|b + \|a x\|2 \|b - \|a +-+ x\|b
+--R - 2atan(----------------) - 2atan(----------------) - 2\|2 atan(-----)
+--R 8+-+ 8+-+ 8+-+
+--R \|a \|a \|a
+--R +
+--R +-----------+
+--R | 1
+--R 8a |-----------
+--R +-----------+ 8| 7
+--R +-+ | 1 8+-+7 8+-+ \|16777216a b
+--R - 16\|2 |----------- \|a \|b atan(----------------)
+--R 8| 7 x
+--R \|16777216a b
+--R +
+--R +-----------+
+--R | 1
+--R 8a |-----------
+--R +-----------+ 8| 7
+--R | 1 8+-+7 8+-+ \|16777216a b
+--R 16 |----------- \|a \|b atan(------------------------)
+--R 8| 7 +-----------+
+--R \|16777216a b | 1 +-+
+--R 8a |----------- - x\|2
+--R 8| 7
+--R \|16777216a b
+--R +
+--R +-----------+
+--R | 1
+--R 8a |-----------
+--R +-----------+ 8| 7
+--R | 1 8+-+7 8+-+ \|16777216a b
+--R - 16 |----------- \|a \|b atan(------------------------)
+--R 8| 7 +-----------+
+--R \|16777216a b | 1 +-+
+--R 8a |----------- + x\|2
+--R 8| 7
+--R \|16777216a b
+--R /
+--R +-+8+-+7 8+-+
+--R 8\|2 \|a \|b
+--R Type: Expression(Integer)
+--E 138
+
+--S 139 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 8 8+-+2 4+-+2 6 4+-+8+-+2 4+-+ 4 8+-+6 4 4+-+2 8+-+8+-+6
+--R (- x \|a \|b - 2x \|a \|a \| + 2x \|a - x \|a \|a)\|b
+--R +
+--R 6 8+-+4 4+-+2 4 4+-+8+-+4 4+-+ 2 4+-+2 8+-+4 2 8+-+4
+--R (- x \|a \|b - 2x \|a \|a \| - x \|a \|a - 2a x )\|b
+--R +
+--R 4 8+-+6 4+-+2 2 4+-+8+-+6 10 2 4+-+ 4+-+2 8+-+6
+--R x \|a \|b + (2x \|a \|a - b x + a x )\|b + \|a \|a
+--R +
+--R 8 8+-+2 8 4+-+
+--R - 2b x \|a + (b x - a)\|a
+--R *
+--R 8+-+2
+--R \|b
+--R +
+--R 10 4+-+2 8 4+-+4+-+ 6 8+-+4 6 4+-+2
+--R b x \|b + 2b x \|a \|b + 2b x \|a + b x \|a
+--R /
+--R 10 2 2 8+-+4
+--R (8a b x - 8a x )\|b
+--R +
+--R 12 4 8+-+6 4+-+2 10 2 4+-+8+-+6 4+-+
+--R (- 4b x + 4a x )\|a \|b + (- 8b x + 8a x )\|a \|a \|b
+--R +
+--R 8 4+-+2 8+-+6
+--R (- 4b x + 4a)\|a \|a
+--R *
+--R 8+-+2
+--R \|b
+--R Type: Expression(Integer)
+--E 139
+
+)clear all
+
+--S 140 of 1369
+t0:=x^9/(1-x^8)
+--R
+--R
+--R 9
+--R x
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 140
+
+--S 141 of 1369
+r0:=-1/2*x^2+1/4*atan(x^2)+1/4*atanh(x^2)
+--R
+--R
+--R 2 2 2
+--R atanh(x ) + atan(x ) - 2x
+--R (2) --------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2
+--R log(x + 1) - log(x - 1) + 2atan(x ) - 4x
+--R (3) -------------------------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 142
+
+--S 143 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2 2
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 143
+
+--S 144 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 144
+
+)clear all
+
+--S 145 of 1369
+t0:=x^7/(1-x^8)
+--R
+--R
+--R 7
+--R x
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 145
+
+--S 146 of 1369
+r0:=-1/8*log(1-x^8)
+--R
+--R
+--R 8
+--R log(- x + 1)
+--R (2) - -------------
+--R 8
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8
+--R log(x - 1)
+--R (3) - -----------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 147
+
+--S 148 of 1369
+m0:=a0-r0
+--R
+--R
+--R 8 8
+--R - log(x - 1) + log(- x + 1)
+--R (4) -----------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 148
+
+--S 149 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 149
+
+)clear all
+
+--S 150 of 1369
+t0:=x^5/(1-x^8)
+--R
+--R
+--R 5
+--R x
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 150
+
+--S 151 of 1369
+r0:=-1/4*atan(x^2)+1/4*atanh(x^2)
+--R
+--R
+--R 2 2
+--R atanh(x ) - atan(x )
+--R (2) --------------------
+--R 4
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R log(x + 1) - log(x - 1) - 2atan(x )
+--R (3) -------------------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 152
+
+--S 153 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2 2
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 153
+
+--S 154 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 154
+
+)clear all
+
+--S 155 of 1369
+t0:=x^3/(1-x^8)
+--R
+--R
+--R 3
+--R x
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 155
+
+--S 156 of 1369
+r0:=1/4*atanh(x^4)
+--R
+--R
+--R 4
+--R atanh(x )
+--R (2) ---------
+--R 4
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4
+--R log(x + 1) - log(x - 1)
+--R (3) -------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 157
+
+--S 158 of 1369
+m0:=a0-r0
+--R
+--R
+--R 4 4 4
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 158
+
+--S 159 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 159
+
+)clear all
+
+--S 160 of 1369
+t0:=x/(1-x^8)
+--R
+--R
+--R x
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 160
+
+--S 161 of 1369
+r0:=1/4*atan(x^2)+1/4*atanh(x^2)
+--R
+--R
+--R 2 2
+--R atanh(x ) + atan(x )
+--R (2) --------------------
+--R 4
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R log(x + 1) - log(x - 1) + 2atan(x )
+--R (3) -------------------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 162
+
+--S 163 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2 2
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 163
+
+--S 164 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 164
+
+)clear all
+
+--S 165 of 1369
+t0:=1/(x*(1-x^8))
+--R
+--R
+--R 1
+--R (1) - ------
+--R 9
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 165
+
+--S 166 of 1369
+r0:=-1/4*atanh(1-2*x^8)
+--R
+--R
+--R 8
+--R atanh(2x - 1)
+--R (2) --------------
+--R 4
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8
+--R - log(x - 1) + 8log(x)
+--R (3) -----------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 167
+
+--S 168 of 1369
+m0:=a0-r0
+--R
+--R
+--R 8 8
+--R - log(x - 1) + 8log(x) - 2atanh(2x - 1)
+--R (4) -----------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 168
+
+--S 169 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 169
+
+)clear all
+
+--S 170 of 1369
+t0:=1/(x^3*(1-x^8))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 11 3
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 170
+
+--S 171 of 1369
+r0:=(-1/2)/x^2-1/4*atan(x^2)+1/4*atanh(x^2)
+--R
+--R
+--R 2 2 2 2
+--R x atanh(x ) - x atan(x ) - 2
+--R (2) ----------------------------
+--R 2
+--R 4x
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2 2 2
+--R x log(x + 1) - x log(x - 1) - 2x atan(x ) - 4
+--R (3) -----------------------------------------------
+--R 2
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 172
+
+--S 173 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2 2
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 173
+
+--S 174 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 174
+
+)clear all
+
+--S 175 of 1369
+t0:=1/(x^5*(1-x^8))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 13 5
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 175
+
+--S 176 of 1369
+r0:=(-1/4)/x^4+1/4*atanh(x^4)
+--R
+--R
+--R 4 4
+--R x atanh(x ) - 1
+--R (2) ---------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4 4 4
+--R x log(x + 1) - x log(x - 1) - 2
+--R (3) ---------------------------------
+--R 4
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 177
+
+--S 178 of 1369
+m0:=a0-r0
+--R
+--R
+--R 4 4 4
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 178
+
+--S 179 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 179
+
+)clear all
+
+--S 180 of 1369
+t0:=1/(x^7*(1-x^8))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 15 7
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 180
+
+--S 181 of 1369
+r0:=(-1/6)/x^6+1/4*atan(x^2)+1/4*atanh(x^2)
+--R
+--R
+--R 6 2 6 2
+--R 3x atanh(x ) + 3x atan(x ) - 2
+--R (2) ------------------------------
+--R 6
+--R 12x
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 2 6 2 6 2
+--R 3x log(x + 1) - 3x log(x - 1) + 6x atan(x ) - 4
+--R (3) -------------------------------------------------
+--R 6
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 182
+
+--S 183 of 1369
+m0:=a0-r0
+--R
+--R
+--R 2 2 2
+--R log(x + 1) - log(x - 1) - 2atanh(x )
+--R (4) --------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 183
+
+--S 184 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 184
+
+)clear all
+
+--S 185 of 1369
+t0:=1/(x^9*(1-x^8))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 17 9
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 185
+
+--S 186 of 1369
+r0:=(-1/8)/x^8-1/4*atanh(1-2*x^8)
+--R
+--R
+--R 8 8
+--R 2x atanh(2x - 1) - 1
+--R (2) ---------------------
+--R 8
+--R 8x
+--R Type: Expression(Integer)
+--E 186
+
+--S 187 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 8 8
+--R - x log(x - 1) + 8x log(x) - 1
+--R (3) -------------------------------
+--R 8
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 187
+
+--S 188 of 1369
+m0:=a0-r0
+--R
+--R
+--R 8 8
+--R - log(x - 1) + 8log(x) - 2atanh(2x - 1)
+--R (4) -----------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 188
+
+--S 189 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 189
+
+)clear all
+
+--S 190 of 1369
+t0:=x^8/(1-x^8)
+--R
+--R
+--R 8
+--R x
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 190
+
+--S 191 of 1369
+r0:=-x+1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_
+ 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/sqrt(2)+_
+ 1/8*log(1+x^2+x*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+
+--R log(x\|2 + x + 1) - log(- x\|2 + x + 1) + 2\|2 atanh(x)
+--R +
+--R +-+ +-+ +-+ +-+
+--R 2atan(x\|2 + 1) + 2atan(x\|2 - 1) + 2\|2 atan(x) - 8x\|2
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ +-+
+--R log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1)
+--R +
+--R +-+ 2 +-+ 2x 1
+--R - log(- x\|2 + x + 1) - \|2 atan(------) - 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1 +-+
+--R - 2atan(---------) - 8x\|2
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 192
+
+--S 193 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+
+--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1)
+--R +
+--R +-+ +-+ +-+ 2x 1
+--R - 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) - 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R - 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 193
+
+--S 194 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 194
+
+)clear all
+
+--S 195 of 1369
+t0:=x^6/(1-x^8)
+--R
+--R
+--R 6
+--R x
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 195
+
+--S 196 of 1369
+r0:=-1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_
+ 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/_
+ sqrt(2)+1/8*log(1+x^2+x*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+
+--R log(x\|2 + x + 1) - log(- x\|2 + x + 1) + 2\|2 atanh(x)
+--R +
+--R +-+ +-+ +-+
+--R - 2atan(x\|2 + 1) - 2atan(x\|2 - 1) - 2\|2 atan(x)
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ +-+
+--R log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1)
+--R +
+--R +-+ 2 +-+ 2x 1
+--R - log(- x\|2 + x + 1) + \|2 atan(------) + 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 197
+
+--S 198 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+
+--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1)
+--R +
+--R +-+ +-+ +-+ 2x 1
+--R 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) + 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 198
+
+--S 199 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 199
+
+)clear all
+
+--S 200 of 1369
+t0:=x^4/(1-x^8)
+--R
+--R
+--R 4
+--R x
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 200
+
+--S 201 of 1369
+r0:=1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_
+ 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/_
+ sqrt(2)-1/8*log(1+x^2+x*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+
+--R - log(x\|2 + x + 1) + log(- x\|2 + x + 1) + 2\|2 atanh(x)
+--R +
+--R +-+ +-+ +-+
+--R - 2atan(x\|2 + 1) - 2atan(x\|2 - 1) + 2\|2 atan(x)
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ +-+
+--R - log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1)
+--R +
+--R +-+ 2 +-+ 2x 1
+--R log(- x\|2 + x + 1) - \|2 atan(------) + 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 202
+
+--S 203 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+
+--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1)
+--R +
+--R +-+ +-+ +-+ 2x 1
+--R 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) + 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 203
+
+--S 204 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 204
+
+)clear all
+
+--S 205 of 1369
+t0:=x^2/(1-x^8)
+--R
+--R
+--R 2
+--R x
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 205
+
+--S 206 of 1369
+r0:=-1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_
+ 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/_
+ sqrt(2)-1/8*log(1+x^2+x*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+
+--R - log(x\|2 + x + 1) + log(- x\|2 + x + 1) + 2\|2 atanh(x)
+--R +
+--R +-+ +-+ +-+
+--R 2atan(x\|2 + 1) + 2atan(x\|2 - 1) - 2\|2 atan(x)
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ +-+
+--R - log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1)
+--R +
+--R +-+ 2 +-+ 2x 1
+--R log(- x\|2 + x + 1) + \|2 atan(------) - 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R - 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 207
+
+--S 208 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+
+--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1)
+--R +
+--R +-+ +-+ +-+ 2x 1
+--R - 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) - 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R - 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 208
+
+--S 209 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 209
+
+)clear all
+
+--S 210 of 1369
+t0:=1/(1-x^8)
+--R
+--R
+--R 1
+--R (1) - ------
+--R 8
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 210
+
+--S 211 of 1369
+r0:=1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_
+ 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/_
+ sqrt(2)+1/8*log(1+x^2+x*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+
+--R log(x\|2 + x + 1) - log(- x\|2 + x + 1) + 2\|2 atanh(x)
+--R +
+--R +-+ +-+ +-+
+--R 2atan(x\|2 + 1) + 2atan(x\|2 - 1) + 2\|2 atan(x)
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ +-+
+--R log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1)
+--R +
+--R +-+ 2 +-+ 2x 1
+--R - log(- x\|2 + x + 1) - \|2 atan(------) - 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R - 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 212
+
+--S 213 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+
+--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1)
+--R +
+--R +-+ +-+ +-+ 2x 1
+--R - 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) - 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R - 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 213
+
+--S 214 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 214
+
+)clear all
+
+--S 215 of 1369
+t0:=1/(x^2*(1-x^8))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 10 2
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 215
+
+--S 216 of 1369
+r0:=(-1)/x-1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_
+ 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/_
+ sqrt(2)+1/8*log(1+x^2+x*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R +-+ 2 +-+ 2 +-+
+--R x log(x\|2 + x + 1) - x log(- x\|2 + x + 1) + 2x\|2 atanh(x)
+--R +
+--R +-+ +-+ +-+ +-+
+--R - 2x atan(x\|2 + 1) - 2x atan(x\|2 - 1) - 2x\|2 atan(x) - 8\|2
+--R /
+--R +-+
+--R 8x\|2
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ +-+
+--R x log(x\|2 + x + 1) + x\|2 log(x + 1) - x\|2 log(x - 1)
+--R +
+--R +-+ 2 +-+ 2x 1
+--R - x log(- x\|2 + x + 1) + x\|2 atan(------) + 2x atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1 +-+
+--R 2x atan(---------) - 8\|2
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8x\|2
+--R Type: Union(Expression(Integer),...)
+--E 217
+
+--S 218 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+
+--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1)
+--R +
+--R +-+ +-+ +-+ 2x 1
+--R 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) + 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 218
+
+--S 219 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 219
+
+)clear all
+
+--S 220 of 1369
+t0:=1/(x^4*(1-x^8))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 12 4
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 220
+
+--S 221 of 1369
+r0:=(-1/3)/x^3+1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_
+ 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/sqrt(2)-_
+ 1/8*log(1+x^2+x*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R 3 +-+ 2 3 +-+ 2 3 +-+
+--R - 3x log(x\|2 + x + 1) + 3x log(- x\|2 + x + 1) + 6x \|2 atanh(x)
+--R +
+--R 3 +-+ 3 +-+ 3 +-+ +-+
+--R - 6x atan(x\|2 + 1) - 6x atan(x\|2 - 1) + 6x \|2 atan(x) - 8\|2
+--R /
+--R 3 +-+
+--R 24x \|2
+--R Type: Expression(Integer)
+--E 221
+
+--S 222 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 +-+ 2 3 +-+ 3 +-+
+--R - 3x log(x\|2 + x + 1) + 3x \|2 log(x + 1) - 3x \|2 log(x - 1)
+--R +
+--R 3 +-+ 2 3 +-+ 2x 3 1
+--R 3x log(- x\|2 + x + 1) - 3x \|2 atan(------) + 6x atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 3 1 +-+
+--R 6x atan(---------) - 8\|2
+--R +-+
+--R x\|2 + 1
+--R /
+--R 3 +-+
+--R 24x \|2
+--R Type: Union(Expression(Integer),...)
+--E 222
+
+--S 223 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+
+--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1)
+--R +
+--R +-+ +-+ +-+ 2x 1
+--R 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) + 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 223
+
+--S 224 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 224
+
+)clear all
+
+--S 225 of 1369
+t0:=1/(x^6*(1-x^8))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 14 6
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 225
+
+--S 226 of 1369
+r0:=(-1/5)/x^5-1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_
+ 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/sqrt(2)-_
+ 1/8*log(1+x^2+x*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R 5 +-+ 2 5 +-+ 2 5 +-+
+--R - 5x log(x\|2 + x + 1) + 5x log(- x\|2 + x + 1) + 10x \|2 atanh(x)
+--R +
+--R 5 +-+ 5 +-+ 5 +-+ +-+
+--R 10x atan(x\|2 + 1) + 10x atan(x\|2 - 1) - 10x \|2 atan(x) - 8\|2
+--R /
+--R 5 +-+
+--R 40x \|2
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 +-+ 2 5 +-+ 5 +-+
+--R - 5x log(x\|2 + x + 1) + 5x \|2 log(x + 1) - 5x \|2 log(x - 1)
+--R +
+--R 5 +-+ 2 5 +-+ 2x 5 1
+--R 5x log(- x\|2 + x + 1) + 5x \|2 atan(------) - 10x atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 5 1 +-+
+--R - 10x atan(---------) - 8\|2
+--R +-+
+--R x\|2 + 1
+--R /
+--R 5 +-+
+--R 40x \|2
+--R Type: Union(Expression(Integer),...)
+--E 227
+
+--S 228 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+
+--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1)
+--R +
+--R +-+ +-+ +-+ 2x 1
+--R - 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) - 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R - 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 228
+
+--S 229 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 229
+
+)clear all
+
+--S 230 of 1369
+t0:=1/(x^8*(1-x^8))
+--R
+--R
+--R 1
+--R (1) - --------
+--R 16 8
+--R x - x
+--R Type: Fraction(Polynomial(Integer))
+--E 230
+
+--S 231 of 1369
+r0:=(-1/7)/x^7+1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_
+ 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/sqrt(2)+_
+ 1/8*log(1+x^2+x*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R 7 +-+ 2 7 +-+ 2 7 +-+
+--R 7x log(x\|2 + x + 1) - 7x log(- x\|2 + x + 1) + 14x \|2 atanh(x)
+--R +
+--R 7 +-+ 7 +-+ 7 +-+ +-+
+--R 14x atan(x\|2 + 1) + 14x atan(x\|2 - 1) + 14x \|2 atan(x) - 8\|2
+--R /
+--R 7 +-+
+--R 56x \|2
+--R Type: Expression(Integer)
+--E 231
+
+--S 232 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 +-+ 2 7 +-+ 7 +-+
+--R 7x log(x\|2 + x + 1) + 7x \|2 log(x + 1) - 7x \|2 log(x - 1)
+--R +
+--R 7 +-+ 2 7 +-+ 2x 7 1
+--R - 7x log(- x\|2 + x + 1) - 7x \|2 atan(------) - 14x atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 7 1 +-+
+--R - 14x atan(---------) - 8\|2
+--R +-+
+--R x\|2 + 1
+--R /
+--R 7 +-+
+--R 56x \|2
+--R Type: Union(Expression(Integer),...)
+--E 232
+
+--S 233 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+ +-+ +-+ +-+
+--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1)
+--R +
+--R +-+ +-+ +-+ 2x 1
+--R - 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) - 2atan(---------)
+--R 2 +-+
+--R x - 1 x\|2 - 1
+--R +
+--R 1
+--R - 2atan(---------)
+--R +-+
+--R x\|2 + 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 233
+
+--S 234 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 234
+
+)clear all
+
+--S 235 of 1369
+t0:=x^9/(1+x^8)
+--R
+--R
+--R 9
+--R x
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 235
+
+--S 236 of 1369
+r0:=1/2*x^2+1/4*atan(1-x^2*sqrt(2))/sqrt(2)-1/4*atan(1+x^2*sqrt(2))/_
+ sqrt(2)+1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)-1/8*log(1+x^4+_
+ x^2*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R 2 +-+ 4 2 +-+ 4 2 +-+
+--R - log(x \|2 + x + 1) + log(- x \|2 + x + 1) - 2atan(x \|2 + 1)
+--R +
+--R 2 +-+ 2 +-+
+--R - 2atan(x \|2 - 1) + 4x \|2
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ 4 +-+ 2 +-+ 4
+--R - \|2 log(x \|2 + x + 1) + \|2 log(- x \|2 + x + 1)
+--R +
+--R +-+ 1 +-+ 1 2
+--R 2\|2 atan(----------) + 2\|2 atan(----------) + 8x
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R /
+--R 16
+--R Type: Union(Expression(Integer),...)
+--E 237
+
+--S 238 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 +-+ 2 +-+ 1 1
+--R atan(x \|2 + 1) + atan(x \|2 - 1) + atan(----------) + atan(----------)
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R -------------------------------------------------------------------------
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 238
+
+--S 239 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 239
+
+)clear all
+
+--S 240 of 1369
+t0:=x^7/(1+x^8)
+--R
+--R
+--R 7
+--R x
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 240
+
+--S 241 of 1369
+r0:=1/8*log(1+x^8)
+--R
+--R
+--R 8
+--R log(x + 1)
+--R (2) -----------
+--R 8
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8
+--R log(x + 1)
+--R (3) -----------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 242
+
+--S 243 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 243
+
+--S 244 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 244
+
+)clear all
+
+--S 245 of 1369
+t0:=x^5/(1+x^8)
+--R
+--R
+--R 5
+--R x
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 245
+
+--S 246 of 1369
+r0:=-1/4*atan(1-x^2*sqrt(2))/sqrt(2)+1/4*atan(1+x^2*sqrt(2))/sqrt(2)+_
+ 1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)-1/8*log(1+x^4+x^2*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R 2 +-+ 4 2 +-+ 4 2 +-+
+--R - log(x \|2 + x + 1) + log(- x \|2 + x + 1) + 2atan(x \|2 + 1)
+--R +
+--R 2 +-+
+--R 2atan(x \|2 - 1)
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ 4 +-+ 2 +-+ 4
+--R - \|2 log(x \|2 + x + 1) + \|2 log(- x \|2 + x + 1)
+--R +
+--R +-+ 1 +-+ 1
+--R - 2\|2 atan(----------) - 2\|2 atan(----------)
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R /
+--R 16
+--R Type: Union(Expression(Integer),...)
+--E 247
+
+--S 248 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 +-+ 2 +-+ 1 1
+--R - atan(x \|2 + 1) - atan(x \|2 - 1) - atan(----------) - atan(----------)
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 248
+
+--S 249 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 249
+
+)clear all
+
+--S 250 of 1369
+t0:=x^3/(1+x^8)
+--R
+--R
+--R 3
+--R x
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 250
+
+--S 251 of 1369
+r0:=1/4*atan(x^4)
+--R
+--R
+--R 4
+--R atan(x )
+--R (2) --------
+--R 4
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R atan(x )
+--R (3) --------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 252
+
+--S 253 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 253
+
+--S 254 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 254
+
+)clear all
+
+--S 255 of 1369
+t0:=x/(1+x^8)
+--R
+--R
+--R x
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 255
+
+--S 256 of 1369
+r0:=-1/4*atan(1-x^2*sqrt(2))/sqrt(2)+1/4*atan(1+x^2*sqrt(2))/sqrt(2)-_
+ 1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)+1/8*log(1+x^4+x^2*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R 2 +-+ 4 2 +-+ 4 2 +-+
+--R log(x \|2 + x + 1) - log(- x \|2 + x + 1) + 2atan(x \|2 + 1)
+--R +
+--R 2 +-+
+--R 2atan(x \|2 - 1)
+--R /
+--R +-+
+--R 8\|2
+--R Type: Expression(Integer)
+--E 256
+
+--S 257 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ 2 +-+ 4 +-+ 2 +-+ 4
+--R \|2 log(x \|2 + x + 1) - \|2 log(- x \|2 + x + 1)
+--R +
+--R +-+ 1 +-+ 1
+--R - 2\|2 atan(----------) - 2\|2 atan(----------)
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R /
+--R 16
+--R Type: Union(Expression(Integer),...)
+--E 257
+
+--S 258 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 +-+ 2 +-+ 1 1
+--R - atan(x \|2 + 1) - atan(x \|2 - 1) - atan(----------) - atan(----------)
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R ---------------------------------------------------------------------------
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 258
+
+--S 259 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 259
+
+)clear all
+
+--S 260 of 1369
+t0:=1/(x*(1+x^8))
+--R
+--R
+--R 1
+--R (1) ------
+--R 9
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 260
+
+--S 261 of 1369
+r0:=-1/4*atanh(1+2*x^8)
+--R
+--R
+--R 8
+--R atanh(2x + 1)
+--R (2) - --------------
+--R 4
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8
+--R - log(x + 1) + 8log(x)
+--R (3) -----------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 262
+
+--S 263 of 1369
+m0:=a0-r0
+--R
+--R
+--R 8 8
+--R - log(x + 1) + 8log(x) + 2atanh(2x + 1)
+--R (4) -----------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 263
+
+--S 264 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 264
+
+)clear all
+
+--S 265 of 1369
+t0:=1/(x^3*(1+x^8))
+--R
+--R
+--R 1
+--R (1) --------
+--R 11 3
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 265
+
+--S 266 of 1369
+r0:=(-1/2)/x^2+1/4*atan(1-x^2*sqrt(2))/sqrt(2)-1/4*atan(1+x^2*_
+ sqrt(2))/sqrt(2)-1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)+_
+ 1/8*log(1+x^4+x^2*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R 2 2 +-+ 4 2 2 +-+ 4 2 2 +-+
+--R x log(x \|2 + x + 1) - x log(- x \|2 + x + 1) - 2x atan(x \|2 + 1)
+--R +
+--R 2 2 +-+ +-+
+--R - 2x atan(x \|2 - 1) - 4\|2
+--R /
+--R 2 +-+
+--R 8x \|2
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ 2 +-+ 4 2 +-+ 2 +-+ 4
+--R x \|2 log(x \|2 + x + 1) - x \|2 log(- x \|2 + x + 1)
+--R +
+--R 2 +-+ 1 2 +-+ 1
+--R 2x \|2 atan(----------) + 2x \|2 atan(----------) - 8
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R /
+--R 2
+--R 16x
+--R Type: Union(Expression(Integer),...)
+--E 267
+
+--S 268 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 +-+ 2 +-+ 1 1
+--R atan(x \|2 + 1) + atan(x \|2 - 1) + atan(----------) + atan(----------)
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R -------------------------------------------------------------------------
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 268
+
+--S 269 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 269
+
+)clear all
+
+--S 270 of 1369
+t0:=1/(x^5*(1+x^8))
+--R
+--R
+--R 1
+--R (1) --------
+--R 13 5
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 270
+
+--S 271 of 1369
+r0:=(-1/4)/x^4-1/4*atan(x^4)
+--R
+--R
+--R 4 4
+--R - x atan(x ) - 1
+--R (2) ----------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4
+--R - x atan(x ) - 1
+--R (3) ----------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 272
+
+--S 273 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 273
+
+--S 274 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 274
+
+)clear all
+
+--S 275 of 1369
+t0:=1/(x^7*(1+x^8))
+--R
+--R
+--R 1
+--R (1) --------
+--R 15 7
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 275
+
+--S 276 of 1369
+r0:=(-1/6)/x^6+1/4*atan(1-x^2*sqrt(2))/sqrt(2)-1/4*atan(1+x^2*sqrt(2))/_
+ sqrt(2)+1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)-1/8*log(1+x^4+_
+ x^2*sqrt(2))/sqrt(2)
+--R
+--R
+--R (2)
+--R 6 2 +-+ 4 6 2 +-+ 4
+--R - 3x log(x \|2 + x + 1) + 3x log(- x \|2 + x + 1)
+--R +
+--R 6 2 +-+ 6 2 +-+ +-+
+--R - 6x atan(x \|2 + 1) - 6x atan(x \|2 - 1) - 4\|2
+--R /
+--R 6 +-+
+--R 24x \|2
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 +-+ 2 +-+ 4 6 +-+ 2 +-+ 4
+--R - 3x \|2 log(x \|2 + x + 1) + 3x \|2 log(- x \|2 + x + 1)
+--R +
+--R 6 +-+ 1 6 +-+ 1
+--R 6x \|2 atan(----------) + 6x \|2 atan(----------) - 8
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R /
+--R 6
+--R 48x
+--R Type: Union(Expression(Integer),...)
+--E 277
+
+--S 278 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 +-+ 2 +-+ 1 1
+--R atan(x \|2 + 1) + atan(x \|2 - 1) + atan(----------) + atan(----------)
+--R 2 +-+ 2 +-+
+--R x \|2 - 1 x \|2 + 1
+--R -------------------------------------------------------------------------
+--R +-+
+--R 4\|2
+--R Type: Expression(Integer)
+--E 278
+
+--S 279 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 279
+
+)clear all
+
+--S 280 of 1369
+t0:=1/(x^9*(1+x^8))
+--R
+--R
+--R 1
+--R (1) --------
+--R 17 9
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 280
+
+--S 281 of 1369
+r0:=(-1/8)/x^8+1/4*atanh(1+2*x^8)
+--R
+--R
+--R 8 8
+--R 2x atanh(2x + 1) - 1
+--R (2) ---------------------
+--R 8
+--R 8x
+--R Type: Expression(Integer)
+--E 281
+
+--S 282 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 8 8
+--R x log(x + 1) - 8x log(x) - 1
+--R (3) -----------------------------
+--R 8
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 282
+
+--S 283 of 1369
+m0:=a0-r0
+--R
+--R
+--R 8 8
+--R log(x + 1) - 8log(x) - 2atanh(2x + 1)
+--R (4) ---------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 283
+
+--S 284 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 284
+
+)clear all
+
+--S 285 of 1369
+t0:=x^8/(1+x^8)
+--R
+--R
+--R 8
+--R x
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 285
+
+--S 286 of 1369
+r0:=x+1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_
+ sqrt(2-sqrt(2))-1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_
+ sqrt(2-sqrt(2))+1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_
+ 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+1/8*_
+ atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_
+ 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_
+ 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_
+ 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))
+--R
+--R
+--R (2)
+--R +--------+ +--------+
+--R | +-+ | +-+ 2
+--R - \|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R | +-+ | +-+ 2
+--R - \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R | +-+ | +-+ 2
+--R \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R | +-+ | +-+ 2
+--R \|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R -
+--R +----------+
+--R | +-+
+--R 2\|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+
+--R | +-+
+--R 2\|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R atan(-----------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R 2\|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R - 2\|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R 16x
+--R /
+--R 16
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+
+--R - \|- 1 log(x\|- 1 \|2 + \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2
+--R \|- 1 \|2 log(- \|- 1 + x) + \|- 1 log(- x\|- 1 \|2 + \|- 1 + x )
+--R +
+--R 8+---+ 8+---+
+--R 8+---+ +-+ \|- 1 8+---+ \|- 1
+--R 2\|- 1 \|2 atan(------) + 2\|- 1 atan(--------------)
+--R x +-+ 8+---+
+--R x\|2 - \|- 1
+--R +
+--R 8+---+
+--R 8+---+ \|- 1 +-+
+--R 2\|- 1 atan(--------------) + 8x\|2
+--R +-+ 8+---+
+--R x\|2 + \|- 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 287
+
+--S 288 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R atan
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R -----------------------------------------------------------------
+--R 2
+--R +
+--R -
+--R +--------+
+--R +-+ | +-+
+--R 2\|2 \|\|2 + 2
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+
+--R - 2\|- 1 log(x\|- 1 \|2 + \|- 1 + x ) - 2\|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2
+--R 2\|- 1 \|2 log(- \|- 1 + x) + 2\|- 1 log(- x\|- 1 \|2 + \|- 1 + x )
+--R +
+--R 8+---+ 8+---+
+--R 8+---+ +-+ \|- 1 8+---+ \|- 1
+--R 4\|- 1 \|2 atan(------) + 4\|- 1 atan(--------------)
+--R x +-+ 8+---+
+--R x\|2 - \|- 1
+--R +
+--R 8+---+
+--R 8+---+ \|- 1
+--R 4\|- 1 atan(--------------)
+--R +-+ 8+---+
+--R x\|2 + \|- 1
+--R /
+--R +-+
+--R 16\|2
+--R Type: Expression(Integer)
+--E 288
+
+--S 289 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 289
+
+)clear all
+
+--S 290 of 1369
+t0:=x^6/(1+x^8)
+--R
+--R
+--R 6
+--R x
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 290
+
+--S 291 of 1369
+r0:=-1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_
+ 1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_
+ 1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_
+ 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_
+ 1/8*atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_
+ 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_
+ 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_
+ 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))
+--R
+--R
+--R (2)
+--R +--------+ +--------+
+--R | +-+ | +-+ 2
+--R - \|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R | +-+ | +-+ 2
+--R - \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R | +-+ | +-+ 2
+--R \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R | +-+ | +-+ 2
+--R \|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+
+--R | +-+
+--R 2\|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +----------+
+--R | +-+
+--R 2\|- \|2 + 2
+--R *
+--R atan
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R -----------------------------------------------------------------
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R - 2\|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R 2\|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R /
+--R 16
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7
+--R \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) + \|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+7
+--R - \|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+7
+--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1
+--R - \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) + 2\|- 1 \|2 atan(-------)
+--R x
+--R +
+--R 8+---+7 8+---+7
+--R 8+---+ \|- 1 8+---+ \|- 1
+--R 2\|- 1 atan(---------------) + 2\|- 1 atan(---------------)
+--R +-+ 8+---+7 +-+ 8+---+7
+--R x\|2 - \|- 1 x\|2 + \|- 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 292
+
+--S 293 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R -
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R atan(-----------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +--------+
+--R +-+ | +-+
+--R 2\|2 \|\|2 + 2
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7
+--R 2\|- 1 log(x \|- 1 \|2 - \|- 1 + x ) + 2\|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+7
+--R - 2\|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+7
+--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1
+--R - 2\|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) + 4\|- 1 \|2 atan(-------)
+--R x
+--R +
+--R 8+---+7 8+---+7
+--R 8+---+ \|- 1 8+---+ \|- 1
+--R 4\|- 1 atan(---------------) + 4\|- 1 atan(---------------)
+--R +-+ 8+---+7 +-+ 8+---+7
+--R x\|2 - \|- 1 x\|2 + \|- 1
+--R /
+--R +-+
+--R 16\|2
+--R Type: Expression(Integer)
+--E 293
+
+--S 294 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 294
+
+)clear all
+
+--S 295 of 1369
+t0:=x^4/(1+x^8)
+--R
+--R
+--R 4
+--R x
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 295
+
+--S 296 of 1369
+r0:=-1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_
+ 1/4*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-_
+ 1/8*log(1+x^2-x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/8*log(1+_
+ x^2+x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/4*atan((-2*x+_
+ sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_
+ 1/4*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+_
+ sqrt(2)))+1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_
+ 1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))
+--R
+--R
+--R (2)
+--R +-----------+ +--------+
+--R | +-+ | +-+ 2
+--R - \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R | +-+ | +-+ 2
+--R \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R | +-+ | +-+ 2
+--R - \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +-----------+ +--------+
+--R | +-+ | +-+ 2
+--R \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+
+--R | +-+
+--R 2\|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +---------+
+--R | +-+
+--R 2\|2\|2 + 4
+--R *
+--R atan
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R -----------------------------------------------------------------
+--R 2
+--R +
+--R +----------+ +--------+
+--R +-----------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R 2\|- 2\|2 + 4 atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +-----------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R - 2\|- 2\|2 + 4 atan(--------------------------------------------------)
+--R 2
+--R /
+--R +-----------+ +---------+
+--R | +-+ | +-+
+--R 8\|- 2\|2 + 4 \|2\|2 + 4
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8+---+ 8+---+5 +-+ 8+---+2 2 8+---+ +-+ 8+---+5
+--R \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+5 8+---+ 8+---+5 +-+ 8+---+2 2
+--R \|- 1 \|2 log(- \|- 1 + x) - \|- 1 log(- x \|- 1 \|2 - \|- 1 + x )
+--R +
+--R 8+---+5 8+---+5
+--R 8+---+ +-+ \|- 1 8+---+ \|- 1
+--R 2\|- 1 \|2 atan(-------) - 2\|- 1 atan(---------------)
+--R x +-+ 8+---+5
+--R x\|2 - \|- 1
+--R +
+--R 8+---+5
+--R 8+---+ \|- 1
+--R - 2\|- 1 atan(---------------)
+--R +-+ 8+---+5
+--R x\|2 + \|- 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 297
+
+--S 298 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +-----------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R -
+--R +---------+
+--R +-+ | +-+
+--R 2\|2 \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R +---------+
+--R +-+ | +-+
+--R 2\|2 \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R atan(-----------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +-----------+
+--R +-+ | +-+
+--R 2\|2 \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R +-----------+
+--R +-+ | +-+
+--R 2\|2 \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R 8+---+ 8+---+5 +-+ 8+---+2 2 8+---+ +-+ 8+---+5
+--R \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+5
+--R \|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+ 8+---+5 +-+ 8+---+2 2
+--R - \|- 1 log(- x \|- 1 \|2 - \|- 1 + x )
+--R +
+--R 8+---+5 8+---+5
+--R 8+---+ +-+ \|- 1 8+---+ \|- 1
+--R 2\|- 1 \|2 atan(-------) - 2\|- 1 atan(---------------)
+--R x +-+ 8+---+5
+--R x\|2 - \|- 1
+--R +
+--R 8+---+5
+--R 8+---+ \|- 1
+--R - 2\|- 1 atan(---------------)
+--R +-+ 8+---+5
+--R x\|2 + \|- 1
+--R *
+--R +-----------+ +---------+
+--R | +-+ | +-+
+--R \|- 2\|2 + 4 \|2\|2 + 4
+--R /
+--R +-----------+ +---------+
+--R +-+ | +-+ | +-+
+--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4
+--R Type: Expression(Integer)
+--E 298
+
+--S 299 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +---------+
+--R 4 +-+ 4 | +-+ | +-+
+--R ((- 3x - 1)\|2 + 4x + 2)\|\|2 + 2 \|2\|2 + 4
+--R +
+--R +-----------+ +----------+
+--R 4 +-+ 4 | +-+ | +-+ 4
+--R ((- 3x - 1)\|2 - 4x - 2)\|- 2\|2 + 4 \|- \|2 + 2 + 8x
+--R /
+--R 8
+--R 8x + 8
+--R Type: Expression(Integer)
+--E 299
+
+)clear all
+
+--S 300 of 1369
+t0:=x^2/(1+x^8)
+--R
+--R
+--R 2
+--R x
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 300
+
+--S 301 of 1369
+r0:=-1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_
+ 1/4*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_
+ 1/8*log(1+x^2-x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-_
+ 1/8*log(1+x^2+x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_
+ 1/4*atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_
+ 1/4*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_
+ 1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+_
+ 1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))
+--R
+--R
+--R (2)
+--R +-----------+ +--------+
+--R | +-+ | +-+ 2
+--R \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R | +-+ | +-+ 2
+--R - \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R | +-+ | +-+ 2
+--R \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +-----------+ +--------+
+--R | +-+ | +-+ 2
+--R - \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+
+--R | +-+
+--R 2\|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +---------+
+--R | +-+
+--R 2\|2\|2 + 4
+--R *
+--R atan
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R -----------------------------------------------------------------
+--R 2
+--R +
+--R +----------+ +--------+
+--R +-----------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R 2\|- 2\|2 + 4 atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +-----------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R - 2\|- 2\|2 + 4 atan(--------------------------------------------------)
+--R 2
+--R /
+--R +-----------+ +---------+
+--R | +-+ | +-+
+--R 8\|- 2\|2 + 4 \|2\|2 + 4
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8+---+ 8+---+3 +-+ 8+---+6 2 8+---+ +-+ 8+---+3
+--R \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+3 8+---+ 8+---+3 +-+ 8+---+6 2
+--R \|- 1 \|2 log(- \|- 1 + x) - \|- 1 log(- x \|- 1 \|2 + \|- 1 + x )
+--R +
+--R 8+---+3 8+---+3
+--R 8+---+ +-+ \|- 1 8+---+ \|- 1
+--R - 2\|- 1 \|2 atan(-------) + 2\|- 1 atan(---------------)
+--R x +-+ 8+---+3
+--R x\|2 - \|- 1
+--R +
+--R 8+---+3
+--R 8+---+ \|- 1
+--R 2\|- 1 atan(---------------)
+--R +-+ 8+---+3
+--R x\|2 + \|- 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 302
+
+--S 303 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +-----------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R -
+--R +---------+
+--R +-+ | +-+
+--R 2\|2 \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R +---------+
+--R +-+ | +-+
+--R 2\|2 \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R atan(-----------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +-----------+
+--R +-+ | +-+
+--R 2\|2 \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R +-----------+
+--R +-+ | +-+
+--R 2\|2 \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R 8+---+ 8+---+3 +-+ 8+---+6 2 8+---+ +-+ 8+---+3
+--R \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+3
+--R \|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+ 8+---+3 +-+ 8+---+6 2
+--R - \|- 1 log(- x \|- 1 \|2 + \|- 1 + x )
+--R +
+--R 8+---+3 8+---+3
+--R 8+---+ +-+ \|- 1 8+---+ \|- 1
+--R - 2\|- 1 \|2 atan(-------) + 2\|- 1 atan(---------------)
+--R x +-+ 8+---+3
+--R x\|2 - \|- 1
+--R +
+--R 8+---+3
+--R 8+---+ \|- 1
+--R 2\|- 1 atan(---------------)
+--R +-+ 8+---+3
+--R x\|2 + \|- 1
+--R *
+--R +-----------+ +---------+
+--R | +-+ | +-+
+--R \|- 2\|2 + 4 \|2\|2 + 4
+--R /
+--R +-----------+ +---------+
+--R +-+ | +-+ | +-+
+--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4
+--R Type: Expression(Integer)
+--E 303
+
+--S 304 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +---------+
+--R 6 2 +-+ 6 2 | +-+ | +-+
+--R ((- x - 3x )\|2 + 2x + 4x )\|\|2 + 2 \|2\|2 + 4
+--R +
+--R +-----------+ +----------+
+--R 6 2 +-+ 6 2 | +-+ | +-+ 2
+--R ((- x - 3x )\|2 - 2x - 4x )\|- 2\|2 + 4 \|- \|2 + 2 + 8x
+--R /
+--R 8
+--R 8x + 8
+--R Type: Expression(Integer)
+--E 304
+
+)clear all
+
+--S 305 of 1369
+t0:=1/(1+x^8)
+--R
+--R
+--R 1
+--R (1) ------
+--R 8
+--R x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 305
+
+--S 306 of 1369
+r0:=-1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_
+ 1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_
+ 1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_
+ 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_
+ 1/8*atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_
+ 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_
+ 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_
+ 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))
+--R
+--R
+--R (2)
+--R +--------+ +--------+
+--R | +-+ | +-+ 2
+--R \|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R | +-+ | +-+ 2
+--R \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R | +-+ | +-+ 2
+--R - \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R | +-+ | +-+ 2
+--R - \|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+
+--R | +-+
+--R 2\|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +----------+
+--R | +-+
+--R 2\|- \|2 + 2
+--R *
+--R atan
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R -----------------------------------------------------------------
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R - 2\|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R 2\|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R /
+--R 16
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+
+--R \|- 1 log(x\|- 1 \|2 + \|- 1 + x ) + \|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2
+--R - \|- 1 \|2 log(- \|- 1 + x) - \|- 1 log(- x\|- 1 \|2 + \|- 1 + x )
+--R +
+--R 8+---+ 8+---+
+--R 8+---+ +-+ \|- 1 8+---+ \|- 1
+--R - 2\|- 1 \|2 atan(------) - 2\|- 1 atan(--------------)
+--R x +-+ 8+---+
+--R x\|2 - \|- 1
+--R +
+--R 8+---+
+--R 8+---+ \|- 1
+--R - 2\|- 1 atan(--------------)
+--R +-+ 8+---+
+--R x\|2 + \|- 1
+--R /
+--R +-+
+--R 8\|2
+--R Type: Union(Expression(Integer),...)
+--E 307
+
+--S 308 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R -
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R atan(-----------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +--------+
+--R +-+ | +-+
+--R 2\|2 \|\|2 + 2
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+
+--R 2\|- 1 log(x\|- 1 \|2 + \|- 1 + x ) + 2\|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2
+--R - 2\|- 1 \|2 log(- \|- 1 + x) - 2\|- 1 log(- x\|- 1 \|2 + \|- 1 + x )
+--R +
+--R 8+---+ 8+---+
+--R 8+---+ +-+ \|- 1 8+---+ \|- 1
+--R - 4\|- 1 \|2 atan(------) - 4\|- 1 atan(--------------)
+--R x +-+ 8+---+
+--R x\|2 - \|- 1
+--R +
+--R 8+---+
+--R 8+---+ \|- 1
+--R - 4\|- 1 atan(--------------)
+--R +-+ 8+---+
+--R x\|2 + \|- 1
+--R /
+--R +-+
+--R 16\|2
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 309
+
+)clear all
+
+--S 310 of 1369
+t0:=1/(x^2*(1+x^8))
+--R
+--R
+--R 1
+--R (1) --------
+--R 10 2
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 310
+
+--S 311 of 1369
+r0:=(-1)/x+1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_
+ sqrt(2-sqrt(2))-1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_
+ sqrt(2-sqrt(2))-1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_
+ 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+1/8*_
+ atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_
+ 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_
+ 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_
+ 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))
+--R
+--R
+--R (2)
+--R +--------+ +--------+
+--R | +-+ | +-+ 2
+--R x\|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R | +-+ | +-+ 2
+--R x\|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R | +-+ | +-+ 2
+--R - x\|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R | +-+ | +-+ 2
+--R - x\|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R -
+--R +----------+
+--R | +-+
+--R 2x\|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+
+--R | +-+
+--R 2x\|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R atan(-----------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R 2x\|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R - 2x\|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R - 16
+--R /
+--R 16x
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7
+--R - x\|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - x\|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+7
+--R x\|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+7
+--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1
+--R x\|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) - 2x\|- 1 \|2 atan(-------)
+--R x
+--R +
+--R 8+---+7 8+---+7
+--R 8+---+ \|- 1 8+---+ \|- 1 +-+
+--R - 2x\|- 1 atan(---------------) - 2x\|- 1 atan(---------------) - 8\|2
+--R +-+ 8+---+7 +-+ 8+---+7
+--R x\|2 - \|- 1 x\|2 + \|- 1
+--R /
+--R +-+
+--R 8x\|2
+--R Type: Union(Expression(Integer),...)
+--E 312
+
+--S 313 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R atan
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R -----------------------------------------------------------------
+--R 2
+--R +
+--R -
+--R +--------+
+--R +-+ | +-+
+--R 2\|2 \|\|2 + 2
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7
+--R - 2\|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - 2\|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+7
+--R 2\|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+7
+--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1
+--R 2\|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) - 4\|- 1 \|2 atan(-------)
+--R x
+--R +
+--R 8+---+7 8+---+7
+--R 8+---+ \|- 1 8+---+ \|- 1
+--R - 4\|- 1 atan(---------------) - 4\|- 1 atan(---------------)
+--R +-+ 8+---+7 +-+ 8+---+7
+--R x\|2 - \|- 1 x\|2 + \|- 1
+--R /
+--R +-+
+--R 16\|2
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 314
+
+)clear all
+
+--S 315 of 1369
+t0:=1/(x^4*(1+x^8))
+--R
+--R
+--R 1
+--R (1) --------
+--R 12 4
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 315
+
+--S 316 of 1369
+r0:=(-1/3)/x^3+1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/_
+ sqrt(2*(2-sqrt(2)))-1/4*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-_
+ sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/8*log(1+x^2-x*sqrt(2-sqrt(2)))/_
+ sqrt(2*(2-sqrt(2)))-1/8*log(1+x^2+x*sqrt(2-sqrt(2)))/_
+ sqrt(2*(2-sqrt(2)))-1/4*atan((-2*x+sqrt(2-sqrt(2)))/_
+ sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+1/4*atan((2*x+_
+ sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_
+ 1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+_
+ 1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))
+--R
+--R
+--R (2)
+--R +-----------+ +--------+
+--R 3 | +-+ | +-+ 2
+--R 3x \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R 3 | +-+ | +-+ 2
+--R - 3x \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R 3 | +-+ | +-+ 2
+--R 3x \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +-----------+ +--------+
+--R 3 | +-+ | +-+ 2
+--R - 3x \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R -
+--R +---------+
+--R 3 | +-+
+--R 6x \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R +---------+
+--R 3 | +-+
+--R 6x \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R atan(-----------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +-----------+
+--R 3 | +-+
+--R 6x \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +-----------+ +-+ | +-+ +-+ | +-+
+--R 3 | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R 6x \|- 2\|2 + 4 atan(--------------------------------------------------)
+--R 2
+--R +
+--R +-----------+ +---------+
+--R | +-+ | +-+
+--R - 8\|- 2\|2 + 4 \|2\|2 + 4
+--R /
+--R +-----------+ +---------+
+--R 3 | +-+ | +-+
+--R 24x \|- 2\|2 + 4 \|2\|2 + 4
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 8+---+ 8+---+5 +-+ 8+---+2 2
+--R - 3x \|- 1 log(x \|- 1 \|2 - \|- 1 + x )
+--R +
+--R 3 8+---+ +-+ 8+---+5 3 8+---+ +-+ 8+---+5
+--R 3x \|- 1 \|2 log(\|- 1 + x - 3x \|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+5
+--R 3 8+---+ 8+---+5 +-+ 8+---+2 2 3 8+---+ +-+ \|- 1
+--R 3x \|- 1 log(- x \|- 1 \|2 - \|- 1 + x - 6x \|- 1 \|2 atan(-------)
+--R x
+--R +
+--R 8+---+5 8+---+5
+--R 3 8+---+ \|- 1 3 8+---+ \|- 1 +-+
+--R 6x \|- 1 atan(--------------- + 6x \|- 1 atan(--------------- - 8\|2
+--R +-+ 8+---+5 +-+ 8+---+5
+--R x\|2 - \|- 1 x\|2 + \|- 1
+--R /
+--R 3 +-+
+--R 24x \|2
+--R Type: Union(Expression(Integer),...)
+--E 317
+
+--S 318 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +-----------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+
+--R +-+ | +-+
+--R 2\|2 \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +---------+
+--R +-+ | +-+
+--R 2\|2 \|2\|2 + 4
+--R *
+--R atan
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R -----------------------------------------------------------------
+--R 2
+--R +
+--R +-----------+
+--R +-+ | +-+
+--R 2\|2 \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +-----------+
+--R +-+ | +-+
+--R 2\|2 \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R 8+---+ 8+---+5 +-+ 8+---+2 2
+--R - \|- 1 log(x \|- 1 \|2 - \|- 1 + x )
+--R +
+--R 8+---+ +-+ 8+---+5 8+---+ +-+ 8+---+5
+--R \|- 1 \|2 log(\|- 1 + x) - \|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+5
+--R 8+---+ 8+---+5 +-+ 8+---+2 2 8+---+ +-+ \|- 1
+--R \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) - 2\|- 1 \|2 atan(-------)
+--R x
+--R +
+--R 8+---+5 8+---+5
+--R 8+---+ \|- 1 8+---+ \|- 1
+--R 2\|- 1 atan(---------------) + 2\|- 1 atan(---------------)
+--R +-+ 8+---+5 +-+ 8+---+5
+--R x\|2 - \|- 1 x\|2 + \|- 1
+--R *
+--R +-----------+ +---------+
+--R | +-+ | +-+
+--R \|- 2\|2 + 4 \|2\|2 + 4
+--R /
+--R +-----------+ +---------+
+--R +-+ | +-+ | +-+
+--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +---------+
+--R 4 +-+ 4 | +-+ | +-+
+--R ((3x + 1)\|2 - 4x - 2)\|\|2 + 2 \|2\|2 + 4
+--R +
+--R +-----------+ +----------+
+--R 4 +-+ 4 | +-+ | +-+ 4
+--R ((3x + 1)\|2 + 4x + 2)\|- 2\|2 + 4 \|- \|2 + 2 - 8x
+--R /
+--R 8
+--R 8x + 8
+--R Type: Expression(Integer)
+--E 319
+
+)clear all
+
+--S 320 of 1369
+t0:=1/(x^6*(1+x^8))
+--R
+--R
+--R 1
+--R (1) --------
+--R 14 6
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 320
+
+--S 321 of 1369
+r0:=(-1/5)/x^5+1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/_
+ sqrt(2*(2-sqrt(2)))-1/4*atan((2*x+sqrt(2+sqrt(2)))/_
+ sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-1/8*log(1+x^2-x*_
+ sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/8*log(1+x^2+x*_
+ sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-1/4*atan((-2*x+_
+ sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+_
+ 1/4*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/_
+ sqrt(2*(2+sqrt(2)))+1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/_
+ sqrt(2*(2+sqrt(2)))-1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/_
+ sqrt(2*(2+sqrt(2)))
+--R
+--R
+--R (2)
+--R +-----------+ +--------+
+--R 5 | +-+ | +-+ 2
+--R - 5x \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R 5 | +-+ | +-+ 2
+--R 5x \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R 5 | +-+ | +-+ 2
+--R - 5x \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +-----------+ +--------+
+--R 5 | +-+ | +-+ 2
+--R 5x \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R -
+--R +---------+
+--R 5 | +-+
+--R 10x \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R +---------+
+--R 5 | +-+
+--R 10x \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R atan(-----------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +-----------+
+--R 5 | +-+
+--R 10x \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R +-----------+
+--R 5 | +-+
+--R 10x \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R +-----------+ +---------+
+--R | +-+ | +-+
+--R - 8\|- 2\|2 + 4 \|2\|2 + 4
+--R /
+--R +-----------+ +---------+
+--R 5 | +-+ | +-+
+--R 40x \|- 2\|2 + 4 \|2\|2 + 4
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 8+---+ 8+---+3 +-+ 8+---+6 2
+--R - 5x \|- 1 log(x \|- 1 \|2 + \|- 1 + x )
+--R +
+--R 5 8+---+ +-+ 8+---+3 5 8+---+ +-+ 8+---+3
+--R 5x \|- 1 \|2 log(\|- 1 + x - 5x \|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 5 8+---+ 8+---+3 +-+ 8+---+6 2
+--R 5x \|- 1 log(- x \|- 1 \|2 + \|- 1 + x )
+--R +
+--R 8+---+3 8+---+3
+--R 5 8+---+ +-+ \|- 1 5 8+---+ \|- 1
+--R 10x \|- 1 \|2 atan(------- - 10x \|- 1 atan(---------------)
+--R x +-+ 8+---+3
+--R x\|2 - \|- 1
+--R +
+--R 8+---+3
+--R 5 8+---+ \|- 1 +-+
+--R - 10x \|- 1 atan(--------------- - 8\|2
+--R +-+ 8+---+3
+--R x\|2 + \|- 1
+--R /
+--R 5 +-+
+--R 40x \|2
+--R Type: Union(Expression(Integer),...)
+--E 322
+
+--S 323 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +---------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +-----------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R +---------+
+--R +-+ | +-+
+--R 2\|2 \|2\|2 + 4
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +---------+
+--R +-+ | +-+
+--R 2\|2 \|2\|2 + 4
+--R *
+--R atan
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R -----------------------------------------------------------------
+--R 2
+--R +
+--R +-----------+
+--R +-+ | +-+
+--R 2\|2 \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +-----------+
+--R +-+ | +-+
+--R 2\|2 \|- 2\|2 + 4
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R 8+---+ 8+---+3 +-+ 8+---+6 2
+--R - \|- 1 log(x \|- 1 \|2 + \|- 1 + x )
+--R +
+--R 8+---+ +-+ 8+---+3 8+---+ +-+ 8+---+3
+--R \|- 1 \|2 log(\|- 1 + x) - \|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+3
+--R 8+---+ 8+---+3 +-+ 8+---+6 2 8+---+ +-+ \|- 1
+--R \|- 1 log(- x \|- 1 \|2 + \|- 1 + x ) + 2\|- 1 \|2 atan(-------)
+--R x
+--R +
+--R 8+---+3 8+---+3
+--R 8+---+ \|- 1 8+---+ \|- 1
+--R - 2\|- 1 atan(---------------) - 2\|- 1 atan(---------------)
+--R +-+ 8+---+3 +-+ 8+---+3
+--R x\|2 - \|- 1 x\|2 + \|- 1
+--R *
+--R +-----------+ +---------+
+--R | +-+ | +-+
+--R \|- 2\|2 + 4 \|2\|2 + 4
+--R /
+--R +-----------+ +---------+
+--R +-+ | +-+ | +-+
+--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4
+--R Type: Expression(Integer)
+--E 323
+
+--S 324 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +---------+
+--R 6 2 +-+ 6 2 | +-+ | +-+
+--R ((x + 3x )\|2 - 2x - 4x )\|\|2 + 2 \|2\|2 + 4
+--R +
+--R +-----------+ +----------+
+--R 6 2 +-+ 6 2 | +-+ | +-+ 2
+--R ((x + 3x )\|2 + 2x + 4x )\|- 2\|2 + 4 \|- \|2 + 2 - 8x
+--R /
+--R 8
+--R 8x + 8
+--R Type: Expression(Integer)
+--E 324
+
+)clear all
+
+--S 325 of 1369
+t0:=1/(x^8*(1+x^8))
+--R
+--R
+--R 1
+--R (1) --------
+--R 16 8
+--R x + x
+--R Type: Fraction(Polynomial(Integer))
+--E 325
+
+--S 326 of 1369
+r0:=(-1/7)/x^7+1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_
+ sqrt(2-sqrt(2))-1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_
+ sqrt(2-sqrt(2))+1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_
+ 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+1/8*_
+ atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_
+ 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_
+ 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_
+ 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))
+--R
+--R
+--R (2)
+--R +--------+ +--------+
+--R 7 | +-+ | +-+ 2
+--R - 7x \|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R 7 | +-+ | +-+ 2
+--R - 7x \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R 7 | +-+ | +-+ 2
+--R 7x \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R 7 | +-+ | +-+ 2
+--R 7x \|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R -
+--R +----------+
+--R 7 | +-+
+--R 14x \|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+
+--R 7 | +-+
+--R 14x \|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R atan(-----------------------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R 7 | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R 14x \|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R 7 | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R - 14x \|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R - 16
+--R /
+--R 7
+--R 112x
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 8+---+ 8+---+ +-+ 8+---+2 2 7 8+---+ +-+ 8+---+
+--R - 7x \|- 1 log(x\|- 1 \|2 + \|- 1 + x - 7x \|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 7 8+---+ +-+ 8+---+
+--R 7x \|- 1 \|2 log(- \|- 1 + x)
+--R +
+--R 8+---+
+--R 7 8+---+ 8+---+ +-+ 8+---+2 2 7 8+---+ +-+ \|- 1
+--R 7x \|- 1 log(- x\|- 1 \|2 + \|- 1 + x + 14x \|- 1 \|2 atan(------)
+--R x
+--R +
+--R 8+---+ 8+---+
+--R 7 8+---+ \|- 1 7 8+---+ \|- 1 +-+
+--R 14x \|- 1 atan(-------------- + 14x \|- 1 atan(-------------- - 8\|2
+--R +-+ 8+---+ +-+ 8+---+
+--R x\|2 - \|- 1 x\|2 + \|- 1
+--R /
+--R 7 +-+
+--R 56x \|2
+--R Type: Union(Expression(Integer),...)
+--E 327
+
+--S 328 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1)
+--R +
+--R +----------+ +----------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1)
+--R +
+--R +--------+ +--------+
+--R +-+ | +-+ | +-+ 2
+--R - \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1)
+--R +
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2
+--R atan(---------------------------------------------------------------)
+--R 2
+--R +
+--R -
+--R +----------+
+--R +-+ | +-+
+--R 2\|2 \|- \|2 + 2
+--R *
+--R atan
+--R +----------+ +--------+ +----------+
+--R +-+ | +-+ | +-+ +-+ | +-+
+--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2
+--R -----------------------------------------------------------------
+--R 2
+--R +
+--R -
+--R +--------+
+--R +-+ | +-+
+--R 2\|2 \|\|2 + 2
+--R *
+--R +----------+ +--------+
+--R +-+ | +-+ +-+ | +-+
+--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2
+--R atan(--------------------------------------------------)
+--R 2
+--R +
+--R +----------+ +--------+
+--R +--------+ +-+ | +-+ +-+ | +-+
+--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2
+--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------)
+--R 2
+--R +
+--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+
+--R - 2\|- 1 log(x\|- 1 \|2 + \|- 1 + x ) - 2\|- 1 \|2 log(\|- 1 + x)
+--R +
+--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2
+--R 2\|- 1 \|2 log(- \|- 1 + x) + 2\|- 1 log(- x\|- 1 \|2 + \|- 1 + x )
+--R +
+--R 8+---+ 8+---+
+--R 8+---+ +-+ \|- 1 8+---+ \|- 1
+--R 4\|- 1 \|2 atan(------) + 4\|- 1 atan(--------------)
+--R x +-+ 8+---+
+--R x\|2 - \|- 1
+--R +
+--R 8+---+
+--R 8+---+ \|- 1
+--R 4\|- 1 atan(--------------)
+--R +-+ 8+---+
+--R x\|2 + \|- 1
+--R /
+--R +-+
+--R 16\|2
+--R Type: Expression(Integer)
+--E 328
+
+--S 329 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 329
+
+)clear all
+
+--S 330 of 1369
+t0:=x^3*sqrt(1+x^8)
+--R
+--R
+--R +------+
+--R 3 | 8
+--R (1) x \|x + 1
+--R Type: Expression(Integer)
+--E 330
+
+--S 331 of 1369
+r0:=1/8*asinh(x^4)+1/8*x^4*sqrt(1+x^8)
+--R
+--R
+--R +------+
+--R 4 | 8 4
+--R x \|x + 1 + asinh(x )
+--R (2) -----------------------
+--R 8
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+ +------+
+--R 4 | 8 8 | 8 4 12 4 | 8
+--R (- 2x \|x + 1 + 2x + 1)log(\|x + 1 - x ) + (- 2x - x )\|x + 1
+--R +
+--R 16 8
+--R 2x + 2x
+--R /
+--R +------+
+--R 4 | 8 8
+--R 16x \|x + 1 - 16x - 8
+--R Type: Union(Expression(Integer),...)
+--E 332
+
+--S 333 of 1369
+m0:=a0-r0
+--R
+--R
+--R +------+
+--R | 8 4 4
+--R - log(\|x + 1 - x ) - asinh(x )
+--R (4) ---------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 333
+
+--S 334 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 334
+
+)clear all
+
+--S 335 of 1369
+t0:=x*sqrt(1+x^8)
+--R
+--R
+--R +------+
+--R | 8
+--R (1) x\|x + 1
+--R Type: Expression(Integer)
+--E 335
+
+--S 336 of 1369
+--r0:=-1/3*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x^2),-1)+1/6*x^2*sqrt(1+x^8)
+--E 336
+
+--S 337 of 1369
+--a0:=integrate(t0,x)
+--E 337
+
+--S 338 of 1369
+--m0:=a0-r0
+--E 338
+
+--S 339 of 1369
+--d0:=D(m0,x)
+--E 339
+
+)clear all
+
+--S 340 of 1369
+t0:=sqrt(1+x^8)/x
+--R
+--R
+--R +------+
+--R | 8
+--R \|x + 1
+--R (1) ---------
+--R x
+--R Type: Expression(Integer)
+--E 340
+
+--S 341 of 1369
+r0:=-1/4*atanh(sqrt(1+x^8))+1/4*sqrt(1+x^8)
+--R
+--R
+--R +------+ +------+
+--R | 8 | 8
+--R - atanh(\|x + 1 ) + \|x + 1
+--R (2) ------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+ +------+ +------+
+--R | 8 | 8 | 8
+--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2\|x + 1
+--R (3) ------------------------------------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 342
+
+--S 343 of 1369
+m0:=a0-r0
+--R
+--R
+--R +------+ +------+ +------+
+--R | 8 | 8 | 8
+--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 )
+--R (4) -------------------------------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 343
+
+--S 344 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 344
+
+)clear all
+
+--S 345 of 1369
+t0:=sqrt(1+x^8)/x^3
+--R
+--R
+--R +------+
+--R | 8
+--R \|x + 1
+--R (1) ---------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 345
+
+--S 346 of 1369
+--r0:=-(-1)^(1/4)*elliptic_e(asin((-1)^(1/4)*x^2),-1)+(-1)^(1/4)*_
+-- elliptic_f(asin((-1)^(1/4)*x^2),-1)-1/2*sqrt(1+x^8)/x^2
+--E 346
+
+--S 347 of 1369
+--a0:=integrate(t0,x)
+--E 347
+
+--S 348 of 1369
+--m0:=a0-r0
+--E 348
+
+--S 349 of 1369
+--d0:=D(m0,x)
+--E 349
+
+)clear all
+
+--S 350 of 1369
+t0:=x^3*sqrt(-2+x^8)
+--R
+--R
+--R +------+
+--R 3 | 8
+--R (1) x \|x - 2
+--R Type: Expression(Integer)
+--E 350
+
+--S 351 of 1369
+r0:=-1/4*atanh(x^4/sqrt(-2+x^8))+1/8*x^4*sqrt(-2+x^8)
+--R
+--R
+--R 4 +------+
+--R x 4 | 8
+--R - 2atanh(---------) + x \|x - 2
+--R +------+
+--R | 8
+--R \|x - 2
+--R (2) ---------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+ +------+ +------+
+--R 4 | 8 8 | 8 4 12 4 | 8 16
+--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x
+--R +
+--R 8
+--R - 2x
+--R /
+--R +------+
+--R 4 | 8 8
+--R 8x \|x - 2 - 8x + 8
+--R Type: Union(Expression(Integer),...)
+--E 352
+
+--S 353 of 1369
+m0:=a0-r0
+--R
+--R
+--R +------+ 4
+--R | 8 4 x
+--R log(\|x - 2 - x ) + atanh(---------)
+--R +------+
+--R | 8
+--R \|x - 2
+--R (4) --------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 353
+
+--S 354 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 354
+
+)clear all
+
+--S 355 of 1369
+t0:=x^3/sqrt(1+x^8)
+--R
+--R
+--R 3
+--R x
+--R (1) ---------
+--R +------+
+--R | 8
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 355
+
+--S 356 of 1369
+r0:=1/4*asinh(x^4)
+--R
+--R
+--R 4
+--R asinh(x )
+--R (2) ---------
+--R 4
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R | 8 4
+--R log(\|x + 1 - x )
+--R (3) - -------------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 357
+
+--S 358 of 1369
+m0:=a0-r0
+--R
+--R
+--R +------+
+--R | 8 4 4
+--R - log(\|x + 1 - x ) - asinh(x )
+--R (4) ---------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 358
+
+--S 359 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 359
+
+)clear all
+
+--S 360 of 1369
+t0:=x/sqrt(1+x^8)
+--R
+--R
+--R x
+--R (1) ---------
+--R +------+
+--R | 8
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 360
+
+--S 361 of 1369
+--r0:=-1/2*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x^2),-1)
+--E 361
+
+--S 362 of 1369
+--a0:=integrate(t0,x)
+--E 362
+
+--S 363 of 1369
+--m0:=a0-r0
+--E 363
+
+--S 364 of 1369
+--d0:=D(m0,x)
+--E 364
+
+)clear all
+
+--S 365 of 1369
+t0:=1/(x*sqrt(1+x^8))
+--R
+--R
+--R 1
+--R (1) ----------
+--R +------+
+--R | 8
+--R x\|x + 1
+--R Type: Expression(Integer)
+--E 365
+
+--S 366 of 1369
+r0:=-1/4*atanh(sqrt(1+x^8))
+--R
+--R
+--R +------+
+--R | 8
+--R atanh(\|x + 1 )
+--R (2) - ----------------
+--R 4
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+ +------+
+--R | 8 | 8
+--R - log(\|x + 1 + 1) + log(\|x + 1 - 1)
+--R (3) -----------------------------------------
+--R 8
+--R Type: Union(Expression(Integer),...)
+--E 367
+
+--S 368 of 1369
+m0:=a0-r0
+--R
+--R
+--R +------+ +------+ +------+
+--R | 8 | 8 | 8
+--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 )
+--R (4) -------------------------------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 369
+
+)clear all
+
+--S 370 of 1369
+t0:=1/(x^3*sqrt(1+x^8))
+--R
+--R
+--R 1
+--R (1) -----------
+--R +------+
+--R 3 | 8
+--R x \|x + 1
+--R Type: Expression(Integer)
+--E 370
+
+--S 371 of 1369
+--r0:=-1/2*(-1)^(1/4)*elliptic_e(asin((-1)^(1/4)*x^2),-1)+_
+-- 1/2*(-1)^(1/4)*elliptic_f(asin((-1)^(1/4)*x^2),-1)-1/2*sqrt(1+x^8)/x^2
+--E 371
+
+--S 372 of 1369
+--a0:=integrate(t0,x)
+--E 372
+
+--S 373 of 1369
+--m0:=a0-r0
+--E 373
+
+--S 374 of 1369
+--d0:=D(m0,x)
+--E 374
+
+)clear all
+
+--S 375 of 1369
+t0:=1/(1-x^10)
+--R
+--R
+--R 1
+--R (1) - -------
+--R 10
+--R x - 1
+--R Type: Fraction(Polynomial(Integer))
+--E 375
+
+--S 376 of 1369
+r0:=1/5*atanh(x)+1/20*atanh(1/2*x*(1-sqrt(5))/(1+x^2))*_
+ (1-sqrt(5))+1/20*atanh(1/2*x*(1+sqrt(5))/(1+x^2))*_
+ (1+sqrt(5))+1/20*atan(1/2*x*sqrt(10-2*sqrt(5))/(1-x^2))*_
+ sqrt(10-2*sqrt(5))+1/20*atan(1/2*x*sqrt(10+2*sqrt(5))/_
+ (1-x^2))*sqrt(10+2*sqrt(5)),1/5*atanh(x)-1/20*log(1+x^2-_
+ x*sqrt(1/2*(3-sqrt(5))))*sqrt(1/2*(3-sqrt(5)))+1/20*_
+ log(1+x^2+x*sqrt(1/2*(3-sqrt(5))))*sqrt(1/2*(3-sqrt(5)))-_
+ 1/10*atan((-2*x+sqrt(1/2*(3+sqrt(5))))*sqrt(1/10*_
+ (5+sqrt(5))))*sqrt(1/2*(5-sqrt(5)))+1/10*atan((2*x+_
+ sqrt(1/2*(3+sqrt(5))))*sqrt(1/10*(5+sqrt(5))))*_
+ sqrt(1/2*(5-sqrt(5)))-1/20*log(1+x^2-x*sqrt(1/2*(3+sqrt(5))))*_
+ sqrt(1/2*(3+sqrt(5)))+1/20*log(1+x^2+x*sqrt(1/2*(3+sqrt(5))))*_
+ sqrt(1/2*(3+sqrt(5)))-1/10*atan((-2*x+sqrt(1/2*(3-sqrt(5))))*_
+ sqrt(2/(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))+1/10*_
+ atan((2*x+sqrt(1/2*(3-sqrt(5))))*sqrt(2/(5+sqrt(5))))*_
+ sqrt(1/2*(5+sqrt(5)))
+--R
+--R
+--R (2)
+--R [
+--R +----------+
+--R +----------+ | +-+
+--R | +-+ x\|2\|5 + 10
+--R - \|2\|5 + 10 atan(--------------)
+--R 2
+--R 2x - 2
+--R +
+--R +------------+
+--R +------------+ | +-+ +-+
+--R | +-+ x\|- 2\|5 + 10 +-+ x\|5 + x
+--R - \|- 2\|5 + 10 atan(----------------) + (\|5 + 1)atanh(---------)
+--R 2 2
+--R 2x - 2 2x + 2
+--R +
+--R +-+
+--R +-+ x\|5 - x
+--R (\|5 - 1)atanh(---------) + 4atanh(x)
+--R 2
+--R 2x + 2
+--R /
+--R 20
+--R ,
+--R
+--R +--------+
+--R +--------+ | +-+ 2 +-+
+--R | +-+ x\|\|5 + 3 + (x + 1)\|2
+--R \|\|5 + 3 log(---------------------------)
+--R +-+
+--R \|2
+--R +
+--R +----------+
+--R +----------+ | +-+ 2 +-+
+--R | +-+ x\|- \|5 + 3 + (x + 1)\|2
+--R \|- \|5 + 3 log(-----------------------------)
+--R +-+
+--R \|2
+--R +
+--R +----------+
+--R +----------+ | +-+ 2 +-+
+--R | +-+ - x\|- \|5 + 3 + (x + 1)\|2
+--R - \|- \|5 + 3 log(-------------------------------)
+--R +-+
+--R \|2
+--R +
+--R +--------+
+--R +--------+ | +-+ 2 +-+
+--R | +-+ - x\|\|5 + 3 + (x + 1)\|2
+--R - \|\|5 + 3 log(-----------------------------)
+--R +-+
+--R \|2
+--R +
+--R +--------+ +--------+
+--R +----------+ | +-+ +-+ | +-+
+--R | +-+ (\|\|5 + 3 + 2x\|2 )\|\|5 + 5
+--R 2\|- \|5 + 5 atan(---------------------------------)
+--R +-+ +--+
+--R \|2 \|10
+--R +
+--R +--------+ +--------+
+--R +----------+ | +-+ +-+ | +-+
+--R | +-+ (\|\|5 + 3 - 2x\|2 )\|\|5 + 5
+--R - 2\|- \|5 + 5 atan(---------------------------------)
+--R +-+ +--+
+--R \|2 \|10
+--R +
+--R +----------+ +----------+
+--R +--------+ | +-+ +-+ | +-+
+--R | +-+ (\|- \|5 + 3 + 2x\|2 )\|- \|5 + 5
+--R 2\|\|5 + 5 atan(-------------------------------------)
+--R +-+ +--+
+--R \|2 \|10
+--R +
+--R +----------+ +----------+
+--R +--------+ | +-+ +-+ | +-+
+--R | +-+ (\|- \|5 + 3 - 2x\|2 )\|- \|5 + 5 +-+
+--R - 2\|\|5 + 5 atan(-------------------------------------) + 4\|2 atanh(x)
+--R +-+ +--+
+--R \|2 \|10
+--R /
+--R +-+
+--R 20\|2
+--R ]
+--R Type: Tuple(Expression(Integer))
+--E 376
+
+--S 377 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3
+--R +
+--R - 10%%CD1 - 10%%CD0 + 1
+--R *
+--R log
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3
+--R +
+--R - 10%%CD1 - 10%%CD0 + 2x + 1
+--R +
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3
+--R +
+--R - 10%%CE1 - 10%%CE0 - 1
+--R *
+--R log
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3
+--R +
+--R - 10%%CE1 - 10%%CE0 + 2x - 1
+--R +
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R - \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3
+--R +
+--R - 10%%CE1 - 10%%CE0 - 1
+--R *
+--R log
+--R -
+--R ROOT
+--R 2 2
+--R - 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0
+--R +
+--R - 3
+--R +
+--R - 10%%CE1 - 10%%CE0 + 2x - 1
+--R +
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R - \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3
+--R +
+--R - 10%%CD1 - 10%%CD0 + 1
+--R *
+--R log
+--R -
+--R ROOT
+--R 2 2
+--R - 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0
+--R +
+--R - 3
+--R +
+--R - 10%%CD1 - 10%%CD0 + 2x + 1
+--R +
+--R 20%%CE1 log(10%%CE1 + x) + 20%%CD1 log(10%%CD1 + x)
+--R +
+--R 20%%CE0 log(10%%CE0 + x) + 20%%CD0 log(10%%CD0 + x) + 2log(x + 1)
+--R +
+--R - 2log(x - 1)
+--R /
+--R 20
+--R Type: Union(Expression(Integer),...)
+--E 377
+
+--S 378 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3
+--R +
+--R - 10%%CD1 - 10%%CD0 + 1
+--R *
+--R log
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3
+--R +
+--R - 10%%CD1 - 10%%CD0 + 2x + 1
+--R +
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3
+--R +
+--R - 10%%CE1 - 10%%CE0 - 1
+--R *
+--R log
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3
+--R +
+--R - 10%%CE1 - 10%%CE0 + 2x - 1
+--R +
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R - \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3
+--R +
+--R - 10%%CE1 - 10%%CE0 - 1
+--R *
+--R log
+--R -
+--R ROOT
+--R 2 2
+--R - 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0
+--R +
+--R - 3
+--R +
+--R - 10%%CE1 - 10%%CE0 + 2x - 1
+--R +
+--R +--------------------------------------------------------------+
+--R | 2 2
+--R - \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3
+--R +
+--R - 10%%CD1 - 10%%CD0 + 1
+--R *
+--R log
+--R -
+--R ROOT
+--R 2 2
+--R - 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0
+--R +
+--R - 3
+--R +
+--R - 10%%CD1 - 10%%CD0 + 2x + 1
+--R +
+--R 20%%CE1 log(10%%CE1 + x) + 20%%CD1 log(10%%CD1 + x)
+--R +
+--R 20%%CE0 log(10%%CE0 + x) + 20%%CD0 log(10%%CD0 + x)
+--R +
+--R +----------+ +------------+
+--R +----------+ | +-+ +------------+ | +-+
+--R | +-+ x\|2\|5 + 10 | +-+ x\|- 2\|5 + 10
+--R \|2\|5 + 10 atan(--------------) + \|- 2\|5 + 10 atan(----------------)
+--R 2 2
+--R 2x - 2 2x - 2
+--R +
+--R +-+
+--R +-+ x\|5 + x
+--R 2log(x + 1) - 2log(x - 1) + (- \|5 - 1)atanh(---------)
+--R 2
+--R 2x + 2
+--R +
+--R +-+
+--R +-+ x\|5 - x
+--R (- \|5 + 1)atanh(---------) - 4atanh(x)
+--R 2
+--R 2x + 2
+--R /
+--R 20
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 379
+
+)clear all
+
+--S 380 of 1369
+t0:=x^4/sqrt(1-x^10)
+--R
+--R
+--R 4
+--R x
+--R (1) ------------
+--R +---------+
+--R | 10
+--R \|- x + 1
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 1369
+r0:=1/5*asin(x^5)
+--R
+--R
+--R 5
+--R asin(x )
+--R (2) --------
+--R 5
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +---------+
+--R | 10
+--R \|- x + 1 - 1
+--R 2atan(----------------)
+--R 5
+--R x
+--R (3) - -----------------------
+--R 5
+--R Type: Union(Expression(Integer),...)
+--E 382
+
+--S 383 of 1369
+m0:=a0-r0
+--R
+--R
+--R +---------+
+--R | 10
+--R \|- x + 1 - 1 5
+--R - 2atan(----------------) - asin(x )
+--R 5
+--R x
+--R (4) ------------------------------------
+--R 5
+--R Type: Expression(Integer)
+--E 383
+
+--S 384 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 384
+
+)clear all
+
+--S 385 of 1369
+t0:=x^4/sqrt(-2+x^10)
+--R
+--R
+--R 4
+--R x
+--R (1) ----------
+--R +-------+
+--R | 10
+--R \|x - 2
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 1369
+r0:=1/5*atanh(x^5/sqrt(-2+x^10))
+--R
+--R
+--R 5
+--R x
+--R atanh(----------)
+--R +-------+
+--R | 10
+--R \|x - 2
+--R (2) -----------------
+--R 5
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 10 5
+--R log(\|x - 2 - x )
+--R (3) - --------------------
+--R 5
+--R Type: Union(Expression(Integer),...)
+--E 387
+
+--S 388 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+ 5
+--R | 10 5 x
+--R - log(\|x - 2 - x ) - atanh(----------)
+--R +-------+
+--R | 10
+--R \|x - 2
+--R (4) ------------------------------------------
+--R 5
+--R Type: Expression(Integer)
+--E 388
+
+--S 389 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 389
+
+)clear all
+
+--S 390 of 1369
+t0:=x^5/(9+x^12)
+--R
+--R
+--R 5
+--R x
+--R (1) -------
+--R 12
+--R x + 9
+--R Type: Fraction(Polynomial(Integer))
+--E 390
+
+--S 391 of 1369
+r0:=1/18*atan(1/3*x^6)
+--R
+--R
+--R 6
+--R x
+--R atan(--)
+--R 3
+--R (2) --------
+--R 18
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 6
+--R x
+--R atan(--)
+--R 3
+--R (3) --------
+--R 18
+--R Type: Union(Expression(Integer),...)
+--E 392
+
+--S 393 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 393
+
+--S 394 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 394
+
+)clear all
+
+--S 395 of 1369
+t0:=x^5/(9-x^12)
+--R
+--R
+--R 5
+--R x
+--R (1) - -------
+--R 12
+--R x - 9
+--R Type: Fraction(Polynomial(Integer))
+--E 395
+
+--S 396 of 1369
+r0:=1/18*atanh(1/3*x^6)
+--R
+--R
+--R 6
+--R x
+--R atanh(--)
+--R 3
+--R (2) ---------
+--R 18
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 6
+--R log(x + 3) - log(x - 3)
+--R (3) -------------------------
+--R 36
+--R Type: Union(Expression(Integer),...)
+--E 397
+
+--S 398 of 1369
+m0:=a0-r0
+--R
+--R
+--R 6
+--R 6 6 x
+--R log(x + 3) - log(x - 3) - 2atanh(--)
+--R 3
+--R (4) --------------------------------------
+--R 36
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 399
+
+)clear all
+
+--S 400 of 1369
+t0:=x^5*sqrt(9+x^12)
+--R
+--R
+--R +-------+
+--R 5 | 12
+--R (1) x \|x + 9
+--R Type: Expression(Integer)
+--E 400
+
+--S 401 of 1369
+r0:=3/4*asinh(1/3*x^6)+1/12*x^6*sqrt(9+x^12)
+--R
+--R
+--R +-------+ 6
+--R 6 | 12 x
+--R x \|x + 9 + 9asinh(--)
+--R 3
+--R (2) -------------------------
+--R 12
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R 6 | 12 12 | 12 6
+--R (- 18x \|x + 9 + 18x + 81)log(\|x + 9 - x )
+--R +
+--R +-------+
+--R 18 6 | 12 24 12
+--R (- 2x - 9x )\|x + 9 + 2x + 18x
+--R /
+--R +-------+
+--R 6 | 12 12
+--R 24x \|x + 9 - 24x - 108
+--R Type: Union(Expression(Integer),...)
+--E 402
+
+--S 403 of 1369
+m0:=a0-r0
+--R
+--R
+--R +-------+ 6
+--R | 12 6 x
+--R - 3log(\|x + 9 - x ) - 3asinh(--)
+--R 3
+--R (4) ------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 403
+
+--S 404 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 404
+
+)clear all
+
+--S 405 of 1369
+t0:=(a+b/x)*x^6
+--R
+--R
+--R 6 5
+--R (1) a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 405
+
+--S 406 of 1369
+r0:=1/6*b*x^6+1/7*a*x^7
+--R
+--R
+--R 1 7 1 6
+--R (2) - a x + - b x
+--R 7 6
+--R Type: Polynomial(Fraction(Integer))
+--E 406
+
+--S 407 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 7 6
+--R 6a x + 7b x
+--R (3) -------------
+--R 42
+--R Type: Union(Expression(Integer),...)
+--E 407
+
+--S 408 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 408
+
+--S 409 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 409
+
+)clear all
+
+--S 410 of 1369
+t0:=(a+b/x)*x^5
+--R
+--R
+--R 5 4
+--R (1) a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 410
+
+--S 411 of 1369
+r0:=1/5*b*x^5+1/6*a*x^6
+--R
+--R
+--R 1 6 1 5
+--R (2) - a x + - b x
+--R 6 5
+--R Type: Polynomial(Fraction(Integer))
+--E 411
+
+--S 412 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 5
+--R 5a x + 6b x
+--R (3) -------------
+--R 30
+--R Type: Union(Expression(Integer),...)
+--E 412
+
+--S 413 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 413
+
+--S 414 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 414
+
+)clear all
+
+--S 415 of 1369
+t0:=(a+b/x)*x^4
+--R
+--R
+--R 4 3
+--R (1) a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 415
+
+--S 416 of 1369
+r0:=1/4*b*x^4+1/5*a*x^5
+--R
+--R
+--R 1 5 1 4
+--R (2) - a x + - b x
+--R 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 416
+
+--S 417 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4
+--R 4a x + 5b x
+--R (3) -------------
+--R 20
+--R Type: Union(Expression(Integer),...)
+--E 417
+
+--S 418 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 418
+
+--S 419 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 419
+
+)clear all
+
+--S 420 of 1369
+t0:=(a+b/x)*x^3
+--R
+--R
+--R 3 2
+--R (1) a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 420
+
+--S 421 of 1369
+r0:=1/3*b*x^3+1/4*a*x^4
+--R
+--R
+--R 1 4 1 3
+--R (2) - a x + - b x
+--R 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 421
+
+--S 422 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 3
+--R 3a x + 4b x
+--R (3) -------------
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 422
+
+--S 423 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 423
+
+--S 424 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 424
+
+)clear all
+
+--S 425 of 1369
+t0:=(a+b/x)*x^2
+--R
+--R
+--R 2
+--R (1) a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 425
+
+--S 426 of 1369
+r0:=1/2*b*x^2+1/3*a*x^3
+--R
+--R
+--R 1 3 1 2
+--R (2) - a x + - b x
+--R 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 426
+
+--S 427 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2
+--R 2a x + 3b x
+--R (3) -------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 427
+
+--S 428 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 429
+
+)clear all
+
+--S 430 of 1369
+t0:=(a+b/x)*x
+--R
+--R
+--R (1) a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 430
+
+--S 431 of 1369
+r0:=b*x+1/2*a*x^2
+--R
+--R
+--R 1 2
+--R (2) - a x + b x
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 431
+
+--S 432 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R a x + 2b x
+--R (3) -----------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 432
+
+--S 433 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 433
+
+--S 434 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 434
+
+)clear all
+
+--S 435 of 1369
+t0:=a+b/x
+--R
+--R
+--R a x + b
+--R (1) -------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 435
+
+--S 436 of 1369
+r0:=a*x+b*log(x)
+--R
+--R
+--R (2) b log(x) + a x
+--R Type: Expression(Integer)
+--E 436
+
+--S 437 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3) b log(x) + a x
+--R Type: Union(Expression(Integer),...)
+--E 437
+
+--S 438 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 438
+
+--S 439 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 439
+
+)clear all
+
+--S 440 of 1369
+t0:=(a+b/x)/x
+--R
+--R
+--R a x + b
+--R (1) -------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 440
+
+--S 441 of 1369
+r0:=-b/x+a*log(x)
+--R
+--R
+--R a x log(x) - b
+--R (2) --------------
+--R x
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R a x log(x) - b
+--R (3) --------------
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 442
+
+--S 443 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 443
+
+--S 444 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 444
+
+)clear all
+
+--S 445 of 1369
+t0:=(a+b/x)/x^2
+--R
+--R
+--R a x + b
+--R (1) -------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 445
+
+--S 446 of 1369
+r0:=-1/2*b/x^2-a/x
+--R
+--R
+--R 1
+--R - a x - - b
+--R 2
+--R (2) -----------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 446
+
+--S 447 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - 2a x - b
+--R (3) ----------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 447
+
+--S 448 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 449
+
+)clear all
+
+--S 450 of 1369
+t0:=(a+b/x)/x^3
+--R
+--R
+--R a x + b
+--R (1) -------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 450
+
+--S 451 of 1369
+r0:=-1/3*b/x^3-1/2*a/x^2
+--R
+--R
+--R 1 1
+--R - - a x - - b
+--R 2 3
+--R (2) -------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 451
+
+--S 452 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - 3a x - 2b
+--R (3) -----------
+--R 3
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 452
+
+--S 453 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 453
+
+--S 454 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 454
+
+)clear all
+
+--S 455 of 1369
+t0:=(a+b/x)/x^4
+--R
+--R
+--R a x + b
+--R (1) -------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 455
+
+--S 456 of 1369
+r0:=-1/4*b/x^4-1/3*a/x^3
+--R
+--R
+--R 1 1
+--R - - a x - - b
+--R 3 4
+--R (2) -------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 456
+
+--S 457 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - 4a x - 3b
+--R (3) -----------
+--R 4
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 457
+
+--S 458 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 458
+
+--S 459 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 459
+
+)clear all
+
+--S 460 of 1369
+t0:=(a+b/x)/x^5
+--R
+--R
+--R a x + b
+--R (1) -------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 460
+
+--S 461 of 1369
+r0:=-1/5*b/x^5-1/4*a/x^4
+--R
+--R
+--R 1 1
+--R - - a x - - b
+--R 4 5
+--R (2) -------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 461
+
+--S 462 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - 5a x - 4b
+--R (3) -----------
+--R 5
+--R 20x
+--R Type: Union(Expression(Integer),...)
+--E 462
+
+--S 463 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 464
+
+)clear all
+
+--S 465 of 1369
+t0:=(a+b/x)/x^6
+--R
+--R
+--R a x + b
+--R (1) -------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 465
+
+--S 466 of 1369
+r0:=-1/6*b/x^6-1/5*a/x^5
+--R
+--R
+--R 1 1
+--R - - a x - - b
+--R 5 6
+--R (2) -------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 466
+
+--S 467 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - 6a x - 5b
+--R (3) -----------
+--R 6
+--R 30x
+--R Type: Union(Expression(Integer),...)
+--E 467
+
+--S 468 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 468
+
+--S 469 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 469
+
+)clear all
+
+--S 470 of 1369
+t0:=(a+b/x)^2*x^6
+--R
+--R
+--R 2 6 5 2 4
+--R (1) a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 470
+
+--S 471 of 1369
+r0:=1/5*b^2*x^5+1/3*a*b*x^6+1/7*a^2*x^7
+--R
+--R
+--R 1 2 7 1 6 1 2 5
+--R (2) - a x + - a b x + - b x
+--R 7 3 5
+--R Type: Polynomial(Fraction(Integer))
+--E 471
+
+--S 472 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 7 6 2 5
+--R 15a x + 35a b x + 21b x
+--R (3) --------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 472
+
+--S 473 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 473
+
+--S 474 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 474
+
+)clear all
+
+--S 475 of 1369
+t0:=(a+b/x)^2*x^5
+--R
+--R
+--R 2 5 4 2 3
+--R (1) a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 475
+
+--S 476 of 1369
+r0:=1/4*b^2*x^4+2/5*a*b*x^5+1/6*a^2*x^6
+--R
+--R
+--R 1 2 6 2 5 1 2 4
+--R (2) - a x + - a b x + - b x
+--R 6 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 476
+
+--S 477 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 5 2 4
+--R 10a x + 24a b x + 15b x
+--R (3) --------------------------
+--R 60
+--R Type: Union(Expression(Integer),...)
+--E 477
+
+--S 478 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 478
+
+--S 479 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 479
+
+)clear all
+
+--S 480 of 1369
+t0:=(a+b/x)^2*x^4
+--R
+--R
+--R 2 4 3 2 2
+--R (1) a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 480
+
+--S 481 of 1369
+r0:=1/3*b^2*x^3+1/2*a*b*x^4+1/5*a^2*x^5
+--R
+--R
+--R 1 2 5 1 4 1 2 3
+--R (2) - a x + - a b x + - b x
+--R 5 2 3
+--R Type: Polynomial(Fraction(Integer))
+--E 481
+
+--S 482 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 5 4 2 3
+--R 6a x + 15a b x + 10b x
+--R (3) -------------------------
+--R 30
+--R Type: Union(Expression(Integer),...)
+--E 482
+
+--S 483 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 483
+
+--S 484 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 484
+
+)clear all
+
+--S 485 of 1369
+t0:=(a+b/x)^2*x^3
+--R
+--R
+--R 2 3 2 2
+--R (1) a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 485
+
+--S 486 of 1369
+r0:=1/2*b^2*x^2+2/3*a*b*x^3+1/4*a^2*x^4
+--R
+--R
+--R 1 2 4 2 3 1 2 2
+--R (2) - a x + - a b x + - b x
+--R 4 3 2
+--R Type: Polynomial(Fraction(Integer))
+--E 486
+
+--S 487 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 3 2 2
+--R 3a x + 8a b x + 6b x
+--R (3) -----------------------
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 487
+
+--S 488 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 488
+
+--S 489 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 489
+
+)clear all
+
+--S 490 of 1369
+t0:=(a+b/x)^2*x^2
+--R
+--R
+--R 2 2 2
+--R (1) a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 490
+
+--S 491 of 1369
+r0:=1/3*(a+b/x)^3*x^3/a
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (2) ----------------------------
+--R 3a
+--R Type: Fraction(Polynomial(Integer))
+--E 491
+
+--S 492 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2 2
+--R a x + 3a b x + 3b x
+--R (3) ---------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 492
+
+--S 493 of 1369
+m0:=a0-r0
+--R
+--R
+--R 3
+--R b
+--R (4) - --
+--R 3a
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 494
+
+)clear all
+
+--S 495 of 1369
+t0:=(a+b/x)^2*x
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 495
+
+--S 496 of 1369
+r0:=2*a*b*x+1/2*a^2*x^2+b^2*log(x)
+--R
+--R
+--R 2 2 2
+--R 2b log(x) + a x + 4a b x
+--R (2) -------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R 2b log(x) + a x + 4a b x
+--R (3) -------------------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 497
+
+--S 498 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 499
+
+)clear all
+
+--S 500 of 1369
+t0:=(a+b/x)^2
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 500
+
+--S 501 of 1369
+r0:=-b^2/x+a^2*x+2*a*b*log(x)
+--R
+--R
+--R 2 2 2
+--R 2a b x log(x) + a x - b
+--R (2) -------------------------
+--R x
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R 2a b x log(x) + a x - b
+--R (3) -------------------------
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 502
+
+--S 503 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 503
+
+--S 504 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 504
+
+)clear all
+
+--S 505 of 1369
+t0:=(a+b/x)^2/x
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 505
+
+--S 506 of 1369
+r0:=-1/2*b^2/x^2-2*a*b/x+a^2*log(x)
+--R
+--R
+--R 2 2 2
+--R 2a x log(x) - 4a b x - b
+--R (2) -------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 506
+
+--S 507 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R 2a x log(x) - 4a b x - b
+--R (3) -------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 507
+
+--S 508 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 508
+
+--S 509 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 509
+
+)clear all
+
+--S 510 of 1369
+t0:=(a+b/x)^2/x^2
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 510
+
+--S 511 of 1369
+r0:=-1/3*(a+b/x)^3/b
+--R
+--R
+--R 3 3 2 2 2 3
+--R - a x - 3a b x - 3a b x - b
+--R (2) ------------------------------
+--R 3
+--R 3b x
+--R Type: Fraction(Polynomial(Integer))
+--E 511
+
+--S 512 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R - 3a x - 3a b x - b
+--R (3) ---------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 512
+
+--S 513 of 1369
+m0:=a0-r0
+--R
+--R
+--R 3
+--R a
+--R (4) --
+--R 3b
+--R Type: Expression(Integer)
+--E 513
+
+--S 514 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 514
+
+)clear all
+
+--S 515 of 1369
+t0:=(a+b/x)^2/x^3
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 515
+
+--S 516 of 1369
+r0:=-1/4*b^2/x^4-2/3*a*b/x^3-1/2*a^2/x^2
+--R
+--R
+--R 1 2 2 2 1 2
+--R - - a x - - a b x - - b
+--R 2 3 4
+--R (2) -------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 516
+
+--S 517 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R - 6a x - 8a b x - 3b
+--R (3) ----------------------
+--R 4
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 517
+
+--S 518 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 518
+
+--S 519 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 519
+
+)clear all
+
+--S 520 of 1369
+t0:=(a+b/x)^2/x^4
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 520
+
+--S 521 of 1369
+r0:=-1/5*b^2/x^5-1/2*a*b/x^4-1/3*a^2/x^3
+--R
+--R
+--R 1 2 2 1 1 2
+--R - - a x - - a b x - - b
+--R 3 2 5
+--R (2) -------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 521
+
+--S 522 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R - 10a x - 15a b x - 6b
+--R (3) ------------------------
+--R 5
+--R 30x
+--R Type: Union(Expression(Integer),...)
+--E 522
+
+--S 523 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 523
+
+--S 524 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 524
+
+)clear all
+
+--S 525 of 1369
+t0:=(a+b/x)^2/x^5
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 525
+
+--S 526 of 1369
+r0:=-1/6*b^2/x^6-2/5*a*b/x^5-1/4*a^2/x^4
+--R
+--R
+--R 1 2 2 2 1 2
+--R - - a x - - a b x - - b
+--R 4 5 6
+--R (2) -------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 526
+
+--S 527 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R - 15a x - 24a b x - 10b
+--R (3) -------------------------
+--R 6
+--R 60x
+--R Type: Union(Expression(Integer),...)
+--E 527
+
+--S 528 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 528
+
+--S 529 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 529
+
+)clear all
+
+--S 530 of 1369
+t0:=(a+b/x)^2/x^6
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 530
+
+--S 531 of 1369
+r0:=-1/7*b^2/x^7-1/3*a*b/x^6-1/5*a^2/x^5
+--R
+--R
+--R 1 2 2 1 1 2
+--R - - a x - - a b x - - b
+--R 5 3 7
+--R (2) -------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 531
+
+--S 532 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R - 21a x - 35a b x - 15b
+--R (3) -------------------------
+--R 7
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 532
+
+--S 533 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 533
+
+--S 534 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 534
+
+)clear all
+
+--S 535 of 1369
+t0:=(a+b/x)^3*x^6
+--R
+--R
+--R 3 6 2 5 2 4 3 3
+--R (1) a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 535
+
+--S 536 of 1369
+r0:=1/4*b^3*x^4+3/5*a*b^2*x^5+1/2*a^2*b*x^6+1/7*a^3*x^7
+--R
+--R
+--R 1 3 7 1 2 6 3 2 5 1 3 4
+--R (2) - a x + - a b x + - a b x + - b x
+--R 7 2 5 4
+--R Type: Polynomial(Fraction(Integer))
+--E 536
+
+--S 537 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 7 2 6 2 5 3 4
+--R 20a x + 70a b x + 84a b x + 35b x
+--R (3) -------------------------------------
+--R 140
+--R Type: Union(Expression(Integer),...)
+--E 537
+
+--S 538 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 538
+
+--S 539 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 539
+
+)clear all
+
+--S 540 of 1369
+t0:=(a+b/x)^3*x^5
+--R
+--R
+--R 3 5 2 4 2 3 3 2
+--R (1) a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 540
+
+--S 541 of 1369
+r0:=1/3*b^3*x^3+3/4*a*b^2*x^4+3/5*a^2*b*x^5+1/6*a^3*x^6
+--R
+--R
+--R 1 3 6 3 2 5 3 2 4 1 3 3
+--R (2) - a x + - a b x + - a b x + - b x
+--R 6 5 4 3
+--R Type: Polynomial(Fraction(Integer))
+--E 541
+
+--S 542 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 5 2 4 3 3
+--R 10a x + 36a b x + 45a b x + 20b x
+--R (3) -------------------------------------
+--R 60
+--R Type: Union(Expression(Integer),...)
+--E 542
+
+--S 543 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 543
+
+--S 544 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 544
+
+)clear all
+
+--S 545 of 1369
+t0:=(a+b/x)^3*x^4
+--R
+--R
+--R 3 4 2 3 2 2 3
+--R (1) a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 545
+
+--S 546 of 1369
+r0:=-1/4*b*(b+a*x)^4/a^2+1/5*(b+a*x)^5/a^2
+--R
+--R
+--R 1 5 5 3 4 4 3 2 3 1 2 3 2 1 5
+--R - a x + - a b x + a b x + - a b x - -- b
+--R 5 4 2 20
+--R (2) ---------------------------------------------
+--R 2
+--R a
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 546
+
+--S 547 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 5 2 4 2 3 3 2
+--R 4a x + 15a b x + 20a b x + 10b x
+--R (3) ------------------------------------
+--R 20
+--R Type: Union(Expression(Integer),...)
+--E 547
+
+--S 548 of 1369
+m0:=a0-r0
+--R
+--R
+--R 5
+--R b
+--R (4) ----
+--R 2
+--R 20a
+--R Type: Expression(Integer)
+--E 548
+
+--S 549 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 549
+
+)clear all
+
+--S 550 of 1369
+t0:=(a+b/x)^3*x^3
+--R
+--R
+--R 3 3 2 2 2 3
+--R (1) a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 550
+
+--S 551 of 1369
+r0:=1/4*(a+b/x)^4*x^4/a
+--R
+--R
+--R 4 4 3 3 2 2 2 3 4
+--R a x + 4a b x + 6a b x + 4a b x + b
+--R (2) --------------------------------------
+--R 4a
+--R Type: Fraction(Polynomial(Integer))
+--E 551
+
+--S 552 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 4 2 3 2 2 3
+--R a x + 4a b x + 6a b x + 4b x
+--R (3) -------------------------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 552
+
+--S 553 of 1369
+m0:=a0-r0
+--R
+--R
+--R 4
+--R b
+--R (4) - --
+--R 4a
+--R Type: Expression(Integer)
+--E 553
+
+--S 554 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 554
+
+)clear all
+
+--S 555 of 1369
+t0:=(a+b/x)^3*x^2
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 555
+
+--S 556 of 1369
+r0:=3*a*b^2*x+3/2*a^2*b*x^2+1/3*a^3*x^3+b^3*log(x)
+--R
+--R
+--R 3 3 3 2 2 2
+--R 6b log(x) + 2a x + 9a b x + 18a b x
+--R (2) -------------------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3 2 2 2
+--R 6b log(x) + 2a x + 9a b x + 18a b x
+--R (3) -------------------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 557
+
+--S 558 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 558
+
+--S 559 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 559
+
+)clear all
+
+--S 560 of 1369
+t0:=(a+b/x)^3*x
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 560
+
+--S 561 of 1369
+r0:=-b^3/x+3*a^2*b*x+1/2*a^3*x^2+3*a*b^2*log(x)
+--R
+--R
+--R 2 3 3 2 2 3
+--R 6a b x log(x) + a x + 6a b x - 2b
+--R (2) ------------------------------------
+--R 2x
+--R Type: Expression(Integer)
+--E 561
+
+--S 562 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 3 2 2 3
+--R 6a b x log(x) + a x + 6a b x - 2b
+--R (3) ------------------------------------
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 562
+
+--S 563 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 564
+
+)clear all
+
+--S 565 of 1369
+t0:=(a+b/x)^3
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 565
+
+--S 566 of 1369
+r0:=-1/2*b^3/x^2-3*a*b^2/x+a^3*x+3*a^2*b*log(x)
+--R
+--R
+--R 2 2 3 3 2 3
+--R 6a b x log(x) + 2a x - 6a b x - b
+--R (2) -----------------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 566
+
+--S 567 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 3 3 2 3
+--R 6a b x log(x) + 2a x - 6a b x - b
+--R (3) -----------------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 567
+
+--S 568 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 569
+
+)clear all
+
+--S 570 of 1369
+t0:=(a+b/x)^3/x
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 570
+
+--S 571 of 1369
+r0:=-1/3*b^3/x^3-3/2*a*b^2/x^2-3*a^2*b/x+a^3*log(x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R 6a x log(x) - 18a b x - 9a b x - 2b
+--R (2) -------------------------------------
+--R 3
+--R 6x
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R 6a x log(x) - 18a b x - 9a b x - 2b
+--R (3) -------------------------------------
+--R 3
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 572
+
+--S 573 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 574
+
+)clear all
+
+--S 575 of 1369
+t0:=(a+b/x)^3/x^2
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 575
+
+--S 576 of 1369
+r0:=-1/4*(a+b/x)^4/b
+--R
+--R
+--R 4 4 3 3 2 2 2 3 4
+--R - a x - 4a b x - 6a b x - 4a b x - b
+--R (2) ----------------------------------------
+--R 4
+--R 4b x
+--R Type: Fraction(Polynomial(Integer))
+--E 576
+
+--S 577 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 4a x - 6a b x - 4a b x - b
+--R (3) -------------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 577
+
+--S 578 of 1369
+m0:=a0-r0
+--R
+--R
+--R 4
+--R a
+--R (4) --
+--R 4b
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 579
+
+)clear all
+
+--S 580 of 1369
+t0:=(a+b/x)^3/x^3
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 580
+
+--S 581 of 1369
+r0:=-1/5*b^3/x^5-3/4*a*b^2/x^4-a^2*b/x^3-1/2*a^3/x^2
+--R
+--R
+--R 1 3 3 2 2 3 2 1 3
+--R - - a x - a b x - - a b x - - b
+--R 2 4 5
+--R (2) ----------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 581
+
+--S 582 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 10a x - 20a b x - 15a b x - 4b
+--R (3) -----------------------------------
+--R 5
+--R 20x
+--R Type: Union(Expression(Integer),...)
+--E 582
+
+--S 583 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 584
+
+)clear all
+
+--S 585 of 1369
+t0:=(a+b/x)^3/x^4
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 585
+
+--S 586 of 1369
+r0:=-1/6*b^3/x^6-3/5*a*b^2/x^5-3/4*a^2*b/x^4-1/3*a^3/x^3
+--R
+--R
+--R 1 3 3 3 2 2 3 2 1 3
+--R - - a x - - a b x - - a b x - - b
+--R 3 4 5 6
+--R (2) ------------------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 586
+
+--S 587 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 20a x - 45a b x - 36a b x - 10b
+--R (3) ------------------------------------
+--R 6
+--R 60x
+--R Type: Union(Expression(Integer),...)
+--E 587
+
+--S 588 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 589
+
+)clear all
+
+--S 590 of 1369
+t0:=(a+b/x)^3/x^5
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 590
+
+--S 591 of 1369
+r0:=-1/7*b^3/x^7-1/2*a*b^2/x^6-3/5*a^2*b/x^5-1/4*a^3/x^4
+--R
+--R
+--R 1 3 3 3 2 2 1 2 1 3
+--R - - a x - - a b x - - a b x - - b
+--R 4 5 2 7
+--R (2) ------------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 591
+
+--S 592 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 35a x - 84a b x - 70a b x - 20b
+--R (3) ------------------------------------
+--R 7
+--R 140x
+--R Type: Union(Expression(Integer),...)
+--E 592
+
+--S 593 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 593
+
+--S 594 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 594
+
+)clear all
+
+--S 595 of 1369
+t0:=(a+b/x)^3/x^6
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 595
+
+--S 596 of 1369
+r0:=-1/8*b^3/x^8-3/7*a*b^2/x^7-1/2*a^2*b/x^6-1/5*a^3/x^5
+--R
+--R
+--R 1 3 3 1 2 2 3 2 1 3
+--R - - a x - - a b x - - a b x - - b
+--R 5 2 7 8
+--R (2) ------------------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 596
+
+--S 597 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 56a x - 140a b x - 120a b x - 35b
+--R (3) --------------------------------------
+--R 8
+--R 280x
+--R Type: Union(Expression(Integer),...)
+--E 597
+
+--S 598 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 598
+
+--S 599 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 599
+
+)clear all
+
+--S 600 of 1369
+t0:=x^4/(a+b/x)
+--R
+--R
+--R 5
+--R x
+--R (1) -------
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 600
+
+--S 601 of 1369
+r0:=b^4*x/a^5-1/2*b^3*x^2/a^4+1/3*b^2*x^3/a^3-1/4*b*x^4/a^2+_
+ 1/5*x^5/a-b^5*log(b+a*x)/a^6
+--R
+--R
+--R 5 5 5 4 4 3 2 3 2 3 2 4
+--R - 60b log(a x + b) + 12a x - 15a b x + 20a b x - 30a b x + 60a b x
+--R (2) ----------------------------------------------------------------------
+--R 6
+--R 60a
+--R Type: Expression(Integer)
+--E 601
+
+--S 602 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5 5 4 4 3 2 3 2 3 2 4
+--R - 60b log(a x + b) + 12a x - 15a b x + 20a b x - 30a b x + 60a b x
+--R (3) ----------------------------------------------------------------------
+--R 6
+--R 60a
+--R Type: Union(Expression(Integer),...)
+--E 602
+
+--S 603 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 603
+
+--S 604 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 604
+
+)clear all
+
+--S 605 of 1369
+t0:=x^3/(a+b/x)
+--R
+--R
+--R 4
+--R x
+--R (1) -------
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 605
+
+--S 606 of 1369
+r0:=-b^3*x/a^4+1/2*b^2*x^2/a^3-1/3*b*x^3/a^2+1/4*x^4/a+b^4*log(b+a*x)/a^5
+--R
+--R
+--R 4 4 4 3 3 2 2 2 3
+--R 12b log(a x + b) + 3a x - 4a b x + 6a b x - 12a b x
+--R (2) ------------------------------------------------------
+--R 5
+--R 12a
+--R Type: Expression(Integer)
+--E 606
+
+--S 607 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4 4 3 3 2 2 2 3
+--R 12b log(a x + b) + 3a x - 4a b x + 6a b x - 12a b x
+--R (3) ------------------------------------------------------
+--R 5
+--R 12a
+--R Type: Union(Expression(Integer),...)
+--E 607
+
+--S 608 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 609
+
+)clear all
+
+--S 610 of 1369
+t0:=x^2/(a+b/x)
+--R
+--R
+--R 3
+--R x
+--R (1) -------
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 610
+
+--S 611 of 1369
+r0:=b^2*x/a^3-1/2*b*x^2/a^2+1/3*x^3/a-b^3*log(b+a*x)/a^4
+--R
+--R
+--R 3 3 3 2 2 2
+--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x
+--R (2) --------------------------------------------
+--R 4
+--R 6a
+--R Type: Expression(Integer)
+--E 611
+
+--S 612 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3 2 2 2
+--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x
+--R (3) --------------------------------------------
+--R 4
+--R 6a
+--R Type: Union(Expression(Integer),...)
+--E 612
+
+--S 613 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 613
+
+--S 614 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 614
+
+)clear all
+
+--S 615 of 1369
+t0:=x/(a+b/x)
+--R
+--R
+--R 2
+--R x
+--R (1) -------
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 615
+
+--S 616 of 1369
+r0:=-b*x/a^2+1/2*x^2/a+b^2*log(b+a*x)/a^3
+--R
+--R
+--R 2 2 2
+--R 2b log(a x + b) + a x - 2a b x
+--R (2) -------------------------------
+--R 3
+--R 2a
+--R Type: Expression(Integer)
+--E 616
+
+--S 617 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R 2b log(a x + b) + a x - 2a b x
+--R (3) -------------------------------
+--R 3
+--R 2a
+--R Type: Union(Expression(Integer),...)
+--E 617
+
+--S 618 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 618
+
+--S 619 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 619
+
+)clear all
+
+--S 620 of 1369
+t0:=1/(a+b/x)
+--R
+--R
+--R x
+--R (1) -------
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 620
+
+--S 621 of 1369
+r0:=x/a-b*log(b+a*x)/a^2
+--R
+--R
+--R - b log(a x + b) + a x
+--R (2) ----------------------
+--R 2
+--R a
+--R Type: Expression(Integer)
+--E 621
+
+--S 622 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - b log(a x + b) + a x
+--R (3) ----------------------
+--R 2
+--R a
+--R Type: Union(Expression(Integer),...)
+--E 622
+
+--S 623 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 624
+
+)clear all
+
+--S 625 of 1369
+t0:=1/((a+b/x)*x)
+--R
+--R
+--R 1
+--R (1) -------
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 625
+
+--S 626 of 1369
+r0:=log(b+a*x)/a
+--R
+--R
+--R log(a x + b)
+--R (2) ------------
+--R a
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R log(a x + b)
+--R (3) ------------
+--R a
+--R Type: Union(Expression(Integer),...)
+--E 627
+
+--S 628 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 628
+
+--S 629 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 629
+
+)clear all
+
+--S 630 of 1369
+t0:=1/((a+b/x)*x^2)
+--R
+--R
+--R 1
+--R (1) ----------
+--R 2
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 630
+
+--S 631 of 1369
+r0:=-log(a+b/x)/b
+--R
+--R
+--R a x + b
+--R log(-------)
+--R x
+--R (2) - ------------
+--R b
+--R Type: Expression(Integer)
+--E 631
+
+--S 632 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - log(a x + b) + log(x)
+--R (3) -----------------------
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 632
+
+--S 633 of 1369
+m0:=a0-r0
+--R
+--R
+--R a x + b
+--R - log(a x + b) + log(x) + log(-------)
+--R x
+--R (4) --------------------------------------
+--R b
+--R Type: Expression(Integer)
+--E 633
+
+--S 634 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 634
+
+)clear all
+
+--S 635 of 1369
+t0:=1/((a+b/x)*x^3)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 3 2
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 635
+
+--S 636 of 1369
+r0:=(-1)/(b*x)-a*log(x)/b^2+a*log(b+a*x)/b^2
+--R
+--R
+--R a x log(a x + b) - a x log(x) - b
+--R (2) ---------------------------------
+--R 2
+--R b x
+--R Type: Expression(Integer)
+--E 636
+
+--S 637 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R a x log(a x + b) - a x log(x) - b
+--R (3) ---------------------------------
+--R 2
+--R b x
+--R Type: Union(Expression(Integer),...)
+--E 637
+
+--S 638 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 639
+
+)clear all
+
+--S 640 of 1369
+t0:=1/((a+b/x)*x^4)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 4 3
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 640
+
+--S 641 of 1369
+r0:=(-1/2)/(b*x^2)+a/(b^2*x)+a^2*log(x)/b^3-a^2*log(b+a*x)/b^3
+--R
+--R
+--R 2 2 2 2 2
+--R - 2a x log(a x + b) + 2a x log(x) + 2a b x - b
+--R (2) -----------------------------------------------
+--R 3 2
+--R 2b x
+--R Type: Expression(Integer)
+--E 641
+
+--S 642 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2 2
+--R - 2a x log(a x + b) + 2a x log(x) + 2a b x - b
+--R (3) -----------------------------------------------
+--R 3 2
+--R 2b x
+--R Type: Union(Expression(Integer),...)
+--E 642
+
+--S 643 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 643
+
+--S 644 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 644
+
+)clear all
+
+--S 645 of 1369
+t0:=1/((a+b/x)*x^5)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 5 4
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 645
+
+--S 646 of 1369
+r0:=(-1/3)/(b*x^3)+1/2*a/(b^2*x^2)-a^2/(b^3*x)-a^3*log(x)/b^4+_
+ a^3*log(b+a*x)/b^4
+--R
+--R
+--R 3 3 3 3 2 2 2 3
+--R 6a x log(a x + b) - 6a x log(x) - 6a b x + 3a b x - 2b
+--R (2) --------------------------------------------------------
+--R 4 3
+--R 6b x
+--R Type: Expression(Integer)
+--E 646
+
+--S 647 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3 3 2 2 2 3
+--R 6a x log(a x + b) - 6a x log(x) - 6a b x + 3a b x - 2b
+--R (3) --------------------------------------------------------
+--R 4 3
+--R 6b x
+--R Type: Union(Expression(Integer),...)
+--E 647
+
+--S 648 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 649
+
+)clear all
+
+--S 650 of 1369
+t0:=1/((a+b/x)*x^6)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 6 5
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 650
+
+--S 651 of 1369
+r0:=(-1/4)/(b*x^4)+1/3*a/(b^2*x^3)-1/2*a^2/(b^3*x^2)+a^3/(b^4*x)+_
+ a^4*log(x)/b^5-a^4*log(b+a*x)/b^5
+--R
+--R
+--R (2)
+--R 4 4 4 4 3 3 2 2 2 3 4
+--R - 12a x log(a x + b) + 12a x log(x) + 12a b x - 6a b x + 4a b x - 3b
+--R -----------------------------------------------------------------------
+--R 5 4
+--R 12b x
+--R Type: Expression(Integer)
+--E 651
+
+--S 652 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 4 4 3 3 2 2 2 3 4
+--R - 12a x log(a x + b) + 12a x log(x) + 12a b x - 6a b x + 4a b x - 3b
+--R -----------------------------------------------------------------------
+--R 5 4
+--R 12b x
+--R Type: Union(Expression(Integer),...)
+--E 652
+
+--S 653 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 653
+
+--S 654 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 654
+
+)clear all
+
+--S 655 of 1369
+t0:=1/((a+b/x)*x^7)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 7 6
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 655
+
+--S 656 of 1369
+r0:=(-1/5)/(b*x^5)+1/4*a/(b^2*x^4)-1/3*a^2/(b^3*x^3)+_
+ 1/2*a^3/(b^4*x^2)-a^4/(b^5*x)-a^5*log(x)/b^6+a^5*log(b+a*x)/b^6
+--R
+--R
+--R (2)
+--R 5 5 5 5 4 4 3 2 3 2 3 2
+--R 60a x log(a x + b) - 60a x log(x) - 60a b x + 30a b x - 20a b x
+--R +
+--R 4 5
+--R 15a b x - 12b
+--R /
+--R 6 5
+--R 60b x
+--R Type: Expression(Integer)
+--E 656
+
+--S 657 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 5 5 4 4 3 2 3 2 3 2
+--R 60a x log(a x + b) - 60a x log(x) - 60a b x + 30a b x - 20a b x
+--R +
+--R 4 5
+--R 15a b x - 12b
+--R /
+--R 6 5
+--R 60b x
+--R Type: Union(Expression(Integer),...)
+--E 657
+
+--S 658 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 659
+
+)clear all
+
+--S 660 of 1369
+t0:=x^5/(a+b/x)^2
+--R
+--R
+--R 7
+--R x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 660
+
+--S 661 of 1369
+r0:=-6*b^5*x/a^7+5/2*b^4*x^2/a^6-4/3*b^3*x^3/a^5+3/4*b^2*x^4/a^4-_
+ 2/5*b*x^5/a^3+1/6*x^6/a^2+b^7/(a^8*(b+a*x))+7*b^6*log(b+a*x)/a^8
+--R
+--R
+--R (2)
+--R 6 7 7 7 6 6 5 2 5 4 3 4
+--R (420a b x + 420b )log(a x + b) + 10a x - 14a b x + 21a b x - 35a b x
+--R +
+--R 3 4 3 2 5 2 6 7
+--R 70a b x - 210a b x - 360a b x + 60b
+--R /
+--R 9 8
+--R 60a x + 60a b
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 7 7 7 6 6 5 2 5 4 3 4
+--R (420a b x + 420b )log(a x + b) + 10a x - 14a b x + 21a b x - 35a b x
+--R +
+--R 3 4 3 2 5 2 6 7
+--R 70a b x - 210a b x - 360a b x + 60b
+--R /
+--R 9 8
+--R 60a x + 60a b
+--R Type: Union(Expression(Integer),...)
+--E 662
+
+--S 663 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 664
+
+)clear all
+
+--S 665 of 1369
+t0:=x^4/(a+b/x)^2
+--R
+--R
+--R 6
+--R x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 665
+
+--S 666 of 1369
+r0:=5*b^4*x/a^6-2*b^3*x^2/a^5+b^2*x^3/a^4-1/2*b*x^4/a^3+1/5*x^5/a^2-_
+ b^6/(a^7*(b+a*x))-6*b^5*log(b+a*x)/a^7
+--R
+--R
+--R (2)
+--R 5 6 6 6 5 5 4 2 4 3 3 3
+--R (- 60a b x - 60b )log(a x + b) + 2a x - 3a b x + 5a b x - 10a b x
+--R +
+--R 2 4 2 5 6
+--R 30a b x + 50a b x - 10b
+--R /
+--R 8 7
+--R 10a x + 10a b
+--R Type: Expression(Integer)
+--E 666
+
+--S 667 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 6 6 6 5 5 4 2 4 3 3 3
+--R (- 60a b x - 60b )log(a x + b) + 2a x - 3a b x + 5a b x - 10a b x
+--R +
+--R 2 4 2 5 6
+--R 30a b x + 50a b x - 10b
+--R /
+--R 8 7
+--R 10a x + 10a b
+--R Type: Union(Expression(Integer),...)
+--E 667
+
+--S 668 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 669
+
+)clear all
+
+--S 670 of 1369
+t0:=x^3/(a+b/x)^2
+--R
+--R
+--R 5
+--R x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 670
+
+--S 671 of 1369
+r0:=-4*b^3*x/a^5+3/2*b^2*x^2/a^4-2/3*b*x^3/a^3+1/4*x^4/a^2+_
+ b^5/(a^6*(b+a*x))+5*b^4*log(b+a*x)/a^6
+--R
+--R
+--R (2)
+--R 4 5 5 5 4 4 3 2 3 2 3 2
+--R (60a b x + 60b )log(a x + b) + 3a x - 5a b x + 10a b x - 30a b x
+--R +
+--R 4 5
+--R - 48a b x + 12b
+--R /
+--R 7 6
+--R 12a x + 12a b
+--R Type: Expression(Integer)
+--E 671
+
+--S 672 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 5 5 5 4 4 3 2 3 2 3 2
+--R (60a b x + 60b )log(a x + b) + 3a x - 5a b x + 10a b x - 30a b x
+--R +
+--R 4 5
+--R - 48a b x + 12b
+--R /
+--R 7 6
+--R 12a x + 12a b
+--R Type: Union(Expression(Integer),...)
+--E 672
+
+--S 673 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 674
+
+)clear all
+
+--S 675 of 1369
+t0:=x^2/(a+b/x)^2
+--R
+--R
+--R 4
+--R x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 675
+
+--S 676 of 1369
+r0:=3*b^2*x/a^4-b*x^2/a^3+1/3*x^3/a^2-b^4/(a^5*(b+a*x))-4*b^3*log(b+a*x)/a^5
+--R
+--R
+--R (2)
+--R 3 4 4 4 3 3 2 2 2 3 4
+--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b
+--R ------------------------------------------------------------------------
+--R 6 5
+--R 3a x + 3a b
+--R Type: Expression(Integer)
+--E 676
+
+--S 677 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 4 4 3 3 2 2 2 3 4
+--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b
+--R ------------------------------------------------------------------------
+--R 6 5
+--R 3a x + 3a b
+--R Type: Union(Expression(Integer),...)
+--E 677
+
+--S 678 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 679
+
+)clear all
+
+--S 680 of 1369
+t0:=x/(a+b/x)^2
+--R
+--R
+--R 3
+--R x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 680
+
+--S 681 of 1369
+r0:=-2*b*x/a^3+1/2*x^2/a^2+b^3/(a^4*(b+a*x))+3*b^2*log(b+a*x)/a^4
+--R
+--R
+--R 2 3 3 3 2 2 2 3
+--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b
+--R (2) ----------------------------------------------------------
+--R 5 4
+--R 2a x + 2a b
+--R Type: Expression(Integer)
+--E 681
+
+--S 682 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 3 3 2 2 2 3
+--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b
+--R (3) ----------------------------------------------------------
+--R 5 4
+--R 2a x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 682
+
+--S 683 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 684
+
+)clear all
+
+--S 685 of 1369
+t0:=1/(a+b/x)^2
+--R
+--R
+--R 2
+--R x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 685
+
+--S 686 of 1369
+r0:=x/a^2-b^2/(a^3*(b+a*x))-2*b*log(b+a*x)/a^3
+--R
+--R
+--R 2 2 2 2
+--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b
+--R (2) ------------------------------------------------
+--R 4 3
+--R a x + a b
+--R Type: Expression(Integer)
+--E 686
+
+--S 687 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2
+--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b
+--R (3) ------------------------------------------------
+--R 4 3
+--R a x + a b
+--R Type: Union(Expression(Integer),...)
+--E 687
+
+--S 688 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 688
+
+--S 689 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 689
+
+)clear all
+
+--S 690 of 1369
+t0:=1/((a+b/x)^2*x)
+--R
+--R
+--R x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 690
+
+--S 691 of 1369
+r0:=b/(a^2*(b+a*x))+log(b+a*x)/a^2
+--R
+--R
+--R (a x + b)log(a x + b) + b
+--R (2) -------------------------
+--R 3 2
+--R a x + a b
+--R Type: Expression(Integer)
+--E 691
+
+--S 692 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (a x + b)log(a x + b) + b
+--R (3) -------------------------
+--R 3 2
+--R a x + a b
+--R Type: Union(Expression(Integer),...)
+--E 692
+
+--S 693 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 694
+
+)clear all
+
+--S 695 of 1369
+t0:=1/((a+b/x)^2*x^2)
+--R
+--R
+--R 1
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 695
+
+--S 696 of 1369
+r0:=1/(b*(a+b/x))
+--R
+--R
+--R x
+--R (2) ----------
+--R 2
+--R a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 696
+
+--S 697 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ---------
+--R 2
+--R a x + a b
+--R Type: Union(Expression(Integer),...)
+--E 697
+
+--S 698 of 1369
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - ---
+--R a b
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 699
+
+)clear all
+
+--S 700 of 1369
+t0:=1/((a+b/x)^2*x^3)
+--R
+--R
+--R 1
+--R (1) --------------------
+--R 2 3 2 2
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 700
+
+--S 701 of 1369
+r0:=1/(b*(b+a*x))+log(x)/b^2-log(b+a*x)/b^2
+--R
+--R
+--R (- a x - b)log(a x + b) + (a x + b)log(x) + b
+--R (2) ---------------------------------------------
+--R 2 3
+--R a b x + b
+--R Type: Expression(Integer)
+--E 701
+
+--S 702 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (- a x - b)log(a x + b) + (a x + b)log(x) + b
+--R (3) ---------------------------------------------
+--R 2 3
+--R a b x + b
+--R Type: Union(Expression(Integer),...)
+--E 702
+
+--S 703 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 704
+
+)clear all
+
+--S 705 of 1369
+t0:=1/((a+b/x)^2*x^4)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 4 3 2 2
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 705
+
+--S 706 of 1369
+r0:=(-1)/(b^2*x)-a/(b^2*(b+a*x))-2*a*log(x)/b^3+2*a*log(b+a*x)/b^3
+--R
+--R
+--R 2 2 2 2 2
+--R (2a x + 2a b x)log(a x + b) + (- 2a x - 2a b x)log(x) - 2a b x - b
+--R (2) ---------------------------------------------------------------------
+--R 3 2 4
+--R a b x + b x
+--R Type: Expression(Integer)
+--E 706
+
+--S 707 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2 2
+--R (2a x + 2a b x)log(a x + b) + (- 2a x - 2a b x)log(x) - 2a b x - b
+--R (3) ---------------------------------------------------------------------
+--R 3 2 4
+--R a b x + b x
+--R Type: Union(Expression(Integer),...)
+--E 707
+
+--S 708 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 709
+
+)clear all
+
+--S 710 of 1369
+t0:=1/((a+b/x)^2*x^5)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 5 4 2 3
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 710
+
+--S 711 of 1369
+r0:=(-1/2)/(b^2*x^2)+2*a/(b^3*x)+a^2/(b^3*(b+a*x))+3*a^2*log(x)/b^4-_
+ 3*a^2*log(b+a*x)/b^4
+--R
+--R
+--R (2)
+--R 3 3 2 2 3 3 2 2 2 2
+--R (- 6a x - 6a b x )log(a x + b) + (6a x + 6a b x )log(x) + 6a b x
+--R +
+--R 2 3
+--R 3a b x - b
+--R /
+--R 4 3 5 2
+--R 2a b x + 2b x
+--R Type: Expression(Integer)
+--E 711
+
+--S 712 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 3 3 2 2 2 2
+--R (- 6a x - 6a b x )log(a x + b) + (6a x + 6a b x )log(x) + 6a b x
+--R +
+--R 2 3
+--R 3a b x - b
+--R /
+--R 4 3 5 2
+--R 2a b x + 2b x
+--R Type: Union(Expression(Integer),...)
+--E 712
+
+--S 713 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 713
+
+--S 714 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 714
+
+)clear all
+
+--S 715 of 1369
+t0:=1/((a+b/x)^2*x^6)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 6 5 2 4
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 715
+
+--S 716 of 1369
+r0:=(-1/3)/(b^2*x^3)+a/(b^3*x^2)-3*a^2/(b^4*x)-a^3/(b^4*(b+a*x))-_
+ 4*a^3*log(x)/b^5+4*a^3*log(b+a*x)/b^5
+--R
+--R
+--R (2)
+--R 4 4 3 3 4 4 3 3 3 3
+--R (12a x + 12a b x )log(a x + b) + (- 12a x - 12a b x )log(x) - 12a b x
+--R +
+--R 2 2 2 3 4
+--R - 6a b x + 2a b x - b
+--R /
+--R 5 4 6 3
+--R 3a b x + 3b x
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 3 3 4 4 3 3 3 3
+--R (12a x + 12a b x )log(a x + b) + (- 12a x - 12a b x )log(x) - 12a b x
+--R +
+--R 2 2 2 3 4
+--R - 6a b x + 2a b x - b
+--R /
+--R 5 4 6 3
+--R 3a b x + 3b x
+--R Type: Union(Expression(Integer),...)
+--E 717
+
+--S 718 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 719
+
+)clear all
+
+--S 720 of 1369
+t0:=1/((a+b/x)^2*x^7)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 7 6 2 5
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 720
+
+--S 721 of 1369
+r0:=(-1/4)/(b^2*x^4)+2/3*a/(b^3*x^3)-3/2*a^2/(b^4*x^2)+4*a^3/(b^5*x)+_
+ a^4/(b^5*(b+a*x))+5*a^4*log(x)/b^6-5*a^4*log(b+a*x)/b^6
+--R
+--R
+--R (2)
+--R 5 5 4 4 5 5 4 4 4 4
+--R (- 60a x - 60a b x )log(a x + b) + (60a x + 60a b x )log(x) + 60a b x
+--R +
+--R 3 2 3 2 3 2 4 5
+--R 30a b x - 10a b x + 5a b x - 3b
+--R /
+--R 6 5 7 4
+--R 12a b x + 12b x
+--R Type: Expression(Integer)
+--E 721
+
+--S 722 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 4 4 5 5 4 4 4 4
+--R (- 60a x - 60a b x )log(a x + b) + (60a x + 60a b x )log(x) + 60a b x
+--R +
+--R 3 2 3 2 3 2 4 5
+--R 30a b x - 10a b x + 5a b x - 3b
+--R /
+--R 6 5 7 4
+--R 12a b x + 12b x
+--R Type: Union(Expression(Integer),...)
+--E 722
+
+--S 723 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 724
+
+)clear all
+
+--S 725 of 1369
+t0:=1/((a+b/x)^2*x^8)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 8 7 2 6
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 725
+
+--S 726 of 1369
+r0:=(-1/5)/(b^2*x^5)+1/2*a/(b^3*x^4)-a^2/(b^4*x^3)+2*a^3/(b^5*x^2)-_
+ 5*a^4/(b^6*x)-a^5/(b^6*(b+a*x))-6*a^5*log(x)/b^7+6*a^5*log(b+a*x)/b^7
+--R
+--R
+--R (2)
+--R 6 6 5 5 6 6 5 5 5 5
+--R (60a x + 60a b x )log(a x + b) + (- 60a x - 60a b x )log(x) - 60a b x
+--R +
+--R 4 2 4 3 3 3 2 4 2 5 6
+--R - 30a b x + 10a b x - 5a b x + 3a b x - 2b
+--R /
+--R 7 6 8 5
+--R 10a b x + 10b x
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 6 5 5 6 6 5 5 5 5
+--R (60a x + 60a b x )log(a x + b) + (- 60a x - 60a b x )log(x) - 60a b x
+--R +
+--R 4 2 4 3 3 3 2 4 2 5 6
+--R - 30a b x + 10a b x - 5a b x + 3a b x - 2b
+--R /
+--R 7 6 8 5
+--R 10a b x + 10b x
+--R Type: Union(Expression(Integer),...)
+--E 727
+
+--S 728 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 729
+
+)clear all
+
+--S 730 of 1369
+t0:=x^4/(a+b/x)^3
+--R
+--R
+--R 7
+--R x
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 730
+
+--S 731 of 1369
+r0:=15*b^4*x/a^7-5*b^3*x^2/a^6+2*b^2*x^3/a^5-3/4*b*x^4/a^4+1/5*x^5/a^3+_
+ 1/2*b^7/(a^8*(b+a*x)^2)-7*b^6/(a^8*(b+a*x))-21*b^5*log(b+a*x)/a^8
+--R
+--R
+--R (2)
+--R 2 5 2 6 7 7 7 6 6 5 2 5
+--R (- 420a b x - 840a b x - 420b )log(a x + b) + 4a x - 7a b x + 14a b x
+--R +
+--R 4 3 4 3 4 3 2 5 2 6 7
+--R - 35a b x + 140a b x + 500a b x + 160a b x - 130b
+--R /
+--R 10 2 9 8 2
+--R 20a x + 40a b x + 20a b
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5 2 6 7 7 7 6 6 5 2 5
+--R (- 420a b x - 840a b x - 420b )log(a x + b) + 4a x - 7a b x + 14a b x
+--R +
+--R 4 3 4 3 4 3 2 5 2 6 7
+--R - 35a b x + 140a b x + 500a b x + 160a b x - 130b
+--R /
+--R 10 2 9 8 2
+--R 20a x + 40a b x + 20a b
+--R Type: Union(Expression(Integer),...)
+--E 732
+
+--S 733 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 734
+
+)clear all
+
+--S 735 of 1369
+t0:=x^3/(a+b/x)^3
+--R
+--R
+--R 6
+--R x
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 735
+
+--S 736 of 1369
+r0:=-10*b^3*x/a^6+3*b^2*x^2/a^5-b*x^3/a^4+1/4*x^4/a^3-_
+ 1/2*b^6/(a^7*(b+a*x)^2)+6*b^5/(a^7*(b+a*x))+15*b^4*log(b+a*x)/a^7
+--R
+--R
+--R (2)
+--R 2 4 2 5 6 6 6 5 5 4 2 4
+--R (60a b x + 120a b x + 60b )log(a x + b) + a x - 2a b x + 5a b x
+--R +
+--R 3 3 3 2 4 2 5 6
+--R - 20a b x - 68a b x - 16a b x + 22b
+--R /
+--R 9 2 8 7 2
+--R 4a x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 736
+
+--S 737 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 5 6 6 6 5 5 4 2 4
+--R (60a b x + 120a b x + 60b )log(a x + b) + a x - 2a b x + 5a b x
+--R +
+--R 3 3 3 2 4 2 5 6
+--R - 20a b x - 68a b x - 16a b x + 22b
+--R /
+--R 9 2 8 7 2
+--R 4a x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 737
+
+--S 738 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 739
+
+)clear all
+
+--S 740 of 1369
+t0:=x^2/(a+b/x)^3
+--R
+--R
+--R 5
+--R x
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 740
+
+--S 741 of 1369
+r0:=6*b^2*x/a^5-3/2*b*x^2/a^4+1/3*x^3/a^3+1/2*b^5/(a^6*(b+a*x)^2)-_
+ 5*b^4/(a^6*(b+a*x))-10*b^3*log(b+a*x)/a^6
+--R
+--R
+--R (2)
+--R 2 3 2 4 5 5 5 4 4 3 2 3
+--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x + 20a b x
+--R +
+--R 2 3 2 4 5
+--R 63a b x + 6a b x - 27b
+--R /
+--R 8 2 7 6 2
+--R 6a x + 12a b x + 6a b
+--R Type: Expression(Integer)
+--E 741
+
+--S 742 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 4 5 5 5 4 4 3 2 3
+--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x + 20a b x
+--R +
+--R 2 3 2 4 5
+--R 63a b x + 6a b x - 27b
+--R /
+--R 8 2 7 6 2
+--R 6a x + 12a b x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 742
+
+--S 743 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 744
+
+)clear all
+
+--S 745 of 1369
+t0:=x/(a+b/x)^3
+--R
+--R
+--R 4
+--R x
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 745
+
+--S 746 of 1369
+r0:=-3*b*x/a^4+1/2*x^2/a^3-1/2*b^4/(a^5*(b+a*x)^2)+4*b^3/(a^5*(b+a*x))+_
+ 6*b^2*log(b+a*x)/a^5
+--R
+--R
+--R (2)
+--R 2 2 2 3 4 4 4 3 3 2 2 2
+--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x
+--R +
+--R 3 4
+--R 2a b x + 7b
+--R /
+--R 7 2 6 5 2
+--R 2a x + 4a b x + 2a b
+--R Type: Expression(Integer)
+--E 746
+
+--S 747 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 4 4 4 3 3 2 2 2
+--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x
+--R +
+--R 3 4
+--R 2a b x + 7b
+--R /
+--R 7 2 6 5 2
+--R 2a x + 4a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 747
+
+--S 748 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 748
+
+--S 749 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 749
+
+)clear all
+
+--S 750 of 1369
+t0:=1/(a+b/x)^3
+--R
+--R
+--R 3
+--R x
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 750
+
+--S 751 of 1369
+r0:=x/a^3+1/2*b^3/(a^4*(b+a*x)^2)-3*b^2/(a^4*(b+a*x))-3*b*log(b+a*x)/a^4
+--R
+--R
+--R (2)
+--R 2 2 2 3 3 3 2 2 2 3
+--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b
+--R ------------------------------------------------------------------------
+--R 6 2 5 4 2
+--R 2a x + 4a b x + 2a b
+--R Type: Expression(Integer)
+--E 751
+
+--S 752 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 3 3 2 2 2 3
+--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b
+--R ------------------------------------------------------------------------
+--R 6 2 5 4 2
+--R 2a x + 4a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 752
+
+--S 753 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 753
+
+--S 754 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 754
+
+)clear all
+
+--S 755 of 1369
+t0:=1/((a+b/x)^3*x)
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 755
+
+--S 756 of 1369
+r0:=-1/2*b^2/(a^3*(b+a*x)^2)+2*b/(a^3*(b+a*x))+log(b+a*x)/a^3
+--R
+--R
+--R 2 2 2 2
+--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b
+--R (2) -------------------------------------------------
+--R 5 2 4 3 2
+--R 2a x + 4a b x + 2a b
+--R Type: Expression(Integer)
+--E 756
+
+--S 757 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2
+--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b
+--R (3) -------------------------------------------------
+--R 5 2 4 3 2
+--R 2a x + 4a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 757
+
+--S 758 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 758
+
+--S 759 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 759
+
+)clear all
+
+--S 760 of 1369
+t0:=1/((a+b/x)^3*x^2)
+--R
+--R
+--R x
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 760
+
+--S 761 of 1369
+r0:=1/2/(b*(a+b/x)^2)
+--R
+--R
+--R 2
+--R x
+--R (2) ----------------------
+--R 2 2 2 3
+--R 2a b x + 4a b x + 2b
+--R Type: Fraction(Polynomial(Integer))
+--E 761
+
+--S 762 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - 2a x - b
+--R (3) ----------------------
+--R 4 2 3 2 2
+--R 2a x + 4a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 762
+
+--S 763 of 1369
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - ----
+--R 2
+--R 2a b
+--R Type: Expression(Integer)
+--E 763
+
+--S 764 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 764
+
+)clear all
+
+--S 765 of 1369
+t0:=1/((a+b/x)^3*x^3)
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 765
+
+--S 766 of 1369
+r0:=(-1/2)/(a*(a+b/x)^2*x^2)
+--R
+--R
+--R 1
+--R (2) - ----------------------
+--R 3 2 2 2
+--R 2a x + 4a b x + 2a b
+--R Type: Fraction(Polynomial(Integer))
+--E 766
+
+--S 767 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ----------------------
+--R 3 2 2 2
+--R 2a x + 4a b x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 767
+
+--S 768 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 768
+
+--S 769 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 769
+
+)clear all
+
+--S 770 of 1369
+t0:=1/((a+b/x)^3*x^4)
+--R
+--R
+--R 1
+--R (1) ------------------------------
+--R 3 4 2 3 2 2 3
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 770
+
+--S 771 of 1369
+r0:=1/2/(b*(b+a*x)^2)+1/(b^2*(b+a*x))+log(x)/b^3-log(b+a*x)/b^3
+--R
+--R
+--R (2)
+--R 2 2 2 2 2 2
+--R (- 2a x - 4a b x - 2b )log(a x + b) + (2a x + 4a b x + 2b )log(x)
+--R +
+--R 2
+--R 2a b x + 3b
+--R /
+--R 2 3 2 4 5
+--R 2a b x + 4a b x + 2b
+--R Type: Expression(Integer)
+--E 771
+
+--S 772 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 2 2
+--R (- 2a x - 4a b x - 2b )log(a x + b) + (2a x + 4a b x + 2b )log(x)
+--R +
+--R 2
+--R 2a b x + 3b
+--R /
+--R 2 3 2 4 5
+--R 2a b x + 4a b x + 2b
+--R Type: Union(Expression(Integer),...)
+--E 772
+
+--S 773 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 773
+
+--S 774 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 774
+
+)clear all
+
+--S 775 of 1369
+t0:=1/((a+b/x)^3*x^5)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 5 2 4 2 3 3 2
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 775
+
+--S 776 of 1369
+r0:=(-1)/(b^3*x)-1/2*a/(b^2*(b+a*x)^2)-2*a/(b^3*(b+a*x))-3*a*log(x)/b^4+_
+ 3*a*log(b+a*x)/b^4
+--R
+--R
+--R (2)
+--R 3 3 2 2 2
+--R (6a x + 12a b x + 6a b x)log(a x + b)
+--R +
+--R 3 3 2 2 2 2 2 2 3
+--R (- 6a x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2b
+--R /
+--R 2 4 3 5 2 6
+--R 2a b x + 4a b x + 2b x
+--R Type: Expression(Integer)
+--E 776
+
+--S 777 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2
+--R (6a x + 12a b x + 6a b x)log(a x + b)
+--R +
+--R 3 3 2 2 2 2 2 2 3
+--R (- 6a x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2b
+--R /
+--R 2 4 3 5 2 6
+--R 2a b x + 4a b x + 2b x
+--R Type: Union(Expression(Integer),...)
+--E 777
+
+--S 778 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 778
+
+--S 779 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 779
+
+)clear all
+
+--S 780 of 1369
+t0:=1/((a+b/x)^3*x^6)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 6 2 5 2 4 3 3
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 780
+
+--S 781 of 1369
+r0:=(-1/2)/(b^3*x^2)+3*a/(b^4*x)+1/2*a^2/(b^3*(b+a*x)^2)+_
+ 3*a^2/(b^4*(b+a*x))+6*a^2*log(x)/b^5-6*a^2*log(b+a*x)/b^5
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2
+--R (- 12a x - 24a b x - 12a b x )log(a x + b)
+--R +
+--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4
+--R (12a x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - b
+--R /
+--R 2 5 4 6 3 7 2
+--R 2a b x + 4a b x + 2b x
+--R Type: Expression(Integer)
+--E 781
+
+--S 782 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 3 3 2 2 2
+--R (- 12a x - 24a b x - 12a b x )log(a x + b)
+--R +
+--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4
+--R (12a x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - b
+--R /
+--R 2 5 4 6 3 7 2
+--R 2a b x + 4a b x + 2b x
+--R Type: Union(Expression(Integer),...)
+--E 782
+
+--S 783 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 783
+
+--S 784 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 784
+
+)clear all
+
+--S 785 of 1369
+t0:=1/((a+b/x)^3*x^7)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 7 2 6 2 5 3 4
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 785
+
+--S 786 of 1369
+r0:=(-1/3)/(b^3*x^3)+3/2*a/(b^4*x^2)-6*a^2/(b^5*x)-_
+ 1/2*a^3/(b^4*(b+a*x)^2)-4*a^3/(b^5*(b+a*x))-10*a^3*log(x)/b^6+_
+ 10*a^3*log(b+a*x)/b^6
+--R
+--R
+--R (2)
+--R 5 5 4 4 3 2 3
+--R (60a x + 120a b x + 60a b x )log(a x + b)
+--R +
+--R 5 5 4 4 3 2 3 4 4 3 2 3 2 3 2
+--R (- 60a x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x
+--R +
+--R 4 5
+--R 5a b x - 2b
+--R /
+--R 2 6 5 7 4 8 3
+--R 6a b x + 12a b x + 6b x
+--R Type: Expression(Integer)
+--E 786
+
+--S 787 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 4 4 3 2 3
+--R (60a x + 120a b x + 60a b x )log(a x + b)
+--R +
+--R 5 5 4 4 3 2 3 4 4 3 2 3 2 3 2
+--R (- 60a x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x
+--R +
+--R 4 5
+--R 5a b x - 2b
+--R /
+--R 2 6 5 7 4 8 3
+--R 6a b x + 12a b x + 6b x
+--R Type: Union(Expression(Integer),...)
+--E 787
+
+--S 788 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 788
+
+--S 789 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 789
+
+)clear all
+
+--S 790 of 1369
+t0:=1/((a+b/x)^3*x^8)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 8 2 7 2 6 3 5
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 790
+
+--S 791 of 1369
+r0:=(-1/4)/(b^3*x^4)+a/(b^4*x^3)-3*a^2/(b^5*x^2)+10*a^3/(b^6*x)+_
+ 1/2*a^4/(b^5*(b+a*x)^2)+5*a^4/(b^6*(b+a*x))+15*a^4*log(x)/b^7-_
+ 15*a^4*log(b+a*x)/b^7
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 4
+--R (- 60a x - 120a b x - 60a b x )log(a x + b)
+--R +
+--R 6 6 5 5 4 2 4 5 5 4 2 4 3 3 3
+--R (60a x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x
+--R +
+--R 2 4 2 5 6
+--R - 5a b x + 2a b x - b
+--R /
+--R 2 7 6 8 5 9 4
+--R 4a b x + 8a b x + 4b x
+--R Type: Expression(Integer)
+--E 791
+
+--S 792 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 6 5 5 4 2 4
+--R (- 60a x - 120a b x - 60a b x )log(a x + b)
+--R +
+--R 6 6 5 5 4 2 4 5 5 4 2 4 3 3 3
+--R (60a x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x
+--R +
+--R 2 4 2 5 6
+--R - 5a b x + 2a b x - b
+--R /
+--R 2 7 6 8 5 9 4
+--R 4a b x + 8a b x + 4b x
+--R Type: Union(Expression(Integer),...)
+--E 792
+
+--S 793 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 793
+
+--S 794 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 794
+
+)clear all
+
+--S 795 of 1369
+t0:=1/((a+b/x)^3*x^9)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 9 2 8 2 7 3 6
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 795
+
+--S 796 of 1369
+r0:=(-1/5)/(b^3*x^5)+3/4*a/(b^4*x^4)-2*a^2/(b^5*x^3)+5*a^3/(b^6*x^2)-_
+ 15*a^4/(b^7*x)-1/2*a^5/(b^6*(b+a*x)^2)-6*a^5/(b^7*(b+a*x))-_
+ 21*a^5*log(x)/b^8+21*a^5*log(b+a*x)/b^8
+--R
+--R
+--R (2)
+--R 7 7 6 6 5 2 5
+--R (420a x + 840a b x + 420a b x )log(a x + b)
+--R +
+--R 7 7 6 6 5 2 5 6 6 5 2 5
+--R (- 420a x - 840a b x - 420a b x )log(x) - 420a b x - 630a b x
+--R +
+--R 4 3 4 3 4 3 2 5 2 6 7
+--R - 140a b x + 35a b x - 14a b x + 7a b x - 4b
+--R /
+--R 2 8 7 9 6 10 5
+--R 20a b x + 40a b x + 20b x
+--R Type: Expression(Integer)
+--E 796
+
+--S 797 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 7 6 6 5 2 5
+--R (420a x + 840a b x + 420a b x )log(a x + b)
+--R +
+--R 7 7 6 6 5 2 5 6 6 5 2 5
+--R (- 420a x - 840a b x - 420a b x )log(x) - 420a b x - 630a b x
+--R +
+--R 4 3 4 3 4 3 2 5 2 6 7
+--R - 140a b x + 35a b x - 14a b x + 7a b x - 4b
+--R /
+--R 2 8 7 9 6 10 5
+--R 20a b x + 40a b x + 20b x
+--R Type: Union(Expression(Integer),...)
+--E 797
+
+--S 798 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 798
+
+--S 799 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 799
+
+)clear all
+
+--S 800 of 1369
+t0:=x^3*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R 3 |a x + b
+--R (1) x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 800
+
+--S 801 of 1369
+r0:=-5/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)+5/64*b^3*x*_
+ sqrt(a+b/x)/a^3-5/96*b^2*x^2*sqrt(a+b/x)/a^2+1/24*b*x^3*_
+ sqrt(a+b/x)/a+1/4*x^4*sqrt(a+b/x)
+--R
+--R
+--R (2)
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 4 \| x 3 4 2 3 2 2 3 +-+ |a x + b
+--R - 15b atanh(----------) + (48a x + 8a b x - 10a b x + 15b x)\|a |-------
+--R +-+ \| x
+--R \|a
+--R -----------------------------------------------------------------------------
+--R 3 +-+
+--R 192a \|a
+--R Type: Expression(Integer)
+--E 801
+
+--S 802 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 4 |a x + b +-+
+--R 15b log(- 2a x |------- + (2a x + b)\|a )
+--R \| x
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +-+ |a x + b
+--R (96a x + 16a b x - 20a b x + 30b x)\|a |-------
+--R \| x
+--R /
+--R 3 +-+
+--R 384a \|a
+--R ,
+--R
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |-------
+--R 4 \| x
+--R - 15b atan(----------------)
+--R a
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +---+ |a x + b
+--R (48a x + 8a b x - 10a b x + 15b x)\|- a |-------
+--R \| x
+--R /
+--R 3 +---+
+--R 192a \|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 802
+
+--S 803 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 4 |a x + b +-+ 4 \| x
+--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) -----------------------------------------------------------------
+--R 3 +-+
+--R 128a \|a
+--R Type: Expression(Integer)
+--E 803
+
+--S 804 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 804
+
+--S 805 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 4 +---+ \| x 4 +-+ \| x
+--R 5b \|- a atanh(----------) - 5b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------------
+--R 3 +---+ +-+
+--R 64a \|- a \|a
+--R Type: Expression(Integer)
+--E 805
+
+--S 806 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 806
+
+)clear all
+
+--S 807 of 1369
+t0:=x^2*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R 2 |a x + b
+--R (1) x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 807
+
+--S 808 of 1369
+r0:=1/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-1/8*b^2*x*_
+ sqrt(a+b/x)/a^2+1/12*b*x^2*sqrt(a+b/x)/a+1/3*x^3*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 3 \| x 2 3 2 2 +-+ |a x + b
+--R 3b atanh(----------) + (8a x + 2a b x - 3b x)\|a |-------
+--R +-+ \| x
+--R \|a
+--R (2) -------------------------------------------------------------
+--R 2 +-+
+--R 24a \|a
+--R Type: Expression(Integer)
+--E 808
+
+--S 809 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 3 |a x + b +-+
+--R 3b log(2a x |------- + (2a x + b)\|a )
+--R \| x
+--R +
+--R +-------+
+--R 2 3 2 2 +-+ |a x + b
+--R (16a x + 4a b x - 6b x)\|a |-------
+--R \| x
+--R /
+--R 2 +-+
+--R 48a \|a
+--R ,
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |------- +-------+
+--R 3 \| x 2 3 2 2 +---+ |a x + b
+--R 3b atan(----------------) + (8a x + 2a b x - 3b x)\|- a |-------
+--R a \| x
+--R --------------------------------------------------------------------]
+--R 2 +---+
+--R 24a \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 809
+
+--S 810 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 3 |a x + b +-+ 3 \| x
+--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) -------------------------------------------------------------
+--R 2 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 810
+
+--S 811 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 811
+
+--S 812 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 3 +---+ \| x 3 +-+ \| x
+--R - b \|- a atanh(----------) + b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------------
+--R 2 +---+ +-+
+--R 8a \|- a \|a
+--R Type: Expression(Integer)
+--E 812
+
+--S 813 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 813
+
+)clear all
+
+--S 814 of 1369
+t0:=x*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (1) x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 814
+
+--S 815 of 1369
+r0:=-1/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+1/4*b*x*sqrt(a+b/x)/a+_
+ 1/2*x^2*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 2 \| x 2 +-+ |a x + b
+--R - b atanh(----------) + (2a x + b x)\|a |-------
+--R +-+ \| x
+--R \|a
+--R (2) ---------------------------------------------------
+--R +-+
+--R 4a\|a
+--R Type: Expression(Integer)
+--E 815
+
+--S 816 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R 2 |a x + b +-+ 2 +-+ |a x + b
+--R b log(- 2a x |------- + (2a x + b)\|a ) + (4a x + 2b x)\|a |-------
+--R \| x \| x
+--R [-----------------------------------------------------------------------,
+--R +-+
+--R 8a\|a
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |------- +-------+
+--R 2 \| x 2 +---+ |a x + b
+--R - b atan(----------------) + (2a x + b x)\|- a |-------
+--R a \| x
+--R ----------------------------------------------------------]
+--R +---+
+--R 4a\|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 816
+
+--S 817 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 |a x + b +-+ 2 \| x
+--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------------
+--R +-+
+--R 8a\|a
+--R Type: Expression(Integer)
+--E 817
+
+--S 818 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 818
+
+--S 819 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 2 +---+ \| x 2 +-+ \| x
+--R b \|- a atanh(----------) - b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R 4a\|- a \|a
+--R Type: Expression(Integer)
+--E 819
+
+--S 820 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 820
+
+)clear all
+
+--S 821 of 1369
+t0:=sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (1) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 821
+
+--S 822 of 1369
+r0:=b*atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)+x*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R \| x +-+ |a x + b
+--R b atanh(----------) + x\|a |-------
+--R +-+ \| x
+--R \|a
+--R (2) -------------------------------------
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R |a x + b +-+ +-+ |a x + b
+--R b log(2a x |------- + (2a x + b)\|a ) + 2x\|a |-------
+--R \| x \| x
+--R [---------------------------------------------------------,
+--R +-+
+--R 2\|a
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |------- +-------+
+--R \| x +---+ |a x + b
+--R b atan(----------------) + x\|- a |-------
+--R a \| x
+--R --------------------------------------------]
+--R +---+
+--R \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 823
+
+--S 824 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b +-+ \| x
+--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) -------------------------------------------------------------
+--R +-+
+--R 2\|a
+--R Type: Expression(Integer)
+--E 824
+
+--S 825 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 825
+
+--S 826 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R +---+ \| x +-+ \| x
+--R - b\|- a atanh(----------) + b\|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R \|- a \|a
+--R Type: Expression(Integer)
+--E 826
+
+--S 827 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 827
+
+)clear all
+
+--S 828 of 1369
+t0:=sqrt(a+b/x)/x
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R x
+--R Type: Expression(Integer)
+--E 828
+
+--S 829 of 1369
+r0:=2*atanh(sqrt(a+b/x)/sqrt(a))*sqrt(a)-2*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R +-+ \| x |a x + b
+--R (2) 2\|a atanh(----------) - 2 |-------
+--R +-+ \| x
+--R \|a
+--R Type: Expression(Integer)
+--E 829
+
+--S 830 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R +-+ +-+ |a x + b |a x + b
+--R [\|a log(2x\|a |------- + 2a x + b) - 2 |-------,
+--R \| x \| x
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R +---+ \| x |a x + b
+--R 2\|- a atan(----------) - 2 |-------]
+--R +---+ \| x
+--R \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 830
+
+--S 831 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R +-+ +-+ |a x + b +-+ \| x
+--R (4) \|a log(2x\|a |------- + 2a x + b) - 2\|a atanh(----------)
+--R \| x +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 831
+
+--S 832 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 832
+
+--S 833 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b |a x + b
+--R |------- |-------
+--R +-+ \| x +---+ \| x
+--R (6) - 2\|a atanh(----------) + 2\|- a atan(----------)
+--R +-+ +---+
+--R \|a \|- a
+--R Type: Expression(Integer)
+--E 833
+
+--S 834 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 834
+
+)clear all
+
+--S 835 of 1369
+t0:=sqrt(a+b/x)/x^2
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 835
+
+--S 836 of 1369
+r0:=-2/3*(a+b/x)^(3/2)/b
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (- 2a x - 2b) |-------
+--R \| x
+--R (2) -----------------------
+--R 3b x
+--R Type: Expression(Integer)
+--E 836
+
+--S 837 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (- 2a x - 2b) |-------
+--R \| x
+--R (3) -----------------------
+--R 3b x
+--R Type: Union(Expression(Integer),...)
+--E 837
+
+--S 838 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 838
+
+--S 839 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 839
+
+)clear all
+
+--S 840 of 1369
+t0:=sqrt(a+b/x)/x^3
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 840
+
+--S 841 of 1369
+r0:=2/3*a*(a+b/x)^(3/2)/b^2-2/5*(a+b/x)^(5/2)/b^2
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (4a x - 2a b x - 6b ) |-------
+--R \| x
+--R (2) --------------------------------
+--R 2 2
+--R 15b x
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (4a x - 2a b x - 6b ) |-------
+--R \| x
+--R (3) --------------------------------
+--R 2 2
+--R 15b x
+--R Type: Union(Expression(Integer),...)
+--E 842
+
+--S 843 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 843
+
+--S 844 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 844
+
+)clear all
+
+--S 845 of 1369
+t0:=sqrt(a+b/x)/x^4
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 845
+
+--S 846 of 1369
+r0:=-2/3*a^2*(a+b/x)^(3/2)/b^3+4/5*a*(a+b/x)^(5/2)/b^3-2/7*(a+b/x)^(7/2)/b^3
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 30b ) |-------
+--R \| x
+--R (2) ----------------------------------------------
+--R 3 3
+--R 105b x
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 30b ) |-------
+--R \| x
+--R (3) ----------------------------------------------
+--R 3 3
+--R 105b x
+--R Type: Union(Expression(Integer),...)
+--E 847
+
+--S 848 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 848
+
+--S 849 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 849
+
+)clear all
+
+--S 850 of 1369
+t0:=sqrt(a+b/x)/x^5
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 850
+
+--S 851 of 1369
+r0:=2/3*a^3*(a+b/x)^(3/2)/b^4-6/5*a^2*(a+b/x)^(5/2)/b^4+6/7*_
+ a*(a+b/x)^(7/2)/b^4-2/9*(a+b/x)^(9/2)/b^4
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b
+--R (32a x - 16a b x + 12a b x - 10a b x - 70b ) |-------
+--R \| x
+--R (2) ---------------------------------------------------------
+--R 4 4
+--R 315b x
+--R Type: Expression(Integer)
+--E 851
+
+--S 852 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b
+--R (32a x - 16a b x + 12a b x - 10a b x - 70b ) |-------
+--R \| x
+--R (3) ---------------------------------------------------------
+--R 4 4
+--R 315b x
+--R Type: Union(Expression(Integer),...)
+--E 852
+
+--S 853 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 853
+
+--S 854 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 854
+
+)clear all
+
+--S 855 of 1369
+t0:=sqrt(a+b/x)/x^6
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 855
+
+--S 856 of 1369
+r0:=-2/3*a^4*(a+b/x)^(3/2)/b^5+8/5*a^3*(a+b/x)^(5/2)/b^5-_
+ 12/7*a^2*(a+b/x)^(7/2)/b^5+8/9*a*(a+b/x)^(9/2)/b^5-2/11*_
+ (a+b/x)^(11/2)/b^5
+--R
+--R
+--R (2)
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b
+--R (- 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 630b ) |-------
+--R \| x
+--R -------------------------------------------------------------------------
+--R 5 5
+--R 3465b x
+--R Type: Expression(Integer)
+--E 856
+
+--S 857 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b
+--R (- 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 630b ) |-------
+--R \| x
+--R -------------------------------------------------------------------------
+--R 5 5
+--R 3465b x
+--R Type: Union(Expression(Integer),...)
+--E 857
+
+--S 858 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 858
+
+--S 859 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 859
+
+)clear all
+
+--S 860 of 1369
+t0:=(a+b/x)^(3/2)*x^3
+--R
+--R
+--R +-------+
+--R 3 2 |a x + b
+--R (1) (a x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 860
+
+--S 861 of 1369
+r0:=1/4*(a+b/x)^(3/2)*x^4+3/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-_
+ 3/64*b^3*x*sqrt(a+b/x)/a^2+1/32*b^2*x^2*sqrt(a+b/x)/a+_
+ 1/8*b*x^3*sqrt(a+b/x)
+--R
+--R
+--R (2)
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 4 \| x 3 4 2 3 2 2 3 +-+ |a x + b
+--R 3b atanh(----------) + (16a x + 24a b x + 2a b x - 3b x)\|a |-------
+--R +-+ \| x
+--R \|a
+--R -------------------------------------------------------------------------
+--R 2 +-+
+--R 64a \|a
+--R Type: Expression(Integer)
+--E 861
+
+--S 862 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 4 |a x + b +-+
+--R 3b log(2a x |------- + (2a x + b)\|a )
+--R \| x
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +-+ |a x + b
+--R (32a x + 48a b x + 4a b x - 6b x)\|a |-------
+--R \| x
+--R /
+--R 2 +-+
+--R 128a \|a
+--R ,
+--R
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |-------
+--R 4 \| x
+--R 3b atan(----------------)
+--R a
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +---+ |a x + b
+--R (16a x + 24a b x + 2a b x - 3b x)\|- a |-------
+--R \| x
+--R /
+--R 2 +---+
+--R 64a \|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 862
+
+--S 863 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 4 |a x + b +-+ 4 \| x
+--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) --------------------------------------------------------------
+--R 2 +-+
+--R 128a \|a
+--R Type: Expression(Integer)
+--E 863
+
+--S 864 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 864
+
+--S 865 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 4 +---+ \| x 4 +-+ \| x
+--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R 2 +---+ +-+
+--R 64a \|- a \|a
+--R Type: Expression(Integer)
+--E 865
+
+--S 866 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 866
+
+)clear all
+
+--S 867 of 1369
+t0:=(a+b/x)^(3/2)*x^2
+--R
+--R
+--R +-------+
+--R 2 |a x + b
+--R (1) (a x + b x) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 867
+
+--S 868 of 1369
+r0:=1/3*(a+b/x)^(3/2)*x^3-1/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+_
+ 1/8*b^2*x*sqrt(a+b/x)/a+1/4*b*x^2*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 3 \| x 2 3 2 2 +-+ |a x + b
+--R - 3b atanh(----------) + (8a x + 14a b x + 3b x)\|a |-------
+--R +-+ \| x
+--R \|a
+--R (2) ----------------------------------------------------------------
+--R +-+
+--R 24a\|a
+--R Type: Expression(Integer)
+--E 868
+
+--S 869 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 3 |a x + b +-+
+--R 3b log(- 2a x |------- + (2a x + b)\|a )
+--R \| x
+--R +
+--R +-------+
+--R 2 3 2 2 +-+ |a x + b
+--R (16a x + 28a b x + 6b x)\|a |-------
+--R \| x
+--R /
+--R +-+
+--R 48a\|a
+--R ,
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |------- +-------+
+--R 3 \| x 2 3 2 2 +---+ |a x + b
+--R - 3b atan(----------------) + (8a x + 14a b x + 3b x)\|- a |-------
+--R a \| x
+--R -----------------------------------------------------------------------]
+--R +---+
+--R 24a\|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 869
+
+--S 870 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 3 |a x + b +-+ 3 \| x
+--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------------
+--R +-+
+--R 16a\|a
+--R Type: Expression(Integer)
+--E 870
+
+--S 871 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 3 +---+ \| x 3 +-+ \| x
+--R b \|- a atanh(----------) - b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R 8a\|- a \|a
+--R Type: Expression(Integer)
+--E 872
+
+--S 873 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 873
+
+)clear all
+
+--S 874 of 1369
+t0:=(a+b/x)^(3/2)*x
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (1) (a x + b) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 1369
+r0:=1/2*(a+b/x)^(3/2)*x^2+3/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)+_
+ 3/4*b*x*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 2 \| x 2 +-+ |a x + b
+--R 3b atanh(----------) + (2a x + 5b x)\|a |-------
+--R +-+ \| x
+--R \|a
+--R (2) ---------------------------------------------------
+--R +-+
+--R 4\|a
+--R Type: Expression(Integer)
+--E 875
+
+--S 876 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R 2 |a x + b +-+ 2 +-+ |a x + b
+--R 3b log(2a x |------- + (2a x + b)\|a ) + (4a x + 10b x)\|a |-------
+--R \| x \| x
+--R [-----------------------------------------------------------------------,
+--R +-+
+--R 8\|a
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |------- +-------+
+--R 2 \| x 2 +---+ |a x + b
+--R 3b atan(----------------) + (2a x + 5b x)\|- a |-------
+--R a \| x
+--R ----------------------------------------------------------]
+--R +---+
+--R 4\|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 876
+
+--S 877 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 |a x + b +-+ 2 \| x
+--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) --------------------------------------------------------------
+--R +-+
+--R 8\|a
+--R Type: Expression(Integer)
+--E 877
+
+--S 878 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 878
+
+--S 879 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 2 +---+ \| x 2 +-+ \| x
+--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R +---+ +-+
+--R 4\|- a \|a
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 880
+
+)clear all
+
+--S 881 of 1369
+t0:=(a+b/x)^(3/2)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R x
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1369
+r0:=(a+b/x)^(3/2)*x+3*b*atanh(sqrt(a+b/x)/sqrt(a))*sqrt(a)-3*b*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R +-+ \| x |a x + b
+--R (2) 3b\|a atanh(----------) + (a x - 2b) |-------
+--R +-+ \| x
+--R \|a
+--R Type: Expression(Integer)
+--E 882
+
+--S 883 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R +-+ +-+ |a x + b |a x + b
+--R 3b\|a log(2x\|a |------- + 2a x + b) + (2a x - 4b) |-------
+--R \| x \| x
+--R [--------------------------------------------------------------,
+--R 2
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R +---+ \| x |a x + b
+--R 3b\|- a atan(----------) + (a x - 2b) |------- ]
+--R +---+ \| x
+--R \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 883
+
+--S 884 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R +-+ +-+ |a x + b +-+ \| x
+--R 3b\|a log(2x\|a |------- + 2a x + b) - 6b\|a atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ----------------------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 884
+
+--S 885 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 885
+
+--S 886 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b |a x + b
+--R |------- |-------
+--R +-+ \| x +---+ \| x
+--R (6) - 3b\|a atanh(----------) + 3b\|- a atan(----------)
+--R +-+ +---+
+--R \|a \|- a
+--R Type: Expression(Integer)
+--E 886
+
+--S 887 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 887
+
+)clear all
+
+--S 888 of 1369
+t0:=(a+b/x)^(3/2)/x
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 888
+
+--S 889 of 1369
+r0:=-2/3*(a+b/x)^(3/2)+2*a^(3/2)*atanh(sqrt(a+b/x)/sqrt(a))-2*a*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R +-+ \| x |a x + b
+--R 6a x\|a atanh(----------) + (- 8a x - 2b) |-------
+--R +-+ \| x
+--R \|a
+--R (2) ---------------------------------------------------
+--R 3x
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R +-+ +-+ |a x + b |a x + b
+--R 3a x\|a log(2x\|a |------- + 2a x + b) + (- 8a x - 2b) |-------
+--R \| x \| x
+--R [------------------------------------------------------------------,
+--R 3x
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R +---+ \| x |a x + b
+--R 6a x\|- a atan(----------) + (- 8a x - 2b) |-------
+--R +---+ \| x
+--R \|- a
+--R ----------------------------------------------------]
+--R 3x
+--R Type: Union(List(Expression(Integer)),...)
+--E 890
+
+--S 891 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R +-+ +-+ |a x + b +-+ \| x
+--R (4) a\|a log(2x\|a |------- + 2a x + b) - 2a\|a atanh(----------)
+--R \| x +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 891
+
+--S 892 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 892
+
+--S 893 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b |a x + b
+--R |------- |-------
+--R +-+ \| x +---+ \| x
+--R (6) - 2a\|a atanh(----------) + 2a\|- a atan(----------)
+--R +-+ +---+
+--R \|a \|- a
+--R Type: Expression(Integer)
+--E 893
+
+--S 894 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 894
+
+)clear all
+
+--S 895 of 1369
+t0:=(a+b/x)^(3/2)/x^2
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 895
+
+--S 896 of 1369
+r0:=-2/5*(a+b/x)^(5/2)/b
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (- 2a x - 4a b x - 2b ) |-------
+--R \| x
+--R (2) ----------------------------------
+--R 2
+--R 5b x
+--R Type: Expression(Integer)
+--E 896
+
+--S 897 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (- 2a x - 4a b x - 2b ) |-------
+--R \| x
+--R (3) ----------------------------------
+--R 2
+--R 5b x
+--R Type: Union(Expression(Integer),...)
+--E 897
+
+--S 898 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 898
+
+--S 899 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 899
+
+)clear all
+
+--S 900 of 1369
+t0:=(a+b/x)^(3/2)/x^3
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 900
+
+--S 901 of 1369
+r0:=2/5*a*(a+b/x)^(5/2)/b^2-2/7*(a+b/x)^(7/2)/b^2
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b
+--R (4a x - 2a b x - 16a b x - 10b ) |-------
+--R \| x
+--R (2) --------------------------------------------
+--R 2 3
+--R 35b x
+--R Type: Expression(Integer)
+--E 901
+
+--S 902 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b
+--R (4a x - 2a b x - 16a b x - 10b ) |-------
+--R \| x
+--R (3) --------------------------------------------
+--R 2 3
+--R 35b x
+--R Type: Union(Expression(Integer),...)
+--E 902
+
+--S 903 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 903
+
+--S 904 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 904
+
+)clear all
+
+--S 905 of 1369
+t0:=(a+b/x)^(3/2)/x^4
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 905
+
+--S 906 of 1369
+r0:=-2/5*a^2*(a+b/x)^(5/2)/b^3+4/7*a*(a+b/x)^(7/2)/b^3-2/9*(a+b/x)^(9/2)/b^3
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |-------
+--R \| x
+--R (2) ----------------------------------------------------------
+--R 3 4
+--R 315b x
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |-------
+--R \| x
+--R (3) ----------------------------------------------------------
+--R 3 4
+--R 315b x
+--R Type: Union(Expression(Integer),...)
+--E 907
+
+--S 908 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 908
+
+--S 909 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 909
+
+)clear all
+
+--S 910 of 1369
+t0:=(a+b/x)^(3/2)/x^5
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 910
+
+--S 911 of 1369
+r0:=2/5*a^3*(a+b/x)^(5/2)/b^4-6/7*a^2*(a+b/x)^(7/2)/b^4+2/3*a*_
+ (a+b/x)^(9/2)/b^4-2/11*(a+b/x)^(11/2)/b^4
+--R
+--R
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b
+--R (32a x - 16a b x + 12a b x - 10a b x - 280a b x - 210b ) |-------
+--R \| x
+--R (2) ----------------------------------------------------------------------
+--R 4 5
+--R 1155b x
+--R Type: Expression(Integer)
+--E 911
+
+--S 912 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b
+--R (32a x - 16a b x + 12a b x - 10a b x - 280a b x - 210b ) |-------
+--R \| x
+--R (3) ----------------------------------------------------------------------
+--R 4 5
+--R 1155b x
+--R Type: Union(Expression(Integer),...)
+--E 912
+
+--S 913 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 913
+
+--S 914 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 914
+
+)clear all
+
+--S 915 of 1369
+t0:=(a+b/x)^(3/2)/x^6
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 915
+
+--S 916 of 1369
+r0:=-2/5*a^4*(a+b/x)^(5/2)/b^5+8/7*a^3*(a+b/x)^(7/2)/b^5-_
+ 4/3*a^2*(a+b/x)^(9/2)/b^5+8/11*a*(a+b/x)^(11/2)/b^5-_
+ 2/13*(a+b/x)^(13/2)/b^5
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5
+--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 2940a b x
+--R +
+--R 6
+--R - 2310b
+--R *
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R /
+--R 5 6
+--R 15015b x
+--R Type: Expression(Integer)
+--E 916
+
+--S 917 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5
+--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 2940a b x
+--R +
+--R 6
+--R - 2310b
+--R *
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R /
+--R 5 6
+--R 15015b x
+--R Type: Union(Expression(Integer),...)
+--E 917
+
+--S 918 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 918
+
+--S 919 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 919
+
+)clear all
+
+--S 920 of 1369
+t0:=(a+b/x)^(3/2)/x^7
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 920
+
+--S 921 of 1369
+r0:=2/5*a^5*(a+b/x)^(5/2)/b^6-10/7*a^4*(a+b/x)^(7/2)/b^6+_
+ 20/9*a^3*(a+b/x)^(9/2)/b^6-20/11*a^2*(a+b/x)^(11/2)/b^6+_
+ 10/13*a*(a+b/x)^(13/2)/b^6-2/15*(a+b/x)^(15/2)/b^6
+--R
+--R
+--R (2)
+--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2
+--R 512a x - 256a b x + 192a b x - 160a b x + 140a b x - 126a b x
+--R +
+--R 6 7
+--R - 7392a b x - 6006b
+--R *
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R /
+--R 6 7
+--R 45045b x
+--R Type: Expression(Integer)
+--E 921
+
+--S 922 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2
+--R 512a x - 256a b x + 192a b x - 160a b x + 140a b x - 126a b x
+--R +
+--R 6 7
+--R - 7392a b x - 6006b
+--R *
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R /
+--R 6 7
+--R 45045b x
+--R Type: Union(Expression(Integer),...)
+--E 922
+
+--S 923 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 923
+
+--S 924 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 924
+
+)clear all
+
+--S 925 of 1369
+t0:=(a+b/x)^(5/2)*x^3
+--R
+--R
+--R +-------+
+--R 2 3 2 2 |a x + b
+--R (1) (a x + 2a b x + b x) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 925
+
+--S 926 of 1369
+r0:=5/24*b*(a+b/x)^(3/2)*x^3+1/4*(a+b/x)^(5/2)*x^4-_
+ 5/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+5/64*b^3*x*_
+ sqrt(a+b/x)/a+5/32*b^2*x^2*sqrt(a+b/x)
+--R
+--R
+--R (2)
+--R +-------+
+--R |a x + b
+--R |-------
+--R 4 \| x
+--R - 15b atanh(----------)
+--R +-+
+--R \|a
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +-+ |a x + b
+--R (48a x + 136a b x + 118a b x + 15b x)\|a |-------
+--R \| x
+--R /
+--R +-+
+--R 192a\|a
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 4 |a x + b +-+
+--R 15b log(- 2a x |------- + (2a x + b)\|a )
+--R \| x
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +-+ |a x + b
+--R (96a x + 272a b x + 236a b x + 30b x)\|a |-------
+--R \| x
+--R /
+--R +-+
+--R 384a\|a
+--R ,
+--R
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |-------
+--R 4 \| x
+--R - 15b atan(----------------)
+--R a
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +---+ |a x + b
+--R (48a x + 136a b x + 118a b x + 15b x)\|- a |-------
+--R \| x
+--R /
+--R +---+
+--R 192a\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 927
+
+--S 928 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 4 |a x + b +-+ 4 \| x
+--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) -----------------------------------------------------------------
+--R +-+
+--R 128a\|a
+--R Type: Expression(Integer)
+--E 928
+
+--S 929 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 929
+
+--S 930 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 4 +---+ \| x 4 +-+ \| x
+--R 5b \|- a atanh(----------) - 5b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------------
+--R +---+ +-+
+--R 64a\|- a \|a
+--R Type: Expression(Integer)
+--E 930
+
+--S 931 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 931
+
+)clear all
+
+--S 932 of 1369
+t0:=(a+b/x)^(5/2)*x^2
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (1) (a x + 2a b x + b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 932
+
+--S 933 of 1369
+r0:=5/12*b*(a+b/x)^(3/2)*x^2+1/3*(a+b/x)^(5/2)*x^3+5/8*b^3*_
+ atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)+5/8*b^2*x*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 3 \| x 2 3 2 2 +-+ |a x + b
+--R 15b atanh(----------) + (8a x + 26a b x + 33b x)\|a |-------
+--R +-+ \| x
+--R \|a
+--R (2) ----------------------------------------------------------------
+--R +-+
+--R 24\|a
+--R Type: Expression(Integer)
+--E 933
+
+--S 934 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 3 |a x + b +-+
+--R 15b log(2a x |------- + (2a x + b)\|a )
+--R \| x
+--R +
+--R +-------+
+--R 2 3 2 2 +-+ |a x + b
+--R (16a x + 52a b x + 66b x)\|a |-------
+--R \| x
+--R /
+--R +-+
+--R 48\|a
+--R ,
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |------- +-------+
+--R 3 \| x 2 3 2 2 +---+ |a x + b
+--R 15b atan(----------------) + (8a x + 26a b x + 33b x)\|- a |-------
+--R a \| x
+--R -----------------------------------------------------------------------]
+--R +---+
+--R 24\|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 934
+
+--S 935 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 3 |a x + b +-+ 3 \| x
+--R 5b log(2a x |------- + (2a x + b)\|a ) - 10b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------------
+--R +-+
+--R 16\|a
+--R Type: Expression(Integer)
+--E 935
+
+--S 936 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 936
+
+--S 937 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 3 +---+ \| x 3 +-+ \| x
+--R - 5b \|- a atanh(----------) + 5b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R +---+ +-+
+--R 8\|- a \|a
+--R Type: Expression(Integer)
+--E 937
+
+--S 938 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 938
+
+)clear all
+
+--S 939 of 1369
+t0:=(a+b/x)^(5/2)*x
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 1369
+r0:=5/4*b*(a+b/x)^(3/2)*x+1/2*(a+b/x)^(5/2)*x^2+15/4*b^2*_
+ atanh(sqrt(a+b/x)/sqrt(a))*sqrt(a)-15/4*b^2*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 2 +-+ \| x 2 2 2 |a x + b
+--R 15b \|a atanh(----------) + (2a x + 9a b x - 8b ) |-------
+--R +-+ \| x
+--R \|a
+--R (2) ------------------------------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 940
+
+--S 941 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 2 +-+ +-+ |a x + b
+--R 15b \|a log(2x\|a |------- + 2a x + b)
+--R \| x
+--R +
+--R +-------+
+--R 2 2 2 |a x + b
+--R (4a x + 18a b x - 16b ) |-------
+--R \| x
+--R /
+--R 8
+--R ,
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 2 +---+ \| x 2 2 2 |a x + b
+--R 15b \|- a atan(----------) + (2a x + 9a b x - 8b ) |-------
+--R +---+ \| x
+--R \|- a
+--R -------------------------------------------------------------]
+--R 4
+--R Type: Union(List(Expression(Integer)),...)
+--E 941
+
+--S 942 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 +-+ +-+ |a x + b 2 +-+ \| x
+--R 15b \|a log(2x\|a |------- + 2a x + b) - 30b \|a atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) --------------------------------------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 942
+
+--S 943 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 943
+
+--S 944 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b |a x + b
+--R |------- |-------
+--R 2 +-+ \| x 2 +---+ \| x
+--R - 15b \|a atanh(----------) + 15b \|- a atan(----------)
+--R +-+ +---+
+--R \|a \|- a
+--R (6) --------------------------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 945
+
+)clear all
+
+--S 946 of 1369
+t0:=(a+b/x)^(5/2)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 1369
+r0:=-5/3*b*(a+b/x)^(3/2)+(a+b/x)^(5/2)*x+5*a^(3/2)*b*_
+ atanh(sqrt(a+b/x)/sqrt(a))-5*a*b*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R +-+ \| x 2 2 2 |a x + b
+--R 15a b x\|a atanh(----------) + (3a x - 14a b x - 2b ) |-------
+--R +-+ \| x
+--R \|a
+--R (2) ----------------------------------------------------------------
+--R 3x
+--R Type: Expression(Integer)
+--E 947
+
+--S 948 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R +-+ +-+ |a x + b
+--R 15a b x\|a log(2x\|a |------- + 2a x + b)
+--R \| x
+--R +
+--R +-------+
+--R 2 2 2 |a x + b
+--R (6a x - 28a b x - 4b ) |-------
+--R \| x
+--R /
+--R 6x
+--R ,
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R +---+ \| x 2 2 2 |a x + b
+--R 15a b x\|- a atan(----------) + (3a x - 14a b x - 2b ) |-------
+--R +---+ \| x
+--R \|- a
+--R -----------------------------------------------------------------]
+--R 3x
+--R Type: Union(List(Expression(Integer)),...)
+--E 948
+
+--S 949 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R +-+ +-+ |a x + b +-+ \| x
+--R 5a b\|a log(2x\|a |------- + 2a x + b) - 10a b\|a atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 950
+
+--S 951 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b |a x + b
+--R |------- |-------
+--R +-+ \| x +---+ \| x
+--R (6) - 5a b\|a atanh(----------) + 5a b\|- a atan(----------)
+--R +-+ +---+
+--R \|a \|- a
+--R Type: Expression(Integer)
+--E 951
+
+--S 952 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 952
+
+)clear all
+
+--S 953 of 1369
+t0:=(a+b/x)^(5/2)/x
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 953
+
+--S 954 of 1369
+r0:=-2/3*a*(a+b/x)^(3/2)-2/5*(a+b/x)^(5/2)+2*a^(5/2)*_
+ atanh(sqrt(a+b/x)/sqrt(a))-2*a^2*sqrt(a+b/x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 2 2 +-+ \| x 2 2 2 |a x + b
+--R 30a x \|a atanh(----------) + (- 46a x - 22a b x - 6b ) |-------
+--R +-+ \| x
+--R \|a
+--R (2) ------------------------------------------------------------------
+--R 2
+--R 15x
+--R Type: Expression(Integer)
+--E 954
+
+--S 955 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 2 2 +-+ +-+ |a x + b
+--R 15a x \|a log(2x\|a |------- + 2a x + b)
+--R \| x
+--R +
+--R +-------+
+--R 2 2 2 |a x + b
+--R (- 46a x - 22a b x - 6b ) |-------
+--R \| x
+--R /
+--R 2
+--R 15x
+--R ,
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 2 2 +---+ \| x 2 2 2 |a x + b
+--R 30a x \|- a atan(----------) + (- 46a x - 22a b x - 6b ) |-------
+--R +---+ \| x
+--R \|- a
+--R -------------------------------------------------------------------]
+--R 2
+--R 15x
+--R Type: Union(List(Expression(Integer)),...)
+--E 955
+
+--S 956 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 +-+ +-+ |a x + b 2 +-+ \| x
+--R (4) a \|a log(2x\|a |------- + 2a x + b) - 2a \|a atanh(----------)
+--R \| x +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 956
+
+--S 957 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 957
+
+--S 958 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b |a x + b
+--R |------- |-------
+--R 2 +-+ \| x 2 +---+ \| x
+--R (6) - 2a \|a atanh(----------) + 2a \|- a atan(----------)
+--R +-+ +---+
+--R \|a \|- a
+--R Type: Expression(Integer)
+--E 958
+
+--S 959 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 959
+
+)clear all
+
+--S 960 of 1369
+t0:=(a+b/x)^(5/2)/x^2
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 960
+
+--S 961 of 1369
+r0:=-2/7*(a+b/x)^(7/2)/b
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b
+--R (- 2a x - 6a b x - 6a b x - 2b ) |-------
+--R \| x
+--R (2) --------------------------------------------
+--R 3
+--R 7b x
+--R Type: Expression(Integer)
+--E 961
+
+--S 962 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b
+--R (- 2a x - 6a b x - 6a b x - 2b ) |-------
+--R \| x
+--R (3) --------------------------------------------
+--R 3
+--R 7b x
+--R Type: Union(Expression(Integer),...)
+--E 962
+
+--S 963 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 963
+
+--S 964 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 964
+
+)clear all
+
+--S 965 of 1369
+t0:=(a+b/x)^(5/2)/x^3
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 965
+
+--S 966 of 1369
+r0:=2/7*a*(a+b/x)^(7/2)/b^2-2/9*(a+b/x)^(9/2)/b^2
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b
+--R (4a x - 2a b x - 30a b x - 38a b x - 14b ) |-------
+--R \| x
+--R (2) -------------------------------------------------------
+--R 2 4
+--R 63b x
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b
+--R (4a x - 2a b x - 30a b x - 38a b x - 14b ) |-------
+--R \| x
+--R (3) -------------------------------------------------------
+--R 2 4
+--R 63b x
+--R Type: Union(Expression(Integer),...)
+--E 967
+
+--S 968 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 968
+
+--S 969 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 969
+
+)clear all
+
+--S 970 of 1369
+t0:=(a+b/x)^(5/2)/x^4
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 970
+
+--S 971 of 1369
+r0:=-2/7*a^2*(a+b/x)^(7/2)/b^3+4/9*a*(a+b/x)^(9/2)/b^3-2/11*(a+b/x)^(11/2)/b^3
+--R
+--R
+--R (2)
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 226a b x - 322a b x - 126b ) |-------
+--R \| x
+--R -----------------------------------------------------------------------
+--R 3 5
+--R 693b x
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 226a b x - 322a b x - 126b ) |-------
+--R \| x
+--R -----------------------------------------------------------------------
+--R 3 5
+--R 693b x
+--R Type: Union(Expression(Integer),...)
+--E 972
+
+--S 973 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 973
+
+--S 974 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 974
+
+)clear all
+
+--S 975 of 1369
+t0:=(a+b/x)^(5/2)/x^5
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 975
+
+--S 976 of 1369
+r0:=2/7*a^3*(a+b/x)^(7/2)/b^4-2/3*a^2*(a+b/x)^(9/2)/b^4+_
+ 6/11*a*(a+b/x)^(11/2)/b^4-2/13*(a+b/x)^(13/2)/b^4
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6
+--R (32a x - 16a b x + 12a b x - 10a b x - 742a b x - 1134a b x - 462b )
+--R *
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R /
+--R 4 6
+--R 3003b x
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6
+--R (32a x - 16a b x + 12a b x - 10a b x - 742a b x - 1134a b x - 462b )
+--R *
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R /
+--R 4 6
+--R 3003b x
+--R Type: Union(Expression(Integer),...)
+--E 977
+
+--S 978 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 978
+
+--S 979 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 979
+
+)clear all
+
+--S 980 of 1369
+t0:=(a+b/x)^(5/2)/x^6
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 980
+
+--S 981 of 1369
+r0:=-2/7*a^4*(a+b/x)^(7/2)/b^5+8/9*a^3*(a+b/x)^(9/2)/b^5-_
+ 12/11*a^2*(a+b/x)^(11/2)/b^5+8/13*a*(a+b/x)^(13/2)/b^5-_
+ 2/15*(a+b/x)^(15/2)/b^5
+--R
+--R
+--R (2)
+--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2
+--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 8946a b x
+--R +
+--R 6 7
+--R - 14322a b x - 6006b
+--R *
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R /
+--R 5 7
+--R 45045b x
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2
+--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 8946a b x
+--R +
+--R 6 7
+--R - 14322a b x - 6006b
+--R *
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R /
+--R 5 7
+--R 45045b x
+--R Type: Union(Expression(Integer),...)
+--E 982
+
+--S 983 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 983
+
+--S 984 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 984
+
+)clear all
+
+--S 985 of 1369
+t0:=x^3/sqrt(a+b/x)
+--R
+--R
+--R 3
+--R x
+--R (1) ----------
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 985
+
+--S 986 of 1369
+r0:=35/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(9/2)-35/64*b^3*x*_
+ sqrt(a+b/x)/a^4+35/96*b^2*x^2*sqrt(a+b/x)/a^3-7/24*b*x^3*_
+ sqrt(a+b/x)/a^2+1/4*x^4*sqrt(a+b/x)/a
+--R
+--R
+--R (2)
+--R +-------+
+--R |a x + b
+--R |-------
+--R 4 \| x
+--R 105b atanh(----------)
+--R +-+
+--R \|a
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +-+ |a x + b
+--R (48a x - 56a b x + 70a b x - 105b x)\|a |-------
+--R \| x
+--R /
+--R 4 +-+
+--R 192a \|a
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 4 |a x + b +-+
+--R 105b log(2a x |------- + (2a x + b)\|a )
+--R \| x
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +-+ |a x + b
+--R (96a x - 112a b x + 140a b x - 210b x)\|a |-------
+--R \| x
+--R /
+--R 4 +-+
+--R 384a \|a
+--R ,
+--R
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |-------
+--R 4 \| x
+--R 105b atan(----------------)
+--R a
+--R +
+--R +-------+
+--R 3 4 2 3 2 2 3 +---+ |a x + b
+--R (48a x - 56a b x + 70a b x - 105b x)\|- a |-------
+--R \| x
+--R /
+--R 4 +---+
+--R 192a \|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 987
+
+--S 988 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 4 |a x + b +-+ 4 \| x
+--R 35b log(2a x |------- + (2a x + b)\|a ) - 70b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ----------------------------------------------------------------
+--R 4 +-+
+--R 128a \|a
+--R Type: Expression(Integer)
+--E 988
+
+--S 989 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 989
+
+--S 990 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 4 +---+ \| x 4 +-+ \| x
+--R - 35b \|- a atanh(----------) + 35b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------------
+--R 4 +---+ +-+
+--R 64a \|- a \|a
+--R Type: Expression(Integer)
+--E 990
+
+--S 991 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 991
+
+)clear all
+
+--S 992 of 1369
+t0:=x^2/sqrt(a+b/x)
+--R
+--R
+--R 2
+--R x
+--R (1) ----------
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 992
+
+--S 993 of 1369
+r0:=-5/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)+5/8*b^2*x*_
+ sqrt(a+b/x)/a^3-5/12*b*x^2*sqrt(a+b/x)/a^2+1/3*x^3*sqrt(a+b/x)/a
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 3 \| x 2 3 2 2 +-+ |a x + b
+--R - 15b atanh(----------) + (8a x - 10a b x + 15b x)\|a |-------
+--R +-+ \| x
+--R \|a
+--R (2) ------------------------------------------------------------------
+--R 3 +-+
+--R 24a \|a
+--R Type: Expression(Integer)
+--E 993
+
+--S 994 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+
+--R 3 |a x + b +-+
+--R 15b log(- 2a x |------- + (2a x + b)\|a )
+--R \| x
+--R +
+--R +-------+
+--R 2 3 2 2 +-+ |a x + b
+--R (16a x - 20a b x + 30b x)\|a |-------
+--R \| x
+--R /
+--R 3 +-+
+--R 48a \|a
+--R ,
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |------- +-------+
+--R 3 \| x 2 3 2 2 +---+ |a x + b
+--R - 15b atan(----------------) + (8a x - 10a b x + 15b x)\|- a |-------
+--R a \| x
+--R -------------------------------------------------------------------------]
+--R 3 +---+
+--R 24a \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 994
+
+--S 995 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 3 |a x + b +-+ 3 \| x
+--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) -----------------------------------------------------------------
+--R 3 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 995
+
+--S 996 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 996
+
+--S 997 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 3 +---+ \| x 3 +-+ \| x
+--R 5b \|- a atanh(----------) - 5b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------------
+--R 3 +---+ +-+
+--R 8a \|- a \|a
+--R Type: Expression(Integer)
+--E 997
+
+--S 998 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 998
+
+)clear all
+
+--S 999 of 1369
+t0:=x/sqrt(a+b/x)
+--R
+--R
+--R x
+--R (1) ----------
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 999
+
+--S 1000 of 1369
+r0:=3/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-3/4*b*x*_
+ sqrt(a+b/x)/a^2+1/2*x^2*sqrt(a+b/x)/a
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R 2 \| x 2 +-+ |a x + b
+--R 3b atanh(----------) + (2a x - 3b x)\|a |-------
+--R +-+ \| x
+--R \|a
+--R (2) ---------------------------------------------------
+--R 2 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 1000
+
+--S 1001 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R 2 |a x + b +-+ 2 +-+ |a x + b
+--R 3b log(2a x |------- + (2a x + b)\|a ) + (4a x - 6b x)\|a |-------
+--R \| x \| x
+--R [----------------------------------------------------------------------,
+--R 2 +-+
+--R 8a \|a
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |------- +-------+
+--R 2 \| x 2 +---+ |a x + b
+--R 3b atan(----------------) + (2a x - 3b x)\|- a |-------
+--R a \| x
+--R ----------------------------------------------------------]
+--R 2 +---+
+--R 4a \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 1001
+
+--S 1002 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 |a x + b +-+ 2 \| x
+--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) --------------------------------------------------------------
+--R 2 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1002
+
+--S 1003 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1003
+
+--S 1004 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 2 +---+ \| x 2 +-+ \| x
+--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R 2 +---+ +-+
+--R 4a \|- a \|a
+--R Type: Expression(Integer)
+--E 1004
+
+--S 1005 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1005
+
+)clear all
+
+--S 1006 of 1369
+t0:=1/sqrt(a+b/x)
+--R
+--R
+--R 1
+--R (1) ----------
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1006
+
+--S 1007 of 1369
+r0:=-b*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+x*sqrt(a+b/x)/a
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |------- +-------+
+--R \| x +-+ |a x + b
+--R - b atanh(----------) + x\|a |-------
+--R +-+ \| x
+--R \|a
+--R (2) ---------------------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 1007
+
+--S 1008 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R |a x + b +-+ +-+ |a x + b
+--R b log(- 2a x |------- + (2a x + b)\|a ) + 2x\|a |-------
+--R \| x \| x
+--R [-----------------------------------------------------------,
+--R +-+
+--R 2a\|a
+--R +-------+
+--R +---+ |a x + b
+--R \|- a |------- +-------+
+--R \| x +---+ |a x + b
+--R - b atan(----------------) + x\|- a |-------
+--R a \| x
+--R ----------------------------------------------]
+--R +---+
+--R a\|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 1008
+
+--S 1009 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b +-+ \| x
+--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------------
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 1009
+
+--S 1010 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1010
+
+--S 1011 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R +---+ \| x +-+ \| x
+--R b\|- a atanh(----------) - b\|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------
+--R +---+ +-+
+--R a\|- a \|a
+--R Type: Expression(Integer)
+--E 1011
+
+--S 1012 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1012
+
+)clear all
+
+--S 1013 of 1369
+t0:=1/(x*sqrt(a+b/x))
+--R
+--R
+--R 1
+--R (1) -----------
+--R +-------+
+--R |a x + b
+--R x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1013
+
+--S 1014 of 1369
+r0:=2*atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R 2atanh(----------)
+--R +-+
+--R \|a
+--R (2) ------------------
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 1014
+
+--S 1015 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R +---+ |a x + b
+--R +-------+ \|- a |-------
+--R |a x + b +-+ \| x
+--R log(2a x |------- + (2a x + b)\|a ) 2atan(----------------)
+--R \| x a
+--R (3) [------------------------------------,-----------------------]
+--R +-+ +---+
+--R \|a \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 1015
+
+--S 1016 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b +-+ \| x
+--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 1016
+
+--S 1017 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1017
+
+--S 1018 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R +---+ \| x +-+ \| x
+--R - 2\|- a atanh(----------) + 2\|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R \|- a \|a
+--R Type: Expression(Integer)
+--E 1018
+
+--S 1019 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1019
+
+)clear all
+
+--S 1020 of 1369
+t0:=1/(x^2*sqrt(a+b/x))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 2 |a x + b
+--R x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1020
+
+--S 1021 of 1369
+r0:=-2*sqrt(a+b/x)/b
+--R
+--R
+--R +-------+
+--R |a x + b
+--R 2 |-------
+--R \| x
+--R (2) - -----------
+--R b
+--R Type: Expression(Integer)
+--E 1021
+
+--S 1022 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R 2 |-------
+--R \| x
+--R (3) - -----------
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 1022
+
+--S 1023 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1023
+
+--S 1024 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1024
+
+)clear all
+
+--S 1025 of 1369
+t0:=1/(x^3*sqrt(a+b/x))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 3 |a x + b
+--R x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1025
+
+--S 1026 of 1369
+r0:=-2/3*(a+b/x)^(3/2)/b^2+2*a*sqrt(a+b/x)/b^2
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (4a x - 2b) |-------
+--R \| x
+--R (2) ---------------------
+--R 2
+--R 3b x
+--R Type: Expression(Integer)
+--E 1026
+
+--S 1027 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (4a x - 2b) |-------
+--R \| x
+--R (3) ---------------------
+--R 2
+--R 3b x
+--R Type: Union(Expression(Integer),...)
+--E 1027
+
+--S 1028 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1028
+
+--S 1029 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1029
+
+)clear all
+
+--S 1030 of 1369
+t0:=1/(x^4*sqrt(a+b/x))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 4 |a x + b
+--R x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1030
+
+--S 1031 of 1369
+r0:=4/3*a*(a+b/x)^(3/2)/b^3-2/5*(a+b/x)^(5/2)/b^3-2*a^2*sqrt(a+b/x)/b^3
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (- 16a x + 8a b x - 6b ) |-------
+--R \| x
+--R (2) -----------------------------------
+--R 3 2
+--R 15b x
+--R Type: Expression(Integer)
+--E 1031
+
+--S 1032 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (- 16a x + 8a b x - 6b ) |-------
+--R \| x
+--R (3) -----------------------------------
+--R 3 2
+--R 15b x
+--R Type: Union(Expression(Integer),...)
+--E 1032
+
+--S 1033 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1033
+
+--S 1034 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1034
+
+)clear all
+
+--S 1035 of 1369
+t0:=1/(x^5*sqrt(a+b/x))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 5 |a x + b
+--R x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1035
+
+--S 1036 of 1369
+r0:=-2*a^2*(a+b/x)^(3/2)/b^4+6/5*a*(a+b/x)^(5/2)/b^4-_
+ 2/7*(a+b/x)^(7/2)/b^4+2*a^3*sqrt(a+b/x)/b^4
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b
+--R (32a x - 16a b x + 12a b x - 10b ) |-------
+--R \| x
+--R (2) ----------------------------------------------
+--R 4 3
+--R 35b x
+--R Type: Expression(Integer)
+--E 1036
+
+--S 1037 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b
+--R (32a x - 16a b x + 12a b x - 10b ) |-------
+--R \| x
+--R (3) ----------------------------------------------
+--R 4 3
+--R 35b x
+--R Type: Union(Expression(Integer),...)
+--E 1037
+
+--S 1038 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1038
+
+--S 1039 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1039
+
+)clear all
+
+--S 1040 of 1369
+t0:=1/(x^6*sqrt(a+b/x))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R 6 |a x + b
+--R x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1040
+
+--S 1041 of 1369
+r0:=8/3*a^3*(a+b/x)^(3/2)/b^5-12/5*a^2*(a+b/x)^(5/2)/b^5+_
+ 8/7*a*(a+b/x)^(7/2)/b^5-2/9*(a+b/x)^(9/2)/b^5-2*a^4*sqrt(a+b/x)/b^5
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b
+--R (- 256a x + 128a b x - 96a b x + 80a b x - 70b ) |-------
+--R \| x
+--R (2) -------------------------------------------------------------
+--R 5 4
+--R 315b x
+--R Type: Expression(Integer)
+--E 1041
+
+--S 1042 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b
+--R (- 256a x + 128a b x - 96a b x + 80a b x - 70b ) |-------
+--R \| x
+--R (3) -------------------------------------------------------------
+--R 5 4
+--R 315b x
+--R Type: Union(Expression(Integer),...)
+--E 1042
+
+--S 1043 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1043
+
+--S 1044 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1044
+
+)clear all
+
+--S 1045 of 1369
+t0:=x^2/(a+b/x)^(3/2)
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1045
+
+--S 1046 of 1369
+r0:=-35/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(9/2)-2*x^3/(a*sqrt(a+b/x))+_
+ 35/8*b^2*x*sqrt(a+b/x)/a^4-35/12*b*x^2*sqrt(a+b/x)/a^3+_
+ 7/3*x^3*sqrt(a+b/x)/a^2
+--R
+--R
+--R (2)
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 3 |a x + b \| x 3 3 2 2 2 3 +-+
+--R - 105b |------- atanh(----------) + (8a x - 14a b x + 35a b x + 105b )\|a
+--R \| x +-+
+--R \|a
+--R -----------------------------------------------------------------------------
+--R +-------+
+--R 4 +-+ |a x + b
+--R 24a \|a |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1046
+
+--S 1047 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+ +-------+
+--R 3 |a x + b |a x + b +-+
+--R 105b |------- log(- 2a x |------- + (2a x + b)\|a )
+--R \| x \| x
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (16a x - 28a b x + 70a b x + 210b )\|a
+--R /
+--R +-------+
+--R 4 +-+ |a x + b
+--R 48a \|a |-------
+--R \| x
+--R ,
+--R
+--R +-------+
+--R +---+ |a x + b
+--R +-------+ \|- a |-------
+--R 3 |a x + b \| x
+--R - 105b |------- atan(----------------)
+--R \| x a
+--R +
+--R 3 3 2 2 2 3 +---+
+--R (8a x - 14a b x + 35a b x + 105b )\|- a
+--R /
+--R +-------+
+--R 4 +---+ |a x + b
+--R 24a \|- a |-------
+--R \| x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1047
+
+--S 1048 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 3 |a x + b +-+ 3 \| x
+--R 35b log(- 2a x |------- + (2a x + b)\|a ) + 70b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ------------------------------------------------------------------
+--R 4 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 1048
+
+--S 1049 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1049
+
+--S 1050 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 3 +---+ \| x 3 +-+ \| x
+--R 35b \|- a atanh(----------) - 35b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) ------------------------------------------------------------
+--R 4 +---+ +-+
+--R 8a \|- a \|a
+--R Type: Expression(Integer)
+--E 1050
+
+--S 1051 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1051
+
+)clear all
+
+--S 1052 of 1369
+t0:=x/(a+b/x)^(3/2)
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1052
+
+--S 1053 of 1369
+r0:=15/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)-2*x^2/(a*sqrt(a+b/x))-_
+ 15/4*b*x*sqrt(a+b/x)/a^3+5/2*x^2*sqrt(a+b/x)/a^2
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 |a x + b \| x 2 2 2 +-+
+--R 15b |------- atanh(----------) + (2a x - 5a b x - 15b )\|a
+--R \| x +-+
+--R \|a
+--R (2) -------------------------------------------------------------
+--R +-------+
+--R 3 +-+ |a x + b
+--R 4a \|a |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1053
+
+--S 1054 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+ +-------+
+--R 2 |a x + b |a x + b +-+
+--R 15b |------- log(2a x |------- + (2a x + b)\|a )
+--R \| x \| x
+--R +
+--R 2 2 2 +-+
+--R (4a x - 10a b x - 30b )\|a
+--R /
+--R +-------+
+--R 3 +-+ |a x + b
+--R 8a \|a |-------
+--R \| x
+--R ,
+--R +-------+
+--R +---+ |a x + b
+--R +-------+ \|- a |-------
+--R 2 |a x + b \| x 2 2 2 +---+
+--R 15b |------- atan(----------------) + (2a x - 5a b x - 15b )\|- a
+--R \| x a
+--R --------------------------------------------------------------------]
+--R +-------+
+--R 3 +---+ |a x + b
+--R 4a \|- a |-------
+--R \| x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1054
+
+--S 1055 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 |a x + b +-+ 2 \| x
+--R 15b log(2a x |------- + (2a x + b)\|a ) - 30b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ----------------------------------------------------------------
+--R 3 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1055
+
+--S 1056 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1056
+
+--S 1057 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 2 +---+ \| x 2 +-+ \| x
+--R - 15b \|- a atanh(----------) + 15b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------------
+--R 3 +---+ +-+
+--R 4a \|- a \|a
+--R Type: Expression(Integer)
+--E 1057
+
+--S 1058 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1058
+
+)clear all
+
+--S 1059 of 1369
+t0:=1/(a+b/x)^(3/2)
+--R
+--R
+--R x
+--R (1) -------------------
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1059
+
+--S 1060 of 1369
+r0:=-3*b*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-2*x/(a*sqrt(a+b/x))+_
+ 3*x*sqrt(a+b/x)/a^2
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b \| x +-+
+--R - 3b |------- atanh(----------) + (a x + 3b)\|a
+--R \| x +-+
+--R \|a
+--R (2) ------------------------------------------------
+--R +-------+
+--R 2 +-+ |a x + b
+--R a \|a |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1060
+
+--S 1061 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R |a x + b |a x + b +-+ +-+
+--R 3b |------- log(- 2a x |------- + (2a x + b)\|a ) + (2a x + 6b)\|a
+--R \| x \| x
+--R [--------------------------------------------------------------------,
+--R +-------+
+--R 2 +-+ |a x + b
+--R 2a \|a |-------
+--R \| x
+--R +-------+
+--R +---+ |a x + b
+--R +-------+ \|- a |-------
+--R |a x + b \| x +---+
+--R - 3b |------- atan(----------------) + (a x + 3b)\|- a
+--R \| x a
+--R -------------------------------------------------------]
+--R +-------+
+--R 2 +---+ |a x + b
+--R a \|- a |-------
+--R \| x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1061
+
+--S 1062 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b +-+ \| x
+--R 3b log(- 2a x |------- + (2a x + b)\|a ) + 6b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ----------------------------------------------------------------
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 1062
+
+--S 1063 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1063
+
+--S 1064 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R +---+ \| x +-+ \| x
+--R 3b\|- a atanh(----------) - 3b\|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R 2 +---+ +-+
+--R a \|- a \|a
+--R Type: Expression(Integer)
+--E 1064
+
+--S 1065 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1065
+
+)clear all
+
+--S 1066 of 1369
+t0:=1/((a+b/x)^(3/2)*x)
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1066
+
+--S 1067 of 1369
+r0:=2*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+(-2)/(a*sqrt(a+b/x))
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b \| x +-+
+--R 2 |------- atanh(---------- - 2\|a
+--R \| x +-+
+--R \|a
+--R (2) ------------------------------------
+--R +-------+
+--R +-+ |a x + b
+--R a\|a |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1067
+
+--S 1068 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+
+--R |a x + b |a x + b +-+ +-+
+--R |------- log(2a x |------- + (2a x + b)\|a ) - 2\|a
+--R \| x \| x
+--R [------------------------------------------------------,
+--R +-------+
+--R +-+ |a x + b
+--R a\|a |-------
+--R \| x
+--R +-------+
+--R +---+ |a x + b
+--R +-------+ \|- a |-------
+--R |a x + b \| x +---+
+--R 2 |------- atan(---------------- - 2\|- a
+--R \| x a
+--R -------------------------------------------]
+--R +-------+
+--R +---+ |a x + b
+--R a\|- a |-------
+--R \| x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1068
+
+--S 1069 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b +-+ \| x
+--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 1069
+
+--S 1070 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1070
+
+--S 1071 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R +---+ \| x +-+ \| x
+--R - 2\|- a atanh(----------) + 2\|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R a\|- a \|a
+--R Type: Expression(Integer)
+--E 1071
+
+--S 1072 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1072
+
+)clear all
+
+--S 1073 of 1369
+t0:=1/((a+b/x)^(3/2)*x^2)
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +-------+
+--R 2 |a x + b
+--R (a x + b x) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1073
+
+--S 1074 of 1369
+r0:=2/(b*sqrt(a+b/x))
+--R
+--R
+--R 2
+--R (2) -----------
+--R +-------+
+--R |a x + b
+--R b |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1074
+
+--S 1075 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (3) -----------
+--R +-------+
+--R |a x + b
+--R b |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1075
+
+--S 1076 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1076
+
+--S 1077 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1077
+
+)clear all
+
+--S 1078 of 1369
+t0:=1/((a+b/x)^(3/2)*x^3)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +-------+
+--R 3 2 |a x + b
+--R (a x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1078
+
+--S 1079 of 1369
+r0:=-2*a/(b^2*sqrt(a+b/x))-2*sqrt(a+b/x)/b^2
+--R
+--R
+--R - 4a x - 2b
+--R (2) -------------
+--R +-------+
+--R 2 |a x + b
+--R b x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1079
+
+--S 1080 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - 4a x - 2b
+--R (3) -------------
+--R +-------+
+--R 2 |a x + b
+--R b x |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1080
+
+--S 1081 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1081
+
+--S 1082 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1082
+
+)clear all
+
+--S 1083 of 1369
+t0:=1/((a+b/x)^(3/2)*x^4)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +-------+
+--R 4 3 |a x + b
+--R (a x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1083
+
+--S 1084 of 1369
+r0:=-2/3*(a+b/x)^(3/2)/b^3+2*a^2/(b^3*sqrt(a+b/x))+4*a*sqrt(a+b/x)/b^3
+--R
+--R
+--R 2 2 2
+--R 16a x + 8a b x - 2b
+--R (2) ---------------------
+--R +-------+
+--R 3 2 |a x + b
+--R 3b x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1084
+
+--S 1085 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R 16a x + 8a b x - 2b
+--R (3) ---------------------
+--R +-------+
+--R 3 2 |a x + b
+--R 3b x |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1085
+
+--S 1086 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1086
+
+--S 1087 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1087
+
+)clear all
+
+--S 1088 of 1369
+t0:=1/((a+b/x)^(3/2)*x^5)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +-------+
+--R 5 4 |a x + b
+--R (a x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1088
+
+--S 1089 of 1369
+r0:=2*a*(a+b/x)^(3/2)/b^4-2/5*(a+b/x)^(5/2)/b^4-2*a^3/(b^4*sqrt(a+b/x))-_
+ 6*a^2*sqrt(a+b/x)/b^4
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 32a x - 16a b x + 4a b x - 2b
+--R (2) ----------------------------------
+--R +-------+
+--R 4 3 |a x + b
+--R 5b x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1089
+
+--S 1090 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 32a x - 16a b x + 4a b x - 2b
+--R (3) ----------------------------------
+--R +-------+
+--R 4 3 |a x + b
+--R 5b x |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1090
+
+--S 1091 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1091
+
+--S 1092 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1092
+
+)clear all
+
+--S 1093 of 1369
+t0:=1/((a+b/x)^(3/2)*x^6)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +-------+
+--R 6 5 |a x + b
+--R (a x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1093
+
+--S 1094 of 1369
+r0:=-4*a^2*(a+b/x)^(3/2)/b^5+8/5*a*(a+b/x)^(5/2)/b^5-_
+ 2/7*(a+b/x)^(7/2)/b^5+2*a^4/(b^5*sqrt(a+b/x))+8*a^3*sqrt(a+b/x)/b^5
+--R
+--R
+--R 4 4 3 3 2 2 2 3 4
+--R 256a x + 128a b x - 32a b x + 16a b x - 10b
+--R (2) -----------------------------------------------
+--R +-------+
+--R 5 4 |a x + b
+--R 35b x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1094
+
+--S 1095 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4 3 3 2 2 2 3 4
+--R 256a x + 128a b x - 32a b x + 16a b x - 10b
+--R (3) -----------------------------------------------
+--R +-------+
+--R 5 4 |a x + b
+--R 35b x |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1095
+
+--S 1096 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1096
+
+--S 1097 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1097
+
+)clear all
+
+--S 1098 of 1369
+t0:=1/((a+b/x)^(3/2)*x^7)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +-------+
+--R 7 6 |a x + b
+--R (a x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1098
+
+--S 1099 of 1369
+r0:=20/3*a^3*(a+b/x)^(3/2)/b^6-4*a^2*(a+b/x)^(5/2)/b^6+_
+ 10/7*a*(a+b/x)^(7/2)/b^6-2/9*(a+b/x)^(9/2)/b^6-_
+ 2*a^5/(b^6*sqrt(a+b/x))-10*a^4*sqrt(a+b/x)/b^6
+--R
+--R
+--R 5 5 4 4 3 2 3 2 3 2 4 5
+--R - 512a x - 256a b x + 64a b x - 32a b x + 20a b x - 14b
+--R (2) ------------------------------------------------------------
+--R +-------+
+--R 6 5 |a x + b
+--R 63b x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1099
+
+--S 1100 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5 4 4 3 2 3 2 3 2 4 5
+--R - 512a x - 256a b x + 64a b x - 32a b x + 20a b x - 14b
+--R (3) ------------------------------------------------------------
+--R +-------+
+--R 6 5 |a x + b
+--R 63b x |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1100
+
+--S 1101 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1101
+
+--S 1102 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1102
+
+)clear all
+
+--S 1103 of 1369
+t0:=x^2/(a+b/x)^(5/2)
+--R
+--R
+--R 4
+--R x
+--R (1) ------------------------------
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1103
+
+--S 1104 of 1369
+r0:=-2/3*x^3/(a*(a+b/x)^(3/2))-105/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/_
+ a^(11/2)-6*x^3/(a^2*sqrt(a+b/x))+105/8*b^2*x*sqrt(a+b/x)/a^5-_
+ 35/4*b*x^2*sqrt(a+b/x)/a^4+7*x^3*sqrt(a+b/x)/a^3
+--R
+--R
+--R (2)
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 3 4 |a x + b \| x
+--R (- 315a b x - 315b ) |------- atanh(----------)
+--R \| x +-+
+--R \|a
+--R +
+--R 4 4 3 3 2 2 2 3 4 +-+
+--R (8a x - 18a b x + 63a b x + 420a b x + 315b )\|a
+--R /
+--R +-------+
+--R 6 5 +-+ |a x + b
+--R (24a x + 24a b)\|a |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1104
+
+--S 1105 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+ +-------+
+--R 3 4 |a x + b |a x + b +-+
+--R (315a b x + 315b ) |------- log(- 2a x |------- + (2a x + b)\|a )
+--R \| x \| x
+--R +
+--R 4 4 3 3 2 2 2 3 4 +-+
+--R (16a x - 36a b x + 126a b x + 840a b x + 630b )\|a
+--R /
+--R +-------+
+--R 6 5 +-+ |a x + b
+--R (48a x + 48a b)\|a |-------
+--R \| x
+--R ,
+--R
+--R +-------+
+--R +---+ |a x + b
+--R +-------+ \|- a |-------
+--R 3 4 |a x + b \| x
+--R (- 315a b x - 315b ) |------- atan(----------------)
+--R \| x a
+--R +
+--R 4 4 3 3 2 2 2 3 4 +---+
+--R (8a x - 18a b x + 63a b x + 420a b x + 315b )\|- a
+--R /
+--R +-------+
+--R 6 5 +---+ |a x + b
+--R (24a x + 24a b)\|- a |-------
+--R \| x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1105
+
+--S 1106 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 3 |a x + b +-+ 3 \| x
+--R 105b log(- 2a x |------- + (2a x + b)\|a ) + 210b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) --------------------------------------------------------------------
+--R 5 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 1106
+
+--S 1107 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1107
+
+--S 1108 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 3 +---+ \| x 3 +-+ \| x
+--R 105b \|- a atanh(----------) - 105b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------------
+--R 5 +---+ +-+
+--R 8a \|- a \|a
+--R Type: Expression(Integer)
+--E 1108
+
+--S 1109 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1109
+
+)clear all
+
+--S 1110 of 1369
+t0:=x/(a+b/x)^(5/2)
+--R
+--R
+--R 3
+--R x
+--R (1) ------------------------------
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1110
+
+--S 1111 of 1369
+r0:=-2/3*x^2/(a*(a+b/x)^(3/2))+35/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/_
+ a^(9/2)-14/3*x^2/(a^2*sqrt(a+b/x))-35/4*b*x*sqrt(a+b/x)/a^4+_
+ 35/6*x^2*sqrt(a+b/x)/a^3
+--R
+--R
+--R (2)
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 3 |a x + b \| x
+--R (105a b x + 105b ) |------- atanh(----------)
+--R \| x +-+
+--R \|a
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (6a x - 21a b x - 140a b x - 105b )\|a
+--R /
+--R +-------+
+--R 5 4 +-+ |a x + b
+--R (12a x + 12a b)\|a |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1111
+
+--S 1112 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+ +-------+
+--R 2 3 |a x + b |a x + b +-+
+--R (105a b x + 105b ) |------- log(2a x |------- + (2a x + b)\|a )
+--R \| x \| x
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (12a x - 42a b x - 280a b x - 210b )\|a
+--R /
+--R +-------+
+--R 5 4 +-+ |a x + b
+--R (24a x + 24a b)\|a |-------
+--R \| x
+--R ,
+--R
+--R +-------+
+--R +---+ |a x + b
+--R +-------+ \|- a |-------
+--R 2 3 |a x + b \| x
+--R (105a b x + 105b ) |------- atan(----------------)
+--R \| x a
+--R +
+--R 3 3 2 2 2 3 +---+
+--R (6a x - 21a b x - 140a b x - 105b )\|- a
+--R /
+--R +-------+
+--R 5 4 +---+ |a x + b
+--R (12a x + 12a b)\|- a |-------
+--R \| x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1112
+
+--S 1113 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 |a x + b +-+ 2 \| x
+--R 35b log(2a x |------- + (2a x + b)\|a ) - 70b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ----------------------------------------------------------------
+--R 4 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 1113
+
+--S 1114 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1114
+
+--S 1115 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R 2 +---+ \| x 2 +-+ \| x
+--R - 35b \|- a atanh(----------) + 35b \|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------------
+--R 4 +---+ +-+
+--R 4a \|- a \|a
+--R Type: Expression(Integer)
+--E 1115
+
+--S 1116 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1116
+
+)clear all
+
+--S 1117 of 1369
+t0:=1/(a+b/x)^(5/2)
+--R
+--R
+--R 2
+--R x
+--R (1) ------------------------------
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1117
+
+--S 1118 of 1369
+r0:=-2/3*x/(a*(a+b/x)^(3/2))-5*b*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)-_
+ 10/3*x/(a^2*sqrt(a+b/x))+5*x*sqrt(a+b/x)/a^3
+--R
+--R
+--R (2)
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R 2 |a x + b \| x 2 2 2 +-+
+--R (- 15a b x - 15b ) |------- atanh(----------) + (3a x + 20a b x + 15b )\|a
+--R \| x +-+
+--R \|a
+--R ----------------------------------------------------------------------------
+--R +-------+
+--R 4 3 +-+ |a x + b
+--R (3a x + 3a b)\|a |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1118
+
+--S 1119 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+ +-------+
+--R 2 |a x + b |a x + b +-+
+--R (15a b x + 15b ) |------- log(- 2a x |------- + (2a x + b)\|a )
+--R \| x \| x
+--R +
+--R 2 2 2 +-+
+--R (6a x + 40a b x + 30b )\|a
+--R /
+--R +-------+
+--R 4 3 +-+ |a x + b
+--R (6a x + 6a b)\|a |-------
+--R \| x
+--R ,
+--R
+--R +-------+
+--R +---+ |a x + b
+--R +-------+ \|- a |-------
+--R 2 |a x + b \| x
+--R (- 15a b x - 15b ) |------- atan(----------------)
+--R \| x a
+--R +
+--R 2 2 2 +---+
+--R (3a x + 20a b x + 15b )\|- a
+--R /
+--R +-------+
+--R 4 3 +---+ |a x + b
+--R (3a x + 3a b)\|- a |-------
+--R \| x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1119
+
+--S 1120 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b +-+ \| x
+--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) -----------------------------------------------------------------
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 1120
+
+--S 1121 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1121
+
+--S 1122 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R +---+ \| x +-+ \| x
+--R 5b\|- a atanh(----------) - 5b\|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R 3 +---+ +-+
+--R a \|- a \|a
+--R Type: Expression(Integer)
+--E 1122
+
+--S 1123 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1123
+
+)clear all
+
+--S 1124 of 1369
+t0:=1/((a+b/x)^(5/2)*x)
+--R
+--R
+--R x
+--R (1) ------------------------------
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1124
+
+--S 1125 of 1369
+r0:=(-2/3)/(a*(a+b/x)^(3/2))+2*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)+_
+ (-2)/(a^2*sqrt(a+b/x))
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b \| x +-+
+--R (6a x + 6b) |------- atanh(----------) + (- 8a x - 6b)\|a
+--R \| x +-+
+--R \|a
+--R (2) ----------------------------------------------------------
+--R +-------+
+--R 3 2 +-+ |a x + b
+--R (3a x + 3a b)\|a |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1125
+
+--S 1126 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-------+ +-------+
+--R |a x + b |a x + b +-+
+--R (3a x + 3b) |------- log(2a x |------- + (2a x + b)\|a )
+--R \| x \| x
+--R +
+--R +-+
+--R (- 8a x - 6b)\|a
+--R /
+--R +-------+
+--R 3 2 +-+ |a x + b
+--R (3a x + 3a b)\|a |-------
+--R \| x
+--R ,
+--R +-------+
+--R +---+ |a x + b
+--R +-------+ \|- a |-------
+--R |a x + b \| x +---+
+--R (6a x + 6b) |------- atan(----------------) + (- 8a x - 6b)\|- a
+--R \| x a
+--R -----------------------------------------------------------------]
+--R +-------+
+--R 3 2 +---+ |a x + b
+--R (3a x + 3a b)\|- a |-------
+--R \| x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1126
+
+--S 1127 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-------+
+--R |a x + b
+--R +-------+ |-------
+--R |a x + b +-+ \| x
+--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------)
+--R \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1127
+
+--S 1128 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1128
+
+--S 1129 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-------+ +-------+
+--R |a x + b +---+ |a x + b
+--R |------- \|- a |-------
+--R +---+ \| x +-+ \| x
+--R - 2\|- a atanh(----------) + 2\|a atan(----------------)
+--R +-+ a
+--R \|a
+--R (6) --------------------------------------------------------
+--R 2 +---+ +-+
+--R a \|- a \|a
+--R Type: Expression(Integer)
+--E 1129
+
+--S 1130 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1130
+
+)clear all
+
+--S 1131 of 1369
+t0:=1/((a+b/x)^(5/2)*x^2)
+--R
+--R
+--R 1
+--R (1) ------------------------------
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1131
+
+--S 1132 of 1369
+r0:=2/3/(b*(a+b/x)^(3/2))
+--R
+--R
+--R 2x
+--R (2) ------------------------
+--R +-------+
+--R 2 |a x + b
+--R (3a b x + 3b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1132
+
+--S 1133 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2x
+--R (3) ------------------------
+--R +-------+
+--R 2 |a x + b
+--R (3a b x + 3b ) |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1133
+
+--S 1134 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1134
+
+--S 1135 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1135
+
+)clear all
+
+--S 1136 of 1369
+t0:=1/((a+b/x)^(5/2)*x^3)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +-------+
+--R 2 3 2 2 |a x + b
+--R (a x + 2a b x + b x) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1136
+
+--S 1137 of 1369
+r0:=-2/3*a/(b^2*(a+b/x)^(3/2))+2/(b^2*sqrt(a+b/x))
+--R
+--R
+--R 4a x + 6b
+--R (2) ------------------------
+--R +-------+
+--R 2 3 |a x + b
+--R (3a b x + 3b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1137
+
+--S 1138 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4a x + 6b
+--R (3) ------------------------
+--R +-------+
+--R 2 3 |a x + b
+--R (3a b x + 3b ) |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1138
+
+--S 1139 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1139
+
+--S 1140 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1140
+
+)clear all
+
+--S 1141 of 1369
+t0:=1/((a+b/x)^(5/2)*x^4)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R +-------+
+--R 2 4 3 2 2 |a x + b
+--R (a x + 2a b x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1141
+
+--S 1142 of 1369
+r0:=2/3*a^2/(b^3*(a+b/x)^(3/2))-4*a/(b^3*sqrt(a+b/x))-2*sqrt(a+b/x)/b^3
+--R
+--R
+--R 2 2 2
+--R - 16a x - 24a b x - 6b
+--R (2) --------------------------
+--R +-------+
+--R 3 2 4 |a x + b
+--R (3a b x + 3b x) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1142
+
+--S 1143 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R - 16a x - 24a b x - 6b
+--R (3) --------------------------
+--R +-------+
+--R 3 2 4 |a x + b
+--R (3a b x + 3b x) |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1143
+
+--S 1144 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1144
+
+--S 1145 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1145
+
+)clear all
+
+--S 1146 of 1369
+t0:=1/((a+b/x)^(5/2)*x^5)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R +-------+
+--R 2 5 4 2 3 |a x + b
+--R (a x + 2a b x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1146
+
+--S 1147 of 1369
+r0:=-2/3*a^3/(b^4*(a+b/x)^(3/2))-2/3*(a+b/x)^(3/2)/b^4+_
+ 6*a^2/(b^4*sqrt(a+b/x))+6*a*sqrt(a+b/x)/b^4
+--R
+--R
+--R 3 3 2 2 2 3
+--R 32a x + 48a b x + 12a b x - 2b
+--R (2) ---------------------------------
+--R +-------+
+--R 4 3 5 2 |a x + b
+--R (3a b x + 3b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1147
+
+--S 1148 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R 32a x + 48a b x + 12a b x - 2b
+--R (3) ---------------------------------
+--R +-------+
+--R 4 3 5 2 |a x + b
+--R (3a b x + 3b x ) |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1148
+
+--S 1149 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1149
+
+--S 1150 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1150
+
+)clear all
+
+--S 1151 of 1369
+t0:=1/((a+b/x)^(5/2)*x^6)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R +-------+
+--R 2 6 5 2 4 |a x + b
+--R (a x + 2a b x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1151
+
+--S 1152 of 1369
+r0:=2/3*a^4/(b^5*(a+b/x)^(3/2))+8/3*a*(a+b/x)^(3/2)/b^5-_
+ 2/5*(a+b/x)^(5/2)/b^5-8*a^3/(b^5*sqrt(a+b/x))-12*a^2*sqrt(a+b/x)/b^5
+--R
+--R
+--R 4 4 3 3 2 2 2 3 4
+--R - 256a x - 384a b x - 96a b x + 16a b x - 6b
+--R (2) ------------------------------------------------
+--R +-------+
+--R 5 4 6 3 |a x + b
+--R (15a b x + 15b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1152
+
+--S 1153 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 4 3 3 2 2 2 3 4
+--R - 256a x - 384a b x - 96a b x + 16a b x - 6b
+--R (3) ------------------------------------------------
+--R +-------+
+--R 5 4 6 3 |a x + b
+--R (15a b x + 15b x ) |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1153
+
+--S 1154 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1154
+
+--S 1155 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1155
+
+)clear all
+
+--S 1156 of 1369
+t0:=1/((a+b/x)^(5/2)*x^7)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R +-------+
+--R 2 7 6 2 5 |a x + b
+--R (a x + 2a b x + b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1156
+
+--S 1157 of 1369
+r0:=-2/3*a^5/(b^6*(a+b/x)^(3/2))-20/3*a^2*(a+b/x)^(3/2)/b^6+_
+ 2*a*(a+b/x)^(5/2)/b^6-2/7*(a+b/x)^(7/2)/b^6+_
+ 10*a^4/(b^6*sqrt(a+b/x))+20*a^3*sqrt(a+b/x)/b^6
+--R
+--R
+--R 5 5 4 4 3 2 3 2 3 2 4 5
+--R 512a x + 768a b x + 192a b x - 32a b x + 12a b x - 6b
+--R (2) ----------------------------------------------------------
+--R +-------+
+--R 6 5 7 4 |a x + b
+--R (21a b x + 21b x ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 1157
+
+--S 1158 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 5 4 4 3 2 3 2 3 2 4 5
+--R 512a x + 768a b x + 192a b x - 32a b x + 12a b x - 6b
+--R (3) ----------------------------------------------------------
+--R +-------+
+--R 6 5 7 4 |a x + b
+--R (21a b x + 21b x ) |-------
+--R \| x
+--R Type: Union(Expression(Integer),...)
+--E 1158
+
+--S 1159 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1159
+
+--S 1160 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1160
+
+)clear all
+
+--S 1161 of 1369
+t0:=(a+b/x)*x^(5/2)
+--R
+--R
+--R 2 +-+
+--R (1) (a x + b x)\|x
+--R Type: Expression(Integer)
+--E 1161
+
+--S 1162 of 1369
+r0:=2/5*b*x^(5/2)+2/7*a*x^(7/2)
+--R
+--R
+--R 3 2 +-+
+--R (10a x + 14b x )\|x
+--R (2) ---------------------
+--R 35
+--R Type: Expression(Integer)
+--E 1162
+
+--S 1163 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +-+
+--R (10a x + 14b x )\|x
+--R (3) ---------------------
+--R 35
+--R Type: Union(Expression(Integer),...)
+--E 1163
+
+--S 1164 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1164
+
+--S 1165 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1165
+
+)clear all
+
+--S 1166 of 1369
+t0:=(a+b/x)*x^(3/2)
+--R
+--R
+--R +-+
+--R (1) (a x + b)\|x
+--R Type: Expression(Integer)
+--E 1166
+
+--S 1167 of 1369
+r0:=2/3*b*x^(3/2)+2/5*a*x^(5/2)
+--R
+--R
+--R 2 +-+
+--R (6a x + 10b x)\|x
+--R (2) -------------------
+--R 15
+--R Type: Expression(Integer)
+--E 1167
+
+--S 1168 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R (6a x + 10b x)\|x
+--R (3) -------------------
+--R 15
+--R Type: Union(Expression(Integer),...)
+--E 1168
+
+--S 1169 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1169
+
+--S 1170 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1170
+
+)clear all
+
+--S 1171 of 1369
+t0:=(a+b/x)*x^(1/2)
+--R
+--R
+--R +-+
+--R (a x + b)\|x
+--R (1) -------------
+--R x
+--R Type: Expression(Integer)
+--E 1171
+
+--S 1172 of 1369
+r0:=2/3*a*x^(3/2)+2*b*sqrt(x)
+--R
+--R
+--R +-+
+--R (2a x + 6b)\|x
+--R (2) ---------------
+--R 3
+--R Type: Expression(Integer)
+--E 1172
+
+--S 1173 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R (2a x + 6b)\|x
+--R (3) ---------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 1173
+
+--S 1174 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1174
+
+--S 1175 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1175
+
+)clear all
+
+--S 1176 of 1369
+t0:=(a+b/x)/x^(1/2)
+--R
+--R
+--R a x + b
+--R (1) -------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 1176
+
+--S 1177 of 1369
+r0:=-2*b/sqrt(x)+2*a*sqrt(x)
+--R
+--R
+--R 2a x - 2b
+--R (2) ---------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 1177
+
+--S 1178 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2a x - 2b
+--R (3) ---------
+--R +-+
+--R \|x
+--R Type: Union(Expression(Integer),...)
+--E 1178
+
+--S 1179 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1179
+
+--S 1180 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1180
+
+)clear all
+
+--S 1181 of 1369
+t0:=(a+b/x)/x^(3/2)
+--R
+--R
+--R a x + b
+--R (1) -------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1181
+
+--S 1182 of 1369
+r0:=-2/3*b/x^(3/2)-2*a/sqrt(x)
+--R
+--R
+--R - 6a x - 2b
+--R (2) -----------
+--R +-+
+--R 3x\|x
+--R Type: Expression(Integer)
+--E 1182
+
+--S 1183 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - 6a x - 2b
+--R (3) -----------
+--R +-+
+--R 3x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1183
+
+--S 1184 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1184
+
+--S 1185 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1185
+
+)clear all
+
+--S 1186 of 1369
+t0:=(a+b/x)/x^(5/2)
+--R
+--R
+--R a x + b
+--R (1) -------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1186
+
+--S 1187 of 1369
+r0:=-2/5*b/x^(5/2)-2/3*a/x^(3/2)
+--R
+--R
+--R - 10a x - 6b
+--R (2) ------------
+--R 2 +-+
+--R 15x \|x
+--R Type: Expression(Integer)
+--E 1187
+
+--S 1188 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R - 10a x - 6b
+--R (3) ------------
+--R 2 +-+
+--R 15x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1188
+
+--S 1189 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1189
+
+--S 1190 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1190
+
+)clear all
+
+--S 1191 of 1369
+t0:=(a+b/x)^2*x^(5/2)
+--R
+--R
+--R 2 2 2 +-+
+--R (1) (a x + 2a b x + b )\|x
+--R Type: Expression(Integer)
+--E 1191
+
+--S 1192 of 1369
+r0:=2/3*b^2*x^(3/2)+4/5*a*b*x^(5/2)+2/7*a^2*x^(7/2)
+--R
+--R
+--R 2 3 2 2 +-+
+--R (30a x + 84a b x + 70b x)\|x
+--R (2) -------------------------------
+--R 105
+--R Type: Expression(Integer)
+--E 1192
+
+--S 1193 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2 2 +-+
+--R (30a x + 84a b x + 70b x)\|x
+--R (3) -------------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 1193
+
+--S 1194 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1194
+
+--S 1195 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1195
+
+)clear all
+
+--S 1196 of 1369
+t0:=(a+b/x)^2*x^(3/2)
+--R
+--R
+--R 2 2 2 +-+
+--R (a x + 2a b x + b )\|x
+--R (1) ------------------------
+--R x
+--R Type: Expression(Integer)
+--E 1196
+
+--S 1197 of 1369
+r0:=4/3*a*b*x^(3/2)+2/5*a^2*x^(5/2)+2*b^2*sqrt(x)
+--R
+--R
+--R 2 2 2 +-+
+--R (6a x + 20a b x + 30b )\|x
+--R (2) ----------------------------
+--R 15
+--R Type: Expression(Integer)
+--E 1197
+
+--S 1198 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 +-+
+--R (6a x + 20a b x + 30b )\|x
+--R (3) ----------------------------
+--R 15
+--R Type: Union(Expression(Integer),...)
+--E 1198
+
+--S 1199 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1199
+
+--S 1200 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1200
+
+)clear all
+
+--S 1201 of 1369
+t0:=(a+b/x)^2*x^(1/2)
+--R
+--R
+--R 2 2 2 +-+
+--R (a x + 2a b x + b )\|x
+--R (1) ------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 1201
+
+--S 1202 of 1369
+r0:=2/3*a^2*x^(3/2)-2*b^2/sqrt(x)+4*a*b*sqrt(x)
+--R
+--R
+--R 2 2 2
+--R 2a x + 12a b x - 6b
+--R (2) ---------------------
+--R +-+
+--R 3\|x
+--R Type: Expression(Integer)
+--E 1202
+
+--S 1203 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R 2a x + 12a b x - 6b
+--R (3) ---------------------
+--R +-+
+--R 3\|x
+--R Type: Union(Expression(Integer),...)
+--E 1203
+
+--S 1204 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1204
+
+--S 1205 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1205
+
+)clear all
+
+--S 1206 of 1369
+t0:=(a+b/x)^2/x^(1/2)
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1206
+
+--S 1207 of 1369
+r0:=-2/3*b^2/x^(3/2)-4*a*b/sqrt(x)+2*a^2*sqrt(x)
+--R
+--R
+--R 2 2 2
+--R 6a x - 12a b x - 2b
+--R (2) ---------------------
+--R +-+
+--R 3x\|x
+--R Type: Expression(Integer)
+--E 1207
+
+--S 1208 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R 6a x - 12a b x - 2b
+--R (3) ---------------------
+--R +-+
+--R 3x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1208
+
+--S 1209 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1209
+
+--S 1210 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1210
+
+)clear all
+
+--S 1211 of 1369
+t0:=(a+b/x)^2/x^(3/2)
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1211
+
+--S 1212 of 1369
+r0:=-2/5*b^2/x^(5/2)-4/3*a*b/x^(3/2)-2*a^2/sqrt(x)
+--R
+--R
+--R 2 2 2
+--R - 30a x - 20a b x - 6b
+--R (2) ------------------------
+--R 2 +-+
+--R 15x \|x
+--R Type: Expression(Integer)
+--E 1212
+
+--S 1213 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R - 30a x - 20a b x - 6b
+--R (3) ------------------------
+--R 2 +-+
+--R 15x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1213
+
+--S 1214 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1214
+
+--S 1215 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1215
+
+)clear all
+
+--S 1216 of 1369
+t0:=(a+b/x)^2/x^(5/2)
+--R
+--R
+--R 2 2 2
+--R a x + 2a b x + b
+--R (1) ------------------
+--R 4 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1216
+
+--S 1217 of 1369
+r0:=-2/7*b^2/x^(7/2)-4/5*a*b/x^(5/2)-2/3*a^2/x^(3/2)
+--R
+--R
+--R 2 2 2
+--R - 70a x - 84a b x - 30b
+--R (2) -------------------------
+--R 3 +-+
+--R 105x \|x
+--R Type: Expression(Integer)
+--E 1217
+
+--S 1218 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R - 70a x - 84a b x - 30b
+--R (3) -------------------------
+--R 3 +-+
+--R 105x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1218
+
+--S 1219 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1219
+
+--S 1220 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1220
+
+)clear all
+
+--S 1221 of 1369
+t0:=(a+b/x)^3*x^(5/2)
+--R
+--R
+--R 3 3 2 2 2 3 +-+
+--R (a x + 3a b x + 3a b x + b )\|x
+--R (1) ----------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 1221
+
+--S 1222 of 1369
+r0:=2*a*b^2*x^(3/2)+6/5*a^2*b*x^(5/2)+2/7*a^3*x^(7/2)+2*b^3*sqrt(x)
+--R
+--R
+--R 3 3 2 2 2 3 +-+
+--R (10a x + 42a b x + 70a b x + 70b )\|x
+--R (2) ----------------------------------------
+--R 35
+--R Type: Expression(Integer)
+--E 1222
+
+--S 1223 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3 +-+
+--R (10a x + 42a b x + 70a b x + 70b )\|x
+--R (3) ----------------------------------------
+--R 35
+--R Type: Union(Expression(Integer),...)
+--E 1223
+
+--S 1224 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1224
+
+--S 1225 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1225
+
+)clear all
+
+--S 1226 of 1369
+t0:=(a+b/x)^3*x^(3/2)
+--R
+--R
+--R 3 3 2 2 2 3 +-+
+--R (a x + 3a b x + 3a b x + b )\|x
+--R (1) ----------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 1226
+
+--S 1227 of 1369
+r0:=2*a^2*b*x^(3/2)+2/5*a^3*x^(5/2)-2*b^3/sqrt(x)+6*a*b^2*sqrt(x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R 2a x + 10a b x + 30a b x - 10b
+--R (2) ---------------------------------
+--R +-+
+--R 5\|x
+--R Type: Expression(Integer)
+--E 1227
+
+--S 1228 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R 2a x + 10a b x + 30a b x - 10b
+--R (3) ---------------------------------
+--R +-+
+--R 5\|x
+--R Type: Union(Expression(Integer),...)
+--E 1228
+
+--S 1229 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1229
+
+--S 1230 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1230
+
+)clear all
+
+--S 1231 of 1369
+t0:=(a+b/x)^3*x^(1/2)
+--R
+--R
+--R 3 3 2 2 2 3 +-+
+--R (a x + 3a b x + 3a b x + b )\|x
+--R (1) ----------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 1231
+
+--S 1232 of 1369
+r0:=-2/3*b^3/x^(3/2)+2/3*a^3*x^(3/2)-6*a*b^2/sqrt(x)+6*a^2*b*sqrt(x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R 2a x + 18a b x - 18a b x - 2b
+--R (2) --------------------------------
+--R +-+
+--R 3x\|x
+--R Type: Expression(Integer)
+--E 1232
+
+--S 1233 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R 2a x + 18a b x - 18a b x - 2b
+--R (3) --------------------------------
+--R +-+
+--R 3x\|x
+--R Type: Union(Expression(Integer),...)
+--E 1233
+
+--S 1234 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1234
+
+--S 1235 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1235
+
+)clear all
+
+--S 1236 of 1369
+t0:=(a+b/x)^3/x^(1/2)
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1236
+
+--S 1237 of 1369
+r0:=-2/5*b^3/x^(5/2)-2*a*b^2/x^(3/2)-6*a^2*b/sqrt(x)+2*a^3*sqrt(x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R 10a x - 30a b x - 10a b x - 2b
+--R (2) ---------------------------------
+--R 2 +-+
+--R 5x \|x
+--R Type: Expression(Integer)
+--E 1237
+
+--S 1238 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R 10a x - 30a b x - 10a b x - 2b
+--R (3) ---------------------------------
+--R 2 +-+
+--R 5x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1238
+
+--S 1239 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1239
+
+--S 1240 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1240
+
+)clear all
+
+--S 1241 of 1369
+t0:=(a+b/x)^3/x^(3/2)
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 4 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1241
+
+--S 1242 of 1369
+r0:=-2/7*b^3/x^(7/2)-6/5*a*b^2/x^(5/2)-2*a^2*b/x^(3/2)-2*a^3/sqrt(x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 70a x - 70a b x - 42a b x - 10b
+--R (2) ------------------------------------
+--R 3 +-+
+--R 35x \|x
+--R Type: Expression(Integer)
+--E 1242
+
+--S 1243 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 70a x - 70a b x - 42a b x - 10b
+--R (3) ------------------------------------
+--R 3 +-+
+--R 35x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1243
+
+--S 1244 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1244
+
+--S 1245 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1245
+
+)clear all
+
+--S 1246 of 1369
+t0:=(a+b/x)^3/x^(5/2)
+--R
+--R
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) ----------------------------
+--R 5 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 1246
+
+--S 1247 of 1369
+r0:=-2/9*b^3/x^(9/2)-6/7*a*b^2/x^(7/2)-6/5*a^2*b/x^(5/2)-2/3*a^3/x^(3/2)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 210a x - 378a b x - 270a b x - 70b
+--R (2) ---------------------------------------
+--R 4 +-+
+--R 315x \|x
+--R Type: Expression(Integer)
+--E 1247
+
+--S 1248 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 2 3
+--R - 210a x - 378a b x - 270a b x - 70b
+--R (3) ---------------------------------------
+--R 4 +-+
+--R 315x \|x
+--R Type: Union(Expression(Integer),...)
+--E 1248
+
+--S 1249 of 1369
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1249
+
+--S 1250 of 1369
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1250
+
+)clear all
+
+--S 1251 of 1369
+t0:=x^(5/2)/(a+b/x)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) -------
+--R a x + b
+--R Type: Expression(Integer)
+--E 1251
+
+--S 1252 of 1369
+r0:=2/3*b^2*x^(3/2)/a^3-2/5*b*x^(5/2)/a^2+2/7*x^(7/2)/a+2*b^(7/2)*_
+ atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(9/2)-2*b^3*sqrt(x)/a^4
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 3 +-+ \|a \|x 3 3 2 2 2 3 +-+ +-+
+--R 210b \|b atan(--------) + (30a x - 42a b x + 70a b x - 210b )\|a \|x
+--R +-+
+--R \|b
+--R -----------------------------------------------------------------------
+--R 4 +-+
+--R 105a \|a
+--R Type: Expression(Integer)
+--E 1252
+
+--S 1253 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b
+--R 3 | b \| a
+--R 105b |- - log(----------------------)
+--R \| a a x + b
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (30a x - 42a b x + 70a b x - 210b )\|x
+--R /
+--R 4
+--R 105a
+--R ,
+--R +-+ +-+
+--R 3 |b \|x 3 3 2 2 2 3 +-+
+--R 210b |- atan(----) + (30a x - 42a b x + 70a b x - 210b )\|x
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R ---------------------------------------------------------------]
+--R 4
+--R 105a
+--R Type: Union(List(Expression(Integer)),...)
+--E 1253
+
+--S 1254 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b +-+ +-+
+--R 3 | b +-+ \| a 3 +-+ \|a \|x
+--R b |- - \|a log(----------------------) - 2b \|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) ---------------------------------------------------------------
+--R 4 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1254
+
+--S 1255 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1255
+
+--S 1256 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R 3 +-+ |b \|x 3 +-+ \|a \|x
+--R 2b \|a |- atan(----) - 2b \|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) ---------------------------------------------
+--R 4 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1256
+
+--S 1257 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1257
+
+)clear all
+
+--S 1258 of 1369
+t0:=x^(3/2)/(a+b/x)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) -------
+--R a x + b
+--R Type: Expression(Integer)
+--E 1258
+
+--S 1259 of 1369
+r0:=-2/3*b*x^(3/2)/a^2+2/5*x^(5/2)/a-2*b^(5/2)*atan(sqrt(a)*_
+ sqrt(x)/sqrt(b))/a^(7/2)+2*b^2*sqrt(x)/a^3
+--R
+--R
+--R +-+ +-+
+--R 2 +-+ \|a \|x 2 2 2 +-+ +-+
+--R - 30b \|b atan(--------) + (6a x - 10a b x + 30b )\|a \|x
+--R +-+
+--R \|b
+--R (2) -----------------------------------------------------------
+--R 3 +-+
+--R 15a \|a
+--R Type: Expression(Integer)
+--E 1259
+
+--S 1260 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b
+--R 2 | b \| a 2 2 2 +-+
+--R 15b |- - log(------------------------) + (6a x - 10a b x + 30b )\|x
+--R \| a a x + b
+--R [----------------------------------------------------------------------,
+--R 3
+--R 15a
+--R +-+ +-+
+--R 2 |b \|x 2 2 2 +-+
+--R - 30b |- atan(----) + (6a x - 10a b x + 30b )\|x
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R ---------------------------------------------------]
+--R 3
+--R 15a
+--R Type: Union(List(Expression(Integer)),...)
+--E 1260
+
+--S 1261 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b +-+ +-+
+--R 2 | b +-+ \| a 2 +-+ \|a \|x
+--R b |- - \|a log(------------------------) + 2b \|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) -----------------------------------------------------------------
+--R 3 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1261
+
+--S 1262 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1262
+
+--S 1263 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R 2 +-+ |b \|x 2 +-+ \|a \|x
+--R - 2b \|a |- atan(----) + 2b \|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) -----------------------------------------------
+--R 3 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1263
+
+--S 1264 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1264
+
+)clear all
+
+--S 1265 of 1369
+t0:=x^(1/2)/(a+b/x)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) -------
+--R a x + b
+--R Type: Expression(Integer)
+--E 1265
+
+--S 1266 of 1369
+r0:=2/3*x^(3/2)/a+2*b^(3/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(5/2)-_
+ 2*b*sqrt(x)/a^2
+--R
+--R
+--R +-+ +-+
+--R +-+ \|a \|x +-+ +-+
+--R 6b\|b atan(--------) + (2a x - 6b)\|a \|x
+--R +-+
+--R \|b
+--R (2) ------------------------------------------
+--R 2 +-+
+--R 3a \|a
+--R Type: Expression(Integer)
+--E 1266
+
+--S 1267 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b
+--R | b \| a +-+
+--R 3b |- - log(----------------------) + (2a x - 6b)\|x
+--R \| a a x + b
+--R [-----------------------------------------------------,
+--R 2
+--R 3a
+--R +-+ +-+
+--R |b \|x +-+
+--R 6b |- atan(----) + (2a x - 6b)\|x
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R ----------------------------------]
+--R 2
+--R 3a
+--R Type: Union(List(Expression(Integer)),...)
+--E 1267
+
+--S 1268 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b +-+ +-+
+--R | b +-+ \| a +-+ \|a \|x
+--R b |- - \|a log(----------------------) - 2b\|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1268
+
+--S 1269 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1269
+
+--S 1270 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R +-+ |b \|x +-+ \|a \|x
+--R 2b\|a |- atan(----) - 2b\|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) -------------------------------------------
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1270
+
+--S 1271 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1271
+
+)clear all
+
+--S 1272 of 1369
+t0:=1/((a+b/x)*x^(1/2))
+--R
+--R
+--R x
+--R (1) -------------
+--R +-+
+--R (a x + b)\|x
+--R Type: Expression(Integer)
+--E 1272
+
+--S 1273 of 1369
+r0:=-2*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(b)/a^(3/2)+2*sqrt(x)/a
+--R
+--R
+--R +-+ +-+
+--R +-+ \|a \|x +-+ +-+
+--R - 2\|b atan(--------) + 2\|a \|x
+--R +-+
+--R \|b
+--R (2) ---------------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 1273
+
+--S 1274 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+
+--R +---+ |b \|x +-+
+--R | b +-+ - 2 |- atan(---- + 2\|x
+--R +---+ - 2a |- - \|x + a x - b \|a +-+
+--R | b \| a +-+ |b
+--R |- - log(------------------------) + 2\|x |-
+--R \| a a x + b \|a
+--R [-------------------------------------------,-------------------------]
+--R a a
+--R Type: Union(List(Expression(Integer)),...)
+--E 1274
+
+--S 1275 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b +-+ +-+
+--R | b +-+ \| a +-+ \|a \|x
+--R |- - \|a log(------------------------) + 2\|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 1275
+
+--S 1276 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1276
+
+--S 1277 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R +-+ |b \|x +-+ \|a \|x
+--R - 2\|a |- atan(----) + 2\|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) -------------------------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 1277
+
+--S 1278 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1278
+
+)clear all
+
+--S 1279 of 1369
+t0:=1/((a+b/x)*x^(3/2))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +-+
+--R (a x + b)\|x
+--R Type: Expression(Integer)
+--E 1279
+
+--S 1280 of 1369
+r0:=2*atan(sqrt(a)*sqrt(x)/sqrt(b))/(sqrt(a)*sqrt(b))
+--R
+--R
+--R +-+ +-+
+--R \|a \|x
+--R 2atan(--------)
+--R +-+
+--R \|b
+--R (2) ---------------
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 1280
+
+--S 1281 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +-----+ +---+ +-+
+--R 2a b\|x + (a x - b)\|- a b \|a b \|x
+--R log(----------------------------) 2atan(----------)
+--R a x + b b
+--R (3) [---------------------------------,-----------------]
+--R +-----+ +---+
+--R \|- a b \|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1281
+
+--S 1282 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-+ +-----+ +-+ +-+
+--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x
+--R \|a \|b log(----------------------------) - 2\|- a b atan(--------)
+--R a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1282
+
+--S 1283 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1283
+
+--S 1284 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+ +-+ +-+
+--R +-+ +-+ \|a b \|x +---+ \|a \|x
+--R 2\|a \|b atan(----------) - 2\|a b atan(--------)
+--R b +-+
+--R \|b
+--R (6) -------------------------------------------------
+--R +-+ +-+ +---+
+--R \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1284
+
+--S 1285 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1285
+
+)clear all
+
+--S 1286 of 1369
+t0:=1/((a+b/x)*x^(5/2))
+--R
+--R
+--R 1
+--R (1) ----------------
+--R 2 +-+
+--R (a x + b x)\|x
+--R Type: Expression(Integer)
+--E 1286
+
+--S 1287 of 1369
+r0:=-2*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(a)/b^(3/2)+(-2)/(b*sqrt(x))
+--R
+--R
+--R +-+ +-+
+--R +-+ +-+ \|a \|x +-+
+--R - 2\|a \|x atan(--------) - 2\|b
+--R +-+
+--R \|b
+--R (2) ---------------------------------
+--R +-+ +-+
+--R b\|b \|x
+--R Type: Expression(Integer)
+--E 1287
+
+--S 1288 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+
+--R +---+ |a +-+ a\|x
+--R | a +-+ - 2 |- \|x atan(----- - 2
+--R +---+ - 2b |- - \|x + a x - b \|b +-+
+--R | a +-+ \| b |a
+--R |- - \|x log(------------------------) - 2 b |-
+--R \| b a x + b \|b
+--R [-------------------------------------------,--------------------------]
+--R +-+ +-+
+--R b\|x b\|x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1288
+
+--S 1289 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b +-+ +-+
+--R | a +-+ \| b +-+ \|a \|x
+--R |- - \|b log(------------------------) + 2\|a atan(--------)
+--R \| b a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 1289
+
+--S 1290 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1290
+
+--S 1291 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R |a +-+ a\|x +-+ \|a \|x
+--R - 2 |- \|b atan(----- + 2\|a atan(--------)
+--R \|b +-+ +-+
+--R |a \|b
+--R b |-
+--R \|b
+--R (6) --------------------------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 1291
+
+--S 1292 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1292
+
+)clear all
+
+--S 1293 of 1369
+t0:=1/((a+b/x)*x^(7/2))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R 3 2 +-+
+--R (a x + b x )\|x
+--R Type: Expression(Integer)
+--E 1293
+
+--S 1294 of 1369
+r0:=(-2/3)/(b*x^(3/2))+2*a^(3/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/b^(5/2)+_
+ 2*a/(b^2*sqrt(x))
+--R
+--R
+--R +-+ +-+
+--R +-+ +-+ \|a \|x +-+
+--R 6a x\|a \|x atan(--------) + (6a x - 2b)\|b
+--R +-+
+--R \|b
+--R (2) --------------------------------------------
+--R 2 +-+ +-+
+--R 3b x\|b \|x
+--R Type: Expression(Integer)
+--E 1294
+
+--S 1295 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a +-+
+--R +---+ 2b |- - \|x + a x - b
+--R | a +-+ \| b
+--R 3a x |- - \|x log(----------------------) + 6a x - 2b
+--R \| b a x + b
+--R [-----------------------------------------------------,
+--R 2 +-+
+--R 3b x\|x
+--R +-+ +-+
+--R |a +-+ a\|x
+--R 6a x |- \|x atan(-----) + 6a x - 2b
+--R \|b +-+
+--R |a
+--R b |-
+--R \|b
+--R -----------------------------------]
+--R 2 +-+
+--R 3b x\|x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1295
+
+--S 1296 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a +-+
+--R +---+ 2b |- - \|x + a x - b +-+ +-+
+--R | a +-+ \| b +-+ \|a \|x
+--R a |- - \|b log(----------------------) - 2a\|a atan(--------)
+--R \| b a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------
+--R 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 1296
+
+--S 1297 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1297
+
+--S 1298 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R |a +-+ a\|x +-+ \|a \|x
+--R 2a |- \|b atan(-----) - 2a\|a atan(--------)
+--R \|b +-+ +-+
+--R |a \|b
+--R b |-
+--R \|b
+--R (6) --------------------------------------------
+--R 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 1298
+
+--S 1299 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1299
+
+)clear all
+
+--S 1300 of 1369
+t0:=1/((a+b/x)*x^(9/2))
+--R
+--R
+--R 1
+--R (1) -----------------
+--R 4 3 +-+
+--R (a x + b x )\|x
+--R Type: Expression(Integer)
+--E 1300
+
+--S 1301 of 1369
+r0:=(-2/5)/(b*x^(5/2))+2/3*a/(b^2*x^(3/2))-2*a^(5/2)*atan(sqrt(a)*_
+ sqrt(x)/sqrt(b))/b^(7/2)-2*a^2/(b^3*sqrt(x))
+--R
+--R
+--R +-+ +-+
+--R 2 2 +-+ +-+ \|a \|x 2 2 2 +-+
+--R - 30a x \|a \|x atan(--------) + (- 30a x + 10a b x - 6b )\|b
+--R +-+
+--R \|b
+--R (2) ---------------------------------------------------------------
+--R 3 2 +-+ +-+
+--R 15b x \|b \|x
+--R Type: Expression(Integer)
+--E 1301
+
+--S 1302 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b
+--R 2 2 | a +-+ \| b 2 2 2
+--R 15a x |- - \|x log(------------------------) - 30a x + 10a b x - 6b
+--R \| b a x + b
+--R [----------------------------------------------------------------------,
+--R 3 2 +-+
+--R 15b x \|x
+--R +-+ +-+
+--R 2 2 |a +-+ a\|x 2 2 2
+--R - 30a x |- \|x atan(-----) - 30a x + 10a b x - 6b
+--R \|b +-+
+--R |a
+--R b |-
+--R \|b
+--R ----------------------------------------------------]
+--R 3 2 +-+
+--R 15b x \|x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1302
+
+--S 1303 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b +-+ +-+
+--R 2 | a +-+ \| b 2 +-+ \|a \|x
+--R a |- - \|b log(------------------------) + 2a \|a atan(--------)
+--R \| b a x + b +-+
+--R \|b
+--R (4) -----------------------------------------------------------------
+--R 3 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 1303
+
+--S 1304 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1304
+
+--S 1305 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R 2 |a +-+ a\|x 2 +-+ \|a \|x
+--R - 2a |- \|b atan(-----) + 2a \|a atan(--------)
+--R \|b +-+ +-+
+--R |a \|b
+--R b |-
+--R \|b
+--R (6) ------------------------------------------------
+--R 3 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 1305
+
+--S 1306 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1306
+
+)clear all
+
+--S 1307 of 1369
+t0:=x^(5/2)/(a+b/x)^2
+--R
+--R
+--R 4 +-+
+--R x \|x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Expression(Integer)
+--E 1307
+
+--S 1308 of 1369
+r0:=3*b^2*x^(3/2)/a^4-9/5*b*x^(5/2)/a^3+9/7*x^(7/2)/a^2-x^(9/2)/_
+ (a*(b+a*x))+9*b^(7/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(11/2)-_
+ 9*b^3*sqrt(x)/a^5
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 3 4 +-+ \|a \|x
+--R (315a b x + 315b )\|b atan(--------)
+--R +-+
+--R \|b
+--R +
+--R 4 4 3 3 2 2 2 3 4 +-+ +-+
+--R (10a x - 18a b x + 42a b x - 210a b x - 315b )\|a \|x
+--R /
+--R 6 5 +-+
+--R (35a x + 35a b)\|a
+--R Type: Expression(Integer)
+--E 1308
+
+--S 1309 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b
+--R 3 4 | b \| a
+--R (315a b x + 315b ) |- - log(----------------------)
+--R \| a a x + b
+--R +
+--R 4 4 3 3 2 2 2 3 4 +-+
+--R (20a x - 36a b x + 84a b x - 420a b x - 630b )\|x
+--R /
+--R 6 5
+--R 70a x + 70a b
+--R ,
+--R
+--R +-+ +-+
+--R 3 4 |b \|x
+--R (315a b x + 315b ) |- atan(----)
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R +
+--R 4 4 3 3 2 2 2 3 4 +-+
+--R (10a x - 18a b x + 42a b x - 210a b x - 315b )\|x
+--R /
+--R 6 5
+--R 35a x + 35a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1309
+
+--S 1310 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b +-+ +-+
+--R 3 | b +-+ \| a 3 +-+ \|a \|x
+--R 9b |- - \|a log(----------------------) - 18b \|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) -----------------------------------------------------------------
+--R 5 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 1310
+
+--S 1311 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1311
+
+--S 1312 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R 3 +-+ |b \|x 3 +-+ \|a \|x
+--R 9b \|a |- atan(----) - 9b \|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) ---------------------------------------------
+--R 5 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1312
+
+--S 1313 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1313
+
+)clear all
+
+--S 1314 of 1369
+t0:=x^(3/2)/(a+b/x)^2
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Expression(Integer)
+--E 1314
+
+--S 1315 of 1369
+r0:=-7/3*b*x^(3/2)/a^3+7/5*x^(5/2)/a^2-x^(7/2)/(a*(b+a*x))-_
+ 7*b^(5/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(9/2)+7*b^2*sqrt(x)/a^4
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 2 3 +-+ \|a \|x
+--R (- 105a b x - 105b )\|b atan(--------)
+--R +-+
+--R \|b
+--R +
+--R 3 3 2 2 2 3 +-+ +-+
+--R (6a x - 14a b x + 70a b x + 105b )\|a \|x
+--R /
+--R 5 4 +-+
+--R (15a x + 15a b)\|a
+--R Type: Expression(Integer)
+--E 1315
+
+--S 1316 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b
+--R 2 3 | b \| a
+--R (105a b x + 105b ) |- - log(------------------------)
+--R \| a a x + b
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (12a x - 28a b x + 140a b x + 210b )\|x
+--R /
+--R 5 4
+--R 30a x + 30a b
+--R ,
+--R
+--R +-+ +-+
+--R 2 3 |b \|x
+--R (- 105a b x - 105b ) |- atan(----)
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (6a x - 14a b x + 70a b x + 105b )\|x
+--R /
+--R 5 4
+--R 15a x + 15a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1316
+
+--S 1317 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b +-+ +-+
+--R 2 | b +-+ \| a 2 +-+ \|a \|x
+--R 7b |- - \|a log(------------------------) + 14b \|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------------
+--R 4 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 1317
+
+--S 1318 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1318
+
+--S 1319 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R 2 +-+ |b \|x 2 +-+ \|a \|x
+--R - 7b \|a |- atan(----) + 7b \|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) -----------------------------------------------
+--R 4 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1319
+
+--S 1320 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1320
+
+)clear all
+
+--S 1321 of 1369
+t0:=x^(1/2)/(a+b/x)^2
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ------------------
+--R 2 2 2
+--R a x + 2a b x + b
+--R Type: Expression(Integer)
+--E 1321
+
+--S 1322 of 1369
+r0:=5/3*x^(3/2)/a^2-x^(5/2)/(a*(b+a*x))+5*b^(3/2)*atan(sqrt(a)*_
+ sqrt(x)/sqrt(b))/a^(7/2)-5*b*sqrt(x)/a^3
+--R
+--R
+--R +-+ +-+
+--R 2 +-+ \|a \|x 2 2 2 +-+ +-+
+--R (15a b x + 15b )\|b atan(--------) + (2a x - 10a b x - 15b )\|a \|x
+--R +-+
+--R \|b
+--R (2) ---------------------------------------------------------------------
+--R 4 3 +-+
+--R (3a x + 3a b)\|a
+--R Type: Expression(Integer)
+--E 1322
+
+--S 1323 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b
+--R 2 | b \| a
+--R (15a b x + 15b ) |- - log(----------------------)
+--R \| a a x + b
+--R +
+--R 2 2 2 +-+
+--R (4a x - 20a b x - 30b )\|x
+--R /
+--R 4 3
+--R 6a x + 6a b
+--R ,
+--R +-+ +-+
+--R 2 |b \|x 2 2 2 +-+
+--R (15a b x + 15b ) |- atan(----) + (2a x - 10a b x - 15b )\|x
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R -------------------------------------------------------------]
+--R 4 3
+--R 3a x + 3a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1323
+
+--S 1324 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b +-+ +-+
+--R | b +-+ \| a +-+ \|a \|x
+--R 5b |- - \|a log(----------------------) - 10b\|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) ---------------------------------------------------------------
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 1324
+
+--S 1325 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1325
+
+--S 1326 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R +-+ |b \|x +-+ \|a \|x
+--R 5b\|a |- atan(----) - 5b\|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) -------------------------------------------
+--R 3 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1326
+
+--S 1327 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1327
+
+)clear all
+
+--S 1328 of 1369
+t0:=1/((a+b/x)^2*x^(1/2))
+--R
+--R
+--R 2
+--R x
+--R (1) ------------------------
+--R 2 2 2 +-+
+--R (a x + 2a b x + b )\|x
+--R Type: Expression(Integer)
+--E 1328
+
+--S 1329 of 1369
+r0:=-x^(3/2)/(a*(b+a*x))-3*atan(sqrt(a)*sqrt(x)/sqrt(b))*_
+ sqrt(b)/a^(5/2)+3*sqrt(x)/a^2
+--R
+--R
+--R +-+ +-+
+--R +-+ \|a \|x +-+ +-+
+--R (- 3a x - 3b)\|b atan(--------) + (2a x + 3b)\|a \|x
+--R +-+
+--R \|b
+--R (2) -----------------------------------------------------
+--R 3 2 +-+
+--R (a x + a b)\|a
+--R Type: Expression(Integer)
+--E 1329
+
+--S 1330 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b
+--R | b \| a +-+
+--R (3a x + 3b) |- - log(------------------------) + (4a x + 6b)\|x
+--R \| a a x + b
+--R [----------------------------------------------------------------,
+--R 3 2
+--R 2a x + 2a b
+--R +-+ +-+
+--R |b \|x +-+
+--R (- 3a x - 3b) |- atan(----) + (2a x + 3b)\|x
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R ---------------------------------------------]
+--R 3 2
+--R a x + a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1330
+
+--S 1331 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b +-+ +-+
+--R | b +-+ \| a +-+ \|a \|x
+--R 3 |- - \|a log(------------------------ + 6\|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) --------------------------------------------------------------
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 1331
+
+--S 1332 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1332
+
+--S 1333 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R +-+ |b \|x +-+ \|a \|x
+--R - 3\|a |- atan(----) + 3\|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) -------------------------------------------
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 1333
+
+--S 1334 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1334
+
+)clear all
+
+--S 1335 of 1369
+t0:=1/((a+b/x)^2*x^(3/2))
+--R
+--R
+--R x
+--R (1) ------------------------
+--R 2 2 2 +-+
+--R (a x + 2a b x + b )\|x
+--R Type: Expression(Integer)
+--E 1335
+
+--S 1336 of 1369
+r0:=atan(sqrt(a)*sqrt(x)/sqrt(b))/(a^(3/2)*sqrt(b))-sqrt(x)/(a*(b+a*x))
+--R
+--R
+--R +-+ +-+
+--R \|a \|x +-+ +-+ +-+
+--R (a x + b)atan(--------) - \|a \|b \|x
+--R +-+
+--R \|b
+--R (2) --------------------------------------
+--R 2 +-+ +-+
+--R (a x + a b)\|a \|b
+--R Type: Expression(Integer)
+--E 1336
+
+--S 1337 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-----+
+--R 2a b\|x + (a x - b)\|- a b +-----+ +-+
+--R (a x + b)log(----------------------------) - 2\|- a b \|x
+--R a x + b
+--R [----------------------------------------------------------,
+--R 2 +-----+
+--R (2a x + 2a b)\|- a b
+--R +---+ +-+
+--R \|a b \|x +---+ +-+
+--R (a x + b)atan(----------) - \|a b \|x
+--R b
+--R --------------------------------------]
+--R 2 +---+
+--R (a x + a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1337
+
+--S 1338 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-+ +-----+ +-+ +-+
+--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x
+--R \|a \|b log(----------------------------) - 2\|- a b atan(--------)
+--R a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 2a\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1338
+
+--S 1339 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1339
+
+--S 1340 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+ +-+ +-+
+--R +-+ +-+ \|a b \|x +---+ \|a \|x
+--R \|a \|b atan(----------) - \|a b atan(--------)
+--R b +-+
+--R \|b
+--R (6) -----------------------------------------------
+--R +-+ +-+ +---+
+--R a\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1340
+
+--S 1341 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1341
+
+)clear all
+
+--S 1342 of 1369
+t0:=1/((a+b/x)^2*x^(5/2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R 2 2 2 +-+
+--R (a x + 2a b x + b )\|x
+--R Type: Expression(Integer)
+--E 1342
+
+--S 1343 of 1369
+r0:=atan(sqrt(a)*sqrt(x)/sqrt(b))/(b^(3/2)*sqrt(a))+sqrt(x)/(b*(b+a*x))
+--R
+--R
+--R +-+ +-+
+--R \|a \|x +-+ +-+ +-+
+--R (a x + b)atan(--------) + \|a \|b \|x
+--R +-+
+--R \|b
+--R (2) --------------------------------------
+--R 2 +-+ +-+
+--R (a b x + b )\|a \|b
+--R Type: Expression(Integer)
+--E 1343
+
+--S 1344 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-----+
+--R 2a b\|x + (a x - b)\|- a b +-----+ +-+
+--R (a x + b)log(----------------------------) + 2\|- a b \|x
+--R a x + b
+--R [----------------------------------------------------------,
+--R 2 +-----+
+--R (2a b x + 2b )\|- a b
+--R +---+ +-+
+--R \|a b \|x +---+ +-+
+--R (a x + b)atan(----------) + \|a b \|x
+--R b
+--R --------------------------------------]
+--R 2 +---+
+--R (a b x + b )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 1344
+
+--S 1345 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +-+ +-----+ +-+ +-+
+--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x
+--R \|a \|b log(----------------------------) - 2\|- a b atan(--------)
+--R a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 2b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1345
+
+--S 1346 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1346
+
+--S 1347 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+ +-+ +-+
+--R +-+ +-+ \|a b \|x +---+ \|a \|x
+--R \|a \|b atan(----------) - \|a b atan(--------)
+--R b +-+
+--R \|b
+--R (6) -----------------------------------------------
+--R +-+ +-+ +---+
+--R b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1347
+
+--S 1348 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1348
+
+)clear all
+
+--S 1349 of 1369
+t0:=1/((a+b/x)^2*x^(7/2))
+--R
+--R
+--R 1
+--R (1) --------------------------
+--R 2 3 2 2 +-+
+--R (a x + 2a b x + b x)\|x
+--R Type: Expression(Integer)
+--E 1349
+
+--S 1350 of 1369
+r0:=-3*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(a)/b^(5/2)+(-3)/_
+ (b^2*sqrt(x))+1/(b*(b+a*x)*sqrt(x))
+--R
+--R
+--R +-+ +-+
+--R +-+ +-+ \|a \|x +-+
+--R (- 3a x - 3b)\|a \|x atan(--------) + (- 3a x - 2b)\|b
+--R +-+
+--R \|b
+--R (2) -------------------------------------------------------
+--R 2 3 +-+ +-+
+--R (a b x + b )\|b \|x
+--R Type: Expression(Integer)
+--E 1350
+
+--S 1351 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b
+--R | a +-+ \| b
+--R (3a x + 3b) |- - \|x log(------------------------) - 6a x - 4b
+--R \| b a x + b
+--R [--------------------------------------------------------------,
+--R 2 3 +-+
+--R (2a b x + 2b )\|x
+--R +-+ +-+
+--R |a +-+ a\|x
+--R (- 3a x - 3b) |- \|x atan(-----) - 3a x - 2b
+--R \|b +-+
+--R |a
+--R b |-
+--R \|b
+--R --------------------------------------------]
+--R 2 3 +-+
+--R (a b x + b )\|x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1351
+
+--S 1352 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b +-+ +-+
+--R | a +-+ \| b +-+ \|a \|x
+--R 3 |- - \|b log(------------------------ + 6\|a atan(--------)
+--R \| b a x + b +-+
+--R \|b
+--R (4) --------------------------------------------------------------
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 1352
+
+--S 1353 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1353
+
+--S 1354 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R |a +-+ a\|x +-+ \|a \|x
+--R - 3 |- \|b atan(----- + 3\|a atan(--------)
+--R \|b +-+ +-+
+--R |a \|b
+--R b |-
+--R \|b
+--R (6) --------------------------------------------
+--R 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 1354
+
+--S 1355 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1355
+
+)clear all
+
+--S 1356 of 1369
+t0:=1/((a+b/x)^2*x^(9/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R 2 4 3 2 2 +-+
+--R (a x + 2a b x + b x )\|x
+--R Type: Expression(Integer)
+--E 1356
+
+--S 1357 of 1369
+r0:=(-5/3)/(b^2*x^(3/2))+1/(b*x^(3/2)*(b+a*x))+5*a^(3/2)*atan(sqrt(a)*_
+ sqrt(x)/sqrt(b))/b^(7/2)+5*a/(b^3*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 2 2 +-+ +-+ \|a \|x 2 2 2 +-+
+--R (15a x + 15a b x)\|a \|x atan(--------) + (15a x + 10a b x - 2b )\|b
+--R +-+
+--R \|b
+--R -----------------------------------------------------------------------
+--R 3 2 4 +-+ +-+
+--R (3a b x + 3b x)\|b \|x
+--R Type: Expression(Integer)
+--E 1357
+
+--S 1358 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a +-+
+--R +---+ 2b |- - \|x + a x - b
+--R 2 2 | a +-+ \| b 2 2
+--R (15a x + 15a b x) |- - \|x log(----------------------) + 30a x
+--R \| b a x + b
+--R +
+--R 2
+--R 20a b x - 4b
+--R /
+--R 3 2 4 +-+
+--R (6a b x + 6b x)\|x
+--R ,
+--R +-+ +-+
+--R 2 2 |a +-+ a\|x 2 2 2
+--R (15a x + 15a b x) |- \|x atan(-----) + 15a x + 10a b x - 2b
+--R \|b +-+
+--R |a
+--R b |-
+--R \|b
+--R --------------------------------------------------------------]
+--R 3 2 4 +-+
+--R (3a b x + 3b x)\|x
+--R Type: Union(List(Expression(Integer)),...)
+--E 1358
+
+--S 1359 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a +-+
+--R +---+ 2b |- - \|x + a x - b +-+ +-+
+--R | a +-+ \| b +-+ \|a \|x
+--R 5a |- - \|b log(----------------------) - 10a\|a atan(--------)
+--R \| b a x + b +-+
+--R \|b
+--R (4) ---------------------------------------------------------------
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 1359
+
+--S 1360 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1360
+
+--S 1361 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R |a +-+ a\|x +-+ \|a \|x
+--R 5a |- \|b atan(-----) - 5a\|a atan(--------)
+--R \|b +-+ +-+
+--R |a \|b
+--R b |-
+--R \|b
+--R (6) --------------------------------------------
+--R 3 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 1361
+
+--S 1362 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1362
+
+)clear all
+
+--S 1363 of 1369
+t0:=1/((a+b/x)^2*x^(11/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R 2 5 4 2 3 +-+
+--R (a x + 2a b x + b x )\|x
+--R Type: Expression(Integer)
+--E 1363
+
+--S 1364 of 1369
+r0:=(-7/5)/(b^2*x^(5/2))+7/3*a/(b^3*x^(3/2))+1/(b*x^(5/2)*(b+a*x))-_
+ 7*a^(5/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/b^(9/2)-7*a^2/(b^4*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 3 3 2 2 +-+ +-+ \|a \|x
+--R (- 105a x - 105a b x )\|a \|x atan(--------)
+--R +-+
+--R \|b
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (- 105a x - 70a b x + 14a b x - 6b )\|b
+--R /
+--R 4 3 5 2 +-+ +-+
+--R (15a b x + 15b x )\|b \|x
+--R Type: Expression(Integer)
+--E 1364
+
+--S 1365 of 1369
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b
+--R 3 3 2 2 | a +-+ \| b 3 3
+--R (105a x + 105a b x ) |- - \|x log(------------------------) - 210a x
+--R \| b a x + b
+--R +
+--R 2 2 2 3
+--R - 140a b x + 28a b x - 12b
+--R /
+--R 4 3 5 2 +-+
+--R (30a b x + 30b x )\|x
+--R ,
+--R
+--R +-+ +-+
+--R 3 3 2 2 |a +-+ a\|x 3 3 2 2
+--R (- 105a x - 105a b x ) |- \|x atan(-----) - 105a x - 70a b x
+--R \|b +-+
+--R |a
+--R b |-
+--R \|b
+--R +
+--R 2 3
+--R 14a b x - 6b
+--R /
+--R 4 3 5 2 +-+
+--R (15a b x + 15b x )\|x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1365
+
+--S 1366 of 1369
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b +-+ +-+
+--R 2 | a +-+ \| b 2 +-+ \|a \|x
+--R 7a |- - \|b log(------------------------) + 14a \|a atan(--------)
+--R \| b a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------------
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 1366
+
+--S 1367 of 1369
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1367
+
+--S 1368 of 1369
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R 2 |a +-+ a\|x 2 +-+ \|a \|x
+--R - 7a |- \|b atan(-----) + 7a \|a atan(--------)
+--R \|b +-+ +-+
+--R |a \|b
+--R b |-
+--R \|b
+--R (6) ------------------------------------------------
+--R 4 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 1368
+
+--S 1369 of 1369
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 1369
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich4f.input.pdf b/src/axiom-website/CATS/rich4f.input.pdf
new file mode 100644
index 0000000..2c09231
Binary files /dev/null and b/src/axiom-website/CATS/rich4f.input.pdf differ
diff --git a/src/axiom-website/CATS/rich4g.input.pamphlet b/src/axiom-website/CATS/rich4g.input.pamphlet
new file mode 100644
index 0000000..845cb44
--- /dev/null
+++ b/src/axiom-website/CATS/rich4g.input.pamphlet
@@ -0,0 +1,29082 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich4g.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 255 supplied "optimal results".
+\item 188 matching answers.
+\item 98 cases where Axiom differs from Rubi
+\item 52 cases where Axiom supplied 2 results.
+\item 24 cases that Axiom failed to integrate.
+\item 2 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich4g.output
+)spool rich4g.output
+)set message test on
+)set message auto off
+)clear all
+
+
+--S 1 of 1379
+t0:=x^(3/2)/(a+b/x)^3
+--R
+--R
+--R 4 +-+
+--R x \|x
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1379
+r0:=-21/4*b*x^(3/2)/a^4+63/20*x^(5/2)/a^3-1/2*x^(9/2)/(a*(b+a*x)^2)-_
+ 9/4*x^(7/2)/(a^2*(b+a*x))-63/4*b^(5/2)*atan(sqrt(a)*sqrt(x)/_
+ sqrt(b))/a^(11/2)+63/4*b^2*sqrt(x)/a^5
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 2 2 2 3 4 +-+ \|a \|x
+--R (- 315a b x - 630a b x - 315b )\|b atan(--------)
+--R +-+
+--R \|b
+--R +
+--R 4 4 3 3 2 2 2 3 4 +-+ +-+
+--R (8a x - 24a b x + 168a b x + 525a b x + 315b )\|a \|x
+--R /
+--R 7 2 6 5 2 +-+
+--R (20a x + 40a b x + 20a b )\|a
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b
+--R 2 2 2 3 4 | b \| a
+--R (315a b x + 630a b x + 315b ) |- - log(------------------------)
+--R \| a a x + b
+--R +
+--R 4 4 3 3 2 2 2 3 4 +-+
+--R (16a x - 48a b x + 336a b x + 1050a b x + 630b )\|x
+--R /
+--R 7 2 6 5 2
+--R 40a x + 80a b x + 40a b
+--R ,
+--R
+--R +-+ +-+
+--R 2 2 2 3 4 |b \|x
+--R (- 315a b x - 630a b x - 315b ) |- atan(----)
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R +
+--R 4 4 3 3 2 2 2 3 4 +-+
+--R (8a x - 24a b x + 168a b x + 525a b x + 315b )\|x
+--R /
+--R 7 2 6 5 2
+--R 20a x + 40a b x + 20a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 3
+
+--S 4 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b +-+ +-+
+--R 2 | b +-+ \| a 2 +-+ \|a \|x
+--R 63b |- - \|a log(------------------------) + 126b \|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) ---------------------------------------------------------------------
+--R 5 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+--S 6 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R 2 +-+ |b \|x 2 +-+ \|a \|x
+--R - 63b \|a |- atan(----) + 63b \|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) -------------------------------------------------
+--R 5 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 7
+
+)clear all
+
+--S 8 of 1379
+t0:=x^(1/2)/(a+b/x)^3
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ----------------------------
+--R 3 3 2 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Expression(Integer)
+--E 8
+
+--S 9 of 1379
+r0:=35/12*x^(3/2)/a^3-1/2*x^(7/2)/(a*(b+a*x)^2)-7/4*x^(5/2)/(a^2*(b+a*x))+_
+ 35/4*b^(3/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(9/2)-35/4*b*sqrt(x)/a^4
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 2 2 2 3 +-+ \|a \|x
+--R (105a b x + 210a b x + 105b )\|b atan(--------)
+--R +-+
+--R \|b
+--R +
+--R 3 3 2 2 2 3 +-+ +-+
+--R (8a x - 56a b x - 175a b x - 105b )\|a \|x
+--R /
+--R 6 2 5 4 2 +-+
+--R (12a x + 24a b x + 12a b )\|a
+--R Type: Expression(Integer)
+--E 9
+
+--S 10 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b
+--R 2 2 2 3 | b \| a
+--R (105a b x + 210a b x + 105b ) |- - log(----------------------)
+--R \| a a x + b
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (16a x - 112a b x - 350a b x - 210b )\|x
+--R /
+--R 6 2 5 4 2
+--R 24a x + 48a b x + 24a b
+--R ,
+--R
+--R +-+ +-+
+--R 2 2 2 3 |b \|x
+--R (105a b x + 210a b x + 105b ) |- atan(----)
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (8a x - 56a b x - 175a b x - 105b )\|x
+--R /
+--R 6 2 5 4 2
+--R 12a x + 24a b x + 12a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 10
+
+--S 11 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ 2a |- - \|x + a x - b +-+ +-+
+--R | b +-+ \| a +-+ \|a \|x
+--R 35b |- - \|a log(----------------------) - 70b\|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) ----------------------------------------------------------------
+--R 4 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 12
+
+--S 13 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R +-+ |b \|x +-+ \|a \|x
+--R 35b\|a |- atan(----) - 35b\|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) ---------------------------------------------
+--R 4 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 13
+
+--S 14 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 14
+
+)clear all
+
+--S 15 of 1379
+t0:=1/((a+b/x)^3*x^(1/2))
+--R
+--R
+--R 3
+--R x
+--R (1) ----------------------------------
+--R 3 3 2 2 2 3 +-+
+--R (a x + 3a b x + 3a b x + b )\|x
+--R Type: Expression(Integer)
+--E 15
+
+--S 16 of 1379
+r0:=-1/2*x^(5/2)/(a*(b+a*x)^2)-5/4*x^(3/2)/(a^2*(b+a*x))-_
+ 15/4*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(b)/a^(7/2)+15/4*sqrt(x)/a^3
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 2 2 2 +-+ \|a \|x
+--R (- 15a x - 30a b x - 15b )\|b atan(--------)
+--R +-+
+--R \|b
+--R +
+--R 2 2 2 +-+ +-+
+--R (8a x + 25a b x + 15b )\|a \|x
+--R /
+--R 5 2 4 3 2 +-+
+--R (4a x + 8a b x + 4a b )\|a
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b
+--R 2 2 2 | b \| a
+--R (15a x + 30a b x + 15b ) |- - log(------------------------)
+--R \| a a x + b
+--R +
+--R 2 2 2 +-+
+--R (16a x + 50a b x + 30b )\|x
+--R /
+--R 5 2 4 3 2
+--R 8a x + 16a b x + 8a b
+--R ,
+--R +-+ +-+
+--R 2 2 2 |b \|x 2 2 2 +-+
+--R (- 15a x - 30a b x - 15b ) |- atan(----) + (8a x + 25a b x + 15b )\|x
+--R \|a +-+
+--R |b
+--R |-
+--R \|a
+--R ------------------------------------------------------------------------]
+--R 5 2 4 3 2
+--R 4a x + 8a b x + 4a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 17
+
+--S 18 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b +-+
+--R +---+ - 2a |- - \|x + a x - b +-+ +-+
+--R | b +-+ \| a +-+ \|a \|x
+--R 15 |- - \|a log(------------------------ + 30\|b atan(--------)
+--R \| a a x + b +-+
+--R \|b
+--R (4) ----------------------------------------------------------------
+--R 3 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 18
+
+--S 19 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 19
+
+--S 20 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R +-+ |b \|x +-+ \|a \|x
+--R - 15\|a |- atan(----) + 15\|b atan(--------)
+--R \|a +-+ +-+
+--R |b \|b
+--R |-
+--R \|a
+--R (6) ---------------------------------------------
+--R 3 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 20
+
+--S 21 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 21
+
+)clear all
+
+--S 22 of 1379
+t0:=1/((a+b/x)^3*x^(3/2))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------------------
+--R 3 3 2 2 2 3 +-+
+--R (a x + 3a b x + 3a b x + b )\|x
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 1379
+r0:=-1/2*x^(3/2)/(a*(b+a*x)^2)+3/4*atan(sqrt(a)*sqrt(x)/sqrt(b))/_
+ (a^(5/2)*sqrt(b))-3/4*sqrt(x)/(a^2*(b+a*x))
+--R
+--R
+--R +-+ +-+
+--R 2 2 2 \|a \|x +-+ +-+ +-+
+--R (3a x + 6a b x + 3b )atan(--------) + (- 5a x - 3b)\|a \|b \|x
+--R +-+
+--R \|b
+--R (2) ----------------------------------------------------------------
+--R 4 2 3 2 2 +-+ +-+
+--R (4a x + 8a b x + 4a b )\|a \|b
+--R Type: Expression(Integer)
+--E 23
+
+--S 24 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-+ +-----+
+--R 2 2 2 2a b\|x + (a x - b)\|- a b
+--R (3a x + 6a b x + 3b )log(----------------------------)
+--R a x + b
+--R +
+--R +-----+ +-+
+--R (- 10a x - 6b)\|- a b \|x
+--R /
+--R 4 2 3 2 2 +-----+
+--R (8a x + 16a b x + 8a b )\|- a b
+--R ,
+--R +---+ +-+
+--R 2 2 2 \|a b \|x +---+ +-+
+--R (3a x + 6a b x + 3b )atan(----------) + (- 5a x - 3b)\|a b \|x
+--R b
+--R ----------------------------------------------------------------]
+--R 4 2 3 2 2 +---+
+--R (4a x + 8a b x + 4a b )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 24
+
+--S 25 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +-+ +-----+ +-+ +-+
+--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x
+--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------)
+--R a x + b +-+
+--R \|b
+--R (4) --------------------------------------------------------------------
+--R 2 +-----+ +-+ +-+
+--R 8a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 25
+
+--S 26 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+ +-+ +-+
+--R +-+ +-+ \|a b \|x +---+ \|a \|x
+--R 3\|a \|b atan(----------) - 3\|a b atan(--------)
+--R b +-+
+--R \|b
+--R (6) -------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 4a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 27
+
+--S 28 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 28
+
+)clear all
+
+--S 29 of 1379
+t0:=1/((a+b/x)^3*x^(5/2))
+--R
+--R
+--R x
+--R (1) ----------------------------------
+--R 3 3 2 2 2 3 +-+
+--R (a x + 3a b x + 3a b x + b )\|x
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 1379
+r0:=1/4*atan(sqrt(a)*sqrt(x)/sqrt(b))/(a^(3/2)*b^(3/2))-_
+ 1/2*sqrt(x)/(a*(b+a*x)^2)+1/4*sqrt(x)/(a*b*(b+a*x))
+--R
+--R
+--R +-+ +-+
+--R 2 2 2 \|a \|x +-+ +-+ +-+
+--R (a x + 2a b x + b )atan(--------) + (a x - b)\|a \|b \|x
+--R +-+
+--R \|b
+--R (2) ----------------------------------------------------------
+--R 3 2 2 2 3 +-+ +-+
+--R (4a b x + 8a b x + 4a b )\|a \|b
+--R Type: Expression(Integer)
+--E 30
+
+--S 31 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-+ +-----+
+--R 2 2 2 2a b\|x + (a x - b)\|- a b
+--R (a x + 2a b x + b )log(----------------------------)
+--R a x + b
+--R +
+--R +-----+ +-+
+--R (2a x - 2b)\|- a b \|x
+--R /
+--R 3 2 2 2 3 +-----+
+--R (8a b x + 16a b x + 8a b )\|- a b
+--R ,
+--R +---+ +-+
+--R 2 2 2 \|a b \|x +---+ +-+
+--R (a x + 2a b x + b )atan(----------) + (a x - b)\|a b \|x
+--R b
+--R ----------------------------------------------------------]
+--R 3 2 2 2 3 +---+
+--R (4a b x + 8a b x + 4a b )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 31
+
+--S 32 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +-+ +-----+ +-+ +-+
+--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x
+--R \|a \|b log(----------------------------) - 2\|- a b atan(--------)
+--R a x + b +-+
+--R \|b
+--R (4) -------------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 8a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 33
+
+--S 34 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+ +-+ +-+
+--R +-+ +-+ \|a b \|x +---+ \|a \|x
+--R \|a \|b atan(----------) - \|a b atan(--------)
+--R b +-+
+--R \|b
+--R (6) -----------------------------------------------
+--R +-+ +-+ +---+
+--R 4a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 1379
+t0:=1/((a+b/x)^3*x^(7/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R 3 3 2 2 2 3 +-+
+--R (a x + 3a b x + 3a b x + b )\|x
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 1379
+r0:=3/4*atan(sqrt(a)*sqrt(x)/sqrt(b))/(b^(5/2)*sqrt(a))+_
+ 1/2*sqrt(x)/(b*(b+a*x)^2)+3/4*sqrt(x)/(b^2*(b+a*x))
+--R
+--R
+--R +-+ +-+
+--R 2 2 2 \|a \|x +-+ +-+ +-+
+--R (3a x + 6a b x + 3b )atan(--------) + (3a x + 5b)\|a \|b \|x
+--R +-+
+--R \|b
+--R (2) --------------------------------------------------------------
+--R 2 2 2 3 4 +-+ +-+
+--R (4a b x + 8a b x + 4b )\|a \|b
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-+ +-----+
+--R 2 2 2 2a b\|x + (a x - b)\|- a b
+--R (3a x + 6a b x + 3b )log(----------------------------)
+--R a x + b
+--R +
+--R +-----+ +-+
+--R (6a x + 10b)\|- a b \|x
+--R /
+--R 2 2 2 3 4 +-----+
+--R (8a b x + 16a b x + 8b )\|- a b
+--R ,
+--R +---+ +-+
+--R 2 2 2 \|a b \|x +---+ +-+
+--R (3a x + 6a b x + 3b )atan(----------) + (3a x + 5b)\|a b \|x
+--R b
+--R --------------------------------------------------------------]
+--R 2 2 2 3 4 +---+
+--R (4a b x + 8a b x + 4b )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 38
+
+--S 39 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +-+ +-----+ +-+ +-+
+--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x
+--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------)
+--R a x + b +-+
+--R \|b
+--R (4) --------------------------------------------------------------------
+--R 2 +-----+ +-+ +-+
+--R 8b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+--S 41 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+ +-+ +-+
+--R +-+ +-+ \|a b \|x +---+ \|a \|x
+--R 3\|a \|b atan(----------) - 3\|a b atan(--------)
+--R b +-+
+--R \|b
+--R (6) -------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 4b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 42
+
+)clear all
+
+--S 43 of 1379
+t0:=1/((a+b/x)^3*x^(9/2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R 3 4 2 3 2 2 3 +-+
+--R (a x + 3a b x + 3a b x + b x)\|x
+--R Type: Expression(Integer)
+--E 43
+
+--S 44 of 1379
+r0:=-15/4*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(a)/b^(7/2)+_
+ (-15/4)/(b^3*sqrt(x))+1/2/(b*(b+a*x)^2*sqrt(x))+5/4/(b^2*(b+a*x)*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 2 2 2 +-+ +-+ \|a \|x
+--R (- 15a x - 30a b x - 15b )\|a \|x atan(--------)
+--R +-+
+--R \|b
+--R +
+--R 2 2 2 +-+
+--R (- 15a x - 25a b x - 8b )\|b
+--R /
+--R 2 3 2 4 5 +-+ +-+
+--R (4a b x + 8a b x + 4b )\|b \|x
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b
+--R 2 2 2 | a +-+ \| b
+--R (15a x + 30a b x + 15b ) |- - \|x log(------------------------)
+--R \| b a x + b
+--R +
+--R 2 2 2
+--R - 30a x - 50a b x - 16b
+--R /
+--R 2 3 2 4 5 +-+
+--R (8a b x + 16a b x + 8b )\|x
+--R ,
+--R +-+ +-+
+--R 2 2 2 |a +-+ a\|x 2 2 2
+--R (- 15a x - 30a b x - 15b ) |- \|x atan(-----) - 15a x - 25a b x - 8b
+--R \|b +-+
+--R |a
+--R b |-
+--R \|b
+--R -----------------------------------------------------------------------]
+--R 2 3 2 4 5 +-+
+--R (4a b x + 8a b x + 4b )\|x
+--R Type: Union(List(Expression(Integer)),...)
+--E 45
+
+--S 46 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b +-+ +-+
+--R | a +-+ \| b +-+ \|a \|x
+--R 15 |- - \|b log(------------------------ + 30\|a atan(--------)
+--R \| b a x + b +-+
+--R \|b
+--R (4) ----------------------------------------------------------------
+--R 3 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R |a +-+ a\|x +-+ \|a \|x
+--R - 15 |- \|b atan(----- + 15\|a atan(--------)
+--R \|b +-+ +-+
+--R |a \|b
+--R b |-
+--R \|b
+--R (6) ----------------------------------------------
+--R 3 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 48
+
+--S 49 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 49
+
+)clear all
+
+--S 50 of 1379
+t0:=1/((a+b/x)^3*x^(11/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R 3 5 2 4 2 3 3 2 +-+
+--R (a x + 3a b x + 3a b x + b x )\|x
+--R Type: Expression(Integer)
+--E 50
+
+--S 51 of 1379
+r0:=(-35/12)/(b^3*x^(3/2))+1/2/(b*x^(3/2)*(b+a*x)^2)+_
+ 7/4/(b^2*x^(3/2)*(b+a*x))+35/4*a^(3/2)*atan(sqrt(a)*_
+ sqrt(x)/sqrt(b))/b^(9/2)+35/4*a/(b^4*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 3 3 2 2 2 +-+ +-+ \|a \|x
+--R (105a x + 210a b x + 105a b x)\|a \|x atan(--------)
+--R +-+
+--R \|b
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (105a x + 175a b x + 56a b x - 8b )\|b
+--R /
+--R 2 4 3 5 2 6 +-+ +-+
+--R (12a b x + 24a b x + 12b x)\|b \|x
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a +-+
+--R +---+ 2b |- - \|x + a x - b
+--R 3 3 2 2 2 | a +-+ \| b
+--R (105a x + 210a b x + 105a b x) |- - \|x log(----------------------)
+--R \| b a x + b
+--R +
+--R 3 3 2 2 2 3
+--R 210a x + 350a b x + 112a b x - 16b
+--R /
+--R 2 4 3 5 2 6 +-+
+--R (24a b x + 48a b x + 24b x)\|x
+--R ,
+--R
+--R +-+ +-+
+--R 3 3 2 2 2 |a +-+ a\|x 3 3
+--R (105a x + 210a b x + 105a b x) |- \|x atan(-----) + 105a x
+--R \|b +-+
+--R |a
+--R b |-
+--R \|b
+--R +
+--R 2 2 2 3
+--R 175a b x + 56a b x - 8b
+--R /
+--R 2 4 3 5 2 6 +-+
+--R (12a b x + 24a b x + 12b x)\|x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 52
+
+--S 53 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a +-+
+--R +---+ 2b |- - \|x + a x - b +-+ +-+
+--R | a +-+ \| b +-+ \|a \|x
+--R 35a |- - \|b log(----------------------) - 70a\|a atan(--------)
+--R \| b a x + b +-+
+--R \|b
+--R (4) ----------------------------------------------------------------
+--R 4 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 53
+
+--S 54 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R |a +-+ a\|x +-+ \|a \|x
+--R 35a |- \|b atan(-----) - 35a\|a atan(--------)
+--R \|b +-+ +-+
+--R |a \|b
+--R b |-
+--R \|b
+--R (6) ----------------------------------------------
+--R 4 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 55
+
+--S 56 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 56
+
+)clear all
+
+--S 57 of 1379
+t0:=1/((a+b/x)^3*x^(13/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R 3 6 2 5 2 4 3 3 +-+
+--R (a x + 3a b x + 3a b x + b x )\|x
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 1379
+r0:=(-63/20)/(b^3*x^(5/2))+21/4*a/(b^4*x^(3/2))+_
+ 1/2/(b*x^(5/2)*(b+a*x)^2)+9/4/(b^2*x^(5/2)*(b+a*x))-_
+ 63/4*a^(5/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/b^(11/2)-_
+ 63/4*a^2/(b^5*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-+
+--R 4 4 3 3 2 2 2 +-+ +-+ \|a \|x
+--R (- 315a x - 630a b x - 315a b x )\|a \|x atan(--------)
+--R +-+
+--R \|b
+--R +
+--R 4 4 3 3 2 2 2 3 4 +-+
+--R (- 315a x - 525a b x - 168a b x + 24a b x - 8b )\|b
+--R /
+--R 2 5 4 6 3 7 2 +-+ +-+
+--R (20a b x + 40a b x + 20b x )\|b \|x
+--R Type: Expression(Integer)
+--E 58
+
+--S 59 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 4 4 3 3 2 2 2 | a +-+
+--R (315a x + 630a b x + 315a b x ) |- - \|x
+--R \| b
+--R *
+--R +---+
+--R | a +-+
+--R - 2b |- - \|x + a x - b
+--R \| b
+--R log(------------------------)
+--R a x + b
+--R +
+--R 4 4 3 3 2 2 2 3 4
+--R - 630a x - 1050a b x - 336a b x + 48a b x - 16b
+--R /
+--R 2 5 4 6 3 7 2 +-+
+--R (40a b x + 80a b x + 40b x )\|x
+--R ,
+--R
+--R +-+ +-+
+--R 4 4 3 3 2 2 2 |a +-+ a\|x 4 4
+--R (- 315a x - 630a b x - 315a b x ) |- \|x atan(-----) - 315a x
+--R \|b +-+
+--R |a
+--R b |-
+--R \|b
+--R +
+--R 3 3 2 2 2 3 4
+--R - 525a b x - 168a b x + 24a b x - 8b
+--R /
+--R 2 5 4 6 3 7 2 +-+
+--R (20a b x + 40a b x + 20b x )\|x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 59
+
+--S 60 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a +-+
+--R +---+ - 2b |- - \|x + a x - b +-+ +-+
+--R 2 | a +-+ \| b 2 +-+ \|a \|x
+--R 63a |- - \|b log(------------------------) + 126a \|a atan(--------)
+--R \| b a x + b +-+
+--R \|b
+--R (4) ---------------------------------------------------------------------
+--R 5 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 60
+
+--S 61 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R 2 |a +-+ a\|x 2 +-+ \|a \|x
+--R - 63a |- \|b atan(-----) + 63a \|a atan(--------)
+--R \|b +-+ +-+
+--R |a \|b
+--R b |-
+--R \|b
+--R (6) --------------------------------------------------
+--R 5 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 63
+
+)clear all
+
+--S 64 of 1379
+t0:=(a+b/x)^(1/2)*x^(7/2)
+--R
+--R
+--R +-------+
+--R 3 |a x + b +-+
+--R (1) x |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 1379
+r0:=-32/315*b^3*(a+b/x)^(3/2)*x^(3/2)/a^4+16/105*b^2*(a+b/x)^(3/2)*_
+ x^(5/2)/a^3-4/21*b*(a+b/x)^(3/2)*x^(7/2)/a^2+2/9*(a+b/x)^(3/2)*x^(9/2)/a
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b +-+
+--R (70a x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x
+--R \| x
+--R (2) -------------------------------------------------------------
+--R 4
+--R 315a
+--R Type: Expression(Integer)
+--E 65
+
+--S 66 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b +-+
+--R (70a x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x
+--R \| x
+--R (3) -------------------------------------------------------------
+--R 4
+--R 315a
+--R Type: Union(Expression(Integer),...)
+--E 66
+
+--S 67 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 68
+
+)clear all
+
+--S 69 of 1379
+t0:=(a+b/x)^(1/2)*x^(5/2)
+--R
+--R
+--R +-------+
+--R 2 |a x + b +-+
+--R (1) x |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 1379
+r0:=16/105*b^2*(a+b/x)^(3/2)*x^(3/2)/a^3-8/35*b*(a+b/x)^(3/2)*x^(5/2)/_
+ a^2+2/7*(a+b/x)^(3/2)*x^(7/2)/a
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b +-+
+--R (30a x + 6a b x - 8a b x + 16b ) |------- \|x
+--R \| x
+--R (2) ------------------------------------------------
+--R 3
+--R 105a
+--R Type: Expression(Integer)
+--E 70
+
+--S 71 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b +-+
+--R (30a x + 6a b x - 8a b x + 16b ) |------- \|x
+--R \| x
+--R (3) ------------------------------------------------
+--R 3
+--R 105a
+--R Type: Union(Expression(Integer),...)
+--E 71
+
+--S 72 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 73
+
+)clear all
+
+--S 74 of 1379
+t0:=(a+b/x)^(1/2)*x^(3/2)
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R (1) x |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 1379
+r0:=-4/15*b*(a+b/x)^(3/2)*x^(3/2)/a^2+2/5*(a+b/x)^(3/2)*x^(5/2)/a
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (6a x + 2a b x - 4b ) |------- \|x
+--R \| x
+--R (2) ------------------------------------
+--R 2
+--R 15a
+--R Type: Expression(Integer)
+--E 75
+
+--S 76 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (6a x + 2a b x - 4b ) |------- \|x
+--R \| x
+--R (3) ------------------------------------
+--R 2
+--R 15a
+--R Type: Union(Expression(Integer),...)
+--E 76
+
+--S 77 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 78
+
+)clear all
+
+--S 79 of 1379
+t0:=(a+b/x)^(1/2)*x^(1/2)
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R (1) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 1379
+r0:=2/3*(a+b/x)^(3/2)*x^(3/2)/a
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R (2a x + 2b) |------- \|x
+--R \| x
+--R (2) -------------------------
+--R 3a
+--R Type: Expression(Integer)
+--E 80
+
+--S 81 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R (2a x + 2b) |------- \|x
+--R \| x
+--R (3) -------------------------
+--R 3a
+--R Type: Union(Expression(Integer),...)
+--E 81
+
+--S 82 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 83
+
+)clear all
+
+--S 84 of 1379
+t0:=(a+b/x)^(1/2)/x^(1/2)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 1379
+r0:=-2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))*sqrt(b)+2*sqrt(a+b/x)*sqrt(x)
+--R
+--R
+--R +-+ +-------+
+--R +-+ \|b |a x + b +-+
+--R (2) - 2\|b atanh(--------------) + 2 |------- \|x
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 85
+
+--S 86 of 1379
+--a0:=integrate(t0,x)
+--E 86
+
+--S 87 of 1379
+--m0:=a0-r0
+--E 87
+
+--S 88 of 1379
+--d0:=D(m0,x)
+--E 88
+
+)clear all
+
+--S 89 of 1379
+t0:=(a+b/x)^(1/2)/x^(3/2)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 1379
+r0:=-a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)-sqrt(a+b/x)/sqrt(x)
+--R
+--R
+--R +-+ +-------+
+--R +-+ \|b |a x + b +-+
+--R - a\|x atanh(--------------) - |------- \|b
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) ---------------------------------------------
+--R +-+ +-+
+--R \|b \|x
+--R Type: Expression(Integer)
+--E 90
+
+--S 91 of 1379
+--a0:=integrate(t0,x)
+--E 91
+
+--S 92 of 1379
+--m0:=a0-r0
+--E 92
+
+--S 93 of 1379
+--d0:=D(m0,x)
+--E 93
+
+)clear all
+
+--S 94 of 1379
+t0:=(a+b/x)^(1/2)/x^(5/2)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 1379
+r0:=1/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)-_
+ 1/2*sqrt(a+b/x)/x^(3/2)-1/4*a*sqrt(a+b/x)/(b*sqrt(x))
+--R
+--R
+--R +-+ +-------+
+--R 2 +-+ \|b |a x + b +-+
+--R a x\|x atanh(--------------) + (- a x - 2b) |------- \|b
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) ---------------------------------------------------------
+--R +-+ +-+
+--R 4b x\|b \|x
+--R Type: Expression(Integer)
+--E 95
+
+--S 96 of 1379
+--a0:=integrate(t0,x)
+--E 96
+
+--S 97 of 1379
+--m0:=a0-r0
+--E 97
+
+--S 98 of 1379
+--d0:=D(m0,x)
+--E 98
+
+)clear all
+
+--S 99 of 1379
+t0:=(a+b/x)^(1/2)/x^(7/2)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R (1) ----------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 1379
+r0:=-1/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(5/2)-_
+ 1/3*sqrt(a+b/x)/x^(5/2)-1/12*a*sqrt(a+b/x)/(b*x^(3/2))+_
+ 1/8*a^2*sqrt(a+b/x)/(b^2*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 2 +-+ \|b 2 2 2 |a x + b +-+
+--R - 3a x \|x atanh(--------------) + (3a x - 2a b x - 8b ) |------- \|b
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R -----------------------------------------------------------------------
+--R 2 2 +-+ +-+
+--R 24b x \|b \|x
+--R Type: Expression(Integer)
+--E 100
+
+--S 101 of 1379
+--a0:=integrate(t0,x)
+--E 101
+
+--S 102 of 1379
+--m0:=a0-r0
+--E 102
+
+--S 103 of 1379
+--d0:=D(m0,x)
+--E 103
+
+)clear all
+
+--S 104 of 1379
+t0:=(a+b/x)^(3/2)*x^(9/2)
+--R
+--R
+--R +-------+
+--R 4 3 |a x + b +-+
+--R (1) (a x + b x ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 1379
+r0:=-32/1155*b^3*(a+b/x)^(5/2)*x^(5/2)/a^4+16/231*b^2*(a+b/x)^(5/2)*_
+ x^(7/2)/a^3-4/33*b*(a+b/x)^(5/2)*x^(9/2)/a^2+_
+ 2/11*(a+b/x)^(5/2)*x^(11/2)/a
+--R
+--R
+--R (2)
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+
+--R (210a x + 280a b x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x
+--R \| x
+--R --------------------------------------------------------------------------
+--R 4
+--R 1155a
+--R Type: Expression(Integer)
+--E 105
+
+--S 106 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+
+--R (210a x + 280a b x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x
+--R \| x
+--R --------------------------------------------------------------------------
+--R 4
+--R 1155a
+--R Type: Union(Expression(Integer),...)
+--E 106
+
+--S 107 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 108
+
+)clear all
+
+--S 109 of 1379
+t0:=(a+b/x)^(3/2)*x^(7/2)
+--R
+--R
+--R +-------+
+--R 3 2 |a x + b +-+
+--R (1) (a x + b x ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 1379
+r0:=16/315*b^2*(a+b/x)^(5/2)*x^(5/2)/a^3-8/63*b*(a+b/x)^(5/2)*_
+ x^(7/2)/a^2+2/9*(a+b/x)^(5/2)*x^(9/2)/a
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b +-+
+--R (70a x + 100a b x + 6a b x - 8a b x + 16b ) |------- \|x
+--R \| x
+--R (2) ------------------------------------------------------------
+--R 3
+--R 315a
+--R Type: Expression(Integer)
+--E 110
+
+--S 111 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b +-+
+--R (70a x + 100a b x + 6a b x - 8a b x + 16b ) |------- \|x
+--R \| x
+--R (3) ------------------------------------------------------------
+--R 3
+--R 315a
+--R Type: Union(Expression(Integer),...)
+--E 111
+
+--S 112 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 113
+
+)clear all
+
+--S 114 of 1379
+t0:=(a+b/x)^(3/2)*x^(5/2)
+--R
+--R
+--R +-------+
+--R 2 |a x + b +-+
+--R (1) (a x + b x) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 1379
+r0:=-4/35*b*(a+b/x)^(5/2)*x^(5/2)/a^2+2/7*(a+b/x)^(5/2)*x^(7/2)/a
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b +-+
+--R (10a x + 16a b x + 2a b x - 4b ) |------- \|x
+--R \| x
+--R (2) ------------------------------------------------
+--R 2
+--R 35a
+--R Type: Expression(Integer)
+--E 115
+
+--S 116 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b +-+
+--R (10a x + 16a b x + 2a b x - 4b ) |------- \|x
+--R \| x
+--R (3) ------------------------------------------------
+--R 2
+--R 35a
+--R Type: Union(Expression(Integer),...)
+--E 116
+
+--S 117 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 118
+
+)clear all
+
+--S 119 of 1379
+t0:=(a+b/x)^(3/2)*x^(3/2)
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R (1) (a x + b) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 1379
+r0:=2/5*(a+b/x)^(5/2)*x^(5/2)/a
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (2a x + 4a b x + 2b ) |------- \|x
+--R \| x
+--R (2) ------------------------------------
+--R 5a
+--R Type: Expression(Integer)
+--E 120
+
+--S 121 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (2a x + 4a b x + 2b ) |------- \|x
+--R \| x
+--R (3) ------------------------------------
+--R 5a
+--R Type: Union(Expression(Integer),...)
+--E 121
+
+--S 122 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 123
+
+)clear all
+
+--S 124 of 1379
+t0:=(a+b/x)^(3/2)*x^(1/2)
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R (a x + b) |------- \|x
+--R \| x
+--R (1) -----------------------
+--R x
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 1379
+r0:=2/3*(a+b/x)^(3/2)*x^(3/2)-2*b^(3/2)*atanh(sqrt(b)/_
+ (sqrt(a+b/x)*sqrt(x)))+2*b*sqrt(a+b/x)*sqrt(x)
+--R
+--R
+--R +-+ +-------+
+--R +-+ \|b |a x + b +-+
+--R - 6b\|b atanh(--------------) + (2a x + 8b) |------- \|x
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) ---------------------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 125
+
+--S 126 of 1379
+--a0:=integrate(t0,x)
+--E 126
+
+--S 127 of 1379
+--m0:=a0-r0
+--E 127
+
+--S 128 of 1379
+--d0:=D(m0,x)
+--E 128
+
+)clear all
+
+--S 129 of 1379
+t0:=(a+b/x)^(3/2)/x^(1/2)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 1379
+r0:=-3*a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))*sqrt(b)-_
+ 3*b*sqrt(a+b/x)/sqrt(x)+2*(a+b/x)^(3/2)*sqrt(x)
+--R
+--R
+--R +-+ +-------+
+--R +-+ +-+ \|b |a x + b
+--R - 3a\|b \|x atanh(--------------) + (2a x - b) |-------
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) --------------------------------------------------------
+--R +-+
+--R \|x
+--R Type: Expression(Integer)
+--E 130
+
+--S 131 of 1379
+--a0:=integrate(t0,x)
+--E 131
+
+--S 132 of 1379
+--m0:=a0-r0
+--E 132
+
+--S 133 of 1379
+--d0:=D(m0,x)
+--E 133
+
+)clear all
+
+--S 134 of 1379
+t0:=(a+b/x)^(3/2)/x^(3/2)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 134
+
+--S 135 of 1379
+r0:=-3/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)-_
+ 1/2*(a+b/x)^(3/2)/sqrt(x)-3/4*a*sqrt(a+b/x)/sqrt(x)
+--R
+--R
+--R +-+ +-------+
+--R 2 +-+ \|b |a x + b +-+
+--R - 3a x\|x atanh(--------------) + (- 5a x - 2b) |------- \|b
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) -------------------------------------------------------------
+--R +-+ +-+
+--R 4x\|b \|x
+--R Type: Expression(Integer)
+--E 135
+
+--S 136 of 1379
+--a0:=integrate(t0,x)
+--E 136
+
+--S 137 of 1379
+--m0:=a0-r0
+--E 137
+
+--S 138 of 1379
+--d0:=D(m0,x)
+--E 138
+
+)clear all
+
+--S 139 of 1379
+t0:=(a+b/x)^(3/2)/x^(5/2)
+--R
+--R
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R (1) -------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 1379
+r0:=-1/3*(a+b/x)^(3/2)/x^(3/2)+1/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*_
+ sqrt(x)))/b^(3/2)-1/4*a*sqrt(a+b/x)/x^(3/2)-1/8*a^2*_
+ sqrt(a+b/x)/(b*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 2 +-+ \|b 2 2 2 |a x + b +-+
+--R 3a x \|x atanh(--------------) + (- 3a x - 14a b x - 8b ) |------- \|b
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R ------------------------------------------------------------------------
+--R 2 +-+ +-+
+--R 24b x \|b \|x
+--R Type: Expression(Integer)
+--E 140
+
+--S 141 of 1379
+--a0:=integrate(t0,x)
+--E 141
+
+--S 142 of 1379
+--m0:=a0-r0
+--E 142
+
+--S 143 of 1379
+--d0:=D(m0,x)
+--E 143
+
+)clear all
+
+--S 144 of 1379
+t0:=(a+b/x)^(5/2)*x^(11/2)
+--R
+--R
+--R +-------+
+--R 2 5 4 2 3 |a x + b +-+
+--R (1) (a x + 2a b x + b x ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 144
+
+--S 145 of 1379
+r0:=-32/3003*b^3*(a+b/x)^(7/2)*x^(7/2)/a^4+16/429*b^2*(a+b/x)^(7/2)*_
+ x^(9/2)/a^3-12/143*b*(a+b/x)^(7/2)*x^(11/2)/a^2+_
+ 2/13*(a+b/x)^(7/2)*x^(13/2)/a
+--R
+--R
+--R (2)
+--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6
+--R (462a x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32b )
+--R *
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R /
+--R 4
+--R 3003a
+--R Type: Expression(Integer)
+--E 145
+
+--S 146 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6
+--R (462a x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32b )
+--R *
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R /
+--R 4
+--R 3003a
+--R Type: Union(Expression(Integer),...)
+--E 146
+
+--S 147 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 148
+
+)clear all
+
+--S 149 of 1379
+t0:=(a+b/x)^(5/2)*x^(9/2)
+--R
+--R
+--R +-------+
+--R 2 4 3 2 2 |a x + b +-+
+--R (1) (a x + 2a b x + b x ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 1379
+r0:=16/693*b^2*(a+b/x)^(7/2)*x^(7/2)/a^3-8/99*b*(a+b/x)^(7/2)*_
+ x^(9/2)/a^2+2/11*(a+b/x)^(7/2)*x^(11/2)/a
+--R
+--R
+--R (2)
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+
+--R (126a x + 322a b x + 226a b x + 6a b x - 8a b x + 16b ) |------- \|x
+--R \| x
+--R -------------------------------------------------------------------------
+--R 3
+--R 693a
+--R Type: Expression(Integer)
+--E 150
+
+--S 151 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+
+--R (126a x + 322a b x + 226a b x + 6a b x - 8a b x + 16b ) |------- \|x
+--R \| x
+--R -------------------------------------------------------------------------
+--R 3
+--R 693a
+--R Type: Union(Expression(Integer),...)
+--E 151
+
+--S 152 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 153
+
+)clear all
+
+--S 154 of 1379
+t0:=(a+b/x)^(5/2)*x^(7/2)
+--R
+--R
+--R +-------+
+--R 2 3 2 2 |a x + b +-+
+--R (1) (a x + 2a b x + b x) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 1379
+r0:=-4/63*b*(a+b/x)^(7/2)*x^(7/2)/a^2+2/9*(a+b/x)^(7/2)*x^(9/2)/a
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b +-+
+--R (14a x + 38a b x + 30a b x + 2a b x - 4b ) |------- \|x
+--R \| x
+--R (2) -----------------------------------------------------------
+--R 2
+--R 63a
+--R Type: Expression(Integer)
+--E 155
+
+--S 156 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b +-+
+--R (14a x + 38a b x + 30a b x + 2a b x - 4b ) |------- \|x
+--R \| x
+--R (3) -----------------------------------------------------------
+--R 2
+--R 63a
+--R Type: Union(Expression(Integer),...)
+--E 156
+
+--S 157 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 158
+
+)clear all
+
+--S 159 of 1379
+t0:=(a+b/x)^(5/2)*x^(5/2)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (1) (a x + 2a b x + b ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 1379
+r0:=2/7*(a+b/x)^(7/2)*x^(7/2)/a
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b +-+
+--R (2a x + 6a b x + 6a b x + 2b ) |------- \|x
+--R \| x
+--R (2) ----------------------------------------------
+--R 7a
+--R Type: Expression(Integer)
+--E 160
+
+--S 161 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b +-+
+--R (2a x + 6a b x + 6a b x + 2b ) |------- \|x
+--R \| x
+--R (3) ----------------------------------------------
+--R 7a
+--R Type: Union(Expression(Integer),...)
+--E 161
+
+--S 162 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 162
+
+--S 163 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 163
+
+)clear all
+
+--S 164 of 1379
+t0:=(a+b/x)^(5/2)*x^(3/2)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (a x + 2a b x + b ) |------- \|x
+--R \| x
+--R (1) ----------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 1379
+r0:=2/3*b*(a+b/x)^(3/2)*x^(3/2)+2/5*(a+b/x)^(5/2)*x^(5/2)-2*b^(5/2)*_
+ atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))+2*b^2*sqrt(a+b/x)*sqrt(x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 +-+ \|b 2 2 2 |a x + b +-+
+--R - 30b \|b atanh(--------------) + (6a x + 22a b x + 46b ) |------- \|x
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R ------------------------------------------------------------------------
+--R 15
+--R Type: Expression(Integer)
+--E 165
+
+--S 166 of 1379
+--a0:=integrate(t0,x)
+--E 166
+
+--S 167 of 1379
+--m0:=a0-r0
+--E 167
+
+--S 168 of 1379
+--d0:=D(m0,x)
+--E 168
+
+)clear all
+
+--S 169 of 1379
+t0:=(a+b/x)^(5/2)*x^(1/2)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (a x + 2a b x + b ) |------- \|x
+--R \| x
+--R (1) ----------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 169
+
+--S 170 of 1379
+r0:=2/3*(a+b/x)^(5/2)*x^(3/2)-5*a*b^(3/2)*atanh(sqrt(b)/(sqrt(a+b/x)*_
+ sqrt(x)))-5*b^2*sqrt(a+b/x)/sqrt(x)+10/3*b*(a+b/x)^(3/2)*sqrt(x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R +-+ +-+ \|b 2 2 2 |a x + b
+--R - 15a b\|b \|x atanh(--------------) + (2a x + 14a b x - 3b ) |-------
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R ------------------------------------------------------------------------
+--R +-+
+--R 3\|x
+--R Type: Expression(Integer)
+--E 170
+
+--S 171 of 1379
+--a0:=integrate(t0,x)
+--E 171
+
+--S 172 of 1379
+--m0:=a0-r0
+--E 172
+
+--S 173 of 1379
+--d0:=D(m0,x)
+--E 173
+
+)clear all
+
+--S 174 of 1379
+t0:=(a+b/x)^(5/2)/x^(1/2)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 2 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 1379
+r0:=-15/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))*sqrt(b)-_
+ 5/2*b*(a+b/x)^(3/2)/sqrt(x)-15/4*a*b*sqrt(a+b/x)/sqrt(x)+_
+ 2*(a+b/x)^(5/2)*sqrt(x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 2 +-+ +-+ \|b 2 2 2 |a x + b
+--R - 15a x\|b \|x atanh(--------------) + (8a x - 9a b x - 2b ) |-------
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R -----------------------------------------------------------------------
+--R +-+
+--R 4x\|x
+--R Type: Expression(Integer)
+--E 175
+
+--S 176 of 1379
+--a0:=integrate(t0,x)
+--E 176
+
+--S 177 of 1379
+--m0:=a0-r0
+--E 177
+
+--S 178 of 1379
+--d0:=D(m0,x)
+--E 178
+
+)clear all
+
+--S 179 of 1379
+t0:=(a+b/x)^(5/2)/x^(3/2)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 3 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 1379
+r0:=-5/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)-_
+ 5/12*a*(a+b/x)^(3/2)/sqrt(x)-1/3*(a+b/x)^(5/2)/sqrt(x)-_
+ 5/8*a^2*sqrt(a+b/x)/sqrt(x)
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 2 +-+ \|b 2 2 2 |a x + b +-+
+--R - 15a x \|x atanh(--------------) + (- 33a x - 26a b x - 8b ) |------- \|b
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R ----------------------------------------------------------------------------
+--R 2 +-+ +-+
+--R 24x \|b \|x
+--R Type: Expression(Integer)
+--E 180
+
+--S 181 of 1379
+--a0:=integrate(t0,x)
+--E 181
+
+--S 182 of 1379
+--m0:=a0-r0
+--E 182
+
+--S 183 of 1379
+--d0:=D(m0,x)
+--E 183
+
+)clear all
+
+--S 184 of 1379
+t0:=(a+b/x)^(5/2)/x^(5/2)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R (1) ------------------------------
+--R 4 +-+
+--R x \|x
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 1379
+r0:=-5/24*a*(a+b/x)^(3/2)/x^(3/2)-1/4*(a+b/x)^(5/2)/x^(3/2)+_
+ 5/64*a^4*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)-_
+ 5/32*a^2*sqrt(a+b/x)/x^(3/2)-5/64*a^3*sqrt(a+b/x)/(b*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+
+--R 4 3 +-+ \|b
+--R 15a x \|x atanh(--------------)
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b +-+
+--R (- 15a x - 118a b x - 136a b x - 48b ) |------- \|b
+--R \| x
+--R /
+--R 3 +-+ +-+
+--R 192b x \|b \|x
+--R Type: Expression(Integer)
+--E 185
+
+--S 186 of 1379
+--a0:=integrate(t0,x)
+--E 186
+
+--S 187 of 1379
+--m0:=a0-r0
+--E 187
+
+--S 188 of 1379
+--d0:=D(m0,x)
+--E 188
+
+)clear all
+
+--S 189 of 1379
+t0:=x^(7/2)/(a+b/x)^(1/2)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ----------
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 1379
+r0:=-128/315*b^3*x^(3/2)*sqrt(a+b/x)/a^4+32/105*b^2*x^(5/2)*_
+ sqrt(a+b/x)/a^3-16/63*b*x^(7/2)*sqrt(a+b/x)/a^2+2/9*x^(9/2)*_
+ sqrt(a+b/x)/a+256/315*b^4*sqrt(a+b/x)*sqrt(x)/a^5
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b +-+
+--R (70a x - 80a b x + 96a b x - 128a b x + 256b ) |------- \|x
+--R \| x
+--R (2) ---------------------------------------------------------------
+--R 5
+--R 315a
+--R Type: Expression(Integer)
+--E 190
+
+--S 191 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 4 4 3 3 2 2 2 3 4 |a x + b +-+
+--R (70a x - 80a b x + 96a b x - 128a b x + 256b ) |------- \|x
+--R \| x
+--R (3) ---------------------------------------------------------------
+--R 5
+--R 315a
+--R Type: Union(Expression(Integer),...)
+--E 191
+
+--S 192 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 193
+
+)clear all
+
+--S 194 of 1379
+t0:=x^(5/2)/(a+b/x)^(1/2)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ----------
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 1379
+r0:=16/35*b^2*x^(3/2)*sqrt(a+b/x)/a^3-12/35*b*x^(5/2)*sqrt(a+b/x)/a^2+_
+ 2/7*x^(7/2)*sqrt(a+b/x)/a-32/35*b^3*sqrt(a+b/x)*sqrt(x)/a^4
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b +-+
+--R (10a x - 12a b x + 16a b x - 32b ) |------- \|x
+--R \| x
+--R (2) --------------------------------------------------
+--R 4
+--R 35a
+--R Type: Expression(Integer)
+--E 195
+
+--S 196 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 3 3 2 2 2 3 |a x + b +-+
+--R (10a x - 12a b x + 16a b x - 32b ) |------- \|x
+--R \| x
+--R (3) --------------------------------------------------
+--R 4
+--R 35a
+--R Type: Union(Expression(Integer),...)
+--E 196
+
+--S 197 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 198
+
+)clear all
+
+--S 199 of 1379
+t0:=x^(3/2)/(a+b/x)^(1/2)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) ----------
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 1379
+r0:=-8/15*b*x^(3/2)*sqrt(a+b/x)/a^2+2/5*x^(5/2)*sqrt(a+b/x)/a+_
+ 16/15*b^2*sqrt(a+b/x)*sqrt(x)/a^3
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (6a x - 8a b x + 16b ) |------- \|x
+--R \| x
+--R (2) -------------------------------------
+--R 3
+--R 15a
+--R Type: Expression(Integer)
+--E 200
+
+--S 201 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (6a x - 8a b x + 16b ) |------- \|x
+--R \| x
+--R (3) -------------------------------------
+--R 3
+--R 15a
+--R Type: Union(Expression(Integer),...)
+--E 201
+
+--S 202 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 203
+
+)clear all
+
+--S 204 of 1379
+t0:=x^(1/2)/(a+b/x)^(1/2)
+--R
+--R
+--R +-+
+--R \|x
+--R (1) ----------
+--R +-------+
+--R |a x + b
+--R |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 1379
+r0:=2/3*x^(3/2)*sqrt(a+b/x)/a-4/3*b*sqrt(a+b/x)*sqrt(x)/a^2
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R (2a x - 4b) |------- \|x
+--R \| x
+--R (2) -------------------------
+--R 2
+--R 3a
+--R Type: Expression(Integer)
+--E 205
+
+--S 206 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R (2a x - 4b) |------- \|x
+--R \| x
+--R (3) -------------------------
+--R 2
+--R 3a
+--R Type: Union(Expression(Integer),...)
+--E 206
+
+--S 207 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 208
+
+)clear all
+
+--S 209 of 1379
+t0:=1/((a+b/x)^(1/2)*x^(1/2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 1379
+r0:=2*sqrt(a+b/x)*sqrt(x)/a
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R 2 |------- \|x
+--R \| x
+--R (2) ---------------
+--R a
+--R Type: Expression(Integer)
+--E 210
+
+--S 211 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R |a x + b +-+
+--R 2 |------- \|x
+--R \| x
+--R (3) ---------------
+--R a
+--R Type: Union(Expression(Integer),...)
+--E 211
+
+--S 212 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 213
+
+)clear all
+
+--S 214 of 1379
+t0:=1/((a+b/x)^(1/2)*x^(3/2))
+--R
+--R
+--R 1
+--R (1) ---------------
+--R +-------+
+--R |a x + b +-+
+--R x |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 1379
+r0:=-2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)
+--R
+--R
+--R +-+
+--R \|b
+--R 2atanh(--------------)
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) - ----------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 215
+
+--S 216 of 1379
+--a0:=integrate(t0,x)
+--E 216
+
+--S 217 of 1379
+--m0:=a0-r0
+--E 217
+
+--S 218 of 1379
+--d0:=D(m0,x)
+--E 218
+
+)clear all
+
+--S 219 of 1379
+t0:=1/((a+b/x)^(1/2)*x^(5/2))
+--R
+--R
+--R 1
+--R (1) ----------------
+--R +-------+
+--R 2 |a x + b +-+
+--R x |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 1379
+r0:=a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)-sqrt(a+b/x)/(b*sqrt(x))
+--R
+--R
+--R +-+ +-------+
+--R +-+ \|b |a x + b +-+
+--R a\|x atanh(--------------) - |------- \|b
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) -------------------------------------------
+--R +-+ +-+
+--R b\|b \|x
+--R Type: Expression(Integer)
+--E 220
+
+--S 221 of 1379
+--a0:=integrate(t0,x)
+--E 221
+
+--S 222 of 1379
+--m0:=a0-r0
+--E 222
+
+--S 223 of 1379
+--d0:=D(m0,x)
+--E 223
+
+)clear all
+
+--S 224 of 1379
+t0:=1/((a+b/x)^(1/2)*x^(7/2))
+--R
+--R
+--R 1
+--R (1) ----------------
+--R +-------+
+--R 3 |a x + b +-+
+--R x |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 1379
+r0:=-3/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(5/2)-_
+ 1/2*sqrt(a+b/x)/(b*x^(3/2))+3/4*a*sqrt(a+b/x)/(b^2*sqrt(x))
+--R
+--R
+--R +-+ +-------+
+--R 2 +-+ \|b |a x + b +-+
+--R - 3a x\|x atanh(--------------) + (3a x - 2b) |------- \|b
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) -----------------------------------------------------------
+--R 2 +-+ +-+
+--R 4b x\|b \|x
+--R Type: Expression(Integer)
+--E 225
+
+--S 226 of 1379
+--a0:=integrate(t0,x)
+--E 226
+
+--S 227 of 1379
+--m0:=a0-r0
+--E 227
+
+--S 228 of 1379
+--d0:=D(m0,x)
+--E 228
+
+)clear all
+
+--S 229 of 1379
+t0:=1/((a+b/x)^(1/2)*x^(9/2))
+--R
+--R
+--R 1
+--R (1) ----------------
+--R +-------+
+--R 4 |a x + b +-+
+--R x |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 1379
+r0:=5/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(7/2)-_
+ 1/3*sqrt(a+b/x)/(b*x^(5/2))+5/12*a*sqrt(a+b/x)/(b^2*x^(3/2))-_
+ 5/8*a^2*sqrt(a+b/x)/(b^3*sqrt(x))
+--R
+--R
+--R (2)
+--R +-+ +-------+
+--R 3 2 +-+ \|b 2 2 2 |a x + b +-+
+--R 15a x \|x atanh(--------------) + (- 15a x + 10a b x - 8b ) |------- \|b
+--R +-------+ \| x
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R --------------------------------------------------------------------------
+--R 3 2 +-+ +-+
+--R 24b x \|b \|x
+--R Type: Expression(Integer)
+--E 230
+
+--S 231 of 1379
+--a0:=integrate(t0,x)
+--E 231
+
+--S 232 of 1379
+--m0:=a0-r0
+--E 232
+
+--S 233 of 1379
+--d0:=D(m0,x)
+--E 233
+
+)clear all
+
+--S 234 of 1379
+t0:=x^(5/2)/(a+b/x)^(3/2)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) -------------------
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 1379
+r0:=-2*x^(7/2)/(a*sqrt(a+b/x))+128/35*b^2*x^(3/2)*sqrt(a+b/x)/a^4-_
+ 96/35*b*x^(5/2)*sqrt(a+b/x)/a^3+16/7*x^(7/2)*sqrt(a+b/x)/a^2-_
+ 256/35*b^3*sqrt(a+b/x)*sqrt(x)/a^5
+--R
+--R
+--R 4 4 3 3 2 2 2 3 4 +-+
+--R (10a x - 16a b x + 32a b x - 128a b x - 256b )\|x
+--R (2) -----------------------------------------------------
+--R +-------+
+--R 5 |a x + b
+--R 35a x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 235
+
+--S 236 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 5 4 3 2 4 3 2 3 3 2 2
+--R (30a b + 30a )x + (- 48a b - 48a b)x + (96a b + 96a b )x
+--R +
+--R 4 2 3 5 4
+--R (- 384a b - 384a b )x - 768b - 768a b
+--R *
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R 5 2 4 3 2 3 4 3 2
+--R 1152a b + (1728a + 128a)b + (432a + 64a )b + (- 72a - 16a )b
+--R +
+--R 5 4 6 5
+--R (27a + 8a )b - 45a - 5a
+--R *
+--R x
+--R +
+--R 6 5 2 4 3 2 3
+--R 1152b + (1728a + 128)b + (432a + 64a)b + (- 72a - 16a )b
+--R +
+--R 4 3 2 5 4
+--R (27a + 8a )b + (- 45a - 5a )b
+--R /
+--R 6 7 5 2 6
+--R (105a b + 105a )x + 105a b + 105a b
+--R Type: Union(Expression(Integer),...)
+--E 236
+
+--S 237 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 4 2 3 3 2 2
+--R 1152b + (1728a + 128)b + (432a + 64a)b + (- 72a - 16a )b
+--R +
+--R 4 3 5 4
+--R (27a + 8a )b - 45a - 5a
+--R /
+--R 5 6
+--R 105a b + 105a
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 238
+
+)clear all
+
+--S 239 of 1379
+t0:=x^(3/2)/(a+b/x)^(3/2)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) -------------------
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 1379
+r0:=-2*x^(5/2)/(a*sqrt(a+b/x))-16/5*b*x^(3/2)*sqrt(a+b/x)/a^3+_
+ 12/5*x^(5/2)*sqrt(a+b/x)/a^2+32/5*b^2*sqrt(a+b/x)*sqrt(x)/a^4
+--R
+--R
+--R 3 3 2 2 2 3 +-+
+--R (2a x - 4a b x + 16a b x + 32b )\|x
+--R (2) --------------------------------------
+--R +-------+
+--R 4 |a x + b
+--R 5a x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 240
+
+--S 241 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 4 3 2 2 3 2 3 2 2 4
+--R (8a b + 8a )x + (- 16a b - 16a b)x + (64a b + 64a b )x + 128b
+--R +
+--R 3
+--R 128a b
+--R *
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R 4 2 3 3 2 2 4 3 5
+--R 256a b + (384a + 16a)b + (96a + 8a )b + (- 16a - 2a )b + 16a
+--R +
+--R 4
+--R a
+--R *
+--R x
+--R +
+--R 5 4 2 3 3 2 2 4 3
+--R 256b + (384a + 16)b + (96a + 8a)b + (- 16a - 2a )b + (16a + a )b
+--R /
+--R 5 6 4 2 5
+--R (20a b + 20a )x + 20a b + 20a b
+--R Type: Union(Expression(Integer),...)
+--E 241
+
+--S 242 of 1379
+m0:=a0-r0
+--R
+--R
+--R 4 3 2 2 3 2 4 3
+--R 256b + (384a + 16)b + (96a + 8a)b + (- 16a - 2a )b + 16a + a
+--R (4) -------------------------------------------------------------------
+--R 4 5
+--R 20a b + 20a
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 243
+
+)clear all
+
+--S 244 of 1379
+t0:=x^(1/2)/(a+b/x)^(3/2)
+--R
+--R
+--R +-+
+--R x\|x
+--R (1) -------------------
+--R +-------+
+--R |a x + b
+--R (a x + b) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 1379
+r0:=-2*x^(3/2)/(a*sqrt(a+b/x))+8/3*x^(3/2)*sqrt(a+b/x)/a^2-_
+ 16/3*b*sqrt(a+b/x)*sqrt(x)/a^3
+--R
+--R
+--R 2 2 2 +-+
+--R (2a x - 8a b x - 16b )\|x
+--R (2) ---------------------------
+--R +-------+
+--R 3 |a x + b
+--R 3a x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 245
+
+--S 246 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 2 3 2 2 2 3 2 |a x + b +-+
+--R ((6a b + 6a )x + (- 24a b - 24a b)x - 48b - 48a b ) |------- \|x
+--R \| x
+--R +
+--R 3 2 2 3 2 4 3 4
+--R (72a b + (108a + 8a)b + (27a + 4a )b - 9a - a )x + 72b
+--R +
+--R 3 2 2 3 2
+--R (108a + 8)b + (27a + 4a)b + (- 9a - a )b
+--R /
+--R 4 5 3 2 4
+--R (9a b + 9a )x + 9a b + 9a b
+--R Type: Union(Expression(Integer),...)
+--E 246
+
+--S 247 of 1379
+m0:=a0-r0
+--R
+--R
+--R 3 2 2 3 2
+--R 72b + (108a + 8)b + (27a + 4a)b - 9a - a
+--R (4) ---------------------------------------------
+--R 3 4
+--R 9a b + 9a
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 248
+
+)clear all
+
+--S 249 of 1379
+t0:=1/((a+b/x)^(3/2)*x^(1/2))
+--R
+--R
+--R x
+--R (1) -----------------------
+--R +-------+
+--R |a x + b +-+
+--R (a x + b) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 1379
+r0:=-2*sqrt(x)/(a*sqrt(a+b/x))+4*sqrt(a+b/x)*sqrt(x)/a^2
+--R
+--R
+--R +-+
+--R (2a x + 4b)\|x
+--R (2) ---------------
+--R +-------+
+--R 2 |a x + b
+--R a x |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 250
+
+--S 251 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 2 2 |a x + b +-+
+--R ((10a b + 10a )x + 20b + 20a b) |------- \|x
+--R \| x
+--R +
+--R 2 2 3 2 3 2 2
+--R (50a b + (75a + 2a)b + 25a + a )x + 50b + (75a + 2)b + (25a + a)b
+--R /
+--R 3 4 2 2 3
+--R (5a b + 5a )x + 5a b + 5a b
+--R Type: Union(Expression(Integer),...)
+--E 251
+
+--S 252 of 1379
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R 50b + (75a + 2)b + 25a + a
+--R (4) ----------------------------
+--R 2 3
+--R 5a b + 5a
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 253
+
+)clear all
+
+--S 254 of 1379
+t0:=1/((a+b/x)^(3/2)*x^(3/2))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +-------+
+--R |a x + b +-+
+--R (a x + b) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1379
+r0:=(-2)/(a*sqrt(a+b/x)*sqrt(x))
+--R
+--R
+--R 2
+--R (2) - ---------------
+--R +-------+
+--R |a x + b +-+
+--R a |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 255
+
+--S 256 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R |a x + b +-+ 2 2
+--R (- 4b - 4a) |------- \|x + (- 4a b - 4a - a)x - 4b + (- 4a - 1)b
+--R \| x
+--R (3) -------------------------------------------------------------------
+--R 2 3 2 2
+--R (2a b + 2a )x + 2a b + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 256
+
+--S 257 of 1379
+m0:=a0-r0
+--R
+--R
+--R - 4b - 4a - 1
+--R (4) -------------
+--R 2
+--R 2a b + 2a
+--R Type: Expression(Integer)
+--E 257
+
+--S 258 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 258
+
+)clear all
+
+--S 259 of 1379
+t0:=1/((a+b/x)^(3/2)*x^(5/2))
+--R
+--R
+--R 1
+--R (1) --------------------------
+--R +-------+
+--R 2 |a x + b +-+
+--R (a x + b x) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 1379
+r0:=-2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)+2/(b*sqrt(a+b/x)*sqrt(x))
+--R
+--R
+--R +-------+ +-+
+--R |a x + b +-+ \|b +-+
+--R - 2 |------- \|x atanh(-------------- + 2\|b
+--R \| x +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) ----------------------------------------------
+--R +-------+
+--R |a x + b +-+ +-+
+--R b |------- \|b \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 260
+
+--S 261 of 1379
+--a0:=integrate(t0,x)
+--E 261
+
+--S 262 of 1379
+--m0:=a0-r0
+--E 262
+
+--S 263 of 1379
+--d0:=D(m0,x)
+--E 263
+
+)clear all
+
+--S 264 of 1379
+t0:=1/((a+b/x)^(3/2)*x^(7/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R +-------+
+--R 3 2 |a x + b +-+
+--R (a x + b x ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 1379
+r0:=3*a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(5/2)+2/(b*x^(3/2)*_
+ sqrt(a+b/x))-3*sqrt(a+b/x)/(b^2*sqrt(x))
+--R
+--R
+--R +-------+ +-+
+--R |a x + b +-+ \|b +-+
+--R 3a x |------- \|x atanh(--------------) + (- 3a x - b)\|b
+--R \| x +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) ----------------------------------------------------------
+--R +-------+
+--R 2 |a x + b +-+ +-+
+--R b x |------- \|b \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 265
+
+--S 266 of 1379
+--a0:=integrate(t0,x)
+--E 266
+
+--S 267 of 1379
+--m0:=a0-r0
+--E 267
+
+--S 268 of 1379
+--d0:=D(m0,x)
+--E 268
+
+)clear all
+
+--S 269 of 1379
+t0:=1/((a+b/x)^(3/2)*x^(9/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R +-------+
+--R 4 3 |a x + b +-+
+--R (a x + b x ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 1379
+r0:=-15/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(7/2)+2/(b*x^(5/2)*_
+ sqrt(a+b/x))-5/2*sqrt(a+b/x)/(b^2*x^(3/2))+15/4*a*_
+ sqrt(a+b/x)/(b^3*sqrt(x))
+--R
+--R
+--R (2)
+--R +-------+ +-+
+--R 2 2 |a x + b +-+ \|b 2 2 2 +-+
+--R - 15a x |------- \|x atanh(--------------) + (15a x + 5a b x - 2b )\|b
+--R \| x +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R -------------------------------------------------------------------------
+--R +-------+
+--R 3 2 |a x + b +-+ +-+
+--R 4b x |------- \|b \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 270
+
+--S 271 of 1379
+--a0:=integrate(t0,x)
+--E 271
+
+--S 272 of 1379
+--m0:=a0-r0
+--E 272
+
+--S 273 of 1379
+--d0:=D(m0,x)
+--E 273
+
+)clear all
+
+--S 274 of 1379
+t0:=1/((a+b/x)^(3/2)*x^(11/2))
+--R
+--R
+--R 1
+--R (1) ---------------------------
+--R +-------+
+--R 5 4 |a x + b +-+
+--R (a x + b x ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 1379
+r0:=35/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(9/2)+_
+ 2/(b*x^(7/2)*sqrt(a+b/x))-7/3*sqrt(a+b/x)/(b^2*x^(5/2))+_
+ 35/12*a*sqrt(a+b/x)/(b^3*x^(3/2))-35/8*a^2*sqrt(a+b/x)/(b^4*sqrt(x))
+--R
+--R
+--R (2)
+--R +-------+ +-+
+--R 3 3 |a x + b +-+ \|b
+--R 105a x |------- \|x atanh(--------------)
+--R \| x +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (- 105a x - 35a b x + 14a b x - 8b )\|b
+--R /
+--R +-------+
+--R 4 3 |a x + b +-+ +-+
+--R 24b x |------- \|b \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 275
+
+--S 276 of 1379
+--a0:=integrate(t0,x)
+--E 276
+
+--S 277 of 1379
+--m0:=a0-r0
+--E 277
+
+--S 278 of 1379
+--d0:=D(m0,x)
+--E 278
+
+)clear all
+
+--S 279 of 1379
+t0:=x^(5/2)/(a+b/x)^(5/2)
+--R
+--R
+--R 4 +-+
+--R x \|x
+--R (1) ------------------------------
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 1379
+r0:=-2/3*x^(7/2)/(a*(a+b/x)^(3/2))-20/3*x^(7/2)/(a^2*sqrt(a+b/x))+_
+ 256/21*b^2*x^(3/2)*sqrt(a+b/x)/a^5-64/7*b*x^(5/2)*sqrt(a+b/x)/_
+ a^4+160/21*x^(7/2)*sqrt(a+b/x)/a^3-512/21*b^3*sqrt(a+b/x)*sqrt(x)/a^6
+--R
+--R
+--R 5 5 4 4 3 2 3 2 3 2 4 5 +-+
+--R (6a x - 12a b x + 32a b x - 192a b x - 768a b x - 512b )\|x
+--R (2) ----------------------------------------------------------------
+--R +-------+
+--R 7 2 6 |a x + b
+--R (21a x + 21a b x) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 280
+
+--S 281 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 6 7 5 4 3 5 2 6 4
+--R (12a b + 24a b + 12a )x + (- 24a b - 48a b - 24a b)x
+--R +
+--R 3 4 4 3 5 2 3 2 5 3 4 4 3 2
+--R (64a b + 128a b + 64a b )x + (- 384a b - 768a b - 384a b )x
+--R +
+--R 6 2 5 3 4 7 6 2 5
+--R (- 1536a b - 3072a b - 1536a b )x - 1024b - 2048a b - 1024a b
+--R *
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R 2 6 3 2 5 4 3 4 5 4 3
+--R 1024a b + (2560a + 256a )b + (1920a + 384a )b + (320a + 96a )b
+--R +
+--R 6 5 2 7 6 8 7
+--R (- 40a - 16a )b + (12a + 6a )b - 12a - 3a
+--R *
+--R 2
+--R x
+--R +
+--R 7 2 6 3 2 5 4 3 4
+--R 2048a b + (5120a + 512a)b + (3840a + 768a )b + (640a + 192a )b
+--R +
+--R 5 4 3 6 5 2 7 6
+--R (- 80a - 32a )b + (24a + 12a )b + (- 24a - 6a )b
+--R *
+--R x
+--R +
+--R 8 7 2 6 3 2 5
+--R 1024b + (2560a + 256)b + (1920a + 384a)b + (320a + 96a )b
+--R +
+--R 4 3 4 5 4 3 6 5 2
+--R (- 40a - 16a )b + (12a + 6a )b + (- 12a - 3a )b
+--R /
+--R 8 2 9 10 2 7 3 8 2 9 6 4
+--R (42a b + 84a b + 42a )x + (84a b + 168a b + 84a b)x + 42a b
+--R +
+--R 7 3 8 2
+--R 84a b + 42a b
+--R Type: Union(Expression(Integer),...)
+--E 281
+
+--S 282 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 6 5 2 4 3 2 3
+--R 1024b + (2560a + 256)b + (1920a + 384a)b + (320a + 96a )b
+--R +
+--R 4 3 2 5 4 6 5
+--R (- 40a - 16a )b + (12a + 6a )b - 12a - 3a
+--R /
+--R 6 2 7 8
+--R 42a b + 84a b + 42a
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 283
+
+)clear all
+
+--S 284 of 1379
+t0:=x^(3/2)/(a+b/x)^(5/2)
+--R
+--R
+--R 3 +-+
+--R x \|x
+--R (1) ------------------------------
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 1379
+r0:=-2/3*x^(5/2)/(a*(a+b/x)^(3/2))-16/3*x^(5/2)/(a^2*sqrt(a+b/x))-_
+ 128/15*b*x^(3/2)*sqrt(a+b/x)/a^4+32/5*x^(5/2)*sqrt(a+b/x)/_
+ a^3+256/15*b^2*sqrt(a+b/x)*sqrt(x)/a^5
+--R
+--R
+--R 4 4 3 3 2 2 2 3 4 +-+
+--R (6a x - 16a b x + 96a b x + 384a b x + 256b )\|x
+--R (2) ----------------------------------------------------
+--R +-------+
+--R 6 2 5 |a x + b
+--R (15a x + 15a b x) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 285
+
+--S 286 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 5 6 4 3 3 4 2 5 3
+--R (24a b + 48a b + 24a )x + (- 64a b - 128a b - 64a b)x
+--R +
+--R 2 4 3 3 4 2 2 5 2 4 3 3
+--R (384a b + 768a b + 384a b )x + (1536a b + 3072a b + 1536a b )x
+--R +
+--R 6 5 2 4
+--R 1024b + 2048a b + 1024a b
+--R *
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R 2 5 3 2 4 4 3 3 5 4 2
+--R 2048a b + (5120a + 128a )b + (3840a + 192a )b + (640a + 48a )b
+--R +
+--R 6 5 7 6
+--R (- 80a - 8a )b + 48a + 3a
+--R *
+--R 2
+--R x
+--R +
+--R 6 2 5 3 2 4
+--R 4096a b + (10240a + 256a)b + (7680a + 384a )b
+--R +
+--R 4 3 3 5 4 2 6 5
+--R (1280a + 96a )b + (- 160a - 16a )b + (96a + 6a )b
+--R *
+--R x
+--R +
+--R 7 6 2 5 3 2 4
+--R 2048b + (5120a + 128)b + (3840a + 192a)b + (640a + 48a )b
+--R +
+--R 4 3 3 5 4 2
+--R (- 80a - 8a )b + (48a + 3a )b
+--R /
+--R 7 2 8 9 2 6 3 7 2 8 5 4
+--R (60a b + 120a b + 60a )x + (120a b + 240a b + 120a b)x + 60a b
+--R +
+--R 6 3 7 2
+--R 120a b + 60a b
+--R Type: Union(Expression(Integer),...)
+--E 286
+
+--S 287 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 4 2 3 3 2 2
+--R 2048b + (5120a + 128)b + (3840a + 192a)b + (640a + 48a )b
+--R +
+--R 4 3 5 4
+--R (- 80a - 8a )b + 48a + 3a
+--R /
+--R 5 2 6 7
+--R 60a b + 120a b + 60a
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 288
+
+)clear all
+
+--S 289 of 1379
+t0:=x^(1/2)/(a+b/x)^(5/2)
+--R
+--R
+--R 2 +-+
+--R x \|x
+--R (1) ------------------------------
+--R +-------+
+--R 2 2 2 |a x + b
+--R (a x + 2a b x + b ) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 1379
+r0:=-2/3*x^(3/2)/(a*(a+b/x)^(3/2))-4*x^(3/2)/(a^2*sqrt(a+b/x))+_
+ 16/3*x^(3/2)*sqrt(a+b/x)/a^3-32/3*b*sqrt(a+b/x)*sqrt(x)/a^4
+--R
+--R
+--R 3 3 2 2 2 3 +-+
+--R (2a x - 12a b x - 48a b x - 32b )\|x
+--R (2) ---------------------------------------
+--R +-------+
+--R 5 2 4 |a x + b
+--R (3a x + 3a b x) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 290
+
+--S 291 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 5 3 2 3 3 2 4 2
+--R (6a b + 12a b + 6a )x + (- 36a b - 72a b - 36a b)x
+--R +
+--R 4 2 3 3 2 5 4 2 3
+--R (- 144a b - 288a b - 144a b )x - 96b - 192a b - 96a b
+--R *
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R 2 4 3 2 3 4 3 2 5 4 6
+--R 144a b + (360a + 16a )b + (270a + 24a )b + (45a + 6a )b - 9a
+--R +
+--R 5
+--R - a
+--R *
+--R 2
+--R x
+--R +
+--R 5 2 4 3 2 3 4 3 2
+--R 288a b + (720a + 32a)b + (540a + 48a )b + (90a + 12a )b
+--R +
+--R 5 4
+--R (- 18a - 2a )b
+--R *
+--R x
+--R +
+--R 6 5 2 4 3 2 3 4 3 2
+--R 144b + (360a + 16)b + (270a + 24a)b + (45a + 6a )b + (- 9a - a )b
+--R /
+--R 6 2 7 8 2 5 3 6 2 7 4 4 5 3
+--R (9a b + 18a b + 9a )x + (18a b + 36a b + 18a b)x + 9a b + 18a b
+--R +
+--R 6 2
+--R 9a b
+--R Type: Union(Expression(Integer),...)
+--E 291
+
+--S 292 of 1379
+m0:=a0-r0
+--R
+--R
+--R 4 3 2 2 3 2 4 3
+--R 144b + (360a + 16)b + (270a + 24a)b + (45a + 6a )b - 9a - a
+--R (4) ------------------------------------------------------------------
+--R 4 2 5 6
+--R 9a b + 18a b + 9a
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 293
+
+)clear all
+
+--S 294 of 1379
+t0:=1/((a+b/x)^(5/2)*x^(1/2))
+--R
+--R
+--R 2
+--R x
+--R (1) ----------------------------------
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (a x + 2a b x + b ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 1379
+r0:=-2/3*sqrt(x)/(a*(a+b/x)^(3/2))-8/3*sqrt(x)/(a^2*sqrt(a+b/x))+_
+ 16/3*sqrt(a+b/x)*sqrt(x)/a^3
+--R
+--R
+--R 2 2 2 +-+
+--R (6a x + 24a b x + 16b )\|x
+--R (2) ----------------------------
+--R +-------+
+--R 4 2 3 |a x + b
+--R (3a x + 3a b x) |-------
+--R \| x
+--R Type: Expression(Integer)
+--E 295
+
+--S 296 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 4 2 3 2 2 3 4
+--R (30a b + 60a b + 30a )x + (120a b + 240a b + 120a b)x + 80b
+--R +
+--R 3 2 2
+--R 160a b + 80a b
+--R *
+--R +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R 2 3 3 2 2 4 3 5 4 2
+--R (200a b + (500a + 8a )b + (375a + 12a )b + 75a + 3a )x
+--R +
+--R 4 2 3 3 2 2 4 3 5
+--R (400a b + (1000a + 16a)b + (750a + 24a )b + (150a + 6a )b)x + 200b
+--R +
+--R 4 2 3 3 2 2
+--R (500a + 8)b + (375a + 12a)b + (75a + 3a )b
+--R /
+--R 5 2 6 7 2 4 3 5 2 6 3 4 4 3
+--R (15a b + 30a b + 15a )x + (30a b + 60a b + 30a b)x + 15a b + 30a b
+--R +
+--R 5 2
+--R 15a b
+--R Type: Union(Expression(Integer),...)
+--E 296
+
+--S 297 of 1379
+m0:=a0-r0
+--R
+--R
+--R 3 2 2 3 2
+--R 200b + (500a + 8)b + (375a + 12a)b + 75a + 3a
+--R (4) --------------------------------------------------
+--R 3 2 4 5
+--R 15a b + 30a b + 15a
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 298
+
+)clear all
+
+--S 299 of 1379
+t0:=1/((a+b/x)^(5/2)*x^(3/2))
+--R
+--R
+--R x
+--R (1) ----------------------------------
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (a x + 2a b x + b ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 1379
+r0:=(-2/3)/(a*(a+b/x)^(3/2)*sqrt(x))+(-4/3)/(a^2*sqrt(a+b/x)*sqrt(x))
+--R
+--R
+--R - 6a x - 4b
+--R (2) ---------------------------
+--R +-------+
+--R 3 2 |a x + b +-+
+--R (3a x + 3a b) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 300
+
+--S 301 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 2 2 3 3 2 2 |a x + b +-+
+--R ((- 18a b - 36a b - 18a )x - 12b - 24a b - 12a b) |------- \|x
+--R \| x
+--R +
+--R 2 2 3 2 4 3 2
+--R (18a b + (45a + 2a )b + 27a + 3a )x
+--R +
+--R 3 2 2 3 2 4 3
+--R (36a b + (90a + 4a)b + (54a + 6a )b)x + 18b + (45a + 2)b
+--R +
+--R 2 2
+--R (27a + 3a)b
+--R /
+--R 4 2 5 6 2 3 3 4 2 5 2 4 3 3
+--R (9a b + 18a b + 9a )x + (18a b + 36a b + 18a b)x + 9a b + 18a b
+--R +
+--R 4 2
+--R 9a b
+--R Type: Union(Expression(Integer),...)
+--E 301
+
+--S 302 of 1379
+m0:=a0-r0
+--R
+--R
+--R 2 2
+--R 18b + (45a + 2)b + 27a + 3a
+--R (4) -----------------------------
+--R 2 2 3 4
+--R 9a b + 18a b + 9a
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 303
+
+)clear all
+
+--S 304 of 1379
+t0:=1/((a+b/x)^(5/2)*x^(5/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +-------+
+--R 2 2 2 |a x + b +-+
+--R (a x + 2a b x + b ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 1379
+r0:=(-2/3)/(a*(a+b/x)^(3/2)*x^(3/2))
+--R
+--R
+--R 2
+--R (2) - ---------------------------
+--R +-------+
+--R 2 |a x + b +-+
+--R (3a x + 3a b) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 305
+
+--S 306 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+
+--R 2 2 |a x + b +-+ 2 3 2 2
+--R (- 4b - 8a b - 4a ) |------- \|x + (4a b + 4a + a )x
+--R \| x
+--R +
+--R 2 2 3 2
+--R (8a b + (8a + 2a)b)x + 4b + (4a + 1)b
+--R /
+--R 3 2 4 5 2 2 3 3 2 4 4 2 3
+--R (6a b + 12a b + 6a )x + (12a b + 24a b + 12a b)x + 6a b + 12a b
+--R +
+--R 3 2
+--R 6a b
+--R Type: Union(Expression(Integer),...)
+--E 306
+
+--S 307 of 1379
+m0:=a0-r0
+--R
+--R
+--R 4b + 4a + 1
+--R (4) -------------------
+--R 2 2 3
+--R 6a b + 12a b + 6a
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 308
+
+)clear all
+
+--S 309 of 1379
+t0:=1/((a+b/x)^(5/2)*x^(7/2))
+--R
+--R
+--R 1
+--R (1) ------------------------------------
+--R +-------+
+--R 2 3 2 2 |a x + b +-+
+--R (a x + 2a b x + b x) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 309
+
+--S 310 of 1379
+r0:=2/3/(b*(a+b/x)^(3/2)*x^(3/2))-2*atanh(sqrt(b)/(sqrt(a+b/x)*_
+ sqrt(x)))/b^(5/2)+2/(b^2*sqrt(a+b/x)*sqrt(x))
+--R
+--R
+--R +-------+ +-+
+--R |a x + b +-+ \|b +-+
+--R (- 6a x - 6b) |------- \|x atanh(--------------) + (6a x + 8b)\|b
+--R \| x +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R (2) ------------------------------------------------------------------
+--R +-------+
+--R 2 3 |a x + b +-+ +-+
+--R (3a b x + 3b ) |------- \|b \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 310
+
+--S 311 of 1379
+--a0:=integrate(t0,x)
+--E 311
+
+--S 312 of 1379
+--m0:=a0-r0
+--E 312
+
+--S 313 of 1379
+--d0:=D(m0,x)
+--E 313
+
+)clear all
+
+--S 314 of 1379
+t0:=1/((a+b/x)^(5/2)*x^(9/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R +-------+
+--R 2 4 3 2 2 |a x + b +-+
+--R (a x + 2a b x + b x ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 1379
+r0:=2/3/(b*(a+b/x)^(3/2)*x^(5/2))+5*a*atanh(sqrt(b)/(sqrt(a+b/x)*_
+ sqrt(x)))/b^(7/2)+10/3/(b^2*x^(3/2)*sqrt(a+b/x))-_
+ 5*sqrt(a+b/x)/(b^3*sqrt(x))
+--R
+--R
+--R (2)
+--R +-------+ +-+
+--R 2 2 |a x + b +-+ \|b
+--R (15a x + 15a b x) |------- \|x atanh(--------------)
+--R \| x +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R 2 2 2 +-+
+--R (- 15a x - 20a b x - 3b )\|b
+--R /
+--R +-------+
+--R 3 2 4 |a x + b +-+ +-+
+--R (3a b x + 3b x) |------- \|b \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 315
+
+--S 316 of 1379
+--a0:=integrate(t0,x)
+--E 316
+
+--S 317 of 1379
+--m0:=a0-r0
+--E 317
+
+--S 318 of 1379
+--d0:=D(m0,x)
+--E 318
+
+)clear all
+
+--S 319 of 1379
+t0:=1/((a+b/x)^(5/2)*x^(11/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------
+--R +-------+
+--R 2 5 4 2 3 |a x + b +-+
+--R (a x + 2a b x + b x ) |------- \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 1379
+r0:=2/3/(b*(a+b/x)^(3/2)*x^(7/2))-35/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*_
+ sqrt(x)))/b^(9/2)+14/3/(b^2*x^(5/2)*sqrt(a+b/x))-_
+ 35/6*sqrt(a+b/x)/(b^3*x^(3/2))+35/4*a*sqrt(a+b/x)/(b^4*sqrt(x))
+--R
+--R
+--R (2)
+--R +-------+ +-+
+--R 3 3 2 2 |a x + b +-+ \|b
+--R (- 105a x - 105a b x ) |------- \|x atanh(--------------)
+--R \| x +-------+
+--R |a x + b +-+
+--R |------- \|x
+--R \| x
+--R +
+--R 3 3 2 2 2 3 +-+
+--R (105a x + 140a b x + 21a b x - 6b )\|b
+--R /
+--R +-------+
+--R 4 3 5 2 |a x + b +-+ +-+
+--R (12a b x + 12b x ) |------- \|b \|x
+--R \| x
+--R Type: Expression(Integer)
+--E 320
+
+--S 321 of 1379
+--a0:=integrate(t0,x)
+--E 321
+
+--S 322 of 1379
+--m0:=a0-r0
+--E 322
+
+--S 323 of 1379
+--d0:=D(m0,x)
+--E 323
+
+)clear all
+
+--S 324 of 1379
+t0:=(a+b/x^2)*x^6
+--R
+--R
+--R 6 4
+--R (1) a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 324
+
+--S 325 of 1379
+r0:=1/5*b*x^5+1/7*a*x^7
+--R
+--R
+--R 1 7 1 5
+--R (2) - a x + - b x
+--R 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 325
+
+--S 326 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 7 5
+--R 5a x + 7b x
+--R (3) -------------
+--R 35
+--R Type: Union(Expression(Integer),...)
+--E 326
+
+--S 327 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 327
+
+--S 328 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 328
+
+)clear all
+
+--S 329 of 1379
+t0:=(a+b/x^2)*x^5
+--R
+--R
+--R 5 3
+--R (1) a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 329
+
+--S 330 of 1379
+r0:=1/4*b*x^4+1/6*a*x^6
+--R
+--R
+--R 1 6 1 4
+--R (2) - a x + - b x
+--R 6 4
+--R Type: Polynomial(Fraction(Integer))
+--E 330
+
+--S 331 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 6 4
+--R 2a x + 3b x
+--R (3) -------------
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 331
+
+--S 332 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 333
+
+)clear all
+
+--S 334 of 1379
+t0:=(a+b/x^2)*x^4
+--R
+--R
+--R 4 2
+--R (1) a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 334
+
+--S 335 of 1379
+r0:=1/3*b*x^3+1/5*a*x^5
+--R
+--R
+--R 1 5 1 3
+--R (2) - a x + - b x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 335
+
+--S 336 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 3
+--R 3a x + 5b x
+--R (3) -------------
+--R 15
+--R Type: Union(Expression(Integer),...)
+--E 336
+
+--S 337 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 338
+
+)clear all
+
+--S 339 of 1379
+t0:=(a+b/x^2)*x^3
+--R
+--R
+--R 3
+--R (1) a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 339
+
+--S 340 of 1379
+r0:=1/2*b*x^2+1/4*a*x^4
+--R
+--R
+--R 1 4 1 2
+--R (2) - a x + - b x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 340
+
+--S 341 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R a x + 2b x
+--R (3) ------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 341
+
+--S 342 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 343
+
+)clear all
+
+--S 344 of 1379
+t0:=(a+b/x^2)*x^2
+--R
+--R
+--R 2
+--R (1) a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 344
+
+--S 345 of 1379
+r0:=b*x+1/3*a*x^3
+--R
+--R
+--R 1 3
+--R (2) - a x + b x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 345
+
+--S 346 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R a x + 3b x
+--R (3) -----------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 346
+
+--S 347 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 348
+
+)clear all
+
+--S 349 of 1379
+t0:=(a+b/x^2)*x
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 349
+
+--S 350 of 1379
+r0:=1/2*a*x^2+b*log(x)
+--R
+--R
+--R 2
+--R 2b log(x) + a x
+--R (2) ----------------
+--R 2
+--R Type: Expression(Integer)
+--E 350
+
+--S 351 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 2b log(x) + a x
+--R (3) ----------------
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 351
+
+--S 352 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 353
+
+)clear all
+
+--S 354 of 1379
+t0:=a+b/x^2
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 354
+
+--S 355 of 1379
+r0:=-b/x+a*x
+--R
+--R
+--R 2
+--R a x - b
+--R (2) --------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 355
+
+--S 356 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R a x - b
+--R (3) --------
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 356
+
+--S 357 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 358
+
+)clear all
+
+--S 359 of 1379
+t0:=(a+b/x^2)/x
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 359
+
+--S 360 of 1379
+r0:=-1/2*b/x^2+a*log(x)
+--R
+--R
+--R 2
+--R 2a x log(x) - b
+--R (2) ---------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 360
+
+--S 361 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R 2a x log(x) - b
+--R (3) ---------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 361
+
+--S 362 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 363
+
+)clear all
+
+--S 364 of 1379
+t0:=(a+b/x^2)/x^2
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 364
+
+--S 365 of 1379
+r0:=-1/3*b/x^3-a/x
+--R
+--R
+--R 2 1
+--R - a x - - b
+--R 3
+--R (2) ------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 365
+
+--S 366 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 3a x - b
+--R (3) -----------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 366
+
+--S 367 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 368
+
+)clear all
+
+--S 369 of 1379
+t0:=(a+b/x^2)/x^3
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 369
+
+--S 370 of 1379
+r0:=-1/4*b/x^4-1/2*a/x^2
+--R
+--R
+--R 1 2 1
+--R - - a x - - b
+--R 2 4
+--R (2) --------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 370
+
+--S 371 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 2a x - b
+--R (3) -----------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 371
+
+--S 372 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 372
+
+--S 373 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 373
+
+)clear all
+
+--S 374 of 1379
+t0:=(a+b/x^2)/x^4
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 374
+
+--S 375 of 1379
+r0:=-1/5*b/x^5-1/3*a/x^3
+--R
+--R
+--R 1 2 1
+--R - - a x - - b
+--R 3 5
+--R (2) --------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 375
+
+--S 376 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 5a x - 3b
+--R (3) ------------
+--R 5
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 376
+
+--S 377 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 378
+
+)clear all
+
+--S 379 of 1379
+t0:=(a+b/x^2)/x^5
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 379
+
+--S 380 of 1379
+r0:=-1/6*b/x^6-1/4*a/x^4
+--R
+--R
+--R 1 2 1
+--R - - a x - - b
+--R 4 6
+--R (2) --------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 380
+
+--S 381 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 3a x - 2b
+--R (3) ------------
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 381
+
+--S 382 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 383
+
+)clear all
+
+--S 384 of 1379
+t0:=(a+b/x^2)/x^6
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 384
+
+--S 385 of 1379
+r0:=-1/7*b/x^7-1/5*a/x^5
+--R
+--R
+--R 1 2 1
+--R - - a x - - b
+--R 5 7
+--R (2) --------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 385
+
+--S 386 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 7a x - 5b
+--R (3) ------------
+--R 7
+--R 35x
+--R Type: Union(Expression(Integer),...)
+--E 386
+
+--S 387 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 388
+
+)clear all
+
+--S 389 of 1379
+t0:=(a+b/x^2)^2*x^6
+--R
+--R
+--R 2 6 4 2 2
+--R (1) a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 389
+
+--S 390 of 1379
+r0:=1/3*b^2*x^3+2/5*a*b*x^5+1/7*a^2*x^7
+--R
+--R
+--R 1 2 7 2 5 1 2 3
+--R (2) - a x + - a b x + - b x
+--R 7 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 390
+
+--S 391 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 7 5 2 3
+--R 15a x + 42a b x + 35b x
+--R (3) --------------------------
+--R 105
+--R Type: Union(Expression(Integer),...)
+--E 391
+
+--S 392 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 393
+
+)clear all
+
+--S 394 of 1379
+t0:=(a+b/x^2)^2*x^5
+--R
+--R
+--R 2 5 3 2
+--R (1) a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 394
+
+--S 395 of 1379
+r0:=1/6*(a+b/x^2)^3*x^6/a
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (2) -----------------------------
+--R 6a
+--R Type: Fraction(Polynomial(Integer))
+--E 395
+
+--S 396 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 4 2 2
+--R a x + 3a b x + 3b x
+--R (3) ----------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 396
+
+--S 397 of 1379
+m0:=a0-r0
+--R
+--R
+--R 3
+--R b
+--R (4) - --
+--R 6a
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 398
+
+)clear all
+
+--S 399 of 1379
+t0:=(a+b/x^2)^2*x^4
+--R
+--R
+--R 2 4 2 2
+--R (1) a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 399
+
+--S 400 of 1379
+r0:=b^2*x+2/3*a*b*x^3+1/5*a^2*x^5
+--R
+--R
+--R 1 2 5 2 3 2
+--R (2) - a x + - a b x + b x
+--R 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 400
+
+--S 401 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 5 3 2
+--R 3a x + 10a b x + 15b x
+--R (3) ------------------------
+--R 15
+--R Type: Union(Expression(Integer),...)
+--E 401
+
+--S 402 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 403
+
+)clear all
+
+--S 404 of 1379
+t0:=(a+b/x^2)^2*x^3
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 404
+
+--S 405 of 1379
+r0:=a*b*x^2+1/4*a^2*x^4+b^2*log(x)
+--R
+--R
+--R 2 2 4 2
+--R 4b log(x) + a x + 4a b x
+--R (2) --------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 405
+
+--S 406 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 4 2
+--R 4b log(x) + a x + 4a b x
+--R (3) --------------------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 406
+
+--S 407 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 408
+
+)clear all
+
+--S 409 of 1379
+t0:=(a+b/x^2)^2*x^2
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 409
+
+--S 410 of 1379
+r0:=-b^2/x+2*a*b*x+1/3*a^2*x^3
+--R
+--R
+--R 2 4 2 2
+--R a x + 6a b x - 3b
+--R (2) --------------------
+--R 3x
+--R Type: Fraction(Polynomial(Integer))
+--E 410
+
+--S 411 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R a x + 6a b x - 3b
+--R (3) --------------------
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 411
+
+--S 412 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 413
+
+)clear all
+
+--S 414 of 1379
+t0:=(a+b/x^2)^2*x
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 414
+
+--S 415 of 1379
+r0:=-1/2*b^2/x^2+1/2*a^2*x^2+2*a*b*log(x)
+--R
+--R
+--R 2 2 4 2
+--R 4a b x log(x) + a x - b
+--R (2) -------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 415
+
+--S 416 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 4 2
+--R 4a b x log(x) + a x - b
+--R (3) -------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 416
+
+--S 417 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 418
+
+)clear all
+
+--S 419 of 1379
+t0:=(a+b/x^2)^2
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 419
+
+--S 420 of 1379
+r0:=-1/3*b^2/x^3-2*a*b/x+a^2*x
+--R
+--R
+--R 2 4 2 1 2
+--R a x - 2a b x - - b
+--R 3
+--R (2) ---------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 420
+
+--S 421 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R 3a x - 6a b x - b
+--R (3) --------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 421
+
+--S 422 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 423
+
+)clear all
+
+--S 424 of 1379
+t0:=(a+b/x^2)^2/x
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 424
+
+--S 425 of 1379
+r0:=-1/4*b^2/x^4-a*b/x^2+a^2*log(x)
+--R
+--R
+--R 2 4 2 2
+--R 4a x log(x) - 4a b x - b
+--R (2) --------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 425
+
+--S 426 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R 4a x log(x) - 4a b x - b
+--R (3) --------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 426
+
+--S 427 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 428
+
+)clear all
+
+--S 429 of 1379
+t0:=(a+b/x^2)^2/x^2
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 429
+
+--S 430 of 1379
+r0:=-1/5*b^2/x^5-2/3*a*b/x^3-a^2/x
+--R
+--R
+--R 2 4 2 2 1 2
+--R - a x - - a b x - - b
+--R 3 5
+--R (2) ------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 430
+
+--S 431 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 15a x - 10a b x - 3b
+--R (3) -------------------------
+--R 5
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 431
+
+--S 432 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 433
+
+)clear all
+
+--S 434 of 1379
+t0:=(a+b/x^2)^2/x^3
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 434
+
+--S 435 of 1379
+r0:=-1/6*(a+b/x^2)^3/b
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - a x - 3a b x - 3a b x - b
+--R (2) -------------------------------
+--R 6
+--R 6b x
+--R Type: Fraction(Polynomial(Integer))
+--E 435
+
+--S 436 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 3a x - 3a b x - b
+--R (3) ----------------------
+--R 6
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 436
+
+--S 437 of 1379
+m0:=a0-r0
+--R
+--R
+--R 3
+--R a
+--R (4) --
+--R 6b
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 438
+
+)clear all
+
+--S 439 of 1379
+t0:=(a+b/x^2)^2/x^4
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 439
+
+--S 440 of 1379
+r0:=-1/7*b^2/x^7-2/5*a*b/x^5-1/3*a^2/x^3
+--R
+--R
+--R 1 2 4 2 2 1 2
+--R - - a x - - a b x - - b
+--R 3 5 7
+--R (2) --------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 440
+
+--S 441 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 35a x - 42a b x - 15b
+--R (3) --------------------------
+--R 7
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 441
+
+--S 442 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 443
+
+)clear all
+
+--S 444 of 1379
+t0:=(a+b/x^2)^2/x^5
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 444
+
+--S 445 of 1379
+r0:=-1/8*b^2/x^8-1/3*a*b/x^6-1/4*a^2/x^4
+--R
+--R
+--R 1 2 4 1 2 1 2
+--R - - a x - - a b x - - b
+--R 4 3 8
+--R (2) --------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 445
+
+--S 446 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 6a x - 8a b x - 3b
+--R (3) -----------------------
+--R 8
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 446
+
+--S 447 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 448
+
+)clear all
+
+--S 449 of 1379
+t0:=(a+b/x^2)^2/x^6
+--R
+--R
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R (1) -------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 449
+
+--S 450 of 1379
+r0:=-1/9*b^2/x^9-2/7*a*b/x^7-1/5*a^2/x^5
+--R
+--R
+--R 1 2 4 2 2 1 2
+--R - - a x - - a b x - - b
+--R 5 7 9
+--R (2) --------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 450
+
+--S 451 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2
+--R - 63a x - 90a b x - 35b
+--R (3) --------------------------
+--R 9
+--R 315x
+--R Type: Union(Expression(Integer),...)
+--E 451
+
+--S 452 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 453
+
+)clear all
+
+--S 454 of 1379
+t0:=(a+b/x^2)^3*x^6
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R (1) a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 454
+
+--S 455 of 1379
+r0:=b^3*x+a*b^2*x^3+3/5*a^2*b*x^5+1/7*a^3*x^7
+--R
+--R
+--R 1 3 7 3 2 5 2 3 3
+--R (2) - a x + - a b x + a b x + b x
+--R 7 5
+--R Type: Polynomial(Fraction(Integer))
+--E 455
+
+--S 456 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 7 2 5 2 3 3
+--R 5a x + 21a b x + 35a b x + 35b x
+--R (3) -----------------------------------
+--R 35
+--R Type: Union(Expression(Integer),...)
+--E 456
+
+--S 457 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 457
+
+--S 458 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 458
+
+)clear all
+
+--S 459 of 1379
+t0:=(a+b/x^2)^3*x^5
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 459
+
+--S 460 of 1379
+r0:=3/2*a*b^2*x^2+3/4*a^2*b*x^4+1/6*a^3*x^6+b^3*log(x)
+--R
+--R
+--R 3 3 6 2 4 2 2
+--R 12b log(x) + 2a x + 9a b x + 18a b x
+--R (2) ---------------------------------------
+--R 12
+--R Type: Expression(Integer)
+--E 460
+
+--S 461 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 6 2 4 2 2
+--R 12b log(x) + 2a x + 9a b x + 18a b x
+--R (3) ---------------------------------------
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 461
+
+--S 462 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 463
+
+)clear all
+
+--S 464 of 1379
+t0:=(a+b/x^2)^3*x^4
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 464
+
+--S 465 of 1379
+r0:=-b^3/x+3*a*b^2*x+a^2*b*x^3+1/5*a^3*x^5
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 5a b x + 15a b x - 5b
+--R (2) -------------------------------
+--R 5x
+--R Type: Fraction(Polynomial(Integer))
+--E 465
+
+--S 466 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 5a b x + 15a b x - 5b
+--R (3) -------------------------------
+--R 5x
+--R Type: Union(Expression(Integer),...)
+--E 466
+
+--S 467 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 468
+
+)clear all
+
+--S 469 of 1379
+t0:=(a+b/x^2)^3*x^3
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 469
+
+--S 470 of 1379
+r0:=-1/2*b^3/x^2+3/2*a^2*b*x^2+1/4*a^3*x^4+3*a*b^2*log(x)
+--R
+--R
+--R 2 2 3 6 2 4 3
+--R 12a b x log(x) + a x + 6a b x - 2b
+--R (2) -------------------------------------
+--R 2
+--R 4x
+--R Type: Expression(Integer)
+--E 470
+
+--S 471 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 3 6 2 4 3
+--R 12a b x log(x) + a x + 6a b x - 2b
+--R (3) -------------------------------------
+--R 2
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 471
+
+--S 472 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 473
+
+)clear all
+
+--S 474 of 1379
+t0:=(a+b/x^2)^3*x^2
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 474
+
+--S 475 of 1379
+r0:=-1/3*b^3/x^3-3*a*b^2/x+3*a^2*b*x+1/3*a^3*x^3
+--R
+--R
+--R 1 3 6 2 4 2 2 1 3
+--R - a x + 3a b x - 3a b x - - b
+--R 3 3
+--R (2) ---------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 475
+
+--S 476 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 9a b x - 9a b x - b
+--R (3) -----------------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 476
+
+--S 477 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 478
+
+)clear all
+
+--S 479 of 1379
+t0:=(a+b/x^2)^3*x
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 479
+
+--S 480 of 1379
+r0:=-1/4*b^3/x^4-3/2*a*b^2/x^2+1/2*a^3*x^2+3*a^2*b*log(x)
+--R
+--R
+--R 2 4 3 6 2 2 3
+--R 12a b x log(x) + 2a x - 6a b x - b
+--R (2) -------------------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 480
+
+--S 481 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 3 6 2 2 3
+--R 12a b x log(x) + 2a x - 6a b x - b
+--R (3) -------------------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 481
+
+--S 482 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 483
+
+)clear all
+
+--S 484 of 1379
+t0:=(a+b/x^2)^3
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 484
+
+--S 485 of 1379
+r0:=-1/5*b^3/x^5-a*b^2/x^3-3*a^2*b/x+a^3*x
+--R
+--R
+--R 3 6 2 4 2 2 1 3
+--R a x - 3a b x - a b x - - b
+--R 5
+--R (2) ------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 485
+
+--S 486 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 5a x - 15a b x - 5a b x - b
+--R (3) -------------------------------
+--R 5
+--R 5x
+--R Type: Union(Expression(Integer),...)
+--E 486
+
+--S 487 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 488
+
+)clear all
+
+--S 489 of 1379
+t0:=(a+b/x^2)^3/x
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 489
+
+--S 490 of 1379
+r0:=-1/6*b^3/x^6-3/4*a*b^2/x^4-3/2*a^2*b/x^2+a^3*log(x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 12a x log(x) - 18a b x - 9a b x - 2b
+--R (2) ---------------------------------------
+--R 6
+--R 12x
+--R Type: Expression(Integer)
+--E 490
+
+--S 491 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 12a x log(x) - 18a b x - 9a b x - 2b
+--R (3) ---------------------------------------
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 491
+
+--S 492 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 493
+
+)clear all
+
+--S 494 of 1379
+t0:=(a+b/x^2)^3/x^2
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 494
+
+--S 495 of 1379
+r0:=-1/7*b^3/x^7-3/5*a*b^2/x^5-a^2*b/x^3-a^3/x
+--R
+--R
+--R 3 6 2 4 3 2 2 1 3
+--R - a x - a b x - - a b x - - b
+--R 5 7
+--R (2) ---------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 495
+
+--S 496 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 35a x - 35a b x - 21a b x - 5b
+--R (3) ------------------------------------
+--R 7
+--R 35x
+--R Type: Union(Expression(Integer),...)
+--E 496
+
+--S 497 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 498
+
+)clear all
+
+--S 499 of 1379
+t0:=(a+b/x^2)^3/x^3
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 499
+
+--S 500 of 1379
+r0:=-1/8*(a+b/x^2)^4/b
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R - a x - 4a b x - 6a b x - 4a b x - b
+--R (2) -----------------------------------------
+--R 8
+--R 8b x
+--R Type: Fraction(Polynomial(Integer))
+--E 500
+
+--S 501 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 4a x - 6a b x - 4a b x - b
+--R (3) --------------------------------
+--R 8
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 501
+
+--S 502 of 1379
+m0:=a0-r0
+--R
+--R
+--R 4
+--R a
+--R (4) --
+--R 8b
+--R Type: Expression(Integer)
+--E 502
+
+--S 503 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 503
+
+)clear all
+
+--S 504 of 1379
+t0:=(a+b/x^2)^3/x^4
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 504
+
+--S 505 of 1379
+r0:=-1/9*b^3/x^9-3/7*a*b^2/x^7-3/5*a^2*b/x^5-1/3*a^3/x^3
+--R
+--R
+--R 1 3 6 3 2 4 3 2 2 1 3
+--R - - a x - - a b x - - a b x - - b
+--R 3 5 7 9
+--R (2) -------------------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 505
+
+--S 506 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 105a x - 189a b x - 135a b x - 35b
+--R (3) ----------------------------------------
+--R 9
+--R 315x
+--R Type: Union(Expression(Integer),...)
+--E 506
+
+--S 507 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 507
+
+--S 508 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 508
+
+)clear all
+
+--S 509 of 1379
+t0:=(a+b/x^2)^3/x^5
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 509
+
+--S 510 of 1379
+r0:=-1/10*b^3/x^10-3/8*a*b^2/x^8-1/2*a^2*b/x^6-1/4*a^3/x^4
+--R
+--R
+--R 1 3 6 1 2 4 3 2 2 1 3
+--R - - a x - - a b x - - a b x - -- b
+--R 4 2 8 10
+--R (2) --------------------------------------
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 510
+
+--S 511 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 10a x - 20a b x - 15a b x - 4b
+--R (3) ------------------------------------
+--R 10
+--R 40x
+--R Type: Union(Expression(Integer),...)
+--E 511
+
+--S 512 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 512
+
+--S 513 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 513
+
+)clear all
+
+--S 514 of 1379
+t0:=(a+b/x^2)^3/x^6
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R (1) -----------------------------
+--R 12
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 514
+
+--S 515 of 1379
+r0:=-1/11*b^3/x^11-1/3*a*b^2/x^9-3/7*a^2*b/x^7-1/5*a^3/x^5
+--R
+--R
+--R 1 3 6 3 2 4 1 2 2 1 3
+--R - - a x - - a b x - - a b x - -- b
+--R 5 7 3 11
+--R (2) --------------------------------------
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 515
+
+--S 516 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 231a x - 495a b x - 385a b x - 105b
+--R (3) -----------------------------------------
+--R 11
+--R 1155x
+--R Type: Union(Expression(Integer),...)
+--E 516
+
+--S 517 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 518
+
+)clear all
+
+--S 519 of 1379
+t0:=x^6/(a+b/x^2)
+--R
+--R
+--R 8
+--R x
+--R (1) --------
+--R 2
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 519
+
+--S 520 of 1379
+r0:=-b^3*x/a^4+1/3*b^2*x^3/a^3-1/5*b*x^5/a^2+1/7*x^7/a+_
+ b^(7/2)*atan(x*sqrt(a)/sqrt(b))/a^(9/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|a 3 7 2 5 2 3 3 +-+
+--R 105b \|b atan(-----) + (15a x - 21a b x + 35a b x - 105b x)\|a
+--R +-+
+--R \|b
+--R (2) ------------------------------------------------------------------
+--R 4 +-+
+--R 105a \|a
+--R Type: Expression(Integer)
+--E 520
+
+--S 521 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b
+--R 3 | b \| a 3 7 2 5 2 3
+--R 105b |- - log(---------------------) + 30a x - 42a b x + 70a b x
+--R \| a 2
+--R a x + b
+--R +
+--R 3
+--R - 210b x
+--R /
+--R 4
+--R 210a
+--R ,
+--R +-+
+--R |b
+--R +-+ |-
+--R 3 |b \|a 3 7 2 5 2 3 3
+--R - 105b |- atan(----) + 15a x - 21a b x + 35a b x - 105b x
+--R \|a x
+--R -------------------------------------------------------------]
+--R 4
+--R 105a
+--R Type: Union(List(Expression(Integer)),...)
+--E 521
+
+--S 522 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b +-+
+--R 3 | b +-+ \| a 3 +-+ x\|a
+--R b |- - \|a log(---------------------) - 2b \|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) -----------------------------------------------------------
+--R 4 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 523
+
+--S 524 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R 3 +-+ |b \|a 3 +-+ x\|a
+--R - b \|a |- atan(----) - b \|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) ------------------------------------------
+--R 4 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 524
+
+--S 525 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 525
+
+)clear all
+
+--S 526 of 1379
+t0:=x^5/(a+b/x^2)
+--R
+--R
+--R 7
+--R x
+--R (1) --------
+--R 2
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 526
+
+--S 527 of 1379
+r0:=1/2*b^2*x^2/a^3-1/4*b*x^4/a^2+1/6*x^6/a-1/2*b^3*log(b+a*x^2)/a^4
+--R
+--R
+--R 3 2 3 6 2 4 2 2
+--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x
+--R (2) ----------------------------------------------
+--R 4
+--R 12a
+--R Type: Expression(Integer)
+--E 527
+
+--S 528 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 3 6 2 4 2 2
+--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x
+--R (3) ----------------------------------------------
+--R 4
+--R 12a
+--R Type: Union(Expression(Integer),...)
+--E 528
+
+--S 529 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 530
+
+)clear all
+
+--S 531 of 1379
+t0:=x^4/(a+b/x^2)
+--R
+--R
+--R 6
+--R x
+--R (1) --------
+--R 2
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 531
+
+--S 532 of 1379
+r0:=b^2*x/a^3-1/3*b*x^3/a^2+1/5*x^5/a-b^(5/2)*atan(x*sqrt(a)/sqrt(b))/a^(7/2)
+--R
+--R
+--R +-+
+--R 2 +-+ x\|a 2 5 3 2 +-+
+--R - 15b \|b atan(-----) + (3a x - 5a b x + 15b x)\|a
+--R +-+
+--R \|b
+--R (2) -----------------------------------------------------
+--R 3 +-+
+--R 15a \|a
+--R Type: Expression(Integer)
+--E 532
+
+--S 533 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b
+--R 2 | b \| a 2 5 3 2
+--R 15b |- - log(-----------------------) + 6a x - 10a b x + 30b x
+--R \| a 2
+--R a x + b
+--R [-----------------------------------------------------------------,
+--R 3
+--R 30a
+--R +-+
+--R |b
+--R +-+ |-
+--R 2 |b \|a 2 5 3 2
+--R 15b |- atan(----) + 3a x - 5a b x + 15b x
+--R \|a x
+--R --------------------------------------------]
+--R 3
+--R 15a
+--R Type: Union(List(Expression(Integer)),...)
+--E 533
+
+--S 534 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b +-+
+--R 2 | b +-+ \| a 2 +-+ x\|a
+--R b |- - \|a log(-----------------------) + 2b \|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) -------------------------------------------------------------
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 535
+
+--S 536 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R 2 +-+ |b \|a 2 +-+ x\|a
+--R b \|a |- atan(----) + b \|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) ----------------------------------------
+--R 3 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 536
+
+--S 537 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 537
+
+)clear all
+
+--S 538 of 1379
+t0:=x^3/(a+b/x^2)
+--R
+--R
+--R 5
+--R x
+--R (1) --------
+--R 2
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 538
+
+--S 539 of 1379
+r0:=-1/2*b*x^2/a^2+1/4*x^4/a+1/2*b^2*log(b+a*x^2)/a^3
+--R
+--R
+--R 2 2 2 4 2
+--R 2b log(a x + b) + a x - 2a b x
+--R (2) ---------------------------------
+--R 3
+--R 4a
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 4 2
+--R 2b log(a x + b) + a x - 2a b x
+--R (3) ---------------------------------
+--R 3
+--R 4a
+--R Type: Union(Expression(Integer),...)
+--E 540
+
+--S 541 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 542
+
+)clear all
+
+--S 543 of 1379
+t0:=x^2/(a+b/x^2)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 2
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 543
+
+--S 544 of 1379
+r0:=-b*x/a^2+1/3*x^3/a+b^(3/2)*atan(x*sqrt(a)/sqrt(b))/a^(5/2)
+--R
+--R
+--R +-+
+--R +-+ x\|a 3 +-+
+--R 3b\|b atan(-----) + (a x - 3b x)\|a
+--R +-+
+--R \|b
+--R (2) -------------------------------------
+--R 2 +-+
+--R 3a \|a
+--R Type: Expression(Integer)
+--E 544
+
+--S 545 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b
+--R | b \| a 3
+--R 3b |- - log(---------------------) + 2a x - 6b x
+--R \| a 2
+--R a x + b
+--R [-------------------------------------------------,
+--R 2
+--R 6a
+--R +-+
+--R |b
+--R +-+ |-
+--R |b \|a 3
+--R - 3b |- atan(----) + a x - 3b x
+--R \|a x
+--R --------------------------------]
+--R 2
+--R 3a
+--R Type: Union(List(Expression(Integer)),...)
+--E 545
+
+--S 546 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b +-+
+--R | b +-+ \| a +-+ x\|a
+--R b |- - \|a log(---------------------) - 2b\|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) ---------------------------------------------------------
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 546
+
+--S 547 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 547
+
+--S 548 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R +-+ |b \|a +-+ x\|a
+--R - b\|a |- atan(----) - b\|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) ----------------------------------------
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 548
+
+--S 549 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 549
+
+)clear all
+
+--S 550 of 1379
+t0:=x/(a+b/x^2)
+--R
+--R
+--R 3
+--R x
+--R (1) --------
+--R 2
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 550
+
+--S 551 of 1379
+r0:=1/2*x^2/a-1/2*b*log(b+a*x^2)/a^2
+--R
+--R
+--R 2 2
+--R - b log(a x + b) + a x
+--R (2) ------------------------
+--R 2
+--R 2a
+--R Type: Expression(Integer)
+--E 551
+
+--S 552 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R - b log(a x + b) + a x
+--R (3) ------------------------
+--R 2
+--R 2a
+--R Type: Union(Expression(Integer),...)
+--E 552
+
+--S 553 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 553
+
+--S 554 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 554
+
+)clear all
+
+--S 555 of 1379
+t0:=1/(a+b/x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) --------
+--R 2
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 555
+
+--S 556 of 1379
+r0:=x/a-atan(x*sqrt(a)/sqrt(b))*sqrt(b)/a^(3/2)
+--R
+--R
+--R +-+
+--R +-+ x\|a +-+
+--R - \|b atan(-----) + x\|a
+--R +-+
+--R \|b
+--R (2) -------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 556
+
+--S 557 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+
+--R | b 2 +-+
+--R +---+ - 2a x |- - + a x - b |b
+--R | b \| a +-+ |-
+--R |- - log(-----------------------) + 2x |b \|a
+--R \| a 2 |- atan(----) + x
+--R a x + b \|a x
+--R (3) [---------------------------------------,------------------]
+--R 2a a
+--R Type: Union(List(Expression(Integer)),...)
+--E 557
+
+--S 558 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b +-+
+--R | b +-+ \| a +-+ x\|a
+--R |- - \|a log(-----------------------) + 2\|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) ---------------------------------------------------------
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 558
+
+--S 559 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 559
+
+--S 560 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R +-+ |b \|a +-+ x\|a
+--R \|a |- atan(----) + \|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) ------------------------------------
+--R +-+
+--R a\|a
+--R Type: Expression(Integer)
+--E 560
+
+--S 561 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 561
+
+)clear all
+
+--S 562 of 1379
+t0:=1/((a+b/x^2)*x)
+--R
+--R
+--R x
+--R (1) --------
+--R 2
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 562
+
+--S 563 of 1379
+r0:=1/2*log(b+a*x^2)/a
+--R
+--R
+--R 2
+--R log(a x + b)
+--R (2) -------------
+--R 2a
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R log(a x + b)
+--R (3) -------------
+--R 2a
+--R Type: Union(Expression(Integer),...)
+--E 564
+
+--S 565 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 565
+
+--S 566 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 566
+
+)clear all
+
+--S 567 of 1379
+t0:=1/((a+b/x^2)*x^2)
+--R
+--R
+--R 1
+--R (1) --------
+--R 2
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 567
+
+--S 568 of 1379
+r0:=atan(x*sqrt(a)/sqrt(b))/(sqrt(a)*sqrt(b))
+--R
+--R
+--R +-+
+--R x\|a
+--R atan(-----)
+--R +-+
+--R \|b
+--R (2) -----------
+--R +-+ +-+
+--R \|a \|b
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-----+
+--R (a x - b)\|- a b + 2a b x +---+
+--R log(---------------------------) x\|a b
+--R 2 atan(-------)
+--R a x + b b
+--R (3) [--------------------------------,-------------]
+--R +-----+ +---+
+--R 2\|- a b \|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 569
+
+--S 570 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a
+--R \|a \|b log(---------------------------) - 2\|- a b atan(-----)
+--R 2 +-+
+--R a x + b \|b
+--R (4) ---------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 2\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 570
+
+--S 571 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 571
+
+--S 572 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|a
+--R \|a \|b atan(-------) - \|a b atan(-----)
+--R b +-+
+--R \|b
+--R (6) -----------------------------------------
+--R +-+ +-+ +---+
+--R \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 572
+
+--S 573 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 573
+
+)clear all
+
+--S 574 of 1379
+t0:=1/((a+b/x^2)*x^3)
+--R
+--R
+--R 1
+--R (1) ----------
+--R 3
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 574
+
+--S 575 of 1379
+r0:=-1/2*log(a+b/x^2)/b
+--R
+--R
+--R 2
+--R a x + b
+--R log(--------)
+--R 2
+--R x
+--R (2) - -------------
+--R 2b
+--R Type: Expression(Integer)
+--E 575
+
+--S 576 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - log(a x + b) + 2log(x)
+--R (3) -------------------------
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 576
+
+--S 577 of 1379
+m0:=a0-r0
+--R
+--R
+--R 2
+--R 2 a x + b
+--R - log(a x + b) + 2log(x) + log(--------)
+--R 2
+--R x
+--R (4) -----------------------------------------
+--R 2b
+--R Type: Expression(Integer)
+--E 577
+
+--S 578 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 578
+
+)clear all
+
+--S 579 of 1379
+t0:=1/((a+b/x^2)*x^4)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 4 2
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 579
+
+--S 580 of 1379
+r0:=(-1)/(b*x)-atan(x*sqrt(a)/sqrt(b))*sqrt(a)/b^(3/2)
+--R
+--R
+--R +-+
+--R +-+ x\|a +-+
+--R - x\|a atan(-----) - \|b
+--R +-+
+--R \|b
+--R (2) -------------------------
+--R +-+
+--R b x\|b
+--R Type: Expression(Integer)
+--E 580
+
+--S 581 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +---+
+--R | a 2 +-+
+--R +---+ - 2b x |- - + a x - b |a
+--R | a \| b +-+ b |-
+--R x |- - log(-----------------------) - 2 |a \|b
+--R \| b 2 x |- atan(-----) - 1
+--R a x + b \|b a x
+--R (3) [---------------------------------------,--------------------]
+--R 2b x b x
+--R Type: Union(List(Expression(Integer)),...)
+--E 581
+
+--S 582 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + a x - b +-+
+--R | a +-+ \| b +-+ x\|a
+--R |- - \|b log(-----------------------) + 2\|a atan(-----)
+--R \| b 2 +-+
+--R a x + b \|b
+--R (4) ---------------------------------------------------------
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 582
+
+--S 583 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ b |- +-+
+--R |a +-+ \|b +-+ x\|a
+--R |- \|b atan(-----) + \|a atan(-----)
+--R \|b a x +-+
+--R \|b
+--R (6) -------------------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 584
+
+--S 585 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 585
+
+)clear all
+
+--S 586 of 1379
+t0:=1/((a+b/x^2)*x^5)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 5 3
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 586
+
+--S 587 of 1379
+r0:=(-1/2)/(b*x^2)-a*log(x)/b^2+1/2*a*log(b+a*x^2)/b^2
+--R
+--R
+--R 2 2 2
+--R a x log(a x + b) - 2a x log(x) - b
+--R (2) -----------------------------------
+--R 2 2
+--R 2b x
+--R Type: Expression(Integer)
+--E 587
+
+--S 588 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R a x log(a x + b) - 2a x log(x) - b
+--R (3) -----------------------------------
+--R 2 2
+--R 2b x
+--R Type: Union(Expression(Integer),...)
+--E 588
+
+--S 589 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 589
+
+--S 590 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 590
+
+)clear all
+
+--S 591 of 1379
+t0:=1/((a+b/x^2)*x^6)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 6 4
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 591
+
+--S 592 of 1379
+r0:=(-1/3)/(b*x^3)+a/(b^2*x)+a^(3/2)*atan(x*sqrt(a)/sqrt(b))/b^(5/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|a 2 +-+
+--R 3a x \|a atan(-----) + (3a x - b)\|b
+--R +-+
+--R \|b
+--R (2) --------------------------------------
+--R 2 3 +-+
+--R 3b x \|b
+--R Type: Expression(Integer)
+--E 592
+
+--S 593 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + a x - b
+--R 3 | a \| b 2
+--R 3a x |- - log(---------------------) + 6a x - 2b
+--R \| b 2
+--R a x + b
+--R [--------------------------------------------------,
+--R 2 3
+--R 6b x
+--R +-+
+--R |a
+--R +-+ b |-
+--R 3 |a \|b 2
+--R - 3a x |- atan(-----) + 3a x - b
+--R \|b a x
+--R ----------------------------------]
+--R 2 3
+--R 3b x
+--R Type: Union(List(Expression(Integer)),...)
+--E 593
+
+--S 594 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + a x - b +-+
+--R | a +-+ \| b +-+ x\|a
+--R a |- - \|b log(---------------------) - 2a\|a atan(-----)
+--R \| b 2 +-+
+--R a x + b \|b
+--R (4) ---------------------------------------------------------
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 594
+
+--S 595 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 595
+
+--S 596 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ b |- +-+
+--R |a +-+ \|b +-+ x\|a
+--R - a |- \|b atan(-----) - a\|a atan(-----)
+--R \|b a x +-+
+--R \|b
+--R (6) -----------------------------------------
+--R 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 596
+
+--S 597 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 597
+
+)clear all
+
+--S 598 of 1379
+t0:=1/((a+b/x^2)*x^7)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 7 5
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 598
+
+--S 599 of 1379
+r0:=(-1/4)/(b*x^4)+1/2*a/(b^2*x^2)+a^2*log(x)/b^3-1/2*a^2*log(b+a*x^2)/b^3
+--R
+--R
+--R 2 4 2 2 4 2 2
+--R - 2a x log(a x + b) + 4a x log(x) + 2a b x - b
+--R (2) -------------------------------------------------
+--R 3 4
+--R 4b x
+--R Type: Expression(Integer)
+--E 599
+
+--S 600 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2 4 2 2
+--R - 2a x log(a x + b) + 4a x log(x) + 2a b x - b
+--R (3) -------------------------------------------------
+--R 3 4
+--R 4b x
+--R Type: Union(Expression(Integer),...)
+--E 600
+
+--S 601 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 601
+
+--S 602 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 602
+
+)clear all
+
+--S 603 of 1379
+t0:=1/((a+b/x^2)*x^8)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 8 6
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 603
+
+--S 604 of 1379
+r0:=(-1/5)/(b*x^5)+1/3*a/(b^2*x^3)-a^2/(b^3*x)-_
+ a^(5/2)*atan(x*sqrt(a)/sqrt(b))/b^(7/2)
+--R
+--R
+--R +-+
+--R 2 5 +-+ x\|a 2 4 2 2 +-+
+--R - 15a x \|a atan(-----) + (- 15a x + 5a b x - 3b )\|b
+--R +-+
+--R \|b
+--R (2) --------------------------------------------------------
+--R 3 5 +-+
+--R 15b x \|b
+--R Type: Expression(Integer)
+--E 604
+
+--S 605 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + a x - b
+--R 2 5 | a \| b 2 4 2 2
+--R 15a x |- - log(-----------------------) - 30a x + 10a b x - 6b
+--R \| b 2
+--R a x + b
+--R [------------------------------------------------------------------,
+--R 3 5
+--R 30b x
+--R +-+
+--R |a
+--R +-+ b |-
+--R 2 5 |a \|b 2 4 2 2
+--R 15a x |- atan(-----) - 15a x + 5a b x - 3b
+--R \|b a x
+--R ----------------------------------------------]
+--R 3 5
+--R 15b x
+--R Type: Union(List(Expression(Integer)),...)
+--E 605
+
+--S 606 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + a x - b +-+
+--R 2 | a +-+ \| b 2 +-+ x\|a
+--R a |- - \|b log(-----------------------) + 2a \|a atan(-----)
+--R \| b 2 +-+
+--R a x + b \|b
+--R (4) -------------------------------------------------------------
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 606
+
+--S 607 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 607
+
+--S 608 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ b |- +-+
+--R 2 |a +-+ \|b 2 +-+ x\|a
+--R a |- \|b atan(-----) + a \|a atan(-----)
+--R \|b a x +-+
+--R \|b
+--R (6) -----------------------------------------
+--R 3 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 609
+
+)clear all
+
+--S 610 of 1379
+t0:=x^6/(a+b/x^2)^2
+--R
+--R
+--R 10
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 610
+
+--S 611 of 1379
+r0:=-9/2*b^3*x/a^5+3/2*b^2*x^3/a^4-9/10*b*x^5/a^3+9/14*x^7/a^2-_
+ 1/2*x^9/(a*(b+a*x^2))+9/2*b^(7/2)*atan(x*sqrt(a)/sqrt(b))/a^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 4 +-+ x\|a
+--R (315a b x + 315b )\|b atan(-----)
+--R +-+
+--R \|b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (10a x - 18a b x + 42a b x - 210a b x - 315b x)\|a
+--R /
+--R 6 2 5 +-+
+--R (70a x + 70a b)\|a
+--R Type: Expression(Integer)
+--E 611
+
+--S 612 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b
+--R 3 2 4 | b \| a 4 9 3 7
+--R (315a b x + 315b ) |- - log(---------------------) + 20a x - 36a b x
+--R \| a 2
+--R a x + b
+--R +
+--R 2 2 5 3 3 4
+--R 84a b x - 420a b x - 630b x
+--R /
+--R 6 2 5
+--R 140a x + 140a b
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ |-
+--R 3 2 4 |b \|a 4 9 3 7 2 2 5
+--R (- 315a b x - 315b ) |- atan(----) + 10a x - 18a b x + 42a b x
+--R \|a x
+--R +
+--R 3 3 4
+--R - 210a b x - 315b x
+--R /
+--R 6 2 5
+--R 70a x + 70a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 612
+
+--S 613 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b +-+
+--R 3 | b +-+ \| a 3 +-+ x\|a
+--R 9b |- - \|a log(---------------------) - 18b \|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) -------------------------------------------------------------
+--R 5 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 613
+
+--S 614 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 614
+
+--S 615 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R 3 +-+ |b \|a 3 +-+ x\|a
+--R - 9b \|a |- atan(----) - 9b \|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) --------------------------------------------
+--R 5 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 615
+
+--S 616 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 616
+
+)clear all
+
+--S 617 of 1379
+t0:=x^5/(a+b/x^2)^2
+--R
+--R
+--R 9
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 617
+
+--S 618 of 1379
+r0:=3/2*b^2*x^2/a^4-1/2*b*x^4/a^3+1/6*x^6/a^2-1/2*b^4/(a^5*(b+a*x^2))-_
+ 2*b^3*log(b+a*x^2)/a^5
+--R
+--R
+--R (2)
+--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4
+--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b
+--R ---------------------------------------------------------------------------
+--R 6 2 5
+--R 6a x + 6a b
+--R Type: Expression(Integer)
+--E 618
+
+--S 619 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4
+--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b
+--R ---------------------------------------------------------------------------
+--R 6 2 5
+--R 6a x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 619
+
+--S 620 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 620
+
+--S 621 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 621
+
+)clear all
+
+--S 622 of 1379
+t0:=x^4/(a+b/x^2)^2
+--R
+--R
+--R 8
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 622
+
+--S 623 of 1379
+r0:=7/2*b^2*x/a^4-7/6*b*x^3/a^3+7/10*x^5/a^2-1/2*x^7/(a*(b+a*x^2))-_
+ 7/2*b^(5/2)*atan(x*sqrt(a)/sqrt(b))/a^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 3 +-+ x\|a
+--R (- 105a b x - 105b )\|b atan(-----)
+--R +-+
+--R \|b
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (6a x - 14a b x + 70a b x + 105b x)\|a
+--R /
+--R 5 2 4 +-+
+--R (30a x + 30a b)\|a
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b
+--R 2 2 3 | b \| a 3 7
+--R (105a b x + 105b ) |- - log(-----------------------) + 12a x
+--R \| a 2
+--R a x + b
+--R +
+--R 2 5 2 3 3
+--R - 28a b x + 140a b x + 210b x
+--R /
+--R 5 2 4
+--R 60a x + 60a b
+--R ,
+--R +-+
+--R |b
+--R +-+ |-
+--R 2 2 3 |b \|a 3 7 2 5 2 3 3
+--R (105a b x + 105b ) |- atan(----) + 6a x - 14a b x + 70a b x + 105b x
+--R \|a x
+--R ------------------------------------------------------------------------]
+--R 5 2 4
+--R 30a x + 30a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 624
+
+--S 625 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b +-+
+--R 2 | b +-+ \| a 2 +-+ x\|a
+--R 7b |- - \|a log(-----------------------) + 14b \|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) ---------------------------------------------------------------
+--R 4 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 625
+
+--S 626 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R 2 +-+ |b \|a 2 +-+ x\|a
+--R 7b \|a |- atan(----) + 7b \|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) ------------------------------------------
+--R 4 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 627
+
+--S 628 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 628
+
+)clear all
+
+--S 629 of 1379
+t0:=x^3/(a+b/x^2)^2
+--R
+--R
+--R 7
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 629
+
+--S 630 of 1379
+r0:=-b*x^2/a^3+1/4*x^4/a^2+1/2*b^3/(a^4*(b+a*x^2))+3/2*b^2*log(b+a*x^2)/a^4
+--R
+--R
+--R 2 2 3 2 3 6 2 4 2 2 3
+--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b
+--R (2) -------------------------------------------------------------
+--R 5 2 4
+--R 4a x + 4a b
+--R Type: Expression(Integer)
+--E 630
+
+--S 631 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 3 2 3 6 2 4 2 2 3
+--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b
+--R (3) -------------------------------------------------------------
+--R 5 2 4
+--R 4a x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 631
+
+--S 632 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 632
+
+--S 633 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 633
+
+)clear all
+
+--S 634 of 1379
+t0:=x^2/(a+b/x^2)^2
+--R
+--R
+--R 6
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 634
+
+--S 635 of 1379
+r0:=-5/2*b*x/a^3+5/6*x^3/a^2-1/2*x^5/(a*(b+a*x^2))+5/2*b^(3/2)*_
+ atan(x*sqrt(a)/sqrt(b))/a^(7/2)
+--R
+--R
+--R +-+
+--R 2 2 +-+ x\|a 2 5 3 2 +-+
+--R (15a b x + 15b )\|b atan(-----) + (2a x - 10a b x - 15b x)\|a
+--R +-+
+--R \|b
+--R (2) -----------------------------------------------------------------
+--R 4 2 3 +-+
+--R (6a x + 6a b)\|a
+--R Type: Expression(Integer)
+--E 635
+
+--S 636 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b
+--R 2 2 | b \| a 2 5 3 2
+--R (15a b x + 15b ) |- - log(---------------------) + 4a x - 20a b x - 30b x
+--R \| a 2
+--R a x + b
+--R [----------------------------------------------------------------------------
+--R 4 2 3
+--R 12a x + 12a b
+--R ,
+--R +-+
+--R |b
+--R +-+ |-
+--R 2 2 |b \|a 2 5 3 2
+--R (- 15a b x - 15b ) |- atan(----) + 2a x - 10a b x - 15b x
+--R \|a x
+--R ------------------------------------------------------------]
+--R 4 2 3
+--R 6a x + 6a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 636
+
+--S 637 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b +-+
+--R | b +-+ \| a +-+ x\|a
+--R 5b |- - \|a log(---------------------) - 10b\|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) -----------------------------------------------------------
+--R 3 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 637
+
+--S 638 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R +-+ |b \|a +-+ x\|a
+--R - 5b\|a |- atan(----) - 5b\|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) ------------------------------------------
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 639
+
+--S 640 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 640
+
+)clear all
+
+--S 641 of 1379
+t0:=x/(a+b/x^2)^2
+--R
+--R
+--R 5
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 641
+
+--S 642 of 1379
+r0:=1/2*x^2/a^2-1/2*b^2/(a^3*(b+a*x^2))-b*log(b+a*x^2)/a^3
+--R
+--R
+--R 2 2 2 2 4 2 2
+--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b
+--R (2) ---------------------------------------------------
+--R 4 2 3
+--R 2a x + 2a b
+--R Type: Expression(Integer)
+--E 642
+
+--S 643 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 2 4 2 2
+--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b
+--R (3) ---------------------------------------------------
+--R 4 2 3
+--R 2a x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 643
+
+--S 644 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 644
+
+--S 645 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 645
+
+)clear all
+
+--S 646 of 1379
+t0:=1/(a+b/x^2)^2
+--R
+--R
+--R 4
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 646
+
+--S 647 of 1379
+r0:=3/2*x/a^2-1/2*x^3/(a*(b+a*x^2))-3/2*atan(x*sqrt(a)/sqrt(b))*sqrt(b)/a^(5/2)
+--R
+--R
+--R +-+
+--R 2 +-+ x\|a 3 +-+
+--R (- 3a x - 3b)\|b atan(-----) + (2a x + 3b x)\|a
+--R +-+
+--R \|b
+--R (2) --------------------------------------------------
+--R 3 2 2 +-+
+--R (2a x + 2a b)\|a
+--R Type: Expression(Integer)
+--E 647
+
+--S 648 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b
+--R 2 | b \| a 3
+--R (3a x + 3b) |- - log(-----------------------) + 4a x + 6b x
+--R \| a 2
+--R a x + b
+--R [-------------------------------------------------------------,
+--R 3 2 2
+--R 4a x + 4a b
+--R +-+
+--R |b
+--R +-+ |-
+--R 2 |b \|a 3
+--R (3a x + 3b) |- atan(----) + 2a x + 3b x
+--R \|a x
+--R -----------------------------------------]
+--R 3 2 2
+--R 2a x + 2a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 648
+
+--S 649 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b +-+
+--R | b +-+ \| a +-+ x\|a
+--R 3 |- - \|a log(----------------------- + 6\|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) ----------------------------------------------------------
+--R 2 +-+
+--R 4a \|a
+--R Type: Expression(Integer)
+--E 649
+
+--S 650 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 650
+
+--S 651 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R +-+ |b \|a +-+ x\|a
+--R 3\|a |- atan(----) + 3\|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) --------------------------------------
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 651
+
+--S 652 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 652
+
+)clear all
+
+--S 653 of 1379
+t0:=1/((a+b/x^2)^2*x)
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 653
+
+--S 654 of 1379
+r0:=1/2*b/(a^2*(b+a*x^2))+1/2*log(b+a*x^2)/a^2
+--R
+--R
+--R 2 2
+--R (a x + b)log(a x + b) + b
+--R (2) ---------------------------
+--R 3 2 2
+--R 2a x + 2a b
+--R Type: Expression(Integer)
+--E 654
+
+--S 655 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R (a x + b)log(a x + b) + b
+--R (3) ---------------------------
+--R 3 2 2
+--R 2a x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 655
+
+--S 656 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 656
+
+--S 657 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 657
+
+)clear all
+
+--S 658 of 1379
+t0:=1/((a+b/x^2)^2*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 658
+
+--S 659 of 1379
+r0:=-1/2*x/(a*(b+a*x^2))+1/2*atan(x*sqrt(a)/sqrt(b))/(a^(3/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R 2 x\|a +-+ +-+
+--R (a x + b)atan(-----) - x\|a \|b
+--R +-+
+--R \|b
+--R (2) ---------------------------------
+--R 2 2 +-+ +-+
+--R (2a x + 2a b)\|a \|b
+--R Type: Expression(Integer)
+--E 659
+
+--S 660 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R 2 (a x - b)\|- a b + 2a b x +-----+
+--R (a x + b)log(---------------------------) - 2x\|- a b
+--R 2
+--R a x + b
+--R [-------------------------------------------------------,
+--R 2 2 +-----+
+--R (4a x + 4a b)\|- a b
+--R +---+
+--R 2 x\|a b +---+
+--R (a x + b)atan(-------) - x\|a b
+--R b
+--R ---------------------------------]
+--R 2 2 +---+
+--R (2a x + 2a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 660
+
+--S 661 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a
+--R \|a \|b log(---------------------------) - 2\|- a b atan(-----)
+--R 2 +-+
+--R a x + b \|b
+--R (4) ---------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 4a\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 661
+
+--S 662 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 662
+
+--S 663 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|a
+--R \|a \|b atan(-------) - \|a b atan(-----)
+--R b +-+
+--R \|b
+--R (6) -----------------------------------------
+--R +-+ +-+ +---+
+--R 2a\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 664
+
+)clear all
+
+--S 665 of 1379
+t0:=1/((a+b/x^2)^2*x^3)
+--R
+--R
+--R x
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 665
+
+--S 666 of 1379
+r0:=1/2/(b*(a+b/x^2))
+--R
+--R
+--R 2
+--R x
+--R (2) -------------
+--R 2 2
+--R 2a b x + 2b
+--R Type: Fraction(Polynomial(Integer))
+--E 666
+
+--S 667 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ------------
+--R 2 2
+--R 2a x + 2a b
+--R Type: Union(Expression(Integer),...)
+--E 667
+
+--S 668 of 1379
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - ----
+--R 2a b
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 669
+
+)clear all
+
+--S 670 of 1379
+t0:=1/((a+b/x^2)^2*x^4)
+--R
+--R
+--R 1
+--R (1) -------------------
+--R 2 4 2 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 670
+
+--S 671 of 1379
+r0:=1/2*x/(b*(b+a*x^2))+1/2*atan(x*sqrt(a)/sqrt(b))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R 2 x\|a +-+ +-+
+--R (a x + b)atan(-----) + x\|a \|b
+--R +-+
+--R \|b
+--R (2) ---------------------------------
+--R 2 2 +-+ +-+
+--R (2a b x + 2b )\|a \|b
+--R Type: Expression(Integer)
+--E 671
+
+--S 672 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R 2 (a x - b)\|- a b + 2a b x +-----+
+--R (a x + b)log(---------------------------) + 2x\|- a b
+--R 2
+--R a x + b
+--R [-------------------------------------------------------,
+--R 2 2 +-----+
+--R (4a b x + 4b )\|- a b
+--R +---+
+--R 2 x\|a b +---+
+--R (a x + b)atan(-------) + x\|a b
+--R b
+--R ---------------------------------]
+--R 2 2 +---+
+--R (2a b x + 2b )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 672
+
+--S 673 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a
+--R \|a \|b log(---------------------------) - 2\|- a b atan(-----)
+--R 2 +-+
+--R a x + b \|b
+--R (4) ---------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 4b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 674
+
+--S 675 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|a
+--R \|a \|b atan(-------) - \|a b atan(-----)
+--R b +-+
+--R \|b
+--R (6) -----------------------------------------
+--R +-+ +-+ +---+
+--R 2b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 675
+
+--S 676 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 676
+
+)clear all
+
+--S 677 of 1379
+t0:=1/((a+b/x^2)^2*x^5)
+--R
+--R
+--R 1
+--R (1) --------------------
+--R 2 5 3 2
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 677
+
+--S 678 of 1379
+r0:=1/2/(b*(b+a*x^2))+log(x)/b^2-1/2*log(b+a*x^2)/b^2
+--R
+--R
+--R 2 2 2
+--R (- a x - b)log(a x + b) + (2a x + 2b)log(x) + b
+--R (2) --------------------------------------------------
+--R 2 2 3
+--R 2a b x + 2b
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R (- a x - b)log(a x + b) + (2a x + 2b)log(x) + b
+--R (3) --------------------------------------------------
+--R 2 2 3
+--R 2a b x + 2b
+--R Type: Union(Expression(Integer),...)
+--E 679
+
+--S 680 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 680
+
+--S 681 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 681
+
+)clear all
+
+--S 682 of 1379
+t0:=1/((a+b/x^2)^2*x^6)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 6 4 2 2
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 682
+
+--S 683 of 1379
+r0:=(-3/2)/(b^2*x)+1/2/(b*x*(b+a*x^2))-3/2*atan(x*sqrt(a)/sqrt(b))*_
+ sqrt(a)/b^(5/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|a 2 +-+
+--R (- 3a x - 3b x)\|a atan(-----) + (- 3a x - 2b)\|b
+--R +-+
+--R \|b
+--R (2) ----------------------------------------------------
+--R 2 3 3 +-+
+--R (2a b x + 2b x)\|b
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + a x - b
+--R 3 | a \| b 2
+--R (3a x + 3b x) |- - log(-----------------------) - 6a x - 4b
+--R \| b 2
+--R a x + b
+--R [-------------------------------------------------------------,
+--R 2 3 3
+--R 4a b x + 4b x
+--R +-+
+--R |a
+--R +-+ b |-
+--R 3 |a \|b 2
+--R (3a x + 3b x) |- atan(-----) - 3a x - 2b
+--R \|b a x
+--R ------------------------------------------]
+--R 2 3 3
+--R 2a b x + 2b x
+--R Type: Union(List(Expression(Integer)),...)
+--E 684
+
+--S 685 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + a x - b +-+
+--R | a +-+ \| b +-+ x\|a
+--R 3 |- - \|b log(----------------------- + 6\|a atan(-----)
+--R \| b 2 +-+
+--R a x + b \|b
+--R (4) ----------------------------------------------------------
+--R 2 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 685
+
+--S 686 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 686
+
+--S 687 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ b |- +-+
+--R |a +-+ \|b +-+ x\|a
+--R 3 |- \|b atan(----- + 3\|a atan(-----)
+--R \|b a x +-+
+--R \|b
+--R (6) ---------------------------------------
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 687
+
+--S 688 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 688
+
+)clear all
+
+--S 689 of 1379
+t0:=1/((a+b/x^2)^2*x^7)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 7 5 2 3
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 689
+
+--S 690 of 1379
+r0:=(-1)/(b^2*x^2)+1/2/(b*x^2*(b+a*x^2))-2*a*log(x)/b^3+a*log(b+a*x^2)/b^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 2 4 2 2 2
+--R (2a x + 2a b x )log(a x + b) + (- 4a x - 4a b x )log(x) - 2a b x - b
+--R -------------------------------------------------------------------------
+--R 3 4 4 2
+--R 2a b x + 2b x
+--R Type: Expression(Integer)
+--E 690
+
+--S 691 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2 4 2 2 2
+--R (2a x + 2a b x )log(a x + b) + (- 4a x - 4a b x )log(x) - 2a b x - b
+--R -------------------------------------------------------------------------
+--R 3 4 4 2
+--R 2a b x + 2b x
+--R Type: Union(Expression(Integer),...)
+--E 691
+
+--S 692 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 692
+
+--S 693 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 693
+
+)clear all
+
+--S 694 of 1379
+t0:=1/((a+b/x^2)^2*x^8)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 8 6 2 4
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 694
+
+--S 695 of 1379
+r0:=(-5/6)/(b^2*x^3)+5/2*a/(b^3*x)+1/2/(b*x^3*(b+a*x^2))+5/2*a^(3/2)*_
+ atan(x*sqrt(a)/sqrt(b))/b^(7/2)
+--R
+--R
+--R +-+
+--R 2 5 3 +-+ x\|a 2 4 2 2 +-+
+--R (15a x + 15a b x )\|a atan(-----) + (15a x + 10a b x - 2b )\|b
+--R +-+
+--R \|b
+--R (2) ------------------------------------------------------------------
+--R 3 5 4 3 +-+
+--R (6a b x + 6b x )\|b
+--R Type: Expression(Integer)
+--E 695
+
+--S 696 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + a x - b
+--R 2 5 3 | a \| b 2 4 2
+--R (15a x + 15a b x ) |- - log(---------------------) + 30a x + 20a b x
+--R \| b 2
+--R a x + b
+--R +
+--R 2
+--R - 4b
+--R /
+--R 3 5 4 3
+--R 12a b x + 12b x
+--R ,
+--R +-+
+--R |a
+--R +-+ b |-
+--R 2 5 3 |a \|b 2 4 2 2
+--R (- 15a x - 15a b x ) |- atan(-----) + 15a x + 10a b x - 2b
+--R \|b a x
+--R --------------------------------------------------------------]
+--R 3 5 4 3
+--R 6a b x + 6b x
+--R Type: Union(List(Expression(Integer)),...)
+--E 696
+
+--S 697 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + a x - b +-+
+--R | a +-+ \| b +-+ x\|a
+--R 5a |- - \|b log(---------------------) - 10a\|a atan(-----)
+--R \| b 2 +-+
+--R a x + b \|b
+--R (4) -----------------------------------------------------------
+--R 3 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 697
+
+--S 698 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ b |- +-+
+--R |a +-+ \|b +-+ x\|a
+--R - 5a |- \|b atan(-----) - 5a\|a atan(-----)
+--R \|b a x +-+
+--R \|b
+--R (6) -------------------------------------------
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 699
+
+--S 700 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 700
+
+)clear all
+
+--S 701 of 1379
+t0:=1/((a+b/x^2)^2*x^9)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R 2 9 7 2 5
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 701
+
+--S 702 of 1379
+r0:=(-3/4)/(b^2*x^4)+3/2*a/(b^3*x^2)+1/2/(b*x^4*(b+a*x^2))+3*a^2*_
+ log(x)/b^4-3/2*a^2*log(b+a*x^2)/b^4
+--R
+--R
+--R (2)
+--R 3 6 2 4 2 3 6 2 4 2 4
+--R (- 6a x - 6a b x )log(a x + b) + (12a x + 12a b x )log(x) + 6a b x
+--R +
+--R 2 2 3
+--R 3a b x - b
+--R /
+--R 4 6 5 4
+--R 4a b x + 4b x
+--R Type: Expression(Integer)
+--E 702
+
+--S 703 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 6 2 4 2 3 6 2 4 2 4
+--R (- 6a x - 6a b x )log(a x + b) + (12a x + 12a b x )log(x) + 6a b x
+--R +
+--R 2 2 3
+--R 3a b x - b
+--R /
+--R 4 6 5 4
+--R 4a b x + 4b x
+--R Type: Union(Expression(Integer),...)
+--E 703
+
+--S 704 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 704
+
+--S 705 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 705
+
+)clear all
+
+--S 706 of 1379
+t0:=x^5/(a+b/x^2)^3
+--R
+--R
+--R 11
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 706
+
+--S 707 of 1379
+r0:=3*b^2*x^2/a^5-3/4*b*x^4/a^4+1/6*x^6/a^3+1/4*b^5/(a^6*(b+a*x^2)^2)-_
+ 5/2*b^4/(a^6*(b+a*x^2))-5*b^3*log(b+a*x^2)/a^6
+--R
+--R
+--R (2)
+--R 2 3 4 4 2 5 2 5 10 4 8
+--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x
+--R +
+--R 3 2 6 2 3 4 4 2 5
+--R 20a b x + 63a b x + 6a b x - 27b
+--R /
+--R 8 4 7 2 6 2
+--R 12a x + 24a b x + 12a b
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 4 4 2 5 2 5 10 4 8
+--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x
+--R +
+--R 3 2 6 2 3 4 4 2 5
+--R 20a b x + 63a b x + 6a b x - 27b
+--R /
+--R 8 4 7 2 6 2
+--R 12a x + 24a b x + 12a b
+--R Type: Union(Expression(Integer),...)
+--E 708
+
+--S 709 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 709
+
+--S 710 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 710
+
+)clear all
+
+--S 711 of 1379
+t0:=x^4/(a+b/x^2)^3
+--R
+--R
+--R 10
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 711
+
+--S 712 of 1379
+r0:=63/8*b^2*x/a^5-21/8*b*x^3/a^4+63/40*x^5/a^3-1/4*x^9/(a*(b+a*x^2)^2)-_
+ 9/8*x^7/(a^2*(b+a*x^2))-63/8*b^(5/2)*atan(x*sqrt(a)/sqrt(b))/a^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 4 3 2 4 +-+ x\|a
+--R (- 315a b x - 630a b x - 315b )\|b atan(-----)
+--R +-+
+--R \|b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (8a x - 24a b x + 168a b x + 525a b x + 315b x)\|a
+--R /
+--R 7 4 6 2 5 2 +-+
+--R (40a x + 80a b x + 40a b )\|a
+--R Type: Expression(Integer)
+--E 712
+
+--S 713 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b
+--R 2 2 4 3 2 4 | b \| a
+--R (315a b x + 630a b x + 315b ) |- - log(-----------------------)
+--R \| a 2
+--R a x + b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4
+--R 16a x - 48a b x + 336a b x + 1050a b x + 630b x
+--R /
+--R 7 4 6 2 5 2
+--R 80a x + 160a b x + 80a b
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ |-
+--R 2 2 4 3 2 4 |b \|a 4 9 3 7
+--R (315a b x + 630a b x + 315b ) |- atan(----) + 8a x - 24a b x
+--R \|a x
+--R +
+--R 2 2 5 3 3 4
+--R 168a b x + 525a b x + 315b x
+--R /
+--R 7 4 6 2 5 2
+--R 40a x + 80a b x + 40a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 713
+
+--S 714 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b +-+
+--R 2 | b +-+ \| a 2 +-+ x\|a
+--R 63b |- - \|a log(-----------------------) + 126b \|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) -----------------------------------------------------------------
+--R 5 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 714
+
+--S 715 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 715
+
+--S 716 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R 2 +-+ |b \|a 2 +-+ x\|a
+--R 63b \|a |- atan(----) + 63b \|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) --------------------------------------------
+--R 5 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 716
+
+--S 717 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 717
+
+)clear all
+
+--S 718 of 1379
+t0:=x^3/(a+b/x^2)^3
+--R
+--R
+--R 9
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 718
+
+--S 719 of 1379
+r0:=-3/2*b*x^2/a^4+1/4*x^4/a^3-1/4*b^4/(a^5*(b+a*x^2)^2)+2*b^3/_
+ (a^5*(b+a*x^2))+3*b^2*log(b+a*x^2)/a^5
+--R
+--R
+--R (2)
+--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4
+--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x
+--R +
+--R 3 2 4
+--R 2a b x + 7b
+--R /
+--R 7 4 6 2 5 2
+--R 4a x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 719
+
+--S 720 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4
+--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x
+--R +
+--R 3 2 4
+--R 2a b x + 7b
+--R /
+--R 7 4 6 2 5 2
+--R 4a x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 720
+
+--S 721 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 721
+
+--S 722 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 722
+
+)clear all
+
+--S 723 of 1379
+t0:=x^2/(a+b/x^2)^3
+--R
+--R
+--R 8
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 723
+
+--S 724 of 1379
+r0:=-35/8*b*x/a^4+35/24*x^3/a^3-1/4*x^7/(a*(b+a*x^2)^2)-7/8*x^5/_
+ (a^2*(b+a*x^2))+35/8*b^(3/2)*atan(x*sqrt(a)/sqrt(b))/a^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 4 2 2 3 +-+ x\|a
+--R (105a b x + 210a b x + 105b )\|b atan(-----)
+--R +-+
+--R \|b
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (8a x - 56a b x - 175a b x - 105b x)\|a
+--R /
+--R 6 4 5 2 4 2 +-+
+--R (24a x + 48a b x + 24a b )\|a
+--R Type: Expression(Integer)
+--E 724
+
+--S 725 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b
+--R 2 4 2 2 3 | b \| a
+--R (105a b x + 210a b x + 105b ) |- - log(---------------------)
+--R \| a 2
+--R a x + b
+--R +
+--R 3 7 2 5 2 3 3
+--R 16a x - 112a b x - 350a b x - 210b x
+--R /
+--R 6 4 5 2 4 2
+--R 48a x + 96a b x + 48a b
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ |-
+--R 2 4 2 2 3 |b \|a 3 7 2 5
+--R (- 105a b x - 210a b x - 105b ) |- atan(----) + 8a x - 56a b x
+--R \|a x
+--R +
+--R 2 3 3
+--R - 175a b x - 105b x
+--R /
+--R 6 4 5 2 4 2
+--R 24a x + 48a b x + 24a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 725
+
+--S 726 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + a x - b +-+
+--R | b +-+ \| a +-+ x\|a
+--R 35b |- - \|a log(---------------------) - 70b\|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) ------------------------------------------------------------
+--R 4 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 726
+
+--S 727 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 727
+
+--S 728 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R +-+ |b \|a +-+ x\|a
+--R - 35b\|a |- atan(----) - 35b\|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) --------------------------------------------
+--R 4 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 729
+
+)clear all
+
+--S 730 of 1379
+t0:=x/(a+b/x^2)^3
+--R
+--R
+--R 7
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 730
+
+--S 731 of 1379
+r0:=1/2*x^2/a^3+1/4*b^3/(a^4*(b+a*x^2)^2)-3/2*b^2/(a^4*(b+a*x^2))-_
+ 3/2*b*log(b+a*x^2)/a^4
+--R
+--R
+--R (2)
+--R 2 4 2 2 3 2 3 6 2 4 2 2 3
+--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b
+--R ---------------------------------------------------------------------------
+--R 6 4 5 2 4 2
+--R 4a x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 731
+
+--S 732 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 3 2 3 6 2 4 2 2 3
+--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b
+--R ---------------------------------------------------------------------------
+--R 6 4 5 2 4 2
+--R 4a x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 732
+
+--S 733 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 734
+
+)clear all
+
+--S 735 of 1379
+t0:=1/(a+b/x^2)^3
+--R
+--R
+--R 6
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 735
+
+--S 736 of 1379
+r0:=15/8*x/a^3-1/4*x^5/(a*(b+a*x^2)^2)-5/8*x^3/(a^2*(b+a*x^2))-_
+ 15/8*atan(x*sqrt(a)/sqrt(b))*sqrt(b)/a^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 4 2 2 +-+ x\|a 2 5 3 2 +-+
+--R (- 15a x - 30a b x - 15b )\|b atan(-----) + (8a x + 25a b x + 15b x)\|a
+--R +-+
+--R \|b
+--R ----------------------------------------------------------------------------
+--R 5 4 4 2 3 2 +-+
+--R (8a x + 16a b x + 8a b )\|a
+--R Type: Expression(Integer)
+--E 736
+
+--S 737 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b
+--R 2 4 2 2 | b \| a 2 5
+--R (15a x + 30a b x + 15b ) |- - log(-----------------------) + 16a x
+--R \| a 2
+--R a x + b
+--R +
+--R 3 2
+--R 50a b x + 30b x
+--R /
+--R 5 4 4 2 3 2
+--R 16a x + 32a b x + 16a b
+--R ,
+--R +-+
+--R |b
+--R +-+ |-
+--R 2 4 2 2 |b \|a 2 5 3 2
+--R (15a x + 30a b x + 15b ) |- atan(----) + 8a x + 25a b x + 15b x
+--R \|a x
+--R -------------------------------------------------------------------]
+--R 5 4 4 2 3 2
+--R 8a x + 16a b x + 8a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 737
+
+--S 738 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + a x - b +-+
+--R | b +-+ \| a +-+ x\|a
+--R 15 |- - \|a log(----------------------- + 30\|b atan(-----)
+--R \| a 2 +-+
+--R a x + b \|b
+--R (4) ------------------------------------------------------------
+--R 3 +-+
+--R 16a \|a
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 739
+
+--S 740 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ |- +-+
+--R +-+ |b \|a +-+ x\|a
+--R 15\|a |- atan(----) + 15\|b atan(-----)
+--R \|a x +-+
+--R \|b
+--R (6) ----------------------------------------
+--R 3 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 740
+
+--S 741 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 741
+
+)clear all
+
+--S 742 of 1379
+t0:=1/((a+b/x^2)^3*x)
+--R
+--R
+--R 5
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 742
+
+--S 743 of 1379
+r0:=-1/4*b^2/(a^3*(b+a*x^2)^2)+b/(a^3*(b+a*x^2))+1/2*log(b+a*x^2)/a^3
+--R
+--R
+--R 2 4 2 2 2 2 2
+--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b
+--R (2) ----------------------------------------------------
+--R 5 4 4 2 3 2
+--R 4a x + 8a b x + 4a b
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 2 2 2 2
+--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b
+--R (3) ----------------------------------------------------
+--R 5 4 4 2 3 2
+--R 4a x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 744
+
+--S 745 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 745
+
+--S 746 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 746
+
+)clear all
+
+--S 747 of 1379
+t0:=1/((a+b/x^2)^3*x^2)
+--R
+--R
+--R 4
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 747
+
+--S 748 of 1379
+r0:=-1/4*x^3/(a*(b+a*x^2)^2)-3/8*x/(a^2*(b+a*x^2))+_
+ 3/8*atan(x*sqrt(a)/sqrt(b))/(a^(5/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R 2 4 2 2 x\|a 3 +-+ +-+
+--R (3a x + 6a b x + 3b )atan(-----) + (- 5a x - 3b x)\|a \|b
+--R +-+
+--R \|b
+--R (2) -------------------------------------------------------------
+--R 4 4 3 2 2 2 +-+ +-+
+--R (8a x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 748
+
+--S 749 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 4 2 2 (a x - b)\|- a b + 2a b x
+--R (3a x + 6a b x + 3b )log(---------------------------)
+--R 2
+--R a x + b
+--R +
+--R 3 +-----+
+--R (- 10a x - 6b x)\|- a b
+--R /
+--R 4 4 3 2 2 2 +-----+
+--R (16a x + 32a b x + 16a b )\|- a b
+--R ,
+--R +---+
+--R 2 4 2 2 x\|a b 3 +---+
+--R (3a x + 6a b x + 3b )atan(-------) + (- 5a x - 3b x)\|a b
+--R b
+--R -------------------------------------------------------------]
+--R 4 4 3 2 2 2 +---+
+--R (8a x + 16a b x + 8a b )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 749
+
+--S 750 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a
+--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----)
+--R 2 +-+
+--R a x + b \|b
+--R (4) ----------------------------------------------------------------
+--R 2 +-----+ +-+ +-+
+--R 16a \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 750
+
+--S 751 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 751
+
+--S 752 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|a
+--R 3\|a \|b atan(-------) - 3\|a b atan(-----)
+--R b +-+
+--R \|b
+--R (6) -------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8a \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 752
+
+--S 753 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 753
+
+)clear all
+
+--S 754 of 1379
+t0:=1/((a+b/x^2)^3*x^3)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 754
+
+--S 755 of 1379
+r0:=1/4/(b*(a+b/x^2)^2)
+--R
+--R
+--R 4
+--R x
+--R (2) -----------------------
+--R 2 4 2 2 3
+--R 4a b x + 8a b x + 4b
+--R Type: Fraction(Polynomial(Integer))
+--E 755
+
+--S 756 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R - 2a x - b
+--R (3) -----------------------
+--R 4 4 3 2 2 2
+--R 4a x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 756
+
+--S 757 of 1379
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - ----
+--R 2
+--R 4a b
+--R Type: Expression(Integer)
+--E 757
+
+--S 758 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 758
+
+)clear all
+
+--S 759 of 1379
+t0:=1/((a+b/x^2)^3*x^4)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 759
+
+--S 760 of 1379
+r0:=-1/4*x/(a*(b+a*x^2)^2)+1/8*x/(a*b*(b+a*x^2))+_
+ 1/8*atan(x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2))
+--R
+--R
+--R +-+
+--R 2 4 2 2 x\|a 3 +-+ +-+
+--R (a x + 2a b x + b )atan(-----) + (a x - b x)\|a \|b
+--R +-+
+--R \|b
+--R (2) -------------------------------------------------------
+--R 3 4 2 2 2 3 +-+ +-+
+--R (8a b x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 760
+
+--S 761 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 4 2 2 (a x - b)\|- a b + 2a b x
+--R (a x + 2a b x + b )log(---------------------------)
+--R 2
+--R a x + b
+--R +
+--R 3 +-----+
+--R (2a x - 2b x)\|- a b
+--R /
+--R 3 4 2 2 2 3 +-----+
+--R (16a b x + 32a b x + 16a b )\|- a b
+--R ,
+--R +---+
+--R 2 4 2 2 x\|a b 3 +---+
+--R (a x + 2a b x + b )atan(-------) + (a x - b x)\|a b
+--R b
+--R -------------------------------------------------------]
+--R 3 4 2 2 2 3 +---+
+--R (8a b x + 16a b x + 8a b )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 761
+
+--S 762 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a
+--R \|a \|b log(---------------------------) - 2\|- a b atan(-----)
+--R 2 +-+
+--R a x + b \|b
+--R (4) ---------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R 16a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 762
+
+--S 763 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 763
+
+--S 764 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|a
+--R \|a \|b atan(-------) - \|a b atan(-----)
+--R b +-+
+--R \|b
+--R (6) -----------------------------------------
+--R +-+ +-+ +---+
+--R 8a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 764
+
+--S 765 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 765
+
+)clear all
+
+--S 766 of 1379
+t0:=1/((a+b/x^2)^3*x^5)
+--R
+--R
+--R x
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 766
+
+--S 767 of 1379
+r0:=(-1/4)/(a*(a+b/x^2)^2*x^4)
+--R
+--R
+--R 1
+--R (2) - -----------------------
+--R 3 4 2 2 2
+--R 4a x + 8a b x + 4a b
+--R Type: Fraction(Polynomial(Integer))
+--E 767
+
+--S 768 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - -----------------------
+--R 3 4 2 2 2
+--R 4a x + 8a b x + 4a b
+--R Type: Union(Expression(Integer),...)
+--E 768
+
+--S 769 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 769
+
+--S 770 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 770
+
+)clear all
+
+--S 771 of 1379
+t0:=1/((a+b/x^2)^3*x^6)
+--R
+--R
+--R 1
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R a x + 3a b x + 3a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 771
+
+--S 772 of 1379
+r0:=1/4*x/(b*(b+a*x^2)^2)+3/8*x/(b^2*(b+a*x^2))+_
+ 3/8*atan(x*sqrt(a)/sqrt(b))/(b^(5/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R 2 4 2 2 x\|a 3 +-+ +-+
+--R (3a x + 6a b x + 3b )atan(-----) + (3a x + 5b x)\|a \|b
+--R +-+
+--R \|b
+--R (2) -----------------------------------------------------------
+--R 2 2 4 3 2 4 +-+ +-+
+--R (8a b x + 16a b x + 8b )\|a \|b
+--R Type: Expression(Integer)
+--E 772
+
+--S 773 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 4 2 2 (a x - b)\|- a b + 2a b x
+--R (3a x + 6a b x + 3b )log(---------------------------)
+--R 2
+--R a x + b
+--R +
+--R 3 +-----+
+--R (6a x + 10b x)\|- a b
+--R /
+--R 2 2 4 3 2 4 +-----+
+--R (16a b x + 32a b x + 16b )\|- a b
+--R ,
+--R +---+
+--R 2 4 2 2 x\|a b 3 +---+
+--R (3a x + 6a b x + 3b )atan(-------) + (3a x + 5b x)\|a b
+--R b
+--R -----------------------------------------------------------]
+--R 2 2 4 3 2 4 +---+
+--R (8a b x + 16a b x + 8b )\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 773
+
+--S 774 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R 2 +-----+ +-+
+--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a
+--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----)
+--R 2 +-+
+--R a x + b \|b
+--R (4) ----------------------------------------------------------------
+--R 2 +-----+ +-+ +-+
+--R 16b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 774
+
+--S 775 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 775
+
+--S 776 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|a
+--R 3\|a \|b atan(-------) - 3\|a b atan(-----)
+--R b +-+
+--R \|b
+--R (6) -------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 776
+
+--S 777 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 777
+
+)clear all
+
+--S 778 of 1379
+t0:=1/((a+b/x^2)^3*x^7)
+--R
+--R
+--R 1
+--R (1) ------------------------------
+--R 3 7 2 5 2 3 3
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 778
+
+--S 779 of 1379
+r0:=1/4/(b*(b+a*x^2)^2)+1/2/(b^2*(b+a*x^2))+log(x)/b^3-1/2*log(b+a*x^2)/b^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 2 2 4 2 2
+--R (- 2a x - 4a b x - 2b )log(a x + b) + (4a x + 8a b x + 4b )log(x)
+--R +
+--R 2 2
+--R 2a b x + 3b
+--R /
+--R 2 3 4 4 2 5
+--R 4a b x + 8a b x + 4b
+--R Type: Expression(Integer)
+--E 779
+
+--S 780 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 2 2 4 2 2
+--R (- 2a x - 4a b x - 2b )log(a x + b) + (4a x + 8a b x + 4b )log(x)
+--R +
+--R 2 2
+--R 2a b x + 3b
+--R /
+--R 2 3 4 4 2 5
+--R 4a b x + 8a b x + 4b
+--R Type: Union(Expression(Integer),...)
+--E 780
+
+--S 781 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 781
+
+--S 782 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 782
+
+)clear all
+
+--S 783 of 1379
+t0:=1/((a+b/x^2)^3*x^8)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 8 2 6 2 4 3 2
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 783
+
+--S 784 of 1379
+r0:=(-15/8)/(b^3*x)+1/4/(b*x*(b+a*x^2)^2)+5/8/(b^2*x*(b+a*x^2))-_
+ 15/8*atan(x*sqrt(a)/sqrt(b))*sqrt(a)/b^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 5 3 2 +-+ x\|a
+--R (- 15a x - 30a b x - 15b x)\|a atan(-----)
+--R +-+
+--R \|b
+--R +
+--R 2 4 2 2 +-+
+--R (- 15a x - 25a b x - 8b )\|b
+--R /
+--R 2 3 5 4 3 5 +-+
+--R (8a b x + 16a b x + 8b x)\|b
+--R Type: Expression(Integer)
+--E 784
+
+--S 785 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + a x - b
+--R 2 5 3 2 | a \| b 2 4
+--R (15a x + 30a b x + 15b x) |- - log(-----------------------) - 30a x
+--R \| b 2
+--R a x + b
+--R +
+--R 2 2
+--R - 50a b x - 16b
+--R /
+--R 2 3 5 4 3 5
+--R 16a b x + 32a b x + 16b x
+--R ,
+--R +-+
+--R |a
+--R +-+ b |-
+--R 2 5 3 2 |a \|b 2 4 2 2
+--R (15a x + 30a b x + 15b x) |- atan(-----) - 15a x - 25a b x - 8b
+--R \|b a x
+--R --------------------------------------------------------------------]
+--R 2 3 5 4 3 5
+--R 8a b x + 16a b x + 8b x
+--R Type: Union(List(Expression(Integer)),...)
+--E 785
+
+--S 786 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + a x - b +-+
+--R | a +-+ \| b +-+ x\|a
+--R 15 |- - \|b log(----------------------- + 30\|a atan(-----)
+--R \| b 2 +-+
+--R a x + b \|b
+--R (4) ------------------------------------------------------------
+--R 3 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 786
+
+--S 787 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 787
+
+--S 788 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ b |- +-+
+--R |a +-+ \|b +-+ x\|a
+--R 15 |- \|b atan(----- + 15\|a atan(-----)
+--R \|b a x +-+
+--R \|b
+--R (6) -----------------------------------------
+--R 3 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 788
+
+--S 789 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 789
+
+)clear all
+
+--S 790 of 1379
+t0:=1/((a+b/x^2)^3*x^9)
+--R
+--R
+--R 1
+--R (1) -------------------------------
+--R 3 9 2 7 2 5 3 3
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 790
+
+--S 791 of 1379
+r0:=(-3/2)/(b^3*x^2)+1/4/(b*x^2*(b+a*x^2)^2)+3/4/(b^2*x^2*(b+a*x^2))-_
+ 3*a*log(x)/b^4+3/2*a*log(b+a*x^2)/b^4
+--R
+--R
+--R (2)
+--R 3 6 2 4 2 2 2
+--R (6a x + 12a b x + 6a b x )log(a x + b)
+--R +
+--R 3 6 2 4 2 2 2 4 2 2 3
+--R (- 12a x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2b
+--R /
+--R 2 4 6 5 4 6 2
+--R 4a b x + 8a b x + 4b x
+--R Type: Expression(Integer)
+--E 791
+
+--S 792 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 6 2 4 2 2 2
+--R (6a x + 12a b x + 6a b x )log(a x + b)
+--R +
+--R 3 6 2 4 2 2 2 4 2 2 3
+--R (- 12a x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2b
+--R /
+--R 2 4 6 5 4 6 2
+--R 4a b x + 8a b x + 4b x
+--R Type: Union(Expression(Integer),...)
+--E 792
+
+--S 793 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 793
+
+--S 794 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 794
+
+)clear all
+
+--S 795 of 1379
+t0:=1/((a+b/x^2)^3*x^10)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 3 10 2 8 2 6 3 4
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 795
+
+--S 796 of 1379
+r0:=(-35/24)/(b^3*x^3)+35/8*a/(b^4*x)+1/4/(b*x^3*(b+a*x^2)^2)+_
+ 7/8/(b^2*x^3*(b+a*x^2))+35/8*a^(3/2)*atan(x*sqrt(a)/sqrt(b))/b^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 7 2 5 2 3 +-+ x\|a
+--R (105a x + 210a b x + 105a b x )\|a atan(-----)
+--R +-+
+--R \|b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (105a x + 175a b x + 56a b x - 8b )\|b
+--R /
+--R 2 4 7 5 5 6 3 +-+
+--R (24a b x + 48a b x + 24b x )\|b
+--R Type: Expression(Integer)
+--E 796
+
+--S 797 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + a x - b
+--R 3 7 2 5 2 3 | a \| b
+--R (105a x + 210a b x + 105a b x ) |- - log(---------------------)
+--R \| b 2
+--R a x + b
+--R +
+--R 3 6 2 4 2 2 3
+--R 210a x + 350a b x + 112a b x - 16b
+--R /
+--R 2 4 7 5 5 6 3
+--R 48a b x + 96a b x + 48b x
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ b |-
+--R 3 7 2 5 2 3 |a \|b 3 6
+--R (- 105a x - 210a b x - 105a b x ) |- atan(-----) + 105a x
+--R \|b a x
+--R +
+--R 2 4 2 2 3
+--R 175a b x + 56a b x - 8b
+--R /
+--R 2 4 7 5 5 6 3
+--R 24a b x + 48a b x + 24b x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 797
+
+--S 798 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + a x - b +-+
+--R | a +-+ \| b +-+ x\|a
+--R 35a |- - \|b log(---------------------) - 70a\|a atan(-----)
+--R \| b 2 +-+
+--R a x + b \|b
+--R (4) ------------------------------------------------------------
+--R 4 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 798
+
+--S 799 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 799
+
+--S 800 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ b |- +-+
+--R |a +-+ \|b +-+ x\|a
+--R - 35a |- \|b atan(-----) - 35a\|a atan(-----)
+--R \|b a x +-+
+--R \|b
+--R (6) ---------------------------------------------
+--R 4 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 800
+
+--S 801 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 801
+
+)clear all
+
+--S 802 of 1379
+t0:=1/((a+b/x^2)^3*x^11)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R 3 11 2 9 2 7 3 5
+--R a x + 3a b x + 3a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 802
+
+--S 803 of 1379
+r0:=(-3/2)/(b^3*x^4)+3*a/(b^4*x^2)+1/4/(b*x^4*(b+a*x^2)^2)+_
+ 1/(b^2*x^4*(b+a*x^2))+6*a^2*log(x)/b^5-3*a^2*log(b+a*x^2)/b^5
+--R
+--R
+--R (2)
+--R 4 8 3 6 2 2 4 2
+--R (- 12a x - 24a b x - 12a b x )log(a x + b)
+--R +
+--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4
+--R (24a x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - b
+--R /
+--R 2 5 8 6 6 7 4
+--R 4a b x + 8a b x + 4b x
+--R Type: Expression(Integer)
+--E 803
+
+--S 804 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 8 3 6 2 2 4 2
+--R (- 12a x - 24a b x - 12a b x )log(a x + b)
+--R +
+--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4
+--R (24a x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - b
+--R /
+--R 2 5 8 6 6 7 4
+--R 4a b x + 8a b x + 4b x
+--R Type: Union(Expression(Integer),...)
+--E 804
+
+--S 805 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 805
+
+--S 806 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 806
+
+)clear all
+
+--S 807 of 1379
+t0:=(a+b/x^2)^(1/2)*x^3
+--R
+--R
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (1) x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 807
+
+--S 808 of 1379
+r0:=-1/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(3/2)+1/8*b*x^2*_
+ sqrt(a+b/x^2)/a+1/4*x^4*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R 2 \| x 4 2 +-+ |a x + b
+--R - b atanh(-----------) + (2a x + b x )\|a |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) ------------------------------------------------------
+--R +-+
+--R 8a\|a
+--R Type: Expression(Integer)
+--E 808
+
+--S 809 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +-+ | 2
+--R (- 2a x - 17a b x - 24a b x - 8b x)\|a \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b
+--R /
+--R +--------+
+--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+
+--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a
+--R ,
+--R
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((- 8a b x - 16b )\|b \|a x + b + 2a b x + 16a b x + 16b )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +---+ | 2
+--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|b
+--R /
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (32a x + 64a b)\|- a \|b \|a x + b
+--R +
+--R 3 4 2 2 2 +---+
+--R (- 8a x - 64a b x - 64a b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 809
+
+--S 810 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 +-+ |a x + b +-+
+--R (- 8a x - 20a b x - 8b x )\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (- 2a x - 17a b x - 24a b x - 8b x)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +-+ |a x + b
+--R (2a x + 17a b x + 24a b x + 8b x )\|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+
+--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a
+--R Type: Expression(Integer)
+--E 810
+
+--S 811 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 6 14 5 12 4 2 10 3 3 8
+--R - 11a x - 231a b x - 1452a b x - 4048a b x
+--R +
+--R 2 4 6 5 4 6 2
+--R - 5632a b x - 3840a b x - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x
+--R +
+--R 2 5 4 6 2
+--R - 3840a b x - 1024a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x
+--R +
+--R 2 5 5 6 3
+--R - 3328a b x - 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x
+--R +
+--R 2 5 5 6 3 7
+--R - 7424a b x - 4352a b x - 1024b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x
+--R +
+--R 2 5 5 6 3
+--R 3840a b x + 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x
+--R +
+--R 2 5 5 6 3 7
+--R 9472a b x + 4864a b x + 1024b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 16 6 14 5 2 12 4 3 10 3 4 8
+--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x
+--R +
+--R 2 5 6 6 4 7 2
+--R 7424a b x + 4352a b x + 1024b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8 3 5 6
+--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x + 7424a b x
+--R +
+--R 2 6 4 7 2
+--R 4352a b x + 1024a b x
+--R /
+--R 6 11 5 9 4 2 7 3 3 5 2 4 3
+--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x
+--R +
+--R 5
+--R 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x
+--R +
+--R 5 2 6
+--R 3328a b x + 1024b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x
+--R +
+--R 5 2 6
+--R - 3840a b x - 1024b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 13 6 11 5 2 9 4 3 7 3 4 5
+--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x
+--R +
+--R 2 5 3 6
+--R - 3328a b x - 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 811
+
+--S 812 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 3 +---+ +-+ | 2
+--R (4a b x + 8b )\|- a \|b \|a x + b
+--R +
+--R 2 2 4 3 2 4 +---+
+--R (- a b x - 8a b x - 8b )\|- a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 3 +-+ +-+ | 2
+--R (- 8a b x - 16b )\|a \|b \|a x + b
+--R +
+--R 2 2 4 3 2 4 +-+
+--R (2a b x + 16a b x + 16b )\|a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 +---+ +-+ |a x + b +-+
+--R (- 8a x - 20a b x - 8b x )\|- a \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+ +-+
+--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b
+--R (2a x + 17a b x + 24a b x + 8b x )\|- a \|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 2 +---+ +-+ +-+ | 2
+--R (32a x + 64a b)\|- a \|a \|b \|a x + b
+--R +
+--R 3 4 2 2 2 +---+ +-+
+--R (- 8a x - 64a b x - 64a b )\|- a \|a
+--R Type: Expression(Integer)
+--E 812
+
+--S 813 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2
+--R 4 10 3 8 2 2 6 3 4 4 2 |a x + b
+--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R - a x - 33a b x - 192a b x - 416a b x - 384a b x - 128b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+
+--R (8a x + 96a b x + 360a b x + 592a b x + 448a b x + 128b x)\|b
+--R +
+--R 5 12 4 10 3 2 8 2 3 6 4 4 5 2
+--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2
+--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+
+--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 813
+
+)clear all
+
+--S 814 of 1379
+t0:=(a+b/x^2)^(1/2)*x^2
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (1) x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 814
+
+--S 815 of 1379
+r0:=1/3*(a+b/x^2)^(3/2)*x^3/a
+--R
+--R
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (a x + b x) |--------
+--R | 2
+--R \| x
+--R (2) -----------------------
+--R 3a
+--R Type: Expression(Integer)
+--E 815
+
+--S 816 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 4 2 2 | 2 2 6 4 2 2 +-+
+--R (- 3a b x - 6b x )\|a x + b + (a x + 6a b x + 6b x )\|b
+--R (3) -------------------------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b
+--R Type: Union(Expression(Integer),...)
+--E 816
+
+--S 817 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 2 5 3 2 |a x + b +-+ 2 4 2 2 | 2
+--R ((- a x - 5a b x - 4b x) |-------- \|b - 3a b x - 6a b x )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 +-+ 2 5 2 3 3 |a x + b
+--R (a x + 6a b x + 6a b x )\|b + (3a b x + 7a b x + 4b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 2 2
+--R (3a x + 12a b)\|b \|a x + b - 9a b x - 12a b
+--R Type: Expression(Integer)
+--E 817
+
+--S 818 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8
+--R (- 6a x - 38a b x - 64a b x - 32b x) |-------- \|b - a x
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 2 4 3 2 4
+--R - 19a b x - 66a b x - 80a b x - 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (6a x + 44a b x + 102a b x + 96a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (a x + 19a b x + 66a b x + 80a b x + 32b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 6 2 4 2 2 3 |a x + b | 2
+--R (a x + 18a b x + 48a b x + 32b ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 3 |a x + b +-+
+--R (- 6a x - 38a b x - 64a b x - 32b ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 818
+
+)clear all
+
+--S 819 of 1379
+t0:=(a+b/x^2)^(1/2)*x
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R (1) x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 819
+
+--S 820 of 1379
+r0:=1/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))/sqrt(a)+1/2*x^2*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R \| x 2 +-+ |a x + b
+--R b atanh(-----------) + x \|a |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) ----------------------------------------
+--R +-+
+--R 2\|a
+--R Type: Expression(Integer)
+--E 820
+
+--S 821 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (2b\|b \|a x + b - a b x - 2b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 +-+
+--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 2 +---+ +-+
+--R +-+ | 2 2 2 \|- a \|a x + b - \|- a \|b
+--R (4b\|b \|a x + b - 2a b x - 4b )atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 +---+
+--R 4\|- a \|b \|a x + b + (- 2a x - 4b)\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 821
+
+--S 822 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ | 2 2 2
+--R (2b\|b \|a x + b - a b x - 2b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R +--------+ | 2
+--R +-+ | 2 2 2 \| x
+--R (- 2b\|b \|a x + b + a b x + 2b )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 +-+ |a x + b +-+ 3 +-+ | 2
+--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 +-+ +-+ 4 2 +-+ |a x + b
+--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 +-+
+--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b
+--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |--------
+--R | 2
+--R \| x
+--R +
+--R 5 9 4 7 3 2 5 2 3 3 4
+--R - 7a x - 63a b x - 168a b x - 176a b x - 64a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (a x + 26a b x + 129a b x + 248a b x + 208a b x + 64b )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b
+--R (7a x + 63a b x + 168a b x + 176a b x + 64a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+
+--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x)\|a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 6 11 5 9 4 2 7 3 3 5 2 4 3 5
+--R a x + 26a b x + 129a b x + 248a b x + 208a b x + 64a b x
+--R /
+--R +--------+
+--R | 2
+--R 4 8 3 6 2 2 4 3 2 |a x + b +-+
+--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+
+--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 823
+
+--S 824 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R +--------+ | 2
+--R +---+ +-+ | 2 2 2 +---+ \| x
+--R (- 2b\|- a \|b \|a x + b + (a b x + 2b )\|- a )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R +-+ +-+ | 2 2 2 +-+
+--R (4b\|a \|b \|a x + b + (- 2a b x - 4b )\|a )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2
+--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b
+--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R +---+ +-+ +-+ | 2 2 +---+ +-+
+--R 4\|- a \|a \|b \|a x + b + (- 2a x - 4b)\|- a \|a
+--R Type: Expression(Integer)
+--E 824
+
+--S 825 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4
+--R (- 4a x - 12a b x - 8b x) |-------- \|b - a x - 9a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 3
+--R - 16a b x - 8b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (4a x + 16a b x + 20a b x + 8b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (a x + 9a b x + 16a b x + 8b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 5 3 2 |a x + b | 2
+--R (a x + 8a b x + 8b x) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+
+--R (- 4a x - 12a b x - 8b x) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 825
+
+)clear all
+
+--S 826 of 1379
+t0:=(a+b/x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R (1) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 826
+
+--S 827 of 1379
+r0:=-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))*sqrt(b)+x*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R +-+ \|b |a x + b
+--R (2) - \|b atanh(------------) + x |--------
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 827
+
+--S 828 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 +-+ \|a x + b - \|b 2 +-+
+--R (b\|a x + b - b\|b )log(------------------) + a x \|b
+--R x
+--R (3) --------------------------------------------------------
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R Type: Union(Expression(Integer),...)
+--E 828
+
+--S 829 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 +-+ \|a x + b - \|b
+--R (b\|a x + b - b\|b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R +--------+ +-+ | 2 +--------+
+--R | 2 +-+ \|b |a x + b +-+ | 2
+--R (b\|a x + b - b\|b )atanh(------------) - x |-------- \|b \|a x + b
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 +-+ |a x + b
+--R a x \|b + b x |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R Type: Expression(Integer)
+--E 829
+
+--S 830 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R ((- 3a x - 7a b x - 4b )\|b + (- a x - 5a b x - 4b x) |-------- )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3
+--R (3a x + 7a b x + 4b x) |-------- \|b + a x + 6a b x + 9a b x + 4b
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 4 2 |a x + b +-+ | 2
+--R (3a x + 4b x ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 |a x + b
+--R (- a x - 5a b x - 4b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 830
+
+)clear all
+
+--S 831 of 1379
+t0:=(a+b/x^2)^(1/2)/x
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R (1) -----------
+--R x
+--R Type: Expression(Integer)
+--E 831
+
+--S 832 of 1379
+r0:=atanh(sqrt(a+b/x^2)/sqrt(a))*sqrt(a)-sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R +-+ \| x |a x + b
+--R (2) \|a atanh(-----------) - |--------
+--R +-+ | 2
+--R \|a \| x
+--R Type: Expression(Integer)
+--E 832
+
+--S 833 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R (x\|a \|a x + b - x\|a \|b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R +-+ | 2 2
+--R \|b \|a x + b - a x - b
+--R /
+--R +--------+
+--R | 2 +-+
+--R x\|a x + b - x\|b
+--R ,
+--R
+--R +--------+
+--R +--------+ | 2 +-+
+--R +---+ | 2 +---+ +-+ \|a x + b - \|b
+--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------+
+--R +-+ | 2 2
+--R \|b \|a x + b - a x - b
+--R /
+--R +--------+
+--R | 2 +-+
+--R x\|a x + b - x\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 833
+
+--S 834 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R (x\|a \|a x + b - x\|a \|b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R +--------+ | 2
+--R +-+ | 2 +-+ +-+ \| x
+--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +-+ |a x + b | 2 |a x + b +-+ 2
+--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b
+--R | 2 | 2
+--R \| x \| x
+--R /
+--R +--------+
+--R | 2 +-+
+--R x\|a x + b - x\|b
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (5a x + 25a b x + 36a b x + 16b x) |--------
+--R | 2
+--R \| x
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (- 5a x - 25a b x - 36a b x - 16b x)\|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8
+--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 2 4 3 2 4
+--R 14a b x + 41a b x + 44a b x + 16b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8
+--R (5a x + 25a b x + 36a b x + 16b x )\|a |-------- - 5a x
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 2 4 3 2 4
+--R - 30a b x - 61a b x - 52a b x - 16b
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (- a x - 14a b x - 41a b x - 44a b x - 16b x) |--------
+--R | 2
+--R \| x
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (a x + 14a b x + 41a b x + 44a b x + 16b x)\|a
+--R /
+--R +--------+
+--R | 2
+--R 2 8 6 2 4 +-+ |a x + b +-+
+--R (5a x + 20a b x + 16b x )\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 9 2 7 2 5 3 3 |a x + b
+--R (- a x - 13a b x - 28a b x - 16b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 3 9 2 7 2 5 3 3 |a x + b +-+
+--R (5a x + 25a b x + 36a b x + 16b x ) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 10 2 8 2 6 3 4 +-+ |a x + b
+--R (- a x - 13a b x - 28a b x - 16b x )\|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 835
+
+--S 836 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R +--------+ | 2
+--R +-+ | 2 +-+ +-+ \| x
+--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R +--------+ | 2 +-+
+--R +---+ | 2 +---+ +-+ \|a x + b - \|b
+--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +-+ |a x + b | 2 |a x + b +-+ 2
+--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b
+--R | 2 | 2
+--R \| x \| x
+--R /
+--R +--------+
+--R | 2 +-+
+--R x\|a x + b - x\|b
+--R Type: Expression(Integer)
+--E 836
+
+--S 837 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2 +--------+
+--R 3 |a x + b +-+ 2 4 2 2 | 2
+--R ((- 2a x - 2b x) |-------- \|b - a x - 3a b x - 2b )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R (2a x + 4a b x + 2b )\|b + (a x + 3a b x + 2b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R 5 3 |a x + b | 2 5 3 |a x + b +-+
+--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 837
+
+)clear all
+
+--S 838 of 1379
+t0:=(a+b/x^2)^(1/2)/x^2
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R (1) -----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 838
+
+--S 839 of 1379
+r0:=-1/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/sqrt(b)-1/2*sqrt(a+b/x^2)/x
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R \|b |a x + b +-+
+--R - a x atanh(------------) - |-------- \|b
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) -------------------------------------------
+--R +-+
+--R 2x\|b
+--R Type: Expression(Integer)
+--E 839
+
+--S 840 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 | 2 2 4 2 +-+ \|a x + b - \|b
+--R (2a b x \|a x + b + (- a x - 2a b x )\|b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a b x + 2b )\|a x + b + (- 2a b x - 2b )\|b
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R 4b x \|b \|a x + b - 2a b x - 4b x
+--R Type: Union(Expression(Integer),...)
+--E 840
+
+--S 841 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 +-+ | 2 2 4 2 \|a x + b - \|b
+--R (2a x \|b \|a x + b - a x - 2a b x )log(------------------)
+--R x
+--R +
+--R +--------+ +-+
+--R 2 +-+ | 2 2 4 2 \|b
+--R (2a x \|b \|a x + b - a x - 2a b x )atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 +-+ |a x + b | 2
+--R ((a x + 2b)\|b + 2b x |-------- )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 |a x + b +-+ 2 2
+--R (- a x - 2b x) |-------- \|b - 2a b x - 2b
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 | 2 4 2 +-+
+--R 4b x \|a x + b + (- 2a x - 4b x )\|b
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 6 2 4 2 2 3 +-+
+--R (- 5a x - 25a b x - 36a b x - 16b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (- a x - 13a b x - 28a b x - 16b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6
+--R (5a x + 25a b x + 36a b x + 16b x) |-------- \|b + a x + 14a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 4 3 2 4
+--R 41a b x + 44a b x + 16b
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 8 6 2 4 |a x + b +-+ | 2
+--R (5a x + 20a b x + 16b x ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 10 2 8 2 6 3 4 |a x + b
+--R (- a x - 13a b x - 28a b x - 16b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 842
+
+)clear all
+
+--S 843 of 1379
+t0:=(a+b/x^2)^(1/2)/x^3
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R (1) -----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 843
+
+--S 844 of 1379
+r0:=-1/3*(a+b/x^2)^(3/2)/b
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (- a x - b) |--------
+--R | 2
+--R \| x
+--R (2) -----------------------
+--R 2
+--R 3b x
+--R Type: Expression(Integer)
+--E 844
+
+--S 845 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3
+--R (3a x + 7a b x + 4b )\|b \|a x + b - a x - 6a b x - 9a b x - 4b
+--R -----------------------------------------------------------------------
+--R +--------+
+--R 5 2 3 | 2 5 2 3 +-+
+--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b
+--R Type: Union(Expression(Integer),...)
+--E 845
+
+--S 846 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R ((3a x + 7a b x + 4b )\|b + (a x + 5a b x + 4b x) |-------- )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3
+--R (- 3a x - 7a b x - 4b x) |-------- \|b - a x - 6a b x - 9a b x - 4b
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 5 2 3 | 2 5 2 3 +-+
+--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8
+--R (- 6a x - 38a b x - 64a b x - 32b x) |-------- \|b - a x
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 2 4 3 2 4
+--R - 19a b x - 66a b x - 80a b x - 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (6a x + 44a b x + 102a b x + 96a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (a x + 19a b x + 66a b x + 80a b x + 32b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 11 2 9 2 7 3 5 |a x + b | 2
+--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 11 2 9 2 7 3 5 |a x + b +-+
+--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 847
+
+)clear all
+
+--S 848 of 1379
+t0:=(a+b/x^2)^(1/2)/x^4
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R (1) -----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 848
+
+--S 849 of 1379
+r0:=1/8*a^2*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)-_
+ 1/4*sqrt(a+b/x^2)/x^3-1/8*a*sqrt(a+b/x^2)/(b*x)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R 2 3 \|b 2 |a x + b +-+
+--R a x atanh(------------) + (- a x - 2b) |-------- \|b
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) ------------------------------------------------------
+--R 3 +-+
+--R 8b x \|b
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 6 2 2 4 | 2 4 8 3 6 2 2 4 +-+
+--R ((- 4a b x - 8a b x )\|a x + b + (a x + 8a b x + 8a b x )\|b )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 6 2 2 4 3 2 4 | 2
+--R (a b x + 10a b x + 24a b x + 16b )\|a x + b
+--R +
+--R 3 6 2 2 4 3 2 4 +-+
+--R (- 4a b x - 20a b x - 32a b x - 16b )\|b
+--R /
+--R +--------+
+--R 2 6 3 4 +-+ | 2 2 2 8 3 6 4 4
+--R (32a b x + 64b x )\|b \|a x + b - 8a b x - 64a b x - 64b x
+--R Type: Union(Expression(Integer),...)
+--E 850
+
+--S 851 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4
+--R ((- 4a x - 8a b x )\|b \|a x + b + a x + 8a b x + 8a b x )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4
+--R ((- 4a x - 8a b x )\|b \|a x + b + a x + 8a b x + 8a b x )
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (a x + 10a b x + 24a b x + 16b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 2 3 3 |a x + b
+--R (4a b x + 16a b x + 16b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 3 6
+--R (- a x - 10a b x - 24a b x - 16b x) |-------- \|b - 4a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 4 3 2 4
+--R - 20a b x - 32a b x - 16b
+--R /
+--R +--------+
+--R 2 6 3 4 | 2 2 8 2 6 3 4 +-+
+--R (32a b x + 64b x )\|a x + b + (- 8a b x - 64a b x - 64b x )\|b
+--R Type: Expression(Integer)
+--E 851
+
+--S 852 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R (- 9a x - 129a b x - 552a b x - 1008a b x - 832a b x - 256b )
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 6
+--R a x + 42a b x + 321a b x + 968a b x + 1392a b x + 960a b x + 256b
+--R /
+--R +--------+
+--R | 2
+--R 4 14 3 12 2 2 10 3 8 4 6 |a x + b +-+
+--R (9a x + 120a b x + 432a b x + 576a b x + 256b x ) |-------- \|b
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 852
+
+)clear all
+
+--S 853 of 1379
+t0:=(a+b/x^2)^(3/2)*x^3
+--R
+--R
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (1) (a x + b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 853
+
+--S 854 of 1379
+r0:=1/4*(a+b/x^2)^(3/2)*x^4+3/8*b^2*atanh(sqrt(a+b/x^2)/_
+ sqrt(a))/sqrt(a)+3/8*b*x^2*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R 2 \| x 4 2 +-+ |a x + b
+--R 3b atanh(-----------) + (2a x + 5b x )\|a |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) ------------------------------------------------------
+--R +-+
+--R 8\|a
+--R Type: Expression(Integer)
+--E 854
+
+--S 855 of 1379
+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 + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +-+ | 2
+--R (- 2a x - 21a b x - 56a b x - 40b x)\|a \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8a x + 44a b x + 76a b x + 40b x)\|a \|b
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 4 2 2 +-+
+--R (32a x + 64b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64b )\|a
+--R ,
+--R
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((24a b x + 48b )\|b \|a x + b - 6a b x - 48a b x - 48b )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +---+ | 2
+--R (- 2a x - 21a b x - 56a b x - 40b x)\|- a \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (8a x + 44a b x + 76a b x + 40b x)\|- a \|b
+--R /
+--R +--------+
+--R 2 +---+ +-+ | 2 2 4 2 2 +---+
+--R (32a x + 64b)\|- a \|b \|a x + b + (- 8a x - 64a b x - 64b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 855
+
+--S 856 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((- 12a b x - 24b )\|b \|a x + b + 3a b x + 24a b x + 24b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 +-+ |a x + b +-+
+--R (- 8a x - 36a b x - 40b x )\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (- 2a x - 21a b x - 56a b x - 40b x)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8a x + 44a b x + 76a b x + 40b x)\|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +-+ |a x + b
+--R (2a x + 21a b x + 56a b x + 40b x )\|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 4 2 2 +-+
+--R (32a x + 64b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64b )\|a
+--R Type: Expression(Integer)
+--E 856
+
+--S 857 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x
+--R +
+--R 2 5 5 6 3 7
+--R 9472a b x + 4864a b x + 1024b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 8 15 7 13 6 2 11 5 3 9 4 4 7
+--R - 11a x - 242a b x - 1683a b x - 5500a b x - 9680a b x
+--R +
+--R 3 5 5 2 6 3 7
+--R - 9472a b x - 4864a b x - 1024a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x
+--R +
+--R 3 5 6 2 6 4 7 2
+--R - 7424a b x - 4352a b x - 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R a x + 63a b x + 743a b x + 3653a b x + 9420a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R 13872a b x + 11776a b x + 5376a b x + 1024b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x
+--R +
+--R 3 5 6 2 6 4 7 2
+--R 9472a b x + 4864a b x + 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R - 11a x - 253a b x - 1925a b x - 7183a b x - 15180a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R - 19152a b x - 14336a b x - 5888a b x - 1024b
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R - 13872a b x - 11776a b x - 5376a b x - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 9 17 8 15 7 2 13 6 3 11 5 4 9 4 5 7
+--R a x + 63a b x + 743a b x + 3653a b x + 9420a b x + 13872a b x
+--R +
+--R 3 6 5 2 7 3 8
+--R 11776a b x + 5376a b x + 1024a b x
+--R /
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x
+--R +
+--R 5 2
+--R 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x
+--R +
+--R 5 3 6
+--R - 3328a b x - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x
+--R +
+--R 5 3 6
+--R 3840a b x + 1024b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x
+--R +
+--R 2 5 4 6 2
+--R - 3328a b x - 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 857
+
+--S 858 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 3 +---+ +-+ | 2
+--R (- 12a b x - 24b )\|- a \|b \|a x + b
+--R +
+--R 2 2 4 3 2 4 +---+
+--R (3a b x + 24a b x + 24b )\|- a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 3 +-+ +-+ | 2
+--R (24a b x + 48b )\|a \|b \|a x + b
+--R +
+--R 2 2 4 3 2 4 +-+
+--R (- 6a b x - 48a b x - 48b )\|a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 +---+ +-+ |a x + b +-+
+--R (- 8a x - 36a b x - 40b x )\|- a \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (- 2a x - 21a b x - 56a b x - 40b x)\|- a \|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+ +-+
+--R (8a x + 44a b x + 76a b x + 40b x)\|- a \|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b
+--R (2a x + 21a b x + 56a b x + 40b x )\|- a \|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 +---+ +-+ +-+ | 2
+--R (32a x + 64b)\|- a \|a \|b \|a x + b
+--R +
+--R 2 4 2 2 +---+ +-+
+--R (- 8a x - 64a b x - 64b )\|- a \|a
+--R Type: Expression(Integer)
+--E 858
+
+--S 859 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (- 8a x - 96a b x - 360a b x - 592a b x - 448a b x - 128b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2
+--R - a x - 34a b x - 225a b x - 608a b x - 800a b x - 512a b x
+--R +
+--R 6
+--R - 128b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2
+--R 8a x + 104a b x + 456a b x + 952a b x + 1040a b x + 576a b x
+--R +
+--R 6
+--R 128b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3
+--R a x + 34a b x + 225a b x + 608a b x + 800a b x + 512a b x
+--R +
+--R 6
+--R 128b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b | 2
+--R (a x + 32a b x + 160a b x + 256a b x + 128b x) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b x) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 859
+
+)clear all
+
+--S 860 of 1379
+t0:=(a+b/x^2)^(3/2)*x^2
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (1) (a x + b) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 860
+
+--S 861 of 1379
+r0:=1/3*(a+b/x^2)^(3/2)*x^3-b^(3/2)*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))+_
+ b*x*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R +-+ \|b 3 |a x + b
+--R - 3b\|b atanh(------------) + (a x + 4b x) |--------
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) ------------------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 861
+
+--S 862 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 2 3 | 2 2 2 3 +-+
+--R ((3a b x + 12b )\|a x + b + (- 9a b x - 12b )\|b )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+
+--R (- 3a b x - 12a b x )\|a x + b + (a x + 9a b x + 12a b x )\|b
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b
+--R Type: Union(Expression(Integer),...)
+--E 862
+
+--S 863 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 3 | 2 2 2 3 +-+
+--R ((3a b x + 12b )\|a x + b + (- 9a b x - 12b )\|b )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+ +-+
+--R 2 2 3 | 2 2 2 3 +-+ \|b
+--R ((3a b x + 12b )\|a x + b + (- 9a b x - 12b )\|b )atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 2 4 2 2
+--R ((- a x - 8a b x - 16b x) |-------- \|b - 3a b x - 12a b x )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 +-+ 2 5 2 3 3 |a x + b
+--R (a x + 9a b x + 12a b x )\|b + (3a b x + 16a b x + 16b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b
+--R Type: Expression(Integer)
+--E 863
+
+--S 864 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (7a x + 70a b x + 231a b x + 344a b x + 240a b x + 64b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 6
+--R a x + 27a b x + 155a b x + 377a b x + 456a b x + 272a b x + 64b
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 8 2 6 2 4 3 2 |a x + b +-+ | 2
+--R (7a x + 56a b x + 112a b x + 64b x ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 10 3 8 2 2 6 3 4 4 2 |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 864
+
+)clear all
+
+--S 865 of 1379
+t0:=(a+b/x^2)^(3/2)*x
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R (1) ---------------------
+--R x
+--R Type: Expression(Integer)
+--E 865
+
+--S 866 of 1379
+r0:=1/2*(a+b/x^2)^(3/2)*x^2+3/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))*sqrt(a)-_
+ 3/2*b*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R +-+ \| x 2 |a x + b
+--R 3b\|a atanh(-----------) + (a x - 2b) |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) -------------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 866
+
+--S 867 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 2 +-+ | 2 3 2 +-+ +-+
+--R ((3a b x + 12b x)\|a \|a x + b + (- 9a b x - 12b x)\|a \|b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3
+--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x - 8b
+--R /
+--R +--------+
+--R 3 | 2 3 +-+
+--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b
+--R ,
+--R
+--R +--------+
+--R 3 2 +---+ | 2 3 2 +---+ +-+
+--R ((6a b x + 24b x)\|- a \|a x + b + (- 18a b x - 24b x)\|- a \|b )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3
+--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x - 8b
+--R /
+--R +--------+
+--R 3 | 2 3 +-+
+--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 867
+
+--S 868 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 2 +-+ | 2 3 2 +-+ +-+
+--R ((3a b x + 12b x)\|a \|a x + b + (- 9a b x - 12b x)\|a \|b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 3 2 +-+ | 2 3 2 +-+ +-+
+--R ((- 3a b x - 12b x)\|a \|a x + b + (9a b x + 12b x)\|a \|b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R ((- 3a x + 2a b x + 8b )\|b + (- a x - 2a b x + 8b x) |-------- )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3
+--R (3a x - 2a b x - 8b x) |-------- \|b + a x + 3a b x - 6a b x - 8b
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 3 | 2 3 +-+
+--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b
+--R Type: Expression(Integer)
+--E 868
+
+--S 869 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 5 3 6
+--R 1088a b x + 256b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x
+--R +
+--R 5 3 6
+--R - 1088a b x - 256b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 14 5 12 4 2 10 3 3 8 2 4 6
+--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x
+--R +
+--R 5 4 6 2
+--R - 960a b x - 256b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4
+--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x
+--R +
+--R 6 2 7
+--R 1216a b x + 256b
+--R *
+--R +--------+
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+--R \|a x + b
+--R +
+--R 6 14 5 12 4 2 10 3 3 8 2 4 6
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 5 4 6 2
+--R 1088a b x + 256b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x
+--R +
+--R 2 5 4 6 2 7
+--R - 2928a b x - 1344a b x - 256b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x
+--R +
+--R 2 5 5 6 3 7
+--R - 2352a b x - 1216a b x - 256b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7 2 5 5
+--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x
+--R +
+--R 6 3 7
+--R 1216a b x + 256b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 12 3 10 2 2 8 3 6 4 4 +-+
+--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3
+--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 3 2 +-+ | 2 3 2 +-+ +-+
+--R ((- 3a b x - 12b x)\|a \|a x + b + (9a b x + 12b x)\|a \|b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 3 2 +---+ | 2 3 2 +---+ +-+
+--R ((6a b x + 24b x)\|- a \|a x + b + (- 18a b x - 24b x)\|- a \|b )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R ((- 3a x + 2a b x + 8b )\|b + (- a x - 2a b x + 8b x) |-------- )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3
+--R (3a x - 2a b x - 8b x) |-------- \|b + a x + 3a b x - 6a b x - 8b
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 3 | 2 3 +-+
+--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b
+--R Type: Expression(Integer)
+--E 870
+
+--S 871 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 9 2 7 2 5 3 3 |a x + b | 2
+--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 9 2 7 2 5 3 3 |a x + b +-+
+--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 871
+
+)clear all
+
+--S 872 of 1379
+t0:=(a+b/x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R (1) ---------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 872
+
+--S 873 of 1379
+r0:=-1/2*(a+b/x^2)^(3/2)*x-3/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))*_
+ sqrt(b)+3/2*a*x*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R +-+ \|b 2 |a x + b
+--R - 3a x\|b atanh(------------) + (2a x - b) |--------
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) ------------------------------------------------------
+--R 2x
+--R Type: Expression(Integer)
+--E 873
+
+--S 874 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 | 2 2 4 2 2 +-+
+--R ((3a b x + 12a b x )\|a x + b + (- 9a b x - 12a b x )\|b )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 2 3 | 2
+--R (- 4a b x + 3a b x + 4b )\|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (2a x + 3a b x - 5a b x - 4b )\|b
+--R /
+--R +--------+
+--R 4 2 +-+ | 2 4 2 2
+--R (2a x + 8b x )\|b \|a x + b - 6a b x - 8b x
+--R Type: Union(Expression(Integer),...)
+--E 874
+
+--S 875 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 4 2 2 | 2 2 4 2 2 +-+
+--R ((3a b x + 12a b x )\|a x + b + (- 9a b x - 12a b x )\|b )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 2 | 2 2 4 2 2 +-+
+--R ((3a b x + 12a b x )\|a x + b + (- 9a b x - 12a b x )\|b )
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 2 4 2 2 3
+--R ((- 2a x - 7a b x + 4b x) |-------- \|b - 4a b x + 3a b x + 4b )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (2a x + 3a b x - 5a b x - 4b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 2 3 3 |a x + b
+--R (6a b x + 5a b x - 4b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 4 2 +-+ | 2 4 2 2
+--R (2a x + 8b x )\|b \|a x + b - 6a b x - 8b x
+--R Type: Expression(Integer)
+--E 875
+
+--S 876 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (7a x + 70a b x + 231a b x + 344a b x + 240a b x + 64b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 6
+--R a x + 27a b x + 155a b x + 377a b x + 456a b x + 272a b x + 64b
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 10 2 8 2 6 3 4 |a x + b +-+ | 2
+--R (7a x + 56a b x + 112a b x + 64b x ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 876
+
+)clear all
+
+--S 877 of 1379
+t0:=(a+b/x^2)^(3/2)/x
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R (1) ---------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 877
+
+--S 878 of 1379
+r0:=-1/3*(a+b/x^2)^(3/2)+a^(3/2)*atanh(sqrt(a+b/x^2)/sqrt(a))-a*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R 2 +-+ \| x 2 |a x + b
+--R 3a x \|a atanh(-----------) + (- 4a x - b) |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) ------------------------------------------------------
+--R 2
+--R 3x
+--R Type: Expression(Integer)
+--E 878
+
+--S 879 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+
+--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2
+--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x
+--R +
+--R 3
+--R - 4b
+--R /
+--R +--------+
+--R 5 3 | 2 5 3 +-+
+--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b
+--R ,
+--R
+--R +--------+
+--R 2 5 3 +---+ | 2
+--R (6a x + 24a b x )\|- a \|a x + b
+--R +
+--R 2 5 3 +---+ +-+
+--R (- 18a x - 24a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2
+--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x
+--R +
+--R 3
+--R - 4b
+--R /
+--R +--------+
+--R 5 3 | 2 5 3 +-+
+--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 879
+
+--S 880 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+
+--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+
+--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R ((12a x + 19a b x + 4b )\|b + (4a x + 17a b x + 4b x) |-------- )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2
+--R (- 12a x - 19a b x - 4b x) |-------- \|b - 4a x - 21a b x - 21a b x
+--R | 2
+--R \| x
+--R +
+--R 3
+--R - 4b
+--R /
+--R +--------+
+--R 5 3 | 2 5 3 +-+
+--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b
+--R Type: Expression(Integer)
+--E 880
+
+--S 881 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 5 3 6
+--R 1088a b x + 256b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x
+--R +
+--R 5 3 6
+--R - 1088a b x - 256b x
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+--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x
+--R +
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+--R - 960a b x - 256b x
+--R *
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+--R +-+ |a x + b
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+--R | 2
+--R \| x
+--R +
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+--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x
+--R +
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+--R 1216a b x + 256b
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+--R 6 14 5 12 4 2 10 3 3 8 2 4 6
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 5 4 6 2
+--R 1088a b x + 256b x
+--R *
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+--R | 2
+--R +-+ |a x + b
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+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x
+--R +
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+--R - 2928a b x - 1344a b x - 256b
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+--R +
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+--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x
+--R +
+--R 2 5 5 6 3 7
+--R - 2352a b x - 1216a b x - 256b x
+--R *
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+--R |a x + b
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+--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x
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+--R /
+--R 4 14 3 12 2 2 10 3 8 4 6 +-+
+--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a
+--R *
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+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 15 4 13 3 2 11 2 3 9 4 7
+--R - a x - 41a b x - 280a b x - 688a b x - 704a b x
+--R +
+--R 5 5
+--R - 256b x
+--R *
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+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5
+--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x )
+--R *
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+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+
+--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 5 3 +---+ | 2 2 5 3 +---+ +-+
+--R ((6a x + 24a b x )\|- a \|a x + b + (- 18a x - 24a b x )\|- a \|b )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R ((12a x + 19a b x + 4b )\|b + (4a x + 17a b x + 4b x) |-------- )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2
+--R (- 12a x - 19a b x - 4b x) |-------- \|b - 4a x - 21a b x - 21a b x
+--R | 2
+--R \| x
+--R +
+--R 3
+--R - 4b
+--R /
+--R +--------+
+--R 5 3 | 2 5 3 +-+
+--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b
+--R Type: Expression(Integer)
+--E 882
+
+--S 883 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 11 2 9 2 7 3 5 |a x + b | 2
+--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 11 2 9 2 7 3 5 |a x + b +-+
+--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 883
+
+)clear all
+
+--S 884 of 1379
+t0:=(a+b/x^2)^(3/2)/x^2
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R (1) ---------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 884
+
+--S 885 of 1379
+r0:=-1/4*(a+b/x^2)^(3/2)/x-3/8*a^2*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/_
+ sqrt(b)-3/8*a*sqrt(a+b/x^2)/x
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R 2 3 \|b 2 |a x + b +-+
+--R - 3a x atanh(------------) + (- 5a x - 2b) |-------- \|b
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) ----------------------------------------------------------
+--R 3 +-+
+--R 8x \|b
+--R Type: Expression(Integer)
+--E 885
+
+--S 886 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 6 2 2 4 | 2
+--R (12a b x + 24a b x )\|a x + b
+--R +
+--R 4 8 3 6 2 2 4 +-+
+--R (- 3a x - 24a b x - 24a b x )\|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 6 2 2 4 3 2 4 | 2
+--R (5a b x + 42a b x + 56a b x + 16b )\|a x + b
+--R +
+--R 3 6 2 2 4 3 2 4 +-+
+--R (- 20a b x - 68a b x - 64a b x - 16b )\|b
+--R /
+--R +--------+
+--R 6 2 4 +-+ | 2 2 8 2 6 3 4
+--R (32a b x + 64b x )\|b \|a x + b - 8a b x - 64a b x - 64b x
+--R Type: Union(Expression(Integer),...)
+--E 886
+
+--S 887 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4
+--R ((12a x + 24a b x )\|b \|a x + b - 3a x - 24a b x - 24a b x )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4
+--R ((12a x + 24a b x )\|b \|a x + b - 3a x - 24a b x - 24a b x )
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (5a x + 42a b x + 56a b x + 16b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 2 3 3 |a x + b
+--R (20a b x + 48a b x + 16b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 3 6
+--R (- 5a x - 42a b x - 56a b x - 16b x) |-------- \|b - 20a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 4 3 2 4
+--R - 68a b x - 64a b x - 16b
+--R /
+--R +--------+
+--R 6 2 4 | 2 2 8 6 2 4 +-+
+--R (32a b x + 64b x )\|a x + b + (- 8a x - 64a b x - 64b x )\|b
+--R Type: Expression(Integer)
+--E 887
+
+--S 888 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x
+--R +
+--R 5 2 6
+--R - 1088a b x - 256b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x
+--R +
+--R 5 3 6
+--R - 960a b x - 256b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 5 3 6
+--R 1088a b x + 256b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4
+--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x
+--R +
+--R 6 2 7
+--R 1216a b x + 256b
+--R /
+--R +--------+
+--R | 2
+--R 4 14 3 12 2 2 10 3 8 4 6 |a x + b +-+
+--R (9a x + 120a b x + 432a b x + 576a b x + 256b x ) |-------- \|b
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 888
+
+)clear all
+
+--S 889 of 1379
+t0:=(a+b/x^2)^(3/2)/x^3
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R (1) ---------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 1379
+r0:=-1/5*(a+b/x^2)^(5/2)/b
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (- a x - 2a b x - b ) |--------
+--R | 2
+--R \| x
+--R (2) ----------------------------------
+--R 4
+--R 5b x
+--R Type: Expression(Integer)
+--E 890
+
+--S 891 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10
+--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|b \|a x + b - a x
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R - 15a b x - 55a b x - 85a b x - 60a b x - 16b
+--R /
+--R +--------+
+--R 2 9 2 7 3 5 | 2
+--R (5a b x + 60a b x + 80b x )\|a x + b
+--R +
+--R 2 9 2 7 3 5 +-+
+--R (- 25a b x - 100a b x - 80b x )\|b
+--R Type: Union(Expression(Integer),...)
+--E 891
+
+--S 892 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (a x + 14a b x + 41a b x + 44a b x + 16b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ 5 10
+--R (- 5a x - 30a b x - 61a b x - 52a b x - 16b x) |-------- \|b - a x
+--R | 2
+--R \| x
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R - 15a b x - 55a b x - 85a b x - 60a b x - 16b
+--R /
+--R +--------+
+--R 2 9 2 7 3 5 | 2
+--R (5a b x + 60a b x + 80b x )\|a x + b
+--R +
+--R 2 9 2 7 3 5 +-+
+--R (- 25a b x - 100a b x - 80b x )\|b
+--R Type: Expression(Integer)
+--E 892
+
+--S 893 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R - 10a x - 180a b x - 1002a b x - 2528a b x - 3232a b x
+--R +
+--R 5 3 6
+--R - 2048a b x - 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R - a x - 52a b x - 501a b x - 1970a b x - 3920a b x
+--R +
+--R 2 5 4 6 2 7
+--R - 4192a b x - 2304a b x - 512b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R 10a x + 190a b x + 1182a b x + 3530a b x + 5760a b x
+--R +
+--R 2 5 4 6 2 7
+--R 5280a b x + 2560a b x + 512b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7 2 5 5
+--R a x + 52a b x + 501a b x + 1970a b x + 3920a b x + 4192a b x
+--R +
+--R 6 3 7
+--R 2304a b x + 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 5 17 4 15 3 2 13 2 3 11 4 9 5 7
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 17 4 15 3 2 13 2 3 11 4 9
+--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x
+--R +
+--R 5 7
+--R - 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 893
+
+)clear all
+
+--S 894 of 1379
+t0:=(a+b/x^2)^(3/2)/x^4
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R (1) ---------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 894
+
+--S 895 of 1379
+r0:=-1/6*(a+b/x^2)^(3/2)/x^3+1/16*a^3*atanh(sqrt(b)/_
+ (x*sqrt(a+b/x^2)))/b^(3/2)-1/8*a*sqrt(a+b/x^2)/x^3-1/16*a^2*_
+ sqrt(a+b/x^2)/(b*x)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R 3 5 \|b 2 4 2 2 |a x + b +-+
+--R 3a x atanh(------------) + (- 3a x - 14a b x - 8b ) |-------- \|b
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) --------------------------------------------------------------------
+--R 5 +-+
+--R 48b x \|b
+--R Type: Expression(Integer)
+--E 895
+
+--S 896 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 5 10 4 2 8 3 3 6 | 2
+--R (- 18a b x - 96a b x - 96a b x )\|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 +-+
+--R (3a x + 54a b x + 144a b x + 96a b x )\|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6
+--R (3a b x + 68a b x + 404a b x + 912a b x + 832a b x + 256b )
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +-+
+--R (- 18a b x - 198a b x - 772a b x - 1296a b x - 960a b x - 256b )\|b
+--R /
+--R +--------+
+--R 2 2 10 3 8 4 6 +-+ | 2 3 2 12
+--R (288a b x + 1536a b x + 1536b x )\|b \|a x + b - 48a b x
+--R +
+--R 2 3 10 4 8 5 6
+--R - 864a b x - 2304a b x - 1536b x
+--R Type: Union(Expression(Integer),...)
+--E 896
+
+--S 897 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 5 10 4 8 3 2 6 +-+ | 2 6 12 5 10
+--R (- 18a x - 96a b x - 96a b x )\|b \|a x + b + 3a x + 54a b x
+--R +
+--R 4 2 8 3 3 6
+--R 144a b x + 96a b x
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 5 10 4 8 3 2 6 +-+ | 2 6 12 5 10
+--R (- 18a x - 96a b x - 96a b x )\|b \|a x + b + 3a x + 54a b x
+--R +
+--R 4 2 8 3 3 6
+--R 144a b x + 96a b x
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (3a x + 68a b x + 404a b x + 912a b x + 832a b x + 256b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b
+--R (18a b x + 180a b x + 592a b x + 704a b x + 256b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (- 3a x - 68a b x - 404a b x - 912a b x - 832a b x - 256b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6
+--R - 18a b x - 198a b x - 772a b x - 1296a b x - 960a b x - 256b
+--R /
+--R +--------+
+--R 2 2 10 3 8 4 6 | 2
+--R (288a b x + 1536a b x + 1536b x )\|a x + b
+--R +
+--R 3 12 2 2 10 3 8 4 6 +-+
+--R (- 48a b x - 864a b x - 2304a b x - 1536b x )\|b
+--R Type: Expression(Integer)
+--E 897
+
+--S 898 of 1379
+d0:=D(m0,x)
+--R
+--R
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+--R - 13a x - 390a b x - 3653a b x - 16172a b x - 39520a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R - 56576a b x - 47360a b x - 21504a b x - 4096b
+--R *
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+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R - a x - 86a b x - 1289a b x - 7700a b x - 23392a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R - 39680a b x - 38144a b x - 19456a b x - 4096b x
+--R *
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+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R 56576a b x + 47360a b x + 21504a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 9 18 8 16 7 2 14 6 3 12 5 4 10
+--R a x + 87a b x + 1375a b x + 8989a b x + 31092a b x
+--R +
+--R 4 5 8 3 6 6 2 7 4 8 2 9
+--R 63072a b x + 77824a b x + 57600a b x + 23552a b x + 4096b
+--R /
+--R 6 20 5 18 4 2 16 3 3 14 2 4 12
+--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x
+--R +
+--R 5 10 6 8
+--R 13312a b x + 4096b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 7 22 6 20 5 2 18 4 3 16 3 4 14
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 12 6 10 7 8
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 898
+
+)clear all
+
+--S 899 of 1379
+t0:=(a+b/x^2)^(5/2)*x^3
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R (1) --------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 899
+
+--S 900 of 1379
+r0:=5/8*b*(a+b/x^2)^(3/2)*x^2+1/4*(a+b/x^2)^(5/2)*x^4+_
+ 15/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))*sqrt(a)-15/8*b^2*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R 2 +-+ \| x 2 4 2 2 |a x + b
+--R 15b \|a atanh(-----------) + (2a x + 9a b x - 8b ) |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) ---------------------------------------------------------------
+--R 8
+--R Type: Expression(Integer)
+--E 900
+
+--S 901 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 5 3 3 4 +-+ | 2
+--R (15a b x + 180a b x + 240b x)\|a \|a x + b
+--R +
+--R 2 2 5 3 3 4 +-+ +-+
+--R (- 75a b x - 300a b x - 240b x)\|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b
+--R /
+--R +--------+
+--R 2 5 3 2 | 2
+--R (8a x + 96a b x + 128b x)\|a x + b
+--R +
+--R 2 5 3 2 +-+
+--R (- 40a x - 160a b x - 128b x)\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 5 3 3 4 +---+ | 2
+--R (30a b x + 360a b x + 480b x)\|- a \|a x + b
+--R +
+--R 2 2 5 3 3 4 +---+ +-+
+--R (- 150a b x - 600a b x - 480b x)\|- a \|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b
+--R /
+--R +--------+
+--R 2 5 3 2 | 2
+--R (8a x + 96a b x + 128b x)\|a x + b
+--R +
+--R 2 5 3 2 +-+
+--R (- 40a x - 160a b x - 128b x)\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 901
+
+--S 902 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 5 3 3 4 +-+ | 2
+--R (15a b x + 180a b x + 240b x)\|a \|a x + b
+--R +
+--R 2 2 5 3 3 4 +-+ +-+
+--R (- 75a b x - 300a b x - 240b x)\|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 2 5 3 3 4 +-+ | 2
+--R (- 15a b x - 180a b x - 240b x)\|a \|a x + b
+--R +
+--R 2 2 5 3 3 4 +-+ +-+
+--R (75a b x + 300a b x + 240b x)\|a \|b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (- 2a x - 33a b x - 132a b x - 48a b x + 128b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (10a x + 85a b x + 172a b x - 16a b x - 128b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b
+--R /
+--R +--------+
+--R 2 5 3 2 | 2
+--R (8a x + 96a b x + 128b x)\|a x + b
+--R +
+--R 2 5 3 2 +-+
+--R (- 40a x - 160a b x - 128b x)\|b
+--R Type: Expression(Integer)
+--E 902
+
+--S 903 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 9 19 8 17 7 2 15 6 3 13
+--R 13a x + 403a b x + 4043a b x + 19825a b x
+--R +
+--R 5 4 11 4 5 9 3 6 7 2 7 5
+--R 55692a b x + 96096a b x + 103936a b x + 68864a b x
+--R +
+--R 8 3 9
+--R 25600a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 9 19 8 17 7 2 15 6 3 13
+--R - 13a x - 403a b x - 4043a b x - 19825a b x
+--R +
+--R 5 4 11 4 5 9 3 6 7 2 7 5
+--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x
+--R +
+--R 8 3 9
+--R - 25600a b x - 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 9 20 8 18 7 2 16 6 3 14 5 4 12
+--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x
+--R +
+--R 4 5 10 3 6 8 2 7 6 8 4 9 2
+--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 10 20 9 18 8 2 16 7 3 14 6 4 12
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 10 4 6 8 3 7 6 2 8 4
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 2 10
+--R 27648a b x + 4096b
+--R *
+--R +--------+
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+--R \|a x + b
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+--R 9 20 8 18 7 2 16 6 3 14 5 4 12
+--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x
+--R +
+--R 4 5 10 3 6 8 2 7 6 8 4 9 2
+--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 10 20 9 18 8 2 16 7 3 14 6 4 12
+--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x
+--R +
+--R 5 5 10 4 6 8 3 7 6 2 8 4
+--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x
+--R +
+--R 9 2 10
+--R - 29696a b x - 4096b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 10 21 9 19 8 2 17 7 3 15 6 4 13
+--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x
+--R +
+--R 5 5 11 4 6 9 3 7 7 2 8 5
+--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x
+--R +
+--R 9 3 10
+--R - 27648a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 10 21 9 19 8 2 17 7 3 15 6 4 13
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 11 4 6 9 3 7 7 2 8 5
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 3 10
+--R 27648a b x + 4096b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 16 5 14 4 2 12 3 3 10 2 4 8
+--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x
+--R +
+--R 5 6 6 4
+--R 13312a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 17 6 15 5 2 13 4 3 11 3 4 9
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 7 6 5 7 3
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 17 6 15 5 2 13 4 3 11 3 4 9
+--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x
+--R +
+--R 2 5 7 6 5 7 3
+--R 29952a b x + 17408a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 18 6 16 5 2 14 4 3 12 3 4 10
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 8 6 6 7 4
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 903
+
+--S 904 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 5 3 3 4 +-+ | 2
+--R (- 15a b x - 180a b x - 240b x)\|a \|a x + b
+--R +
+--R 2 2 5 3 3 4 +-+ +-+
+--R (75a b x + 300a b x + 240b x)\|a \|b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 5 3 3 4 +---+ | 2
+--R (30a b x + 360a b x + 480b x)\|- a \|a x + b
+--R +
+--R 2 2 5 3 3 4 +---+ +-+
+--R (- 150a b x - 600a b x - 480b x)\|- a \|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (- 2a x - 33a b x - 132a b x - 48a b x + 128b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (10a x + 85a b x + 172a b x - 16a b x - 128b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b
+--R /
+--R +--------+
+--R 2 5 3 2 | 2
+--R (8a x + 96a b x + 128b x)\|a x + b
+--R +
+--R 2 5 3 2 +-+
+--R (- 40a x - 160a b x - 128b x)\|b
+--R Type: Expression(Integer)
+--E 904
+
+--S 905 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x
+--R +
+--R 2 5 5 6 3 7
+--R - 5280a b x - 2560a b x - 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R - 8112a b x - 6496a b x - 2816a b x - 512b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R 11040a b x + 7840a b x + 3072a b x + 512b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R 8112a b x + 6496a b x + 2816a b x + 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 13 4 11 3 2 9 2 3 7 4 5
+--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x
+--R +
+--R 5 3
+--R - 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 905
+
+)clear all
+
+--S 906 of 1379
+t0:=(a+b/x^2)^(5/2)*x^2
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R (1) --------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 1379
+r0:=5/3*b*(a+b/x^2)^(3/2)*x+1/3*(a+b/x^2)^(5/2)*x^3-_
+ 5/2*a*b^(3/2)*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))-5/2*b^2*sqrt(a+b/x^2)/x
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R +-+ \|b 2 4 2 2 |a x + b
+--R - 15a b x\|b atanh(------------) + (2a x + 14a b x - 3b ) |--------
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) ----------------------------------------------------------------------
+--R 6x
+--R Type: Expression(Integer)
+--E 907
+
+--S 908 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 2 6 2 3 4 4 2 | 2
+--R (15a b x + 180a b x + 240a b x )\|a x + b
+--R +
+--R 3 2 6 2 3 4 4 2 +-+
+--R (- 75a b x - 300a b x - 240a b x )\|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 8 3 2 6 2 3 4 4 2 5 | 2
+--R (- 10a b x - 96a b x - 129a b x + 60a b x + 48b )\|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (2a x + 40a b x + 165a b x + 105a b x - 84a b x - 48b )\|b
+--R /
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2
+--R (6a x + 72a b x + 96b x )\|b \|a x + b - 30a b x - 120a b x - 96b x
+--R Type: Union(Expression(Integer),...)
+--E 908
+
+--S 909 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 2 6 2 3 4 4 2 | 2
+--R (15a b x + 180a b x + 240a b x )\|a x + b
+--R +
+--R 3 2 6 2 3 4 4 2 +-+
+--R (- 75a b x - 300a b x - 240a b x )\|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 3 2 6 2 3 4 4 2 | 2
+--R (15a b x + 180a b x + 240a b x )\|a x + b
+--R +
+--R 3 2 6 2 3 4 4 2 +-+
+--R (- 75a b x - 300a b x - 240a b x )\|b
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 2a x - 38a b x - 197a b x - 188a b x + 48b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R - 10a b x - 96a b x - 129a b x + 60a b x + 48b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (2a x + 40a b x + 165a b x + 105a b x - 84a b x - 48b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b
+--R (10a b x + 110a b x + 297a b x + 164a b x - 48b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2
+--R (6a x + 72a b x + 96b x )\|b \|a x + b - 30a b x - 120a b x - 96b x
+--R Type: Expression(Integer)
+--E 909
+
+--S 910 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R - 11a x - 253a b x - 1925a b x - 7183a b x - 15180a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R - 19152a b x - 14336a b x - 5888a b x - 1024b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R - 13872a b x - 11776a b x - 5376a b x - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R 11a x + 253a b x + 1925a b x + 7183a b x + 15180a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R 19152a b x + 14336a b x + 5888a b x + 1024b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 9 18 8 16 7 2 14 6 3 12 5 4 10 4 5 8
+--R a x + 64a b x + 806a b x + 4396a b x + 13073a b x + 23292a b x
+--R +
+--R 3 6 6 2 7 4 8 2 9
+--R 25648a b x + 17152a b x + 6400a b x + 1024b
+--R /
+--R 5 14 4 12 3 2 10 2 3 8 4 6
+--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x
+--R +
+--R 5 4
+--R 1024b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 6 16 5 14 4 2 12 3 3 10 2 4 8
+--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x
+--R +
+--R 5 6 6 4
+--R - 3328a b x - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 910
+
+)clear all
+
+--S 911 of 1379
+t0:=(a+b/x^2)^(5/2)*x
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R (1) --------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 911
+
+--S 912 of 1379
+r0:=-5/6*b*(a+b/x^2)^(3/2)+1/2*(a+b/x^2)^(5/2)*x^2+5/2*a^(3/2)*b*_
+ atanh(sqrt(a+b/x^2)/sqrt(a))-5/2*a*b*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R 2 +-+ \| x 2 4 2 2 |a x + b
+--R 15a b x \|a atanh(-----------) + (3a x - 14a b x - 2b ) |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) --------------------------------------------------------------------
+--R 2
+--R 6x
+--R Type: Expression(Integer)
+--E 912
+
+--S 913 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 7 2 2 5 3 3 +-+ | 2
+--R (15a b x + 180a b x + 240a b x )\|a \|a x + b
+--R +
+--R 3 7 2 2 5 3 3 +-+ +-+
+--R (- 75a b x - 300a b x - 240a b x )\|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b
+--R /
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (6a x + 72a b x + 96b x )\|a x + b
+--R +
+--R 2 7 5 2 3 +-+
+--R (- 30a x - 120a b x - 96b x )\|b
+--R ,
+--R
+--R +--------+
+--R 3 7 2 2 5 3 3 +---+ | 2
+--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b
+--R +
+--R 3 7 2 2 5 3 3 +---+ +-+
+--R (- 150a b x - 600a b x - 480a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b
+--R /
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (6a x + 72a b x + 96b x )\|a x + b
+--R +
+--R 2 7 5 2 3 +-+
+--R (- 30a x - 120a b x - 96b x )\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 913
+
+--S 914 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 7 2 2 5 3 3 +-+ | 2
+--R (15a b x + 180a b x + 240a b x )\|a \|a x + b
+--R +
+--R 3 7 2 2 5 3 3 +-+ +-+
+--R (- 75a b x - 300a b x - 240a b x )\|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 3 7 2 2 5 3 3 +-+ | 2
+--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b
+--R +
+--R 3 7 2 2 5 3 3 +-+ +-+
+--R (75a b x + 300a b x + 240a b x )\|a \|b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (15a x - 10a b x - 242a b x - 264a b x - 32b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b
+--R /
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (6a x + 72a b x + 96b x )\|a x + b
+--R +
+--R 2 7 5 2 3 +-+
+--R (- 30a x - 120a b x - 96b x )\|b
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 9 19 8 17 7 2 15 6 3 13
+--R 13a x + 403a b x + 4043a b x + 19825a b x
+--R +
+--R 5 4 11 4 5 9 3 6 7 2 7 5
+--R 55692a b x + 96096a b x + 103936a b x + 68864a b x
+--R +
+--R 8 3 9
+--R 25600a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 9 19 8 17 7 2 15 6 3 13
+--R - 13a x - 403a b x - 4043a b x - 19825a b x
+--R +
+--R 5 4 11 4 5 9 3 6 7 2 7 5
+--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x
+--R +
+--R 8 3 9
+--R - 25600a b x - 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 9 20 8 18 7 2 16 6 3 14 5 4 12
+--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x
+--R +
+--R 4 5 10 3 6 8 2 7 6 8 4 9 2
+--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 10 20 9 18 8 2 16 7 3 14 6 4 12
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 10 4 6 8 3 7 6 2 8 4
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 2 10
+--R 27648a b x + 4096b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 9 20 8 18 7 2 16 6 3 14 5 4 12
+--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x
+--R +
+--R 4 5 10 3 6 8 2 7 6 8 4 9 2
+--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 10 20 9 18 8 2 16 7 3 14 6 4 12
+--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x
+--R +
+--R 5 5 10 4 6 8 3 7 6 2 8 4
+--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x
+--R +
+--R 9 2 10
+--R - 29696a b x - 4096b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 10 21 9 19 8 2 17 7 3 15 6 4 13
+--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x
+--R +
+--R 5 5 11 4 6 9 3 7 7 2 8 5
+--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x
+--R +
+--R 9 3 10
+--R - 27648a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 10 21 9 19 8 2 17 7 3 15 6 4 13
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 11 4 6 9 3 7 7 2 8 5
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 3 10
+--R 27648a b x + 4096b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 18 5 16 4 2 14 3 3 12 2 4 10
+--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x
+--R +
+--R 5 8 6 6
+--R 13312a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 19 6 17 5 2 15 4 3 13 3 4 11
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 9 6 7 7 5
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 19 6 17 5 2 15 4 3 13 3 4 11
+--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x
+--R +
+--R 2 5 9 6 7 7 5
+--R 29952a b x + 17408a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 20 6 18 5 2 16 4 3 14 3 4 12
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 10 6 8 7 6
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 915
+
+--S 916 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 3 7 2 2 5 3 3 +-+ | 2
+--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b
+--R +
+--R 3 7 2 2 5 3 3 +-+ +-+
+--R (75a b x + 300a b x + 240a b x )\|a \|b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 3 7 2 2 5 3 3 +---+ | 2
+--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b
+--R +
+--R 3 7 2 2 5 3 3 +---+ +-+
+--R (- 150a b x - 600a b x - 480a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (15a x - 10a b x - 242a b x - 264a b x - 32b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b
+--R /
+--R +--------+
+--R 2 7 5 2 3 | 2
+--R (6a x + 72a b x + 96b x )\|a x + b
+--R +
+--R 2 7 5 2 3 +-+
+--R (- 30a x - 120a b x - 96b x )\|b
+--R Type: Expression(Integer)
+--E 916
+
+--S 917 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x
+--R +
+--R 2 5 5 6 3 7
+--R - 5280a b x - 2560a b x - 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R - 8112a b x - 6496a b x - 2816a b x - 512b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R 11040a b x + 7840a b x + 3072a b x + 512b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R 8112a b x + 6496a b x + 2816a b x + 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 15 4 13 3 2 11 2 3 9 4 7
+--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x
+--R +
+--R 5 5
+--R - 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 917
+
+)clear all
+
+--S 918 of 1379
+t0:=(a+b/x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R (1) --------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 918
+
+--S 919 of 1379
+r0:=-5/8*a*(a+b/x^2)^(3/2)*x-1/4*(a+b/x^2)^(5/2)*x-15/8*a^2*_
+ atanh(sqrt(b)/(x*sqrt(a+b/x^2)))*sqrt(b)+15/8*a^2*x*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R 2 3 +-+ \|b 2 4 2 2 |a x + b
+--R - 15a x \|b atanh(------------) + (8a x - 9a b x - 2b ) |--------
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) --------------------------------------------------------------------
+--R 3
+--R 8x
+--R Type: Expression(Integer)
+--E 919
+
+--S 920 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 8 3 2 6 2 3 4 | 2
+--R (15a b x + 180a b x + 240a b x )\|a x + b
+--R +
+--R 4 8 3 2 6 2 3 4 +-+
+--R (- 75a b x - 300a b x - 240a b x )\|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 8 3 2 6 2 3 4 4 2 5 | 2
+--R (- 32a b x - 19a b x + 190a b x + 184a b x + 32b )\|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (8a x + 55a b x - 55a b x - 278a b x - 200a b x - 32b )\|b
+--R /
+--R +--------+
+--R 2 8 6 2 4 +-+ | 2 2 8 2 6
+--R (8a x + 96a b x + 128b x )\|b \|a x + b - 40a b x - 160a b x
+--R +
+--R 3 4
+--R - 128b x
+--R Type: Union(Expression(Integer),...)
+--E 920
+
+--S 921 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 4 8 3 2 6 2 3 4 | 2
+--R (15a b x + 180a b x + 240a b x )\|a x + b
+--R +
+--R 4 8 3 2 6 2 3 4 +-+
+--R (- 75a b x - 300a b x - 240a b x )\|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 8 3 2 6 2 3 4 | 2
+--R (15a b x + 180a b x + 240a b x )\|a x + b
+--R +
+--R 4 8 3 2 6 2 3 4 +-+
+--R (- 75a b x - 300a b x - 240a b x )\|b
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 8a x - 87a b x - 18a b x + 168a b x + 32b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R - 32a b x - 19a b x + 190a b x + 184a b x + 32b
+--R *
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+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (8a x + 55a b x - 55a b x - 278a b x - 200a b x - 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b
+--R (40a b x + 115a b x - 62a b x - 184a b x - 32b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 8 6 2 4 +-+ | 2 2 8 2 6
+--R (8a x + 96a b x + 128b x )\|b \|a x + b - 40a b x - 160a b x
+--R +
+--R 3 4
+--R - 128b x
+--R Type: Expression(Integer)
+--E 921
+
+--S 922 of 1379
+d0:=D(m0,x)
+--R
+--R
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+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R - 11a x - 253a b x - 1925a b x - 7183a b x - 15180a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R - 19152a b x - 14336a b x - 5888a b x - 1024b
+--R *
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+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R - 13872a b x - 11776a b x - 5376a b x - 1024b x
+--R *
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+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R 11a x + 253a b x + 1925a b x + 7183a b x + 15180a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R 19152a b x + 14336a b x + 5888a b x + 1024b x
+--R *
+--R +--------+
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+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 9 18 8 16 7 2 14 6 3 12 5 4 10 4 5 8
+--R a x + 64a b x + 806a b x + 4396a b x + 13073a b x + 23292a b x
+--R +
+--R 3 6 6 2 7 4 8 2 9
+--R 25648a b x + 17152a b x + 6400a b x + 1024b
+--R /
+--R 5 16 4 14 3 2 12 2 3 10 4 8
+--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x
+--R +
+--R 5 6
+--R 1024b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 6 18 5 16 4 2 14 3 3 12 2 4 10
+--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x
+--R +
+--R 5 8 6 6
+--R - 3328a b x - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 922
+
+)clear all
+
+--S 923 of 1379
+t0:=(a+b/x^2)^(5/2)/x
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R (1) --------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 923
+
+--S 924 of 1379
+r0:=-1/3*a*(a+b/x^2)^(3/2)-1/5*(a+b/x^2)^(5/2)+a^(5/2)*_
+ atanh(sqrt(a+b/x^2)/sqrt(a))-a^2*sqrt(a+b/x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R 2 4 +-+ \| x 2 4 2 2 |a x + b
+--R 15a x \|a atanh(-----------) + (- 23a x - 11a b x - 3b ) |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) ---------------------------------------------------------------------
+--R 4
+--R 15x
+--R Type: Expression(Integer)
+--E 924
+
+--S 925 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 4 9 3 7 2 2 5 +-+ | 2
+--R (15a x + 180a b x + 240a b x )\|a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 +-+ +-+
+--R (- 75a x - 300a b x - 240a b x )\|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b
+--R /
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (15a x + 180a b x + 240b x )\|a x + b
+--R +
+--R 2 9 7 2 5 +-+
+--R (- 75a x - 300a b x - 240b x )\|b
+--R ,
+--R
+--R +--------+
+--R 4 9 3 7 2 2 5 +---+ | 2
+--R (30a x + 360a b x + 480a b x )\|- a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 +---+ +-+
+--R (- 150a x - 600a b x - 480a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b
+--R /
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (15a x + 180a b x + 240b x )\|a x + b
+--R +
+--R 2 9 7 2 5 +-+
+--R (- 75a x - 300a b x - 240b x )\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 925
+
+--S 926 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 4 9 3 7 2 2 5 +-+ | 2
+--R (15a x + 180a b x + 240a b x )\|a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 +-+ +-+
+--R (- 75a x - 300a b x - 240a b x )\|a \|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b
+--R log(------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 4 9 3 7 2 2 5 +-+ | 2
+--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 +-+ +-+
+--R (75a x + 300a b x + 240a b x )\|a \|b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (23a x + 287a b x + 503a b x + 212a b x + 48b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b
+--R /
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (15a x + 180a b x + 240b x )\|a x + b
+--R +
+--R 2 9 7 2 5 +-+
+--R (- 75a x - 300a b x - 240b x )\|b
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 9 19 8 17 7 2 15 6 3 13
+--R 13a x + 403a b x + 4043a b x + 19825a b x
+--R +
+--R 5 4 11 4 5 9 3 6 7 2 7 5
+--R 55692a b x + 96096a b x + 103936a b x + 68864a b x
+--R +
+--R 8 3 9
+--R 25600a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 9 19 8 17 7 2 15 6 3 13
+--R - 13a x - 403a b x - 4043a b x - 19825a b x
+--R +
+--R 5 4 11 4 5 9 3 6 7 2 7 5
+--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x
+--R +
+--R 8 3 9
+--R - 25600a b x - 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 9 20 8 18 7 2 16 6 3 14 5 4 12
+--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x
+--R +
+--R 4 5 10 3 6 8 2 7 6 8 4 9 2
+--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 10 20 9 18 8 2 16 7 3 14 6 4 12
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 10 4 6 8 3 7 6 2 8 4
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 2 10
+--R 27648a b x + 4096b
+--R *
+--R +--------+
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+--R \|a x + b
+--R +
+--R 9 20 8 18 7 2 16 6 3 14 5 4 12
+--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x
+--R +
+--R 4 5 10 3 6 8 2 7 6 8 4 9 2
+--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 10 20 9 18 8 2 16 7 3 14 6 4 12
+--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x
+--R +
+--R 5 5 10 4 6 8 3 7 6 2 8 4
+--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x
+--R +
+--R 9 2 10
+--R - 29696a b x - 4096b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 10 21 9 19 8 2 17 7 3 15 6 4 13
+--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x
+--R +
+--R 5 5 11 4 6 9 3 7 7 2 8 5
+--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x
+--R +
+--R 9 3 10
+--R - 27648a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 10 21 9 19 8 2 17 7 3 15 6 4 13
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 11 4 6 9 3 7 7 2 8 5
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 3 10
+--R 27648a b x + 4096b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 20 5 18 4 2 16 3 3 14 2 4 12
+--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x
+--R +
+--R 5 10 6 8
+--R 13312a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 21 6 19 5 2 17 4 3 15 3 4 13
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 11 6 9 7 7
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 21 6 19 5 2 17 4 3 15 3 4 13
+--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x
+--R +
+--R 2 5 11 6 9 7 7
+--R 29952a b x + 17408a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 22 6 20 5 2 18 4 3 16 3 4 14
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 12 6 10 7 8
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 927
+
+--S 928 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 4 9 3 7 2 2 5 +-+ | 2
+--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 +-+ +-+
+--R (75a x + 300a b x + 240a b x )\|a \|b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 9 3 7 2 2 5 +---+ | 2
+--R (30a x + 360a b x + 480a b x )\|- a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 +---+ +-+
+--R (- 150a x - 600a b x - 480a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R +---+
+--R x\|- a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (23a x + 287a b x + 503a b x + 212a b x + 48b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b
+--R /
+--R +--------+
+--R 2 9 7 2 5 | 2
+--R (15a x + 180a b x + 240b x )\|a x + b
+--R +
+--R 2 9 7 2 5 +-+
+--R (- 75a x - 300a b x - 240b x )\|b
+--R Type: Expression(Integer)
+--E 928
+
+--S 929 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x
+--R +
+--R 2 5 5 6 3 7
+--R - 5280a b x - 2560a b x - 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R - 8112a b x - 6496a b x - 2816a b x - 512b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R 11040a b x + 7840a b x + 3072a b x + 512b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 8 17 7 15 6 2 13 5 3 11 4 4 9
+--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x
+--R +
+--R 3 5 7 2 6 5 7 3 8
+--R 8112a b x + 6496a b x + 2816a b x + 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 5 17 4 15 3 2 13 2 3 11 4 9 5 7
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 17 4 15 3 2 13 2 3 11 4 9
+--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x
+--R +
+--R 5 7
+--R - 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 929
+
+)clear all
+
+--S 930 of 1379
+t0:=(a+b/x^2)^(5/2)/x^2
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R (1) --------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 930
+
+--S 931 of 1379
+r0:=-5/24*a*(a+b/x^2)^(3/2)/x-1/6*(a+b/x^2)^(5/2)/x-_
+ 5/16*a^3*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/sqrt(b)-5/16*a^2*_
+ sqrt(a+b/x^2)/x
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 2
+--R 3 5 \|b 2 4 2 2 |a x + b +-+
+--R - 15a x atanh(------------) + (- 33a x - 26a b x - 8b ) |-------- \|b
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
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+
+--S 932 of 1379
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+--E 932
+
+--S 933 of 1379
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+--R (- 48a x - 864a b x - 2304a b x - 1536b x )\|b
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+
+--S 934 of 1379
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+--R |a x + b
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+--E 934
+
+)clear all
+
+--S 935 of 1379
+t0:=(a+b/x^2)^(5/2)/x^3
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+--E 935
+
+--S 936 of 1379
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+--R
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+--R \| x
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+--R 7b x
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+--E 936
+
+--S 937 of 1379
+a0:=integrate(t0,x)
+--R
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+--R +
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+--R +
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+--R - 336a b x - 64b
+--R /
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+--R 3 13 2 2 11 3 9 4 7 +-+
+--R (- 49a b x - 392a b x - 784a b x - 448b x )\|b
+--R Type: Union(Expression(Integer),...)
+--E 937
+
+--S 938 of 1379
+m0:=a0-r0
+--R
+--R
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+--R a x + 27a b x + 155a b x + 377a b x + 456a b x + 272a b x
+--R +
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+--R *
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+--R \|a x + b
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+--R +
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+--R - 64b x
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+--R +
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+--R /
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+--R (7a b x + 168a b x + 560a b x + 448b x )\|a x + b
+--R +
+--R 3 13 2 2 11 3 9 4 7 +-+
+--R (- 49a b x - 392a b x - 784a b x - 448b x )\|b
+--R Type: Expression(Integer)
+--E 938
+
+--S 939 of 1379
+d0:=D(m0,x)
+--R
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+--R - 86784a b x - 159168a b x - 181760a b x - 126464a b x
+--R +
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+--R - 49152a b x - 8192b x
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+--R +
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+--R - 149856a b x - 236992a b x - 239360a b x - 150016a b x
+--R +
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+--R - 53248a b x - 8192b
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+--R 14a x + 504a b x + 5908a b x + 34232a b x + 115598a b x
+--R +
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+--R 245952a b x + 340928a b x + 308224a b x + 175616a b x
+--R +
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+--R a x + 101a b x + 1865a b x + 14407a b x + 59906a b x
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+--R 149856a b x + 236992a b x + 239360a b x + 150016a b x
+--R +
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+--R 53248a b x + 8192b x
+--R *
+--R +--------+
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+--R |a x + b
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+--R \| x
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+--R 7 23 6 21 5 2 19 4 3 17 3 4 15
+--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x
+--R +
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+--R 39424a b x + 28672a b x + 8192b x
+--R *
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+--R |-------- \|a x + b
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+--R \| x
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+--R - 14a x - 462a b x - 4480a b x - 19392a b x - 43520a b x
+--R +
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+--R - 52736a b x - 32768a b x - 8192b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
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+--E 939
+
+)clear all
+
+--S 940 of 1379
+t0:=(a+b/x^2)^(5/2)/x^4
+--R
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+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R (1) --------------------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 940
+
+--S 941 of 1379
+r0:=-5/48*a*(a+b/x^2)^(3/2)/x^3-1/8*(a+b/x^2)^(5/2)/x^3+5/128*a^4*_
+ atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)-5/64*a^2*_
+ sqrt(a+b/x^2)/x^3-5/128*a^3*sqrt(a+b/x^2)/(b*x)
+--R
+--R
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+--R +-+
+--R 4 7 \|b
+--R 15a x atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
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+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 3 |a x + b +-+
+--R (- 15a x - 118a b x - 136a b x - 48b ) |-------- \|b
+--R | 2
+--R \| x
+--R /
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+--R 384b x \|b
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
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+--R (- 120a b x - 1200a b x - 2880a b x - 1920a b x )\|a x + b
+--R +
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+--R (15a x + 480a b x + 2400a b x + 3840a b x + 1920a b x )\|b
+--R *
+--R +--------+
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+--R \|a x + b - \|b
+--R log(------------------)
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+--R 15a b x + 598a b x + 6312a b x + 27120a b x + 55424a b x
+--R +
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+--R 57600a b x + 29696a b x + 6144b
+--R *
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+--R - 120a b x - 2264a b x - 15552a b x - 49248a b x - 80896a b x
+--R +
+--R 2 6 4 7 2 8
+--R - 71680a b x - 32768a b x - 6144b
+--R *
+--R +-+
+--R \|b
+--R /
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+--R 3 2 14 2 3 12 4 10 5 8 +-+ | 2
+--R (3072a b x + 30720a b x + 73728a b x + 49152b x )\|b \|a x + b
+--R +
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+--R - 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152b x
+--R Type: Union(Expression(Integer),...)
+--E 942
+
+--S 943 of 1379
+m0:=a0-r0
+--R
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+--R +--------+
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+--R 15a x + 480a b x + 2400a b x + 3840a b x + 1920a b x
+--R *
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+--R \|a x + b - \|b
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+--R +
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+--R 15a x + 480a b x + 2400a b x + 3840a b x + 1920a b x
+--R *
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+--R atanh(------------)
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+--R |a x + b
+--R x |--------
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+--R \| x
+--R +
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+--R 15a x + 598a b x + 6312a b x + 27120a b x + 55424a b x
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+--R 120a b x + 2144a b x + 13408a b x + 35840a b x
+--R +
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+--R 45056a b x + 26624a b x + 6144b x
+--R *
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+--R |a x + b
+--R |--------
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+--R \| x
+--R *
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+--R | 2
+--R \|a x + b
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+--R - 15a x - 598a b x - 6312a b x - 27120a b x - 55424a b x
+--R +
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+--R - 57600a b x - 29696a b x - 6144b x
+--R *
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+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
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+--R - 120a b x - 2264a b x - 15552a b x - 49248a b x - 80896a b x
+--R +
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+--R - 71680a b x - 32768a b x - 6144b
+--R /
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+--R +
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+--R (- 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152b x )\|b
+--R Type: Expression(Integer)
+--E 943
+
+--S 944 of 1379
+d0:=D(m0,x)
+--R
+--R
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+--R +
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+--R - 489872a b x - 1397536a b x - 2635136a b x - 3337984a b x
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+--R - 2213888a b x - 1306624a b x - 442368a b x - 65536b x
+--R *
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+--R |a x + b
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+--R \|a x + b
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+--R 17a x + 867a b x + 13923a b x + 108545a b x + 489872a b x
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+--R +
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+--R 1519616a b x + 475136a b x + 65536b x
+--R *
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+--R |a x + b +-+
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+--R \| x
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+--R a x + 148a b x + 3942a b x + 43876a b x + 265729a b x
+--R +
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+--R 990736a b x + 2426144a b x + 4030336a b x + 4583168a b x
+--R +
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+--R 3520512a b x + 1748992a b x + 507904a b x + 65536b
+--R /
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+--R 17a x + 816a b x + 11424a b x + 71808a b x + 239360a b x
+--R +
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+--R 452608a b x + 487424a b x + 278528a b x + 65536b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 9 28 8 26 7 2 24 6 3 22 5 4 20
+--R - a x - 145a b x - 3504a b x - 32928a b x - 156288a b x
+--R +
+--R 4 5 18 3 6 16 2 7 14 8 12
+--R - 419584a b x - 665600a b x - 618496a b x - 311296a b x
+--R +
+--R 9 10
+--R - 65536b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 944
+
+)clear all
+
+--S 945 of 1379
+t0:=x^3/(a+b/x^2)^(1/2)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 945
+
+--S 946 of 1379
+r0:=3/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(5/2)-3/8*b*x^2*_
+ sqrt(a+b/x^2)/a^2+1/4*x^4*sqrt(a+b/x^2)/a
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R 2 \| x 4 2 +-+ |a x + b
+--R 3b atanh(-----------) + (2a x - 3b x )\|a |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) ------------------------------------------------------
+--R 2 +-+
+--R 8a \|a
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 1379
+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 + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +-+ | 2
+--R (- 2a x - 13a b x + 8a b x + 24b x)\|a \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b
+--R /
+--R +--------+
+--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+
+--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a
+--R ,
+--R
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((24a b x + 48b )\|b \|a x + b - 6a b x - 48a b x - 48b )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +---+ | 2
+--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|b
+--R /
+--R +--------+
+--R 3 2 2 +---+ +-+ | 2
+--R (32a x + 64a b)\|- a \|b \|a x + b
+--R +
+--R 4 4 3 2 2 2 +---+
+--R (- 8a x - 64a b x - 64a b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 947
+
+--S 948 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((- 12a b x - 24b )\|b \|a x + b + 3a b x + 24a b x + 24b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 +-+ |a x + b +-+
+--R (- 8a x - 4a b x + 24b x )\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (- 2a x - 13a b x + 8a b x + 24b x)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +-+ |a x + b
+--R (2a x + 13a b x - 8a b x - 24b x )\|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+
+--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a
+--R Type: Expression(Integer)
+--E 948
+
+--S 949 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 5 14 4 12 3 2 10 2 3 8 4 6
+--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x
+--R +
+--R 5 4
+--R 1024b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 6 14 5 12 4 2 10 3 3 8 2 4 6
+--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x
+--R +
+--R 5 4
+--R - 1024a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 15 5 13 4 2 11 3 3 9 2 4 7
+--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x
+--R +
+--R 5 5
+--R - 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 6 15 5 13 4 2 11 3 3 9 2 4 7
+--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x
+--R +
+--R 5 5 6 3
+--R 3328a b x + 1024b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 15 5 13 4 2 11 3 3 9 2 4 7
+--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x
+--R +
+--R 5 5
+--R 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 6 15 5 13 4 2 11 3 3 9 2 4 7
+--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x
+--R +
+--R 5 5 6 3
+--R - 3840a b x - 1024b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 16 5 14 4 2 12 3 3 10 2 4 8
+--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x
+--R +
+--R 5 6 6 4
+--R - 3328a b x - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 7 16 6 14 5 2 12 4 3 10 3 4 8 2 5 6
+--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x
+--R +
+--R 6 4
+--R 1024a b x
+--R /
+--R 6 11 5 9 4 2 7 3 3 5 2 4 3
+--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x
+--R +
+--R 5
+--R 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x
+--R +
+--R 5 2 6
+--R - 3328a b x - 1024b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x
+--R +
+--R 5 2 6
+--R 3840a b x + 1024b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 13 6 11 5 2 9 4 3 7 3 4 5
+--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x
+--R +
+--R 2 5 3 6
+--R - 3328a b x - 1024a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 2 3 +---+ +-+ | 2
+--R (- 12a b x - 24b )\|- a \|b \|a x + b
+--R +
+--R 2 2 4 3 2 4 +---+
+--R (3a b x + 24a b x + 24b )\|- a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 2 3 +-+ +-+ | 2
+--R (24a b x + 48b )\|a \|b \|a x + b
+--R +
+--R 2 2 4 3 2 4 +-+
+--R (- 6a b x - 48a b x - 48b )\|a
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 +---+ +-+ |a x + b +-+
+--R (- 8a x - 4a b x + 24b x )\|- a \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+ +-+
+--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b
+--R (2a x + 13a b x - 8a b x - 24b x )\|- a \|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 3 2 2 +---+ +-+ +-+ | 2
+--R (32a x + 64a b)\|- a \|a \|b \|a x + b
+--R +
+--R 4 4 3 2 2 2 +---+ +-+
+--R (- 8a x - 64a b x - 64a b )\|- a \|a
+--R Type: Expression(Integer)
+--E 950
+
+--S 951 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2
+--R 3 10 2 8 2 6 3 4 |a x + b +-+ 4 11
+--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x
+--R | 2
+--R \| x
+--R +
+--R 3 9 2 2 7 3 5 4 3
+--R - 32a b x - 160a b x - 256a b x - 128b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 11 3 9 2 2 7 3 5 4 3 +-+
+--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b
+--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2
+--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+
+--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 951
+
+)clear all
+
+--S 952 of 1379
+t0:=x/(a+b/x^2)^(1/2)
+--R
+--R
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 952
+
+--S 953 of 1379
+r0:=-1/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(3/2)+1/2*x^2*sqrt(a+b/x^2)/a
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 | 2
+--R \| x 2 +-+ |a x + b
+--R - b atanh(-----------) + x \|a |--------
+--R +-+ | 2
+--R \|a \| x
+--R (2) ------------------------------------------
+--R +-+
+--R 2a\|a
+--R Type: Expression(Integer)
+--E 953
+
+--S 954 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (2b\|b \|a x + b - a b x - 2b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 +-+
+--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (- 4b\|b \|a x + b + 2a b x + 4b )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 2 +---+
+--R 4a\|- a \|b \|a x + b + (- 2a x - 4a b)\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 954
+
+--S 955 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ | 2 2 2
+--R (2b\|b \|a x + b - a b x - 2b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R +--------+ | 2
+--R +-+ | 2 2 2 \| x
+--R (2b\|b \|a x + b - a b x - 2b )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 +-+ |a x + b +-+ 3 +-+ | 2
+--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 +-+ +-+ 4 2 +-+ |a x + b
+--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 +-+
+--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a
+--R Type: Expression(Integer)
+--E 955
+
+--S 956 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8
+--R (- 7a x - 56a b x - 112a b x - 64b x )\|a |-------- - 7a x
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 2 4 3 2
+--R - 56a b x - 112a b x - 64a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 |a x + b
+--R (- a x - 24a b x - 80a b x - 64a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 |a x + b
+--R (7a x + 56a b x + 112a b x + 64a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+
+--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 4 10 3 8 2 2 6 3 4 4 2 +-+ |a x + b
+--R (a x + 25a b x + 104a b x + 144a b x + 64b x )\|a |--------
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2
+--R a x + 25a b x + 104a b x + 144a b x + 64a b x
+--R /
+--R +--------+
+--R | 2
+--R 4 7 3 5 2 2 3 3 |a x + b +-+
+--R (7a x + 56a b x + 112a b x + 64a b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b
+--R (a x + 25a b x + 104a b x + 144a b x + 64b )\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +-+
+--R (- 7a x - 63a b x - 168a b x - 176a b x - 64b )\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 9 4 7 3 2 5 2 3 3 4 |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 956
+
+--S 957 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R +--------+ | 2
+--R +---+ +-+ | 2 2 2 +---+ \| x
+--R (2b\|- a \|b \|a x + b + (- a b x - 2b )\|- a )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R +-+ +-+ | 2 2 2 +-+
+--R (- 4b\|a \|b \|a x + b + (2a b x + 4b )\|a )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2
+--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b
+--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R +---+ +-+ +-+ | 2 2 2 +---+ +-+
+--R 4a\|- a \|a \|b \|a x + b + (- 2a x - 4a b)\|- a \|a
+--R Type: Expression(Integer)
+--E 957
+
+--S 958 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2 +--------+
+--R 4 2 |a x + b +-+ 2 5 3 2 | 2
+--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x)\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +-+ 2 6 4 2 2 |a x + b
+--R (4a x + 12a b x + 8b x)\|b + (a x + 8a b x + 8b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 4 2 2 |a x + b | 2
+--R (a x + 8a b x + 8b ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b +-+
+--R (- 4a x - 12a b x - 8b ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 958
+
+)clear all
+
+--S 959 of 1379
+t0:=1/((a+b/x^2)^(1/2)*x)
+--R
+--R
+--R 1
+--R (1) ------------
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 1379
+r0:=atanh(sqrt(a+b/x^2)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R (2) ------------------
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 960
+
+--S 961 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R [-------------------------------------------------------------,
+--R +-+
+--R \|a
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R 2atan(------------------------------)
+--R a x
+--R -------------------------------------]
+--R +---+
+--R \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 961
+
+--S 962 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R - atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 3 +-+ |a x + b 2 3 +-+
+--R ((3a x + 4b x)\|a |-------- - 3a x - 4a b x)\|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 |a x + b 2 4 2 2 +-+
+--R (- a x - 4a b x ) |-------- + (a x + 5a b x + 4b )\|a
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 |a x + b 2 4 2 2 +-+ +-+
+--R ((3a x + 4a b x ) |-------- + (- 3a x - 7a b x - 4b )\|a )\|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +-+ |a x + b 3 5 2 3 2
+--R (- a x - 5a b x - 4b x)\|a |-------- + a x + 5a b x + 4a b x
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2
+--R 2 4 2 |a x + b +-+
+--R (3a x + 4a b x ) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +-+ |a x + b
+--R (- a x - 5a b x - 4b x)\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +-+ |a x + b +-+
+--R (3a x + 7a b x + 4b x)\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 |a x + b
+--R (- a x - 5a b x - 4a b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 963
+
+--S 964 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |-------- +--------+
+--R | 2 +---+ | 2 +---+ +-+
+--R +---+ \| x +-+ \|- a \|a x + b - \|- a \|b
+--R - \|- a atanh(-----------) + 2\|a atan(------------------------------)
+--R +-+ a x
+--R \|a
+--R (6) ----------------------------------------------------------------------
+--R +---+ +-+
+--R \|- a \|a
+--R Type: Expression(Integer)
+--E 964
+
+--S 965 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 2
+--R | 2 |a x + b
+--R - \|a x + b + x |--------
+--R | 2
+--R \| x
+--R (7) ----------------------------
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R x |-------- \|a x + b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 965
+
+)clear all
+
+--S 966 of 1379
+t0:=1/((a+b/x^2)^(1/2)*x^3)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 1379
+r0:=-sqrt(a+b/x^2)/b
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R (2) - -----------
+--R b
+--R Type: Expression(Integer)
+--E 967
+
+--S 968 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +-+ | 2 2
+--R \|b \|a x + b - a x - b
+--R (3) --------------------------
+--R +--------+
+--R | 2 +-+
+--R b x\|a x + b - b x\|b
+--R Type: Union(Expression(Integer),...)
+--E 968
+
+--S 969 of 1379
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +-+ |a x + b | 2 |a x + b +-+ 2
+--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b
+--R | 2 | 2
+--R \| x \| x
+--R (4) --------------------------------------------------------------
+--R +--------+
+--R | 2 +-+
+--R b x\|a x + b - b x\|b
+--R Type: Expression(Integer)
+--E 969
+
+--S 970 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ 2 | 2 2 +-+
+--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (a x + 2b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R 5 3 |a x + b | 2 5 3 |a x + b +-+
+--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 970
+
+)clear all
+
+--S 971 of 1379
+t0:=1/((a+b/x^2)^(1/2)*x^5)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 2
+--R 5 |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 1379
+r0:=-1/3*(a+b/x^2)^(3/2)/b^2+a*sqrt(a+b/x^2)/b^2
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (2a x - b) |--------
+--R | 2
+--R \| x
+--R (2) ----------------------
+--R 2 2
+--R 3b x
+--R Type: Expression(Integer)
+--E 972
+
+--S 973 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3
+--R (- 6a x - 5a b x + 4b )\|b \|a x + b + 2a x + 9a b x + 3a b x - 4b
+--R --------------------------------------------------------------------------
+--R +--------+
+--R 2 5 3 3 | 2 2 5 3 3 +-+
+--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b
+--R Type: Union(Expression(Integer),...)
+--E 973
+
+--S 974 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R ((- 6a x - 5a b x + 4b )\|b + (- 2a x - 7a b x + 4b x) |-------- )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3
+--R (6a x + 5a b x - 4b x) |-------- \|b + 2a x + 9a b x + 3a b x - 4b
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 5 3 3 | 2 2 5 3 3 +-+
+--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4
+--R (- 6a x - 32a b x - 32b x) |-------- \|b - a x - 18a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 3
+--R - 48a b x - 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (6a x + 38a b x + 64a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 11 2 9 2 7 3 5 |a x + b | 2
+--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 11 2 9 2 7 3 5 |a x + b +-+
+--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 975
+
+)clear all
+
+--S 976 of 1379
+t0:=1/((a+b/x^2)^(1/2)*x^7)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 2
+--R 7 |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 1379
+r0:=2/3*a*(a+b/x^2)^(3/2)/b^3-1/5*(a+b/x^2)^(5/2)/b^3-a^2*sqrt(a+b/x^2)/b^3
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (- 8a x + 4a b x - 3b ) |--------
+--R | 2
+--R \| x
+--R (2) ------------------------------------
+--R 3 4
+--R 15b x
+--R Type: Expression(Integer)
+--E 977
+
+--S 978 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10
+--R (40a x + 140a b x + 63a b x - 4a b x + 48b )\|b \|a x + b - 8a x
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R - 100a b x - 175a b x - 55a b x - 20a b x - 48b
+--R /
+--R +--------+
+--R 2 3 9 4 7 5 5 | 2
+--R (15a b x + 180a b x + 240b x )\|a x + b
+--R +
+--R 2 3 9 4 7 5 5 +-+
+--R (- 75a b x - 300a b x - 240b x )\|b
+--R Type: Union(Expression(Integer),...)
+--E 978
+
+--S 979 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (40a x + 140a b x + 63a b x - 4a b x + 48b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (8a x + 92a b x + 83a b x - 28a b x + 48b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 40a x - 140a b x - 63a b x + 4a b x - 48b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R - 8a x - 100a b x - 175a b x - 55a b x - 20a b x - 48b
+--R /
+--R +--------+
+--R 2 3 9 4 7 5 5 | 2
+--R (15a b x + 180a b x + 240b x )\|a x + b
+--R +
+--R 2 3 9 4 7 5 5 +-+
+--R (- 75a b x - 300a b x - 240b x )\|b
+--R Type: Expression(Integer)
+--E 979
+
+--S 980 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b )\|b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 5 17 4 15 3 2 13 2 3 11 4 9 5 7
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 17 4 15 3 2 13 2 3 11 4 9
+--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x
+--R +
+--R 5 7
+--R - 512b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 980
+
+)clear all
+
+--S 981 of 1379
+t0:=1/((a+b/x^2)^(1/2)*x^9)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 2
+--R 9 |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 1379
+r0:=-a^2*(a+b/x^2)^(3/2)/b^4+3/5*a*(a+b/x^2)^(5/2)/b^4-_
+ 1/7*(a+b/x^2)^(7/2)/b^4+a^3*sqrt(a+b/x^2)/b^4
+--R
+--R
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 3 |a x + b
+--R (16a x - 8a b x + 6a b x - 5b ) |--------
+--R | 2
+--R \| x
+--R (2) ---------------------------------------------
+--R 4 6
+--R 35b x
+--R Type: Expression(Integer)
+--E 982
+
+--S 983 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - 112a x - 840a b x - 1386a b x - 429a b x + 120a b x
+--R +
+--R 5 2 6
+--R 176a b x + 320b
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4
+--R 16a x + 392a b x + 1470a b x + 1617a b x + 371a b x - 168a b x
+--R +
+--R 6 2 7
+--R - 336a b x - 320b
+--R /
+--R +--------+
+--R 3 4 13 2 5 11 6 9 7 7 | 2
+--R (35a b x + 840a b x + 2800a b x + 2240b x )\|a x + b
+--R +
+--R 3 4 13 2 5 11 6 9 7 7 +-+
+--R (- 245a b x - 1960a b x - 3920a b x - 2240b x )\|b
+--R Type: Union(Expression(Integer),...)
+--E 983
+
+--S 984 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - 112a x - 840a b x - 1386a b x - 429a b x + 120a b x
+--R +
+--R 5 2 6
+--R 176a b x + 320b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R - 16a x - 376a b x - 1094a b x - 523a b x + 152a b x
+--R +
+--R 5 3 6
+--R 16a b x + 320b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R 112a x + 840a b x + 1386a b x + 429a b x - 120a b x
+--R +
+--R 5 3 6
+--R - 176a b x - 320b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4
+--R 16a x + 392a b x + 1470a b x + 1617a b x + 371a b x - 168a b x
+--R +
+--R 6 2 7
+--R - 336a b x - 320b
+--R /
+--R +--------+
+--R 3 4 13 2 5 11 6 9 7 7 | 2
+--R (35a b x + 840a b x + 2800a b x + 2240b x )\|a x + b
+--R +
+--R 3 4 13 2 5 11 6 9 7 7 +-+
+--R (- 245a b x - 1960a b x - 3920a b x - 2240b x )\|b
+--R Type: Expression(Integer)
+--E 984
+
+--S 985 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R - 14a x - 448a b x - 4032a b x - 15360a b x - 28160a b x
+--R +
+--R 5 3 6
+--R - 24576a b x - 8192b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R - a x - 98a b x - 1568a b x - 9408a b x - 26880a b x
+--R +
+--R 2 5 4 6 2 7
+--R - 39424a b x - 28672a b x - 8192b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R 14a x + 462a b x + 4480a b x + 19392a b x + 43520a b x
+--R +
+--R 2 5 4 6 2 7
+--R 52736a b x + 32768a b x + 8192b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 15 6 13 5 2 11 4 3 9 3 4 7
+--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x
+--R +
+--R 2 5 5 6 3 7
+--R 39424a b x + 28672a b x + 8192b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 7 23 6 21 5 2 19 4 3 17 3 4 15
+--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x
+--R +
+--R 2 5 13 6 11 7 9
+--R 39424a b x + 28672a b x + 8192b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 7 23 6 21 5 2 19 4 3 17 3 4 15
+--R - 14a x - 462a b x - 4480a b x - 19392a b x - 43520a b x
+--R +
+--R 2 5 13 6 11 7 9
+--R - 52736a b x - 32768a b x - 8192b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 985
+
+)clear all
+
+--S 986 of 1379
+t0:=x^4/(a+b/x^2)^(1/2)
+--R
+--R
+--R 4
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 1379
+r0:=8/15*b^2*x*sqrt(a+b/x^2)/a^3-4/15*b*x^3*sqrt(a+b/x^2)/a^2+_
+ 1/5*x^5*sqrt(a+b/x^2)/a
+--R
+--R
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b
+--R (3a x - 4a b x + 8b x) |--------
+--R | 2
+--R \| x
+--R (2) -----------------------------------
+--R 3
+--R 15a
+--R Type: Expression(Integer)
+--E 987
+
+--S 988 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 8 2 6 | 2 2 10 8 2 6 +-+
+--R (- 15a b x - 40b x )\|a x + b + (3a x + 35a b x + 40b x )\|b
+--R --------------------------------------------------------------------------
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (15a x + 180a b x + 240b )\|b \|a x + b - 75a b x - 300a b x - 240b
+--R Type: Union(Expression(Integer),...)
+--E 988
+
+--S 989 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 3a x - 32a b x - 8a b x - 32a b x - 128b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 4 8 3 2 6
+--R - 15a b x - 40a b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 +-+
+--R (3a x + 35a b x + 40a b x )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b
+--R (15a b x + 40a b x + 8a b x + 96a b x + 128b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 5 4 4 2 3 2 +-+ | 2 5 4 4 2 2
+--R (15a x + 180a b x + 240a b )\|b \|a x + b - 75a b x - 300a b x
+--R +
+--R 3 3
+--R - 240a b
+--R Type: Expression(Integer)
+--E 989
+
+--S 990 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 4 13 3 11 2 2 9 3 7 4 5
+--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4
+--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4
+--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b x )
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R (- 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x - 512b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 990
+
+)clear all
+
+--S 991 of 1379
+t0:=x^2/(a+b/x^2)^(1/2)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 1379
+r0:=-2/3*b*x*sqrt(a+b/x^2)/a^2+1/3*x^3*sqrt(a+b/x^2)/a
+--R
+--R
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (a x - 2b x) |--------
+--R | 2
+--R \| x
+--R (2) ------------------------
+--R 2
+--R 3a
+--R Type: Expression(Integer)
+--E 992
+
+--S 993 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 4 | 2 6 4 +-+
+--R - 3b x \|a x + b + (a x + 3b x )\|b
+--R (3) ---------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b
+--R Type: Union(Expression(Integer),...)
+--E 993
+
+--S 994 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 2 5 3 2 |a x + b +-+ 2 4 | 2
+--R ((- a x - 2a b x + 8b x) |-------- \|b - 3a b x )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 +-+ 2 5 2 3 3 |a x + b
+--R (a x + 3a b x )\|b + (3a b x - 2a b x - 8b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 3 2 2 +-+ | 2 3 2 2 2
+--R (3a x + 12a b)\|b \|a x + b - 9a b x - 12a b
+--R Type: Expression(Integer)
+--E 994
+
+--S 995 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 2 7 5 2 3 |a x + b +-+ 3 8 2 6
+--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x
+--R | 2
+--R \| x
+--R +
+--R 2 4 3 2
+--R - 48a b x - 32b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 8 2 6 2 4 3 2 +-+
+--R (6a x + 38a b x + 64a b x + 32b x )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 9 2 7 2 5 3 3 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 6 2 4 2 2 3 |a x + b | 2
+--R (a x + 18a b x + 48a b x + 32b ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 3 |a x + b +-+
+--R (- 6a x - 38a b x - 64a b x - 32b ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 995
+
+)clear all
+
+--S 996 of 1379
+t0:=1/(a+b/x^2)^(1/2)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 996
+
+--S 997 of 1379
+r0:=x*sqrt(a+b/x^2)/a
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) ------------
+--R a
+--R Type: Expression(Integer)
+--E 997
+
+--S 998 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R x \|b
+--R (3) -------------------
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R Type: Union(Expression(Integer),...)
+--E 998
+
+--S 999 of 1379
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R |a x + b +-+ | 2 2 +-+ |a x + b
+--R - x |-------- \|b \|a x + b + a x \|b + b x |--------
+--R | 2 | 2
+--R \| x \| x
+--R (4) ---------------------------------------------------------
+--R +--------+
+--R +-+ | 2
+--R a\|b \|a x + b - a b
+--R Type: Expression(Integer)
+--E 999
+
+--S 1000 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ 2 | 2 2 +-+
+--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (a x + 2b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R 2 |a x + b | 2 2 |a x + b +-+
+--R (a x + 2b) |-------- \|a x + b + (- 2a x - 2b) |-------- \|b
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1000
+
+)clear all
+
+--S 1001 of 1379
+t0:=1/((a+b/x^2)^(1/2)*x^2)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1001
+
+--S 1002 of 1379
+r0:=-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/sqrt(b)
+--R
+--R
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) - -------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1002
+
+--S 1003 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R +-+ \|a x + b - \|b
+--R \|b log(------------------)
+--R x
+--R (3) ---------------------------
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 1003
+
+--S 1004 of 1379
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R | 2 +-+ +-+
+--R \|a x + b - \|b \|b
+--R log(------------------) + atanh(------------)
+--R x +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (4) ---------------------------------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1004
+
+--S 1005 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +-+ |a x + b | 2 |a x + b +-+ 2
+--R (- \|b - x |-------- )\|a x + b + x |-------- \|b + a x + b
+--R | 2 | 2
+--R \| x \| x
+--R (5) ----------------------------------------------------------------
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R 2 |a x + b +-+ | 2 4 2 |a x + b
+--R x |-------- \|b \|a x + b + (- a x - b x ) |--------
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1005
+
+)clear all
+
+--S 1006 of 1379
+t0:=1/((a+b/x^2)^(1/2)*x^4)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 2
+--R 4 |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1006
+
+--S 1007 of 1379
+r0:=1/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)-1/2*sqrt(a+b/x^2)/(b*x)
+--R
+--R
+--R +--------+
+--R +-+ | 2
+--R \|b |a x + b +-+
+--R a x atanh(------------) - |-------- \|b
+--R +--------+ | 2
+--R | 2 \| x
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) -----------------------------------------
+--R +-+
+--R 2b x\|b
+--R Type: Expression(Integer)
+--E 1007
+
+--S 1008 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 | 2 2 4 2 +-+ \|a x + b - \|b
+--R (- 2a b x \|a x + b + (a x + 2a b x )\|b )log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 2 | 2 2 2 +-+
+--R (a b x + 2b )\|a x + b + (- 2a b x - 2b )\|b
+--R /
+--R +--------+
+--R 2 2 +-+ | 2 2 4 3 2
+--R 4b x \|b \|a x + b - 2a b x - 4b x
+--R Type: Union(Expression(Integer),...)
+--E 1008
+
+--S 1009 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2 +-+
+--R 2 +-+ | 2 2 4 2 \|a x + b - \|b
+--R (- 2a x \|b \|a x + b + a x + 2a b x )log(------------------)
+--R x
+--R +
+--R +--------+ +-+
+--R 2 +-+ | 2 2 4 2 \|b
+--R (- 2a x \|b \|a x + b + a x + 2a b x )atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 +-+ |a x + b | 2
+--R ((a x + 2b)\|b + 2b x |-------- )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 |a x + b +-+ 2 2
+--R (- a x - 2b x) |-------- \|b - 2a b x - 2b
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R 2 2 | 2 4 2 2 +-+
+--R 4b x \|a x + b + (- 2a b x - 4b x )\|b
+--R Type: Expression(Integer)
+--E 1009
+
+--S 1010 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 2 4 2 2 +-+
+--R (- 5a x - 20a b x - 16b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b
+--R (- a x - 12a b x - 16b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2
+--R (5a x + 20a b x + 16b x) |-------- \|b + a x + 13a b x + 28a b x
+--R | 2
+--R \| x
+--R +
+--R 3
+--R 16b
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 8 6 2 4 |a x + b +-+ | 2
+--R (5a x + 20a b x + 16b x ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 10 2 8 2 6 3 4 |a x + b
+--R (- a x - 13a b x - 28a b x - 16b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1010
+
+)clear all
+
+--S 1011 of 1379
+t0:=1/(x*sqrt(-a+b/x^2))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +----------+
+--R | 2
+--R |- a x + b
+--R x |----------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1011
+
+--S 1012 of 1379
+r0:=-atan(sqrt(-a+b/x^2)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +----------+
+--R | 2
+--R |- a x + b
+--R |----------
+--R | 2
+--R \| x
+--R atan(-------------)
+--R +-+
+--R \|a
+--R (2) - -------------------
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 1012
+
+--S 1013 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----------+ +----------+
+--R | 2 +---+ +-+ 2 +---+ | 2
+--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a + a x\|- a x + b
+--R log(---------------------------------------------------------------------)
+--R +----------+
+--R | 2 +-+
+--R \|- a x + b \|b - b
+--R [--------------------------------------------------------------------------,
+--R +---+
+--R \|- a
+--R +----------+
+--R +-+ +-+ | 2 +-+
+--R \|a \|b - \|- a x + b \|a
+--R 2atan(----------------------------)
+--R a x
+--R -----------------------------------]
+--R +-+
+--R \|a
+--R Type: Union(List(Expression(Integer)),...)
+--E 1013
+
+--S 1014 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-+
+--R \|a
+--R *
+--R log
+--R +----------+
+--R | 2 +---+ +-+ 2 +---+
+--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a
+--R +
+--R +----------+
+--R | 2
+--R a x\|- a x + b
+--R /
+--R +----------+
+--R | 2 +-+
+--R \|- a x + b \|b - b
+--R +
+--R +----------+
+--R | 2
+--R |- a x + b
+--R |----------
+--R | 2
+--R +---+ \| x
+--R \|- a atan(-------------)
+--R +-+
+--R \|a
+--R /
+--R +---+ +-+
+--R \|- a \|a
+--R Type: Expression(Integer)
+--E 1014
+
+--S 1015 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +----------+
+--R +----------+ | 2
+--R 3 | 2 +---+ 2 4 2 |- a x + b
+--R ((- 3a x + 4b x)\|- a x + b \|- a + 3a x - 4a b x ) |----------
+--R | 2
+--R \| x
+--R +
+--R +----------+
+--R 2 4 2 2 +---+ 2 3 | 2
+--R (- 3a x + 7a b x - 4b )\|- a + (- 3a x + 4a b x)\|- a x + b
+--R *
+--R +-+
+--R \|b
+--R +
+--R +----------+
+--R 2 5 3 2 +---+ 2 4 2 | 2
+--R ((- a x + 5a b x - 4b x)\|- a + (- a x + 4a b x )\|- a x + b )
+--R *
+--R +----------+
+--R | 2
+--R |- a x + b
+--R |----------
+--R | 2
+--R \| x
+--R +
+--R +----------+
+--R 2 4 2 2 | 2 +---+ 3 5 2 3 2
+--R (a x - 5a b x + 4b )\|- a x + b \|- a - a x + 5a b x - 4a b x
+--R /
+--R +----------+
+--R 2 5 3 2 +---+ 2 4 2 | 2
+--R ((3a x - 7a b x + 4b x)\|- a + (3a x - 4a b x )\|- a x + b )
+--R *
+--R +----------+
+--R | 2
+--R |- a x + b +-+
+--R |---------- \|b
+--R | 2
+--R \| x
+--R +
+--R +----------+
+--R 2 5 3 2 | 2 +---+ 3 6 2 4
+--R (- a x + 5a b x - 4b x)\|- a x + b \|- a + a x - 5a b x
+--R +
+--R 2 2
+--R 4a b x
+--R *
+--R +----------+
+--R | 2
+--R |- a x + b
+--R |----------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1015
+
+--S 1016 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R +----------+
+--R | 2
+--R |- a x + b
+--R +----------+ |----------
+--R +-+ +-+ | 2 +-+ | 2
+--R \|a \|b - \|- a x + b \|a \| x
+--R 2atan(----------------------------) + atan(-------------)
+--R a x +-+
+--R \|a
+--R (6) ---------------------------------------------------------
+--R +-+
+--R \|a
+--R Type: Expression(Integer)
+--E 1016
+
+--S 1017 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R +----------+
+--R | 2 +----------+
+--R |- a x + b | 2
+--R x |---------- - \|- a x + b
+--R | 2
+--R \| x
+--R (7) ------------------------------
+--R +----------+
+--R +----------+ | 2
+--R | 2 |- a x + b
+--R x\|- a x + b |----------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1017
+
+)clear all
+
+--S 1018 of 1379
+t0:=1/(x^2*sqrt(2+b/x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R | 2
+--R 2 |2x + b
+--R x |-------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1018
+
+--S 1019 of 1379
+r0:=-asinh(sqrt(b)/(x*sqrt(2)))/sqrt(b)
+--R
+--R
+--R +-+
+--R \|b
+--R asinh(-----)
+--R +-+
+--R x\|2
+--R (2) - ------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1019
+
+--S 1020 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 2 +-+
+--R +-+ \|2x + b - \|b
+--R \|b log(-----------------)
+--R x
+--R (3) --------------------------
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 1020
+
+--S 1021 of 1379
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 +-+ +-+
+--R \|2x + b - \|b \|b
+--R log(-----------------) + asinh(-----)
+--R x +-+
+--R x\|2
+--R (4) -------------------------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1021
+
+--S 1022 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +-------+ +-------+
+--R | 2 +-------+ | 2
+--R +-+ +-+ |2x + b | 2 |2x + b +-+ 2 +-+
+--R (- \|2 \|b - 2x |------- )\|2x + b + 2x |------- \|b + (2x + b)\|2
+--R | 2 | 2
+--R \| 2x \| 2x
+--R ------------------------------------------------------------------------
+--R +-------+ +-------+
+--R | 2 +-------+ | 2
+--R 2 |2x + b +-+ | 2 4 2 |2x + b
+--R 2x |------- \|b \|2x + b + (- 4x - 2b x ) |-------
+--R | 2 | 2
+--R \| 2x \| 2x
+--R Type: Expression(Integer)
+--E 1022
+
+)clear all
+
+--S 1023 of 1379
+t0:=1/(x^2*sqrt(2-b/x^2))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-------+
+--R | 2
+--R 2 |2x - b
+--R x |-------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1023
+
+--S 1024 of 1379
+r0:=-asin(sqrt(b)/(x*sqrt(2)))/sqrt(b)
+--R
+--R
+--R +-+
+--R \|b
+--R asin(-----)
+--R +-+
+--R x\|2
+--R (2) - -----------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 1024
+
+--S 1025 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+
+--R | 2 +---+
+--R +---+ \|2x - b - \|- b
+--R \|- b log(-------------------)
+--R x
+--R (3) - ------------------------------
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 1025
+
+--S 1026 of 1379
+m0:=a0-r0
+--R
+--R
+--R +-------+
+--R | 2 +---+ +-+
+--R +---+ +-+ \|2x - b - \|- b \|b
+--R - \|- b \|b log(-------------------) + b asin(-----)
+--R x +-+
+--R x\|2
+--R (4) ----------------------------------------------------
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 1026
+
+--S 1027 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +-------+ +-------+
+--R | 2 +-------+ | 2
+--R |2x - b +-+ +---+ | 2 +---+ |2x - b 2 +-+
+--R (- 2x |------- - \|2 \|- b )\|2x - b + 2x\|- b |------- + (2x - b)\|2
+--R | 2 | 2
+--R \| 2x \| 2x
+--R ----------------------------------------------------------------------------
+--R +-------+ +-------+
+--R | 2 +-------+ | 2
+--R 2 +---+ |2x - b | 2 4 2 |2x - b
+--R 2x \|- b |------- \|2x - b + (- 4x + 2b x ) |-------
+--R | 2 | 2
+--R \| 2x \| 2x
+--R Type: Expression(Integer)
+--E 1027
+
+)clear all
+
+--S 1028 of 1379
+t0:=x^3/(a+b/x^2)^(3/2)
+--R
+--R
+--R 5
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1028
+
+--S 1029 of 1379
+r0:=15/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(7/2)-x^4/(a*sqrt(a+b/x^2))-_
+ 15/8*b*x^2*sqrt(a+b/x^2)/a^3+5/4*x^4*sqrt(a+b/x^2)/a^2
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R +--------+ |--------
+--R | 2 | 2
+--R 2 |a x + b \| x 2 4 2 2 +-+
+--R 15b |-------- atanh(-----------) + (2a x - 5a b x - 15b )\|a
+--R | 2 +-+
+--R \| x \|a
+--R (2) ----------------------------------------------------------------
+--R +--------+
+--R | 2
+--R 3 +-+ |a x + b
+--R 8a \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1029
+
+--S 1030 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 4 3 2 4 +-+ | 2 3 2 6
+--R (75a b x + 300a b x + 240b )\|b \|a x + b - 15a b x
+--R +
+--R 2 3 4 4 2 5
+--R - 195a b x - 420a b x - 240b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2
+--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+ +-+
+--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|a \|b
+--R /
+--R +--------+
+--R 5 4 4 2 3 2 +-+ +-+ | 2
+--R (40a x + 160a b x + 128a b )\|a \|b \|a x + b
+--R +
+--R 6 6 5 4 4 2 2 3 3 +-+
+--R (- 8a x - 104a b x - 224a b x - 128a b )\|a
+--R ,
+--R
+--R +--------+
+--R 2 2 4 3 2 4 +-+ | 2 3 2 6
+--R (150a b x + 600a b x + 480b )\|b \|a x + b - 30a b x
+--R +
+--R 2 3 4 4 2 5
+--R - 390a b x - 840a b x - 480b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R 4 9 3 7 2 2 5 3 3 4 +---+ | 2
+--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|- a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+
+--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|- a \|b
+--R /
+--R +--------+
+--R 5 4 4 2 3 2 +---+ +-+ | 2
+--R (40a x + 160a b x + 128a b )\|- a \|b \|a x + b
+--R +
+--R 6 6 5 4 4 2 2 3 3 +---+
+--R (- 8a x - 104a b x - 224a b x - 128a b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1030
+
+--S 1031 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 2 2 4 3 2 4 |a x + b +-+ | 2
+--R (75a b x + 300a b x + 240b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 2 6 2 3 4 4 2 5 |a x + b
+--R (- 15a b x - 195a b x - 420a b x - 240b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 2 4 3 2 4 |a x + b +-+ | 2
+--R (- 75a b x - 300a b x - 240b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 2 6 2 3 4 4 2 5 |a x + b
+--R (15a b x + 195a b x + 420a b x + 240b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+ +-+
+--R (- 10a x - 15a b x + 143a b x + 380a b x + 240b )\|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b
+--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+
+--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (2a x + 21a b x - 24a b x - 303a b x - 500a b x - 240b )\|a
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 5 4 4 2 3 2 +-+ |a x + b +-+ | 2
+--R (40a x + 160a b x + 128a b )\|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 6 6 5 4 4 2 2 3 3 +-+ |a x + b
+--R (- 8a x - 104a b x - 224a b x - 128a b )\|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1031
+
+--S 1032 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 6 18 5 16 4 2 14 3 3 12
+--R 13a x + 364a b x + 2912a b x + 9984a b x
+--R +
+--R 2 4 10 5 8 6 6
+--R 16640a b x + 13312a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 7 18 6 16 5 2 14 4 3 12 3 4 10
+--R - 13a x - 364a b x - 2912a b x - 9984a b x - 16640a b x
+--R +
+--R 2 5 8 6 6
+--R - 13312a b x - 4096a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 19 6 17 5 2 15 4 3 13 3 4 11
+--R - a x - 84a b x - 1120a b x - 5376a b x - 11520a b x
+--R +
+--R 2 5 9 6 7
+--R - 11264a b x - 4096a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 7 19 6 17 5 2 15 4 3 13 3 4 11
+--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x
+--R +
+--R 2 5 9 6 7 7 5
+--R 22784a b x + 15360a b x + 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 19 6 17 5 2 15 4 3 13 3 4 11
+--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x
+--R +
+--R 2 5 9 6 7
+--R 13312a b x + 4096a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 7 19 6 17 5 2 15 4 3 13
+--R - 13a x - 377a b x - 3276a b x - 12896a b x
+--R +
+--R 3 4 11 2 5 9 6 7 7 5
+--R - 26624a b x - 29952a b x - 17408a b x - 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 20 6 18 5 2 16 4 3 14 3 4 12
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 10 6 8 7 6
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 8 20 7 18 6 2 16 5 3 14 4 4 12
+--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x
+--R +
+--R 3 5 10 2 6 8 7 6
+--R 22784a b x + 15360a b x + 4096a b x
+--R /
+--R 8 15 7 13 6 2 11 5 3 9 4 4 7
+--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x
+--R +
+--R 3 5 5 2 6 3 7
+--R 29952a b x + 17408a b x + 4096a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R - a x - 86a b x - 1289a b x - 7700a b x - 23392a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R - 39680a b x - 38144a b x - 19456a b x - 4096b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R 56576a b x + 47360a b x + 21504a b x + 4096b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 9 17 8 15 7 2 13 6 3 11 5 4 9
+--R - a x - 86a b x - 1289a b x - 7700a b x - 23392a b x
+--R +
+--R 4 5 7 3 6 5 2 7 3 8
+--R - 39680a b x - 38144a b x - 19456a b x - 4096a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1032
+
+--S 1033 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2 +--------+
+--R 2 2 4 3 2 4 +---+ |a x + b +-+ | 2
+--R (- 75a b x - 300a b x - 240b )\|- a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 2 6 2 3 4 4 2 5 +---+ |a x + b
+--R (15a b x + 195a b x + 420a b x + 240b )\|- a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 2 4 3 2 4 +-+ |a x + b +-+ | 2
+--R (150a b x + 600a b x + 480b )\|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 2 6 2 3 4 4 2 5 +-+ |a x + b
+--R (- 30a b x - 390a b x - 840a b x - 480b )\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +---+ +-+ +-+
+--R (- 10a x - 15a b x + 143a b x + 380a b x + 240b )\|- a \|a \|b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+
+--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|- a \|a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+
+--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|- a \|a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +---+ +-+
+--R (2a x + 21a b x - 24a b x - 303a b x - 500a b x - 240b )\|- a \|a
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 5 4 4 2 3 2 +---+ +-+ |a x + b +-+ | 2
+--R (40a x + 160a b x + 128a b )\|- a \|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 6 6 5 4 4 2 2 3 3 +---+ +-+ |a x + b
+--R (- 8a x - 104a b x - 224a b x - 128a b )\|- a \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1033
+
+--S 1034 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 4 14 3 12 2 2 10 3 8 4 6
+--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5
+--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5
+--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b x )
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2
+--R a x + 51a b x + 450a b x + 1520a b x + 2400a b x + 1792a b x
+--R +
+--R 6
+--R 512b
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - 10a x - 180a b x - 1002a b x - 2528a b x - 3232a b x
+--R +
+--R 5 2 6
+--R - 2048a b x - 512b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1034
+
+)clear all
+
+--S 1035 of 1379
+t0:=x/(a+b/x^2)^(3/2)
+--R
+--R
+--R 3
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1035
+
+--S 1036 of 1379
+r0:=-3/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(5/2)-x^2/(a*sqrt(a+b/x^2))+_
+ 3/2*x^2*sqrt(a+b/x^2)/a^2
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R +--------+ |--------
+--R | 2 | 2
+--R |a x + b \| x 2 +-+
+--R - 3b |-------- atanh(-----------) + (a x + 3b)\|a
+--R | 2 +-+
+--R \| x \|a
+--R (2) ---------------------------------------------------
+--R +--------+
+--R | 2
+--R 2 +-+ |a x + b
+--R 2a \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1036
+
+--S 1037 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 +-+ | 2 2 4 2 2 3
+--R ((9a b x + 12b )\|b \|a x + b - 3a b x - 15a b x - 12b )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
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+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (- a x - 7a b x - 12b x)\|a \|a x + b
+--R +
+--R 2 5 3 2 +-+ +-+
+--R (3a x + 13a b x + 12b x)\|a \|b
+--R /
+--R +--------+
+--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+
+--R (6a x + 8a b)\|a \|b \|a x + b + (- 2a x - 10a b x - 8a b )\|a
+--R ,
+--R
+--R +--------+
+--R 2 2 +-+ | 2 2 4 2 2 3
+--R ((- 18a b x - 24b )\|b \|a x + b + 6a b x + 30a b x + 24b )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R 2 5 3 2 +---+ | 2
+--R (- a x - 7a b x - 12b x)\|- a \|a x + b
+--R +
+--R 2 5 3 2 +---+ +-+
+--R (3a x + 13a b x + 12b x)\|- a \|b
+--R /
+--R +--------+
+--R 3 2 2 +---+ +-+ | 2 4 4 3 2 2 2 +---+
+--R (6a x + 8a b)\|- a \|b \|a x + b + (- 2a x - 10a b x - 8a b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1037
+
+--S 1038 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 2 2 |a x + b +-+ | 2
+--R (9a b x + 12b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 3 |a x + b
+--R (- 3a b x - 15a b x - 12b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 2 |a x + b +-+ | 2
+--R (9a b x + 12b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 3 |a x + b
+--R (- 3a b x - 15a b x - 12b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 +-+ +-+
+--R (- 3a x - 13a b x - 12b )\|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +-+ |a x + b
+--R (- a x - 7a b x - 12b x)\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +-+ |a x + b +-+
+--R (3a x + 13a b x + 12b x)\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (a x + 8a b x + 19a b x + 12b )\|a
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 2 2 +-+ |a x + b +-+ | 2
+--R (6a x + 8a b)\|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 4 3 2 2 2 +-+ |a x + b
+--R (- 2a x - 10a b x - 8a b )\|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1038
+
+--S 1039 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 4 12 3 10 2 2 8 3 6 4 4 +-+
+--R (- 9a x - 120a b x - 432a b x - 576a b x - 256b x )\|a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 5 12 4 10 3 2 8 2 3 6 4 4
+--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b
+--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +-+
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )\|a
+--R *
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+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b
+--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 5 13 4 11 3 2 9 2 3 7 4 5
+--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x
+--R +
+--R 5 3
+--R 256b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +-+
+--R (a x + 41a b x + 280a b x + 688a b x + 704a b x + 256b x )\|a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 6 14 5 12 4 2 10 3 3 8 2 4 6 5 4
+--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x
+--R /
+--R 6 11 5 9 4 2 7 3 3 5 2 4 3
+--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x
+--R +
+--R 5
+--R 256a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R a x + 42a b x + 321a b x + 968a b x + 1392a b x
+--R +
+--R 5 2 6
+--R 960a b x + 256b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x
+--R +
+--R 5 2 6
+--R - 1088a b x - 256b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 13 6 11 5 2 9 4 3 7 3 4 5 2 5 3
+--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x - 960a b x
+--R +
+--R 6
+--R - 256a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1039
+
+--S 1040 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2 +--------+
+--R 2 2 +---+ |a x + b +-+ | 2
+--R (9a b x + 12b )\|- a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 3 +---+ |a x + b
+--R (- 3a b x - 15a b x - 12b )\|- a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 2 +-+ |a x + b +-+ | 2
+--R (- 18a b x - 24b )\|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 3 +-+ |a x + b
+--R (6a b x + 30a b x + 24b )\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R 2 4 2 2 +---+ +-+ +-+
+--R (- 3a x - 13a b x - 12b )\|- a \|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +---+ +-+ |a x + b
+--R (- a x - 7a b x - 12b x)\|- a \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +---+ +-+ |a x + b +-+
+--R (3a x + 13a b x + 12b x)\|- a \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 4 2 2 3 +---+ +-+
+--R (a x + 8a b x + 19a b x + 12b )\|- a \|a
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 2 2 +---+ +-+ |a x + b +-+ | 2
+--R (6a x + 8a b)\|- a \|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 4 3 2 2 2 +---+ +-+ |a x + b
+--R (- 2a x - 10a b x - 8a b )\|- a \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1040
+
+--S 1041 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2
+--R 2 8 6 2 4 |a x + b +-+ 3 9 2 7
+--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x
+--R | 2
+--R \| x
+--R +
+--R 2 5 3 3
+--R - 48a b x - 32b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 9 2 7 2 5 3 3 +-+
+--R (6a x + 38a b x + 64a b x + 32b x )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 10 2 8 2 6 3 4 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2
+--R (a x + 19a b x + 66a b x + 80a b x + 32b ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+
+--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1041
+
+)clear all
+
+--S 1042 of 1379
+t0:=1/((a+b/x^2)^(3/2)*x)
+--R
+--R
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1042
+
+--S 1043 of 1379
+r0:=atanh(sqrt(a+b/x^2)/sqrt(a))/a^(3/2)+(-1)/(a*sqrt(a+b/x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R +--------+ |--------
+--R | 2 | 2
+--R |a x + b \| x +-+
+--R |-------- atanh(-----------) - \|a
+--R | 2 +-+
+--R \| x \|a
+--R (2) ------------------------------------
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R a\|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1043
+
+--S 1044 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2
+--R (\|b \|a x + b - a x - b)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R x\|a \|a x + b - x\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 +-+
+--R a\|a \|b \|a x + b + (- a x - a b)\|a
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 2 +---+ +-+
+--R +-+ | 2 2 \|- a \|a x + b - \|- a \|b
+--R (2\|b \|a x + b - 2a x - 2b)atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R x\|- a \|a x + b - x\|- a \|b
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 2 +---+
+--R a\|- a \|b \|a x + b + (- a x - a b)\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1044
+
+--S 1045 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R |a x + b +-+ | 2 2 |a x + b
+--R ( |-------- \|b \|a x + b + (- a x - b) |-------- )
+--R | 2 | 2
+--R \| x \| x
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 2
+--R |a x + b
+--R +--------+ +--------+ |--------
+--R | 2 +--------+ | 2 | 2
+--R |a x + b +-+ | 2 2 |a x + b \| x
+--R (- |-------- \|b \|a x + b + (a x + b) |-------- )atanh(-----------)
+--R | 2 | 2 +-+
+--R \| x \| x \|a
+--R +
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +-+ +-+ +-+ |a x + b | 2 +-+ |a x + b +-+
+--R (\|a \|b + x\|a |-------- )\|a x + b - x\|a |-------- \|b
+--R | 2 | 2
+--R \| x \| x
+--R +
+--R 2 +-+
+--R (- a x - b)\|a
+--R /
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +-+ |a x + b +-+ | 2 2 2 +-+ |a x + b
+--R a\|a |-------- \|b \|a x + b + (- a x - a b)\|a |--------
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1045
+
+--S 1046 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 +-+ |a x + b 3 6 2 4
+--R (5a x + 20a b x + 16b x )\|a |-------- - 5a x - 20a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2
+--R - 16a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 |a x + b
+--R (- a x - 12a b x - 16a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (a x + 13a b x + 28a b x + 16b x)\|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 |a x + b
+--R (5a x + 20a b x + 16a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (- 5a x - 25a b x - 36a b x - 16b x)\|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 3 6
+--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x + 13a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 4 3 2
+--R 28a b x + 16a b x
+--R /
+--R +--------+
+--R | 2
+--R 4 7 3 5 2 2 3 3 |a x + b +-+
+--R (5a x + 25a b x + 36a b x + 16a b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b
+--R (- a x - 14a b x - 41a b x - 44a b x - 16b )\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +-+
+--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 9 4 7 3 2 5 2 3 3 4 |a x + b
+--R (- a x - 14a b x - 41a b x - 44a b x - 16a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1046
+
+--S 1047 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +---+ |a x + b +-+ | 2 2 +---+ |a x + b
+--R (- \|- a |-------- \|b \|a x + b + (a x + b)\|- a |-------- )
+--R | 2 | 2
+--R \| x \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +-+ |a x + b +-+ | 2 2 +-+ |a x + b
+--R (2\|a |-------- \|b \|a x + b + (- 2a x - 2b)\|a |-------- )
+--R | 2 | 2
+--R \| x \| x
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R | 2 +--------+
+--R +---+ +-+ +-+ +---+ +-+ |a x + b | 2
+--R (\|- a \|a \|b + x\|- a \|a |-------- )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R +---+ +-+ |a x + b +-+ 2 +---+ +-+
+--R - x\|- a \|a |-------- \|b + (- a x - b)\|- a \|a
+--R | 2
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +---+ +-+ |a x + b +-+ | 2 2 2 +---+ +-+ |a x + b
+--R a\|- a \|a |-------- \|b \|a x + b + (- a x - a b)\|- a \|a |--------
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1047
+
+--S 1048 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2 +--------+
+--R 2 |a x + b +-+ 3 | 2 3 +-+
+--R (- 2x |-------- \|b - a x - 2b x)\|a x + b + (2a x + 2b x)\|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 2 |a x + b
+--R (a x + 2b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 4 2 2 |a x + b | 2
+--R (a x + 3a b x + 2b ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b +-+
+--R (- 2a x - 4a b x - 2b ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1048
+
+)clear all
+
+--S 1049 of 1379
+t0:=1/((a+b/x^2)^(3/2)*x^3)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (a x + b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1049
+
+--S 1050 of 1379
+r0:=1/(b*sqrt(a+b/x^2))
+--R
+--R
+--R 1
+--R (2) ------------
+--R +--------+
+--R | 2
+--R |a x + b
+--R b |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1050
+
+--S 1051 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R - x\|a x + b + x\|b
+--R (3) ------------------------------
+--R +--------+
+--R +-+ | 2 2 2
+--R b\|b \|a x + b - a b x - b
+--R Type: Union(Expression(Integer),...)
+--E 1051
+
+--S 1052 of 1379
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R +-+ |a x + b | 2 |a x + b +-+ 2
+--R (- \|b - x |-------- )\|a x + b + x |-------- \|b + a x + b
+--R | 2 | 2
+--R \| x \| x
+--R (4) ----------------------------------------------------------------
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R |a x + b +-+ | 2 2 2 |a x + b
+--R b |-------- \|b \|a x + b + (- a b x - b ) |--------
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1052
+
+--S 1053 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ 2 | 2 2 +-+
+--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (a x + 2b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 5 3 2 |a x + b | 2
+--R (a x + 3a b x + 2b x) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+
+--R (- 2a x - 4a b x - 2b x) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1053
+
+)clear all
+
+--S 1054 of 1379
+t0:=1/((a+b/x^2)^(3/2)*x^5)
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R | 2
+--R 5 3 |a x + b
+--R (a x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1054
+
+--S 1055 of 1379
+r0:=-a/(b^2*sqrt(a+b/x^2))-sqrt(a+b/x^2)/b^2
+--R
+--R
+--R 2
+--R - 2a x - b
+--R (2) ---------------
+--R +--------+
+--R | 2
+--R 2 2 |a x + b
+--R b x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1055
+
+--S 1056 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 +-+ | 2 2 4 2 2
+--R (4a x + 2b)\|b \|a x + b - 2a x - 5a b x - 2b
+--R (3) ---------------------------------------------------
+--R +--------+
+--R 2 3 3 | 2 2 3 3 +-+
+--R (a b x + 2b x)\|a x + b + (- 2a b x - 2b x)\|b
+--R Type: Union(Expression(Integer),...)
+--E 1056
+
+--S 1057 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 3 |a x + b +-+ 2 4 2 2 | 2
+--R ((4a x + 2b x) |-------- \|b + 2a x + 5a b x + 2b )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R (- 4a x - 6a b x - 2b )\|b + (- 2a x - 5a b x - 2b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R 2 4 3 2 |a x + b | 2 2 4 3 2 |a x + b +-+
+--R (a b x + 2b x ) |-------- \|a x + b + (- 2a b x - 2b x ) |-------- \|b
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1057
+
+--S 1058 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2 +--------+
+--R 3 |a x + b +-+ 2 4 2 2 | 2
+--R ((- 4a x - 8b x) |-------- \|b - a x - 8a b x - 8b )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 +-+ 2 5 3 2 |a x + b
+--R (4a x + 12a b x + 8b )\|b + (a x + 8a b x + 8b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 9 2 7 2 5 3 3 |a x + b | 2
+--R (a x + 9a b x + 16a b x + 8b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 9 2 7 2 5 3 3 |a x + b +-+
+--R (- 4a x - 16a b x - 20a b x - 8b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1058
+
+)clear all
+
+--S 1059 of 1379
+t0:=1/((a+b/x^2)^(3/2)*x^7)
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R | 2
+--R 7 5 |a x + b
+--R (a x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1059
+
+--S 1060 of 1379
+r0:=-1/3*(a+b/x^2)^(3/2)/b^3+a^2/(b^3*sqrt(a+b/x^2))+2*a*sqrt(a+b/x^2)/b^3
+--R
+--R
+--R 2 4 2 2
+--R 8a x + 4a b x - b
+--R (2) --------------------
+--R +--------+
+--R | 2
+--R 3 4 |a x + b
+--R 3b x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1060
+
+--S 1061 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6
+--R (- 32a x - 80a b x - 28a b x + 8b )\|b \|a x + b + 8a x + 68a b x
+--R +
+--R 2 2 4 3 2 4
+--R 95a b x + 24a b x - 8b
+--R /
+--R +--------+
+--R 2 3 7 4 5 5 3 | 2
+--R (3a b x + 24a b x + 24b x )\|a x + b
+--R +
+--R 2 3 7 4 5 5 3 +-+
+--R (- 12a b x - 36a b x - 24b x )\|b
+--R Type: Union(Expression(Integer),...)
+--E 1061
+
+--S 1062 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8
+--R (- 32a x - 80a b x - 28a b x + 8b x) |-------- \|b - 8a x
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 2 4 3 2 4
+--R - 68a b x - 95a b x - 24a b x + 8b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (32a x + 112a b x + 108a b x + 20a b x - 8b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (8a x + 68a b x + 95a b x + 24a b x - 8b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 3 8 4 6 5 4 |a x + b | 2
+--R (3a b x + 24a b x + 24b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 3 8 4 6 5 4 |a x + b +-+
+--R (- 12a b x - 36a b x - 24b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1062
+
+--S 1063 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8
+--R (- 8a x - 80a b x - 192a b x - 128b x) |-------- \|b - a x
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 2 4 3 2 4
+--R - 32a b x - 160a b x - 256a b x - 128b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (8a x + 88a b x + 272a b x + 320a b x + 128b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (a x + 32a b x + 160a b x + 256a b x + 128b x) |--------
+--R | 2
+--R \| x
+--R /
+--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5
+--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b x )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5
+--R (- 8a x - 96a b x - 360a b x - 592a b x - 448a b x - 128b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1063
+
+)clear all
+
+--S 1064 of 1379
+t0:=1/((a+b/x^2)^(3/2)*x^9)
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R | 2
+--R 9 7 |a x + b
+--R (a x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1064
+
+--S 1065 of 1379
+r0:=a*(a+b/x^2)^(3/2)/b^4-1/5*(a+b/x^2)^(5/2)/b^4-a^3/(b^4*_
+ sqrt(a+b/x^2))-3*a^2*sqrt(a+b/x^2)/b^4
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R - 16a x - 8a b x + 2a b x - b
+--R (2) ---------------------------------
+--R +--------+
+--R | 2
+--R 4 6 |a x + b
+--R 5b x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1065
+
+--S 1066 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (96a x + 560a b x + 756a b x + 198a b x - 32a b x + 32b )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2
+--R - 16a x - 296a b x - 910a b x - 861a b x - 178a b x + 16a b x
+--R +
+--R 6
+--R - 32b
+--R /
+--R +--------+
+--R 3 4 11 2 5 9 6 7 7 5 | 2
+--R (5a b x + 90a b x + 240a b x + 160b x )\|a x + b
+--R +
+--R 3 4 11 2 5 9 6 7 7 5 +-+
+--R (- 30a b x - 190a b x - 320a b x - 160b x )\|b
+--R Type: Union(Expression(Integer),...)
+--E 1066
+
+--S 1067 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (96a x + 560a b x + 756a b x + 198a b x - 32a b x + 32b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2
+--R 16a x + 296a b x + 910a b x + 861a b x + 178a b x - 16a b x
+--R +
+--R 6
+--R 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 6 +-+
+--R (- 96a x - 656a b x - 1316a b x - 954a b x - 166a b x - 32b )\|b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3
+--R - 16a x - 296a b x - 910a b x - 861a b x - 178a b x + 16a b x
+--R +
+--R 6
+--R - 32b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 4 12 2 5 10 6 8 7 6 |a x + b | 2
+--R (5a b x + 90a b x + 240a b x + 160b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 4 12 2 5 10 6 8 7 6 |a x + b +-+
+--R (- 30a b x - 190a b x - 320a b x - 160b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1067
+
+--S 1068 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 5 11 4 9 3 2 7 2 3 5 4 3
+--R - 12a x - 280a b x - 1792a b x - 4608a b x - 5120a b x
+--R +
+--R 5
+--R - 2048b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - a x - 72a b x - 840a b x - 3584a b x - 6912a b x
+--R +
+--R 5 2 6
+--R - 6144a b x - 2048b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R 12a x + 292a b x + 2072a b x + 6400a b x + 9728a b x
+--R +
+--R 5 2 6
+--R 7168a b x + 2048b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3
+--R a x + 72a b x + 840a b x + 3584a b x + 6912a b x + 6144a b x
+--R +
+--R 6
+--R 2048b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 7 21 6 19 5 2 17 4 3 15 3 4 13
+--R a x + 73a b x + 912a b x + 4424a b x + 10496a b x
+--R +
+--R 2 5 11 6 9 7 7
+--R 13056a b x + 8192a b x + 2048b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 7 21 6 19 5 2 17 4 3 15 3 4 13
+--R - 12a x - 304a b x - 2364a b x - 8472a b x - 16128a b x
+--R +
+--R 2 5 11 6 9 7 7
+--R - 16896a b x - 9216a b x - 2048b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1068
+
+)clear all
+
+--S 1069 of 1379
+t0:=x^2/(a+b/x^2)^(3/2)
+--R
+--R
+--R 4
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1069
+
+--S 1070 of 1379
+r0:=-x^3/(a*sqrt(a+b/x^2))-8/3*b*x*sqrt(a+b/x^2)/a^3+4/3*x^3*sqrt(a+b/x^2)/a^2
+--R
+--R
+--R 2 4 2 2
+--R a x - 4a b x - 8b
+--R (2) --------------------
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R 3a x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1070
+
+--S 1071 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 6 | 2 8 6 +-+
+--R - 4b x \|a x + b + (a x + 4b x )\|b
+--R (3) ---------------------------------------------------------------------
+--R +--------+
+--R 2 4 2 2 +-+ | 2 2 4 2 2 3
+--R (3a x + 24a b x + 24b )\|b \|a x + b - 12a b x - 36a b x - 24b
+--R Type: Union(Expression(Integer),...)
+--E 1071
+
+--S 1072 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- a x - 4a b x + 32a b x + 96a b x + 64b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 |a x + b
+--R - 4a b x |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 |a x + b +-+ 4 8 3 2 6 2 3 4
+--R (a x + 4a b x ) |-------- \|b + 4a b x - 4a b x - 72a b x
+--R | 2
+--R \| x
+--R +
+--R 4 2 5
+--R - 128a b x - 64b
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 5 5 4 3 3 2 |a x + b +-+ | 2
+--R (3a x + 24a b x + 24a b x) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 5 4 2 3 3 3 |a x + b
+--R (- 12a b x - 36a b x - 24a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1072
+
+--S 1073 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 3 11 2 9 2 7 3 5 |a x + b +-+ 4 12
+--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x
+--R | 2
+--R \| x
+--R +
+--R 3 10 2 2 8 3 6 4 4
+--R - 32a b x - 160a b x - 256a b x - 128b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 12 3 10 2 2 8 3 6 4 4 +-+
+--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 13 3 11 2 2 9 3 7 4 5 |a x + b
+--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R (- 8a x - 96a b x - 360a b x - 592a b x - 448a b x - 128b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1073
+
+)clear all
+
+--S 1074 of 1379
+t0:=1/(a+b/x^2)^(3/2)
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1074
+
+--S 1075 of 1379
+r0:=-x/(a*sqrt(a+b/x^2))+2*x*sqrt(a+b/x^2)/a^2
+--R
+--R
+--R 2
+--R a x + 2b
+--R (2) --------------
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R a x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1075
+
+--S 1076 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 +-+
+--R x \|b
+--R (3) ------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2
+--R (a x + 2b)\|b \|a x + b - 2a b x - 2b
+--R Type: Union(Expression(Integer),...)
+--E 1076
+
+--S 1077 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +--------+ | 2
+--R 2 4 2 2 +-+ | 2 2 5 |a x + b +-+ 2 4
+--R (- a x - 4a b x - 4b )\|b \|a x + b + a x |-------- \|b + 2a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 3
+--R 6a b x + 4b
+--R /
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R 3 3 2 |a x + b +-+ | 2 3 3 2 2 |a x + b
+--R (a x + 2a b x) |-------- \|b \|a x + b + (- 2a b x - 2a b x) |--------
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1077
+
+--S 1078 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2 +--------+
+--R 5 3 |a x + b +-+ 2 6 4 2 2 | 2
+--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 +-+ 2 7 5 2 3 |a x + b
+--R (4a x + 12a b x + 8b x )\|b + (a x + 8a b x + 8b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 6 2 4 2 2 3 |a x + b | 2
+--R (a x + 9a b x + 16a b x + 8b ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 3 |a x + b +-+
+--R (- 4a x - 16a b x - 20a b x - 8b ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1078
+
+)clear all
+
+--S 1079 of 1379
+t0:=1/((a+b/x^2)^(3/2)*x^2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R 2 |a x + b
+--R (a x + b) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1079
+
+--S 1080 of 1379
+r0:=(-1)/(a*x*sqrt(a+b/x^2))
+--R
+--R
+--R 1
+--R (2) - --------------
+--R +--------+
+--R | 2
+--R |a x + b
+--R a x |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1080
+
+--S 1081 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+
+--R x \|b
+--R (3) ------------------------------
+--R +--------+
+--R +-+ | 2 2 2
+--R b\|b \|a x + b - a b x - b
+--R Type: Union(Expression(Integer),...)
+--E 1081
+
+--S 1082 of 1379
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R +--------+ | 2
+--R +-+ | 2 3 |a x + b +-+ 2 2
+--R b\|b \|a x + b + a x |-------- \|b - a b x - b
+--R | 2
+--R \| x
+--R (4) ---------------------------------------------------------------
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R |a x + b +-+ | 2 2 3 2 |a x + b
+--R a b x |-------- \|b \|a x + b + (- a b x - a b x) |--------
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1082
+
+--S 1083 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ 2 | 2 2 +-+
+--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (a x + 2b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 4 2 2 |a x + b | 2
+--R (a x + 3a b x + 2b ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b +-+
+--R (- 2a x - 4a b x - 2b ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1083
+
+)clear all
+
+--S 1084 of 1379
+t0:=1/((a+b/x^2)^(3/2)*x^4)
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R | 2
+--R 4 2 |a x + b
+--R (a x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1084
+
+--S 1085 of 1379
+r0:=-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)+1/(b*x*sqrt(a+b/x^2))
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R |a x + b \|b +-+
+--R - x |-------- atanh(------------) + \|b
+--R | 2 +--------+
+--R \| x | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) ----------------------------------------
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R b x |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1085
+
+--S 1086 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 2 +-+
+--R | 2 2 +-+ \|a x + b - \|b 2 +-+
+--R (b\|a x + b + (- a x - b)\|b )log(------------------) - a x \|b
+--R x
+--R (3) -------------------------------------------------------------------
+--R +--------+
+--R 2 +-+ | 2 2 2 3
+--R b \|b \|a x + b - a b x - b
+--R Type: Union(Expression(Integer),...)
+--E 1086
+
+--S 1087 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R |a x + b +-+ | 2 3 |a x + b
+--R (x |-------- \|b \|a x + b + (- a x - b x) |-------- )
+--R | 2 | 2
+--R \| x \| x
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R |a x + b +-+ | 2 3 |a x + b
+--R (x |-------- \|b \|a x + b + (- a x - b x) |-------- )
+--R | 2 | 2
+--R \| x \| x
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R +--------+ | 2
+--R | 2 2 +-+ 3 |a x + b
+--R - b\|a x + b + (a x + b)\|b - a x |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 2 +--------+ | 2
+--R 2 |a x + b | 2 3 2 |a x + b +-+
+--R b x |-------- \|a x + b + (- a b x - b x) |-------- \|b
+--R | 2 | 2
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1087
+
+--S 1088 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ 2 | 2 2 +-+
+--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 |a x + b
+--R (a x + 2b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 6 4 2 2 |a x + b | 2
+--R (a x + 3a b x + 2b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 |a x + b +-+
+--R (- 2a x - 4a b x - 2b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1088
+
+)clear all
+
+--S 1089 of 1379
+t0:=1/((a+b/x^2)^(3/2)*x^6)
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R | 2
+--R 6 4 |a x + b
+--R (a x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1089
+
+--S 1090 of 1379
+r0:=3/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(5/2)+_
+ 1/(b*x^3*sqrt(a+b/x^2))-3/2*sqrt(a+b/x^2)/(b^2*x)
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R 3 |a x + b \|b 2 +-+
+--R 3a x |-------- atanh(------------) + (- 3a x - b)\|b
+--R | 2 +--------+
+--R \| x | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) -------------------------------------------------------
+--R +--------+
+--R | 2
+--R 2 3 |a x + b +-+
+--R 2b x |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1090
+
+--S 1091 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+
+--R ((- 9a b x - 12a b x )\|a x + b + (3a x + 15a b x + 12a b x )\|b )
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 2 3 | 2
+--R (- 3a b x + 5a b x + 4b )\|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (2a x + a b x - 7a b x - 4b )\|b
+--R /
+--R +--------+
+--R 3 4 4 2 +-+ | 2 2 3 6 4 4 5 2
+--R (6a b x + 8b x )\|b \|a x + b - 2a b x - 10a b x - 8b x
+--R Type: Union(Expression(Integer),...)
+--E 1091
+
+--S 1092 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 2 5 3 |a x + b +-+ | 2
+--R (- 9a x - 12a b x ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 |a x + b
+--R (3a x + 15a b x + 12a b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 5 3 |a x + b +-+ | 2
+--R (- 9a x - 12a b x ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 |a x + b
+--R (3a x + 15a b x + 12a b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 2 4 2 2 3
+--R ((- 3a x + 5a b x + 4b x) |-------- \|b + 9a b x + 15a b x + 4b )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 3a x - 16a b x - 17a b x - 4b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (2a x + a b x - 7a b x - 4b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 5 4 3 |a x + b | 2
+--R (6a b x + 8b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 2 7 3 5 4 3 |a x + b +-+
+--R (- 2a b x - 10a b x - 8b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1092
+
+--S 1093 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 6 2 4 2 2 3 +-+
+--R (- 7a x - 56a b x - 112a b x - 64b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (- a x - 24a b x - 80a b x - 64b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6
+--R (7a x + 56a b x + 112a b x + 64b x) |-------- \|b + a x + 25a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 4 3 2 4
+--R 104a b x + 144a b x + 64b
+--R /
+--R +--------+
+--R | 2
+--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +-+
+--R (7a x + 63a b x + 168a b x + 176a b x + 64b x ) |-------- \|b
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4
+--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1093
+
+)clear all
+
+--S 1094 of 1379
+t0:=1/((a+b/x^2)^(3/2)*x^8)
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R | 2
+--R 8 6 |a x + b
+--R (a x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1094
+
+--S 1095 of 1379
+r0:=-15/8*a^2*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(7/2)+_
+ 1/(b*x^5*sqrt(a+b/x^2))-5/4*sqrt(a+b/x^2)/(b^2*x^3)+_
+ 15/8*a*sqrt(a+b/x^2)/(b^3*x)
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R 2 5 |a x + b \|b 2 4 2 2 +-+
+--R - 15a x |-------- atanh(------------) + (15a x + 5a b x - 2b )\|b
+--R | 2 +--------+
+--R \| x | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) ---------------------------------------------------------------------
+--R +--------+
+--R | 2
+--R 3 5 |a x + b +-+
+--R 8b x |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1095
+
+--S 1096 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 8 3 2 6 2 3 4 | 2
+--R (75a b x + 300a b x + 240a b x )\|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 +-+
+--R (- 15a x - 195a b x - 420a b x - 240a b x )\|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 8 3 2 6 2 3 4 4 2 5 | 2
+--R (25a b x - 25a b x - 170a b x - 56a b x + 32b )\|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (- 8a x - 29a b x + 101a b x + 202a b x + 40a b x - 32b )\|b
+--R /
+--R +--------+
+--R 2 4 8 5 6 6 4 +-+ | 2 3 4 10 2 5 8
+--R (40a b x + 160a b x + 128b x )\|b \|a x + b - 8a b x - 104a b x
+--R +
+--R 6 6 7 4
+--R - 224a b x - 128b x
+--R Type: Union(Expression(Integer),...)
+--E 1096
+
+--S 1097 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 4 9 3 7 2 2 5 |a x + b +-+ | 2
+--R (75a x + 300a b x + 240a b x ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 11 4 9 3 2 7 2 3 5 |a x + b
+--R (- 15a x - 195a b x - 420a b x - 240a b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 4 9 3 7 2 2 5 |a x + b +-+ | 2
+--R (75a x + 300a b x + 240a b x ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 11 4 9 3 2 7 2 3 5 |a x + b
+--R (- 15a x - 195a b x - 420a b x - 240a b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (25a x - 25a b x - 170a b x - 56a b x + 32b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R - 75a b x - 325a b x - 330a b x - 40a b x + 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (15a x + 200a b x + 483a b x + 354a b x + 24a b x - 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b
+--R (- 8a x - 29a b x + 101a b x + 202a b x + 40a b x - 32b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 4 9 5 7 6 5 |a x + b | 2
+--R (40a b x + 160a b x + 128b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 3 11 2 4 9 5 7 6 5 |a x + b +-+
+--R (- 8a b x - 104a b x - 224a b x - 128b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1097
+
+--S 1098 of 1379
+d0:=D(m0,x)
+--R
+--R
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+--R 5 10 4 8 3 2 6 2 3 4 4 2
+--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x
+--R +
+--R 5
+--R - 1024b
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+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3
+--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x
+--R +
+--R 5
+--R - 1024b x
+--R *
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+--R |a x + b
+--R |--------
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+--R \| x
+--R *
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+--R | 2
+--R \|a x + b
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+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x + 1024b x)
+--R *
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+--R | 2
+--R \| x
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+--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x
+--R +
+--R 6
+--R 1024b
+--R /
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+--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x
+--R +
+--R 5 8 6 6
+--R 3840a b x + 1024b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 7 20 6 18 5 2 16 4 3 14 3 4 12
+--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x
+--R +
+--R 2 5 10 6 8 7 6
+--R - 7424a b x - 4352a b x - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1098
+
+)clear all
+
+--S 1099 of 1379
+t0:=x^3/(a+b/x^2)^(5/2)
+--R
+--R
+--R 7
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1099
+
+--S 1100 of 1379
+r0:=-1/3*x^4/(a*(a+b/x^2)^(3/2))+35/8*b^2*atanh(sqrt(a+b/x^2)/_
+ sqrt(a))/a^(9/2)-7/3*x^4/(a^2*sqrt(a+b/x^2))-35/8*b*x^2*_
+ sqrt(a+b/x^2)/a^4+35/12*x^4*sqrt(a+b/x^2)/a^3
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R |a x + b
+--R +--------+ |--------
+--R | 2 | 2
+--R 2 2 3 |a x + b \| x
+--R (105a b x + 105b ) |-------- atanh(-----------)
+--R | 2 +-+
+--R \| x \|a
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (6a x - 21a b x - 140a b x - 105b )\|a
+--R /
+--R +--------+
+--R | 2
+--R 5 2 4 +-+ |a x + b
+--R (24a x + 24a b)\|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1100
+
+--S 1101 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
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+--R (735a b x + 6615a b x + 17640a b x + 18480a b x + 6720b )\|b
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+--R - 105a b x - 2730a b x - 13545a b x - 26040a b x - 21840a b x
+--R +
+--R 7
+--R - 6720b
+--R *
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+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
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+--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x
+--R +
+--R 5 3 6
+--R 17360a b x + 6720b x
+--R *
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+--R +-+ | 2
+--R \|a \|a x + b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x
+--R +
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+--R - 20720a b x - 6720b x
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+--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|a \|b
+--R *
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+--R \|a x + b
+--R +
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+--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x
+--R +
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+--R - 1536a b
+--R *
+--R +-+
+--R \|a
+--R ,
+--R
+--R 4 2 8 3 3 6 2 4 4 5 2 6
+--R (1470a b x + 13230a b x + 35280a b x + 36960a b x + 13440b )
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b
+--R +
+--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2
+--R - 210a b x - 5460a b x - 27090a b x - 52080a b x - 43680a b x
+--R +
+--R 7
+--R - 13440b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x
+--R +
+--R 5 3 6
+--R 17360a b x + 6720b x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- a \|a x + b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x
+--R +
+--R 5 3 6
+--R - 20720a b x - 6720b x
+--R *
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+--R /
+--R 8 8 7 6 6 2 4 5 3 2 4 4 +---+ +-+
+--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|- a \|b
+--R *
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+--R | 2
+--R \|a x + b
+--R +
+--R 9 10 8 8 7 2 6 6 3 4 5 4 2
+--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x
+--R +
+--R 4 5
+--R - 1536a b
+--R *
+--R +---+
+--R \|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1101
+
+--S 1102 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 2 8 3 3 6 2 4 4 5 2 6
+--R (735a b x + 6615a b x + 17640a b x + 18480a b x + 6720b )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
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+--R 5 2 10 4 3 8 3 4 6 2 5 4
+--R - 105a b x - 2730a b x - 13545a b x - 26040a b x
+--R +
+--R 6 2 7
+--R - 21840a b x - 6720b
+--R *
+--R +--------+
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+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R 4 2 8 3 3 6 2 4 4 5 2 6
+--R (- 735a b x - 6615a b x - 17640a b x - 18480a b x - 6720b )
+--R *
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+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
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+--R 105a b x + 2730a b x + 13545a b x + 26040a b x + 21840a b x
+--R +
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+--R 6720b
+--R *
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+--R |a x + b
+--R |--------
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+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
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+--R - 42a x - 189a b x + 1484a b x + 10543a b x + 22904a b x
+--R +
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+--R 20720a b x + 6720b
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+--R \|a \|b
+--R +
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+--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x
+--R +
+--R 5 3 6
+--R 17360a b x + 6720b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
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+--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x
+--R +
+--R 5 3 6
+--R - 20720a b x - 6720b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R 6a x + 129a b x - 41a b x - 4925a b x - 19825a b x
+--R +
+--R 2 5 4 6 2 7
+--R - 32424a b x - 24080a b x - 6720b
+--R *
+--R +-+
+--R \|a
+--R /
+--R 8 8 7 6 6 2 4 5 3 2 4 4 +-+
+--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|a
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 9 10 8 8 7 2 6 6 3 4 5 4 2
+--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x
+--R +
+--R 4 5
+--R - 1536a b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1102
+
+--S 1103 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
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+--R 17a x + 816a b x + 11424a b x + 71808a b x
+--R +
+--R 4 4 16 3 5 14 2 6 12 7 10
+--R 239360a b x + 452608a b x + 487424a b x + 278528a b x
+--R +
+--R 8 8
+--R 65536b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
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+--R - 17a x - 816a b x - 11424a b x - 71808a b x
+--R +
+--R 5 4 16 4 5 14 3 6 12 2 7 10
+--R - 239360a b x - 452608a b x - 487424a b x - 278528a b x
+--R +
+--R 8 8
+--R - 65536a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 9 25 8 23 7 2 21 6 3 19 5 4 17
+--R - a x - 144a b x - 3360a b x - 29568a b x - 126720a b x
+--R +
+--R 4 5 15 3 6 13 2 7 11 8 9
+--R - 292864a b x - 372736a b x - 245760a b x - 65536a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 9 25 8 23 7 2 21 6 3 19 5 4 17
+--R a x + 145a b x + 3504a b x + 32928a b x + 156288a b x
+--R +
+--R 4 5 15 3 6 13 2 7 11 8 9
+--R 419584a b x + 665600a b x + 618496a b x + 311296a b x
+--R +
+--R 9 7
+--R 65536b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 9 25 8 23 7 2 21 6 3 19
+--R 17a x + 816a b x + 11424a b x + 71808a b x
+--R +
+--R 5 4 17 4 5 15 3 6 13 2 7 11
+--R 239360a b x + 452608a b x + 487424a b x + 278528a b x
+--R +
+--R 8 9
+--R 65536a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 9 25 8 23 7 2 21 6 3 19
+--R - 17a x - 833a b x - 12240a b x - 83232a b x
+--R +
+--R 5 4 17 4 5 15 3 6 13 2 7 11
+--R - 311168a b x - 691968a b x - 940032a b x - 765952a b x
+--R +
+--R 8 9 9 7
+--R - 344064a b x - 65536b x
+--R *
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+--R *
+--R +-+
+--R \|b
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+--R - a x - 145a b x - 3504a b x - 32928a b x - 156288a b x
+--R +
+--R 4 5 16 3 6 14 2 7 12 8 10
+--R - 419584a b x - 665600a b x - 618496a b x - 311296a b x
+--R +
+--R 9 8
+--R - 65536b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 10 26 9 24 8 2 22 7 3 20 6 4 18
+--R a x + 145a b x + 3504a b x + 32928a b x + 156288a b x
+--R +
+--R 5 5 16 4 6 14 3 7 12 2 8 10 9 8
+--R 419584a b x + 665600a b x + 618496a b x + 311296a b x + 65536a b x
+--R /
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+--R 17a x + 850a b x + 13073a b x + 95472a b x
+--R +
+--R 7 4 13 6 5 11 5 6 9 4 7 7
+--R 394400a b x + 1003136a b x + 1632000a b x + 1705984a b x
+--R +
+--R 3 8 5 2 9 3 10
+--R 1110016a b x + 409600a b x + 65536a b x
+--R *
+--R +--------+
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+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
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+--R - a x - 147a b x - 3795a b x - 40081a b x
+--R +
+--R 7 4 14 6 5 12 5 6 10 4 7 8
+--R - 225648a b x - 765088a b x - 1661056a b x - 2369280a b x
+--R +
+--R 3 8 6 2 9 4 10 2 11
+--R - 2213888a b x - 1306624a b x - 442368a b x - 65536b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 11 22 10 20 9 2 18 8 3 16 7 4 14
+--R 17a x + 867a b x + 13923a b x + 108545a b x + 489872a b x
+--R +
+--R 6 5 12 5 6 10 4 7 8 3 8 6
+--R 1397536a b x + 2635136a b x + 3337984a b x + 2816000a b x
+--R +
+--R 2 9 4 10 2 11
+--R 1519616a b x + 475136a b x + 65536b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 12 23 11 21 10 2 19 9 3 17 8 4 15
+--R - a x - 147a b x - 3795a b x - 40081a b x - 225648a b x
+--R +
+--R 7 5 13 6 6 11 5 7 9 4 8 7
+--R - 765088a b x - 1661056a b x - 2369280a b x - 2213888a b x
+--R +
+--R 3 9 5 2 10 3 11
+--R - 1306624a b x - 442368a b x - 65536a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1103
+
+--S 1104 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 4 2 8 3 3 6 2 4 4 5 2 6
+--R (- 735a b x - 6615a b x - 17640a b x - 18480a b x - 6720b )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R +---+ |a x + b +-+ | 2
+--R \|- a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2
+--R 105a b x + 2730a b x + 13545a b x + 26040a b x + 21840a b x
+--R +
+--R 7
+--R 6720b
+--R *
+--R +--------+
+--R | 2
+--R +---+ |a x + b
+--R \|- a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 2 8 3 3 6 2 4 4 5 2 6
+--R (1470a b x + 13230a b x + 35280a b x + 36960a b x + 13440b )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R +-+ |a x + b +-+ | 2
+--R \|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 2 10 4 3 8 3 4 6 2 5 4
+--R - 210a b x - 5460a b x - 27090a b x - 52080a b x
+--R +
+--R 6 2 7
+--R - 43680a b x - 13440b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - 42a x - 189a b x + 1484a b x + 10543a b x + 22904a b x
+--R +
+--R 5 2 6
+--R 20720a b x + 6720b
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+--R +---+ +-+ +-+
+--R \|- a \|a \|b
+--R +
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+--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x
+--R +
+--R 5 3 6
+--R 17360a b x + 6720b x
+--R *
+--R +--------+
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+--R +---+ +-+ |a x + b
+--R \|- a \|a |--------
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+--R \| x
+--R *
+--R +--------+
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+--R \|a x + b
+--R +
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+--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x
+--R +
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+--R - 20720a b x - 6720b x
+--R *
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+--R | 2
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+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R 6a x + 129a b x - 41a b x - 4925a b x - 19825a b x
+--R +
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+--R - 32424a b x - 24080a b x - 6720b
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+--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|- a \|a
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 9 10 8 8 7 2 6 6 3 4 5 4 2
+--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x
+--R +
+--R 4 5
+--R - 1536a b
+--R *
+--R +--------+
+--R | 2
+--R +---+ +-+ |a x + b
+--R \|- a \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1104
+
+--S 1105 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 6 20 5 18 4 2 16 3 3 14
+--R - 14a x - 448a b x - 4032a b x - 15360a b x
+--R +
+--R 2 4 12 5 10 6 8
+--R - 28160a b x - 24576a b x - 8192b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 21 6 19 5 2 17 4 3 15 3 4 13
+--R - a x - 98a b x - 1568a b x - 9408a b x - 26880a b x
+--R +
+--R 2 5 11 6 9 7 7
+--R - 39424a b x - 28672a b x - 8192b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 21 6 19 5 2 17 4 3 15 3 4 13
+--R 14a x + 462a b x + 4480a b x + 19392a b x + 43520a b x
+--R +
+--R 2 5 11 6 9 7 7
+--R 52736a b x + 32768a b x + 8192b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 22 6 20 5 2 18 4 3 16 3 4 14
+--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x
+--R +
+--R 2 5 12 6 10 7 8
+--R 39424a b x + 28672a b x + 8192b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 9 18 8 16 7 2 14 6 3 12 5 4 10
+--R a x + 100a b x + 1765a b x + 12642a b x + 47264a b x
+--R +
+--R 4 5 8 3 6 6 2 7 4 8 2 9
+--R 102592a b x + 134400a b x + 104960a b x + 45056a b x + 8192b
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 9 18 8 16 7 2 14 6 3 12 5 4 10
+--R - 14a x - 490a b x - 5418a b x - 28814a b x - 86784a b x
+--R +
+--R 4 5 8 3 6 6 2 7 4 8 2 9
+--R - 159168a b x - 181760a b x - 126464a b x - 49152a b x - 8192b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1105
+
+)clear all
+
+--S 1106 of 1379
+t0:=x/(a+b/x^2)^(5/2)
+--R
+--R
+--R 5
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1106
+
+--S 1107 of 1379
+r0:=-1/3*x^2/(a*(a+b/x^2)^(3/2))-5/2*b*atanh(sqrt(a+b/x^2)/_
+ sqrt(a))/a^(7/2)-5/3*x^2/(a^2*sqrt(a+b/x^2))+5/2*x^2*sqrt(a+b/x^2)/a^3
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2
+--R |a x + b
+--R +--------+ |--------
+--R | 2 | 2
+--R 2 2 |a x + b \| x
+--R (- 15a b x - 15b ) |-------- atanh(-----------)
+--R | 2 +-+
+--R \| x \|a
+--R +
+--R 2 4 2 2 +-+
+--R (3a x + 20a b x + 15b )\|a
+--R /
+--R +--------+
+--R | 2
+--R 4 2 3 +-+ |a x + b
+--R (6a x + 6a b)\|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1107
+
+--S 1108 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 6 2 2 4 3 2 4 +-+ | 2
+--R (75a b x + 375a b x + 540a b x + 240b )\|b \|a x + b
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R - 15a b x - 210a b x - 615a b x - 660a b x - 240b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2
+--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +-+ +-+
+--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|a \|b
+--R /
+--R +--------+
+--R 6 6 5 4 4 2 2 3 3 +-+ +-+ | 2
+--R (30a x + 150a b x + 216a b x + 96a b )\|a \|b \|a x + b
+--R +
+--R 7 8 6 6 5 2 4 4 3 2 3 4 +-+
+--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|a
+--R ,
+--R
+--R +--------+
+--R 3 6 2 2 4 3 2 4 +-+ | 2
+--R (- 150a b x - 750a b x - 1080a b x - 480b )\|b \|a x + b
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R 30a b x + 420a b x + 1230a b x + 1320a b x + 480b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R 4 9 3 7 2 2 5 3 3 4 +---+ | 2
+--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|- a \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+
+--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|- a \|b
+--R /
+--R +--------+
+--R 6 6 5 4 4 2 2 3 3 +---+ +-+ | 2
+--R (30a x + 150a b x + 216a b x + 96a b )\|- a \|b \|a x + b
+--R +
+--R 7 8 6 6 5 2 4 4 3 2 3 4 +---+
+--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1108
+
+--S 1109 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 3 6 2 2 4 3 2 4 |a x + b +-+ | 2
+--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 2 6 2 3 4 4 2 5 |a x + b
+--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 3 6 2 2 4 3 2 4 |a x + b +-+ | 2
+--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 2 6 2 3 4 4 2 5 |a x + b
+--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+ +-+
+--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b
+--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+
+--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|a
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 6 6 5 4 4 2 2 3 3 +-+ |a x + b +-+ | 2
+--R (30a x + 150a b x + 216a b x + 96a b )\|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 7 8 6 6 5 2 4 4 3 2 3 4 +-+ |a x + b
+--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1109
+
+--S 1110 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 6 18 5 16 4 2 14 3 3 12
+--R - 13a x - 364a b x - 2912a b x - 9984a b x
+--R +
+--R 2 4 10 5 8 6 6
+--R - 16640a b x - 13312a b x - 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 7 18 6 16 5 2 14 4 3 12 3 4 10
+--R - 13a x - 364a b x - 2912a b x - 9984a b x - 16640a b x
+--R +
+--R 2 5 8 6 6
+--R - 13312a b x - 4096a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 19 6 17 5 2 15 4 3 13 3 4 11
+--R - a x - 84a b x - 1120a b x - 5376a b x - 11520a b x
+--R +
+--R 2 5 9 6 7
+--R - 11264a b x - 4096a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 7 19 6 17 5 2 15 4 3 13 3 4 11
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 9 6 7 7 5
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 19 6 17 5 2 15 4 3 13 3 4 11
+--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x
+--R +
+--R 2 5 9 6 7
+--R 13312a b x + 4096a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 7 19 6 17 5 2 15 4 3 13 3 4 11
+--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x
+--R +
+--R 2 5 9 6 7 7 5
+--R 29952a b x + 17408a b x + 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 20 6 18 5 2 16 4 3 14 3 4 12
+--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x
+--R +
+--R 2 5 10 6 8 7 6
+--R 22784a b x + 15360a b x + 4096b x
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 8 20 7 18 6 2 16 5 3 14 4 4 12
+--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x
+--R +
+--R 3 5 10 2 6 8 7 6
+--R 22784a b x + 15360a b x + 4096a b x
+--R /
+--R 9 17 8 15 7 2 13 6 3 11 5 4 9
+--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x
+--R +
+--R 4 5 7 3 6 5 2 7 3 8
+--R 56576a b x + 47360a b x + 21504a b x + 4096a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 9 18 8 16 7 2 14 6 3 12 5 4 10
+--R a x + 87a b x + 1375a b x + 8989a b x + 31092a b x
+--R +
+--R 4 5 8 3 6 6 2 7 4 8 2 9
+--R 63072a b x + 77824a b x + 57600a b x + 23552a b x + 4096b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 9 18 8 16 7 2 14 6 3 12 5 4 10
+--R - 13a x - 403a b x - 4043a b x - 19825a b x - 55692a b x
+--R +
+--R 4 5 8 3 6 6 2 7 4 8 2 9
+--R - 96096a b x - 103936a b x - 68864a b x - 25600a b x - 4096b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 10 19 9 17 8 2 15 7 3 13 6 4 11
+--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x
+--R +
+--R 5 5 9 4 6 7 3 7 5 2 8 3 9
+--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1110
+
+--S 1111 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2
+--R 3 6 2 2 4 3 2 4 +---+ |a x + b +-+
+--R (75a b x + 375a b x + 540a b x + 240b )\|- a |-------- \|b
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5 +---+
+--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b )\|- a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 2 4 3 2 4 +-+ |a x + b +-+
+--R (- 150a b x - 750a b x - 1080a b x - 480b )\|a |-------- \|b
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 8 3 2 6 2 3 4 4 2 5 +-+ |a x + b
+--R (30a b x + 420a b x + 1230a b x + 1320a b x + 480b )\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +---+ +-+ +-+
+--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|- a \|a \|b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+
+--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|- a \|a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+
+--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|- a \|a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +---+ +-+
+--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|- a \|a
+--R /
+--R +--------+
+--R | 2
+--R 6 6 5 4 4 2 2 3 3 +---+ +-+ |a x + b +-+
+--R (30a x + 150a b x + 216a b x + 96a b )\|- a \|a |-------- \|b
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 7 8 6 6 5 2 4 4 3 2 3 4 +---+ +-+ |a x + b
+--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|- a \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1111
+
+--S 1112 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 4 14 3 12 2 2 10 3 8 4 6
+--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5
+--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5
+--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b x )
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4
+--R a x + 52a b x + 501a b x + 1970a b x + 3920a b x + 4192a b x
+--R +
+--R 6 2 7
+--R 2304a b x + 512b
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x
+--R +
+--R 2 5 4 6 2 7
+--R - 5280a b x - 2560a b x - 512b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1112
+
+)clear all
+
+--S 1113 of 1379
+t0:=1/((a+b/x^2)^(5/2)*x)
+--R
+--R
+--R 3
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1113
+
+--S 1114 of 1379
+r0:=(-1/3)/(a*(a+b/x^2)^(3/2))+atanh(sqrt(a+b/x^2)/sqrt(a))/a^(5/2)+_
+ (-1)/(a^2*sqrt(a+b/x^2))
+--R
+--R
+--R +--------+
+--R | 2
+--R |a x + b
+--R +--------+ |--------
+--R | 2 | 2
+--R 2 |a x + b \| x 2 +-+
+--R (3a x + 3b) |-------- atanh(-----------) + (- 4a x - 3b)\|a
+--R | 2 +-+
+--R \| x \|a
+--R (2) --------------------------------------------------------------
+--R +--------+
+--R | 2
+--R 3 2 2 +-+ |a x + b
+--R (3a x + 3a b)\|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1114
+
+--S 1115 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4
+--R (9a x + 21a b x + 12b )\|b \|a x + b - 3a x - 18a b x
+--R +
+--R 2 2 3
+--R - 27a b x - 12b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 5 3 2 +-+ | 2
+--R (4a x + 19a b x + 12b x)\|a \|a x + b
+--R +
+--R 2 5 3 2 +-+ +-+
+--R (- 12a x - 25a b x - 12b x)\|a \|b
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ +-+ | 2
+--R (9a x + 21a b x + 12a b )\|a \|b \|a x + b
+--R +
+--R 5 6 4 4 3 2 2 2 3 +-+
+--R (- 3a x - 18a b x - 27a b x - 12a b )\|a
+--R ,
+--R
+--R +--------+
+--R 2 4 2 2 +-+ | 2 3 6 2 4
+--R (18a x + 42a b x + 24b )\|b \|a x + b - 6a x - 36a b x
+--R +
+--R 2 2 3
+--R - 54a b x - 24b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R +--------+
+--R 2 5 3 2 +---+ | 2
+--R (4a x + 19a b x + 12b x)\|- a \|a x + b
+--R +
+--R 2 5 3 2 +---+ +-+
+--R (- 12a x - 25a b x - 12b x)\|- a \|b
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +---+ +-+ | 2
+--R (9a x + 21a b x + 12a b )\|- a \|b \|a x + b
+--R +
+--R 5 6 4 4 3 2 2 2 3 +---+
+--R (- 3a x - 18a b x - 27a b x - 12a b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 1115
+
+--S 1116 of 1379
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 2 4 2 2 |a x + b +-+ | 2
+--R (9a x + 21a b x + 12b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 3 |a x + b
+--R (- 3a x - 18a b x - 27a b x - 12b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ 2 +-+
+--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 4 2 2 |a x + b +-+ | 2
+--R (- 9a x - 21a b x - 12b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 3 |a x + b
+--R (3a x + 18a b x + 27a b x + 12b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 +-+ +-+
+--R (12a x + 25a b x + 12b )\|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +-+ |a x + b
+--R (4a x + 19a b x + 12b x)\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +-+ |a x + b +-+
+--R (- 12a x - 25a b x - 12b x)\|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 4a x - 23a b x - 31a b x - 12b )\|a
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 4 4 3 2 2 2 +-+ |a x + b +-+ | 2
+--R (9a x + 21a b x + 12a b )\|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 6 4 4 3 2 2 2 3 +-+ |a x + b
+--R (- 3a x - 18a b x - 27a b x - 12a b )\|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1116
+
+--S 1117 of 1379
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 4 12 3 10 2 2 8 3 6 4 4 +-+
+--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R +
+--R 5 12 4 10 3 2 8 2 3 6 4 4
+--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b
+--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +-+
+--R (a x + 41a b x + 280a b x + 688a b x + 704a b x + 256b x )\|a
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b
+--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) |--------
+--R | 2
+--R \| x
+--R +
+--R 5 13 4 11 3 2 9 2 3 7 4 5
+--R - 9a x - 129a b x - 552a b x - 1008a b x - 832a b x
+--R +
+--R 5 3
+--R - 256b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R +
+--R 6 14 5 12 4 2 10 3 3 8 2 4 6 5 4
+--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x
+--R /
+--R 7 13 6 11 5 2 9 4 3 7 3 4 5
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 2 5 3 6
+--R 1088a b x + 256a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x
+--R +
+--R 2 5 4 6 2 7
+--R - 2352a b x - 1216a b x - 256b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b
+--R \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 7 14 6 12 5 2 10 4 3 8 3 4 6
+--R 9a x + 147a b x + 819a b x + 2241a b x + 3400a b x
+--R +
+--R 2 5 4 6 2 7
+--R 2928a b x + 1344a b x + 256b
+--R *
+--R +--------+
+--R | 2
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 8 15 7 13 6 2 11 5 3 9 4 4 7
+--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x
+--R +
+--R 3 5 5 2 6 3 7
+--R - 2352a b x - 1216a b x - 256a b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1117
+
+--S 1118 of 1379
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 2 +--------+
+--R 2 4 2 2 +---+ |a x + b +-+ | 2
+--R (- 9a x - 21a b x - 12b )\|- a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 3 +---+ |a x + b
+--R (3a x + 18a b x + 27a b x + 12b )\|- a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 4 2 2 +-+ |a x + b +-+ | 2
+--R (18a x + 42a b x + 24b )\|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 4 2 2 3 +-+ |a x + b
+--R (- 6a x - 36a b x - 54a b x - 24b )\|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R a x
+--R +
+--R 2 4 2 2 +---+ +-+ +-+
+--R (12a x + 25a b x + 12b )\|- a \|a \|b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +---+ +-+ |a x + b
+--R (4a x + 19a b x + 12b x)\|- a \|a |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 +---+ +-+ |a x + b +-+
+--R (- 12a x - 25a b x - 12b x)\|- a \|a |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 4 2 2 3 +---+ +-+
+--R (- 4a x - 23a b x - 31a b x - 12b )\|- a \|a
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 4 4 3 2 2 2 +---+ +-+ |a x + b +-+ | 2
+--R (9a x + 21a b x + 12a b )\|- a \|a |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 6 4 4 3 2 2 2 3 +---+ +-+ |a x + b
+--R (- 3a x - 18a b x - 27a b x - 12a b )\|- a \|a |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1118
+
+--S 1119 of 1379
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 2
+--R 2 8 6 2 4 |a x + b +-+ 3 9 2 7
+--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x
+--R | 2
+--R \| x
+--R +
+--R 2 5 3 3
+--R - 48a b x - 32b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 9 2 7 2 5 3 3 +-+
+--R (6a x + 38a b x + 64a b x + 32b x )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 10 2 8 2 6 3 4 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1119
+
+)clear all
+
+--S 1120 of 1379
+t0:=1/((a+b/x^2)^(5/2)*x^3)
+--R
+--R
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1120
+
+--S 1121 of 1379
+r0:=1/3/(b*(a+b/x^2)^(3/2))
+--R
+--R
+--R 2
+--R x
+--R (2) --------------------------
+--R +--------+
+--R | 2
+--R 2 2 |a x + b
+--R (3a b x + 3b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1121
+
+--S 1122 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 5 3 | 2 5 3 +-+
+--R (- a x - 4b x )\|a x + b + (3a x + 4b x )\|b
+--R /
+--R +--------+
+--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4
+--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x
+--R +
+--R 3 2 4
+--R - 27a b x - 12b
+--R Type: Union(Expression(Integer),...)
+--E 1122
+
+--S 1123 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 4 2 +-+ 5 3 |a x + b | 2
+--R ((- 3a x - 4b x )\|b + (- a x - 4b x ) |-------- )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 3 |a x + b +-+ 2 6 4 2 2
+--R (3a x + 4b x ) |-------- \|b + a x + 5a b x + 4b x
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 4 2 2 3 |a x + b +-+ | 2
+--R (9a b x + 21a b x + 12b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 6 2 2 4 3 2 4 |a x + b
+--R (- 3a b x - 18a b x - 27a b x - 12b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1123
+
+--S 1124 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 |a x + b +-+ 3 7 2 5
+--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x
+--R | 2
+--R \| x
+--R +
+--R 2 3 3
+--R - 48a b x - 32b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 7 2 5 2 3 3 +-+
+--R (6a x + 38a b x + 64a b x + 32b x)\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 8 2 6 2 4 3 2 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1124
+
+)clear all
+
+--S 1125 of 1379
+t0:=1/((a+b/x^2)^(5/2)*x^5)
+--R
+--R
+--R 1
+--R (1) ---------------------------------
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b
+--R (a x + 2a b x + b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1125
+
+--S 1126 of 1379
+r0:=-1/3*a/(b^2*(a+b/x^2)^(3/2))+1/(b^2*sqrt(a+b/x^2))
+--R
+--R
+--R 2
+--R 2a x + 3b
+--R (2) --------------------------
+--R +--------+
+--R | 2
+--R 2 2 3 |a x + b
+--R (3a b x + 3b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1126
+
+--S 1127 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 5 3 2 | 2 2 5 3 2 +-+
+--R (- 2a x - 11a b x - 12b x)\|a x + b + (6a x + 17a b x + 12b x)\|b
+--R /
+--R +--------+
+--R 2 2 4 3 2 4 +-+ | 2 3 2 6 2 3 4
+--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x
+--R +
+--R 4 2 5
+--R - 27a b x - 12b
+--R Type: Union(Expression(Integer),...)
+--E 1127
+
+--S 1128 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 4 2 2 +-+
+--R (- 6a x - 17a b x - 12b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b
+--R (- 2a x - 11a b x - 12b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2
+--R (6a x + 17a b x + 12b x) |-------- \|b + 2a x + 13a b x + 23a b x
+--R | 2
+--R \| x
+--R +
+--R 3
+--R 12b
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 2 4 3 2 4 |a x + b +-+ | 2
+--R (9a b x + 21a b x + 12b ) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 2 6 2 3 4 4 2 5 |a x + b
+--R (- 3a b x - 18a b x - 27a b x - 12b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1128
+
+--S 1129 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4
+--R (- 6a x - 32a b x - 32b x) |-------- \|b - a x - 18a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 3
+--R - 48a b x - 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (6a x + 38a b x + 64a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x) |--------
+--R | 2
+--R \| x
+--R /
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x)
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1129
+
+)clear all
+
+--S 1130 of 1379
+t0:=1/((a+b/x^2)^(5/2)*x^7)
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R | 2
+--R 2 7 5 2 3 |a x + b
+--R (a x + 2a b x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1130
+
+--S 1131 of 1379
+r0:=1/3*a^2/(b^3*(a+b/x^2)^(3/2))-2*a/(b^3*sqrt(a+b/x^2))-sqrt(a+b/x^2)/b^3
+--R
+--R
+--R 2 4 2 2
+--R - 8a x - 12a b x - 3b
+--R (2) ----------------------------
+--R +--------+
+--R | 2
+--R 3 4 4 2 |a x + b
+--R (3a b x + 3b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1131
+
+--S 1132 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6
+--R (32a x + 112a b x + 108a b x + 24b )\|b \|a x + b - 8a x - 76a b x
+--R +
+--R 2 2 4 3 2 4
+--R - 163a b x - 120a b x - 24b
+--R /
+--R +--------+
+--R 3 3 7 2 4 5 5 3 6 | 2
+--R (3a b x + 27a b x + 48a b x + 24b x)\|a x + b
+--R +
+--R 3 3 7 2 4 5 5 3 6 +-+
+--R (- 12a b x - 48a b x - 60a b x - 24b x)\|b
+--R Type: Union(Expression(Integer),...)
+--E 1132
+
+--S 1133 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8
+--R (32a x + 112a b x + 108a b x + 24b x) |-------- \|b + 8a x
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 2 4 3 2 4
+--R 76a b x + 163a b x + 120a b x + 24b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- 32a x - 144a b x - 220a b x - 132a b x - 24b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (- 8a x - 76a b x - 163a b x - 120a b x - 24b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 3 8 2 4 6 5 4 6 2 |a x + b | 2
+--R (3a b x + 27a b x + 48a b x + 24b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 3 8 2 4 6 5 4 6 2 |a x + b +-+
+--R (- 12a b x - 48a b x - 60a b x - 24b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1133
+
+--S 1134 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8
+--R (- 8a x - 80a b x - 192a b x - 128b x) |-------- \|b - a x
+--R | 2
+--R \| x
+--R +
+--R 3 6 2 2 4 3 2 4
+--R - 32a b x - 160a b x - 256a b x - 128b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (8a x + 88a b x + 272a b x + 320a b x + 128b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b
+--R (a x + 32a b x + 160a b x + 256a b x + 128b x) |--------
+--R | 2
+--R \| x
+--R /
+--R 6 15 5 13 4 2 11 3 3 9 2 4 7 5 5
+--R a x + 34a b x + 225a b x + 608a b x + 800a b x + 512a b x
+--R +
+--R 6 3
+--R 128b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 6 15 5 13 4 2 11 3 3 9 2 4 7
+--R - 8a x - 104a b x - 456a b x - 952a b x - 1040a b x
+--R +
+--R 5 5 6 3
+--R - 576a b x - 128b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1134
+
+)clear all
+
+--S 1135 of 1379
+t0:=1/((a+b/x^2)^(5/2)*x^9)
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R | 2
+--R 2 9 7 2 5 |a x + b
+--R (a x + 2a b x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1135
+
+--S 1136 of 1379
+r0:=-1/3*a^3/(b^4*(a+b/x^2)^(3/2))-1/3*(a+b/x^2)^(3/2)/b^4+_
+ 3*a^2/(b^4*sqrt(a+b/x^2))+3*a*sqrt(a+b/x^2)/b^4
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R 16a x + 24a b x + 6a b x - b
+--R (2) --------------------------------
+--R +--------+
+--R | 2
+--R 4 6 5 4 |a x + b
+--R (3a b x + 3b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1136
+
+--S 1137 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (- 96a x - 656a b x - 1316a b x - 954a b x - 160a b x + 32b )\|b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2
+--R 16a x + 312a b x + 1206a b x + 1771a b x + 1038a b x + 144a b x
+--R +
+--R 6
+--R - 32b
+--R /
+--R +--------+
+--R 4 4 11 3 5 9 2 6 7 7 5 8 3 | 2
+--R (3a b x + 57a b x + 198a b x + 240a b x + 96b x )\|a x + b
+--R +
+--R 4 4 11 3 5 9 2 6 7 7 5 8 3 +-+
+--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96b x )\|b
+--R Type: Union(Expression(Integer),...)
+--E 1137
+
+--S 1138 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 11 4 9 3 2 7 2 3 5 4 3
+--R - 96a x - 656a b x - 1316a b x - 954a b x - 160a b x
+--R +
+--R 5
+--R 32b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - 16a x - 312a b x - 1206a b x - 1771a b x - 1038a b x
+--R +
+--R 5 2 6
+--R - 144a b x + 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R 96a x + 752a b x + 1972a b x + 2270a b x + 1114a b x
+--R +
+--R 5 2 6
+--R 128a b x - 32b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5
+--R 16a x + 312a b x + 1206a b x + 1771a b x + 1038a b x
+--R +
+--R 5 3 6
+--R 144a b x - 32b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2
+--R 4 4 12 3 5 10 2 6 8 7 6 8 4 |a x + b
+--R (3a b x + 57a b x + 198a b x + 240a b x + 96b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 4 12 3 5 10 2 6 8 7 6 8 4 |a x + b +-+
+--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1138
+
+--S 1139 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 5 11 4 9 3 2 7 2 3 5 4 3
+--R - 12a x - 280a b x - 1792a b x - 4608a b x - 5120a b x
+--R +
+--R 5
+--R - 2048b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - a x - 72a b x - 840a b x - 3584a b x - 6912a b x
+--R +
+--R 5 2 6
+--R - 6144a b x - 2048b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R 12a x + 292a b x + 2072a b x + 6400a b x + 9728a b x
+--R +
+--R 5 2 6
+--R 7168a b x + 2048b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3
+--R a x + 72a b x + 840a b x + 3584a b x + 6912a b x + 6144a b x
+--R +
+--R 6
+--R 2048b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 8 21 7 19 6 2 17 5 3 15 4 4 13
+--R a x + 74a b x + 985a b x + 5336a b x + 14920a b x
+--R +
+--R 3 5 11 2 6 9 7 7 8 5
+--R 23552a b x + 21248a b x + 10240a b x + 2048b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 8 21 7 19 6 2 17 5 3 15 4 4 13
+--R - 12a x - 316a b x - 2668a b x - 10836a b x - 24600a b x
+--R +
+--R 3 5 11 2 6 9 7 7 8 5
+--R - 33024a b x - 26112a b x - 11264a b x - 2048b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1139
+
+)clear all
+
+--S 1140 of 1379
+t0:=x^2/(a+b/x^2)^(5/2)
+--R
+--R
+--R 6
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1140
+
+--S 1141 of 1379
+r0:=-1/3*x^3/(a*(a+b/x^2)^(3/2))-2*x^3/(a^2*sqrt(a+b/x^2))-_
+ 16/3*b*x*sqrt(a+b/x^2)/a^4+8/3*x^3*sqrt(a+b/x^2)/a^3
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R a x - 6a b x - 24a b x - 16b
+--R (2) --------------------------------
+--R +--------+
+--R | 2
+--R 5 3 4 |a x + b
+--R (3a x + 3a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1141
+
+--S 1142 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 10 2 8 | 2 2 12 10 2 8 +-+
+--R (- 6a b x - 12b x )\|a x + b + (a x + 12a b x + 12b x )\|b
+--R /
+--R +--------+
+--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2
+--R (3a x + 57a b x + 198a b x + 240a b x + 96b )\|b \|a x + b
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R - 18a b x - 132a b x - 306a b x - 288a b x - 96b
+--R Type: Union(Expression(Integer),...)
+--E 1142
+
+--S 1143 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - a x - 12a b x + 84a b x + 704a b x + 1632a b x
+--R +
+--R 5 2 6
+--R 1536a b x + 512b
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 2
+--R 5 11 4 2 9 |a x + b
+--R (- 6a b x - 12a b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 6 13 5 11 4 2 9 |a x + b +-+ 6 12 5 2 10
+--R (a x + 12a b x + 12a b x ) |-------- \|b + 6a b x + 2a b x
+--R | 2
+--R \| x
+--R +
+--R 4 3 8 3 4 6 2 5 4 6 2 7
+--R - 308a b x - 1360a b x - 2336a b x - 1792a b x - 512b
+--R /
+--R +--------+
+--R | 2
+--R 8 9 7 7 6 2 5 5 3 3 4 4 |a x + b +-+
+--R (3a x + 57a b x + 198a b x + 240a b x + 96a b x) |-------- \|b
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 8 9 7 2 7 6 3 5 5 4 3 4 5 |a x + b
+--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1143
+
+--S 1144 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 5 17 4 15 3 2 13 2 3 11 4 9
+--R - 12a x - 280a b x - 1792a b x - 4608a b x - 5120a b x
+--R +
+--R 5 7
+--R - 2048b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 18 5 16 4 2 14 3 3 12 2 4 10
+--R - a x - 72a b x - 840a b x - 3584a b x - 6912a b x
+--R +
+--R 5 8 6 6
+--R - 6144a b x - 2048b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 6 18 5 16 4 2 14 3 3 12 2 4 10
+--R 12a x + 292a b x + 2072a b x + 6400a b x + 9728a b x
+--R +
+--R 5 8 6 6
+--R 7168a b x + 2048b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 19 5 17 4 2 15 3 3 13 2 4 11
+--R a x + 72a b x + 840a b x + 3584a b x + 6912a b x
+--R +
+--R 5 9 6 7
+--R 6144a b x + 2048b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R /
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R a x + 74a b x + 985a b x + 5336a b x + 14920a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R 23552a b x + 21248a b x + 10240a b x + 2048b
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 8 16 7 14 6 2 12 5 3 10 4 4 8
+--R - 12a x - 316a b x - 2668a b x - 10836a b x - 24600a b x
+--R +
+--R 3 5 6 2 6 4 7 2 8
+--R - 33024a b x - 26112a b x - 11264a b x - 2048b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1144
+
+)clear all
+
+--S 1145 of 1379
+t0:=1/(a+b/x^2)^(5/2)
+--R
+--R
+--R 4
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1145
+
+--S 1146 of 1379
+r0:=-1/3*x/(a*(a+b/x^2)^(3/2))-4/3*x/(a^2*sqrt(a+b/x^2))+_
+ 8/3*x*sqrt(a+b/x^2)/a^3
+--R
+--R
+--R 2 4 2 2
+--R 3a x + 12a b x + 8b
+--R (2) ---------------------------
+--R +--------+
+--R | 2
+--R 4 3 3 |a x + b
+--R (3a x + 3a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1146
+
+--S 1147 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 6 | 2 8 6 +-+
+--R - 4b x \|a x + b + (3a x + 4b x )\|b
+--R /
+--R +--------+
+--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4
+--R (3a x + 27a b x + 48a b x + 24b )\|b \|a x + b - 12a b x - 48a b x
+--R +
+--R 3 2 4
+--R - 60a b x - 24b
+--R Type: Union(Expression(Integer),...)
+--E 1147
+
+--S 1148 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 8 3 6 2 2 4 3 2 4 +-+
+--R (- 3a x - 36a b x - 128a b x - 160a b x - 64b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 |a x + b
+--R - 4a b x |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 |a x + b +-+ 4 8 3 2 6 2 3 4
+--R (3a x + 4a b x ) |-------- \|b + 12a b x + 84a b x + 200a b x
+--R | 2
+--R \| x
+--R +
+--R 4 2 5
+--R 192a b x + 64b
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 6 7 5 5 4 2 3 3 3 |a x + b +-+ | 2
+--R (3a x + 27a b x + 48a b x + 24a b x) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 6 7 5 2 5 4 3 3 3 4 |a x + b
+--R (- 12a b x - 48a b x - 60a b x - 24a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1148
+
+--S 1149 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 3 11 2 9 2 7 3 5 |a x + b +-+ 4 12
+--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x
+--R | 2
+--R \| x
+--R +
+--R 3 10 2 2 8 3 6 4 4
+--R - 32a b x - 160a b x - 256a b x - 128b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 4 12 3 10 2 2 8 3 6 4 4 +-+
+--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b
+--R +
+--R +--------+
+--R | 2
+--R 4 13 3 11 2 2 9 3 7 4 5 |a x + b
+--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2
+--R a x + 34a b x + 225a b x + 608a b x + 800a b x + 512a b x
+--R +
+--R 6
+--R 128b
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b | 2
+--R |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4
+--R - 8a x - 104a b x - 456a b x - 952a b x - 1040a b x
+--R +
+--R 5 2 6
+--R - 576a b x - 128b
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1149
+
+)clear all
+
+--S 1150 of 1379
+t0:=1/((a+b/x^2)^(5/2)*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1150
+
+--S 1151 of 1379
+r0:=(-1/3)/(a*(a+b/x^2)^(3/2)*x)+(-2/3)/(a^2*x*sqrt(a+b/x^2))
+--R
+--R
+--R 2
+--R - 3a x - 2b
+--R (2) ---------------------------
+--R +--------+
+--R | 2
+--R 3 3 2 |a x + b
+--R (3a x + 3a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1151
+
+--S 1152 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 | 2 6 4 +-+
+--R - 3b x \|a x + b + (2a x + 3b x )\|b
+--R /
+--R +--------+
+--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4
+--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x
+--R +
+--R 3 2 4
+--R - 27a b x - 12b
+--R Type: Union(Expression(Integer),...)
+--E 1152
+
+--S 1153 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 2 4 2 2 3 +-+ 2 5 |a x + b | 2
+--R ((9a b x + 18a b x + 8b )\|b - 3a b x |-------- )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 |a x + b +-+ 3 6 2 2 4 3 2 4
+--R (2a x + 3a b x ) |-------- \|b - 3a b x - 17a b x - 22a b x - 8b
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 4 5 3 2 3 2 3 |a x + b +-+ | 2
+--R (9a b x + 21a b x + 12a b x) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 5 7 4 2 5 3 3 3 2 4 |a x + b
+--R (- 3a b x - 18a b x - 27a b x - 12a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1153
+
+--S 1154 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 2 7 5 2 3 |a x + b +-+ 3 8 2 6
+--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x
+--R | 2
+--R \| x
+--R +
+--R 2 4 3 2
+--R - 48a b x - 32b x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 8 2 6 2 4 3 2 +-+
+--R (6a x + 38a b x + 64a b x + 32b x )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 9 2 7 2 5 3 3 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1154
+
+)clear all
+
+--S 1155 of 1379
+t0:=1/((a+b/x^2)^(5/2)*x^4)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R 2 4 2 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1155
+
+--S 1156 of 1379
+r0:=(-1/3)/(a*(a+b/x^2)^(3/2)*x^3)
+--R
+--R
+--R 1
+--R (2) - ---------------------------
+--R +--------+
+--R | 2
+--R 2 3 |a x + b
+--R (3a x + 3a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1156
+
+--S 1157 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 2 2 | 2 2 6 4 2 2 +-+
+--R (- 3a b x - 6b x )\|a x + b + (a x + 6a b x + 6b x )\|b
+--R /
+--R +--------+
+--R 2 2 4 3 2 4 +-+ | 2 3 2 6 2 3 4
+--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x
+--R +
+--R 4 2 5
+--R - 27a b x - 12b
+--R Type: Union(Expression(Integer),...)
+--E 1157
+
+--S 1158 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 2 2 3 +-+ 2 5 2 3 |a x + b | 2
+--R ((3a b x + 4b )\|b + (- 3a b x - 6a b x ) |-------- )\|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 |a x + b +-+ 2 2 4 3 2 4
+--R (a x + 6a b x + 6a b x ) |-------- \|b - a b x - 5a b x - 4b
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 2 5 2 3 3 4 |a x + b +-+ | 2
+--R (9a b x + 21a b x + 12a b x) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 2 7 3 3 5 2 4 3 5 |a x + b
+--R (- 3a b x - 18a b x - 27a b x - 12a b x) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1158
+
+--S 1159 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 2
+--R 2 5 3 2 |a x + b +-+ 3 6 2 4
+--R (- 6a x - 32a b x - 32b x) |-------- \|b - a x - 18a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 3
+--R - 48a b x - 32b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (6a x + 38a b x + 64a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5
+--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b )
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1159
+
+)clear all
+
+--S 1160 of 1379
+t0:=1/((a+b/x^2)^(5/2)*x^6)
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R | 2
+--R 2 6 4 2 2 |a x + b
+--R (a x + 2a b x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1160
+
+--S 1161 of 1379
+r0:=1/3/(b*(a+b/x^2)^(3/2)*x^3)-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/_
+ b^(5/2)+1/(b^2*x*sqrt(a+b/x^2))
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R 3 |a x + b \|b 2 +-+
+--R (- 3a x - 3b x) |-------- atanh(------------) + (3a x + 4b)\|b
+--R | 2 +--------+
+--R \| x | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R (2) -----------------------------------------------------------------
+--R +--------+
+--R | 2
+--R 2 3 3 |a x + b +-+
+--R (3a b x + 3b x) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1161
+
+--S 1162 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 2 4 2 2 3 | 2
+--R (9a b x + 21a b x + 12b )\|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (- 3a x - 18a b x - 27a b x - 12b )\|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+
+--R (9a b x + 12a b x )\|a x + b + (- 4a x - 15a b x - 12a b x )\|b
+--R /
+--R +--------+
+--R 2 3 4 4 2 5 +-+ | 2 3 3 6 2 4 4
+--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x
+--R +
+--R 5 2 6
+--R - 27a b x - 12b
+--R Type: Union(Expression(Integer),...)
+--E 1162
+
+--S 1163 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 +--------+
+--R 2 5 3 2 |a x + b +-+ | 2
+--R (9a x + 21a b x + 12b x) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (- 3a x - 18a b x - 27a b x - 12b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2 +--------+
+--R 2 5 3 2 |a x + b +-+ | 2
+--R (9a x + 21a b x + 12b x) |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (- 3a x - 18a b x - 27a b x - 12b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 2 5 3 |a x + b +-+ 2 4 2 2 3
+--R ((9a x + 12a b x ) |-------- \|b - 9a b x - 24a b x - 16b )
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 3 6 2 4 2 2 3 +-+
+--R (3a x + 19a b x + 32a b x + 16b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 |a x + b
+--R (- 4a x - 15a b x - 12a b x ) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 2 3 5 4 3 5 |a x + b | 2
+--R (9a b x + 21a b x + 12b x) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 3 2 7 2 3 5 4 3 5 |a x + b +-+
+--R (- 3a b x - 18a b x - 27a b x - 12b x) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1163
+
+--S 1164 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3 6 2 4 2 2 3 +-+
+--R (- 7a x - 56a b x - 112a b x - 64b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b
+--R (- a x - 24a b x - 80a b x - 64b x) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6
+--R (7a x + 56a b x + 112a b x + 64b x) |-------- \|b + a x + 25a b x
+--R | 2
+--R \| x
+--R +
+--R 2 2 4 3 2 4
+--R 104a b x + 144a b x + 64b
+--R /
+--R 5 12 4 10 3 2 8 2 3 6 4 4 5 2
+--R (7a x + 70a b x + 231a b x + 344a b x + 240a b x + 64b x )
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 6 14 5 12 4 2 10 3 3 8 2 4 6 5 4
+--R - a x - 27a b x - 155a b x - 377a b x - 456a b x - 272a b x
+--R +
+--R 6 2
+--R - 64b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1164
+
+)clear all
+
+--S 1165 of 1379
+t0:=1/((a+b/x^2)^(5/2)*x^8)
+--R
+--R
+--R 1
+--R (1) ----------------------------------
+--R +--------+
+--R | 2
+--R 2 8 6 2 4 |a x + b
+--R (a x + 2a b x + b x ) |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1165
+
+--S 1166 of 1379
+r0:=1/3/(b*(a+b/x^2)^(3/2)*x^5)+5/2*a*atanh(sqrt(b)/(x*_
+ sqrt(a+b/x^2)))/b^(7/2)+5/3/(b^2*x^3*sqrt(a+b/x^2))-_
+ 5/2*sqrt(a+b/x^2)/(b^3*x)
+--R
+--R
+--R (2)
+--R +--------+
+--R | 2 +-+
+--R 2 5 3 |a x + b \|b
+--R (15a x + 15a b x ) |-------- atanh(------------)
+--R | 2 +--------+
+--R \| x | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R 2 4 2 2 +-+
+--R (- 15a x - 20a b x - 3b )\|b
+--R /
+--R +--------+
+--R | 2
+--R 3 5 4 3 |a x + b +-+
+--R (6a b x + 6b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1166
+
+--S 1167 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R 4 8 3 2 6 2 3 4 4 2 | 2
+--R (- 75a b x - 375a b x - 540a b x - 240a b x )\|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 +-+
+--R (15a x + 210a b x + 615a b x + 660a b x + 240a b x )\|b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R 4 8 3 2 6 2 3 4 4 2 5 | 2
+--R (- 55a b x - 150a b x - 21a b x + 132a b x + 48b )\|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (14a x + 121a b x + 174a b x - 39a b x - 156a b x - 48b )\|b
+--R /
+--R +--------+
+--R 3 4 8 2 5 6 6 4 7 2 +-+ | 2 4 4 10
+--R (30a b x + 150a b x + 216a b x + 96b x )\|b \|a x + b - 6a b x
+--R +
+--R 3 5 8 2 6 6 7 4 8 2
+--R - 84a b x - 246a b x - 264a b x - 96b x
+--R Type: Union(Expression(Integer),...)
+--E 1167
+
+--S 1168 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 |a x + b +-+
+--R (- 75a x - 375a b x - 540a b x - 240a b x ) |-------- \|b
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 5 11 4 9 3 2 7 2 3 5 4 3 |a x + b
+--R (15a x + 210a b x + 615a b x + 660a b x + 240a b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|a x + b - \|b
+--R log(------------------)
+--R x
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 |a x + b +-+
+--R (- 75a x - 375a b x - 540a b x - 240a b x ) |-------- \|b
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R +--------+
+--R | 2
+--R 5 11 4 9 3 2 7 2 3 5 4 3 |a x + b
+--R (15a x + 210a b x + 615a b x + 660a b x + 240a b x ) |--------
+--R | 2
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R atanh(------------)
+--R +--------+
+--R | 2
+--R |a x + b
+--R x |--------
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+
+--R (- 55a x - 150a b x - 21a b x + 132a b x + 48b x) |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 4 8 3 2 6 2 3 4 4 2 5
+--R 75a b x + 400a b x + 655a b x + 380a b x + 48b
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+
+--R (- 15a x - 215a b x - 683a b x - 839a b x - 404a b x - 48b )\|b
+--R +
+--R +--------+
+--R | 2
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b
+--R (14a x + 121a b x + 174a b x - 39a b x - 156a b x - 48b x) |--------
+--R | 2
+--R \| x
+--R /
+--R +--------+
+--R | 2 +--------+
+--R 3 4 9 2 5 7 6 5 7 3 |a x + b | 2
+--R (30a b x + 150a b x + 216a b x + 96b x ) |-------- \|a x + b
+--R | 2
+--R \| x
+--R +
+--R +--------+
+--R | 2
+--R 4 3 11 3 4 9 2 5 7 6 5 7 3 |a x + b +-+
+--R (- 6a b x - 84a b x - 246a b x - 264a b x - 96b x ) |-------- \|b
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1168
+
+--S 1169 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 5 10 4 8 3 2 6 2 3 4 4 2
+--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x
+--R +
+--R 5
+--R - 1024b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3
+--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x
+--R +
+--R 5
+--R - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R *
+--R +--------+
+--R | 2
+--R \|a x + b
+--R +
+--R 5 11 4 9 3 2 7 2 3 5 4 3 5
+--R (11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x + 1024b x)
+--R *
+--R +--------+
+--R | 2
+--R |a x + b +-+
+--R |-------- \|b
+--R | 2
+--R \| x
+--R +
+--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2
+--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x
+--R +
+--R 6
+--R 1024b
+--R /
+--R 7 18 6 16 5 2 14 4 3 12 3 4 10
+--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x
+--R +
+--R 2 5 8 6 6 7 4
+--R 9472a b x + 4864a b x + 1024b x
+--R *
+--R +--------+
+--R | 2 +--------+
+--R |a x + b +-+ | 2
+--R |-------- \|b \|a x + b
+--R | 2
+--R \| x
+--R +
+--R 8 20 7 18 6 2 16 5 3 14 4 4 12
+--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x
+--R +
+--R 3 5 10 2 6 8 7 6 8 4
+--R - 13872a b x - 11776a b x - 5376a b x - 1024b x
+--R *
+--R +--------+
+--R | 2
+--R |a x + b
+--R |--------
+--R | 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1169
+
+)clear all
+
+--S 1170 of 1379
+t0:=(1+1/x^2)^(1/3)/x^3
+--R
+--R
+--R +------+
+--R | 2
+--R |x + 1
+--R |------
+--R 3| 2
+--R \| x
+--R (1) ---------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 1170
+
+--S 1171 of 1379
+r0:=-3/8*(1+1/x^2)^(4/3)
+--R
+--R
+--R +------+
+--R | 2
+--R 2 |x + 1
+--R (- 3x - 3) |------
+--R 3| 2
+--R \| x
+--R (2) --------------------
+--R 2
+--R 8x
+--R Type: Expression(Integer)
+--E 1171
+
+--S 1172 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+
+--R | 2
+--R 2 |x + 1
+--R (- 3x - 3) |------
+--R 3| 2
+--R \| x
+--R (3) --------------------
+--R 4
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 1172
+
+--S 1173 of 1379
+m0:=a0-r0
+--R
+--R
+--R +------+
+--R | 2
+--R 4 |x + 1
+--R (3x - 3) |------
+--R 3| 2
+--R \| x
+--R (4) ------------------
+--R 4
+--R 8x
+--R Type: Expression(Integer)
+--E 1173
+
+--S 1174 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R 4 2
+--R - x + 6x + 7
+--R (5) --------------
+--R +------+2
+--R | 2
+--R 7 |x + 1
+--R 4x |------
+--R 3| 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1174
+
+)clear all
+
+--S 1175 of 1379
+t0:=(1+1/x^2)^(5/3)/x^3
+--R
+--R
+--R +------+2
+--R | 2
+--R 2 |x + 1
+--R (x + 1) |------
+--R 3| 2
+--R \| x
+--R (1) ------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 1175
+
+--S 1176 of 1379
+r0:=-3/16*(1+1/x^2)^(8/3)
+--R
+--R
+--R +------+2
+--R | 2
+--R 4 2 |x + 1
+--R (- 3x - 6x - 3) |------
+--R 3| 2
+--R \| x
+--R (2) ---------------------------
+--R 4
+--R 16x
+--R Type: Expression(Integer)
+--E 1176
+
+--S 1177 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+2
+--R | 2
+--R 4 2 |x + 1
+--R (- 3x - 6x - 3) |------
+--R 3| 2
+--R \| x
+--R (3) ---------------------------
+--R 8
+--R 16x
+--R Type: Union(Expression(Integer),...)
+--E 1177
+
+--S 1178 of 1379
+m0:=a0-r0
+--R
+--R
+--R +------+2
+--R | 2
+--R 8 6 2 |x + 1
+--R (3x + 6x - 6x - 3) |------
+--R 3| 2
+--R \| x
+--R (4) -------------------------------
+--R 8
+--R 16x
+--R Type: Expression(Integer)
+--E 1178
+
+--S 1179 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R 8 6 4 2
+--R - 4x - 5x + 9x + 17x + 7
+--R (5) ----------------------------
+--R +------+
+--R | 2
+--R 11 |x + 1
+--R 4x |------
+--R 3| 2
+--R \| x
+--R Type: Expression(Integer)
+--E 1179
+
+)clear all
+
+--S 1180 of 1379
+t0:=x^5/(a+b/x^3)
+--R
+--R
+--R 8
+--R x
+--R (1) --------
+--R 3
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1180
+
+--S 1181 of 1379
+r0:=-1/3*b*x^3/a^2+1/6*x^6/a+1/3*b^2*log(b+a*x^3)/a^3
+--R
+--R
+--R 2 3 2 6 3
+--R 2b log(a x + b) + a x - 2a b x
+--R (2) ---------------------------------
+--R 3
+--R 6a
+--R Type: Expression(Integer)
+--E 1181
+
+--S 1182 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 2 6 3
+--R 2b log(a x + b) + a x - 2a b x
+--R (3) ---------------------------------
+--R 3
+--R 6a
+--R Type: Union(Expression(Integer),...)
+--E 1182
+
+--S 1183 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1183
+
+--S 1184 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1184
+
+)clear all
+
+--S 1185 of 1379
+t0:=x^4/(a+b/x^3)
+--R
+--R
+--R 7
+--R x
+--R (1) --------
+--R 3
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1185
+
+--S 1186 of 1379
+r0:=-1/2*b*x^2/a^2+1/5*x^5/a-1/3*b^(5/3)*log(b^(1/3)+a^(1/3)*x)/_
+ a^(8/3)+1/6*b^(5/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/_
+ a^(8/3)-b^(5/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/_
+ (a^(8/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2
+--R 5b\|3 \|b log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+2 3+-+ 3+-+ 3+-+2 \|b - 2x\|a
+--R - 10b\|3 \|b log(\|b + x\|a ) - 30b \|b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R +
+--R 5 2 +-+3+-+2
+--R (6a x - 15b x )\|3 \|a
+--R /
+--R 2 +-+3+-+2
+--R 30a \|3 \|a
+--R Type: Expression(Integer)
+--E 1186
+
+--S 1187 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+2
+--R | 2 | 2
+--R +-+ | b | b
+--R 10b\|3 |- -- log(a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b | b | b 2
+--R - 5b\|3 |- -- log(- a x |- -- - b |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+2
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- - 2b x\|3
+--R | 2 3| 2
+--R | b \| a 5 2 +-+
+--R 30b |- -- atan(------------------------ + (6a x - 15b x )\|3
+--R 3| 2 +----+2
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R /
+--R 2 +-+
+--R 30a \|3
+--R Type: Union(Expression(Integer),...)
+--E 1187
+
+--S 1188 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2
+--R - b\|3 \|b log(\|b - x\|a \|b + x \|a )
+--R +
+--R +----+ +----+2
+--R | 2 | 2
+--R +-+3+-+2 3+-+ 3+-+ +-+ | b 3+-+2 | b
+--R 2b\|3 \|b log(\|b + x\|a ) + 2b\|3 |- -- \|a log(a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 | b | b 2
+--R - b\|3 |- -- \|a log(- a x |- -- - b |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+2
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- - 2b x\|3
+--R | 2 3| 2 3+-+ 3+-+
+--R | b 3+-+2 \| a 3+-+2 \|b - 2x\|a
+--R 6b |- -- \|a atan(------------------------ + 6b \|b atan(-------------)
+--R 3| 2 +----+2 +-+3+-+
+--R \| a | 2 \|3 \|b
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R /
+--R 2 +-+3+-+2
+--R 6a \|3 \|a
+--R Type: Expression(Integer)
+--E 1188
+
+--S 1189 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1189
+
+)clear all
+
+--S 1190 of 1379
+t0:=x^3/(a+b/x^3)
+--R
+--R
+--R 6
+--R x
+--R (1) --------
+--R 3
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1190
+
+--S 1191 of 1379
+r0:=-b*x/a^2+1/4*x^4/a+1/3*b^(4/3)*log(b^(1/3)+a^(1/3)*x)/a^(7/3)-_
+ 1/6*b^(4/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(7/3)-_
+ b^(4/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2
+--R - 2b\|3 \|b log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+ 3+-+ 3+-+ 3+-+ \|b - 2x\|a
+--R 4b\|3 \|b log(\|b + x\|a ) - 12b\|b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R +
+--R 4 +-+3+-+
+--R (3a x - 12b x)\|3 \|a
+--R /
+--R 2 +-+3+-+
+--R 12a \|3 \|a
+--R Type: Expression(Integer)
+--E 1191
+
+--S 1192 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2 +-+ +-+ +-+
+--R +-+ |b |b |b 2 +-+ |b |b
+--R - 2b\|3 3|- log(3|- - x 3|- + x + 4b\|3 3|- log(3|- + x)
+--R \|a \|a \|a \|a \|a
+--R +
+--R +-+
+--R +-+ |b +-+
+--R +-+ \|3 3|- - 2x\|3
+--R |b \|a 4 +-+
+--R - 12b 3|- atan(----------------- + (3a x - 12b x)\|3
+--R \|a +-+
+--R |b
+--R 3 3|-
+--R \|a
+--R /
+--R 2 +-+
+--R 12a \|3
+--R Type: Union(Expression(Integer),...)
+--E 1192
+
+--S 1193 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R b\|3 \|b log(\|b - x\|a \|b + x \|a ) - 2b\|3 \|b log(\|b + x\|a )
+--R +
+--R +-+ +-+2 +-+ +-+ +-+
+--R +-+3+-+ |b |b |b 2 +-+3+-+ |b |b
+--R - b\|3 \|a 3|- log(3|- - x 3|- + x + 2b\|3 \|a 3|- log(3|- + x)
+--R \|a \|a \|a \|a \|a
+--R +
+--R +-+
+--R +-+ |b +-+
+--R +-+ \|3 3|- - 2x\|3 3+-+ 3+-+
+--R 3+-+ |b \|a 3+-+ \|b - 2x\|a
+--R - 6b\|a 3|- atan(----------------- + 6b\|b atan(-------------)
+--R \|a +-+ +-+3+-+
+--R |b \|3 \|b
+--R 3 3|-
+--R \|a
+--R /
+--R 2 +-+3+-+
+--R 6a \|3 \|a
+--R Type: Expression(Integer)
+--E 1193
+
+--S 1194 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1194
+
+)clear all
+
+--S 1195 of 1379
+t0:=x^2/(a+b/x^3)
+--R
+--R
+--R 5
+--R x
+--R (1) --------
+--R 3
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1195
+
+--S 1196 of 1379
+r0:=1/3*x^3/a-1/3*b*log(b+a*x^3)/a^2
+--R
+--R
+--R 3 3
+--R - b log(a x + b) + a x
+--R (2) ------------------------
+--R 2
+--R 3a
+--R Type: Expression(Integer)
+--E 1196
+
+--S 1197 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R - b log(a x + b) + a x
+--R (3) ------------------------
+--R 2
+--R 3a
+--R Type: Union(Expression(Integer),...)
+--E 1197
+
+--S 1198 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1198
+
+--S 1199 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1199
+
+)clear all
+
+--S 1200 of 1379
+t0:=x/(a+b/x^3)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 3
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1200
+
+--S 1201 of 1379
+r0:=1/2*x^2/a+1/3*b^(2/3)*log(b^(1/3)+a^(1/3)*x)/a^(5/3)-_
+ 1/6*b^(2/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(5/3)+_
+ b^(2/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+
+--R - \|3 \|b log(\|b - x\|a \|b + x \|a ) + 2\|3 \|b log(\|b + x\|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 \|b - 2x\|a 2 +-+3+-+2
+--R 6\|b atan(-------------) + 3x \|3 \|a
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R +-+3+-+2
+--R 6a\|3 \|a
+--R Type: Expression(Integer)
+--E 1201
+
+--S 1202 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2
+--R | 2 | 2
+--R +-+ |b |b
+--R 2\|3 |-- log(a |-- + b x)
+--R 3| 2 3| 2
+--R \|a \|a
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |b |b |b 2
+--R - \|3 |-- log(- a x |-- + b |-- + b x )
+--R 3| 2 3| 2 3| 2
+--R \|a \|a \|a
+--R +
+--R +--+2
+--R | 2
+--R +-+ |b +-+
+--R +--+ a\|3 |-- - 2b x\|3
+--R | 2 3| 2
+--R |b \|a 2 +-+
+--R 6 |-- atan(---------------------- + 3x \|3
+--R 3| 2 +--+2
+--R \|a | 2
+--R |b
+--R 3a |--
+--R 3| 2
+--R \|a
+--R /
+--R +-+
+--R 6a\|3
+--R Type: Union(Expression(Integer),...)
+--E 1202
+
+--S 1203 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+2
+--R | 2 | 2
+--R +-+3+-+2 |b |b
+--R 2\|3 \|a |-- log(a |-- + b x)
+--R 3| 2 3| 2
+--R \|a \|a
+--R +
+--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+
+--R \|3 \|b log(\|b - x\|a \|b + x \|a ) - 2\|3 \|b log(\|b + x\|a )
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+3+-+2 |b |b |b 2
+--R - \|3 \|a |-- log(- a x |-- + b |-- + b x )
+--R 3| 2 3| 2 3| 2
+--R \|a \|a \|a
+--R +
+--R +--+2
+--R | 2
+--R +-+ |b +-+
+--R +--+ a\|3 |-- - 2b x\|3
+--R | 2 3| 2 3+-+ 3+-+
+--R 3+-+2 |b \|a 3+-+2 \|b - 2x\|a
+--R 6\|a |-- atan(---------------------- - 6\|b atan(-------------)
+--R 3| 2 +--+2 +-+3+-+
+--R \|a | 2 \|3 \|b
+--R |b
+--R 3a |--
+--R 3| 2
+--R \|a
+--R /
+--R +-+3+-+2
+--R 6a\|3 \|a
+--R Type: Expression(Integer)
+--E 1203
+
+--S 1204 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1204
+
+)clear all
+
+--S 1205 of 1379
+t0:=1/(a+b/x^3)
+--R
+--R
+--R 3
+--R x
+--R (1) --------
+--R 3
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1205
+
+--S 1206 of 1379
+r0:=x/a-1/3*b^(1/3)*log(b^(1/3)+a^(1/3)*x)/a^(4/3)+1/6*b^(1/3)*_
+ log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(4/3)+b^(1/3)*_
+ atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R \|3 \|b log(\|b - x\|a \|b + x \|a ) - 2\|3 \|b log(\|b + x\|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+ \|b - 2x\|a +-+3+-+
+--R 6\|b atan(-------------) + 6x\|3 \|a
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R +-+3+-+
+--R 6a\|3 \|a
+--R Type: Expression(Integer)
+--E 1206
+
+--S 1207 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+2 +---+ +---+ +---+
+--R +-+ | b | b | b 2 +-+ | b | b
+--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x)
+--R \| a \| a \| a \| a \| a
+--R +
+--R +---+
+--R +-+ | b +-+
+--R +---+ \|3 3|- - + 2x\|3
+--R | b \| a +-+
+--R - 6 3|- - atan(------------------- + 6x\|3
+--R \| a +---+
+--R | b
+--R 3 3|- -
+--R \| a
+--R /
+--R +-+
+--R 6a\|3
+--R Type: Union(Expression(Integer),...)
+--E 1207
+
+--S 1208 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R - \|3 \|b log(\|b - x\|a \|b + x \|a ) + 2\|3 \|b log(\|b + x\|a )
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | b 3+-+ | b | b 2
+--R - \|3 3|- - \|a log(3|- - + x 3|- - + x )
+--R \| a \| a \| a
+--R +
+--R +---+
+--R +-+ | b +-+
+--R +---+ +---+ +---+ \|3 3|- - + 2x\|3
+--R +-+ | b 3+-+ | b | b 3+-+ \| a
+--R 2\|3 3|- - \|a log(- 3|- - + x - 6 3|- - \|a atan(-------------------)
+--R \| a \| a \| a +---+
+--R | b
+--R 3 3|- -
+--R \| a
+--R +
+--R 3+-+ 3+-+
+--R 3+-+ \|b - 2x\|a
+--R - 6\|b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R +-+3+-+
+--R 6a\|3 \|a
+--R Type: Expression(Integer)
+--E 1208
+
+--S 1209 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1209
+
+)clear all
+
+--S 1210 of 1379
+t0:=1/((a+b/x^3)*x)
+--R
+--R
+--R 2
+--R x
+--R (1) --------
+--R 3
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1210
+
+--S 1211 of 1379
+r0:=1/3*log(b+a*x^3)/a
+--R
+--R
+--R 3
+--R log(a x + b)
+--R (2) -------------
+--R 3a
+--R Type: Expression(Integer)
+--E 1211
+
+--S 1212 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R log(a x + b)
+--R (3) -------------
+--R 3a
+--R Type: Union(Expression(Integer),...)
+--E 1212
+
+--S 1213 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1213
+
+--S 1214 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1214
+
+)clear all
+
+--S 1215 of 1379
+t0:=1/((a+b/x^3)*x^2)
+--R
+--R
+--R x
+--R (1) --------
+--R 3
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1215
+
+--S 1216 of 1379
+r0:=-1/3*log(b^(1/3)+a^(1/3)*x)/(a^(2/3)*b^(1/3))+1/6*log(b^(2/3)-_
+ a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(2/3)*b^(1/3))-atan((b^(1/3)-_
+ 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+ 3+-+ 3+-+
+--R \|3 log(\|b - x\|a \|b + x \|a ) - 2\|3 log(\|b + x\|a )
+--R +
+--R 3+-+ 3+-+
+--R \|b - 2x\|a
+--R - 6atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R +-+3+-+2 3+-+
+--R 6\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1216
+
+--S 1217 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----+2 +-----+ +-----+2
+--R +-+ 3| 2 2 3| 2 +-+ 3| 2
+--R - \|3 log(x \|- a b + a x \|- a b - a b) + 2\|3 log(x \|- a b + a b)
+--R +
+--R +-----+2
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b - a b\|3
+--R - 6atan(-------------------------)
+--R 3a b
+--R /
+--R +-----+
+--R +-+3| 2
+--R 6\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 1217
+
+--S 1218 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2
+--R - \|3 \|- a b log(\|b - x\|a \|b + x \|a )
+--R +
+--R +-----+
+--R +-+3| 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(\|b + x\|a )
+--R +
+--R +-----+2 +-----+
+--R +-+3+-+2 3+-+ 3| 2 2 3| 2
+--R - \|3 \|a \|b log(x \|- a b + a x \|- a b - a b)
+--R +
+--R +-----+2
+--R +-+3+-+2 3+-+ 3| 2
+--R 2\|3 \|a \|b log(x \|- a b + a b)
+--R +
+--R +-----+2
+--R +-+3| 2 +-+ +-----+ 3+-+ 3+-+
+--R 3+-+2 3+-+ 2x\|3 \|- a b - a b\|3 3| 2 \|b - 2x\|a
+--R - 6\|a \|b atan(------------------------- + 6\|- a b atan(-------------)
+--R 3a b +-+3+-+
+--R \|3 \|b
+--R /
+--R +-----+
+--R +-+3| 2 3+-+2 3+-+
+--R 6\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1218
+
+--S 1219 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1219
+
+)clear all
+
+--S 1220 of 1379
+t0:=1/((a+b/x^3)*x^3)
+--R
+--R
+--R 1
+--R (1) --------
+--R 3
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1220
+
+--S 1221 of 1379
+r0:=1/3*log(b^(1/3)+a^(1/3)*x)/(a^(1/3)*b^(2/3))-1/6*log(b^(2/3)-_
+ a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(1/3)*b^(2/3))-atan((b^(1/3)-_
+ 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+ 3+-+ 3+-+
+--R - \|3 log(\|b - x\|a \|b + x \|a ) + 2\|3 log(\|b + x\|a )
+--R +
+--R 3+-+ 3+-+
+--R \|b - 2x\|a
+--R - 6atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R +-+3+-+3+-+2
+--R 6\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1221
+
+--S 1222 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+2 +----+ +----+
+--R +-+ 2 3| 2 3| 2 2 +-+ 3| 2
+--R - \|3 log(x \|a b - b x\|a b + b ) + 2\|3 log(x\|a b + b)
+--R +
+--R +----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - b\|3
+--R 6atan(---------------------)
+--R 3b
+--R /
+--R +----+
+--R +-+3| 2
+--R 6\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 1222
+
+--S 1223 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----+2 +----+
+--R +-+3+-+3+-+2 2 3| 2 3| 2 2
+--R - \|3 \|a \|b log(x \|a b - b x\|a b + b )
+--R +
+--R +----+
+--R +-+3+-+3+-+2 3| 2
+--R 2\|3 \|a \|b log(x\|a b + b)
+--R +
+--R +----+
+--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2
+--R \|3 \|a b log(\|b - x\|a \|b + x \|a )
+--R +
+--R +----+
+--R +----+ +-+3| 2 +-+
+--R +-+3| 2 3+-+ 3+-+ 3+-+3+-+2 2x\|3 \|a b - b\|3
+--R - 2\|3 \|a b log(\|b + x\|a ) + 6\|a \|b atan(---------------------)
+--R 3b
+--R +
+--R +----+ 3+-+ 3+-+
+--R 3| 2 \|b - 2x\|a
+--R 6\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R +----+
+--R +-+3+-+3+-+2 3| 2
+--R 6\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1223
+
+--S 1224 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1224
+
+)clear all
+
+--S 1225 of 1379
+t0:=1/((a+b/x^3)*x^4)
+--R
+--R
+--R 1
+--R (1) ----------
+--R 4
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 1225
+
+--S 1226 of 1379
+r0:=-1/3*log(a+b/x^3)/b
+--R
+--R
+--R 3
+--R a x + b
+--R log(--------)
+--R 3
+--R x
+--R (2) - -------------
+--R 3b
+--R Type: Expression(Integer)
+--E 1226
+
+--S 1227 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3
+--R - log(a x + b) + 3log(x)
+--R (3) -------------------------
+--R 3b
+--R Type: Union(Expression(Integer),...)
+--E 1227
+
+--S 1228 of 1379
+m0:=a0-r0
+--R
+--R
+--R 3
+--R 3 a x + b
+--R - log(a x + b) + 3log(x) + log(--------)
+--R 3
+--R x
+--R (4) -----------------------------------------
+--R 3b
+--R Type: Expression(Integer)
+--E 1228
+
+--S 1229 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1229
+
+)clear all
+
+--S 1230 of 1379
+t0:=1/((a+b/x^3)*x^5)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 5 2
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 1230
+
+--S 1231 of 1379
+r0:=(-1)/(b*x)+1/3*a^(1/3)*log(b^(1/3)+a^(1/3)*x)/b^(4/3)-1/6*a^(1/3)*_
+ log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/b^(4/3)+a^(1/3)*_
+ atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R - x\|3 \|a log(\|b - x\|a \|b + x \|a ) + 2x\|3 \|a log(\|b + x\|a )
+--R +
+--R 3+-+ 3+-+
+--R 3+-+ \|b - 2x\|a +-+3+-+
+--R 6x\|a atan(-------------) - 6\|3 \|b
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R +-+3+-+
+--R 6b x\|3 \|b
+--R Type: Expression(Integer)
+--E 1231
+
+--S 1232 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2 +-+ +-+2 +-+
+--R +-+ |a |a +-+ |a |a |a 2
+--R 2x\|3 3|- log(b 3|- + a x - x\|3 3|- log(- b x 3|- + b 3|- + a x )
+--R \|b \|b \|b \|b \|b
+--R +
+--R +-+2
+--R +-+ |a +-+
+--R +-+ b\|3 3|- - 2a x\|3
+--R |a \|b +-+
+--R 6x 3|- atan(--------------------- - 6\|3
+--R \|b +-+2
+--R |a
+--R 3b 3|-
+--R \|b
+--R /
+--R +-+
+--R 6b x\|3
+--R Type: Union(Expression(Integer),...)
+--E 1232
+
+--S 1233 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R \|3 \|a log(\|b - x\|a \|b + x \|a ) - 2\|3 \|a log(\|b + x\|a )
+--R +
+--R +-+ +-+2
+--R +-+ |a 3+-+ |a
+--R 2\|3 3|- \|b log(b 3|- + a x)
+--R \|b \|b
+--R +
+--R +-+ +-+2 +-+
+--R +-+ |a 3+-+ |a |a 2
+--R - \|3 3|- \|b log(- b x 3|- + b 3|- + a x )
+--R \|b \|b \|b
+--R +
+--R +-+2
+--R +-+ |a +-+
+--R +-+ b\|3 3|- - 2a x\|3 3+-+ 3+-+
+--R |a 3+-+ \|b 3+-+ \|b - 2x\|a
+--R 6 3|- \|b atan(--------------------- - 6\|a atan(-------------)
+--R \|b +-+2 +-+3+-+
+--R |a \|3 \|b
+--R 3b 3|-
+--R \|b
+--R /
+--R +-+3+-+
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 1233
+
+--S 1234 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1234
+
+)clear all
+
+--S 1235 of 1379
+t0:=1/((a+b/x^3)*x^6)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 6 3
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 1235
+
+--S 1236 of 1379
+r0:=(-1/2)/(b*x^2)-1/3*a^(2/3)*log(b^(1/3)+a^(1/3)*x)/b^(5/3)+_
+ 1/6*a^(2/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/b^(5/3)+_
+ a^(2/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2
+--R x \|3 \|a log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 +-+3+-+2 3+-+ 3+-+ 2 3+-+2 \|b - 2x\|a +-+3+-+2
+--R - 2x \|3 \|a log(\|b + x\|a ) + 6x \|a atan(------------- - 3\|3 \|b
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R 2 +-+3+-+2
+--R 6b x \|3 \|b
+--R Type: Expression(Integer)
+--E 1236
+
+--S 1237 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R 2 +-+ | a 2 | a | a 2 2
+--R - x \|3 |- -- log(b |- -- + a b x |- -- + a x )
+--R 3| 2 3| 2 3| 2
+--R \| b \| b \| b
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R 2 +-+ | a | a
+--R 2x \|3 |- -- log(- b |- -- + a x)
+--R 3| 2 3| 2
+--R \| b \| b
+--R +
+--R +----+
+--R | 2
+--R +-+ | a +-+
+--R +----+ b\|3 |- -- + 2a x\|3
+--R | 2 3| 2
+--R 2 | a \| b +-+
+--R - 6x |- -- atan(----------------------- - 3\|3
+--R 3| 2 +----+
+--R \| b | 2
+--R | a
+--R 3b |- --
+--R 3| 2
+--R \| b
+--R /
+--R 2 +-+
+--R 6b x \|3
+--R Type: Union(Expression(Integer),...)
+--E 1237
+
+--S 1238 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+
+--R - \|3 \|a log(\|b - x\|a \|b + x \|a ) + 2\|3 \|a log(\|b + x\|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | a 3+-+2 2 | a | a 2 2
+--R - \|3 |- -- \|b log(b |- -- + a b x |- -- + a x )
+--R 3| 2 3| 2 3| 2
+--R \| b \| b \| b
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R +-+ | a 3+-+2 | a
+--R 2\|3 |- -- \|b log(- b |- -- + a x)
+--R 3| 2 3| 2
+--R \| b \| b
+--R +
+--R +----+
+--R | 2
+--R +-+ | a +-+
+--R +----+ b\|3 |- -- + 2a x\|3
+--R | 2 3| 2 3+-+ 3+-+
+--R | a 3+-+2 \| b 3+-+2 \|b - 2x\|a
+--R - 6 |- -- \|b atan(----------------------- - 6\|a atan(-------------)
+--R 3| 2 +----+ +-+3+-+
+--R \| b | 2 \|3 \|b
+--R | a
+--R 3b |- --
+--R 3| 2
+--R \| b
+--R /
+--R +-+3+-+2
+--R 6b\|3 \|b
+--R Type: Expression(Integer)
+--E 1238
+
+--S 1239 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1239
+
+)clear all
+
+--S 1240 of 1379
+t0:=1/((a+b/x^3)*x^7)
+--R
+--R
+--R 1
+--R (1) -----------
+--R 7 4
+--R a x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 1240
+
+--S 1241 of 1379
+r0:=(-1/3)/(b*x^3)-a*log(x)/b^2+1/3*a*log(b+a*x^3)/b^2
+--R
+--R
+--R 3 3 3
+--R a x log(a x + b) - 3a x log(x) - b
+--R (2) -----------------------------------
+--R 2 3
+--R 3b x
+--R Type: Expression(Integer)
+--E 1241
+
+--S 1242 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3
+--R a x log(a x + b) - 3a x log(x) - b
+--R (3) -----------------------------------
+--R 2 3
+--R 3b x
+--R Type: Union(Expression(Integer),...)
+--E 1242
+
+--S 1243 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1243
+
+--S 1244 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1244
+
+)clear all
+
+--S 1245 of 1379
+t0:=x^5/(a+b/x^3)^2
+--R
+--R
+--R 11
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1245
+
+--S 1246 of 1379
+r0:=-2/3*b*x^3/a^3+1/6*x^6/a^2+1/3*b^3/(a^4*(b+a*x^3))+b^2*log(b+a*x^3)/a^4
+--R
+--R
+--R 2 3 3 3 3 9 2 6 2 3 3
+--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b
+--R (2) -------------------------------------------------------------
+--R 5 3 4
+--R 6a x + 6a b
+--R Type: Expression(Integer)
+--E 1246
+
+--S 1247 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 3 3 3 3 9 2 6 2 3 3
+--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b
+--R (3) -------------------------------------------------------------
+--R 5 3 4
+--R 6a x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 1247
+
+--S 1248 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1248
+
+--S 1249 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1249
+
+)clear all
+
+--S 1250 of 1379
+t0:=x^4/(a+b/x^3)^2
+--R
+--R
+--R 10
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1250
+
+--S 1251 of 1379
+r0:=-4/3*b*x^2/a^3+8/15*x^5/a^2-1/3*x^8/(a*(b+a*x^3))-8/9*b^(5/3)*_
+ log(b^(1/3)+a^(1/3)*x)/a^(11/3)+4/9*b^(5/3)*log(b^(2/3)-a^(1/3)*_
+ b^(1/3)*x+a^(2/3)*x^2)/a^(11/3)-8/3*b^(5/3)*atan((b^(1/3)-_
+ 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(11/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 2 +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2
+--R (20a b x + 20b )\|3 \|b log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3 2 +-+3+-+2 3+-+ 3+-+
+--R (- 40a b x - 40b )\|3 \|b log(\|b + x\|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 2 3+-+2 \|b - 2x\|a
+--R (- 120a b x - 120b )\|b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R +
+--R 2 8 5 2 2 +-+3+-+2
+--R (9a x - 36a b x - 60b x )\|3 \|a
+--R /
+--R 4 3 3 +-+3+-+2
+--R (45a x + 45a b)\|3 \|a
+--R Type: Expression(Integer)
+--E 1251
+
+--S 1252 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+2
+--R | 2 | 2
+--R 3 2 +-+ | b | b
+--R (40a b x + 40b )\|3 |- -- log(a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R 3 2 +-+ | b | b | b 2
+--R (- 20a b x - 20b )\|3 |- -- log(- a x |- -- - b |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+2
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- - 2b x\|3
+--R | 2 3| 2
+--R 3 2 | b \| a
+--R (120a b x + 120b ) |- -- atan(------------------------)
+--R 3| 2 +----+2
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R 2 8 5 2 2 +-+
+--R (9a x - 36a b x - 60b x )\|3
+--R /
+--R 4 3 3 +-+
+--R (45a x + 45a b)\|3
+--R Type: Union(Expression(Integer),...)
+--E 1252
+
+--S 1253 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2
+--R - 4b\|3 \|b log(\|b - x\|a \|b + x \|a )
+--R +
+--R +----+ +----+2
+--R | 2 | 2
+--R +-+3+-+2 3+-+ 3+-+ +-+ | b 3+-+2 | b
+--R 8b\|3 \|b log(\|b + x\|a ) + 8b\|3 |- -- \|a log(a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 | b | b 2
+--R - 4b\|3 |- -- \|a log(- a x |- -- - b |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+2
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- - 2b x\|3
+--R | 2 3| 2
+--R | b 3+-+2 \| a
+--R 24b |- -- \|a atan(------------------------)
+--R 3| 2 +----+2
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 \|b - 2x\|a
+--R 24b \|b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R 3 +-+3+-+2
+--R 9a \|3 \|a
+--R Type: Expression(Integer)
+--E 1253
+
+--S 1254 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1254
+
+)clear all
+
+--S 1255 of 1379
+t0:=x^3/(a+b/x^3)^2
+--R
+--R
+--R 9
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1255
+
+--S 1256 of 1379
+r0:=-7/3*b*x/a^3+7/12*x^4/a^2-1/3*x^7/(a*(b+a*x^3))+7/9*b^(4/3)*_
+ log(b^(1/3)+a^(1/3)*x)/a^(10/3)-7/18*b^(4/3)*log(b^(2/3)-a^(1/3)*_
+ b^(1/3)*x+a^(2/3)*x^2)/a^(10/3)-7/3*b^(4/3)*atan((b^(1/3)-_
+ 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 2 +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2
+--R (- 14a b x - 14b )\|3 \|b log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3 2 +-+3+-+ 3+-+ 3+-+
+--R (28a b x + 28b )\|3 \|b log(\|b + x\|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 2 3+-+ \|b - 2x\|a
+--R (- 84a b x - 84b )\|b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R +
+--R 2 7 4 2 +-+3+-+
+--R (9a x - 63a b x - 84b x)\|3 \|a
+--R /
+--R 4 3 3 +-+3+-+
+--R (36a x + 36a b)\|3 \|a
+--R Type: Expression(Integer)
+--E 1256
+
+--S 1257 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-+ +-+2 +-+
+--R 3 2 +-+ |b |b |b 2
+--R (- 14a b x - 14b )\|3 3|- log(3|- - x 3|- + x )
+--R \|a \|a \|a
+--R +
+--R +-+ +-+
+--R 3 2 +-+ |b |b
+--R (28a b x + 28b )\|3 3|- log(3|- + x)
+--R \|a \|a
+--R +
+--R +-+
+--R +-+ |b +-+
+--R +-+ \|3 3|- - 2x\|3
+--R 3 2 |b \|a
+--R (- 84a b x - 84b ) 3|- atan(-----------------)
+--R \|a +-+
+--R |b
+--R 3 3|-
+--R \|a
+--R +
+--R 2 7 4 2 +-+
+--R (9a x - 63a b x - 84b x)\|3
+--R /
+--R 4 3 3 +-+
+--R (36a x + 36a b)\|3
+--R Type: Union(Expression(Integer),...)
+--E 1257
+
+--S 1258 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R 7b\|3 \|b log(\|b - x\|a \|b + x \|a ) - 14b\|3 \|b log(\|b + x\|a )
+--R +
+--R +-+ +-+2 +-+ +-+ +-+
+--R +-+3+-+ |b |b |b 2 +-+3+-+ |b |b
+--R - 7b\|3 \|a 3|- log(3|- - x 3|- + x + 14b\|3 \|a 3|- log(3|- + x)
+--R \|a \|a \|a \|a \|a
+--R +
+--R +-+
+--R +-+ |b +-+
+--R +-+ \|3 3|- - 2x\|3 3+-+ 3+-+
+--R 3+-+ |b \|a 3+-+ \|b - 2x\|a
+--R - 42b\|a 3|- atan(----------------- + 42b\|b atan(-------------)
+--R \|a +-+ +-+3+-+
+--R |b \|3 \|b
+--R 3 3|-
+--R \|a
+--R /
+--R 3 +-+3+-+
+--R 18a \|3 \|a
+--R Type: Expression(Integer)
+--E 1258
+
+--S 1259 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1259
+
+)clear all
+
+--S 1260 of 1379
+t0:=x^2/(a+b/x^3)^2
+--R
+--R
+--R 8
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1260
+
+--S 1261 of 1379
+r0:=1/3*x^3/a^2-1/3*b^2/(a^3*(b+a*x^3))-2/3*b*log(b+a*x^3)/a^3
+--R
+--R
+--R 3 2 3 2 6 3 2
+--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b
+--R (2) ---------------------------------------------------
+--R 4 3 3
+--R 3a x + 3a b
+--R Type: Expression(Integer)
+--E 1261
+
+--S 1262 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 3 2 6 3 2
+--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b
+--R (3) ---------------------------------------------------
+--R 4 3 3
+--R 3a x + 3a b
+--R Type: Union(Expression(Integer),...)
+--E 1262
+
+--S 1263 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1263
+
+--S 1264 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1264
+
+)clear all
+
+--S 1265 of 1379
+t0:=x/(a+b/x^3)^2
+--R
+--R
+--R 7
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1265
+
+--S 1266 of 1379
+r0:=5/6*x^2/a^2-1/3*x^5/(a*(b+a*x^3))+5/9*b^(2/3)*log(b^(1/3)+_
+ a^(1/3)*x)/a^(8/3)-5/18*b^(2/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*_
+ x+a^(2/3)*x^2)/a^(8/3)+5/3*b^(2/3)*atan((b^(1/3)-2*a^(1/3)*x)/_
+ (b^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2
+--R (- 5a x - 5b)\|3 \|b log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3 +-+3+-+2 3+-+ 3+-+
+--R (10a x + 10b)\|3 \|b log(\|b + x\|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 3+-+2 \|b - 2x\|a 5 2 +-+3+-+2
+--R (30a x + 30b)\|b atan(-------------) + (9a x + 15b x )\|3 \|a
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R 3 3 2 +-+3+-+2
+--R (18a x + 18a b)\|3 \|a
+--R Type: Expression(Integer)
+--E 1266
+
+--S 1267 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2
+--R | 2 | 2
+--R 3 +-+ |b |b
+--R (10a x + 10b)\|3 |-- log(a |-- + b x)
+--R 3| 2 3| 2
+--R \|a \|a
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R 3 +-+ |b |b |b 2
+--R (- 5a x - 5b)\|3 |-- log(- a x |-- + b |-- + b x )
+--R 3| 2 3| 2 3| 2
+--R \|a \|a \|a
+--R +
+--R +--+2
+--R | 2
+--R +-+ |b +-+
+--R +--+ a\|3 |-- - 2b x\|3
+--R | 2 3| 2
+--R 3 |b \|a 5 2 +-+
+--R (30a x + 30b) |-- atan(---------------------- + (9a x + 15b x )\|3
+--R 3| 2 +--+2
+--R \|a | 2
+--R |b
+--R 3a |--
+--R 3| 2
+--R \|a
+--R /
+--R 3 3 2 +-+
+--R (18a x + 18a b)\|3
+--R Type: Union(Expression(Integer),...)
+--E 1267
+
+--S 1268 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+2
+--R | 2 | 2
+--R +-+3+-+2 |b |b
+--R 10\|3 \|a |-- log(a |-- + b x)
+--R 3| 2 3| 2
+--R \|a \|a
+--R +
+--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+
+--R 5\|3 \|b log(\|b - x\|a \|b + x \|a ) - 10\|3 \|b log(\|b + x\|a )
+--R +
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+3+-+2 |b |b |b 2
+--R - 5\|3 \|a |-- log(- a x |-- + b |-- + b x )
+--R 3| 2 3| 2 3| 2
+--R \|a \|a \|a
+--R +
+--R +--+2
+--R | 2
+--R +-+ |b +-+
+--R +--+ a\|3 |-- - 2b x\|3
+--R | 2 3| 2 3+-+ 3+-+
+--R 3+-+2 |b \|a 3+-+2 \|b - 2x\|a
+--R 30\|a |-- atan(---------------------- - 30\|b atan(-------------)
+--R 3| 2 +--+2 +-+3+-+
+--R \|a | 2 \|3 \|b
+--R |b
+--R 3a |--
+--R 3| 2
+--R \|a
+--R /
+--R 2 +-+3+-+2
+--R 18a \|3 \|a
+--R Type: Expression(Integer)
+--E 1268
+
+--S 1269 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1269
+
+)clear all
+
+--S 1270 of 1379
+t0:=1/(a+b/x^3)^2
+--R
+--R
+--R 6
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1270
+
+--S 1271 of 1379
+r0:=4/3*x/a^2-1/3*x^4/(a*(b+a*x^3))-4/9*b^(1/3)*log(b^(1/3)+_
+ a^(1/3)*x)/a^(7/3)+2/9*b^(1/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*_
+ x+a^(2/3)*x^2)/a^(7/3)+4/3*b^(1/3)*atan((b^(1/3)-2*a^(1/3)*x)/_
+ (b^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2
+--R (2a x + 2b)\|3 \|b log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3 +-+3+-+ 3+-+ 3+-+
+--R (- 4a x - 4b)\|3 \|b log(\|b + x\|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 3+-+ \|b - 2x\|a 4 +-+3+-+
+--R (12a x + 12b)\|b atan(-------------) + (9a x + 12b x)\|3 \|a
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R 3 3 2 +-+3+-+
+--R (9a x + 9a b)\|3 \|a
+--R Type: Expression(Integer)
+--E 1271
+
+--S 1272 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+2 +---+
+--R 3 +-+ | b | b | b 2
+--R (- 2a x - 2b)\|3 3|- - log(3|- - + x 3|- - + x )
+--R \| a \| a \| a
+--R +
+--R +---+ +---+
+--R 3 +-+ | b | b
+--R (4a x + 4b)\|3 3|- - log(- 3|- - + x)
+--R \| a \| a
+--R +
+--R +---+
+--R +-+ | b +-+
+--R +---+ \|3 3|- - + 2x\|3
+--R 3 | b \| a 4 +-+
+--R (- 12a x - 12b) 3|- - atan(------------------- + (9a x + 12b x)\|3
+--R \| a +---+
+--R | b
+--R 3 3|- -
+--R \| a
+--R /
+--R 3 3 2 +-+
+--R (9a x + 9a b)\|3
+--R Type: Union(Expression(Integer),...)
+--E 1272
+
+--S 1273 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+
+--R - 2\|3 \|b log(\|b - x\|a \|b + x \|a ) + 4\|3 \|b log(\|b + x\|a )
+--R +
+--R +---+ +---+2 +---+
+--R +-+ | b 3+-+ | b | b 2
+--R - 2\|3 3|- - \|a log(3|- - + x 3|- - + x )
+--R \| a \| a \| a
+--R +
+--R +---+
+--R +-+ | b +-+
+--R +---+ +---+ +---+ \|3 3|- - + 2x\|3
+--R +-+ | b 3+-+ | b | b 3+-+ \| a
+--R 4\|3 3|- - \|a log(- 3|- - + x - 12 3|- - \|a atan(-------------------)
+--R \| a \| a \| a +---+
+--R | b
+--R 3 3|- -
+--R \| a
+--R +
+--R 3+-+ 3+-+
+--R 3+-+ \|b - 2x\|a
+--R - 12\|b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R 2 +-+3+-+
+--R 9a \|3 \|a
+--R Type: Expression(Integer)
+--E 1273
+
+--S 1274 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1274
+
+)clear all
+
+--S 1275 of 1379
+t0:=1/((a+b/x^3)^2*x)
+--R
+--R
+--R 5
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1275
+
+--S 1276 of 1379
+r0:=1/3*b/(a^2*(b+a*x^3))+1/3*log(b+a*x^3)/a^2
+--R
+--R
+--R 3 3
+--R (a x + b)log(a x + b) + b
+--R (2) ---------------------------
+--R 3 3 2
+--R 3a x + 3a b
+--R Type: Expression(Integer)
+--E 1276
+
+--S 1277 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3
+--R (a x + b)log(a x + b) + b
+--R (3) ---------------------------
+--R 3 3 2
+--R 3a x + 3a b
+--R Type: Union(Expression(Integer),...)
+--E 1277
+
+--S 1278 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1278
+
+--S 1279 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1279
+
+)clear all
+
+--S 1280 of 1379
+t0:=1/((a+b/x^3)^2*x^2)
+--R
+--R
+--R 4
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1280
+
+--S 1281 of 1379
+r0:=-1/3*x^2/(a*(b+a*x^3))-2/9*log(b^(1/3)+a^(1/3)*x)/(a^(5/3)*b^(1/3))+_
+ 1/9*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(5/3)*b^(1/3))-_
+ 2/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(5/3)*_
+ b^(1/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2
+--R (a x + b)\|3 log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a
+--R (- 2a x - 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R +
+--R 2 +-+3+-+2 3+-+
+--R - 3x \|3 \|a \|b
+--R /
+--R 2 3 +-+3+-+2 3+-+
+--R (9a x + 9a b)\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1281
+
+--S 1282 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----+2 +-----+
+--R 3 +-+ 3| 2 2 3| 2
+--R (- a x - b)\|3 log(x \|- a b + a x \|- a b - a b)
+--R +
+--R +-----+2
+--R 3 +-+ 3| 2
+--R (2a x + 2b)\|3 log(x \|- a b + a b)
+--R +
+--R +-----+2
+--R +-+3| 2 +-+ +-----+
+--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2
+--R (- 6a x - 6b)atan(-------------------------) - 3x \|3 \|- a b
+--R 3a b
+--R /
+--R +-----+
+--R 2 3 +-+3| 2
+--R (9a x + 9a b)\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 1282
+
+--S 1283 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2
+--R - \|3 \|- a b log(\|b - x\|a \|b + x \|a )
+--R +
+--R +-----+
+--R +-+3| 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(\|b + x\|a )
+--R +
+--R +-----+2 +-----+
+--R +-+3+-+2 3+-+ 3| 2 2 3| 2
+--R - \|3 \|a \|b log(x \|- a b + a x \|- a b - a b)
+--R +
+--R +-----+2
+--R +-+3+-+2 3+-+ 3| 2
+--R 2\|3 \|a \|b log(x \|- a b + a b)
+--R +
+--R +-----+2
+--R +-+3| 2 +-+ +-----+ 3+-+ 3+-+
+--R 3+-+2 3+-+ 2x\|3 \|- a b - a b\|3 3| 2 \|b - 2x\|a
+--R - 6\|a \|b atan(------------------------- + 6\|- a b atan(-------------)
+--R 3a b +-+3+-+
+--R \|3 \|b
+--R /
+--R +-----+
+--R +-+3| 2 3+-+2 3+-+
+--R 9a\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1283
+
+--S 1284 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1284
+
+)clear all
+
+--S 1285 of 1379
+t0:=1/((a+b/x^3)^2*x^3)
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1285
+
+--S 1286 of 1379
+r0:=-1/3*x/(a*(b+a*x^3))+1/9*log(b^(1/3)+a^(1/3)*x)/(a^(4/3)*b^(2/3))-_
+ 1/18*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(4/3)*b^(2/3))-_
+ 1/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(4/3)*_
+ b^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2
+--R (- a x - b)\|3 log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a
+--R (2a x + 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R +
+--R +-+3+-+3+-+2
+--R - 6x\|3 \|a \|b
+--R /
+--R 2 3 +-+3+-+3+-+2
+--R (18a x + 18a b)\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1286
+
+--S 1287 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+2 +----+
+--R 3 +-+ 2 3| 2 3| 2 2
+--R (- a x - b)\|3 log(x \|a b - b x\|a b + b )
+--R +
+--R +----+
+--R 3 +-+ 3| 2
+--R (2a x + 2b)\|3 log(x\|a b + b)
+--R +
+--R +----+
+--R +-+3| 2 +-+ +----+
+--R 3 2x\|3 \|a b - b\|3 +-+3| 2
+--R (6a x + 6b)atan(---------------------) - 6x\|3 \|a b
+--R 3b
+--R /
+--R +----+
+--R 2 3 +-+3| 2
+--R (18a x + 18a b)\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 1287
+
+--S 1288 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----+2 +----+
+--R +-+3+-+3+-+2 2 3| 2 3| 2 2
+--R - \|3 \|a \|b log(x \|a b - b x\|a b + b )
+--R +
+--R +----+
+--R +-+3+-+3+-+2 3| 2
+--R 2\|3 \|a \|b log(x\|a b + b)
+--R +
+--R +----+
+--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2
+--R \|3 \|a b log(\|b - x\|a \|b + x \|a )
+--R +
+--R +----+
+--R +----+ +-+3| 2 +-+
+--R +-+3| 2 3+-+ 3+-+ 3+-+3+-+2 2x\|3 \|a b - b\|3
+--R - 2\|3 \|a b log(\|b + x\|a ) + 6\|a \|b atan(---------------------)
+--R 3b
+--R +
+--R +----+ 3+-+ 3+-+
+--R 3| 2 \|b - 2x\|a
+--R 6\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R +----+
+--R +-+3+-+3+-+2 3| 2
+--R 18a\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1288
+
+--S 1289 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1289
+
+)clear all
+
+--S 1290 of 1379
+t0:=1/((a+b/x^3)^2*x^4)
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1290
+
+--S 1291 of 1379
+r0:=1/3/(b*(a+b/x^3))
+--R
+--R
+--R 3
+--R x
+--R (2) -------------
+--R 3 2
+--R 3a b x + 3b
+--R Type: Fraction(Polynomial(Integer))
+--E 1291
+
+--S 1292 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - ------------
+--R 2 3
+--R 3a x + 3a b
+--R Type: Union(Expression(Integer),...)
+--E 1292
+
+--S 1293 of 1379
+m0:=a0-r0
+--R
+--R
+--R 1
+--R (4) - ----
+--R 3a b
+--R Type: Expression(Integer)
+--E 1293
+
+--S 1294 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1294
+
+)clear all
+
+--S 1295 of 1379
+t0:=1/((a+b/x^3)^2*x^5)
+--R
+--R
+--R x
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1295
+
+--S 1296 of 1379
+r0:=1/3*x^2/(b*(b+a*x^3))-1/9*log(b^(1/3)+a^(1/3)*x)/(a^(2/3)*b^(4/3))+_
+ 1/18*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(2/3)*b^(4/3))-_
+ 1/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(2/3)*_
+ b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2
+--R (a x + b)\|3 log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a
+--R (- 2a x - 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R +
+--R 2 +-+3+-+2 3+-+
+--R 6x \|3 \|a \|b
+--R /
+--R 3 2 +-+3+-+2 3+-+
+--R (18a b x + 18b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1296
+
+--S 1297 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----+2 +-----+
+--R 3 +-+ 3| 2 2 3| 2
+--R (- a x - b)\|3 log(x \|- a b + a x \|- a b - a b)
+--R +
+--R +-----+2
+--R 3 +-+ 3| 2
+--R (2a x + 2b)\|3 log(x \|- a b + a b)
+--R +
+--R +-----+2
+--R +-+3| 2 +-+ +-----+
+--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2
+--R (- 6a x - 6b)atan(-------------------------) + 6x \|3 \|- a b
+--R 3a b
+--R /
+--R +-----+
+--R 3 2 +-+3| 2
+--R (18a b x + 18b )\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 1297
+
+--S 1298 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2
+--R - \|3 \|- a b log(\|b - x\|a \|b + x \|a )
+--R +
+--R +-----+
+--R +-+3| 2 3+-+ 3+-+
+--R 2\|3 \|- a b log(\|b + x\|a )
+--R +
+--R +-----+2 +-----+
+--R +-+3+-+2 3+-+ 3| 2 2 3| 2
+--R - \|3 \|a \|b log(x \|- a b + a x \|- a b - a b)
+--R +
+--R +-----+2
+--R +-+3+-+2 3+-+ 3| 2
+--R 2\|3 \|a \|b log(x \|- a b + a b)
+--R +
+--R +-----+2
+--R +-+3| 2 +-+ +-----+ 3+-+ 3+-+
+--R 3+-+2 3+-+ 2x\|3 \|- a b - a b\|3 3| 2 \|b - 2x\|a
+--R - 6\|a \|b atan(------------------------- + 6\|- a b atan(-------------)
+--R 3a b +-+3+-+
+--R \|3 \|b
+--R /
+--R +-----+
+--R +-+3| 2 3+-+2 3+-+
+--R 18b\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 1298
+
+--S 1299 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1299
+
+)clear all
+
+--S 1300 of 1379
+t0:=1/((a+b/x^3)^2*x^6)
+--R
+--R
+--R 1
+--R (1) -------------------
+--R 2 6 3 2
+--R a x + 2a b x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 1300
+
+--S 1301 of 1379
+r0:=1/3*x/(b*(b+a*x^3))+2/9*log(b^(1/3)+a^(1/3)*x)/(a^(1/3)*b^(5/3))-_
+ 1/9*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(1/3)*b^(5/3))-_
+ 2/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(1/3)*_
+ b^(5/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2
+--R (- a x - b)\|3 log(\|b - x\|a \|b + x \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a
+--R (2a x + 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R +
+--R +-+3+-+3+-+2
+--R 3x\|3 \|a \|b
+--R /
+--R 3 2 +-+3+-+3+-+2
+--R (9a b x + 9b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 1301
+
+--S 1302 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+2 +----+
+--R 3 +-+ 2 3| 2 3| 2 2
+--R (- a x - b)\|3 log(x \|a b - b x\|a b + b )
+--R +
+--R +----+
+--R 3 +-+ 3| 2
+--R (2a x + 2b)\|3 log(x\|a b + b)
+--R +
+--R +----+
+--R +-+3| 2 +-+ +----+
+--R 3 2x\|3 \|a b - b\|3 +-+3| 2
+--R (6a x + 6b)atan(---------------------) + 3x\|3 \|a b
+--R 3b
+--R /
+--R +----+
+--R 3 2 +-+3| 2
+--R (9a b x + 9b )\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 1302
+
+--S 1303 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----+2 +----+
+--R +-+3+-+3+-+2 2 3| 2 3| 2 2
+--R - \|3 \|a \|b log(x \|a b - b x\|a b + b )
+--R +
+--R +----+
+--R +-+3+-+3+-+2 3| 2
+--R 2\|3 \|a \|b log(x\|a b + b)
+--R +
+--R +----+
+--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2
+--R \|3 \|a b log(\|b - x\|a \|b + x \|a )
+--R +
+--R +----+
+--R +----+ +-+3| 2 +-+
+--R +-+3| 2 3+-+ 3+-+ 3+-+3+-+2 2x\|3 \|a b - b\|3
+--R - 2\|3 \|a b log(\|b + x\|a ) + 6\|a \|b atan(---------------------)
+--R 3b
+--R +
+--R +----+ 3+-+ 3+-+
+--R 3| 2 \|b - 2x\|a
+--R 6\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|b
+--R /
+--R +----+
+--R +-+3+-+3+-+2 3| 2
+--R 9b\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 1303
+
+--S 1304 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1304
+
+)clear all
+
+--S 1305 of 1379
+t0:=1/((a+b/x^3)^2*x^7)
+--R
+--R
+--R 1
+--R (1) --------------------
+--R 2 7 4 2
+--R a x + 2a b x + b x
+--R Type: Fraction(Polynomial(Integer))
+--E 1305
+
+--S 1306 of 1379
+r0:=1/3/(b*(b+a*x^3))+log(x)/b^2-1/3*log(b+a*x^3)/b^2
+--R
+--R
+--R 3 3 3
+--R (- a x - b)log(a x + b) + (3a x + 3b)log(x) + b
+--R (2) --------------------------------------------------
+--R 2 3 3
+--R 3a b x + 3b
+--R Type: Expression(Integer)
+--E 1306
+
+--S 1307 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 3
+--R (- a x - b)log(a x + b) + (3a x + 3b)log(x) + b
+--R (3) --------------------------------------------------
+--R 2 3 3
+--R 3a b x + 3b
+--R Type: Union(Expression(Integer),...)
+--E 1307
+
+--S 1308 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 1308
+
+--S 1309 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 1309
+
+)clear all
+
+--S 1310 of 1379
+t0:=x^5*sqrt(a+b/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R 5 |a x + b
+--R (1) x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 1310
+
+--S 1311 of 1379
+r0:=-1/12*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(3/2)+1/12*b*x^3*_
+ sqrt(a+b/x^3)/a+1/6*x^6*sqrt(a+b/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 2 \| x 6 3 +-+ |a x + b
+--R - b atanh(-----------) + (2a x + b x )\|a |--------
+--R +-+ | 3
+--R \|a \| x
+--R (2) ------------------------------------------------------
+--R +-+
+--R 12a\|a
+--R Type: Expression(Integer)
+--E 1311
+
+--S 1312 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+ +--------+
+--R | 4 | 4 | 3
+--R | b 2 2 | b |a x + b 2 3 3
+--R - 2a |---- log(8a x |---- |-------- + 2a b x + b )
+--R | 3 | 3 \| x
+--R \|16a \|16a
+--R +
+--R +--------+
+--R | 3
+--R 5 2 |a x + b
+--R (2a x + b x ) |--------
+--R \| x
+--R /
+--R 12a
+--R Type: Union(Expression(Integer),...)
+--E 1312
+
+--S 1313 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----+ +----+ +--------+
+--R | 4 | 4 | 3
+--R +-+ | b 2 2 | b |a x + b 2 3 3
+--R - 2a\|a |---- log(8a x |---- |-------- + 2a b x + b )
+--R | 3 | 3 \| x
+--R \|16a \|16a
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 2 \| x 5 2 +-+ |a x + b
+--R b atanh(-----------) + (2a x + b x )\|a |--------
+--R +-+ \| x
+--R \|a
+--R +
+--R +--------+
+--R | 3
+--R 6 3 +-+ |a x + b
+--R (- 2a x - b x )\|a |--------
+--R | 3
+--R \| x
+--R /
+--R +-+
+--R 12a\|a
+--R Type: Expression(Integer)
+--E 1313
+
+--S 1314 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +----+ +--------+ +--------+
+--R | 4 | 3 | 3
+--R 3 7 2 4 | b 2 7 3 4 |a x + b |a x + b
+--R ((- 8a x - 8a b x ) |---- + (2a b x + b x ) |-------- ) |--------
+--R | 3 | 3 \| x
+--R \|16a \| x
+--R +
+--R +--------+ +----+
+--R | 3 | 4
+--R 3 8 2 5 |a x + b | b 2 2 8 3 5 4 2
+--R (8a x + 8a b x ) |-------- |---- - 2a b x - 3a b x - b x
+--R | 3 | 3
+--R \| x \|16a
+--R /
+--R +--------+ +----+ +--------+ +--------+
+--R | 3 | 4 | 3 | 3
+--R 2 2 |a x + b | b |a x + b 2 3 3 |a x + b
+--R 8a x |-------- |---- |-------- + (2a b x + b ) |--------
+--R | 3 | 3 \| x | 3
+--R \| x \|16a \| x
+--R Type: Expression(Integer)
+--E 1314
+
+)clear all
+
+--S 1315 of 1379
+t0:=x^2*sqrt(a+b/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R 2 |a x + b
+--R (1) x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 1315
+
+--S 1316 of 1379
+r0:=1/3*b*atanh(sqrt(a+b/x^3)/sqrt(a))/sqrt(a)+1/3*x^3*sqrt(a+b/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R \| x 3 +-+ |a x + b
+--R b atanh(-----------) + x \|a |--------
+--R +-+ | 3
+--R \|a \| x
+--R (2) ----------------------------------------
+--R +-+
+--R 3\|a
+--R Type: Expression(Integer)
+--E 1316
+
+--S 1317 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--+ +--+ +--------+ +--------+
+--R | 2 | 2 | 3 | 3
+--R |b 2 |b |a x + b 3 2 2 |a x + b
+--R - |-- log(2a x |-- |-------- - 2a b x - b ) + 2x |--------
+--R \| a \| a \| x \| x
+--R (3) -----------------------------------------------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 1317
+
+--S 1318 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+ +--------+
+--R | 2 | 2 | 3
+--R +-+ |b 2 |b |a x + b 3 2
+--R - \|a |-- log(2a x |-- |-------- - 2a b x - b )
+--R \| a \| a \| x
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+ +--------+
+--R | 3 | 3 | 3
+--R \| x 2 +-+ |a x + b 3 +-+ |a x + b
+--R - 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |--------
+--R +-+ \| x | 3
+--R \|a \| x
+--R /
+--R +-+
+--R 6\|a
+--R Type: Expression(Integer)
+--E 1318
+
+--S 1319 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +--+ +--------+
+--R | 3 | 2 | 3
+--R 4 |a x + b |b 4 2 |a x + b
+--R (- 2a x |-------- |-- - 2a b x - b x) |--------
+--R | 3 \| a \| x
+--R \| x
+--R +
+--R +--+ +--------+
+--R | 2 | 3
+--R 2 5 2 |b 5 2 2 |a x + b
+--R (2a x + 2a b x ) |-- + (2a b x + b x ) |--------
+--R \| a | 3
+--R \| x
+--R /
+--R +--+ +--------+
+--R | 2 | 3
+--R 2 |b |a x + b 3 2
+--R 2a x |-- |-------- - 2a b x - b
+--R \| a \| x
+--R Type: Expression(Integer)
+--E 1319
+
+)clear all
+
+--S 1320 of 1379
+t0:=sqrt(a+b/x^3)/x
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R | 3
+--R \| x
+--R (1) -----------
+--R x
+--R Type: Expression(Integer)
+--E 1320
+
+--S 1321 of 1379
+r0:=2/3*atanh(sqrt(a+b/x^3)/sqrt(a))*sqrt(a)-2/3*sqrt(a+b/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R +-+ \| x |a x + b
+--R 2\|a atanh(-----------) - 2 |--------
+--R +-+ | 3
+--R \|a \| x
+--R (2) --------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 1321
+
+--S 1322 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R +--+ 2 +--+ |a x + b 3 |a x + b
+--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4 |--------
+--R \| x \| x
+--R (3) ----------------------------------------------------------
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 1322
+
+--S 1323 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 3
+--R |a x + b
+--R +--------+ |--------
+--R | 3 | 3
+--R +--+ 2 +--+ |a x + b 3 +-+ \| x
+--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4x\|a atanh(-----------)
+--R \| x +-+
+--R \|a
+--R +
+--R +--------+ +--------+
+--R | 3 | 3
+--R |a x + b |a x + b
+--R - 4 |-------- + 4x |--------
+--R \| x | 3
+--R \| x
+--R /
+--R 6x
+--R Type: Expression(Integer)
+--E 1323
+
+--S 1324 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +--------+
+--R | 3 | 3
+--R 5 2 +--+ 5 2 |a x + b |a x + b
+--R ((- a x - b x )\|4a + (- 2a x - b x ) |-------- ) |--------
+--R | 3 \| x
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 6 3 |a x + b +--+ 2 6 3 2
+--R (a x + b x ) |-------- \|4a + 2a x + 3a b x + b
+--R | 3
+--R \| x
+--R /
+--R +--------+ +--------+ +--------+
+--R | 3 | 3 | 3
+--R 6 |a x + b +--+ |a x + b 7 4 |a x + b
+--R x |-------- \|4a |-------- + (- 2a x - b x ) |--------
+--R | 3 \| x | 3
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1324
+
+)clear all
+
+--S 1325 of 1379
+t0:=sqrt(a+b/x^3)/x^4
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R | 3
+--R \| x
+--R (1) -----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 1325
+
+--S 1326 of 1379
+r0:=-2/9*(a+b/x^3)^(3/2)/b
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (- 2a x - 2b) |--------
+--R | 3
+--R \| x
+--R (2) -------------------------
+--R 3
+--R 9b x
+--R Type: Expression(Integer)
+--E 1326
+
+--S 1327 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (- 2a x - 2b) |--------
+--R \| x
+--R (3) -------------------------
+--R 6
+--R 9b x
+--R Type: Union(Expression(Integer),...)
+--E 1327
+
+--S 1328 of 1379
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 |a x + b 6 3 |a x + b
+--R (- 2a x - 2b) |-------- + (2a x + 2b x ) |--------
+--R \| x | 3
+--R \| x
+--R (4) ------------------------------------------------------
+--R 6
+--R 9b x
+--R Type: Expression(Integer)
+--E 1328
+
+--S 1329 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R 4 2 |a x + b 2 6 3 2 |a x + b
+--R (- 9a b x - 9b x) |-------- + (4a x + 17a b x + 13b ) |--------
+--R \| x | 3
+--R \| x
+--R (5) --------------------------------------------------------------------
+--R +--------+ +--------+
+--R | 3 | 3
+--R 8 |a x + b |a x + b
+--R 9b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 1329
+
+)clear all
+
+--S 1330 of 1379
+t0:=sqrt(a+b/x^3)/x^7
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R | 3
+--R \| x
+--R (1) -----------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 1330
+
+--S 1331 of 1379
+r0:=2/9*a*(a+b/x^3)^(3/2)/b^2-2/15*(a+b/x^3)^(5/2)/b^2
+--R
+--R
+--R +--------+
+--R | 3
+--R 2 6 3 2 |a x + b
+--R (4a x - 2a b x - 6b ) |--------
+--R | 3
+--R \| x
+--R (2) ----------------------------------
+--R 2 6
+--R 45b x
+--R Type: Expression(Integer)
+--E 1331
+
+--S 1332 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 2 6 3 2 |a x + b
+--R (4a x - 2a b x - 6b ) |--------
+--R \| x
+--R (3) ----------------------------------
+--R 2 9
+--R 45b x
+--R Type: Union(Expression(Integer),...)
+--E 1332
+
+--S 1333 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 6 3 2 |a x + b 2 9 6 2 3 |a x + b
+--R (4a x - 2a b x - 6b ) |-------- + (- 4a x + 2a b x + 6b x ) |--------
+--R \| x | 3
+--R \| x
+--R ---------------------------------------------------------------------------
+--R 2 9
+--R 45b x
+--R Type: Expression(Integer)
+--E 1333
+
+--S 1334 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 3
+--R 2 4 3 |a x + b
+--R (- 45a b x - 45b x) |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (- 8a x - 4a b x + 61a b x + 57b ) |--------
+--R | 3
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 11 |a x + b |a x + b
+--R 45b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 1334
+
+)clear all
+
+--S 1335 of 1379
+t0:=sqrt(a+b/x^3)/x^10
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R | 3
+--R \| x
+--R (1) -----------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 1335
+
+--S 1336 of 1379
+r0:=-2/9*a^2*(a+b/x^3)^(3/2)/b^3+4/15*a*(a+b/x^3)^(5/2)/b^3-_
+ 2/21*(a+b/x^3)^(7/2)/b^3
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 30b ) |--------
+--R | 3
+--R \| x
+--R (2) ------------------------------------------------
+--R 3 9
+--R 315b x
+--R Type: Expression(Integer)
+--E 1336
+
+--S 1337 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 30b ) |--------
+--R \| x
+--R (3) ------------------------------------------------
+--R 3 12
+--R 315b x
+--R Type: Union(Expression(Integer),...)
+--E 1337
+
+--S 1338 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 30b ) |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 3 12 2 9 2 6 3 3 |a x + b
+--R (16a x - 8a b x + 6a b x + 30b x ) |--------
+--R | 3
+--R \| x
+--R /
+--R 3 12
+--R 315b x
+--R Type: Expression(Integer)
+--E 1338
+
+--S 1339 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 3
+--R 3 4 4 |a x + b
+--R (- 315a b x - 315b x) |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 4 12 3 9 2 2 6 3 3 4 |a x + b
+--R (32a x + 16a b x - 4a b x + 387a b x + 375b ) |--------
+--R | 3
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 14 |a x + b |a x + b
+--R 315b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 1339
+
+)clear all
+
+--S 1340 of 1379
+t0:=(a+b/x^3)^(3/2)*x^5
+--R
+--R
+--R +--------+
+--R | 3
+--R 5 2 |a x + b
+--R (1) (a x + b x ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 1340
+
+--S 1341 of 1379
+r0:=1/6*(a+b/x^3)^(3/2)*x^6+1/4*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/_
+ sqrt(a)+1/4*b*x^3*sqrt(a+b/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 2 \| x 6 3 +-+ |a x + b
+--R 3b atanh(-----------) + (2a x + 5b x )\|a |--------
+--R +-+ | 3
+--R \|a \| x
+--R (2) ------------------------------------------------------
+--R +-+
+--R 12\|a
+--R Type: Expression(Integer)
+--E 1341
+
+--S 1342 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+ +--------+
+--R | 4 | 4 | 3
+--R |9b 2 |9b |a x + b 2 3 3
+--R - 2 |--- log(8a x |--- |-------- - 6a b x - 3b )
+--R \|16a \|16a \| x
+--R +
+--R +--------+
+--R | 3
+--R 5 2 |a x + b
+--R (2a x + 5b x ) |--------
+--R \| x
+--R /
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 1342
+
+--S 1343 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+ +---+ +--------+
+--R | 4 | 4 | 3
+--R +-+ |9b 2 |9b |a x + b 2 3 3
+--R - 2\|a |--- log(8a x |--- |-------- - 6a b x - 3b )
+--R \|16a \|16a \| x
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 2 \| x 5 2 +-+ |a x + b
+--R - 3b atanh(-----------) + (2a x + 5b x )\|a |--------
+--R +-+ \| x
+--R \|a
+--R +
+--R +--------+
+--R | 3
+--R 6 3 +-+ |a x + b
+--R (- 2a x - 5b x )\|a |--------
+--R | 3
+--R \| x
+--R /
+--R +-+
+--R 12\|a
+--R Type: Expression(Integer)
+--E 1343
+
+--S 1344 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +---+
+--R | 4
+--R 3 8 2 5 2 2 |9b
+--R (- 8a x - 16a b x - 8a b x ) |---
+--R \|16a
+--R +
+--R +--------+
+--R | 3
+--R 2 2 8 3 5 4 2 |a x + b
+--R (- 6a b x - 9a b x - 3b x ) |--------
+--R | 3
+--R \| x
+--R *
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R \| x
+--R +
+--R +--------+ +---+
+--R | 3 | 4
+--R 3 9 2 6 2 3 |a x + b |9b 3 2 9 2 3 6
+--R (8a x + 16a b x + 8a b x ) |-------- |--- + 6a b x + 15a b x
+--R | 3 \|16a
+--R \| x
+--R +
+--R 4 3 5
+--R 12a b x + 3b
+--R /
+--R +--------+ +---+ +--------+ +--------+
+--R | 3 | 4 | 3 | 3
+--R 3 |a x + b |9b |a x + b 2 4 3 |a x + b
+--R 8a x |-------- |--- |-------- + (- 6a b x - 3b x) |--------
+--R | 3 \|16a \| x | 3
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1344
+
+)clear all
+
+--S 1345 of 1379
+t0:=(a+b/x^3)^(3/2)*x^2
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (a x + b) |--------
+--R | 3
+--R \| x
+--R (1) ---------------------
+--R x
+--R Type: Expression(Integer)
+--E 1345
+
+--S 1346 of 1379
+r0:=1/3*(a+b/x^3)^(3/2)*x^3+b*atanh(sqrt(a+b/x^3)/sqrt(a))*sqrt(a)-_
+ b*sqrt(a+b/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R +-+ \| x 3 |a x + b
+--R 3b\|a atanh(-----------) + (a x - 2b) |--------
+--R +-+ | 3
+--R \|a \| x
+--R (2) -------------------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 1346
+
+--S 1347 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-----+ +-----+ | 3
+--R | 2 2 | 2 |a x + b 3 2
+--R - x\|9a b log(2x \|9a b |-------- - 6a b x - 3b )
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (2a x - 4b) |--------
+--R \| x
+--R /
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 1347
+
+--S 1348 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-----+ +-----+ | 3
+--R | 2 2 | 2 |a x + b 3 2
+--R - x\|9a b log(2x \|9a b |-------- - 6a b x - 3b )
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R +-+ \| x 3 |a x + b
+--R - 6b x\|a atanh(-----------) + (2a x - 4b) |--------
+--R +-+ \| x
+--R \|a
+--R +
+--R +--------+
+--R | 3
+--R 4 |a x + b
+--R (- 2a x + 4b x) |--------
+--R | 3
+--R \| x
+--R /
+--R 6x
+--R Type: Expression(Integer)
+--E 1348
+
+--S 1349 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +-----+
+--R 2 8 5 2 2 | 2
+--R (- 2a x - 4a b x - 2b x )\|9a b
+--R +
+--R +--------+
+--R | 3
+--R 2 8 2 5 3 2 |a x + b
+--R (- 6a b x - 9a b x - 3b x ) |--------
+--R | 3
+--R \| x
+--R *
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3 +-----+
+--R 2 9 6 2 3 |a x + b | 2 3 9 2 2 6
+--R (2a x + 4a b x + 2b x ) |-------- \|9a b + 6a b x + 15a b x
+--R | 3
+--R \| x
+--R +
+--R 3 3 4
+--R 12a b x + 3b
+--R /
+--R +--------+ +--------+ +--------+
+--R | 3 +-----+ | 3 | 3
+--R 6 |a x + b | 2 |a x + b 7 2 4 |a x + b
+--R 2x |-------- \|9a b |-------- + (- 6a b x - 3b x ) |--------
+--R | 3 \| x | 3
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1349
+
+)clear all
+
+--S 1350 of 1379
+t0:=(a+b/x^3)^(3/2)/x
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (a x + b) |--------
+--R | 3
+--R \| x
+--R (1) ---------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 1350
+
+--S 1351 of 1379
+r0:=-2/9*(a+b/x^3)^(3/2)+2/3*a^(3/2)*atanh(sqrt(a+b/x^3)/sqrt(a))-_
+ 2/3*a*sqrt(a+b/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 3 +-+ \| x 3 |a x + b
+--R 6a x \|a atanh(-----------) + (- 8a x - 2b) |--------
+--R +-+ | 3
+--R \|a \| x
+--R (2) -------------------------------------------------------
+--R 3
+--R 9x
+--R Type: Expression(Integer)
+--E 1351
+
+--S 1352 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +---+ +---+ | 3
+--R 4 | 3 2 | 3 |a x + b 2 3
+--R - 3x \|4a log(x \|4a |-------- - 2a x - a b)
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (- 16a x - 4b) |--------
+--R \| x
+--R /
+--R 4
+--R 18x
+--R Type: Union(Expression(Integer),...)
+--E 1352
+
+--S 1353 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +---+ +---+ | 3
+--R 4 | 3 2 | 3 |a x + b 2 3
+--R - 3x \|4a log(x \|4a |-------- - 2a x - a b)
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 4 +-+ \| x 3 |a x + b
+--R - 12a x \|a atanh(-----------) + (- 16a x - 4b) |--------
+--R +-+ \| x
+--R \|a
+--R +
+--R +--------+
+--R | 3
+--R 4 |a x + b
+--R (16a x + 4b x) |--------
+--R | 3
+--R \| x
+--R /
+--R 4
+--R 18x
+--R Type: Expression(Integer)
+--E 1353
+
+--S 1354 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +---+
+--R 2 8 5 2 2 | 3
+--R (- a x - 2a b x - b x )\|4a
+--R +
+--R +--------+
+--R | 3
+--R 3 8 2 5 2 2 |a x + b
+--R (- 2a x - 3a b x - a b x ) |--------
+--R | 3
+--R \| x
+--R *
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3 +---+
+--R 2 9 6 2 3 |a x + b | 3 4 9 3 6 2 2 3 3
+--R (a x + 2a b x + b x ) |-------- \|4a + 2a x + 5a b x + 4a b x + a b
+--R | 3
+--R \| x
+--R /
+--R +--------+ +--------+ +--------+
+--R | 3 +---+ | 3 | 3
+--R 9 |a x + b | 3 |a x + b 2 10 7 |a x + b
+--R x |-------- \|4a |-------- + (- 2a x - a b x ) |--------
+--R | 3 \| x | 3
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 1354
+
+)clear all
+
+--S 1355 of 1379
+t0:=(a+b/x^3)^(3/2)/x^4
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (a x + b) |--------
+--R | 3
+--R \| x
+--R (1) ---------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 1355
+
+--S 1356 of 1379
+r0:=-2/15*(a+b/x^3)^(5/2)/b
+--R
+--R
+--R +--------+
+--R | 3
+--R 2 6 3 2 |a x + b
+--R (- 2a x - 4a b x - 2b ) |--------
+--R | 3
+--R \| x
+--R (2) ------------------------------------
+--R 6
+--R 15b x
+--R Type: Expression(Integer)
+--E 1356
+
+--S 1357 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 2 6 3 2 |a x + b
+--R (- 2a x - 4a b x - 2b ) |--------
+--R \| x
+--R (3) ------------------------------------
+--R 9
+--R 15b x
+--R Type: Union(Expression(Integer),...)
+--E 1357
+
+--S 1358 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 6 3 2 |a x + b 2 9 6 2 3 |a x + b
+--R (- 2a x - 4a b x - 2b ) |-------- + (2a x + 4a b x + 2b x ) |--------
+--R \| x | 3
+--R \| x
+--R ---------------------------------------------------------------------------
+--R 9
+--R 15b x
+--R Type: Expression(Integer)
+--E 1358
+
+--S 1359 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 3
+--R 2 7 2 4 3 |a x + b
+--R (- 15a b x - 30a b x - 15b x) |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (4a x + 27a b x + 42a b x + 19b ) |--------
+--R | 3
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 3 | 3
+--R 11 |a x + b |a x + b
+--R 15b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 1359
+
+)clear all
+
+--S 1360 of 1379
+t0:=(a+b/x^3)^(3/2)/x^7
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (a x + b) |--------
+--R | 3
+--R \| x
+--R (1) ---------------------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 1360
+
+--S 1361 of 1379
+r0:=2/15*a*(a+b/x^3)^(5/2)/b^2-2/21*(a+b/x^3)^(7/2)/b^2
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (4a x - 2a b x - 16a b x - 10b ) |--------
+--R | 3
+--R \| x
+--R (2) ----------------------------------------------
+--R 2 9
+--R 105b x
+--R Type: Expression(Integer)
+--E 1361
+
+--S 1362 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (4a x - 2a b x - 16a b x - 10b ) |--------
+--R \| x
+--R (3) ----------------------------------------------
+--R 2 12
+--R 105b x
+--R Type: Union(Expression(Integer),...)
+--E 1362
+
+--S 1363 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (4a x - 2a b x - 16a b x - 10b ) |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 3 12 2 9 2 6 3 3 |a x + b
+--R (- 4a x + 2a b x + 16a b x + 10b x ) |--------
+--R | 3
+--R \| x
+--R /
+--R 2 12
+--R 105b x
+--R Type: Expression(Integer)
+--E 1363
+
+--S 1364 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 3
+--R 2 2 7 3 4 4 |a x + b
+--R (- 105a b x - 210a b x - 105b x) |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 4 12 3 9 2 2 6 3 3 4 |a x + b
+--R (- 8a x - 4a b x + 141a b x + 262a b x + 125b ) |--------
+--R | 3
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 14 |a x + b |a x + b
+--R 105b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 1364
+
+)clear all
+
+--S 1365 of 1379
+t0:=(a+b/x^3)^(3/2)/x^10
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (a x + b) |--------
+--R | 3
+--R \| x
+--R (1) ---------------------
+--R 13
+--R x
+--R Type: Expression(Integer)
+--E 1365
+
+--S 1366 of 1379
+r0:=-2/15*a^2*(a+b/x^3)^(5/2)/b^3+4/21*a*(a+b/x^3)^(7/2)/b^3-_
+ 2/27*(a+b/x^3)^(9/2)/b^3
+--R
+--R
+--R +--------+
+--R | 3
+--R 4 12 3 9 2 2 6 3 3 4 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |--------
+--R | 3
+--R \| x
+--R (2) -------------------------------------------------------------
+--R 3 12
+--R 945b x
+--R Type: Expression(Integer)
+--E 1366
+
+--S 1367 of 1379
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 4 12 3 9 2 2 6 3 3 4 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |--------
+--R \| x
+--R (3) -------------------------------------------------------------
+--R 3 15
+--R 945b x
+--R Type: Union(Expression(Integer),...)
+--E 1367
+
+--S 1368 of 1379
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 3
+--R 4 12 3 9 2 2 6 3 3 4 |a x + b
+--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 4 15 3 12 2 2 9 3 6 4 3 |a x + b
+--R (16a x - 8a b x + 6a b x + 100a b x + 70b x ) |--------
+--R | 3
+--R \| x
+--R /
+--R 3 15
+--R 945b x
+--R Type: Expression(Integer)
+--E 1368
+
+--S 1369 of 1379
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 3
+--R 2 3 7 4 4 5 |a x + b
+--R (- 945a b x - 1890a b x - 945b x) |--------
+--R \| x
+--R +
+--R 5 15 4 12 3 2 9 2 3 6 4 3 5
+--R (32a x + 16a b x - 4a b x + 1157a b x + 2230a b x + 1085b )
+--R *
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R | 3
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 17 |a x + b |a x + b
+--R 945b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 1369
+
+)clear all
+
+--S 1370 of 1379
+t0:=x^4*sqrt(8+27/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R 4 |8x + 27
+--R (1) x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 1370
+
+--S 1371 of 1379
+--r0:=81/160*x^2*sqrt(8+27/x^3)+1/5*x^5*sqrt(8+27/x^3)+_
+-- 729/160*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_
+-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3)
+--E 1371
+
+--S 1372 of 1379
+--a0:=integrate(t0,x)
+--E 1372
+
+--S 1373 of 1379
+--m0:=a0-r0
+--E 1373
+
+--S 1374 of 1379
+--d0:=D(m0,x)
+--E 1374
+
+)clear all
+
+--S 1375 of 1379
+t0:=x*sqrt(8+27/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R |8x + 27
+--R (1) x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 1375
+
+--S 1376 of 1379
+--r0:=1/2*x^2*sqrt(8+27/x^3)-27/2*(-1)^(1/4)*elliptic_f(%i*_
+-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_
+-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3)
+--E 1376
+
+--S 1377 of 1379
+--a0:=integrate(t0,x)
+--E 1377
+
+--S 1378 of 1379
+--m0:=a0-r0
+--E 1378
+
+--S 1379 of 1379
+--d0:=D(m0,x)
+--E 1379
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich4g.input.pdf b/src/axiom-website/CATS/rich4g.input.pdf
new file mode 100644
index 0000000..1580459
Binary files /dev/null and b/src/axiom-website/CATS/rich4g.input.pdf differ
diff --git a/src/axiom-website/CATS/rich4h.input.pamphlet b/src/axiom-website/CATS/rich4h.input.pamphlet
new file mode 100644
index 0000000..4f31122
--- /dev/null
+++ b/src/axiom-website/CATS/rich4h.input.pamphlet
@@ -0,0 +1,24104 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich4h.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 255 supplied "optimal results".
+\item 173 matching answers.
+\item 60 cases where Axiom's results differs from Rubi
+\item 25 cases where Axiom supplied 2 results.
+\item 4 cases that Axiom failed to integrate.
+\item 42 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich4h.output
+)spool rich4h.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1325
+t0:=sqrt(8+27/x^3)/x^2
+--R
+--R
+--R +--------+
+--R | 3
+--R |8x + 27
+--R |--------
+--R | 3
+--R \| x
+--R (1) -----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1325
+--r0:=-2/5*sqrt(8+27/x^3)/x-16/5*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+_
+-- 1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-_
+-- sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/_
+-- (3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3)
+--E 2
+
+--S 3 of 1325
+--a0:=integrate(t0,x)
+--E 3
+
+--S 4 of 1325
+--m0:=a0-r0
+--E 4
+
+--S 5 of 1325
+--d0:=D(m0,x)
+--E 5
+
+)clear all
+
+--S 6 of 1325
+t0:=sqrt(8+27/x^3)/x^5
+--R
+--R
+--R +--------+
+--R | 3
+--R |8x + 27
+--R |--------
+--R | 3
+--R \| x
+--R (1) -----------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 6
+
+--S 7 of 1325
+--r0:=-2/11*sqrt(8+27/x^3)/x^4-16/495*sqrt(8+27/x^3)/x+256/1485*_
+-- (-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_
+-- x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/sqrt(8+27/x^3)
+--E 7
+
+--S 8 of 1325
+--a0:=integrate(t0,x)
+--E 8
+
+--S 9 of 1325
+--m0:=a0-r0
+--E 9
+
+--S 10 of 1325
+--d0:=D(m0,x)
+--E 10
+
+)clear all
+
+--S 11 of 1325
+t0:=x^3*sqrt(8+27/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |8x + 27
+--R (1) x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 11
+
+--S 12 of 1325
+--r0:=81/64*x*sqrt(8+27/x^3)+1/4*x^4*sqrt(8+27/x^3)-243/64*(-1)^(1/4)*_
+-- (2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_
+-- x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*_
+-- sqrt((2+3/x)/(3+%i*sqrt(3))))+243/32*(-1)^(1/4)*elliptic_f(%i*_
+-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*_
+-- sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_
+-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3)
+--E 12
+
+--S 13 of 1325
+--a0:=integrate(t0,x)
+--E 13
+
+--S 14 of 1325
+--m0:=a0-r0
+--E 14
+
+--S 15 of 1325
+--d0:=D(m0,x)
+--E 15
+
+)clear all
+
+--S 16 of 1325
+t0:=sqrt(8+27/x^3)
+--R
+--R
+--R +--------+
+--R | 3
+--R |8x + 27
+--R (1) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 16
+
+--S 17 of 1325
+--r0:=x*sqrt(8+27/x^3)-9*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+_
+-- 1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-_
+-- sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/(sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))+18*_
+-- (-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_
+-- x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/sqrt(8+27/x^3)
+--E 17
+
+--S 18 of 1325
+--a0:=integrate(t0,x)
+--E 18
+
+--S 19 of 1325
+--m0:=a0-r0
+--E 19
+
+--S 20 of 1325
+--d0:=D(m0,x)
+--E 20
+
+)clear all
+
+--S 21 of 1325
+t0:=sqrt(8+27/x^3)/x^3
+--R
+--R
+--R +--------+
+--R | 3
+--R |8x + 27
+--R |--------
+--R | 3
+--R \| x
+--R (1) -----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 21
+
+--S 22 of 1325
+--r0:=-2/7*sqrt(8+27/x^3)/x^2-16/21*(-1)^(1/4)*(2+3/x)*_
+-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_
+-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_
+-- sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*_
+-- sqrt((2+3/x)/(3+%i*sqrt(3))))+32/21*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_
+-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_
+-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/sqrt(8+27/x^3)
+--E 22
+
+--S 23 of 1325
+--a0:=integrate(t0,x)
+--E 23
+
+--S 24 of 1325
+--m0:=a0-r0
+--E 24
+
+--S 25 of 1325
+--d0:=D(m0,x)
+--E 25
+
+)clear all
+
+--S 26 of 1325
+t0:=sqrt(8+27/x^3)/x^6
+--R
+--R
+--R +--------+
+--R | 3
+--R |8x + 27
+--R |--------
+--R | 3
+--R \| x
+--R (1) -----------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 1325
+--r0:=-2/13*sqrt(8+27/x^3)/x^5-16/819*sqrt(8+27/x^3)/x^2+_
+-- 512/7371*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_
+-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/_
+-- (sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))-1024/7371*_
+-- (-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_
+-- x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/sqrt(8+27/x^3)
+--E 27
+
+--S 28 of 1325
+--a0:=integrate(t0,x)
+--E 28
+
+--S 29 of 1325
+--m0:=a0-r0
+--E 29
+
+--S 30 of 1325
+--d0:=D(m0,x)
+--E 30
+
+)clear all
+
+--S 31 of 1325
+t0:=x^8/sqrt(a+b/x^3)
+--R
+--R
+--R 8
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 1325
+r0:=-5/24*b^3*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(7/2)+5/24*b^2*x^3*_
+ sqrt(a+b/x^3)/a^3-5/36*b*x^6*sqrt(a+b/x^3)/a^2+1/9*x^9*sqrt(a+b/x^3)/a
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 3 \| x 2 9 6 2 3 +-+ |a x + b
+--R - 15b atanh(-----------) + (8a x - 10a b x + 15b x )\|a |--------
+--R +-+ | 3
+--R \|a \| x
+--R (2) ---------------------------------------------------------------------
+--R 3 +-+
+--R 72a \|a
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+ +--------+
+--R | 6 | 6 | 3
+--R 3 |25b 4 2 |25b |a x + b 3 3 4
+--R - 12a |---- log(16a x |---- |-------- + 10a b x + 5b )
+--R | 7 | 7 \| x
+--R \|64a \|64a
+--R +
+--R +--------+
+--R | 3
+--R 2 8 5 2 2 |a x + b
+--R (8a x - 10a b x + 15b x ) |--------
+--R \| x
+--R /
+--R 3
+--R 72a
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----+ +----+ +--------+
+--R | 6 | 6 | 3
+--R 3 +-+ |25b 4 2 |25b |a x + b 3 3 4
+--R - 12a \|a |---- log(16a x |---- |-------- + 10a b x + 5b )
+--R | 7 | 7 \| x
+--R \|64a \|64a
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 3 \| x 2 8 5 2 2 +-+ |a x + b
+--R 15b atanh(-----------) + (8a x - 10a b x + 15b x )\|a |--------
+--R +-+ \| x
+--R \|a
+--R +
+--R +--------+
+--R | 3
+--R 2 9 6 2 3 +-+ |a x + b
+--R (- 8a x + 10a b x - 15b x )\|a |--------
+--R | 3
+--R \| x
+--R /
+--R 3 +-+
+--R 72a \|a
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +----+ +--------+
+--R | 6 | 3
+--R 5 13 4 10 |25b 3 13 4 10 |a x + b
+--R ((- 16a x - 16a b x ) |---- + (10a b x + 5b x ) |-------- )
+--R | 7 | 3
+--R \|64a \| x
+--R *
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R \| x
+--R +
+--R +--------+ +----+
+--R | 3 | 6
+--R 5 14 4 11 |a x + b |25b 2 3 14 4 11 5 8
+--R (16a x + 16a b x ) |-------- |---- - 10a b x - 15a b x - 5b x
+--R | 3 | 7
+--R \| x \|64a
+--R /
+--R +--------+ +----+ +--------+
+--R | 3 | 6 | 3
+--R 5 5 4 2 |a x + b |25b |a x + b
+--R (16a x + 16a b x ) |-------- |---- |--------
+--R | 3 | 7 \| x
+--R \| x \|64a
+--R +
+--R +--------+
+--R | 3
+--R 2 3 6 4 3 5 |a x + b
+--R (10a b x + 15a b x + 5b ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 1325
+t0:=x^5/sqrt(a+b/x^3)
+--R
+--R
+--R 5
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 1325
+r0:=1/4*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(5/2)-1/4*b*x^3*_
+ sqrt(a+b/x^3)/a^2+1/6*x^6*sqrt(a+b/x^3)/a
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 2 \| x 6 3 +-+ |a x + b
+--R 3b atanh(-----------) + (2a x - 3b x )\|a |--------
+--R +-+ | 3
+--R \|a \| x
+--R (2) ------------------------------------------------------
+--R 2 +-+
+--R 12a \|a
+--R Type: Expression(Integer)
+--E 37
+
+--S 38 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +----+ +----+ +--------+
+--R | 4 | 4 | 3
+--R 2 | 9b 3 2 | 9b |a x + b 2 3 3
+--R - 2a |---- log(8a x |---- |-------- - 6a b x - 3b )
+--R | 5 | 5 \| x
+--R \|16a \|16a
+--R +
+--R +--------+
+--R | 3
+--R 5 2 |a x + b
+--R (2a x - 3b x ) |--------
+--R \| x
+--R /
+--R 2
+--R 12a
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----+ +----+ +--------+
+--R | 4 | 4 | 3
+--R 2 +-+ | 9b 3 2 | 9b |a x + b 2 3 3
+--R - 2a \|a |---- log(8a x |---- |-------- - 6a b x - 3b )
+--R | 5 | 5 \| x
+--R \|16a \|16a
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R 2 \| x 5 2 +-+ |a x + b
+--R - 3b atanh(-----------) + (2a x - 3b x )\|a |--------
+--R +-+ \| x
+--R \|a
+--R +
+--R +--------+
+--R | 3
+--R 6 3 +-+ |a x + b
+--R (- 2a x + 3b x )\|a |--------
+--R | 3
+--R \| x
+--R /
+--R 2 +-+
+--R 12a \|a
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +----+ +--------+
+--R | 4 | 3
+--R 4 10 3 7 | 9b 2 10 3 7 |a x + b
+--R ((- 8a x - 8a b x ) |---- + (- 6a b x - 3b x ) |-------- )
+--R | 5 | 3
+--R \|16a \| x
+--R *
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R \| x
+--R +
+--R +--------+ +----+
+--R | 3 | 4
+--R 4 11 3 8 |a x + b | 9b 2 2 11 3 8 4 5
+--R (8a x + 8a b x ) |-------- |---- + 6a b x + 9a b x + 3b x
+--R | 3 | 5
+--R \| x \|16a
+--R /
+--R +--------+ +----+ +--------+
+--R | 3 | 4 | 3
+--R 4 5 3 2 |a x + b | 9b |a x + b
+--R (8a x + 8a b x ) |-------- |---- |--------
+--R | 3 | 5 \| x
+--R \| x \|16a
+--R +
+--R +--------+
+--R | 3
+--R 2 2 6 3 3 4 |a x + b
+--R (- 6a b x - 9a b x - 3b ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 1325
+t0:=x^2/sqrt(a+b/x^3)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 41
+
+--S 42 of 1325
+r0:=-1/3*b*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(3/2)+1/3*x^3*sqrt(a+b/x^3)/a
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+
+--R | 3 | 3
+--R \| x 3 +-+ |a x + b
+--R - b atanh(-----------) + x \|a |--------
+--R +-+ | 3
+--R \|a \| x
+--R (2) ------------------------------------------
+--R +-+
+--R 3a\|a
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--+ +--+ +--------+ +--------+
+--R | 2 | 2 | 3 | 3
+--R |b 2 2 |b |a x + b 3 2 2 |a x + b
+--R - a |-- log(2a x |-- |-------- + 2a b x + b ) + 2x |--------
+--R | 3 | 3 \| x \| x
+--R \|a \|a
+--R (3) ------------------------------------------------------------------
+--R 6a
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+ +--------+
+--R | 2 | 2 | 3
+--R +-+ |b 2 2 |b |a x + b 3 2
+--R - a\|a |-- log(2a x |-- |-------- + 2a b x + b )
+--R | 3 | 3 \| x
+--R \|a \|a
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R |-------- +--------+ +--------+
+--R | 3 | 3 | 3
+--R \| x 2 +-+ |a x + b 3 +-+ |a x + b
+--R 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |--------
+--R +-+ \| x | 3
+--R \|a \| x
+--R /
+--R +-+
+--R 6a\|a
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--+ +--------+ +--------+
+--R | 2 | 3 | 3
+--R 3 7 2 4 |b 7 2 4 |a x + b |a x + b
+--R ((- 2a x - 2a b x ) |-- + (2a b x + b x ) |-------- ) |--------
+--R | 3 | 3 \| x
+--R \|a \| x
+--R +
+--R +--------+ +--+
+--R | 3 | 2
+--R 3 8 2 5 |a x + b |b 2 8 2 5 3 2
+--R (2a x + 2a b x ) |-------- |-- - 2a b x - 3a b x - b x
+--R | 3 | 3
+--R \| x \|a
+--R /
+--R +--------+ +--+ +--------+
+--R | 3 | 2 | 3
+--R 3 5 2 2 |a x + b |b |a x + b
+--R (2a x + 2a b x ) |-------- |-- |--------
+--R | 3 | 3 \| x
+--R \| x \|a
+--R +
+--R +--------+
+--R | 3
+--R 2 6 2 3 3 |a x + b
+--R (2a b x + 3a b x + b ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 1325
+t0:=1/(x*sqrt(a+b/x^3))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +--------+
+--R | 3
+--R |a x + b
+--R x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 46
+
+--S 47 of 1325
+r0:=2/3*atanh(sqrt(a+b/x^3)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R | 3
+--R \| x
+--R 2atanh(-----------)
+--R +-+
+--R \|a
+--R (2) -------------------
+--R +-+
+--R 3\|a
+--R Type: Expression(Integer)
+--E 47
+
+--S 48 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +-+ +-+ | 3
+--R |1 2 |1 |a x + b 3
+--R |- log(2a x |- |-------- - 2a x - b)
+--R \|a \|a \| x
+--R (3) - -----------------------------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R +--------+ |--------
+--R +-+ +-+ | 3 | 3
+--R |1 +-+ 2 |1 |a x + b 3 \| x
+--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------)
+--R \|a \|a \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------------------
+--R +-+
+--R 3\|a
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +--------+
+--R +-+ | 3 | 3
+--R 3 |1 |a x + b 3 |a x + b
+--R (- 2a x |- |-------- - 2a x - b) |--------
+--R \|a | 3 \| x
+--R \| x
+--R +
+--R +--------+
+--R | 3 +-+
+--R 4 |a x + b 2 4 |1
+--R (2a x + b x) |-------- + (2a x + 2a b x) |-
+--R | 3 \|a
+--R \| x
+--R /
+--R +--------+ +--------+ +--------+
+--R | 3 | 3 +-+ | 3
+--R 4 |a x + b |a x + b 2 5 2 |1 |a x + b
+--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |--------
+--R | 3 \| x \|a | 3
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 1325
+t0:=1/(x^4*sqrt(a+b/x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 3
+--R 4 |a x + b
+--R x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 51
+
+--S 52 of 1325
+r0:=-2/3*sqrt(a+b/x^3)/b
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R 2 |--------
+--R | 3
+--R \| x
+--R (2) - ------------
+--R 3b
+--R Type: Expression(Integer)
+--E 52
+
+--S 53 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R 2 |--------
+--R \| x
+--R (3) - ------------
+--R 3
+--R 3b x
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R |a x + b 3 |a x + b
+--R - 2 |-------- + 2x |--------
+--R \| x | 3
+--R \| x
+--R (4) -------------------------------
+--R 3
+--R 3b x
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R |a x + b 3 |a x + b
+--R - 3b x |-------- + (4a x + 7b) |--------
+--R \| x | 3
+--R \| x
+--R (5) -------------------------------------------
+--R +--------+ +--------+
+--R | 3 | 3
+--R 5 |a x + b |a x + b
+--R 3b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 1325
+t0:=1/(x^7*sqrt(a+b/x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 3
+--R 7 |a x + b
+--R x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1325
+r0:=-2/9*(a+b/x^3)^(3/2)/b^2+2/3*a*sqrt(a+b/x^3)/b^2
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (4a x - 2b) |--------
+--R | 3
+--R \| x
+--R (2) -----------------------
+--R 2 3
+--R 9b x
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (4a x - 2b) |--------
+--R \| x
+--R (3) -----------------------
+--R 2 6
+--R 9b x
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 |a x + b 6 3 |a x + b
+--R (4a x - 2b) |-------- + (- 4a x + 2b x ) |--------
+--R \| x | 3
+--R \| x
+--R (4) ------------------------------------------------------
+--R 2 6
+--R 9b x
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 |a x + b 2 6 3 2 |a x + b
+--R - 9b x |-------- + (- 8a x - 4a b x + 13b ) |--------
+--R \| x | 3
+--R \| x
+--R (5) ---------------------------------------------------------
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 8 |a x + b |a x + b
+--R 9b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 1325
+t0:=1/(x^10*sqrt(a+b/x^3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+
+--R | 3
+--R 10 |a x + b
+--R x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 1325
+r0:=4/9*a*(a+b/x^3)^(3/2)/b^3-2/15*(a+b/x^3)^(5/2)/b^3-2/3*a^2*_
+ sqrt(a+b/x^3)/b^3
+--R
+--R
+--R +--------+
+--R | 3
+--R 2 6 3 2 |a x + b
+--R (- 16a x + 8a b x - 6b ) |--------
+--R | 3
+--R \| x
+--R (2) -------------------------------------
+--R 3 6
+--R 45b x
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 2 6 3 2 |a x + b
+--R (- 16a x + 8a b x - 6b ) |--------
+--R \| x
+--R (3) -------------------------------------
+--R 3 9
+--R 45b x
+--R Type: Union(Expression(Integer),...)
+--E 63
+
+--S 64 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 6 3 2 |a x + b 2 9 6 2 3 |a x + b
+--R (- 16a x + 8a b x - 6b ) |-------- + (16a x - 8a b x + 6b x ) |--------
+--R \| x | 3
+--R \| x
+--R -----------------------------------------------------------------------------
+--R 3 9
+--R 45b x
+--R Type: Expression(Integer)
+--E 64
+
+--S 65 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 |a x + b 3 9 2 6 2 3 3 |a x + b
+--R - 45b x |-------- + (32a x + 16a b x - 4a b x + 57b ) |--------
+--R \| x | 3
+--R \| x
+--R (5) --------------------------------------------------------------------
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 11 |a x + b |a x + b
+--R 45b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 65
+
+)clear all
+
+--S 66 of 1325
+t0:=1/(x^13*sqrt(a+b/x^3))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +--------+
+--R | 3
+--R 13 |a x + b
+--R x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 66
+
+--S 67 of 1325
+r0:=-2/3*a^2*(a+b/x^3)^(3/2)/b^4+2/5*a*(a+b/x^3)^(5/2)/b^4-_
+ 2/21*(a+b/x^3)^(7/2)/b^4+2/3*a^3*sqrt(a+b/x^3)/b^4
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (32a x - 16a b x + 12a b x - 10b ) |--------
+--R | 3
+--R \| x
+--R (2) ------------------------------------------------
+--R 4 9
+--R 105b x
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (32a x - 16a b x + 12a b x - 10b ) |--------
+--R \| x
+--R (3) ------------------------------------------------
+--R 4 12
+--R 105b x
+--R Type: Union(Expression(Integer),...)
+--E 68
+
+--S 69 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (32a x - 16a b x + 12a b x - 10b ) |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 3 12 2 9 2 6 3 3 |a x + b
+--R (- 32a x + 16a b x - 12a b x + 10b x ) |--------
+--R | 3
+--R \| x
+--R /
+--R 4 12
+--R 105b x
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 3
+--R 4 |a x + b
+--R - 105b x |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 4 12 3 9 2 2 6 3 3 4 |a x + b
+--R (- 64a x - 32a b x + 8a b x - 4a b x + 125b ) |--------
+--R | 3
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 3 | 3
+--R 4 14 |a x + b |a x + b
+--R 105b x |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 1325
+t0:=x^5/(a+b/x^3)^(3/2)
+--R
+--R
+--R 8
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (a x + b) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 71
+
+--S 72 of 1325
+r0:=5/4*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(7/2)-2/3*x^6/_
+ (a*sqrt(a+b/x^3))-5/4*b*x^3*sqrt(a+b/x^3)/a^3+5/6*x^6*sqrt(a+b/x^3)/a^2
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R +--------+ |--------
+--R | 3 | 3
+--R 2 |a x + b \| x 2 6 3 2 +-+
+--R 15b |-------- atanh(-----------) + (2a x - 5a b x - 15b )\|a
+--R | 3 +-+
+--R \| x \|a
+--R (2) ----------------------------------------------------------------
+--R +--------+
+--R | 3
+--R 3 +-+ |a x + b
+--R 12a \|a |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----+ +-----+ +--------+
+--R | 4 | 4 | 3
+--R 4 3 3 |225b 4 2 |225b |a x + b 2 3 3
+--R (- 2a x - 2a b) |----- log(8a x |----- |-------- - 30a b x - 15b )
+--R | 7 | 7 \| x
+--R \| 16a \| 16a
+--R +
+--R +--------+
+--R | 3
+--R 2 8 5 2 2 |a x + b
+--R (2a x - 5a b x - 15b x ) |--------
+--R \| x
+--R /
+--R 4 3 3
+--R 12a x + 12a b
+--R Type: Union(Expression(Integer),...)
+--E 73
+
+--S 74 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +-----+
+--R | 3 | 4
+--R 4 3 3 +-+ |a x + b |225b
+--R (- 2a x - 2a b)\|a |-------- |-----
+--R | 3 | 7
+--R \| x \| 16a
+--R *
+--R +-----+ +--------+
+--R | 4 | 3
+--R 4 2 |225b |a x + b 2 3 3
+--R log(8a x |----- |-------- - 30a b x - 15b )
+--R | 7 \| x
+--R \| 16a
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R +--------+ |--------
+--R | 3 | 3
+--R 2 3 3 |a x + b \| x
+--R (- 15a b x - 15b ) |-------- atanh(-----------)
+--R | 3 +-+
+--R \| x \|a
+--R +
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 8 5 2 2 +-+ |a x + b |a x + b
+--R (2a x - 5a b x - 15b x )\|a |-------- |--------
+--R | 3 \| x
+--R \| x
+--R +
+--R 3 9 2 6 2 3 3 +-+
+--R (- 2a x + 3a b x + 20a b x + 15b )\|a
+--R /
+--R +--------+
+--R | 3
+--R 4 3 3 +-+ |a x + b
+--R (12a x + 12a b)\|a |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +-----+ +--------+
+--R | 4 | 3
+--R 5 13 4 10 |225b 2 13 3 10 |a x + b
+--R ((- 8a x - 8a b x ) |----- + (- 30a b x - 15b x ) |-------- )
+--R | 7 | 3
+--R \| 16a \| x
+--R *
+--R +--------+
+--R | 3
+--R |a x + b
+--R |--------
+--R \| x
+--R +
+--R +--------+ +-----+
+--R | 3 | 4
+--R 5 14 4 11 |a x + b |225b 2 2 14 3 11 4 8
+--R (8a x + 8a b x ) |-------- |----- + 30a b x + 45a b x + 15b x
+--R | 3 | 7
+--R \| x \| 16a
+--R /
+--R +--------+ +-----+ +--------+
+--R | 3 | 4 | 3
+--R 6 8 5 5 4 2 2 |a x + b |225b |a x + b
+--R (8a x + 16a b x + 8a b x ) |-------- |----- |--------
+--R | 3 | 7 \| x
+--R \| x \| 16a
+--R +
+--R +--------+
+--R | 3
+--R 3 2 9 2 3 6 4 3 5 |a x + b
+--R (- 30a b x - 75a b x - 60a b x - 15b ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 75
+
+)clear all
+
+--S 76 of 1325
+t0:=x^2/(a+b/x^3)^(3/2)
+--R
+--R
+--R 5
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (a x + b) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 1325
+r0:=-b*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(5/2)-2/3*x^3/(a*sqrt(a+b/x^3))+_
+ x^3*sqrt(a+b/x^3)/a^2
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R +--------+ |--------
+--R | 3 | 3
+--R |a x + b \| x 3 +-+
+--R - 3b |-------- atanh(-----------) + (a x + 3b)\|a
+--R | 3 +-+
+--R \| x \|a
+--R (2) ---------------------------------------------------
+--R +--------+
+--R | 3
+--R 2 +-+ |a x + b
+--R 3a \|a |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+ +--------+
+--R | 2 | 2 | 3
+--R 3 3 2 |9b 3 2 |9b |a x + b 3 2
+--R (- a x - a b) |--- log(2a x |--- |-------- + 6a b x + 3b )
+--R | 5 | 5 \| x
+--R \| a \| a
+--R +
+--R +--------+
+--R | 3
+--R 5 2 |a x + b
+--R (2a x + 6b x ) |--------
+--R \| x
+--R /
+--R 3 3 2
+--R 6a x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +---+
+--R | 3 | 2
+--R 3 3 2 +-+ |a x + b |9b
+--R (- a x - a b)\|a |-------- |---
+--R | 3 | 5
+--R \| x \| a
+--R *
+--R +---+ +--------+
+--R | 2 | 3
+--R 3 2 |9b |a x + b 3 2
+--R log(2a x |--- |-------- + 6a b x + 3b )
+--R | 5 \| x
+--R \| a
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R +--------+ |--------
+--R | 3 | 3
+--R 3 2 |a x + b \| x
+--R (6a b x + 6b ) |-------- atanh(-----------)
+--R | 3 +-+
+--R \| x \|a
+--R +
+--R +--------+ +--------+
+--R | 3 | 3
+--R 5 2 +-+ |a x + b |a x + b 2 6 3 2 +-+
+--R (2a x + 6b x )\|a |-------- |-------- + (- 2a x - 8a b x - 6b )\|a
+--R | 3 \| x
+--R \| x
+--R /
+--R +--------+
+--R | 3
+--R 3 3 2 +-+ |a x + b
+--R (6a x + 6a b)\|a |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +---+ +--------+ +--------+
+--R | 2 | 3 | 3
+--R 4 10 3 7 |9b 10 2 7 |a x + b |a x + b
+--R ((- 2a x - 2a b x ) |--- + (6a b x + 3b x ) |-------- ) |--------
+--R | 5 | 3 \| x
+--R \| a \| x
+--R +
+--R +--------+ +---+
+--R | 3 | 2
+--R 4 11 3 8 |a x + b |9b 2 11 2 8 3 5
+--R (2a x + 2a b x ) |-------- |--- - 6a b x - 9a b x - 3b x
+--R | 3 | 5
+--R \| x \| a
+--R /
+--R +--------+ +---+ +--------+
+--R | 3 | 2 | 3
+--R 5 8 4 5 3 2 2 |a x + b |9b |a x + b
+--R (2a x + 4a b x + 2a b x ) |-------- |--- |--------
+--R | 3 | 5 \| x
+--R \| x \| a
+--R +
+--R +--------+
+--R | 3
+--R 3 9 2 2 6 3 3 4 |a x + b
+--R (6a b x + 15a b x + 12a b x + 3b ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 1325
+t0:=1/((a+b/x^3)^(3/2)*x)
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (a x + b) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 81
+
+--S 82 of 1325
+r0:=2/3*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(3/2)+(-2/3)/(a*sqrt(a+b/x^3))
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R +--------+ |--------
+--R | 3 | 3
+--R |a x + b \| x +-+
+--R 2 |-------- atanh(-----------) - 2\|a
+--R | 3 +-+
+--R \| x \|a
+--R (2) --------------------------------------
+--R +--------+
+--R | 3
+--R +-+ |a x + b
+--R 3a\|a |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 82
+
+--S 83 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+
+--R +--+ +--+ | 3 | 3
+--R 2 3 | 1 2 2 | 1 |a x + b 3 2 |a x + b
+--R (- a x - a b) |-- log(2a x |-- |-------- - 2a x - b) - 2x |--------
+--R | 3 | 3 \| x \| x
+--R \|a \|a
+--R --------------------------------------------------------------------------
+--R 2 3
+--R 3a x + 3a b
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R +--+ | 3 +--+ | 3
+--R 2 3 | 1 +-+ |a x + b 2 2 | 1 |a x + b 3
+--R (- a x - a b) |-- \|a |-------- log(2a x |-- |-------- - 2a x - b)
+--R | 3 | 3 | 3 \| x
+--R \|a \| x \|a
+--R +
+--R +--------+
+--R | 3
+--R |a x + b
+--R +--------+ |--------
+--R | 3 | 3
+--R 3 |a x + b \| x
+--R (- 2a x - 2b) |-------- atanh(-----------)
+--R | 3 +-+
+--R \| x \|a
+--R +
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 +-+ |a x + b |a x + b 3 +-+
+--R - 2x \|a |-------- |-------- + (2a x + 2b)\|a
+--R | 3 \| x
+--R \| x
+--R /
+--R +--------+
+--R | 3
+--R 2 3 +-+ |a x + b
+--R (3a x + 3a b)\|a |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +--------+
+--R | 3 +--+ | 3
+--R 7 4 |a x + b 3 7 2 4 | 1 |a x + b
+--R ((- 2a x - b x ) |-------- + (- 2a x - 2a b x ) |-- ) |--------
+--R | 3 | 3 \| x
+--R \| x \|a
+--R +
+--R +--------+
+--R +--+ | 3
+--R 3 8 2 5 | 1 |a x + b 2 8 5 2 2
+--R (2a x + 2a b x ) |-- |-------- + 2a x + 3a b x + b x
+--R | 3 | 3
+--R \|a \| x
+--R /
+--R +--------+ +--------+
+--R +--+ | 3 | 3
+--R 4 8 3 5 2 2 2 | 1 |a x + b |a x + b
+--R (2a x + 4a b x + 2a b x ) |-- |-------- |--------
+--R | 3 | 3 \| x
+--R \|a \| x
+--R +
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (- 2a x - 5a b x - 4a b x - b ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 1325
+t0:=1/((a+b/x^3)^(3/2)*x^4)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +--------+
+--R | 3
+--R 4 |a x + b
+--R (a x + b x) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 86
+
+--S 87 of 1325
+r0:=2/3/(b*sqrt(a+b/x^3))
+--R
+--R
+--R 2
+--R (2) -------------
+--R +--------+
+--R | 3
+--R |a x + b
+--R 3b |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R |a x + b
+--R 2 |--------
+--R \| x
+--R (3) -------------
+--R 3 2
+--R 3a b x + 3b
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R |a x + b |a x + b 3
+--R 2 |-------- |-------- - 2a x - 2b
+--R | 3 \| x
+--R \| x
+--R (4) ------------------------------------
+--R +--------+
+--R | 3
+--R 3 2 |a x + b
+--R (3a b x + 3b ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R |a x + b 3 |a x + b
+--R - 3b x |-------- + (- 4a x - b) |--------
+--R \| x | 3
+--R \| x
+--R (5) --------------------------------------------
+--R +--------+ +--------+
+--R | 3 | 3
+--R 5 2 2 |a x + b |a x + b
+--R (3a b x + 3b x ) |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 1325
+t0:=1/((a+b/x^3)^(3/2)*x^7)
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +--------+
+--R | 3
+--R 7 4 |a x + b
+--R (a x + b x ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 91
+
+--S 92 of 1325
+r0:=-2/3*a/(b^2*sqrt(a+b/x^3))-2/3*sqrt(a+b/x^3)/b^2
+--R
+--R
+--R 3
+--R - 4a x - 2b
+--R (2) ----------------
+--R +--------+
+--R | 3
+--R 2 3 |a x + b
+--R 3b x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 92
+
+--S 93 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 |a x + b
+--R (- 4a x - 2b) |--------
+--R \| x
+--R (3) -------------------------
+--R 2 6 3 3
+--R 3a b x + 3b x
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 |a x + b |a x + b 2 6 3 2
+--R (- 4a x - 2b) |-------- |-------- + 4a x + 6a b x + 2b
+--R | 3 \| x
+--R \| x
+--R (4) ------------------------------------------------------------
+--R +--------+
+--R | 3
+--R 2 6 3 3 |a x + b
+--R (3a b x + 3b x ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 |a x + b 2 6 3 2 |a x + b
+--R - 3b x |-------- + (8a x + 12a b x + 7b ) |--------
+--R \| x | 3
+--R \| x
+--R (5) -------------------------------------------------------
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 8 3 5 |a x + b |a x + b
+--R (3a b x + 3b x ) |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 1325
+t0:=1/((a+b/x^3)^(3/2)*x^10)
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R +--------+
+--R | 3
+--R 10 7 |a x + b
+--R (a x + b x ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 1325
+r0:=-2/9*(a+b/x^3)^(3/2)/b^3+2/3*a^2/(b^3*sqrt(a+b/x^3))+_
+ 4/3*a*sqrt(a+b/x^3)/b^3
+--R
+--R
+--R 2 6 3 2
+--R 16a x + 8a b x - 2b
+--R (2) ----------------------
+--R +--------+
+--R | 3
+--R 3 6 |a x + b
+--R 9b x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 2 6 3 2 |a x + b
+--R (16a x + 8a b x - 2b ) |--------
+--R \| x
+--R (3) -----------------------------------
+--R 3 9 4 6
+--R 9a b x + 9b x
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 3 | 3
+--R 2 6 3 2 |a x + b |a x + b 3 9 2 6
+--R (16a x + 8a b x - 2b ) |-------- |-------- - 16a x - 24a b x
+--R | 3 \| x
+--R \| x
+--R +
+--R 2 3 3
+--R - 6a b x + 2b
+--R /
+--R +--------+
+--R | 3
+--R 3 9 4 6 |a x + b
+--R (9a b x + 9b x ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 |a x + b 3 9 2 6 2 3 3 |a x + b
+--R - 9b x |-------- + (- 32a x - 48a b x - 12a b x + 13b ) |--------
+--R \| x | 3
+--R \| x
+--R (5) ----------------------------------------------------------------------
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 11 4 8 |a x + b |a x + b
+--R (9a b x + 9b x ) |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 1325
+t0:=1/((a+b/x^3)^(3/2)*x^13)
+--R
+--R
+--R 1
+--R (1) --------------------------
+--R +--------+
+--R | 3
+--R 13 10 |a x + b
+--R (a x + b x ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 1325
+r0:=2/3*a*(a+b/x^3)^(3/2)/b^4-2/15*(a+b/x^3)^(5/2)/b^4-_
+ 2/3*a^3/(b^4*sqrt(a+b/x^3))-2*a^2*sqrt(a+b/x^3)/b^4
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R - 32a x - 16a b x + 4a b x - 2b
+--R (2) -----------------------------------
+--R +--------+
+--R | 3
+--R 4 9 |a x + b
+--R 15b x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 102
+
+--S 103 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 3
+--R 3 9 2 6 2 3 3 |a x + b
+--R (- 32a x - 16a b x + 4a b x - 2b ) |--------
+--R \| x
+--R (3) ------------------------------------------------
+--R 4 12 5 9
+--R 15a b x + 15b x
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 3 | 3
+--R 3 9 2 6 2 3 3 |a x + b |a x + b 4 12
+--R (- 32a x - 16a b x + 4a b x - 2b ) |-------- |-------- + 32a x
+--R | 3 \| x
+--R \| x
+--R +
+--R 3 9 2 2 6 3 3 4
+--R 48a b x + 12a b x - 2a b x + 2b
+--R /
+--R +--------+
+--R | 3
+--R 4 12 5 9 |a x + b
+--R (15a b x + 15b x ) |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 3
+--R 4 |a x + b
+--R - 15b x |--------
+--R \| x
+--R +
+--R +--------+
+--R | 3
+--R 4 12 3 9 2 2 6 3 3 4 |a x + b
+--R (64a x + 96a b x + 24a b x - 4a b x + 19b ) |--------
+--R | 3
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 3 | 3
+--R 4 14 5 11 |a x + b |a x + b
+--R (15a b x + 15b x ) |-------- |--------
+--R | 3 \| x
+--R \| x
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 1325
+t0:=x^4/sqrt(8+27/x^3)
+--R
+--R
+--R 4
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R |8x + 27
+--R |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 106
+
+--S 107 of 1325
+--r0:=-189/1280*x^2*sqrt(8+27/x^3)+1/40*x^5*sqrt(8+27/x^3)-_
+-- 1701/1280*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_
+-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3)
+--E 107
+
+--S 108 of 1325
+--a0:=integrate(t0,x)
+--E 108
+
+--S 109 of 1325
+--m0:=a0-r0
+--E 109
+
+--S 110 of 1325
+--d0:=D(m0,x)
+--E 110
+
+)clear all
+
+--S 111 of 1325
+t0:=x/sqrt(8+27/x^3)
+--R
+--R
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R |8x + 27
+--R |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 1325
+--r0:=1/16*x^2*sqrt(8+27/x^3)+9/16*(-1)^(1/4)*elliptic_f(%i*_
+-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_
+-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3)
+--E 112
+
+--S 113 of 1325
+--a0:=integrate(t0,x)
+--E 113
+
+--S 114 of 1325
+--m0:=a0-r0
+--E 114
+
+--S 115 of 1325
+--d0:=D(m0,x)
+--E 115
+
+)clear all
+
+--S 116 of 1325
+t0:=1/(x^2*sqrt(8+27/x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 3
+--R 2 |8x + 27
+--R x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 116
+
+--S 117 of 1325
+--r0:=-2/3*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_
+-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/sqrt(8+27/x^3)
+--E 117
+
+--S 118 of 1325
+--a0:=integrate(t0,x)
+--E 118
+
+--S 119 of 1325
+--m0:=a0-r0
+--E 119
+
+--S 120 of 1325
+--d0:=D(m0,x)
+--E 120
+
+)clear all
+
+--S 121 of 1325
+t0:=1/(x^5*sqrt(8+27/x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 3
+--R 5 |8x + 27
+--R x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 1325
+--r0:=-2/135*sqrt(8+27/x^3)/x+32/405*(-1)^(1/4)*elliptic_f(%i*_
+-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_
+-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3)
+--E 122
+
+--S 123 of 1325
+--a0:=integrate(t0,x)
+--E 123
+
+--S 124 of 1325
+--m0:=a0-r0
+--E 124
+
+--S 125 of 1325
+--d0:=D(m0,x)
+--E 125
+
+)clear all
+
+--S 126 of 1325
+t0:=x^3/sqrt(8+27/x^3)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------
+--R +--------+
+--R | 3
+--R |8x + 27
+--R |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 1325
+--r0:=-135/512*x*sqrt(8+27/x^3)+1/32*x^4*sqrt(8+27/x^3)+_
+-- 405/512*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_
+-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/_
+-- (sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))-405/256*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_
+-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_
+-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/sqrt(8+27/x^3)
+--E 127
+
+--S 128 of 1325
+--a0:=integrate(t0,x)
+--E 128
+
+--S 129 of 1325
+--m0:=a0-r0
+--E 129
+
+--S 130 of 1325
+--d0:=D(m0,x)
+--E 130
+
+)clear all
+
+--S 131 of 1325
+t0:=1/sqrt(8+27/x^3)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 3
+--R |8x + 27
+--R |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 1325
+--r0:=1/8*x*sqrt(8+27/x^3)-3/8*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*_
+-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_
+-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*_
+-- sqrt(3))))+3/4*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_
+-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3)
+--E 132
+
+--S 133 of 1325
+--a0:=integrate(t0,x)
+--E 133
+
+--S 134 of 1325
+--m0:=a0-r0
+--E 134
+
+--S 135 of 1325
+--d0:=D(m0,x)
+--E 135
+
+)clear all
+
+--S 136 of 1325
+t0:=1/(x^3*sqrt(8+27/x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 3
+--R 3 |8x + 27
+--R x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 1325
+--r0:=-2/9*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_
+-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_
+-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/_
+-- (sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))+4/9*(-1)^(1/4)*_
+-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_
+-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_
+-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_
+-- sqrt(3))/sqrt(8+27/x^3)
+--E 137
+
+--S 138 of 1325
+--a0:=integrate(t0,x)
+--E 138
+
+--S 139 of 1325
+--m0:=a0-r0
+--E 139
+
+--S 140 of 1325
+--d0:=D(m0,x)
+--E 140
+
+)clear all
+
+--S 141 of 1325
+t0:=1/(x^6*sqrt(8+27/x^3))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 3
+--R 6 |8x + 27
+--R x |--------
+--R | 3
+--R \| x
+--R Type: Expression(Integer)
+--E 141
+
+--S 142 of 1325
+--r0:=-2/189*sqrt(8+27/x^3)/x^2+64/1701*(-1)^(1/4)*(2+3/x)*_
+-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_
+-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_
+-- sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*sqrt((2+_
+-- 3/x)/(3+%i*sqrt(3))))-128/1701*(-1)^(1/4)*elliptic_f(%i*_
+-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*_
+-- sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_
+-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3)
+--E 142
+
+--S 143 of 1325
+--a0:=integrate(t0,x)
+--E 143
+
+--S 144 of 1325
+--m0:=a0-r0
+--E 144
+
+--S 145 of 1325
+--d0:=D(m0,x)
+--E 145
+
+)clear all
+
+--S 146 of 1325
+t0:=1/(a+b/x^4)
+--R
+--R
+--R 4
+--R x
+--R (1) --------
+--R 4
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 146
+
+--S 147 of 1325
+r0:=x/a+1/2*b^(1/4)*atan(1-a^(1/4)*x*sqrt(2)/b^(1/4))/(a^(5/4)*sqrt(2))-_
+ 1/2*b^(1/4)*atan(1+a^(1/4)*x*sqrt(2)/b^(1/4))/(a^(5/4)*sqrt(2))+_
+ 1/4*b^(1/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+x^2*sqrt(a)+sqrt(b))/_
+ (a^(5/4)*sqrt(2))-1/4*b^(1/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+_
+ x^2*sqrt(a)+sqrt(b))/(a^(5/4)*sqrt(2))
+--R
+--R
+--R (2)
+--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+
+--R - \|b log(x\|2 \|a \|b + \|b + x \|a )
+--R +
+--R 4+-+ +-+4+-+
+--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+ 4+-+ \|b + x\|2 \|a
+--R \|b log(- x\|2 \|a \|b + \|b + x \|a ) - 2\|b atan(----------------)
+--R 4+-+
+--R \|b
+--R +
+--R 4+-+ +-+4+-+
+--R 4+-+ \|b - x\|2 \|a +-+4+-+
+--R 2\|b atan(----------------) + 4x\|2 \|a
+--R 4+-+
+--R \|b
+--R /
+--R +-+4+-+
+--R 4a\|2 \|a
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-------+ +-------+ +-------+ +-------+
+--R | b | b | b | b
+--R - a |- ----- log(4a |- ----- + x + a |- ----- log(- 4a |- ----- + x)
+--R 4| 5 4| 5 4| 5 4| 5
+--R \| 256a \| 256a \| 256a \| 256a
+--R +
+--R +-------+
+--R | b
+--R 4a |- -----
+--R +-------+ 4| 5
+--R | b \| 256a
+--R 2a |- ----- atan(------------ + x
+--R 4| 5 x
+--R \| 256a
+--R /
+--R a
+--R Type: Union(Expression(Integer),...)
+--E 148
+
+--S 149 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+
+--R \|b log(x\|2 \|a \|b + \|b + x \|a )
+--R +
+--R +-------+ +-------+
+--R +-+ | b 4+-+ | b
+--R - 4a\|2 |- ----- \|a log(4a |- ----- + x)
+--R 4| 5 4| 5
+--R \| 256a \| 256a
+--R +
+--R +-------+ +-------+
+--R +-+ | b 4+-+ | b
+--R 4a\|2 |- ----- \|a log(- 4a |- ----- + x)
+--R 4| 5 4| 5
+--R \| 256a \| 256a
+--R +
+--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+
+--R - \|b log(- x\|2 \|a \|b + \|b + x \|a )
+--R +
+--R +-------+
+--R | b
+--R 4a |- -----
+--R +-------+ 4| 5 4+-+ +-+4+-+
+--R +-+ | b 4+-+ \| 256a 4+-+ \|b + x\|2 \|a
+--R 8a\|2 |- ----- \|a atan(------------ + 2\|b atan(----------------)
+--R 4| 5 x 4+-+
+--R \| 256a \|b
+--R +
+--R 4+-+ +-+4+-+
+--R 4+-+ \|b - x\|2 \|a
+--R - 2\|b atan(----------------)
+--R 4+-+
+--R \|b
+--R /
+--R +-+4+-+
+--R 4a\|2 \|a
+--R Type: Expression(Integer)
+--E 149
+
+--S 150 of 1325
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 150
+
+)clear all
+
+--S 151 of 1325
+t0:=(a+b/x^4)^(1/2)*x^3
+--R
+--R
+--R +--------+
+--R | 4
+--R 3 |a x + b
+--R (1) x |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 151
+
+--S 152 of 1325
+r0:=1/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/sqrt(a)+1/4*x^4*sqrt(a+b/x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |-------- +--------+
+--R | 4 | 4
+--R \| x 4 +-+ |a x + b
+--R b atanh(-----------) + x \|a |--------
+--R +-+ | 4
+--R \|a \| x
+--R (2) ----------------------------------------
+--R +-+
+--R 4\|a
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 4 4 2
+--R (2b\|b \|a x + b - a b x - 2b )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 6 2 +-+ | 4 6 2 +-+ +-+
+--R (- a x - 2b x )\|a \|a x + b + (2a x + 2b x )\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 4 4 +-+
+--R 8\|a \|b \|a x + b + (- 4a x - 8b)\|a
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 4 +---+ +-+
+--R +-+ | 4 4 2 \|- a \|a x + b - \|- a \|b
+--R (4b\|b \|a x + b - 2a b x - 4b )atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R +--------+
+--R 6 2 +---+ | 4 6 2 +---+ +-+
+--R (- a x - 2b x )\|- a \|a x + b + (2a x + 2b x )\|- a \|b
+--R /
+--R +--------+
+--R +---+ +-+ | 4 4 +---+
+--R 8\|- a \|b \|a x + b + (- 4a x - 8b)\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 153
+
+--S 154 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ | 4 4 2
+--R (2b\|b \|a x + b - a b x - 2b )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R +--------+ | 4
+--R +-+ | 4 4 2 \| x
+--R (- 2b\|b \|a x + b + a b x + 2b )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 4 +-+ |a x + b +-+ 6 2 +-+ | 4
+--R (- 2x \|a |-------- \|b + (- a x - 2b x )\|a )\|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 6 2 +-+ +-+ 8 4 +-+ |a x + b
+--R (2a x + 2b x )\|a \|b + (a x + 2b x )\|a |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R +-+ +-+ | 4 4 +-+
+--R 8\|a \|b \|a x + b + (- 4a x - 8b)\|a
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 4 18 3 14 2 2 10 3 6 4 2 +-+
+--R (7a x + 63a b x + 168a b x + 176a b x + 64b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 5 18 4 14 3 2 10 2 3 6 4 2
+--R - 7a x - 63a b x - 168a b x - 176a b x - 64a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 4
+--R 5 20 4 16 3 2 12 2 3 8 4 4 |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |--------
+--R | 4
+--R \| x
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+
+--R (a x + 26a b x + 129a b x + 248a b x + 208a b x + 64b )\|a
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 5 20 4 16 3 2 12 2 3 8 4 4 |a x + b
+--R (7a x + 63a b x + 168a b x + 176a b x + 64a b x ) |--------
+--R | 4
+--R \| x
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+
+--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 22 4 18 3 2 14 2 3 10 4 6 5 2
+--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x )
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 6 22 5 18 4 2 14 3 3 10 2 4 6 5 2
+--R a x + 26a b x + 129a b x + 248a b x + 208a b x + 64a b x
+--R /
+--R +--------+
+--R | 4
+--R 4 15 3 11 2 2 7 3 3 |a x + b +-+
+--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 4 17 3 13 2 2 9 3 5 4 +-+ |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 4 17 3 13 2 2 9 3 5 4 +-+ |a x + b +-+
+--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 5 19 4 15 3 2 11 2 3 7 4 3 |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 155
+
+--S 156 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R +--------+ | 4
+--R +---+ +-+ | 4 4 2 +---+ \| x
+--R (- 2b\|- a \|b \|a x + b + (a b x + 2b )\|- a )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R +-+ +-+ | 4 4 2 +-+
+--R (4b\|a \|b \|a x + b + (- 2a b x - 4b )\|a )
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 4 +---+ +-+ |a x + b +-+ 6 2 +---+ +-+ | 4
+--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x )\|- a \|a )\|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 6 2 +---+ +-+ +-+ 8 4 +---+ +-+ |a x + b
+--R (2a x + 2b x )\|- a \|a \|b + (a x + 2b x )\|- a \|a |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R +---+ +-+ +-+ | 4 4 +---+ +-+
+--R 8\|- a \|a \|b \|a x + b + (- 4a x - 8b)\|- a \|a
+--R Type: Expression(Integer)
+--E 156
+
+--S 157 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8
+--R (- 4a x - 12a b x - 8b x ) |-------- \|b - a x - 9a b x
+--R | 4
+--R \| x
+--R +
+--R 2 4 3
+--R - 16a b x - 8b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 3 12 2 8 2 4 3 +-+
+--R (4a x + 16a b x + 20a b x + 8b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 3 14 2 10 2 6 3 2 |a x + b
+--R (a x + 9a b x + 16a b x + 8b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 2 9 5 2 |a x + b | 4
+--R (a x + 8a b x + 8b x) |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 9 5 2 |a x + b +-+
+--R (- 4a x - 12a b x - 8b x) |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 157
+
+)clear all
+
+--S 158 of 1325
+t0:=(a+b/x^4)^(1/2)*x^2
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 |a x + b
+--R (1) x |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 158
+
+--S 159 of 1325
+--r0:=1/3*x^3*sqrt(a+b/x^4)+2/3*a^(1/4)*(-b)^(3/4)*_
+-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_
+-- sqrt(a+b/x^4)
+--E 159
+
+--S 160 of 1325
+--a0:=integrate(t0,x)
+--E 160
+
+--S 161 of 1325
+--m0:=a0-r0
+--E 161
+
+--S 162 of 1325
+--d0:=D(m0,x)
+--E 162
+
+)clear all
+
+--S 163 of 1325
+t0:=(a+b/x^4)^(1/2)*x
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R (1) x |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 163
+
+--S 164 of 1325
+r0:=-1/2*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))*sqrt(b)+1/2*x^2*sqrt(a+b/x^4)
+--R
+--R
+--R +--------+
+--R +-+ | 4
+--R +-+ \|b 2 |a x + b
+--R - \|b atanh(-------------) + x |--------
+--R +--------+ | 4
+--R | 4 \| x
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R (2) ------------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ | 4 4 +--------+
+--R +-+ - 2\|b \|a x + b + a x + 2b | 4
+--R \|b log(------------------------------) + 2\|a x + b
+--R 4
+--R x
+--R [------------------------------------------------------,
+--R 4
+--R +--------+
+--R | 4 +--------+
+--R +---+ \|a x + b | 4
+--R - \|- b atan(-----------) + \|a x + b
+--R +---+
+--R \|- b
+--R ---------------------------------------]
+--R 2
+--R Type: Union(List(Expression(Integer)),...)
+--E 165
+
+--S 166 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ | 4 4 +-+
+--R +-+ - 2\|b \|a x + b + a x + 2b +-+ \|b
+--R \|b log(------------------------------) + 2\|b atanh(-------------)
+--R 4 +--------+
+--R x | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R +--------+ | 4
+--R | 4 2 |a x + b
+--R 2\|a x + b - 2x |--------
+--R | 4
+--R \| x
+--R /
+--R 4
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 4 +--------+
+--R 2 |a x + b +-+ 4 | 4 4 +-+
+--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 6 2 |a x + b
+--R (a x + 2b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R +-+ | 4 5
+--R 2x\|b \|a x + b - a x - 2b x
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ | 4 +--------+
+--R +-+ \|b +---+ \|a x + b | 4
+--R \|b atanh(-------------) - \|- b atan(-----------) + \|a x + b
+--R +--------+ +---+
+--R | 4 \|- b
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 |a x + b
+--R - x |--------
+--R | 4
+--R \| x
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 168
+
+--S 169 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R +--------+
+--R | 4 +--------+
+--R 2 |a x + b | 4 4
+--R - x |-------- \|a x + b + a x + b
+--R | 4
+--R \| x
+--R (7) -------------------------------------
+--R +--------+
+--R | 4
+--R x\|a x + b
+--R Type: Expression(Integer)
+--E 169
+
+)clear all
+
+--S 170 of 1325
+t0:=(a+b/x^4)^(1/2)
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R (1) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 170
+
+--S 171 of 1325
+--r0:=x*sqrt(a+b/x^4)+2*a^(3/4)*(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/_
+-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/sqrt(a+b/x^4)-2*a^(3/4)*_
+-- (-b)^(1/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/sqrt(a+b/x^4)
+--E 171
+
+--S 172 of 1325
+--a0:=integrate(t0,x)
+--E 172
+
+--S 173 of 1325
+--m0:=a0-r0
+--E 173
+
+--S 174 of 1325
+--d0:=D(m0,x)
+--E 174
+
+)clear all
+
+--S 175 of 1325
+t0:=(a+b/x^4)^(1/2)/x
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R (1) -----------
+--R x
+--R Type: Expression(Integer)
+--E 175
+
+--S 176 of 1325
+r0:=1/2*atanh(sqrt(a+b/x^4)/sqrt(a))*sqrt(a)-1/2*sqrt(a+b/x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |-------- +--------+
+--R | 4 | 4
+--R +-+ \| x |a x + b
+--R \|a atanh(-----------) - |--------
+--R +-+ | 4
+--R \|a \| x
+--R (2) ------------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 176
+
+--S 177 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 +-+ | 4 2 +-+ +-+
+--R (x \|a \|a x + b - x \|a \|b )
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R +-+ | 4 4
+--R \|b \|a x + b - a x - b
+--R /
+--R +--------+
+--R 2 | 4 2 +-+
+--R 2x \|a x + b - 2x \|b
+--R ,
+--R
+--R +--------+
+--R +--------+ | 4 +-+
+--R 2 +---+ | 4 2 +---+ +-+ \|a x + b - \|b
+--R (2x \|- a \|a x + b - 2x \|- a \|b )atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R +--------+
+--R +-+ | 4 4
+--R \|b \|a x + b - a x - b
+--R /
+--R +--------+
+--R 2 | 4 2 +-+
+--R 2x \|a x + b - 2x \|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 177
+
+--S 178 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 +-+ | 4 2 +-+ +-+
+--R (x \|a \|a x + b - x \|a \|b )
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R +--------+ | 4
+--R 2 +-+ | 4 2 +-+ +-+ \| x
+--R (- x \|a \|a x + b + x \|a \|b )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R +-+ 2 |a x + b | 4 2 |a x + b +-+ 4
+--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b
+--R | 4 | 4
+--R \| x \| x
+--R /
+--R +--------+
+--R 2 | 4 2 +-+
+--R 2x \|a x + b - 2x \|b
+--R Type: Expression(Integer)
+--E 178
+
+--S 179 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 4
+--R 3 14 2 10 2 6 3 2 |a x + b
+--R (5a x + 25a b x + 36a b x + 16b x ) |--------
+--R | 4
+--R \| x
+--R +
+--R 3 14 2 10 2 6 3 2 +-+
+--R (- 5a x - 25a b x - 36a b x - 16b x )\|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 4
+--R 3 16 2 12 2 8 3 4 +-+ |a x + b 4 16
+--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x
+--R | 4
+--R \| x
+--R +
+--R 3 12 2 2 8 3 4 4
+--R 14a b x + 41a b x + 44a b x + 16b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 3 16 2 12 2 8 3 4 +-+ |a x + b 4 16
+--R (5a x + 25a b x + 36a b x + 16b x )\|a |-------- - 5a x
+--R | 4
+--R \| x
+--R +
+--R 3 12 2 2 8 3 4 4
+--R - 30a b x - 61a b x - 52a b x - 16b
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b
+--R (- a x - 14a b x - 41a b x - 44a b x - 16b x ) |--------
+--R | 4
+--R \| x
+--R +
+--R 4 18 3 14 2 2 10 3 6 4 2 +-+
+--R (a x + 14a b x + 41a b x + 44a b x + 16b x )\|a
+--R /
+--R +--------+
+--R | 4
+--R 2 15 11 2 7 +-+ |a x + b +-+
+--R (5a x + 20a b x + 16b x )\|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 3 17 2 13 2 9 3 5 |a x + b
+--R (- a x - 13a b x - 28a b x - 16b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 3 17 2 13 2 9 3 5 |a x + b +-+
+--R (5a x + 25a b x + 36a b x + 16b x ) |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 3 19 2 15 2 11 3 7 +-+ |a x + b
+--R (- a x - 13a b x - 28a b x - 16b x )\|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R +--------+ | 4
+--R 2 +-+ | 4 2 +-+ +-+ \| x
+--R (- x \|a \|a x + b + x \|a \|b )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R +--------+ | 4 +-+
+--R 2 +---+ | 4 2 +---+ +-+ \|a x + b - \|b
+--R (2x \|- a \|a x + b - 2x \|- a \|b )atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R +-+ 2 |a x + b | 4 2 |a x + b +-+ 4
+--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b
+--R | 4 | 4
+--R \| x \| x
+--R /
+--R +--------+
+--R 2 | 4 2 +-+
+--R 2x \|a x + b - 2x \|b
+--R Type: Expression(Integer)
+--E 180
+
+--S 181 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 4 +--------+
+--R 6 2 |a x + b +-+ 2 8 4 2 | 4
+--R ((- 2a x - 2b x ) |-------- \|b - a x - 3a b x - 2b )\|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 8 4 2 +-+ 2 10 6 2 2 |a x + b
+--R (2a x + 4a b x + 2b )\|b + (a x + 3a b x + 2b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R 9 5 |a x + b | 4 9 5 |a x + b +-+
+--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b
+--R | 4 | 4
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 181
+
+)clear all
+
+--S 182 of 1325
+t0:=(a+b/x^4)^(1/2)/x^2
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R (1) -----------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 1325
+--r0:=-1/3*sqrt(a+b/x^4)/x-2/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)/_
+-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(1/4)*sqrt(a+b/x^4))
+--E 183
+
+--S 184 of 1325
+--a0:=integrate(t0,x)
+--E 184
+
+--S 185 of 1325
+--m0:=a0-r0
+--E 185
+
+--S 186 of 1325
+--d0:=D(m0,x)
+--E 186
+
+)clear all
+
+--S 187 of 1325
+t0:=(a+b/x^4)^(1/2)/x^3
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R (1) -----------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 1325
+r0:=-1/4*a*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))/sqrt(b)-1/4*sqrt(a+b/x^4)/x^2
+--R
+--R
+--R +--------+
+--R +-+ | 4
+--R 2 \|b |a x + b +-+
+--R - a x atanh(-------------) - |-------- \|b
+--R +--------+ | 4
+--R | 4 \| x
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R (2) --------------------------------------------
+--R 2 +-+
+--R 4x \|b
+--R Type: Expression(Integer)
+--E 188
+
+--S 189 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 4 4 +-+ +--------+
+--R 4 - 2b\|a x + b + (a x + 2b)\|b +-+ | 4
+--R a x log(---------------------------------) - 2\|b \|a x + b
+--R 4
+--R x
+--R [-------------------------------------------------------------,
+--R 4 +-+
+--R 8x \|b
+--R +--------+
+--R +---+ | 4 +--------+
+--R 4 \|- b \|a x + b +---+ | 4
+--R - a x atan(-----------------) - \|- b \|a x + b
+--R b
+--R -------------------------------------------------]
+--R 4 +---+
+--R 4x \|- b
+--R Type: Union(List(Expression(Integer)),...)
+--E 189
+
+--S 190 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 4 4 +-+ +-+
+--R 4 - 2b\|a x + b + (a x + 2b)\|b 4 \|b
+--R a x log(---------------------------------) + 2a x atanh(-------------)
+--R 4 +--------+
+--R x | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R +--------+ | 4
+--R +-+ | 4 2 |a x + b +-+
+--R - 2\|b \|a x + b + 2x |-------- \|b
+--R | 4
+--R \| x
+--R /
+--R 4 +-+
+--R 8x \|b
+--R Type: Expression(Integer)
+--E 190
+
+--S 191 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R | 4 2 |a x + b
+--R \|a x + b - x |--------
+--R | 4
+--R \| x
+--R (5) ---------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 191
+
+--S 192 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 4
+--R 4 +---+ \|b 4 +-+ \|- b \|a x + b
+--R a x \|- b atanh(-------------) - a x \|b atan(-----------------)
+--R +--------+ b
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R +--------+ | 4
+--R +---+ +-+ | 4 2 +---+ |a x + b +-+
+--R - \|- b \|b \|a x + b + x \|- b |-------- \|b
+--R | 4
+--R \| x
+--R /
+--R 4 +---+ +-+
+--R 4x \|- b \|b
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R | 4 2 |a x + b
+--R \|a x + b - x |--------
+--R | 4
+--R \| x
+--R (7) ---------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 193
+
+)clear all
+
+--S 194 of 1325
+t0:=(a+b/x^4)^(1/2)/x^4
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R (1) -----------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 1325
+--r0:=-1/5*sqrt(a+b/x^4)/x^3-2/5*a^(7/4)*elliptic_e(asin((-b)^(1/4)/_
+-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4))+_
+-- 2/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4))
+--E 195
+
+--S 196 of 1325
+--a0:=integrate(t0,x)
+--E 196
+
+--S 197 of 1325
+--m0:=a0-r0
+--E 197
+
+--S 198 of 1325
+--d0:=D(m0,x)
+--E 198
+
+)clear all
+
+--S 199 of 1325
+t0:=(a+b/x^4)^(3/2)*x^3
+--R
+--R
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R (1) ---------------------
+--R x
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 1325
+r0:=1/4*(a+b/x^4)^(3/2)*x^4+3/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))*_
+ sqrt(a)-3/4*b*sqrt(a+b/x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |-------- +--------+
+--R | 4 | 4
+--R +-+ \| x 4 |a x + b
+--R 3b\|a atanh(-----------) + (a x - 2b) |--------
+--R +-+ | 4
+--R \|a \| x
+--R (2) -------------------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 200
+
+--S 201 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+
+--R ((3a b x + 12b x )\|a \|a x + b + (- 9a b x - 12b x )\|a \|b )
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4
+--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x
+--R +
+--R 3
+--R - 8b
+--R /
+--R +--------+
+--R 6 2 | 4 6 2 +-+
+--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b
+--R ,
+--R
+--R +--------+
+--R 6 2 2 +---+ | 4
+--R (6a b x + 24b x )\|- a \|a x + b
+--R +
+--R 6 2 2 +---+ +-+
+--R (- 18a b x - 24b x )\|- a \|b
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4
+--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x
+--R +
+--R 3
+--R - 8b
+--R /
+--R +--------+
+--R 6 2 | 4 6 2 +-+
+--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 201
+
+--S 202 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+
+--R ((3a b x + 12b x )\|a \|a x + b + (- 9a b x - 12b x )\|a \|b )
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+
+--R ((- 3a b x - 12b x )\|a \|a x + b + (9a b x + 12b x )\|a \|b )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 8 4 2 +-+
+--R (- 3a x + 2a b x + 8b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b
+--R (- a x - 2a b x + 8b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 2 4 3
+--R (3a x - 2a b x - 8b x ) |-------- \|b + a x + 3a b x - 6a b x - 8b
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R 6 2 | 4 6 2 +-+
+--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 6 26 5 22 4 2 18 3 3 14 2 4 10
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 5 6 6 2
+--R 1088a b x + 256b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 6 26 5 22 4 2 18 3 3 14
+--R - 9a x - 138a b x - 681a b x - 1560a b x
+--R +
+--R 2 4 10 5 6 6 2
+--R - 1840a b x - 1088a b x - 256b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 28 5 24 4 2 20 3 3 16 2 4 12
+--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x
+--R +
+--R 5 8 6 4
+--R - 960a b x - 256b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 7 28 6 24 5 2 20 4 3 16 3 4 12
+--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x
+--R +
+--R 2 5 8 6 4 7
+--R 2352a b x + 1216a b x + 256b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 6 28 5 24 4 2 20 3 3 16 2 4 12
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 5 8 6 4
+--R 1088a b x + 256b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 7 28 6 24 5 2 20 4 3 16 3 4 12
+--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x
+--R +
+--R 2 5 8 6 4 7
+--R - 2928a b x - 1344a b x - 256b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 30 6 26 5 2 22 4 3 18 3 4 14
+--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x
+--R +
+--R 2 5 10 6 6 7 2
+--R - 2352a b x - 1216a b x - 256b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 7 30 6 26 5 2 22 4 3 18 3 4 14
+--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x
+--R +
+--R 2 5 10 6 6 7 2
+--R 2352a b x + 1216a b x + 256b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 23 3 19 2 2 15 3 11 4 7 +-+
+--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 5 25 4 21 3 2 17 2 3 13 4 9
+--R - a x - 41a b x - 280a b x - 688a b x - 704a b x
+--R +
+--R 5 5
+--R - 256b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 5 25 4 21 3 2 17 2 3 13 4 9 5 5
+--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 5 27 4 23 3 2 19 2 3 15 4 11 5 7
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 203
+
+--S 204 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+
+--R ((- 3a b x - 12b x )\|a \|a x + b + (9a b x + 12b x )\|a \|b )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 6 2 2 +---+ | 4 6 2 2 +---+ +-+
+--R ((6a b x + 24b x )\|- a \|a x + b + (- 18a b x - 24b x )\|- a \|b )
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R 2 8 4 2 +-+
+--R (- 3a x + 2a b x + 8b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b
+--R (- a x - 2a b x + 8b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 2 4 3
+--R (3a x - 2a b x - 8b x ) |-------- \|b + a x + 3a b x - 6a b x - 8b
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R 6 2 | 4 6 2 +-+
+--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b
+--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+
+--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b
+--R +
+--R 5 22 4 18 3 2 14 2 3 10 4 6 5 2
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 3 17 2 13 2 9 3 5 |a x + b | 4
+--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 3 17 2 13 2 9 3 5 |a x + b +-+
+--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 1325
+t0:=(a+b/x^4)^(3/2)*x^2
+--R
+--R
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R (1) ---------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 1325
+--r0:=1/3*(a+b/x^4)^(3/2)*x^3-2/3*b*sqrt(a+b/x^4)/x+4/3*a^(5/4)*_
+-- (-b)^(3/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/sqrt(a+b/x^4)
+--E 207
+
+--S 208 of 1325
+--a0:=integrate(t0,x)
+--E 208
+
+--S 209 of 1325
+--m0:=a0-r0
+--E 209
+
+--S 210 of 1325
+--d0:=D(m0,x)
+--E 210
+
+)clear all
+
+--S 211 of 1325
+t0:=(a+b/x^4)^(3/2)*x
+--R
+--R
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R (1) ---------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 211
+
+--S 212 of 1325
+r0:=1/2*(a+b/x^4)^(3/2)*x^2-3/4*a*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))*_
+ sqrt(b)-3/4*b*sqrt(a+b/x^4)/x^2
+--R
+--R
+--R +--------+
+--R +-+ | 4
+--R 2 +-+ \|b 4 |a x + b
+--R - 3a x \|b atanh(-------------) + (2a x - b) |--------
+--R +--------+ | 4
+--R | 4 \| x
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R (2) --------------------------------------------------------
+--R 2
+--R 4x
+--R Type: Expression(Integer)
+--E 212
+
+--S 213 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ | 4 4 +--------+
+--R 4 +-+ - 2\|b \|a x + b + a x + 2b 4 | 4
+--R 3a x \|b log(------------------------------) + (4a x - 2b)\|a x + b
+--R 4
+--R x
+--R [----------------------------------------------------------------------,
+--R 4
+--R 8x
+--R +--------+
+--R | 4 +--------+
+--R 4 +---+ \|a x + b 4 | 4
+--R - 3a x \|- b atan(-----------) + (2a x - b)\|a x + b
+--R +---+
+--R \|- b
+--R -------------------------------------------------------]
+--R 4
+--R 4x
+--R Type: Union(List(Expression(Integer)),...)
+--E 213
+
+--S 214 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ | 4 4
+--R 4 +-+ - 2\|b \|a x + b + a x + 2b
+--R 3a x \|b log(------------------------------)
+--R 4
+--R x
+--R +
+--R +-+ +--------+
+--R 4 +-+ \|b 4 | 4
+--R 6a x \|b atanh(-------------) + (4a x - 2b)\|a x + b
+--R +--------+
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 6 2 |a x + b
+--R (- 4a x + 2b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R 4
+--R 8x
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 2 8 4 2 +-+
+--R (- 2a x - 4a b x - 2b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b
+--R (- a x - 3a b x - 2b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 2 4 3
+--R (2a x + 4a b x + 2b x ) |-------- \|b + a x + 4a b x + 5a b x + 2b
+--R | 4
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R 7 |a x + b +-+ | 4 11 7 |a x + b
+--R 2x |-------- \|b \|a x + b + (- a x - 2b x ) |--------
+--R | 4 | 4
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 215
+
+--S 216 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ | 4
+--R 4 +-+ \|b 4 +---+ \|a x + b
+--R 3a x \|b atanh(-------------) - 3a x \|- b atan(-----------)
+--R +--------+ +---+
+--R | 4 \|- b
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R +--------+ | 4
+--R 4 | 4 6 2 |a x + b
+--R (2a x - b)\|a x + b + (- 2a x + b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R +--------+ | 4
+--R 2 8 4 2 | 4 2 10 6 2 2 |a x + b
+--R (- a x - 2a b x - b )\|a x + b + (a x + 2a b x + b x ) |--------
+--R | 4
+--R \| x
+--R ------------------------------------------------------------------------
+--R +--------+
+--R | 4 +--------+
+--R 7 |a x + b | 4
+--R x |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 217
+
+)clear all
+
+--S 218 of 1325
+t0:=(a+b/x^4)^(3/2)
+--R
+--R
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R (1) ---------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 218
+
+--S 219 of 1325
+--r0:=-1/5*(a+b/x^4)^(3/2)*x+6/5*a*x*sqrt(a+b/x^4)+12/5*a^(7/4)*_
+-- (-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/sqrt(a+b/x^4)-12/5*a^(7/4)*(-b)^(1/4)*_
+-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_
+-- sqrt(a+b/x^4)
+--E 219
+
+--S 220 of 1325
+--a0:=integrate(t0,x)
+--E 220
+
+--S 221 of 1325
+--m0:=a0-r0
+--E 221
+
+--S 222 of 1325
+--d0:=D(m0,x)
+--E 222
+
+)clear all
+
+--S 223 of 1325
+t0:=(a+b/x^4)^(3/2)/x
+--R
+--R
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R (1) ---------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 223
+
+--S 224 of 1325
+r0:=-1/6*(a+b/x^4)^(3/2)+1/2*a^(3/2)*atanh(sqrt(a+b/x^4)/sqrt(a))-_
+ 1/2*a*sqrt(a+b/x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |-------- +--------+
+--R | 4 | 4
+--R 4 +-+ \| x 4 |a x + b
+--R 3a x \|a atanh(-----------) + (- 4a x - b) |--------
+--R +-+ | 4
+--R \|a \| x
+--R (2) ------------------------------------------------------
+--R 4
+--R 6x
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+
+--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b )
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4
+--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x
+--R +
+--R 3
+--R - 4b
+--R /
+--R +--------+
+--R 10 6 | 4 10 6 +-+
+--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b
+--R ,
+--R
+--R +--------+
+--R 2 10 6 +---+ | 4
+--R (6a x + 24a b x )\|- a \|a x + b
+--R +
+--R 2 10 6 +---+ +-+
+--R (- 18a x - 24a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4
+--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x
+--R +
+--R 3
+--R - 4b
+--R /
+--R +--------+
+--R 10 6 | 4 10 6 +-+
+--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 225
+
+--S 226 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+
+--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b )
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+
+--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 8 4 2 +-+
+--R (12a x + 19a b x + 4b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b
+--R (4a x + 17a b x + 4b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8
+--R (- 12a x - 19a b x - 4b x ) |-------- \|b - 4a x - 21a b x
+--R | 4
+--R \| x
+--R +
+--R 2 4 3
+--R - 21a b x - 4b
+--R /
+--R +--------+
+--R 10 6 | 4 10 6 +-+
+--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b
+--R Type: Expression(Integer)
+--E 226
+
+--S 227 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 6 26 5 22 4 2 18 3 3 14 2 4 10
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 5 6 6 2
+--R 1088a b x + 256b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 6 26 5 22 4 2 18 3 3 14
+--R - 9a x - 138a b x - 681a b x - 1560a b x
+--R +
+--R 2 4 10 5 6 6 2
+--R - 1840a b x - 1088a b x - 256b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 6 28 5 24 4 2 20 3 3 16 2 4 12
+--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x
+--R +
+--R 5 8 6 4
+--R - 960a b x - 256b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 7 28 6 24 5 2 20 4 3 16 3 4 12
+--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x
+--R +
+--R 2 5 8 6 4 7
+--R 2352a b x + 1216a b x + 256b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 6 28 5 24 4 2 20 3 3 16 2 4 12
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 5 8 6 4
+--R 1088a b x + 256b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 7 28 6 24 5 2 20 4 3 16 3 4 12
+--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x
+--R +
+--R 2 5 8 6 4 7
+--R - 2928a b x - 1344a b x - 256b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 30 6 26 5 2 22 4 3 18 3 4 14
+--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x
+--R +
+--R 2 5 10 6 6 7 2
+--R - 2352a b x - 1216a b x - 256b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 7 30 6 26 5 2 22 4 3 18 3 4 14
+--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x
+--R +
+--R 2 5 10 6 6 7 2
+--R 2352a b x + 1216a b x + 256b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 27 3 23 2 2 19 3 15 4 11 +-+
+--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 5 29 4 25 3 2 21 2 3 17 4 13
+--R - a x - 41a b x - 280a b x - 688a b x - 704a b x
+--R +
+--R 5 9
+--R - 256b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9
+--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 5 31 4 27 3 2 23 2 3 19 4 15 5 11
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+
+--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 2 10 6 +---+ | 4
+--R (6a x + 24a b x )\|- a \|a x + b
+--R +
+--R 2 10 6 +---+ +-+
+--R (- 18a x - 24a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R 2 8 4 2 +-+
+--R (12a x + 19a b x + 4b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b
+--R (4a x + 17a b x + 4b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8
+--R (- 12a x - 19a b x - 4b x ) |-------- \|b - 4a x - 21a b x
+--R | 4
+--R \| x
+--R +
+--R 2 4 3
+--R - 21a b x - 4b
+--R /
+--R +--------+
+--R 10 6 | 4 10 6 +-+
+--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b
+--R Type: Expression(Integer)
+--E 228
+
+--S 229 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b
+--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+
+--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b
+--R +
+--R 5 22 4 18 3 2 14 2 3 10 4 6 5 2
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 3 21 2 17 2 13 3 9 |a x + b | 4
+--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 3 21 2 17 2 13 3 9 |a x + b +-+
+--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 229
+
+)clear all
+
+--S 230 of 1325
+t0:=(a+b/x^4)^(3/2)/x^2
+--R
+--R
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R (1) ---------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 230
+
+--S 231 of 1325
+--r0:=-1/7*(a+b/x^4)^(3/2)/x-2/7*a*sqrt(a+b/x^4)/x-4/7*a^(9/4)*_
+-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_
+-- ((-b)^(1/4)*sqrt(a+b/x^4))
+--E 231
+
+--S 232 of 1325
+--a0:=integrate(t0,x)
+--E 232
+
+--S 233 of 1325
+--m0:=a0-r0
+--E 233
+
+--S 234 of 1325
+--d0:=D(m0,x)
+--E 234
+
+)clear all
+
+--S 235 of 1325
+t0:=(a+b/x^4)^(3/2)/x^3
+--R
+--R
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R (1) ---------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 235
+
+--S 236 of 1325
+r0:=-1/8*(a+b/x^4)^(3/2)/x^2-3/16*a^2*atanh(sqrt(b)/(x^2*_
+ sqrt(a+b/x^4)))/sqrt(b)-3/16*a*sqrt(a+b/x^4)/x^2
+--R
+--R
+--R +--------+
+--R +-+ | 4
+--R 2 6 \|b 4 |a x + b +-+
+--R - 3a x atanh(-------------) + (- 5a x - 2b) |-------- \|b
+--R +--------+ | 4
+--R | 4 \| x
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R (2) -----------------------------------------------------------
+--R 6 +-+
+--R 16x \|b
+--R Type: Expression(Integer)
+--E 236
+
+--S 237 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 4 4 +-+ +--------+
+--R 2 8 - 2b\|a x + b + (a x + 2b)\|b 4 +-+ | 4
+--R 3a x log(---------------------------------) + (- 10a x - 4b)\|b \|a x + b
+--R 4
+--R x
+--R [----------------------------------------------------------------------------
+--R 8 +-+
+--R 32x \|b
+--R ,
+--R +--------+
+--R +---+ | 4 +--------+
+--R 2 8 \|- b \|a x + b 4 +---+ | 4
+--R - 3a x atan(-----------------) + (- 5a x - 2b)\|- b \|a x + b
+--R b
+--R ----------------------------------------------------------------]
+--R 8 +---+
+--R 16x \|- b
+--R Type: Union(List(Expression(Integer)),...)
+--E 237
+
+--S 238 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 4 4 +-+ +-+
+--R 2 8 - 2b\|a x + b + (a x + 2b)\|b 2 8 \|b
+--R 3a x log(---------------------------------) + 6a x atanh(-------------)
+--R 4 +--------+
+--R x | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R +--------+ | 4
+--R 4 +-+ | 4 6 2 |a x + b +-+
+--R (- 10a x - 4b)\|b \|a x + b + (10a x + 4b x ) |-------- \|b
+--R | 4
+--R \| x
+--R /
+--R 8 +-+
+--R 32x \|b
+--R Type: Expression(Integer)
+--E 238
+
+--S 239 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b +-+ 2 8 2 4 3
+--R ((- a x - 3a b x - 2b x ) |-------- \|b - 2a b x - 4a b x - 2b )
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 3 12 2 8 2 4 3 +-+
+--R (a x + 4a b x + 5a b x + 2b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 2 6 3 2 |a x + b
+--R (2a b x + 4a b x + 2b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R 11 |a x + b | 4 15 11 |a x + b +-+
+--R 2b x |-------- \|a x + b + (- a x - 2b x ) |-------- \|b
+--R | 4 | 4
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 4
+--R 2 8 +---+ \|b 2 8 +-+ \|- b \|a x + b
+--R 3a x \|- b atanh(-------------) - 3a x \|b atan(-----------------)
+--R +--------+ b
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R +--------+ | 4
+--R 4 +---+ +-+ | 4 6 2 +---+ |a x + b +-+
+--R (- 5a x - 2b)\|- b \|b \|a x + b + (5a x + 2b x )\|- b |-------- \|b
+--R | 4
+--R \| x
+--R /
+--R 8 +---+ +-+
+--R 16x \|- b \|b
+--R Type: Expression(Integer)
+--E 240
+
+--S 241 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R +--------+ | 4
+--R 2 8 4 2 | 4 2 10 6 2 2 |a x + b
+--R (- a x - 2a b x - b )\|a x + b + (a x + 2a b x + b x ) |--------
+--R | 4
+--R \| x
+--R ------------------------------------------------------------------------
+--R +--------+
+--R | 4 +--------+
+--R 11 |a x + b | 4
+--R x |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 241
+
+)clear all
+
+--S 242 of 1325
+t0:=(a+b/x^4)^(3/2)/x^4
+--R
+--R
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R (1) ---------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 242
+
+--S 243 of 1325
+--r0:=-1/9*(a+b/x^4)^(3/2)/x^3-2/15*a*sqrt(a+b/x^4)/x^3-4/15*a^(11/4)*_
+-- elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_
+-- ((-b)^(3/4)*sqrt(a+b/x^4))+4/15*a^(11/4)*elliptic_f(_
+-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*_
+-- sqrt(a+b/x^4))
+--E 243
+
+--S 244 of 1325
+--a0:=integrate(t0,x)
+--E 244
+
+--S 245 of 1325
+--m0:=a0-r0
+--E 245
+
+--S 246 of 1325
+--d0:=D(m0,x)
+--E 246
+
+)clear all
+
+--S 247 of 1325
+t0:=(a+b/x^4)^(5/2)*x^3
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R (1) --------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 1325
+r0:=-5/12*b*(a+b/x^4)^(3/2)+1/4*(a+b/x^4)^(5/2)*x^4+5/4*a^(3/2)*b*_
+ atanh(sqrt(a+b/x^4)/sqrt(a))-5/4*a*b*sqrt(a+b/x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |-------- +--------+
+--R | 4 | 4
+--R 4 +-+ \| x 2 8 4 2 |a x + b
+--R 15a b x \|a atanh(-----------) + (3a x - 14a b x - 2b ) |--------
+--R +-+ | 4
+--R \|a \| x
+--R (2) --------------------------------------------------------------------
+--R 4
+--R 12x
+--R Type: Expression(Integer)
+--E 248
+
+--S 249 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 14 2 2 10 3 6 +-+ | 4
+--R (15a b x + 180a b x + 240a b x )\|a \|a x + b
+--R +
+--R 3 14 2 2 10 3 6 +-+ +-+
+--R (- 75a b x - 300a b x - 240a b x )\|a \|b
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4
+--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b
+--R /
+--R +--------+
+--R 2 14 10 2 6 | 4
+--R (12a x + 144a b x + 192b x )\|a x + b
+--R +
+--R 2 14 10 2 6 +-+
+--R (- 60a x - 240a b x - 192b x )\|b
+--R ,
+--R
+--R +--------+
+--R 3 14 2 2 10 3 6 +---+ | 4
+--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b
+--R +
+--R 3 14 2 2 10 3 6 +---+ +-+
+--R (- 150a b x - 600a b x - 480a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R +--------+
+--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4
+--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b
+--R /
+--R +--------+
+--R 2 14 10 2 6 | 4
+--R (12a x + 144a b x + 192b x )\|a x + b
+--R +
+--R 2 14 10 2 6 +-+
+--R (- 60a x - 240a b x - 192b x )\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 249
+
+--S 250 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 3 14 2 2 10 3 6 +-+ | 4
+--R (15a b x + 180a b x + 240a b x )\|a \|a x + b
+--R +
+--R 3 14 2 2 10 3 6 +-+ +-+
+--R (- 75a b x - 300a b x - 240a b x )\|a \|b
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 3 14 2 2 10 3 6 +-+ | 4
+--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b
+--R +
+--R 3 14 2 2 10 3 6 +-+ +-+
+--R (75a b x + 300a b x + 240a b x )\|a \|b
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 16 3 12 2 2 8 3 4 4 +-+
+--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b
+--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +-+
+--R (15a x - 10a b x - 242a b x - 264a b x - 32b x ) |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b
+--R /
+--R +--------+
+--R 2 14 10 2 6 | 4
+--R (12a x + 144a b x + 192b x )\|a x + b
+--R +
+--R 2 14 10 2 6 +-+
+--R (- 60a x - 240a b x - 192b x )\|b
+--R Type: Expression(Integer)
+--E 250
+
+--S 251 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 9 38 8 34 7 2 30 6 3 26
+--R 13a x + 403a b x + 4043a b x + 19825a b x
+--R +
+--R 5 4 22 4 5 18 3 6 14 2 7 10
+--R 55692a b x + 96096a b x + 103936a b x + 68864a b x
+--R +
+--R 8 6 9 2
+--R 25600a b x + 4096b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 9 38 8 34 7 2 30 6 3 26
+--R - 13a x - 403a b x - 4043a b x - 19825a b x
+--R +
+--R 5 4 22 4 5 18 3 6 14 2 7 10
+--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x
+--R +
+--R 8 6 9 2
+--R - 25600a b x - 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 9 40 8 36 7 2 32 6 3 28 5 4 24
+--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x
+--R +
+--R 4 5 20 3 6 16 2 7 12 8 8
+--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x
+--R +
+--R 9 4
+--R - 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 10 40 9 36 8 2 32 7 3 28 6 4 24
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 20 4 6 16 3 7 12 2 8 8
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 4 10
+--R 27648a b x + 4096b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 9 40 8 36 7 2 32 6 3 28 5 4 24
+--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x
+--R +
+--R 4 5 20 3 6 16 2 7 12 8 8
+--R 96096a b x + 103936a b x + 68864a b x + 25600a b x
+--R +
+--R 9 4
+--R 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 10 40 9 36 8 2 32 7 3 28 6 4 24
+--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x
+--R +
+--R 5 5 20 4 6 16 3 7 12 2 8 8
+--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x
+--R +
+--R 9 4 10
+--R - 29696a b x - 4096b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 10 42 9 38 8 2 34 7 3 30 6 4 26
+--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x
+--R +
+--R 5 5 22 4 6 18 3 7 14 2 8 10
+--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x
+--R +
+--R 9 6 10 2
+--R - 27648a b x - 4096b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 10 42 9 38 8 2 34 7 3 30 6 4 26
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 22 4 6 18 3 7 14 2 8 10
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 6 10 2
+--R 27648a b x + 4096b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 35 5 31 4 2 27 3 3 23 2 4 19
+--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x
+--R +
+--R 5 15 6 11
+--R 13312a b x + 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 7 37 6 33 5 2 29 4 3 25 3 4 21
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 17 6 13 7 9
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 7 37 6 33 5 2 29 4 3 25 3 4 21
+--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x
+--R +
+--R 2 5 17 6 13 7 9
+--R 29952a b x + 17408a b x + 4096b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 7 39 6 35 5 2 31 4 3 27 3 4 23
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 19 6 15 7 11
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 3 14 2 2 10 3 6 +-+ | 4
+--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b
+--R +
+--R 3 14 2 2 10 3 6 +-+ +-+
+--R (75a b x + 300a b x + 240a b x )\|a \|b
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 3 14 2 2 10 3 6 +---+ | 4
+--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b
+--R +
+--R 3 14 2 2 10 3 6 +---+ +-+
+--R (- 150a b x - 600a b x - 480a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R 4 16 3 12 2 2 8 3 4 4 +-+
+--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b
+--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +-+
+--R (15a x - 10a b x - 242a b x - 264a b x - 32b x ) |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b
+--R /
+--R +--------+
+--R 2 14 10 2 6 | 4
+--R (12a x + 144a b x + 192b x )\|a x + b
+--R +
+--R 2 14 10 2 6 +-+
+--R (- 60a x - 240a b x - 192b x )\|b
+--R Type: Expression(Integer)
+--E 252
+
+--S 253 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 7 30 6 26 5 2 22 4 3 18 3 4 14
+--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x
+--R +
+--R 2 5 10 6 6 7 2
+--R - 5280a b x - 2560a b x - 512b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 8 32 7 28 6 2 24 5 3 20 4 4 16
+--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x
+--R +
+--R 3 5 12 2 6 8 7 4 8
+--R - 8112a b x - 6496a b x - 2816a b x - 512b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 8 32 7 28 6 2 24 5 3 20 4 4 16
+--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x
+--R +
+--R 3 5 12 2 6 8 7 4 8
+--R 11040a b x + 7840a b x + 3072a b x + 512b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 8 34 7 30 6 2 26 5 3 22 4 4 18
+--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x
+--R +
+--R 3 5 14 2 6 10 7 6 8 2
+--R 8112a b x + 6496a b x + 2816a b x + 512b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R /
+--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 4 +--------+
+--R |a x + b | 4
+--R |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R 5 29 4 25 3 2 21 2 3 17 4 13
+--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x
+--R +
+--R 5 9
+--R - 512b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 253
+
+)clear all
+
+--S 254 of 1325
+t0:=(a+b/x^4)^(5/2)*x^2
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R (1) --------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1325
+--r0:=-10/21*b*(a+b/x^4)^(3/2)/x+1/3*(a+b/x^4)^(5/2)*x^3-20/21*a*b*_
+-- sqrt(a+b/x^4)/x+40/21*a^(9/4)*(-b)^(3/4)*_
+-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_
+-- sqrt(a+b/x^4)
+--E 255
+
+--S 256 of 1325
+--a0:=integrate(t0,x)
+--E 256
+
+--S 257 of 1325
+--m0:=a0-r0
+--E 257
+
+--S 258 of 1325
+--d0:=D(m0,x)
+--E 258
+
+)clear all
+
+--S 259 of 1325
+t0:=(a+b/x^4)^(5/2)*x
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R (1) --------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 1325
+r0:=-5/8*b*(a+b/x^4)^(3/2)/x^2+1/2*(a+b/x^4)^(5/2)*x^2-15/16*a^2*_
+ atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))*sqrt(b)-15/16*a*b*sqrt(a+b/x^4)/x^2
+--R
+--R
+--R +--------+
+--R +-+ | 4
+--R 2 6 +-+ \|b 2 8 4 2 |a x + b
+--R - 15a x \|b atanh(-------------) + (8a x - 9a b x - 2b ) |--------
+--R +--------+ | 4
+--R | 4 \| x
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R (2) ---------------------------------------------------------------------
+--R 6
+--R 16x
+--R Type: Expression(Integer)
+--E 260
+
+--S 261 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 4 4
+--R 2 8 +-+ - 2\|b \|a x + b + a x + 2b
+--R 15a x \|b log(------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+
+--R 2 8 4 2 | 4
+--R (16a x - 18a b x - 4b )\|a x + b
+--R /
+--R 8
+--R 32x
+--R ,
+--R +--------+
+--R | 4 +--------+
+--R 2 8 +---+ \|a x + b 2 8 4 2 | 4
+--R - 15a x \|- b atan(-----------) + (8a x - 9a b x - 2b )\|a x + b
+--R +---+
+--R \|- b
+--R --------------------------------------------------------------------]
+--R 8
+--R 16x
+--R Type: Union(List(Expression(Integer)),...)
+--E 261
+
+--S 262 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ | 4 4
+--R 2 8 +-+ - 2\|b \|a x + b + a x + 2b
+--R 15a x \|b log(------------------------------)
+--R 4
+--R x
+--R +
+--R +-+ +--------+
+--R 2 8 +-+ \|b 2 8 4 2 | 4
+--R 30a x \|b atanh(-------------) + (16a x - 18a b x - 4b )\|a x + b
+--R +--------+
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b
+--R (- 16a x + 18a b x + 4b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R 8
+--R 32x
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 3 12 2 8 2 4 3 +-+
+--R (- 2a x - 6a b x - 6a b x - 2b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 3 14 2 10 2 6 3 2 |a x + b
+--R (- a x - 4a b x - 5a b x - 2b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 3 14 2 10 2 6 3 2 |a x + b +-+ 4 16 3 12
+--R (2a x + 6a b x + 6a b x + 2b x ) |-------- \|b + a x + 5a b x
+--R | 4
+--R \| x
+--R +
+--R 2 2 8 3 4 4
+--R 9a b x + 7a b x + 2b
+--R /
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R 11 |a x + b +-+ | 4 15 11 |a x + b
+--R 2x |-------- \|b \|a x + b + (- a x - 2b x ) |--------
+--R | 4 | 4
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 263
+
+--S 264 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ | 4
+--R 2 8 +-+ \|b 2 8 +---+ \|a x + b
+--R 15a x \|b atanh(-------------) - 15a x \|- b atan(-----------)
+--R +--------+ +---+
+--R | 4 \|- b
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R 2 8 4 2 | 4
+--R (8a x - 9a b x - 2b )\|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b
+--R (- 8a x + 9a b x + 2b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R 8
+--R 16x
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R 3 12 2 8 2 4 3 | 4
+--R (- a x - 3a b x - 3a b x - b )\|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 3 14 2 10 2 6 3 2 |a x + b
+--R (a x + 3a b x + 3a b x + b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 11 |a x + b | 4
+--R x |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 1325
+t0:=(a+b/x^4)^(5/2)
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R (1) --------------------------------
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 266
+
+--S 267 of 1325
+--r0:=-2/9*a*(a+b/x^4)^(3/2)*x-1/9*(a+b/x^4)^(5/2)*x+4/3*a^2*x*_
+-- sqrt(a+b/x^4)+8/3*a^(11/4)*(-b)^(1/4)*_
+-- elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_
+-- sqrt(a+b/x^4)-8/3*a^(11/4)*(-b)^(1/4)*elliptic_f(_
+-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/sqrt(a+b/x^4)
+--E 267
+
+--S 268 of 1325
+--a0:=integrate(t0,x)
+--E 268
+
+--S 269 of 1325
+--m0:=a0-r0
+--E 269
+
+--S 270 of 1325
+--d0:=D(m0,x)
+--E 270
+
+)clear all
+
+--S 271 of 1325
+t0:=(a+b/x^4)^(5/2)/x
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R (1) --------------------------------
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 271
+
+--S 272 of 1325
+r0:=-1/6*a*(a+b/x^4)^(3/2)-1/10*(a+b/x^4)^(5/2)+1/2*a^(5/2)*_
+ atanh(sqrt(a+b/x^4)/sqrt(a))-1/2*a^2*sqrt(a+b/x^4)
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |-------- +--------+
+--R | 4 | 4
+--R 2 8 +-+ \| x 2 8 4 2 |a x + b
+--R 15a x \|a atanh(-----------) + (- 23a x - 11a b x - 3b ) |--------
+--R +-+ | 4
+--R \|a \| x
+--R (2) ---------------------------------------------------------------------
+--R 8
+--R 30x
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 4 18 3 14 2 2 10 +-+ | 4
+--R (15a x + 180a b x + 240a b x )\|a \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 +-+ +-+
+--R (- 75a x - 300a b x - 240a b x )\|a \|b
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4
+--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b
+--R /
+--R +--------+
+--R 2 18 14 2 10 | 4
+--R (30a x + 360a b x + 480b x )\|a x + b
+--R +
+--R 2 18 14 2 10 +-+
+--R (- 150a x - 600a b x - 480b x )\|b
+--R ,
+--R
+--R +--------+
+--R 4 18 3 14 2 2 10 +---+ | 4
+--R (30a x + 360a b x + 480a b x )\|- a \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 +---+ +-+
+--R (- 150a x - 600a b x - 480a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R +--------+
+--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4
+--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b
+--R /
+--R +--------+
+--R 2 18 14 2 10 | 4
+--R (30a x + 360a b x + 480b x )\|a x + b
+--R +
+--R 2 18 14 2 10 +-+
+--R (- 150a x - 600a b x - 480b x )\|b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 273
+
+--S 274 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 4 18 3 14 2 2 10 +-+ | 4
+--R (15a x + 180a b x + 240a b x )\|a \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 +-+ +-+
+--R (- 75a x - 300a b x - 240a b x )\|a \|b
+--R *
+--R +--------+
+--R +-+ 2 +-+ | 4 2 +-+ +-+ 4
+--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 4 18 3 14 2 2 10 +-+ | 4
+--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 +-+ +-+
+--R (75a x + 300a b x + 240a b x )\|a \|b
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 16 3 12 2 2 8 3 4 4 +-+
+--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b
+--R (23a x + 287a b x + 503a b x + 212a b x + 48b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b
+--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b
+--R /
+--R +--------+
+--R 2 18 14 2 10 | 4
+--R (30a x + 360a b x + 480b x )\|a x + b
+--R +
+--R 2 18 14 2 10 +-+
+--R (- 150a x - 600a b x - 480b x )\|b
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 9 38 8 34 7 2 30 6 3 26
+--R 13a x + 403a b x + 4043a b x + 19825a b x
+--R +
+--R 5 4 22 4 5 18 3 6 14 2 7 10
+--R 55692a b x + 96096a b x + 103936a b x + 68864a b x
+--R +
+--R 8 6 9 2
+--R 25600a b x + 4096b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 9 38 8 34 7 2 30 6 3 26
+--R - 13a x - 403a b x - 4043a b x - 19825a b x
+--R +
+--R 5 4 22 4 5 18 3 6 14 2 7 10
+--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x
+--R +
+--R 8 6 9 2
+--R - 25600a b x - 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 9 40 8 36 7 2 32 6 3 28 5 4 24
+--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x
+--R +
+--R 4 5 20 3 6 16 2 7 12 8 8
+--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x
+--R +
+--R 9 4
+--R - 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 10 40 9 36 8 2 32 7 3 28 6 4 24
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 20 4 6 16 3 7 12 2 8 8
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 4 10
+--R 27648a b x + 4096b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 9 40 8 36 7 2 32 6 3 28 5 4 24
+--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x
+--R +
+--R 4 5 20 3 6 16 2 7 12 8 8
+--R 96096a b x + 103936a b x + 68864a b x + 25600a b x
+--R +
+--R 9 4
+--R 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 10 40 9 36 8 2 32 7 3 28 6 4 24
+--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x
+--R +
+--R 5 5 20 4 6 16 3 7 12 2 8 8
+--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x
+--R +
+--R 9 4 10
+--R - 29696a b x - 4096b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 10 42 9 38 8 2 34 7 3 30 6 4 26
+--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x
+--R +
+--R 5 5 22 4 6 18 3 7 14 2 8 10
+--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x
+--R +
+--R 9 6 10 2
+--R - 27648a b x - 4096b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 10 42 9 38 8 2 34 7 3 30 6 4 26
+--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x
+--R +
+--R 5 5 22 4 6 18 3 7 14 2 8 10
+--R 94164a b x + 140896a b x + 135424a b x + 81152a b x
+--R +
+--R 9 6 10 2
+--R 27648a b x + 4096b x
+--R *
+--R +-+
+--R \|a
+--R /
+--R 6 39 5 35 4 2 31 3 3 27 2 4 23
+--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x
+--R +
+--R 5 19 6 15
+--R 13312a b x + 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 7 41 6 37 5 2 33 4 3 29 3 4 25
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 21 6 17 7 13
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 7 41 6 37 5 2 33 4 3 29 3 4 25
+--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x
+--R +
+--R 2 5 21 6 17 7 13
+--R 29952a b x + 17408a b x + 4096b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 7 43 6 39 5 2 35 4 3 31 3 4 27
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 23 6 19 7 15
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 275
+
+--S 276 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R 4 18 3 14 2 2 10 +-+ | 4
+--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 +-+ +-+
+--R (75a x + 300a b x + 240a b x )\|a \|b
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R 4 18 3 14 2 2 10 +---+ | 4
+--R (30a x + 360a b x + 480a b x )\|- a \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 +---+ +-+
+--R (- 150a x - 600a b x - 480a b x )\|- a \|b
+--R *
+--R +--------+
+--R | 4 +-+
+--R \|a x + b - \|b
+--R atan(------------------)
+--R 2 +---+
+--R x \|- a
+--R +
+--R 4 16 3 12 2 2 8 3 4 4 +-+
+--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b
+--R (23a x + 287a b x + 503a b x + 212a b x + 48b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b
+--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x ) |--------
+--R | 4
+--R \| x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b
+--R /
+--R +--------+
+--R 2 18 14 2 10 | 4
+--R (30a x + 360a b x + 480b x )\|a x + b
+--R +
+--R 2 18 14 2 10 +-+
+--R (- 150a x - 600a b x - 480b x )\|b
+--R Type: Expression(Integer)
+--E 276
+
+--S 277 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 7 30 6 26 5 2 22 4 3 18 3 4 14
+--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x
+--R +
+--R 2 5 10 6 6 7 2
+--R - 5280a b x - 2560a b x - 512b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 8 32 7 28 6 2 24 5 3 20 4 4 16
+--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x
+--R +
+--R 3 5 12 2 6 8 7 4 8
+--R - 8112a b x - 6496a b x - 2816a b x - 512b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 8 32 7 28 6 2 24 5 3 20 4 4 16
+--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x
+--R +
+--R 3 5 12 2 6 8 7 4 8
+--R 11040a b x + 7840a b x + 3072a b x + 512b
+--R *
+--R +-+
+--R \|b
+--R +
+--R 8 34 7 30 6 2 26 5 3 22 4 4 18
+--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x
+--R +
+--R 3 5 14 2 6 10 7 6 8 2
+--R 8112a b x + 6496a b x + 2816a b x + 512b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R /
+--R 5 33 4 29 3 2 25 2 3 21 4 17 5 13
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 4 +--------+
+--R |a x + b | 4
+--R |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R 5 33 4 29 3 2 25 2 3 21 4 17
+--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x
+--R +
+--R 5 13
+--R - 512b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 277
+
+)clear all
+
+--S 278 of 1325
+t0:=(a+b/x^4)^(5/2)/x^2
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R (1) --------------------------------
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 278
+
+--S 279 of 1325
+--r0:=-10/77*a*(a+b/x^4)^(3/2)/x-1/11*(a+b/x^4)^(5/2)/x-20/77*a^2*_
+-- sqrt(a+b/x^4)/x-40/77*a^(13/4)*elliptic_f(asin((-b)^(1/4)/_
+-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(1/4)*sqrt(a+b/x^4))
+--E 279
+
+--S 280 of 1325
+--a0:=integrate(t0,x)
+--E 280
+
+--S 281 of 1325
+--m0:=a0-r0
+--E 281
+
+--S 282 of 1325
+--d0:=D(m0,x)
+--E 282
+
+)clear all
+
+--S 283 of 1325
+t0:=(a+b/x^4)^(5/2)/x^3
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R (1) --------------------------------
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 283
+
+--S 284 of 1325
+r0:=-5/48*a*(a+b/x^4)^(3/2)/x^2-1/12*(a+b/x^4)^(5/2)/x^2-5/32*a^3*_
+ atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))/sqrt(b)-5/32*a^2*sqrt(a+b/x^4)/x^2
+--R
+--R
+--R (2)
+--R +--------+
+--R +-+ | 4
+--R 3 10 \|b 2 8 4 2 |a x + b +-+
+--R - 15a x atanh(-------------) + (- 33a x - 26a b x - 8b ) |-------- \|b
+--R +--------+ | 4
+--R | 4 \| x
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R --------------------------------------------------------------------------
+--R 10 +-+
+--R 96x \|b
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R | 4 4 +-+
+--R 3 12 - 2b\|a x + b + (a x + 2b)\|b
+--R 15a x log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +--------+
+--R 2 8 4 2 +-+ | 4
+--R (- 66a x - 52a b x - 16b )\|b \|a x + b
+--R /
+--R 12 +-+
+--R 192x \|b
+--R ,
+--R
+--R +--------+
+--R +---+ | 4
+--R 3 12 \|- b \|a x + b
+--R - 15a x atan(-----------------)
+--R b
+--R +
+--R +--------+
+--R 2 8 4 2 +---+ | 4
+--R (- 33a x - 26a b x - 8b )\|- b \|a x + b
+--R /
+--R 12 +---+
+--R 96x \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 285
+
+--S 286 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 4 4 +-+
+--R 3 12 - 2b\|a x + b + (a x + 2b)\|b
+--R 15a x log(---------------------------------)
+--R 4
+--R x
+--R +
+--R +-+ +--------+
+--R 3 12 \|b 2 8 4 2 +-+ | 4
+--R 30a x atanh(-------------) + (- 66a x - 52a b x - 16b )\|b \|a x + b
+--R +--------+
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b +-+
+--R (66a x + 52a b x + 16b x ) |-------- \|b
+--R | 4
+--R \| x
+--R /
+--R 12 +-+
+--R 192x \|b
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 4
+--R 3 14 2 10 2 6 3 2 |a x + b +-+ 3 12
+--R (- a x - 4a b x - 5a b x - 2b x ) |-------- \|b - 2a b x
+--R | 4
+--R \| x
+--R +
+--R 2 2 8 3 4 4
+--R - 6a b x - 6a b x - 2b
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 4 16 3 12 2 2 8 3 4 4 +-+
+--R (a x + 5a b x + 9a b x + 7a b x + 2b )\|b
+--R +
+--R +--------+
+--R | 4
+--R 3 14 2 2 10 3 6 4 2 |a x + b
+--R (2a b x + 6a b x + 6a b x + 2b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R 15 |a x + b | 4 19 15 |a x + b +-+
+--R 2b x |-------- \|a x + b + (- a x - 2b x ) |-------- \|b
+--R | 4 | 4
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 4
+--R 3 12 +---+ \|b 3 12 +-+ \|- b \|a x + b
+--R 15a x \|- b atanh(-------------) - 15a x \|b atan(-----------------)
+--R +--------+ b
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R 2 8 4 2 +---+ +-+ | 4
+--R (- 33a x - 26a b x - 8b )\|- b \|b \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +---+ |a x + b +-+
+--R (33a x + 26a b x + 8b x )\|- b |-------- \|b
+--R | 4
+--R \| x
+--R /
+--R 12 +---+ +-+
+--R 96x \|- b \|b
+--R Type: Expression(Integer)
+--E 288
+
+--S 289 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R 3 12 2 8 2 4 3 | 4
+--R (- a x - 3a b x - 3a b x - b )\|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 3 14 2 10 2 6 3 2 |a x + b
+--R (a x + 3a b x + 3a b x + b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 15 |a x + b | 4
+--R x |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 289
+
+)clear all
+
+--S 290 of 1325
+t0:=(a+b/x^4)^(5/2)/x^4
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R (1) --------------------------------
+--R 12
+--R x
+--R Type: Expression(Integer)
+--E 290
+
+--S 291 of 1325
+--r0:=-10/117*a*(a+b/x^4)^(3/2)/x^3-1/13*(a+b/x^4)^(5/2)/x^3-_
+-- 4/39*a^2*sqrt(a+b/x^4)/x^3-8/39*a^(15/4)*elliptic_e(_
+-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*_
+-- sqrt(a+b/x^4))+8/39*a^(15/4)*elliptic_f(asin((-b)^(1/4)/_
+-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4))
+--E 291
+
+--S 292 of 1325
+--a0:=integrate(t0,x)
+--E 292
+
+--S 293 of 1325
+--m0:=a0-r0
+--E 293
+
+--S 294 of 1325
+--d0:=D(m0,x)
+--E 294
+
+)clear all
+
+--S 295 of 1325
+t0:=x^3/(a+b/x^4)^(1/2)
+--R
+--R
+--R 3
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 295
+
+--S 296 of 1325
+r0:=-1/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/a^(3/2)+1/4*x^4*sqrt(a+b/x^4)/a
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |-------- +--------+
+--R | 4 | 4
+--R \| x 4 +-+ |a x + b
+--R - b atanh(-----------) + x \|a |--------
+--R +-+ | 4
+--R \|a \| x
+--R (2) ------------------------------------------
+--R +-+
+--R 4a\|a
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 4 4 2
+--R (2b\|b \|a x + b - a b x - 2b )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 6 2 +-+ | 4 6 2 +-+ +-+
+--R (- a x - 2b x )\|a \|a x + b + (2a x + 2b x )\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 4 2 4 +-+
+--R 8a\|a \|b \|a x + b + (- 4a x - 8a b)\|a
+--R ,
+--R
+--R +--------+
+--R +-+ | 4 4 2
+--R (- 4b\|b \|a x + b + 2a b x + 4b )
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R +--------+
+--R 6 2 +---+ | 4 6 2 +---+ +-+
+--R (- a x - 2b x )\|- a \|a x + b + (2a x + 2b x )\|- a \|b
+--R /
+--R +--------+
+--R +---+ +-+ | 4 2 4 +---+
+--R 8a\|- a \|b \|a x + b + (- 4a x - 8a b)\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 297
+
+--S 298 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ | 4 4 2
+--R (2b\|b \|a x + b - a b x - 2b )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R +--------+ | 4
+--R +-+ | 4 4 2 \| x
+--R (2b\|b \|a x + b - a b x - 2b )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 4 +-+ |a x + b +-+ 6 2 +-+ | 4
+--R (- 2x \|a |-------- \|b + (- a x - 2b x )\|a )\|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 6 2 +-+ +-+ 8 4 +-+ |a x + b
+--R (2a x + 2b x )\|a \|b + (a x + 2b x )\|a |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R +-+ +-+ | 4 2 4 +-+
+--R 8a\|a \|b \|a x + b + (- 4a x - 8a b)\|a
+--R Type: Expression(Integer)
+--E 298
+
+--S 299 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 4
+--R 3 17 2 13 2 9 3 5 +-+ |a x + b
+--R (- 7a x - 56a b x - 112a b x - 64b x )\|a |--------
+--R | 4
+--R \| x
+--R +
+--R 4 17 3 13 2 2 9 3 5
+--R - 7a x - 56a b x - 112a b x - 64a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 4
+--R 4 19 3 15 2 2 11 3 7 |a x + b
+--R (- a x - 24a b x - 80a b x - 64a b x ) |--------
+--R | 4
+--R \| x
+--R +
+--R 4 19 3 15 2 2 11 3 7 4 3 +-+
+--R (- a x - 25a b x - 104a b x - 144a b x - 64b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 4 19 3 15 2 2 11 3 7 |a x + b
+--R (7a x + 56a b x + 112a b x + 64a b x ) |--------
+--R | 4
+--R \| x
+--R +
+--R 4 19 3 15 2 2 11 3 7 4 3 +-+
+--R (7a x + 63a b x + 168a b x + 176a b x + 64b x )\|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 4
+--R 4 21 3 17 2 2 13 3 9 4 5 +-+ |a x + b
+--R (a x + 25a b x + 104a b x + 144a b x + 64b x )\|a |--------
+--R | 4
+--R \| x
+--R +
+--R 5 21 4 17 3 2 13 2 3 9 4 5
+--R a x + 25a b x + 104a b x + 144a b x + 64a b x
+--R /
+--R +--------+
+--R | 4
+--R 4 14 3 10 2 2 6 3 2 |a x + b +-+
+--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b
+--R (a x + 25a b x + 104a b x + 144a b x + 64b )\|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +-+
+--R (- 7a x - 63a b x - 168a b x - 176a b x - 64b )\|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 5 18 4 14 3 2 10 2 3 6 4 2 |a x + b
+--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R +--------+ | 4
+--R +---+ +-+ | 4 4 2 +---+ \| x
+--R (2b\|- a \|b \|a x + b + (- a b x - 2b )\|- a )atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R +-+ +-+ | 4 4 2 +-+
+--R (- 4b\|a \|b \|a x + b + (2a b x + 4b )\|a )
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 4 +---+ +-+ |a x + b +-+ 6 2 +---+ +-+ | 4
+--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x )\|- a \|a )\|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 6 2 +---+ +-+ +-+ 8 4 +---+ +-+ |a x + b
+--R (2a x + 2b x )\|- a \|a \|b + (a x + 2b x )\|- a \|a |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R +---+ +-+ +-+ | 4 2 4 +---+ +-+
+--R 8a\|- a \|a \|b \|a x + b + (- 4a x - 8a b)\|- a \|a
+--R Type: Expression(Integer)
+--E 300
+
+--S 301 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 4 +--------+
+--R 9 5 |a x + b +-+ 2 11 7 2 3 | 4
+--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x )\|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 11 7 2 3 +-+ 2 13 9 2 5 |a x + b
+--R (4a x + 12a b x + 8b x )\|b + (a x + 8a b x + 8b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 2 8 4 2 |a x + b | 4
+--R (a x + 8a b x + 8b ) |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b +-+
+--R (- 4a x - 12a b x - 8b ) |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 301
+
+)clear all
+
+--S 302 of 1325
+t0:=x^2/(a+b/x^4)^(1/2)
+--R
+--R
+--R 2
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 302
+
+--S 303 of 1325
+--r0:=1/3*x^3*sqrt(a+b/x^4)/a-1/3*(-b)^(3/4)*_
+-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(3/4)*sqrt(a+b/x^4))
+--E 303
+
+--S 304 of 1325
+--a0:=integrate(t0,x)
+--E 304
+
+--S 305 of 1325
+--m0:=a0-r0
+--E 305
+
+--S 306 of 1325
+--d0:=D(m0,x)
+--E 306
+
+)clear all
+
+--S 307 of 1325
+t0:=x/(a+b/x^4)^(1/2)
+--R
+--R
+--R x
+--R (1) -----------
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 1325
+r0:=1/2*x^2*sqrt(a+b/x^4)/a
+--R
+--R
+--R +--------+
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R (2) -------------
+--R 2a
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 4
+--R \|a x + b
+--R (3) -----------
+--R 2a
+--R Type: Union(Expression(Integer),...)
+--E 309
+
+--S 310 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R | 4 2 |a x + b
+--R \|a x + b - x |--------
+--R | 4
+--R \| x
+--R (4) ---------------------------
+--R 2a
+--R Type: Expression(Integer)
+--E 310
+
+--S 311 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R | 4 3 |a x + b
+--R - x\|a x + b + x |--------
+--R | 4
+--R \| x
+--R (5) ------------------------------
+--R +--------+
+--R | 4 +--------+
+--R |a x + b | 4
+--R |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 311
+
+)clear all
+
+--S 312 of 1325
+t0:=1/(a+b/x^4)^(1/2)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 1325
+--r0:=x*sqrt(a+b/x^4)/a+(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/_
+-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(1/4)*sqrt(a+b/x^4))-_
+-- (-b)^(1/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(1/4)*sqrt(a+b/x^4))
+--E 313
+
+--S 314 of 1325
+--a0:=integrate(t0,x)
+--E 314
+
+--S 315 of 1325
+--m0:=a0-r0
+--E 315
+
+--S 316 of 1325
+--d0:=D(m0,x)
+--E 316
+
+)clear all
+
+--S 317 of 1325
+t0:=1/((a+b/x^4)^(1/2)*x)
+--R
+--R
+--R 1
+--R (1) ------------
+--R +--------+
+--R | 4
+--R |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 1325
+r0:=1/2*atanh(sqrt(a+b/x^4)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R (2) ------------------
+--R +-+
+--R 2\|a
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R [---------------------------------------------------------------,
+--R +-+
+--R 2\|a
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R ------------------------------------]
+--R +---+
+--R \|- a
+--R Type: Union(List(Expression(Integer)),...)
+--E 319
+
+--S 320 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R - atanh(-----------)
+--R +-+
+--R \|a
+--R /
+--R +-+
+--R 2\|a
+--R Type: Expression(Integer)
+--E 320
+
+--S 321 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 4
+--R 6 2 +-+ |a x + b 2 6 2 +-+
+--R ((3a x + 4b x )\|a |-------- - 3a x - 4a b x )\|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 8 4 |a x + b 2 8 4 2 +-+
+--R (- a x - 4a b x ) |-------- + (a x + 5a b x + 4b )\|a
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 8 4 |a x + b 2 8 4 2 +-+ +-+
+--R ((3a x + 4a b x ) |-------- + (- 3a x - 7a b x - 4b )\|a )\|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +-+ |a x + b 3 10 2 6 2 2
+--R (- a x - 5a b x - 4b x )\|a |-------- + a x + 5a b x + 4a b x
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4
+--R 2 7 3 |a x + b +-+
+--R (3a x + 4a b x ) |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 9 5 2 +-+ |a x + b
+--R (- a x - 5a b x - 4b x)\|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 9 5 2 +-+ |a x + b +-+
+--R (3a x + 7a b x + 4b x)\|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 3 11 2 7 2 3 |a x + b
+--R (- a x - 5a b x - 4a b x ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R |-------- +--------+
+--R | 4 +---+ | 4 +---+ +-+
+--R +---+ \| x +-+ \|- a \|a x + b - \|- a \|b
+--R - \|- a atanh(-----------) + 2\|a atan(------------------------------)
+--R +-+ 2
+--R \|a a x
+--R (6) ----------------------------------------------------------------------
+--R +---+ +-+
+--R 2\|- a \|a
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R | 4 2 |a x + b
+--R - \|a x + b + x |--------
+--R | 4
+--R \| x
+--R (7) -----------------------------
+--R +--------+
+--R | 4 +--------+
+--R |a x + b | 4
+--R x |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 323
+
+)clear all
+
+--S 324 of 1325
+t0:=1/((a+b/x^4)^(1/2)*x^2)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 1325
+--r0:=-a^(1/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/((-b)^(1/4)*sqrt(a+b/x^4))
+--E 325
+
+--S 326 of 1325
+--a0:=integrate(t0,x)
+--E 326
+
+--S 327 of 1325
+--m0:=a0-r0
+--E 327
+
+--S 328 of 1325
+--d0:=D(m0,x)
+--E 328
+
+)clear all
+
+--S 329 of 1325
+t0:=1/((a+b/x^4)^(1/2)*x^3)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 4
+--R 3 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 1325
+r0:=-1/2*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))/sqrt(b)
+--R
+--R
+--R +-+
+--R \|b
+--R atanh(-------------)
+--R +--------+
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R (2) - --------------------
+--R +-+
+--R 2\|b
+--R Type: Expression(Integer)
+--E 330
+
+--S 331 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 4 4 +-+ +--------+
+--R - 2b\|a x + b + (a x + 2b)\|b +---+ | 4
+--R log(---------------------------------) \|- b \|a x + b
+--R 4 atan(-----------------)
+--R x b
+--R (3) [--------------------------------------,- -----------------------]
+--R +-+ +---+
+--R 4\|b 2\|- b
+--R Type: Union(List(Expression(Integer)),...)
+--E 331
+
+--S 332 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R +--------+
+--R | 4 4 +-+ +-+
+--R - 2b\|a x + b + (a x + 2b)\|b \|b
+--R log(---------------------------------) + 2atanh(-------------)
+--R 4 +--------+
+--R x | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R (4) --------------------------------------------------------------
+--R +-+
+--R 4\|b
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 4 +--------+
+--R 4 +-+ 2 |a x + b | 4
+--R ((- a x - 2b)\|b - 2b x |-------- )\|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 6 2 |a x + b +-+ 4 2
+--R (a x + 2b x ) |-------- \|b + 2a b x + 2b
+--R | 4
+--R \| x
+--R /
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R 7 3 |a x + b +-+ | 4 7 2 3 |a x + b
+--R (a x + 2b x ) |-------- \|b \|a x + b + (- 2a b x - 2b x ) |--------
+--R | 4 | 4
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 333
+
+--S 334 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ +---+ | 4
+--R +---+ \|b +-+ \|- b \|a x + b
+--R \|- b atanh(-------------) - \|b atan(-----------------)
+--R +--------+ b
+--R | 4
+--R 2 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R (6) --------------------------------------------------------
+--R +---+ +-+
+--R 2\|- b \|b
+--R Type: Expression(Integer)
+--E 334
+
+--S 335 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R | 4 2 |a x + b
+--R - \|a x + b + x |--------
+--R | 4
+--R \| x
+--R (7) -----------------------------
+--R +--------+
+--R | 4 +--------+
+--R 3 |a x + b | 4
+--R x |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 335
+
+)clear all
+
+--S 336 of 1325
+t0:=1/((a+b/x^4)^(1/2)*x^4)
+--R
+--R
+--R 1
+--R (1) -------------
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R x |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 1325
+--r0:=-a^(3/4)*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4))+a^(3/4)*_
+-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4))
+--E 337
+
+--S 338 of 1325
+--a0:=integrate(t0,x)
+--E 338
+
+--S 339 of 1325
+--m0:=a0-r0
+--E 339
+
+--S 340 of 1325
+--d0:=D(m0,x)
+--E 340
+
+)clear all
+
+--S 341 of 1325
+t0:=x^3/(a+b/x^4)^(3/2)
+--R
+--R
+--R 7
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 341
+
+--S 342 of 1325
+r0:=-3/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/a^(5/2)-_
+ 1/2*x^4/(a*sqrt(a+b/x^4))+3/4*x^4*sqrt(a+b/x^4)/a^2
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R +--------+ |--------
+--R | 4 | 4
+--R |a x + b \| x 4 +-+
+--R - 3b |-------- atanh(-----------) + (a x + 3b)\|a
+--R | 4 +-+
+--R \| x \|a
+--R (2) ---------------------------------------------------
+--R +--------+
+--R | 4
+--R 2 +-+ |a x + b
+--R 4a \|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 4 2 +-+ | 4 2 8 2 4 3
+--R ((9a b x + 12b )\|b \|a x + b - 3a b x - 15a b x - 12b )
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 10 6 2 2 +-+ | 4
+--R (- a x - 7a b x - 12b x )\|a \|a x + b
+--R +
+--R 2 10 6 2 2 +-+ +-+
+--R (3a x + 13a b x + 12b x )\|a \|b
+--R /
+--R +--------+
+--R 3 4 2 +-+ +-+ | 4 4 8 3 4 2 2 +-+
+--R (12a x + 16a b)\|a \|b \|a x + b + (- 4a x - 20a b x - 16a b )\|a
+--R ,
+--R
+--R +--------+
+--R 4 2 +-+ | 4 2 8 2 4 3
+--R ((- 18a b x - 24b )\|b \|a x + b + 6a b x + 30a b x + 24b )
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R +--------+
+--R 2 10 6 2 2 +---+ | 4
+--R (- a x - 7a b x - 12b x )\|- a \|a x + b
+--R +
+--R 2 10 6 2 2 +---+ +-+
+--R (3a x + 13a b x + 12b x )\|- a \|b
+--R /
+--R +--------+
+--R 3 4 2 +---+ +-+ | 4
+--R (12a x + 16a b)\|- a \|b \|a x + b
+--R +
+--R 4 8 3 4 2 2 +---+
+--R (- 4a x - 20a b x - 16a b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 343
+
+--S 344 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 4 +--------+
+--R 4 2 |a x + b +-+ | 4
+--R (9a b x + 12b ) |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 8 2 4 3 |a x + b
+--R (- 3a b x - 15a b x - 12b ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 4 2 |a x + b +-+ | 4
+--R (9a b x + 12b ) |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 8 2 4 3 |a x + b
+--R (- 3a b x - 15a b x - 12b ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 8 4 2 +-+ +-+
+--R (- 3a x - 13a b x - 12b )\|a \|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +-+ |a x + b
+--R (- a x - 7a b x - 12b x )\|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +-+ |a x + b +-+
+--R (3a x + 13a b x + 12b x )\|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 3 12 2 8 2 4 3 +-+
+--R (a x + 8a b x + 19a b x + 12b )\|a
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 3 4 2 +-+ |a x + b +-+ | 4
+--R (12a x + 16a b)\|a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 4 8 3 4 2 2 +-+ |a x + b
+--R (- 4a x - 20a b x - 16a b )\|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 4 25 3 21 2 2 17 3 13 4 9 +-+
+--R (- 9a x - 120a b x - 432a b x - 576a b x - 256b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 5 25 4 21 3 2 17 2 3 13 4 9
+--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 27 4 23 3 2 19 2 3 15 4 11
+--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 5 27 4 23 3 2 19 2 3 15 4 11
+--R - a x - 41a b x - 280a b x - 688a b x - 704a b x
+--R +
+--R 5 7
+--R - 256b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 5 27 4 23 3 2 19 2 3 15 4 11
+--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 5 27 4 23 3 2 19 2 3 15 4 11
+--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x
+--R +
+--R 5 7
+--R 256b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9
+--R (a x + 41a b x + 280a b x + 688a b x + 704a b x + 256b x )
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 6 29 5 25 4 2 21 3 3 17 2 4 13 5 9
+--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x
+--R /
+--R 6 22 5 18 4 2 14 3 3 10 2 4 6
+--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x
+--R +
+--R 5 2
+--R 256a b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 6 24 5 20 4 2 16 3 3 12 2 4 8
+--R a x + 42a b x + 321a b x + 968a b x + 1392a b x
+--R +
+--R 5 4 6
+--R 960a b x + 256b
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 6 24 5 20 4 2 16 3 3 12 2 4 8
+--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x
+--R +
+--R 5 4 6
+--R - 1088a b x - 256b
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 7 26 6 22 5 2 18 4 3 14 3 4 10
+--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x
+--R +
+--R 2 5 6 6 2
+--R - 960a b x - 256a b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 345
+
+--S 346 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 4 +--------+
+--R 4 2 +---+ |a x + b +-+ | 4
+--R (9a b x + 12b )\|- a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 8 2 4 3 +---+ |a x + b
+--R (- 3a b x - 15a b x - 12b )\|- a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 4 2 +-+ |a x + b +-+ | 4
+--R (- 18a b x - 24b )\|a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 8 2 4 3 +-+ |a x + b
+--R (6a b x + 30a b x + 24b )\|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R 2 8 4 2 +---+ +-+ +-+
+--R (- 3a x - 13a b x - 12b )\|- a \|a \|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +---+ +-+ |a x + b
+--R (- a x - 7a b x - 12b x )\|- a \|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +---+ +-+ |a x + b +-+
+--R (3a x + 13a b x + 12b x )\|- a \|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 3 12 2 8 2 4 3 +---+ +-+
+--R (a x + 8a b x + 19a b x + 12b )\|- a \|a
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 3 4 2 +---+ +-+ |a x + b +-+ | 4
+--R (12a x + 16a b)\|- a \|a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 4 8 3 4 2 2 +---+ +-+ |a x + b
+--R (- 4a x - 20a b x - 16a b )\|- a \|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 4
+--R 2 17 13 2 9 |a x + b +-+ 3 19 2 15
+--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x
+--R | 4
+--R \| x
+--R +
+--R 2 11 3 7
+--R - 48a b x - 32b x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 3 19 2 15 2 11 3 7 +-+
+--R (6a x + 38a b x + 64a b x + 32b x )\|b
+--R +
+--R +--------+
+--R | 4
+--R 3 21 2 17 2 13 3 9 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 4 16 3 12 2 2 8 3 4 4 |a x + b | 4
+--R (a x + 19a b x + 66a b x + 80a b x + 32b ) |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 4 16 3 12 2 2 8 3 4 4 |a x + b +-+
+--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b ) |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 347
+
+)clear all
+
+--S 348 of 1325
+t0:=x^2/(a+b/x^4)^(3/2)
+--R
+--R
+--R 6
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 348
+
+--S 349 of 1325
+--r0:=-1/2*x^3/(a*sqrt(a+b/x^4))+5/6*x^3*sqrt(a+b/x^4)/a^2-_
+-- 5/6*(-b)^(3/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(7/4)*sqrt(a+b/x^4))
+--E 349
+
+--S 350 of 1325
+--a0:=integrate(t0,x)
+--E 350
+
+--S 351 of 1325
+--m0:=a0-r0
+--E 351
+
+--S 352 of 1325
+--d0:=D(m0,x)
+--E 352
+
+)clear all
+
+--S 353 of 1325
+t0:=x/(a+b/x^4)^(3/2)
+--R
+--R
+--R 5
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 353
+
+--S 354 of 1325
+r0:=-1/2*x^2/(a*sqrt(a+b/x^4))+x^2*sqrt(a+b/x^4)/a^2
+--R
+--R
+--R 4
+--R a x + 2b
+--R (2) ----------------
+--R +--------+
+--R | 4
+--R 2 2 |a x + b
+--R 2a x |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R a x + 2b
+--R (3) --------------
+--R +--------+
+--R 2 | 4
+--R 2a \|a x + b
+--R Type: Union(Expression(Integer),...)
+--E 355
+
+--S 356 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R 4 | 4 6 2 |a x + b
+--R (- a x - 2b)\|a x + b + (a x + 2b x ) |--------
+--R | 4
+--R \| x
+--R (4) ----------------------------------------------------
+--R +--------+
+--R | 4 +--------+
+--R 2 2 |a x + b | 4
+--R 2a x |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R 5 | 4 7 |a x + b
+--R - x \|a x + b + x |--------
+--R | 4
+--R \| x
+--R (5) --------------------------------
+--R +--------+
+--R | 4 +--------+
+--R 4 |a x + b | 4
+--R (a x + b) |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 357
+
+)clear all
+
+--S 358 of 1325
+t0:=1/(a+b/x^4)^(3/2)
+--R
+--R
+--R 4
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 358
+
+--S 359 of 1325
+--r0:=-1/2*x/(a*sqrt(a+b/x^4))+3/2*x*sqrt(a+b/x^4)/a^2+_
+-- 3/2*(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(5/4)*sqrt(a+b/x^4))-3/2*(-b)^(1/4)*_
+-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(5/4)*sqrt(a+b/x^4))
+--E 359
+
+--S 360 of 1325
+--a0:=integrate(t0,x)
+--E 360
+
+--S 361 of 1325
+--m0:=a0-r0
+--E 361
+
+--S 362 of 1325
+--d0:=D(m0,x)
+--E 362
+
+)clear all
+
+--S 363 of 1325
+t0:=1/((a+b/x^4)^(3/2)*x)
+--R
+--R
+--R 3
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 1325
+r0:=1/2*atanh(sqrt(a+b/x^4)/sqrt(a))/a^(3/2)+(-1/2)/(a*sqrt(a+b/x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R +--------+ |--------
+--R | 4 | 4
+--R |a x + b \| x +-+
+--R |-------- atanh(-----------) - \|a
+--R | 4 +-+
+--R \| x \|a
+--R (2) ------------------------------------
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R 2a\|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 4 4
+--R (\|b \|a x + b - a x - b)
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 +-+ | 4 2 +-+ +-+
+--R x \|a \|a x + b - x \|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 4 2 4 +-+
+--R 2a\|a \|b \|a x + b + (- 2a x - 2a b)\|a
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 4 +---+ +-+
+--R +-+ | 4 4 \|- a \|a x + b - \|- a \|b
+--R (2\|b \|a x + b - 2a x - 2b)atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R +--------+
+--R 2 +---+ | 4 2 +---+ +-+
+--R x \|- a \|a x + b - x \|- a \|b
+--R /
+--R +--------+
+--R +---+ +-+ | 4 2 4 +---+
+--R 2a\|- a \|b \|a x + b + (- 2a x - 2a b)\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 365
+
+--S 366 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R |a x + b +-+ | 4 4 |a x + b
+--R ( |-------- \|b \|a x + b + (- a x - b) |-------- )
+--R | 4 | 4
+--R \| x \| x
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 4
+--R |a x + b
+--R +--------+ +--------+ |--------
+--R | 4 +--------+ | 4 | 4
+--R |a x + b +-+ | 4 4 |a x + b \| x
+--R (- |-------- \|b \|a x + b + (a x + b) |-------- )atanh(-----------)
+--R | 4 | 4 +-+
+--R \| x \| x \|a
+--R +
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R +-+ +-+ 2 +-+ |a x + b | 4 2 +-+ |a x + b +-+
+--R (\|a \|b + x \|a |-------- )\|a x + b - x \|a |-------- \|b
+--R | 4 | 4
+--R \| x \| x
+--R +
+--R 4 +-+
+--R (- a x - b)\|a
+--R /
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R +-+ |a x + b +-+ | 4 2 4 +-+ |a x + b
+--R 2a\|a |-------- \|b \|a x + b + (- 2a x - 2a b)\|a |--------
+--R | 4 | 4
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R +--------+
+--R | 4
+--R 2 13 9 2 5 +-+ |a x + b 3 13 2 9
+--R (5a x + 20a b x + 16b x )\|a |-------- - 5a x - 20a b x
+--R | 4
+--R \| x
+--R +
+--R 2 5
+--R - 16a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 4
+--R 3 15 2 11 2 7 |a x + b
+--R (- a x - 12a b x - 16a b x ) |--------
+--R | 4
+--R \| x
+--R +
+--R 3 15 2 11 2 7 3 3 +-+
+--R (a x + 13a b x + 28a b x + 16b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 3 15 2 11 2 7 |a x + b
+--R (5a x + 20a b x + 16a b x ) |--------
+--R | 4
+--R \| x
+--R +
+--R 3 15 2 11 2 7 3 3 +-+
+--R (- 5a x - 25a b x - 36a b x - 16b x )\|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R +--------+
+--R | 4
+--R 3 17 2 13 2 9 3 5 +-+ |a x + b 4 17
+--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x
+--R | 4
+--R \| x
+--R +
+--R 3 13 2 2 9 3 5
+--R 13a b x + 28a b x + 16a b x
+--R /
+--R +--------+
+--R | 4
+--R 4 14 3 10 2 2 6 3 2 |a x + b +-+
+--R (5a x + 25a b x + 36a b x + 16a b x ) |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b
+--R (- a x - 14a b x - 41a b x - 44a b x - 16b )\|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +-+
+--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 5 18 4 14 3 2 10 2 3 6 4 2 |a x + b
+--R (- a x - 14a b x - 41a b x - 44a b x - 16a b x ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R +---+ |a x + b +-+ | 4 4 +---+ |a x + b
+--R (- \|- a |-------- \|b \|a x + b + (a x + b)\|- a |-------- )
+--R | 4 | 4
+--R \| x \| x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+ +--------+
+--R | 4 +--------+ | 4
+--R +-+ |a x + b +-+ | 4 4 +-+ |a x + b
+--R (2\|a |-------- \|b \|a x + b + (- 2a x - 2b)\|a |-------- )
+--R | 4 | 4
+--R \| x \| x
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R +--------+
+--R | 4 +--------+
+--R +---+ +-+ +-+ 2 +---+ +-+ |a x + b | 4
+--R (\|- a \|a \|b + x \|- a \|a |-------- )\|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 +---+ +-+ |a x + b +-+ 4 +---+ +-+
+--R - x \|- a \|a |-------- \|b + (- a x - b)\|- a \|a
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R +---+ +-+ |a x + b +-+ | 4
+--R 2a\|- a \|a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 4 +---+ +-+ |a x + b
+--R (- 2a x - 2a b)\|- a \|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 4 +--------+
+--R 5 |a x + b +-+ 7 3 | 4 7 3 +-+
+--R (- 2x |-------- \|b - a x - 2b x )\|a x + b + (2a x + 2b x )\|b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 9 5 |a x + b
+--R (a x + 2b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 2 8 4 2 |a x + b | 4
+--R (a x + 3a b x + 2b ) |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b +-+
+--R (- 2a x - 4a b x - 2b ) |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 369
+
+)clear all
+
+--S 370 of 1325
+t0:=1/((a+b/x^4)^(3/2)*x^2)
+--R
+--R
+--R 2
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 370
+
+--S 371 of 1325
+--r0:=(-1/2)/(a*x*sqrt(a+b/x^4))-1/2*elliptic_f(asin((-b)^(1/4)/_
+-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(3/4)*(-b)^(1/4)*sqrt(a+b/x^4))
+--E 371
+
+--S 372 of 1325
+--a0:=integrate(t0,x)
+--E 372
+
+--S 373 of 1325
+--m0:=a0-r0
+--E 373
+
+--S 374 of 1325
+--d0:=D(m0,x)
+--E 374
+
+)clear all
+
+--S 375 of 1325
+t0:=1/((a+b/x^4)^(3/2)*x^3)
+--R
+--R
+--R x
+--R (1) ---------------------
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 375
+
+--S 376 of 1325
+r0:=(-1/2)/(a*x^2*sqrt(a+b/x^4))
+--R
+--R
+--R 1
+--R (2) - ----------------
+--R +--------+
+--R | 4
+--R 2 |a x + b
+--R 2a x |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 376
+
+--S 377 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 1
+--R (3) - -------------
+--R +--------+
+--R | 4
+--R 2a\|a x + b
+--R Type: Union(Expression(Integer),...)
+--E 377
+
+--S 378 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R | 4 2 |a x + b
+--R \|a x + b - x |--------
+--R | 4
+--R \| x
+--R (4) ---------------------------
+--R +--------+
+--R | 4 +--------+
+--R 2 |a x + b | 4
+--R 2a x |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R | 4 3 |a x + b
+--R - x\|a x + b + x |--------
+--R | 4
+--R \| x
+--R (5) --------------------------------
+--R +--------+
+--R | 4 +--------+
+--R 4 |a x + b | 4
+--R (a x + b) |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 379
+
+)clear all
+
+--S 380 of 1325
+t0:=1/((a+b/x^4)^(3/2)*x^4)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R | 4
+--R 4 |a x + b
+--R (a x + b) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 1325
+--r0:=(-1/2)/(a*x^3*sqrt(a+b/x^4))+1/2*elliptic_e(asin((-b)^(1/4)/_
+-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(1/4)*(-b)^(3/4)*_
+-- sqrt(a+b/x^4))-1/2*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(1/4)*(-b)^(3/4)*sqrt(a+b/x^4))
+--E 381
+
+--S 382 of 1325
+--a0:=integrate(t0,x)
+--E 382
+
+--S 383 of 1325
+--m0:=a0-r0
+--E 383
+
+--S 384 of 1325
+--d0:=D(m0,x)
+--E 384
+
+)clear all
+
+--S 385 of 1325
+t0:=x^3/(a+b/x^4)^(5/2)
+--R
+--R
+--R 11
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 1325
+r0:=-1/6*x^4/(a*(a+b/x^4)^(3/2))-5/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/_
+ a^(7/2)-5/6*x^4/(a^2*sqrt(a+b/x^4))+5/4*x^4*sqrt(a+b/x^4)/a^3
+--R
+--R
+--R (2)
+--R +--------+
+--R | 4
+--R |a x + b
+--R +--------+ |--------
+--R | 4 | 4
+--R 4 2 |a x + b \| x
+--R (- 15a b x - 15b ) |-------- atanh(-----------)
+--R | 4 +-+
+--R \| x \|a
+--R +
+--R 2 8 4 2 +-+
+--R (3a x + 20a b x + 15b )\|a
+--R /
+--R +--------+
+--R | 4
+--R 4 4 3 +-+ |a x + b
+--R (12a x + 12a b)\|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 3 12 2 2 8 3 4 4 +-+ | 4
+--R (75a b x + 375a b x + 540a b x + 240b )\|b \|a x + b
+--R +
+--R 4 16 3 2 12 2 3 8 4 4 5
+--R - 15a b x - 210a b x - 615a b x - 660a b x - 240b
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R 4 18 3 14 2 2 10 3 6 4 2 +-+
+--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +-+
+--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|a \|b
+--R /
+--R +--------+
+--R 6 12 5 8 4 2 4 3 3 +-+ +-+ | 4
+--R (60a x + 300a b x + 432a b x + 192a b )\|a \|b \|a x + b
+--R +
+--R 7 16 6 12 5 2 8 4 3 4 3 4 +-+
+--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|a
+--R ,
+--R
+--R +--------+
+--R 3 12 2 2 8 3 4 4 +-+ | 4
+--R (- 150a b x - 750a b x - 1080a b x - 480b )\|b \|a x + b
+--R +
+--R 4 16 3 2 12 2 3 8 4 4 5
+--R 30a b x + 420a b x + 1230a b x + 1320a b x + 480b
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R 4 18 3 14 2 2 10 3 6 4 2 +---+
+--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|- a
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +-+
+--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|- a \|b
+--R /
+--R +--------+
+--R 6 12 5 8 4 2 4 3 3 +---+ +-+ | 4
+--R (60a x + 300a b x + 432a b x + 192a b )\|- a \|b \|a x + b
+--R +
+--R 7 16 6 12 5 2 8 4 3 4 3 4 +---+
+--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 387
+
+--S 388 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 4 +--------+
+--R 3 12 2 2 8 3 4 4 |a x + b +-+ | 4
+--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 4 16 3 2 12 2 3 8 4 4 5 |a x + b
+--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 3 12 2 2 8 3 4 4 |a x + b +-+ | 4
+--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 4 16 3 2 12 2 3 8 4 4 5 |a x + b
+--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 4 16 3 12 2 2 8 3 4 4 +-+ +-+
+--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|a \|b
+--R +
+--R 4 18 3 14 2 2 10 3 6 4 2 +-+
+--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 3 6 4 2 +-+
+--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+
+--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|a
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 6 12 5 8 4 2 4 3 3 +-+ |a x + b +-+ | 4
+--R (60a x + 300a b x + 432a b x + 192a b )\|a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 7 16 6 12 5 2 8 4 3 4 3 4 +-+ |a x + b
+--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 388
+
+--S 389 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 6 37 5 33 4 2 29 3 3 25
+--R - 13a x - 364a b x - 2912a b x - 9984a b x
+--R +
+--R 2 4 21 5 17 6 13
+--R - 16640a b x - 13312a b x - 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 7 37 6 33 5 2 29 4 3 25 3 4 21
+--R - 13a x - 364a b x - 2912a b x - 9984a b x - 16640a b x
+--R +
+--R 2 5 17 6 13
+--R - 13312a b x - 4096a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 39 6 35 5 2 31 4 3 27 3 4 23
+--R - a x - 84a b x - 1120a b x - 5376a b x - 11520a b x
+--R +
+--R 2 5 19 6 15
+--R - 11264a b x - 4096a b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 7 39 6 35 5 2 31 4 3 27 3 4 23
+--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x
+--R +
+--R 2 5 19 6 15 7 11
+--R - 22784a b x - 15360a b x - 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 7 39 6 35 5 2 31 4 3 27 3 4 23
+--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x
+--R +
+--R 2 5 19 6 15
+--R 13312a b x + 4096a b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 7 39 6 35 5 2 31 4 3 27 3 4 23
+--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x
+--R +
+--R 2 5 19 6 15 7 11
+--R 29952a b x + 17408a b x + 4096b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 7 41 6 37 5 2 33 4 3 29 3 4 25
+--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x
+--R +
+--R 2 5 21 6 17 7 13
+--R 22784a b x + 15360a b x + 4096b x
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 8 41 7 37 6 2 33 5 3 29 4 4 25
+--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x
+--R +
+--R 3 5 21 2 6 17 7 13
+--R 22784a b x + 15360a b x + 4096a b x
+--R /
+--R 9 34 8 30 7 2 26 6 3 22 5 4 18
+--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x
+--R +
+--R 4 5 14 3 6 10 2 7 6 8 2
+--R 56576a b x + 47360a b x + 21504a b x + 4096a b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 9 36 8 32 7 2 28 6 3 24 5 4 20
+--R a x + 87a b x + 1375a b x + 8989a b x + 31092a b x
+--R +
+--R 4 5 16 3 6 12 2 7 8 8 4 9
+--R 63072a b x + 77824a b x + 57600a b x + 23552a b x + 4096b
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 9 36 8 32 7 2 28 6 3 24 5 4 20
+--R - 13a x - 403a b x - 4043a b x - 19825a b x - 55692a b x
+--R +
+--R 4 5 16 3 6 12 2 7 8 8 4 9
+--R - 96096a b x - 103936a b x - 68864a b x - 25600a b x - 4096b
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 10 38 9 34 8 2 30 7 3 26 6 4 22
+--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x
+--R +
+--R 5 5 18 4 6 14 3 7 10 2 8 6 9 2
+--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096a b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 4
+--R 3 12 2 2 8 3 4 4 +---+ |a x + b +-+
+--R (75a b x + 375a b x + 540a b x + 240b )\|- a |-------- \|b
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 4 16 3 2 12 2 3 8 4 4 5 +---+
+--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b )\|- a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 4
+--R 3 12 2 2 8 3 4 4 +-+ |a x + b +-+
+--R (- 150a b x - 750a b x - 1080a b x - 480b )\|a |-------- \|b
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 4 16 3 2 12 2 3 8 4 4 5 +-+
+--R (30a b x + 420a b x + 1230a b x + 1320a b x + 480b )\|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R 4 16 3 12 2 2 8 3 4 4 +---+ +-+
+--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|- a \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +-+
+--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|- a \|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +-+
+--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|- a \|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +---+ +-+
+--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|- a \|a
+--R /
+--R +--------+
+--R | 4
+--R 6 12 5 8 4 2 4 3 3 +---+ +-+ |a x + b +-+
+--R (60a x + 300a b x + 432a b x + 192a b )\|- a \|a |-------- \|b
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 7 16 6 12 5 2 8 4 3 4 3 4 +---+ +-+
+--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|- a \|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 390
+
+--S 391 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R 4 29 3 25 2 2 21 3 17 4 13
+--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 5 31 4 27 3 2 23 2 3 19 4 15 5 11
+--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 5 31 4 27 3 2 23 2 3 19 4 15
+--R 10a x + 170a b x + 832a b x + 1696a b x + 1536a b x
+--R +
+--R 5 11
+--R 512b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 33 4 29 3 2 25 2 3 21 4 17 5 13
+--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R /
+--R 7 28 6 24 5 2 20 4 3 16 3 4 12
+--R a x + 52a b x + 501a b x + 1970a b x + 3920a b x
+--R +
+--R 2 5 8 6 4 7
+--R 4192a b x + 2304a b x + 512b
+--R *
+--R +--------+
+--R | 4 +--------+
+--R |a x + b | 4
+--R |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R 7 28 6 24 5 2 20 4 3 16 3 4 12
+--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x
+--R +
+--R 2 5 8 6 4 7
+--R - 5280a b x - 2560a b x - 512b
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 391
+
+)clear all
+
+--S 392 of 1325
+t0:=x^2/(a+b/x^4)^(5/2)
+--R
+--R
+--R 10
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1325
+--r0:=-1/6*x^3/(a*(a+b/x^4)^(3/2))-3/4*x^3/(a^2*sqrt(a+b/x^4))+_
+-- 5/4*x^3*sqrt(a+b/x^4)/a^3-5/4*(-b)^(3/4)*elliptic_f(_
+-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(11/4)*_
+-- sqrt(a+b/x^4))
+--E 393
+
+--S 394 of 1325
+--a0:=integrate(t0,x)
+--E 394
+
+--S 395 of 1325
+--m0:=a0-r0
+--E 395
+
+--S 396 of 1325
+--d0:=D(m0,x)
+--E 396
+
+)clear all
+
+--S 397 of 1325
+t0:=x/(a+b/x^4)^(5/2)
+--R
+--R
+--R 9
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1325
+r0:=-1/6*x^2/(a*(a+b/x^4)^(3/2))-2/3*x^2/(a^2*sqrt(a+b/x^4))+_
+ 4/3*x^2*sqrt(a+b/x^4)/a^3
+--R
+--R
+--R 2 8 4 2
+--R 3a x + 12a b x + 8b
+--R (2) ----------------------------
+--R +--------+
+--R | 4
+--R 4 6 3 2 |a x + b
+--R (6a x + 6a b x ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 8 4 2
+--R 3a x + 12a b x + 8b
+--R (3) -------------------------
+--R +--------+
+--R 4 4 3 | 4
+--R (6a x + 6a b)\|a x + b
+--R Type: Union(Expression(Integer),...)
+--E 399
+
+--S 400 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R 2 8 4 2 | 4
+--R (- 3a x - 12a b x - 8b )\|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 |a x + b
+--R (3a x + 12a b x + 8b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 4 6 3 2 |a x + b | 4
+--R (6a x + 6a b x ) |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 400
+
+--S 401 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R 9 | 4 11 |a x + b
+--R - x \|a x + b + x |--------
+--R | 4
+--R \| x
+--R (5) -------------------------------------------
+--R +--------+
+--R | 4 +--------+
+--R 2 8 4 2 |a x + b | 4
+--R (a x + 2a b x + b ) |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 401
+
+)clear all
+
+--S 402 of 1325
+t0:=1/(a+b/x^4)^(5/2)
+--R
+--R
+--R 8
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 1325
+--r0:=-1/6*x/(a*(a+b/x^4)^(3/2))-7/12*x/(a^2*sqrt(a+b/x^4))+_
+-- 7/4*x*sqrt(a+b/x^4)/a^3+7/4*(-b)^(1/4)*_
+-- elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(9/4)*sqrt(a+b/x^4))-7/4*(-b)^(1/4)*_
+-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(9/4)*sqrt(a+b/x^4))
+--E 403
+
+--S 404 of 1325
+--a0:=integrate(t0,x)
+--E 404
+
+--S 405 of 1325
+--m0:=a0-r0
+--E 405
+
+--S 406 of 1325
+--d0:=D(m0,x)
+--E 406
+
+)clear all
+
+--S 407 of 1325
+t0:=1/((a+b/x^4)^(5/2)*x)
+--R
+--R
+--R 7
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 1325
+r0:=(-1/6)/(a*(a+b/x^4)^(3/2))+1/2*atanh(sqrt(a+b/x^4)/_
+ sqrt(a))/a^(5/2)+(-1/2)/(a^2*sqrt(a+b/x^4))
+--R
+--R
+--R +--------+
+--R | 4
+--R |a x + b
+--R +--------+ |--------
+--R | 4 | 4
+--R 4 |a x + b \| x 4 +-+
+--R (3a x + 3b) |-------- atanh(-----------) + (- 4a x - 3b)\|a
+--R | 4 +-+
+--R \| x \|a
+--R (2) --------------------------------------------------------------
+--R +--------+
+--R | 4
+--R 3 4 2 +-+ |a x + b
+--R (6a x + 6a b)\|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 408
+
+--S 409 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8
+--R (9a x + 21a b x + 12b )\|b \|a x + b - 3a x - 18a b x
+--R +
+--R 2 4 3
+--R - 27a b x - 12b
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R 2 10 6 2 2 +-+ | 4
+--R (4a x + 19a b x + 12b x )\|a \|a x + b
+--R +
+--R 2 10 6 2 2 +-+ +-+
+--R (- 12a x - 25a b x - 12b x )\|a \|b
+--R /
+--R +--------+
+--R 4 8 3 4 2 2 +-+ +-+ | 4
+--R (18a x + 42a b x + 24a b )\|a \|b \|a x + b
+--R +
+--R 5 12 4 8 3 2 4 2 3 +-+
+--R (- 6a x - 36a b x - 54a b x - 24a b )\|a
+--R ,
+--R
+--R +--------+
+--R 2 8 4 2 +-+ | 4 3 12 2 8
+--R (18a x + 42a b x + 24b )\|b \|a x + b - 6a x - 36a b x
+--R +
+--R 2 4 3
+--R - 54a b x - 24b
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R +--------+
+--R 2 10 6 2 2 +---+ | 4
+--R (4a x + 19a b x + 12b x )\|- a \|a x + b
+--R +
+--R 2 10 6 2 2 +---+ +-+
+--R (- 12a x - 25a b x - 12b x )\|- a \|b
+--R /
+--R +--------+
+--R 4 8 3 4 2 2 +---+ +-+ | 4
+--R (18a x + 42a b x + 24a b )\|- a \|b \|a x + b
+--R +
+--R 5 12 4 8 3 2 4 2 3 +---+
+--R (- 6a x - 36a b x - 54a b x - 24a b )\|- a
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 409
+
+--S 410 of 1325
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 4 +--------+
+--R 2 8 4 2 |a x + b +-+ | 4
+--R (9a x + 21a b x + 12b ) |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 3 12 2 8 2 4 3 |a x + b
+--R (- 3a x - 18a b x - 27a b x - 12b ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R +-+ +-+ 2 | 4 2 +-+ 4 +-+
+--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a
+--R log(----------------------------------------------------------)
+--R +--------+
+--R +-+ | 4
+--R \|b \|a x + b - b
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 2 8 4 2 |a x + b +-+ | 4
+--R (- 9a x - 21a b x - 12b ) |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 3 12 2 8 2 4 3 |a x + b
+--R (3a x + 18a b x + 27a b x + 12b ) |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R 2 8 4 2 +-+ +-+
+--R (12a x + 25a b x + 12b )\|a \|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +-+ |a x + b
+--R (4a x + 19a b x + 12b x )\|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +-+ |a x + b +-+
+--R (- 12a x - 25a b x - 12b x )\|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 3 12 2 8 2 4 3 +-+
+--R (- 4a x - 23a b x - 31a b x - 12b )\|a
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 4 8 3 4 2 2 +-+ |a x + b +-+ | 4
+--R (18a x + 42a b x + 24a b )\|a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 5 12 4 8 3 2 4 2 3 +-+ |a x + b
+--R (- 6a x - 36a b x - 54a b x - 24a b )\|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 410
+
+--S 411 of 1325
+d0a:=D(m0a,x)
+--R
+--R
+--R (5)
+--R 4 25 3 21 2 2 17 3 13 4 9 +-+
+--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 5 25 4 21 3 2 17 2 3 13 4 9
+--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 27 4 23 3 2 19 2 3 15 4 11
+--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 5 27 4 23 3 2 19 2 3 15 4 11
+--R a x + 41a b x + 280a b x + 688a b x + 704a b x
+--R +
+--R 5 7
+--R 256b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 5 27 4 23 3 2 19 2 3 15 4 11
+--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R +
+--R 5 27 4 23 3 2 19 2 3 15 4 11
+--R - 9a x - 129a b x - 552a b x - 1008a b x - 832a b x
+--R +
+--R 5 7
+--R - 256b x
+--R *
+--R +-+
+--R \|a
+--R *
+--R +-+
+--R \|b
+--R +
+--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9
+--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R +
+--R 6 29 5 25 4 2 21 3 3 17 2 4 13 5 9
+--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x
+--R /
+--R 7 26 6 22 5 2 18 4 3 14 3 4 10
+--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x
+--R +
+--R 2 5 6 6 2
+--R 1088a b x + 256a b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 7 28 6 24 5 2 20 4 3 16 3 4 12
+--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x
+--R +
+--R 2 5 8 6 4 7
+--R - 2352a b x - 1216a b x - 256b
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b
+--R \|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 7 28 6 24 5 2 20 4 3 16 3 4 12
+--R 9a x + 147a b x + 819a b x + 2241a b x + 3400a b x
+--R +
+--R 2 5 8 6 4 7
+--R 2928a b x + 1344a b x + 256b
+--R *
+--R +--------+
+--R | 4
+--R +-+ |a x + b +-+
+--R \|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 8 30 7 26 6 2 22 5 3 18 4 4 14
+--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x
+--R +
+--R 3 5 10 2 6 6 7 2
+--R - 2352a b x - 1216a b x - 256a b x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 1325
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R | 4 +--------+
+--R 2 8 4 2 +---+ |a x + b +-+ | 4
+--R (- 9a x - 21a b x - 12b )\|- a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 3 12 2 8 2 4 3 +---+ |a x + b
+--R (3a x + 18a b x + 27a b x + 12b )\|- a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R |a x + b
+--R |--------
+--R | 4
+--R \| x
+--R atanh(-----------)
+--R +-+
+--R \|a
+--R +
+--R +--------+
+--R | 4 +--------+
+--R 2 8 4 2 +-+ |a x + b +-+ | 4
+--R (18a x + 42a b x + 24b )\|a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 3 12 2 8 2 4 3 +-+ |a x + b
+--R (- 6a x - 36a b x - 54a b x - 24b )\|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R +---+ | 4 +---+ +-+
+--R \|- a \|a x + b - \|- a \|b
+--R atan(------------------------------)
+--R 2
+--R a x
+--R +
+--R 2 8 4 2 +---+ +-+ +-+
+--R (12a x + 25a b x + 12b )\|- a \|a \|b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +---+ +-+ |a x + b
+--R (4a x + 19a b x + 12b x )\|- a \|a |--------
+--R | 4
+--R \| x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R +--------+
+--R | 4
+--R 2 10 6 2 2 +---+ +-+ |a x + b +-+
+--R (- 12a x - 25a b x - 12b x )\|- a \|a |-------- \|b
+--R | 4
+--R \| x
+--R +
+--R 3 12 2 8 2 4 3 +---+ +-+
+--R (- 4a x - 23a b x - 31a b x - 12b )\|- a \|a
+--R /
+--R +--------+
+--R | 4 +--------+
+--R 4 8 3 4 2 2 +---+ +-+ |a x + b +-+ | 4
+--R (18a x + 42a b x + 24a b )\|- a \|a |-------- \|b \|a x + b
+--R | 4
+--R \| x
+--R +
+--R +--------+
+--R | 4
+--R 5 12 4 8 3 2 4 2 3 +---+ +-+ |a x + b
+--R (- 6a x - 36a b x - 54a b x - 24a b )\|- a \|a |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 412
+
+--S 413 of 1325
+d0b:=D(m0b,x)
+--R
+--R
+--R (7)
+--R +--------+
+--R | 4
+--R 2 17 13 2 9 |a x + b +-+ 3 19 2 15
+--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x
+--R | 4
+--R \| x
+--R +
+--R 2 11 3 7
+--R - 48a b x - 32b x
+--R *
+--R +--------+
+--R | 4
+--R \|a x + b
+--R +
+--R 3 19 2 15 2 11 3 7 +-+
+--R (6a x + 38a b x + 64a b x + 32b x )\|b
+--R +
+--R +--------+
+--R | 4
+--R 3 21 2 17 2 13 3 9 |a x + b
+--R (a x + 18a b x + 48a b x + 32b x ) |--------
+--R | 4
+--R \| x
+--R /
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b )
+--R *
+--R +--------+
+--R | 4 +--------+
+--R |a x + b | 4
+--R |-------- \|a x + b
+--R | 4
+--R \| x
+--R +
+--R 5 20 4 16 3 2 12 2 3 8 4 4 5
+--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b )
+--R *
+--R +--------+
+--R | 4
+--R |a x + b +-+
+--R |-------- \|b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 413
+
+)clear all
+
+--S 414 of 1325
+t0:=1/((a+b/x^4)^(5/2)*x^2)
+--R
+--R
+--R 6
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 1325
+--r0:=(-1/6)/(a*(a+b/x^4)^(3/2)*x)+(-5/12)/(a^2*x*sqrt(a+b/x^4))-_
+-- 5/12*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(7/4)*(-b)^(1/4)*sqrt(a+b/x^4))
+--E 415
+
+--S 416 of 1325
+--a0:=integrate(t0,x)
+--E 416
+
+--S 417 of 1325
+--m0:=a0-r0
+--E 417
+
+--S 418 of 1325
+--d0:=D(m0,x)
+--E 418
+
+)clear all
+
+--S 419 of 1325
+t0:=1/((a+b/x^4)^(5/2)*x^3)
+--R
+--R
+--R 5
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 419
+
+--S 420 of 1325
+r0:=(-1/6)/(a*(a+b/x^4)^(3/2)*x^2)+(-1/3)/(a^2*x^2*sqrt(a+b/x^4))
+--R
+--R
+--R 4
+--R - 3a x - 2b
+--R (2) ----------------------------
+--R +--------+
+--R | 4
+--R 3 6 2 2 |a x + b
+--R (6a x + 6a b x ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 420
+
+--S 421 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 4
+--R - 3a x - 2b
+--R (3) -------------------------
+--R +--------+
+--R 3 4 2 | 4
+--R (6a x + 6a b)\|a x + b
+--R Type: Union(Expression(Integer),...)
+--E 421
+
+--S 422 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R 4 | 4 6 2 |a x + b
+--R (3a x + 2b)\|a x + b + (- 3a x - 2b x ) |--------
+--R | 4
+--R \| x
+--R (4) ------------------------------------------------------
+--R +--------+
+--R | 4 +--------+
+--R 3 6 2 2 |a x + b | 4
+--R (6a x + 6a b x ) |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 422
+
+--S 423 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R +--------+
+--R +--------+ | 4
+--R 5 | 4 7 |a x + b
+--R - x \|a x + b + x |--------
+--R | 4
+--R \| x
+--R (5) -------------------------------------------
+--R +--------+
+--R | 4 +--------+
+--R 2 8 4 2 |a x + b | 4
+--R (a x + 2a b x + b ) |-------- \|a x + b
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 423
+
+)clear all
+
+--S 424 of 1325
+t0:=1/((a+b/x^4)^(5/2)*x^4)
+--R
+--R
+--R 4
+--R x
+--R (1) --------------------------------
+--R +--------+
+--R | 4
+--R 2 8 4 2 |a x + b
+--R (a x + 2a b x + b ) |--------
+--R | 4
+--R \| x
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 1325
+--r0:=(-1/6)/(a*(a+b/x^4)^(3/2)*x^3)+(-1/4)/(a^2*x^3*sqrt(a+b/x^4))+_
+-- 1/4*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(5/4)*(-b)^(3/4)*sqrt(a+b/x^4))-_
+-- 1/4*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_
+-- sqrt((a+b/x^4)/a)/(a^(5/4)*(-b)^(3/4)*sqrt(a+b/x^4))
+--E 425
+
+--S 426 of 1325
+--a0:=integrate(t0,x)
+--E 426
+
+--S 427 of 1325
+--m0:=a0-r0
+--E 427
+
+--S 428 of 1325
+--d0:=D(m0,x)
+--E 428
+
+)clear all
+
+--S 429 of 1325
+t0:=1/(a+b/x^5)
+--R
+--R
+--R 5
+--R x
+--R (1) --------
+--R 5
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 429
+
+--S 430 of 1325
+r0:=x/a-1/5*b^(1/5)*log(b^(1/5)+a^(1/5)*x)/a^(6/5)+1/20*b^(1/5)*_
+ log(2*b^(2/5)+2*a^(2/5)*x^2-a^(1/5)*b^(1/5)*x*(1-sqrt(5)))*_
+ (1-sqrt(5))/a^(6/5)+1/20*b^(1/5)*log(2*b^(2/5)+2*a^(2/5)*x^2-_
+ a^(1/5)*b^(1/5)*x*(1+sqrt(5)))*(1+sqrt(5))/a^(6/5)+1/5*b^(1/5)*_
+ atan(1/2*(-4*a^(1/5)*x+b^(1/5)*(1+sqrt(5)))*sqrt(5+sqrt(5))/_
+ (b^(1/5)*sqrt(10)))*sqrt(1/2*(5-sqrt(5)))/a^(6/5)+1/5*b^(1/5)*_
+ atan((-4*a^(1/5)*x+b^(1/5)*(1-sqrt(5)))/(b^(1/5)*sqrt(2*_
+ (5+sqrt(5)))))*sqrt(1/2*(5+sqrt(5)))/a^(6/5)
+--R
+--R
+--R (2)
+--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2
+--R (- \|2 \|5 + \|2 )\|b log(2\|b + (x\|5 - x)\|a \|b + 2x \|a )
+--R +
+--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2
+--R (\|2 \|5 + \|2 )\|b log(2\|b + (- x\|5 - x)\|a \|b + 2x \|a )
+--R +
+--R +-+5+-+ 5+-+ 5+-+
+--R - 4\|2 \|b log(\|b + x\|a )
+--R +
+--R +--------+
+--R +----------+ +-+ 5+-+ 5+-+ | +-+
+--R | +-+ 5+-+ ((\|5 + 1)\|b - 4x\|a )\|\|5 + 5
+--R 4\|- \|5 + 5 \|b atan(------------------------------------)
+--R +--+5+-+
+--R 2\|10 \|b
+--R +
+--R +--------+ +-+ 5+-+ 5+-+
+--R 5+-+ | +-+ (\|5 - 1)\|b + 4x\|a +-+5+-+
+--R - 4\|b \|\|5 + 5 atan(-----------------------) + 20x\|2 \|a
+--R +----------+
+--R 5+-+ | +-+
+--R \|b \|2\|5 + 10
+--R /
+--R +-+5+-+
+--R 20a\|2 \|a
+--R Type: Expression(Integer)
+--E 430
+
+--S 431 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R 5a
+--R *
+--R ROOT
+--R +---+
+--R 2 2 2 | b
+--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1
+--R \| a
+--R +
+--R +---+ +---+2
+--R 2 2 | b | b
+--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- -
+--R \| a \| a
+--R /
+--R 2
+--R 25a
+--R +
+--R +---+
+--R | b
+--R - 5a %%CZ1 - 5a %%CZ0 - 5|- -
+--R \| a
+--R *
+--R log
+--R 5a
+--R *
+--R ROOT
+--R +---+
+--R 2 2 2 | b
+--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1
+--R \| a
+--R +
+--R +---+ +---+2
+--R 2 2 | b | b
+--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- -
+--R \| a \| a
+--R /
+--R 2
+--R 25a
+--R +
+--R +---+
+--R | b
+--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x
+--R \| a
+--R +
+--R 5a
+--R *
+--R ROOT
+--R +---+
+--R 2 2 2 | b 2 2
+--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 - 75a %%CZ0
+--R \| a
+--R +
+--R +---+ +---+2
+--R | b | b
+--R - 10a 5|- - %%CZ - 3 5|- -
+--R \| a \| a
+--R /
+--R 2
+--R 25a
+--R +
+--R +---+
+--R | b
+--R - 5a %%CZ1 - 5a %%CZ0 - 5|- -
+--R \| a
+--R *
+--R log
+--R -
+--R 5a
+--R *
+--R ROOT
+--R +---+
+--R 2 2 2 | b
+--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1
+--R \| a
+--R +
+--R +---+ +---+2
+--R 2 2 | b | b
+--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- -
+--R \| a \| a
+--R /
+--R 2
+--R 25a
+--R +
+--R +---+
+--R | b
+--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x
+--R \| a
+--R +
+--R 10a %%CZ1 log(- 5a %%CZ1 + x) + 10a %%CZ0 log(- 5a %%CZ0 + x)
+--R +
+--R +---+ +---+
+--R | b | b
+--R 2 5|- - log(- 5|- - + x + 10x
+--R \| a \| a
+--R /
+--R 10a
+--R Type: Union(Expression(Integer),...)
+--E 431
+
+--S 432 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R -
+--R +-+5+-+
+--R 10a\|2 \|a
+--R *
+--R ROOT
+--R +---+
+--R 2 2 2 | b
+--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1
+--R \| a
+--R +
+--R +---+ +---+2
+--R 2 2 | b | b
+--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- -
+--R \| a \| a
+--R /
+--R 2
+--R 25a
+--R +
+--R +---+
+--R +-+5+-+ +-+5+-+ +-+ | b 5+-+
+--R - 10a\|2 \|a %%CZ1 - 10a\|2 \|a %%CZ0 - 2\|2 5|- - \|a
+--R \| a
+--R *
+--R log
+--R 5a
+--R *
+--R ROOT
+--R +---+
+--R 2 2 2 | b
+--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1
+--R \| a
+--R +
+--R +---+ +---+2
+--R 2 2 | b | b
+--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- -
+--R \| a \| a
+--R /
+--R 2
+--R 25a
+--R +
+--R +---+
+--R | b
+--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x
+--R \| a
+--R +
+--R +-+5+-+
+--R 10a\|2 \|a
+--R *
+--R ROOT
+--R +---+
+--R 2 2 2 | b 2 2
+--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 - 75a %%CZ0
+--R \| a
+--R +
+--R +---+ +---+2
+--R | b | b
+--R - 10a 5|- - %%CZ - 3 5|- -
+--R \| a \| a
+--R /
+--R 2
+--R 25a
+--R +
+--R +---+
+--R +-+5+-+ +-+5+-+ +-+ | b 5+-+
+--R - 10a\|2 \|a %%CZ1 - 10a\|2 \|a %%CZ0 - 2\|2 5|- - \|a
+--R \| a
+--R *
+--R log
+--R -
+--R 5a
+--R *
+--R ROOT
+--R +---+
+--R 2 2 2 | b
+--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1
+--R \| a
+--R +
+--R +---+ +---+2
+--R 2 2 | b | b
+--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- -
+--R \| a \| a
+--R /
+--R 2
+--R 25a
+--R +
+--R +---+
+--R | b
+--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x
+--R \| a
+--R +
+--R +-+5+-+
+--R 20a\|2 \|a %%CZ1 log(- 5a %%CZ1 + x)
+--R +
+--R +-+5+-+
+--R 20a\|2 \|a %%CZ0 log(- 5a %%CZ0 + x)
+--R +
+--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2
+--R (\|2 \|5 - \|2 )\|b log(2\|b + (x\|5 - x)\|a \|b + 2x \|a )
+--R +
+--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2
+--R (- \|2 \|5 - \|2 )\|b log(2\|b + (- x\|5 - x)\|a \|b + 2x \|a )
+--R +
+--R +---+ +---+
+--R +-+5+-+ 5+-+ 5+-+ +-+ | b 5+-+ | b
+--R 4\|2 \|b log(\|b + x\|a ) + 4\|2 5|- - \|a log(- 5|- - + x)
+--R \| a \| a
+--R +
+--R +--------+
+--R +----------+ +-+ 5+-+ 5+-+ | +-+
+--R | +-+ 5+-+ ((\|5 + 1)\|b - 4x\|a )\|\|5 + 5
+--R - 4\|- \|5 + 5 \|b atan(------------------------------------)
+--R +--+5+-+
+--R 2\|10 \|b
+--R +
+--R +--------+ +-+ 5+-+ 5+-+
+--R 5+-+ | +-+ (\|5 - 1)\|b + 4x\|a
+--R 4\|b \|\|5 + 5 atan(-----------------------)
+--R +----------+
+--R 5+-+ | +-+
+--R \|b \|2\|5 + 10
+--R /
+--R +-+5+-+
+--R 20a\|2 \|a
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +-+ +-+ +-+ 5+-+4 +-+ +-+ +-+ 5+-+5+-+3
+--R (\|2 \|5 + 5\|2 )\|b + (- 3x\|2 \|5 - 5x\|2 )\|a \|b
+--R +
+--R 2 +-+ +-+ 2 +-+ 5+-+2 5+-+2
+--R (x \|2 \|5 + 5x \|2 )\|a \|b
+--R *
+--R +--------+ +----------+
+--R | +-+ | +-+
+--R \|\|5 + 5 \|2\|5 + 10
+--R +
+--R +----------+
+--R +-+ +--+ | +-+ 5+-+4
+--R 2\|2 \|10 \|- \|5 + 5 \|b
+--R +
+--R +----------+
+--R +-+ +-+ +-+ +--+ | +-+ 5+-+5+-+3
+--R (x\|2 \|5 - x\|2 )\|10 \|- \|5 + 5 \|a \|b
+--R +
+--R +----------+
+--R 2 +-+ +--+ | +-+ 5+-+2 5+-+2
+--R 2x \|2 \|10 \|- \|5 + 5 \|a \|b
+--R *
+--R +--------+
+--R | +-+
+--R \|\|5 + 5
+--R +
+--R +-+ 5+-+4 +-+ 5+-+5+-+3
+--R (- 20\|5 - 100)\|b + (20x\|5 + 100x)\|a \|b
+--R +
+--R 2 +-+ 2 5+-+2 5+-+2
+--R (- 20x \|5 - 100x )\|a \|b
+--R /
+--R +-+ 5+-+4 +-+ 5+-+5+-+3
+--R (40a\|5 + 200a)\|b + (- 40a x\|5 - 200a x)\|a \|b
+--R +
+--R 2 +-+ 2 5+-+2 5+-+2 3 +-+ 3 5+-+3 5+-+
+--R (40a x \|5 + 200a x )\|a \|b + (- 40a x \|5 - 200a x )\|a \|b
+--R +
+--R 4 +-+ 4 5+-+4
+--R (40a x \|5 + 200a x )\|a
+--R Type: Expression(Integer)
+--E 433
+
+)clear all
+
+--S 434 of 1325
+t0:=1/(x*sqrt(a+b/x^5))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +--------+
+--R | 5
+--R |a x + b
+--R x |--------
+--R | 5
+--R \| x
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 1325
+r0:=2/5*atanh(sqrt(a+b/x^5)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +--------+
+--R | 5
+--R |a x + b
+--R |--------
+--R | 5
+--R \| x
+--R 2atanh(-----------)
+--R +-+
+--R \|a
+--R (2) -------------------
+--R +-+
+--R 5\|a
+--R Type: Expression(Integer)
+--E 435
+
+--S 436 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R +-+ +-+ | 5
+--R |1 3 |1 |a x + b 5
+--R |- log(2a x |- |-------- - 2a x - b)
+--R \|a \|a \| x
+--R (3) - -----------------------------------------
+--R 5
+--R Type: Union(Expression(Integer),...)
+--E 436
+
+--S 437 of 1325
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R | 5
+--R |a x + b
+--R +--------+ |--------
+--R +-+ +-+ | 5 | 5
+--R |1 +-+ 3 |1 |a x + b 5 \| x
+--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------)
+--R \|a \|a \| x +-+
+--R \|a
+--R (4) ---------------------------------------------------------------------
+--R +-+
+--R 5\|a
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +--------+ +--------+
+--R +-+ | 5 | 5
+--R 5 |1 |a x + b 5 |a x + b
+--R (- 2a x |- |-------- - 2a x - b) |--------
+--R \|a | 5 \| x
+--R \| x
+--R +
+--R +--------+
+--R | 5 +-+
+--R 7 2 |a x + b 2 7 2 |1
+--R (2a x + b x ) |-------- + (2a x + 2a b x ) |-
+--R | 5 \|a
+--R \| x
+--R /
+--R +--------+ +--------+ +--------+
+--R | 5 | 5 +-+ | 5
+--R 6 |a x + b |a x + b 2 8 3 |1 |a x + b
+--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |--------
+--R | 5 \| x \|a | 5
+--R \| x \| x
+--R Type: Expression(Integer)
+--E 438
+
+)clear all
+
+--S 439 of 1325
+t0:=1/(x*sqrt(-a+b/x^5))
+--R
+--R
+--R 1
+--R (1) --------------
+--R +----------+
+--R | 5
+--R |- a x + b
+--R x |----------
+--R | 5
+--R \| x
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 1325
+r0:=-2/5*atan(sqrt(-a+b/x^5)/sqrt(a))/sqrt(a)
+--R
+--R
+--R +----------+
+--R | 5
+--R |- a x + b
+--R |----------
+--R | 5
+--R \| x
+--R 2atan(-------------)
+--R +-+
+--R \|a
+--R (2) - --------------------
+--R +-+
+--R 5\|a
+--R Type: Expression(Integer)
+--E 440
+
+--S 441 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +----------+
+--R +---+ | 5 +---+
+--R | 1 3 |- a x + b | 1 5
+--R |- - log(2a x |---------- |- - - 2a x + b)
+--R \| a \| x \| a
+--R (3) - -----------------------------------------------
+--R 5
+--R Type: Union(Expression(Integer),...)
+--E 441
+
+--S 442 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +----------+
+--R | 5
+--R |- a x + b
+--R +----------+ |----------
+--R +---+ | 5 +---+ | 5
+--R | 1 +-+ 3 |- a x + b | 1 5 \| x
+--R - |- - \|a log(2a x |---------- |- - - 2a x + b) + 2atan(-------------)
+--R \| a \| x \| a +-+
+--R \|a
+--R ----------------------------------------------------------------------------
+--R +-+
+--R 5\|a
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R +----------+ +----------+
+--R | 5 | 5 +---+
+--R 5 |- a x + b |- a x + b 2 7 2 | 1
+--R (- 2a x |---------- |---------- - 2a x + 2a b x ) |- -
+--R \| x | 5 \| a
+--R \| x
+--R +
+--R +----------+ +----------+
+--R | 5 | 5
+--R 7 2 |- a x + b 5 |- a x + b
+--R (2a x - b x ) |---------- + (- 2a x + b) |----------
+--R | 5 \| x
+--R \| x
+--R /
+--R +----------+
+--R | 5 +---+
+--R 2 8 3 |- a x + b | 1
+--R (2a x - 2a b x ) |---------- |- -
+--R | 5 \| a
+--R \| x
+--R +
+--R +----------+ +----------+
+--R | 5 | 5
+--R 6 |- a x + b |- a x + b
+--R (2a x - b x) |---------- |----------
+--R \| x | 5
+--R \| x
+--R Type: Expression(Integer)
+--E 443
+
+)clear all
+
+--S 444 of 1325
+t0:=1/(a+b/x^6)
+--R
+--R
+--R 6
+--R x
+--R (1) --------
+--R 6
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 444
+
+--S 445 of 1325
+r0:=x/a-1/3*b^(1/6)*atan(a^(1/6)*x/b^(1/6))/a^(7/6)-1/3*atan(a^(1/6)*x*_
+ sqrt(2)/sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))*sqrt(-b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3)))/(a^(7/6)*sqrt(2))-1/3*atanh(a^(1/6)*x*_
+ sqrt(2)/sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))*sqrt(b^(1/3)+_
+ sqrt(3)*sqrt(-b^(2/3)))/(a^(7/6)*sqrt(2))
+--R
+--R
+--R (2)
+--R +---------------------+
+--R | +-------+ +-+6+-+
+--R | +-+ | 3+-+2 3+-+ x\|2 \|a
+--R - \|\|3 \|- \|b + \|b atanh(------------------------)
+--R +---------------------+
+--R | +-------+
+--R | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+6+-+
+--R | +-+ | 3+-+2 3+-+ x\|2 \|a
+--R - \|\|3 \|- \|b - \|b atan(------------------------)
+--R +---------------------+
+--R | +-------+
+--R | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b - \|b
+--R +
+--R 6+-+
+--R +-+6+-+ x\|a +-+6+-+
+--R - \|2 \|b atan(-----) + 3x\|2 \|a
+--R 6+-+
+--R \|b
+--R /
+--R +-+6+-+
+--R 3a\|2 \|a
+--R Type: Expression(Integer)
+--E 445
+
+--S 446 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---------+ +---------+2 +---------+
+--R | b 2 | b | b 2
+--R - a |- ------- log(36a |- ------- + 6a x |- ------- + x )
+--R 6| 7 6| 7 6| 7
+--R \| 46656a \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+2 +---------+
+--R | b 2 | b | b 2
+--R a |- ------- log(36a |- ------- - 6a x |- ------- + x )
+--R 6| 7 6| 7 6| 7
+--R \| 46656a \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+
+--R | b | b
+--R - 2a |- ------- log(6a |- ------- + x)
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+
+--R | b | b
+--R 2a |- ------- log(- 6a |- ------- + x)
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R +---------+
+--R +-+ | b
+--R 3a\|3 |- -------
+--R +---------+ 6| 7
+--R +-+ | b \| 46656a
+--R - 2a\|3 |- ------- atan(------------------)
+--R 6| 7 +---------+
+--R \| 46656a | b
+--R 3a |- ------- - x
+--R 6| 7
+--R \| 46656a
+--R +
+--R +---------+
+--R +-+ | b
+--R 3a\|3 |- -------
+--R +---------+ 6| 7
+--R +-+ | b \| 46656a
+--R 2a\|3 |- ------- atan(------------------ + 2x
+--R 6| 7 +---------+
+--R \| 46656a | b
+--R 3a |- ------- + x
+--R 6| 7
+--R \| 46656a
+--R /
+--R 2a
+--R Type: Union(Expression(Integer),...)
+--E 446
+
+--S 447 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---------------------+
+--R | +-------+ +-+6+-+
+--R | +-+ | 3+-+2 3+-+ x\|2 \|a
+--R 2\|\|3 \|- \|b + \|b atanh(------------------------)
+--R +---------------------+
+--R | +-------+
+--R | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b + \|b
+--R +
+--R +---------------------+
+--R | +-------+ +-+6+-+
+--R | +-+ | 3+-+2 3+-+ x\|2 \|a
+--R 2\|\|3 \|- \|b - \|b atan(------------------------)
+--R +---------------------+
+--R | +-------+
+--R | +-+ | 3+-+2 3+-+
+--R \|\|3 \|- \|b - \|b
+--R +
+--R +---------+ +---------+2 +---------+
+--R +-+ | b 6+-+ 2 | b | b 2
+--R - 3a\|2 |- ------- \|a log(36a |- ------- + 6a x |- ------- + x )
+--R 6| 7 6| 7 6| 7
+--R \| 46656a \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+2 +---------+
+--R +-+ | b 6+-+ 2 | b | b 2
+--R 3a\|2 |- ------- \|a log(36a |- ------- - 6a x |- ------- + x )
+--R 6| 7 6| 7 6| 7
+--R \| 46656a \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+
+--R +-+ | b 6+-+ | b
+--R - 6a\|2 |- ------- \|a log(6a |- ------- + x)
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R +---------+ +---------+
+--R +-+ | b 6+-+ | b
+--R 6a\|2 |- ------- \|a log(- 6a |- ------- + x)
+--R 6| 7 6| 7
+--R \| 46656a \| 46656a
+--R +
+--R +---------+
+--R +-+ | b
+--R 3a\|3 |- -------
+--R +---------+ 6| 7
+--R +-+ +-+ | b 6+-+ \| 46656a
+--R - 6a\|2 \|3 |- ------- \|a atan(------------------)
+--R 6| 7 +---------+
+--R \| 46656a | b
+--R 3a |- ------- - x
+--R 6| 7
+--R \| 46656a
+--R +
+--R +---------+
+--R +-+ | b
+--R 3a\|3 |- -------
+--R +---------+ 6| 7 6+-+
+--R +-+ +-+ | b 6+-+ \| 46656a +-+6+-+ x\|a
+--R 6a\|2 \|3 |- ------- \|a atan(------------------ + 2\|2 \|b atan(-----)
+--R 6| 7 +---------+ 6+-+
+--R \| 46656a | b \|b
+--R 3a |- ------- + x
+--R 6| 7
+--R \| 46656a
+--R /
+--R +-+6+-+
+--R 6a\|2 \|a
+--R Type: Expression(Integer)
+--E 447
+
+--S 448 of 1325
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 448
+
+)clear all
+
+--S 449 of 1325
+t0:=1/(a+b/x^8)
+--R
+--R
+--R 8
+--R x
+--R (1) --------
+--R 8
+--R a x + b
+--R Type: Fraction(Polynomial(Integer))
+--E 449
+
+--S 450 of 1325
+r0:=x/a-1/4*(-b)^(1/8)*atan(a^(1/8)*x/(-b)^(1/8))/a^(9/8)-1/4*(-b)^(1/8)*_
+ atanh(a^(1/8)*x/(-b)^(1/8))/a^(9/8)+1/4*(-b)^(1/8)*atan(1-a^(1/8)*_
+ x*sqrt(2)/(-b)^(1/8))/(a^(9/8)*sqrt(2))-1/4*(-b)^(1/8)*atan(1+_
+ a^(1/8)*x*sqrt(2)/(-b)^(1/8))/(a^(9/8)*sqrt(2))+1/8*(-b)^(1/8)*_
+ log((-b)^(1/4)+a^(1/4)*x^2-a^(1/8)*(-b)^(1/8)*x*sqrt(2))/(a^(9/8)*_
+ sqrt(2))-1/8*(-b)^(1/8)*log((-b)^(1/4)+a^(1/4)*x^2+a^(1/8)*_
+ (-b)^(1/8)*x*sqrt(2))/(a^(9/8)*sqrt(2))
+--R
+--R
+--R (2)
+--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - \|- b log(x\|2 \|- b \|a + x \|a + \|- b )
+--R +
+--R 8+-+
+--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+---+ x\|a
+--R \|- b log(- x\|2 \|- b \|a + x \|a + \|- b ) - 2\|2 \|- b atanh(------)
+--R 8+---+
+--R \|- b
+--R +
+--R +-+8+-+ 8+---+ +-+8+-+ 8+---+
+--R 8+---+ x\|2 \|a + \|- b 8+---+ x\|2 \|a - \|- b
+--R - 2\|- b atan(------------------) - 2\|- b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- b \|- b
+--R +
+--R 8+-+
+--R +-+8+---+ x\|a +-+8+-+
+--R - 2\|2 \|- b atan(------) + 8x\|2 \|a
+--R 8+---+
+--R \|- b
+--R /
+--R +-+8+-+
+--R 8a\|2 \|a
+--R Type: Expression(Integer)
+--E 450
+
+--S 451 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R -
+--R +------------+
+--R | b
+--R a |- ----------
+--R 8| 9
+--R \| 16777216a
+--R *
+--R +------------+2 +------------+
+--R 2 | b +-+ | b 2
+--R log(64a |- ---------- + 8a x\|2 |- ---------- + x )
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+ +------------+2 +------------+
+--R | b 2 | b +-+ | b 2
+--R a |- ---------- log(64a |- ---------- - 8a x\|2 |- ---------- + x )
+--R 8| 9 8| 9 8| 9
+--R \| 16777216a \| 16777216a \| 16777216a
+--R +
+--R +------------+ +------------+
+--R +-+ | b | b
+--R - a\|2 |- ---------- log(8a |- ---------- + x)
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+ +------------+
+--R +-+ | b | b
+--R a\|2 |- ---------- log(- 8a |- ---------- + x)
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+
+--R | b
+--R 8a |- ----------
+--R +------------+ 8| 9
+--R +-+ | b \| 16777216a
+--R 2a\|2 |- ---------- atan(-----------------)
+--R 8| 9 x
+--R \| 16777216a
+--R +
+--R +------------+
+--R | b
+--R 8a |- ----------
+--R +------------+ 8| 9
+--R | b \| 16777216a
+--R - 2a |- ---------- atan(-------------------------)
+--R 8| 9 +------------+
+--R \| 16777216a | b +-+
+--R 8a |- ---------- - x\|2
+--R 8| 9
+--R \| 16777216a
+--R +
+--R +------------+
+--R | b
+--R 8a |- ----------
+--R +------------+ 8| 9
+--R | b \| 16777216a +-+
+--R 2a |- ---------- atan(------------------------- + x\|2
+--R 8| 9 +------------+
+--R \| 16777216a | b +-+
+--R 8a |- ---------- + x\|2
+--R 8| 9
+--R \| 16777216a
+--R /
+--R +-+
+--R a\|2
+--R Type: Union(Expression(Integer),...)
+--E 451
+
+--S 452 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+
+--R \|- b log(x\|2 \|- b \|a + x \|a + \|- b )
+--R +
+--R -
+--R +------------+
+--R | b 8+-+
+--R 8a |- ---------- \|a
+--R 8| 9
+--R \| 16777216a
+--R *
+--R +------------+2 +------------+
+--R 2 | b +-+ | b 2
+--R log(64a |- ---------- + 8a x\|2 |- ---------- + x )
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+
+--R | b 8+-+
+--R 8a |- ---------- \|a
+--R 8| 9
+--R \| 16777216a
+--R *
+--R +------------+2 +------------+
+--R 2 | b +-+ | b 2
+--R log(64a |- ---------- - 8a x\|2 |- ---------- + x )
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+ +------------+
+--R +-+ | b 8+-+ | b
+--R - 8a\|2 |- ---------- \|a log(8a |- ---------- + x)
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R +------------+ +------------+
+--R +-+ | b 8+-+ | b
+--R 8a\|2 |- ---------- \|a log(- 8a |- ---------- + x)
+--R 8| 9 8| 9
+--R \| 16777216a \| 16777216a
+--R +
+--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+
+--R - \|- b log(- x\|2 \|- b \|a + x \|a + \|- b )
+--R +
+--R 8+-+ +-+8+-+ 8+---+
+--R +-+8+---+ x\|a 8+---+ x\|2 \|a + \|- b
+--R 2\|2 \|- b atanh(------) + 2\|- b atan(------------------)
+--R 8+---+ 8+---+
+--R \|- b \|- b
+--R +
+--R +-+8+-+ 8+---+ 8+-+
+--R 8+---+ x\|2 \|a - \|- b +-+8+---+ x\|a
+--R 2\|- b atan(------------------) + 2\|2 \|- b atan(------)
+--R 8+---+ 8+---+
+--R \|- b \|- b
+--R +
+--R +------------+
+--R | b
+--R 8a |- ----------
+--R +------------+ 8| 9
+--R +-+ | b 8+-+ \| 16777216a
+--R 16a\|2 |- ---------- \|a atan(-----------------)
+--R 8| 9 x
+--R \| 16777216a
+--R +
+--R +------------+
+--R | b
+--R 8a |- ----------
+--R +------------+ 8| 9
+--R | b 8+-+ \| 16777216a
+--R - 16a |- ---------- \|a atan(-------------------------)
+--R 8| 9 +------------+
+--R \| 16777216a | b +-+
+--R 8a |- ---------- - x\|2
+--R 8| 9
+--R \| 16777216a
+--R +
+--R +------------+
+--R | b
+--R 8a |- ----------
+--R +------------+ 8| 9
+--R | b 8+-+ \| 16777216a
+--R 16a |- ---------- \|a atan(-------------------------)
+--R 8| 9 +------------+
+--R \| 16777216a | b +-+
+--R 8a |- ---------- + x\|2
+--R 8| 9
+--R \| 16777216a
+--R /
+--R +-+8+-+
+--R 8a\|2 \|a
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 1325
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 453
+
+)clear all
+
+--S 454 of 1325
+t0:=x^m*(a+b*sqrt(x))^p
+--R
+--R
+--R m +-+ p
+--R (1) x (b\|x + a)
+--R Type: Expression(Integer)
+--E 454
+
+--S 455 of 1325
+--r0:=2*x^(1/2*(1+2*m))*(a+b*sqrt(x))^(1+p)/(b*(2+2*m+p))-_
+-- 2*a*(1+2*m)*x^m*hypergeometric(-2*m,1+p,2+p,(a+b*sqrt(x))/a)*_
+-- (a+b*sqrt(x))^(1+p)/(b^2*(1+p)*(2+2*m+p)*(-b*sqrt(x)/a)^(2*m))
+--E 455
+
+--S 456 of 1325
+--a0:=integrate(t0,x)
+--E 456
+
+--S 457 of 1325
+--m0:=a0-r0
+--E 457
+
+--S 458 of 1325
+--d0:=D(m0,x)
+--E 458
+
+)clear all
+
+--S 459 of 1325
+t0:=x^m*(a+b*sqrt(x))
+--R
+--R
+--R m +-+ m
+--R (1) b x \|x + a x
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 1325
+r0:=a*x^(1+m)/(1+m)+2*b*x^(3/2+m)/(3+2*m)
+--R
+--R
+--R 2m + 3
+--R ------
+--R 2 m + 1
+--R (2b m + 2b)x + (2a m + 3a)x
+--R (2) --------------------------------------
+--R 2
+--R 2m + 5m + 3
+--R Type: Expression(Integer)
+--E 460
+
+--S 461 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ m log(x)
+--R ((2b m + 2b)x\|x + (2a m + 3a)x)%e
+--R (3) -------------------------------------------
+--R 2
+--R 2m + 5m + 3
+--R Type: Union(Expression(Integer),...)
+--E 461
+
+--S 462 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2m + 3
+--R ------
+--R +-+ m log(x) 2
+--R ((2b m + 2b)x\|x + (2a m + 3a)x)%e + (- 2b m - 2b)x
+--R +
+--R m + 1
+--R (- 2a m - 3a)x
+--R /
+--R 2
+--R 2m + 5m + 3
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 1325
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 463
+
+)clear all
+
+--S 464 of 1325
+t0:=x^4*(a+b*sqrt(x))
+--R
+--R
+--R 4 +-+ 4
+--R (1) b x \|x + a x
+--R Type: Expression(Integer)
+--E 464
+
+--S 465 of 1325
+r0:=1/5*a*x^5+2/11*b*x^(11/2)
+--R
+--R
+--R 5 +-+ 5
+--R 10b x \|x + 11a x
+--R (2) -------------------
+--R 55
+--R Type: Expression(Integer)
+--E 465
+
+--S 466 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 +-+ 5
+--R 10b x \|x + 11a x
+--R (3) -------------------
+--R 55
+--R Type: Union(Expression(Integer),...)
+--E 466
+
+--S 467 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 468
+
+)clear all
+
+--S 469 of 1325
+t0:=x^3*(a+b*sqrt(x))
+--R
+--R
+--R 3 +-+ 3
+--R (1) b x \|x + a x
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 1325
+r0:=1/4*a*x^4+2/9*b*x^(9/2)
+--R
+--R
+--R 4 +-+ 4
+--R 8b x \|x + 9a x
+--R (2) -----------------
+--R 36
+--R Type: Expression(Integer)
+--E 470
+
+--S 471 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 +-+ 4
+--R 8b x \|x + 9a x
+--R (3) -----------------
+--R 36
+--R Type: Union(Expression(Integer),...)
+--E 471
+
+--S 472 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 473
+
+)clear all
+
+--S 474 of 1325
+t0:=x^2*(a+b*sqrt(x))
+--R
+--R
+--R 2 +-+ 2
+--R (1) b x \|x + a x
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 1325
+r0:=1/3*a*x^3+2/7*b*x^(7/2)
+--R
+--R
+--R 3 +-+ 3
+--R 6b x \|x + 7a x
+--R (2) -----------------
+--R 21
+--R Type: Expression(Integer)
+--E 475
+
+--S 476 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 +-+ 3
+--R 6b x \|x + 7a x
+--R (3) -----------------
+--R 21
+--R Type: Union(Expression(Integer),...)
+--E 476
+
+--S 477 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 478
+
+)clear all
+
+--S 479 of 1325
+t0:=x*(a+b*sqrt(x))
+--R
+--R
+--R +-+
+--R (1) b x\|x + a x
+--R Type: Expression(Integer)
+--E 479
+
+--S 480 of 1325
+r0:=1/2*a*x^2+2/5*b*x^(5/2)
+--R
+--R
+--R 2 +-+ 2
+--R 4b x \|x + 5a x
+--R (2) -----------------
+--R 10
+--R Type: Expression(Integer)
+--E 480
+
+--S 481 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+ 2
+--R 4b x \|x + 5a x
+--R (3) -----------------
+--R 10
+--R Type: Union(Expression(Integer),...)
+--E 481
+
+--S 482 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 483
+
+)clear all
+
+--S 484 of 1325
+t0:=a+b*sqrt(x)
+--R
+--R
+--R +-+
+--R (1) b\|x + a
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 1325
+r0:=a*x+2/3*b*x^(3/2)
+--R
+--R
+--R +-+
+--R 2b x\|x + 3a x
+--R (2) ---------------
+--R 3
+--R Type: Expression(Integer)
+--E 485
+
+--S 486 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R 2b x\|x + 3a x
+--R (3) ---------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 486
+
+--S 487 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 487
+
+--S 488 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 488
+
+)clear all
+
+--S 489 of 1325
+t0:=(a+b*sqrt(x))/x
+--R
+--R
+--R +-+
+--R b\|x + a
+--R (1) ---------
+--R x
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 1325
+r0:=a*log(x)+2*b*sqrt(x)
+--R
+--R
+--R +-+
+--R (2) 2b\|x + a log(x)
+--R Type: Expression(Integer)
+--E 490
+
+--S 491 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +-+
+--R (3) 2a log(\|x ) + 2b\|x
+--R Type: Union(Expression(Integer),...)
+--E 491
+
+--S 492 of 1325
+m0:=a0-r0
+--R
+--R
+--R +-+
+--R (4) 2a log(\|x ) - a log(x)
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 493
+
+)clear all
+
+--S 494 of 1325
+t0:=(a+b*sqrt(x))/x^2
+--R
+--R
+--R +-+
+--R b\|x + a
+--R (1) ---------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 494
+
+--S 495 of 1325
+r0:=-a/x-2*b/sqrt(x)
+--R
+--R
+--R +-+
+--R - a\|x - 2b x
+--R (2) --------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 495
+
+--S 496 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R - 2b\|x - a
+--R (3) ------------
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 496
+
+--S 497 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 497
+
+--S 498 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 498
+
+)clear all
+
+--S 499 of 1325
+t0:=(a+b*sqrt(x))/x^3
+--R
+--R
+--R +-+
+--R b\|x + a
+--R (1) ---------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 499
+
+--S 500 of 1325
+r0:=-1/2*a/x^2-2/3*b/x^(3/2)
+--R
+--R
+--R +-+
+--R - 3a\|x - 4b x
+--R (2) ---------------
+--R 2 +-+
+--R 6x \|x
+--R Type: Expression(Integer)
+--E 500
+
+--S 501 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R - 4b\|x - 3a
+--R (3) -------------
+--R 2
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 501
+
+--S 502 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 502
+
+--S 503 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 503
+
+)clear all
+
+--S 504 of 1325
+t0:=(a+b*sqrt(x))/x^4
+--R
+--R
+--R +-+
+--R b\|x + a
+--R (1) ---------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 1325
+r0:=-1/3*a/x^3-2/5*b/x^(5/2)
+--R
+--R
+--R +-+
+--R - 5a\|x - 6b x
+--R (2) ---------------
+--R 3 +-+
+--R 15x \|x
+--R Type: Expression(Integer)
+--E 505
+
+--S 506 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+
+--R - 6b\|x - 5a
+--R (3) -------------
+--R 3
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 506
+
+--S 507 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 507
+
+--S 508 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 508
+
+)clear all
+
+--S 509 of 1325
+t0:=x^m*(a+b*sqrt(x))^2
+--R
+--R
+--R m +-+ 2 2 m
+--R (1) 2a b x \|x + (b x + a )x
+--R Type: Expression(Integer)
+--E 509
+
+--S 510 of 1325
+r0:=a^2*x^(1+m)/(1+m)+4*a*b*x^(3/2+m)/(3+2*m)+b^2*x^(2+m)/(2+m)
+--R
+--R
+--R (2)
+--R 2m + 3
+--R ------
+--R 2 2 2 2 m + 2 2 2
+--R (2b m + 5b m + 3b )x + (4a b m + 12a b m + 8a b)x
+--R +
+--R 2 2 2 2 m + 1
+--R (2a m + 7a m + 6a )x
+--R /
+--R 3 2
+--R 2m + 9m + 13m + 6
+--R Type: Expression(Integer)
+--E 510
+
+--S 511 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-+ 2 2 2 2 2
+--R (4a b m + 12a b m + 8a b)x\|x + (2b m + 5b m + 3b )x
+--R +
+--R 2 2 2 2
+--R (2a m + 7a m + 6a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 3 2
+--R 2m + 9m + 13m + 6
+--R Type: Union(Expression(Integer),...)
+--E 511
+
+--S 512 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 +-+ 2 2 2 2 2
+--R (4a b m + 12a b m + 8a b)x\|x + (2b m + 5b m + 3b )x
+--R +
+--R 2 2 2 2
+--R (2a m + 7a m + 6a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2m + 3
+--R ------
+--R 2 2 2 2 m + 2 2 2
+--R (- 2b m - 5b m - 3b )x + (- 4a b m - 12a b m - 8a b)x
+--R +
+--R 2 2 2 2 m + 1
+--R (- 2a m - 7a m - 6a )x
+--R /
+--R 3 2
+--R 2m + 9m + 13m + 6
+--R Type: Expression(Integer)
+--E 512
+
+--S 513 of 1325
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 513
+
+)clear all
+
+--S 514 of 1325
+t0:=x^4*(a+b*sqrt(x))^2
+--R
+--R
+--R 4 +-+ 2 5 2 4
+--R (1) 2a b x \|x + b x + a x
+--R Type: Expression(Integer)
+--E 514
+
+--S 515 of 1325
+r0:=1/5*a^2*x^5+4/11*a*b*x^(11/2)+1/6*b^2*x^6
+--R
+--R
+--R 5 +-+ 2 6 2 5
+--R 120a b x \|x + 55b x + 66a x
+--R (2) -------------------------------
+--R 330
+--R Type: Expression(Integer)
+--E 515
+
+--S 516 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 +-+ 2 6 2 5
+--R 120a b x \|x + 55b x + 66a x
+--R (3) -------------------------------
+--R 330
+--R Type: Union(Expression(Integer),...)
+--E 516
+
+--S 517 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 518
+
+)clear all
+
+--S 519 of 1325
+t0:=x^3*(a+b*sqrt(x))^2
+--R
+--R
+--R 3 +-+ 2 4 2 3
+--R (1) 2a b x \|x + b x + a x
+--R Type: Expression(Integer)
+--E 519
+
+--S 520 of 1325
+r0:=1/4*a^2*x^4+4/9*a*b*x^(9/2)+1/5*b^2*x^5
+--R
+--R
+--R 4 +-+ 2 5 2 4
+--R 80a b x \|x + 36b x + 45a x
+--R (2) ------------------------------
+--R 180
+--R Type: Expression(Integer)
+--E 520
+
+--S 521 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 +-+ 2 5 2 4
+--R 80a b x \|x + 36b x + 45a x
+--R (3) ------------------------------
+--R 180
+--R Type: Union(Expression(Integer),...)
+--E 521
+
+--S 522 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 523
+
+)clear all
+
+--S 524 of 1325
+t0:=x^2*(a+b*sqrt(x))^2
+--R
+--R
+--R 2 +-+ 2 3 2 2
+--R (1) 2a b x \|x + b x + a x
+--R Type: Expression(Integer)
+--E 524
+
+--S 525 of 1325
+r0:=1/3*a^2*x^3+4/7*a*b*x^(7/2)+1/4*b^2*x^4
+--R
+--R
+--R 3 +-+ 2 4 2 3
+--R 48a b x \|x + 21b x + 28a x
+--R (2) ------------------------------
+--R 84
+--R Type: Expression(Integer)
+--E 525
+
+--S 526 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 +-+ 2 4 2 3
+--R 48a b x \|x + 21b x + 28a x
+--R (3) ------------------------------
+--R 84
+--R Type: Union(Expression(Integer),...)
+--E 526
+
+--S 527 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 527
+
+--S 528 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 528
+
+)clear all
+
+--S 529 of 1325
+t0:=x*(a+b*sqrt(x))^2
+--R
+--R
+--R +-+ 2 2 2
+--R (1) 2a b x\|x + b x + a x
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 1325
+r0:=1/2*a^2*x^2+4/5*a*b*x^(5/2)+1/3*b^2*x^3
+--R
+--R
+--R 2 +-+ 2 3 2 2
+--R 24a b x \|x + 10b x + 15a x
+--R (2) ------------------------------
+--R 30
+--R Type: Expression(Integer)
+--E 530
+
+--S 531 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+ 2 3 2 2
+--R 24a b x \|x + 10b x + 15a x
+--R (3) ------------------------------
+--R 30
+--R Type: Union(Expression(Integer),...)
+--E 531
+
+--S 532 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 532
+
+--S 533 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 533
+
+)clear all
+
+--S 534 of 1325
+t0:=(a+b*sqrt(x))^2
+--R
+--R
+--R +-+ 2 2
+--R (1) 2a b\|x + b x + a
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 1325
+r0:=a^2*x+4/3*a*b*x^(3/2)+1/2*b^2*x^2
+--R
+--R
+--R +-+ 2 2 2
+--R 8a b x\|x + 3b x + 6a x
+--R (2) -------------------------
+--R 6
+--R Type: Expression(Integer)
+--E 535
+
+--S 536 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ 2 2 2
+--R 8a b x\|x + 3b x + 6a x
+--R (3) -------------------------
+--R 6
+--R Type: Union(Expression(Integer),...)
+--E 536
+
+--S 537 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 537
+
+--S 538 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 538
+
+)clear all
+
+--S 539 of 1325
+t0:=(a+b*sqrt(x))^2/x
+--R
+--R
+--R +-+ 2 2
+--R 2a b\|x + b x + a
+--R (1) -------------------
+--R x
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 1325
+r0:=b^2*x+a^2*log(x)+4*a*b*sqrt(x)
+--R
+--R
+--R +-+ 2 2
+--R (2) 4a b\|x + a log(x) + b x
+--R Type: Expression(Integer)
+--E 540
+
+--S 541 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+ +-+ 2
+--R (3) 2a log(\|x ) + 4a b\|x + b x
+--R Type: Union(Expression(Integer),...)
+--E 541
+
+--S 542 of 1325
+m0:=a0-r0
+--R
+--R
+--R 2 +-+ 2
+--R (4) 2a log(\|x ) - a log(x)
+--R Type: Expression(Integer)
+--E 542
+
+--S 543 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 543
+
+)clear all
+
+--S 544 of 1325
+t0:=(a+b*sqrt(x))^2/x^2
+--R
+--R
+--R +-+ 2 2
+--R 2a b\|x + b x + a
+--R (1) -------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 544
+
+--S 545 of 1325
+r0:=-a^2/x+b^2*log(x)-4*a*b/sqrt(x)
+--R
+--R
+--R 2 2 +-+
+--R (b x log(x) - a )\|x - 4a b x
+--R (2) ------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 545
+
+--S 546 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+ +-+ 2
+--R 2b x log(\|x ) - 4a b\|x - a
+--R (3) ------------------------------
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 546
+
+--S 547 of 1325
+m0:=a0-r0
+--R
+--R
+--R 2 +-+ 2
+--R (4) 2b log(\|x ) - b log(x)
+--R Type: Expression(Integer)
+--E 547
+
+--S 548 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 548
+
+)clear all
+
+--S 549 of 1325
+t0:=(a+b*sqrt(x))^2/x^3
+--R
+--R
+--R +-+ 2 2
+--R 2a b\|x + b x + a
+--R (1) -------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 549
+
+--S 550 of 1325
+r0:=-1/2*a^2/x^2-4/3*a*b/x^(3/2)-b^2/x
+--R
+--R
+--R 2 2 +-+
+--R (- 6b x - 3a )\|x - 8a b x
+--R (2) ---------------------------
+--R 2 +-+
+--R 6x \|x
+--R Type: Expression(Integer)
+--E 550
+
+--S 551 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ 2 2
+--R - 8a b\|x - 6b x - 3a
+--R (3) -----------------------
+--R 2
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 551
+
+--S 552 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 552
+
+--S 553 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 553
+
+)clear all
+
+--S 554 of 1325
+t0:=(a+b*sqrt(x))^2/x^4
+--R
+--R
+--R +-+ 2 2
+--R 2a b\|x + b x + a
+--R (1) -------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 554
+
+--S 555 of 1325
+r0:=-1/3*a^2/x^3-4/5*a*b/x^(5/2)-1/2*b^2/x^2
+--R
+--R
+--R 2 2 +-+
+--R (- 15b x - 10a )\|x - 24a b x
+--R (2) ------------------------------
+--R 3 +-+
+--R 30x \|x
+--R Type: Expression(Integer)
+--E 555
+
+--S 556 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ 2 2
+--R - 24a b\|x - 15b x - 10a
+--R (3) --------------------------
+--R 3
+--R 30x
+--R Type: Union(Expression(Integer),...)
+--E 556
+
+--S 557 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 557
+
+--S 558 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 558
+
+)clear all
+
+--S 559 of 1325
+t0:=(a+b*sqrt(x))^2/x^5
+--R
+--R
+--R +-+ 2 2
+--R 2a b\|x + b x + a
+--R (1) -------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 559
+
+--S 560 of 1325
+r0:=-1/4*a^2/x^4-4/7*a*b/x^(7/2)-1/3*b^2/x^3
+--R
+--R
+--R 2 2 +-+
+--R (- 28b x - 21a )\|x - 48a b x
+--R (2) ------------------------------
+--R 4 +-+
+--R 84x \|x
+--R Type: Expression(Integer)
+--E 560
+
+--S 561 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ 2 2
+--R - 48a b\|x - 28b x - 21a
+--R (3) --------------------------
+--R 4
+--R 84x
+--R Type: Union(Expression(Integer),...)
+--E 561
+
+--S 562 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 562
+
+--S 563 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 563
+
+)clear all
+
+--S 564 of 1325
+t0:=x^m*(a+b*sqrt(x))^3
+--R
+--R
+--R 3 2 m +-+ 2 3 m
+--R (1) (b x + 3a b)x \|x + (3a b x + a )x
+--R Type: Expression(Integer)
+--E 564
+
+--S 565 of 1325
+r0:=a^3*x^(1+m)/(1+m)+6*a^2*b*x^(3/2+m)/(3+2*m)+3*a*b^2*x^(2+m)/(2+m)+_
+ 2*b^3*x^(5/2+m)/(5+2*m)
+--R
+--R
+--R (2)
+--R 2m + 5
+--R ------
+--R 3 3 3 2 3 3 2
+--R (4b m + 18b m + 26b m + 12b )x
+--R +
+--R 2 3 2 2 2 2 m + 2
+--R (12a b m + 60a b m + 93a b m + 45a b )x
+--R +
+--R 2m + 3
+--R ------
+--R 2 3 2 2 2 2 2
+--R (12a b m + 66a b m + 114a b m + 60a b)x
+--R +
+--R 3 3 3 2 3 3 m + 1
+--R (4a m + 24a m + 47a m + 30a )x
+--R /
+--R 4 3 2
+--R 4m + 28m + 71m + 77m + 30
+--R Type: Expression(Integer)
+--E 565
+
+--S 566 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 3 2 3 3 2
+--R (4b m + 18b m + 26b m + 12b )x
+--R +
+--R 2 3 2 2 2 2
+--R (12a b m + 66a b m + 114a b m + 60a b)x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 2 2 2 2 2
+--R (12a b m + 60a b m + 93a b m + 45a b )x
+--R +
+--R 3 3 3 2 3 3
+--R (4a m + 24a m + 47a m + 30a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 4 3 2
+--R 4m + 28m + 71m + 77m + 30
+--R Type: Union(Expression(Integer),...)
+--E 566
+
+--S 567 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 3 2 3 3 2
+--R (4b m + 18b m + 26b m + 12b )x
+--R +
+--R 2 3 2 2 2 2
+--R (12a b m + 66a b m + 114a b m + 60a b)x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 2 3 2 2 2 2 2
+--R (12a b m + 60a b m + 93a b m + 45a b )x
+--R +
+--R 3 3 3 2 3 3
+--R (4a m + 24a m + 47a m + 30a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2m + 5
+--R ------
+--R 3 3 3 2 3 3 2
+--R (- 4b m - 18b m - 26b m - 12b )x
+--R +
+--R 2 3 2 2 2 2 m + 2
+--R (- 12a b m - 60a b m - 93a b m - 45a b )x
+--R +
+--R 2m + 3
+--R ------
+--R 2 3 2 2 2 2 2
+--R (- 12a b m - 66a b m - 114a b m - 60a b)x
+--R +
+--R 3 3 3 2 3 3 m + 1
+--R (- 4a m - 24a m - 47a m - 30a )x
+--R /
+--R 4 3 2
+--R 4m + 28m + 71m + 77m + 30
+--R Type: Expression(Integer)
+--E 567
+
+--S 568 of 1325
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 568
+
+)clear all
+
+--S 569 of 1325
+t0:=x^4*(a+b*sqrt(x))^3
+--R
+--R
+--R 3 5 2 4 +-+ 2 5 3 4
+--R (1) (b x + 3a b x )\|x + 3a b x + a x
+--R Type: Expression(Integer)
+--E 569
+
+--S 570 of 1325
+r0:=1/5*a^3*x^5+6/11*a^2*b*x^(11/2)+1/2*a*b^2*x^6+2/13*b^3*x^(13/2)
+--R
+--R
+--R 3 6 2 5 +-+ 2 6 3 5
+--R (220b x + 780a b x )\|x + 715a b x + 286a x
+--R (2) -----------------------------------------------
+--R 1430
+--R Type: Expression(Integer)
+--E 570
+
+--S 571 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 6 2 5 +-+ 2 6 3 5
+--R (220b x + 780a b x )\|x + 715a b x + 286a x
+--R (3) -----------------------------------------------
+--R 1430
+--R Type: Union(Expression(Integer),...)
+--E 571
+
+--S 572 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 572
+
+--S 573 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 573
+
+)clear all
+
+--S 574 of 1325
+t0:=x^3*(a+b*sqrt(x))^3
+--R
+--R
+--R 3 4 2 3 +-+ 2 4 3 3
+--R (1) (b x + 3a b x )\|x + 3a b x + a x
+--R Type: Expression(Integer)
+--E 574
+
+--S 575 of 1325
+r0:=1/4*a^3*x^4+2/3*a^2*b*x^(9/2)+3/5*a*b^2*x^5+2/11*b^3*x^(11/2)
+--R
+--R
+--R 3 5 2 4 +-+ 2 5 3 4
+--R (120b x + 440a b x )\|x + 396a b x + 165a x
+--R (2) -----------------------------------------------
+--R 660
+--R Type: Expression(Integer)
+--E 575
+
+--S 576 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 5 2 4 +-+ 2 5 3 4
+--R (120b x + 440a b x )\|x + 396a b x + 165a x
+--R (3) -----------------------------------------------
+--R 660
+--R Type: Union(Expression(Integer),...)
+--E 576
+
+--S 577 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 577
+
+--S 578 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 578
+
+)clear all
+
+--S 579 of 1325
+t0:=x^2*(a+b*sqrt(x))^3
+--R
+--R
+--R 3 3 2 2 +-+ 2 3 3 2
+--R (1) (b x + 3a b x )\|x + 3a b x + a x
+--R Type: Expression(Integer)
+--E 579
+
+--S 580 of 1325
+r0:=1/3*a^3*x^3+6/7*a^2*b*x^(7/2)+3/4*a*b^2*x^4+2/9*b^3*x^(9/2)
+--R
+--R
+--R 3 4 2 3 +-+ 2 4 3 3
+--R (56b x + 216a b x )\|x + 189a b x + 84a x
+--R (2) ---------------------------------------------
+--R 252
+--R Type: Expression(Integer)
+--E 580
+
+--S 581 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 4 2 3 +-+ 2 4 3 3
+--R (56b x + 216a b x )\|x + 189a b x + 84a x
+--R (3) ---------------------------------------------
+--R 252
+--R Type: Union(Expression(Integer),...)
+--E 581
+
+--S 582 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 582
+
+--S 583 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 583
+
+)clear all
+
+--S 584 of 1325
+t0:=x*(a+b*sqrt(x))^3
+--R
+--R
+--R 3 2 2 +-+ 2 2 3
+--R (1) (b x + 3a b x)\|x + 3a b x + a x
+--R Type: Expression(Integer)
+--E 584
+
+--S 585 of 1325
+r0:=1/2*a^3*x^2+6/5*a^2*b*x^(5/2)+a*b^2*x^3+2/7*b^3*x^(7/2)
+--R
+--R
+--R 3 3 2 2 +-+ 2 3 3 2
+--R (20b x + 84a b x )\|x + 70a b x + 35a x
+--R (2) -------------------------------------------
+--R 70
+--R Type: Expression(Integer)
+--E 585
+
+--S 586 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 3 2 2 +-+ 2 3 3 2
+--R (20b x + 84a b x )\|x + 70a b x + 35a x
+--R (3) -------------------------------------------
+--R 70
+--R Type: Union(Expression(Integer),...)
+--E 586
+
+--S 587 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 587
+
+--S 588 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 588
+
+)clear all
+
+--S 589 of 1325
+t0:=(a+b*sqrt(x))^3
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (1) (b x + 3a b)\|x + 3a b x + a
+--R Type: Expression(Integer)
+--E 589
+
+--S 590 of 1325
+r0:=-1/2*a*(a+b*sqrt(x))^4/b^2+2/5*(a+b*sqrt(x))^5/b^2
+--R
+--R
+--R 5 2 2 3 +-+ 4 2 3 2 5
+--R (4b x + 20a b x)\|x + 15a b x + 10a b x - a
+--R (2) -----------------------------------------------
+--R 2
+--R 10b
+--R Type: Expression(Integer)
+--E 590
+
+--S 591 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 2 +-+ 2 2 3
+--R (4b x + 20a b x)\|x + 15a b x + 10a x
+--R (3) ----------------------------------------
+--R 10
+--R Type: Union(Expression(Integer),...)
+--E 591
+
+--S 592 of 1325
+m0:=a0-r0
+--R
+--R
+--R 5
+--R a
+--R (4) ----
+--R 2
+--R 10b
+--R Type: Expression(Integer)
+--E 592
+
+--S 593 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 593
+
+)clear all
+
+--S 594 of 1325
+t0:=(a+b*sqrt(x))^3/x
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (b x + 3a b)\|x + 3a b x + a
+--R (1) ------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 594
+
+--S 595 of 1325
+r0:=3*a*b^2*x+2/3*b^3*x^(3/2)+a^3*log(x)+6*a^2*b*sqrt(x)
+--R
+--R
+--R 3 2 +-+ 3 2
+--R (2b x + 18a b)\|x + 3a log(x) + 9a b x
+--R (2) ---------------------------------------
+--R 3
+--R Type: Expression(Integer)
+--E 595
+
+--S 596 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 +-+ 3 2 +-+ 2
+--R 6a log(\|x ) + (2b x + 18a b)\|x + 9a b x
+--R (3) ------------------------------------------
+--R 3
+--R Type: Union(Expression(Integer),...)
+--E 596
+
+--S 597 of 1325
+m0:=a0-r0
+--R
+--R
+--R 3 +-+ 3
+--R (4) 2a log(\|x ) - a log(x)
+--R Type: Expression(Integer)
+--E 597
+
+--S 598 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 598
+
+)clear all
+
+--S 599 of 1325
+t0:=(a+b*sqrt(x))^3/x^2
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (b x + 3a b)\|x + 3a b x + a
+--R (1) ------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 599
+
+--S 600 of 1325
+r0:=-a^3/x+3*a*b^2*log(x)-6*a^2*b/sqrt(x)+2*b^3*sqrt(x)
+--R
+--R
+--R 2 3 +-+ 3 2 2
+--R (3a b x log(x) - a )\|x + 2b x - 6a b x
+--R (2) -----------------------------------------
+--R +-+
+--R x\|x
+--R Type: Expression(Integer)
+--E 600
+
+--S 601 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+ 3 2 +-+ 3
+--R 6a b x log(\|x ) + (2b x - 6a b)\|x - a
+--R (3) -----------------------------------------
+--R x
+--R Type: Union(Expression(Integer),...)
+--E 601
+
+--S 602 of 1325
+m0:=a0-r0
+--R
+--R
+--R 2 +-+ 2
+--R (4) 6a b log(\|x ) - 3a b log(x)
+--R Type: Expression(Integer)
+--E 602
+
+--S 603 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 603
+
+)clear all
+
+--S 604 of 1325
+t0:=(a+b*sqrt(x))^3/x^3
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (b x + 3a b)\|x + 3a b x + a
+--R (1) ------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 604
+
+--S 605 of 1325
+r0:=-1/2*(a+b*sqrt(x))^4/(a*x^2)
+--R
+--R
+--R 3 3 +-+ 4 2 2 2 4
+--R (- 4a b x - 4a b)\|x - b x - 6a b x - a
+--R (2) ------------------------------------------
+--R 2
+--R 2a x
+--R Type: Expression(Integer)
+--E 605
+
+--S 606 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (- 4b x - 4a b)\|x - 6a b x - a
+--R (3) ---------------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 606
+
+--S 607 of 1325
+m0:=a0-r0
+--R
+--R
+--R 4
+--R b
+--R (4) --
+--R 2a
+--R Type: Expression(Integer)
+--E 607
+
+--S 608 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 608
+
+)clear all
+
+--S 609 of 1325
+t0:=(a+b*sqrt(x))^3/x^4
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (b x + 3a b)\|x + 3a b x + a
+--R (1) ------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 609
+
+--S 610 of 1325
+r0:=-1/3*a^3/x^3-6/5*a^2*b/x^(5/2)-3/2*a*b^2/x^2-2/3*b^3/x^(3/2)
+--R
+--R
+--R 2 3 +-+ 3 2 2
+--R (- 45a b x - 10a )\|x - 20b x - 36a b x
+--R (2) -----------------------------------------
+--R 3 +-+
+--R 30x \|x
+--R Type: Expression(Integer)
+--E 610
+
+--S 611 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (- 20b x - 36a b)\|x - 45a b x - 10a
+--R (3) --------------------------------------
+--R 3
+--R 30x
+--R Type: Union(Expression(Integer),...)
+--E 611
+
+--S 612 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 612
+
+--S 613 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 613
+
+)clear all
+
+--S 614 of 1325
+t0:=(a+b*sqrt(x))^3/x^5
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (b x + 3a b)\|x + 3a b x + a
+--R (1) ------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 614
+
+--S 615 of 1325
+r0:=-1/4*a^3/x^4-6/7*a^2*b/x^(7/2)-a*b^2/x^3-2/5*b^3/x^(5/2)
+--R
+--R
+--R 2 3 +-+ 3 2 2
+--R (- 140a b x - 35a )\|x - 56b x - 120a b x
+--R (2) -------------------------------------------
+--R 4 +-+
+--R 140x \|x
+--R Type: Expression(Integer)
+--E 615
+
+--S 616 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (- 56b x - 120a b)\|x - 140a b x - 35a
+--R (3) ----------------------------------------
+--R 4
+--R 140x
+--R Type: Union(Expression(Integer),...)
+--E 616
+
+--S 617 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 617
+
+--S 618 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 618
+
+)clear all
+
+--S 619 of 1325
+t0:=(a+b*sqrt(x))^3/x^6
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (b x + 3a b)\|x + 3a b x + a
+--R (1) ------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 619
+
+--S 620 of 1325
+r0:=-1/5*a^3/x^5-2/3*a^2*b/x^(9/2)-3/4*a*b^2/x^4-2/7*b^3/x^(7/2)
+--R
+--R
+--R 2 3 +-+ 3 2 2
+--R (- 315a b x - 84a )\|x - 120b x - 280a b x
+--R (2) --------------------------------------------
+--R 5 +-+
+--R 420x \|x
+--R Type: Expression(Integer)
+--E 620
+
+--S 621 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +-+ 2 3
+--R (- 120b x - 280a b)\|x - 315a b x - 84a
+--R (3) -----------------------------------------
+--R 5
+--R 420x
+--R Type: Union(Expression(Integer),...)
+--E 621
+
+--S 622 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 622
+
+--S 623 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 623
+
+)clear all
+
+--S 624 of 1325
+t0:=x^m*(a+b*sqrt(x))^5
+--R
+--R
+--R 5 2 2 3 4 m +-+ 4 2 3 2 5 m
+--R (1) (b x + 10a b x + 5a b)x \|x + (5a b x + 10a b x + a )x
+--R Type: Expression(Integer)
+--E 624
+
+--S 625 of 1325
+r0:=a^5*x^(1+m)/(1+m)+10*a^4*b*x^(3/2+m)/(3+2*m)+10*a^3*_
+ b^2*x^(2+m)/(2+m)+20*a^2*b^3*x^(5/2+m)/(5+2*m)+5*a*_
+ b^4*x^(3+m)/(3+m)+2*b^5*x^(7/2+m)/(7+2*m)
+--R
+--R
+--R (2)
+--R 2m + 7
+--R ------
+--R 5 5 5 4 5 3 5 2 5 5 2
+--R (8b m + 80b m + 310b m + 580b m + 522b m + 180b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4 4
+--R (40a b m + 420a b m + 1690a b m + 3255a b m + 2995a b m + 1050a b )
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3
+--R (80a b m + 880a b m + 3700a b m + 7400a b m + 7020a b m + 2520a b )
+--R *
+--R 2m + 5
+--R ------
+--R 2
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 3 2
+--R (80a b m + 920a b m + 4060a b m + 8530a b m + 8460a b m + 3150a b )
+--R *
+--R m + 2
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4 4
+--R (40a b m + 480a b m + 2230a b m + 4980a b m + 5290a b m + 2100a b)
+--R *
+--R 2m + 3
+--R ------
+--R 2
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5 m + 1
+--R (8a m + 100a m + 490a m + 1175a m + 1377a m + 630a )x
+--R /
+--R 6 5 4 3 2
+--R 8m + 108m + 590m + 1665m + 2552m + 2007m + 630
+--R Type: Expression(Integer)
+--E 625
+
+--S 626 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 5 4 5 3 5 2 5 5 3
+--R (8b m + 80b m + 310b m + 580b m + 522b m + 180b )x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R 80a b m + 880a b m + 3700a b m + 7400a b m + 7020a b m
+--R +
+--R 2 3
+--R 2520a b
+--R *
+--R 2
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 40a b m + 480a b m + 2230a b m + 4980a b m + 5290a b m
+--R +
+--R 4
+--R 2100a b
+--R *
+--R x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 40a b m + 420a b m + 1690a b m + 3255a b m + 2995a b m
+--R +
+--R 4
+--R 1050a b
+--R *
+--R 3
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R 80a b m + 920a b m + 4060a b m + 8530a b m + 8460a b m
+--R +
+--R 3 2
+--R 3150a b
+--R *
+--R 2
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5
+--R (8a m + 100a m + 490a m + 1175a m + 1377a m + 630a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 6 5 4 3 2
+--R 8m + 108m + 590m + 1665m + 2552m + 2007m + 630
+--R Type: Union(Expression(Integer),...)
+--E 626
+
+--S 627 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 5 5 4 5 3 5 2 5 5 3
+--R (8b m + 80b m + 310b m + 580b m + 522b m + 180b )x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R 80a b m + 880a b m + 3700a b m + 7400a b m + 7020a b m
+--R +
+--R 2 3
+--R 2520a b
+--R *
+--R 2
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 40a b m + 480a b m + 2230a b m + 4980a b m + 5290a b m
+--R +
+--R 4
+--R 2100a b
+--R *
+--R x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R 40a b m + 420a b m + 1690a b m + 3255a b m + 2995a b m
+--R +
+--R 4
+--R 1050a b
+--R *
+--R 3
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R 80a b m + 920a b m + 4060a b m + 8530a b m + 8460a b m
+--R +
+--R 3 2
+--R 3150a b
+--R *
+--R 2
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5
+--R (8a m + 100a m + 490a m + 1175a m + 1377a m + 630a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2m + 7
+--R ------
+--R 5 5 5 4 5 3 5 2 5 5 2
+--R (- 8b m - 80b m - 310b m - 580b m - 522b m - 180b )x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R - 40a b m - 420a b m - 1690a b m - 3255a b m - 2995a b m
+--R +
+--R 4
+--R - 1050a b
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3
+--R - 80a b m - 880a b m - 3700a b m - 7400a b m - 7020a b m
+--R +
+--R 2 3
+--R - 2520a b
+--R *
+--R 2m + 5
+--R ------
+--R 2
+--R x
+--R +
+--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2
+--R - 80a b m - 920a b m - 4060a b m - 8530a b m - 8460a b m
+--R +
+--R 3 2
+--R - 3150a b
+--R *
+--R m + 2
+--R x
+--R +
+--R 4 5 4 4 4 3 4 2 4
+--R - 40a b m - 480a b m - 2230a b m - 4980a b m - 5290a b m
+--R +
+--R 4
+--R - 2100a b
+--R *
+--R 2m + 3
+--R ------
+--R 2
+--R x
+--R +
+--R 5 5 5 4 5 3 5 2 5 5 m + 1
+--R (- 8a m - 100a m - 490a m - 1175a m - 1377a m - 630a )x
+--R /
+--R 6 5 4 3 2
+--R 8m + 108m + 590m + 1665m + 2552m + 2007m + 630
+--R Type: Expression(Integer)
+--E 627
+
+--S 628 of 1325
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 628
+
+)clear all
+
+--S 629 of 1325
+t0:=x^4*(a+b*sqrt(x))^5
+--R
+--R
+--R 5 6 2 3 5 4 4 +-+ 4 6 3 2 5 5 4
+--R (1) (b x + 10a b x + 5a b x )\|x + 5a b x + 10a b x + a x
+--R Type: Expression(Integer)
+--E 629
+
+--S 630 of 1325
+r0:=1/5*a^5*x^5+10/11*a^4*b*x^(11/2)+5/3*a^3*b^2*x^6+20/13*a^2*_
+ b^3*x^(13/2)+5/7*a*b^4*x^7+2/15*b^5*x^(15/2)
+--R
+--R
+--R (2)
+--R 5 7 2 3 6 4 5 +-+ 4 7 3 2 6
+--R (2002b x + 23100a b x + 13650a b x )\|x + 10725a b x + 25025a b x
+--R +
+--R 5 5
+--R 3003a x
+--R /
+--R 15015
+--R Type: Expression(Integer)
+--E 630
+
+--S 631 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 7 2 3 6 4 5 +-+ 4 7 3 2 6
+--R (2002b x + 23100a b x + 13650a b x )\|x + 10725a b x + 25025a b x
+--R +
+--R 5 5
+--R 3003a x
+--R /
+--R 15015
+--R Type: Union(Expression(Integer),...)
+--E 631
+
+--S 632 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 632
+
+--S 633 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 633
+
+)clear all
+
+--S 634 of 1325
+t0:=x^3*(a+b*sqrt(x))^5
+--R
+--R
+--R 5 5 2 3 4 4 3 +-+ 4 5 3 2 4 5 3
+--R (1) (b x + 10a b x + 5a b x )\|x + 5a b x + 10a b x + a x
+--R Type: Expression(Integer)
+--E 634
+
+--S 635 of 1325
+r0:=1/4*a^5*x^4+10/9*a^4*b*x^(9/2)+2*a^3*b^2*x^5+20/11*a^2*_
+ b^3*x^(11/2)+5/6*a*b^4*x^6+2/13*b^5*x^(13/2)
+--R
+--R
+--R (2)
+--R 5 6 2 3 5 4 4 +-+ 4 6 3 2 5 5 4
+--R (792b x + 9360a b x + 5720a b x )\|x + 4290a b x + 10296a b x + 1287a x
+--R -----------------------------------------------------------------------------
+--R 5148
+--R Type: Expression(Integer)
+--E 635
+
+--S 636 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 6 2 3 5 4 4 +-+ 4 6 3 2 5 5 4
+--R (792b x + 9360a b x + 5720a b x )\|x + 4290a b x + 10296a b x + 1287a x
+--R -----------------------------------------------------------------------------
+--R 5148
+--R Type: Union(Expression(Integer),...)
+--E 636
+
+--S 637 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 637
+
+--S 638 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 638
+
+)clear all
+
+--S 639 of 1325
+t0:=x^2*(a+b*sqrt(x))^5
+--R
+--R
+--R 5 4 2 3 3 4 2 +-+ 4 4 3 2 3 5 2
+--R (1) (b x + 10a b x + 5a b x )\|x + 5a b x + 10a b x + a x
+--R Type: Expression(Integer)
+--E 639
+
+--S 640 of 1325
+r0:=1/3*a^5*x^3+10/7*a^4*b*x^(7/2)+5/2*a^3*b^2*x^4+20/9*a^2*_
+ b^3*x^(9/2)+a*b^4*x^5+2/11*b^5*x^(11/2)
+--R
+--R
+--R (2)
+--R 5 5 2 3 4 4 3 +-+ 4 5 3 2 4 5 3
+--R (252b x + 3080a b x + 1980a b x )\|x + 1386a b x + 3465a b x + 462a x
+--R ---------------------------------------------------------------------------
+--R 1386
+--R Type: Expression(Integer)
+--E 640
+
+--S 641 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 2 3 4 4 3 +-+ 4 5 3 2 4 5 3
+--R (252b x + 3080a b x + 1980a b x )\|x + 1386a b x + 3465a b x + 462a x
+--R ---------------------------------------------------------------------------
+--R 1386
+--R Type: Union(Expression(Integer),...)
+--E 641
+
+--S 642 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 642
+
+--S 643 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 643
+
+)clear all
+
+--S 644 of 1325
+t0:=x*(a+b*sqrt(x))^5
+--R
+--R
+--R 5 3 2 3 2 4 +-+ 4 3 3 2 2 5
+--R (1) (b x + 10a b x + 5a b x)\|x + 5a b x + 10a b x + a x
+--R Type: Expression(Integer)
+--E 644
+
+--S 645 of 1325
+r0:=1/2*a^5*x^2+2*a^4*b*x^(5/2)+10/3*a^3*b^2*x^3+20/7*a^2*_
+ b^3*x^(7/2)+5/4*a*b^4*x^4+2/9*b^5*x^(9/2)
+--R
+--R
+--R 5 4 2 3 3 4 2 +-+ 4 4 3 2 3 5 2
+--R (56b x + 720a b x + 504a b x )\|x + 315a b x + 840a b x + 126a x
+--R (2) ----------------------------------------------------------------------
+--R 252
+--R Type: Expression(Integer)
+--E 645
+
+--S 646 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 4 2 3 3 4 2 +-+ 4 4 3 2 3 5 2
+--R (56b x + 720a b x + 504a b x )\|x + 315a b x + 840a b x + 126a x
+--R (3) ----------------------------------------------------------------------
+--R 252
+--R Type: Union(Expression(Integer),...)
+--E 646
+
+--S 647 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 647
+
+--S 648 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 648
+
+)clear all
+
+--S 649 of 1325
+t0:=(a+b*sqrt(x))^5
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (1) (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a
+--R Type: Expression(Integer)
+--E 649
+
+--S 650 of 1325
+r0:=-1/3*a*(a+b*sqrt(x))^6/b^2+2/7*(a+b*sqrt(x))^7/b^2
+--R
+--R
+--R 7 3 2 5 2 4 3 +-+ 6 3 3 4 2 5 2 7
+--R (6b x + 84a b x + 70a b x)\|x + 35a b x + 105a b x + 21a b x - a
+--R (2) ----------------------------------------------------------------------
+--R 2
+--R 21b
+--R Type: Expression(Integer)
+--E 650
+
+--S 651 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 3 2 3 2 4 +-+ 4 3 3 2 2 5
+--R (6b x + 84a b x + 70a b x)\|x + 35a b x + 105a b x + 21a x
+--R (3) ---------------------------------------------------------------
+--R 21
+--R Type: Union(Expression(Integer),...)
+--E 651
+
+--S 652 of 1325
+m0:=a0-r0
+--R
+--R
+--R 7
+--R a
+--R (4) ----
+--R 2
+--R 21b
+--R Type: Expression(Integer)
+--E 652
+
+--S 653 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 653
+
+)clear all
+
+--S 654 of 1325
+t0:=(a+b*sqrt(x))^5/x
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a
+--R (1) ----------------------------------------------------
+--R x
+--R Type: Expression(Integer)
+--E 654
+
+--S 655 of 1325
+r0:=10*a^3*b^2*x+20/3*a^2*b^3*x^(3/2)+5/2*a*b^4*x^2+2/5*b^5*x^(5/2)+_
+ a^5*log(x)+10*a^4*b*sqrt(x)
+--R
+--R
+--R 5 2 2 3 4 +-+ 5 4 2 3 2
+--R (12b x + 200a b x + 300a b)\|x + 30a log(x) + 75a b x + 300a b x
+--R (2) -------------------------------------------------------------------
+--R 30
+--R Type: Expression(Integer)
+--E 655
+
+--S 656 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 +-+ 5 2 2 3 4 +-+ 4 2 3 2
+--R 60a log(\|x ) + (12b x + 200a b x + 300a b)\|x + 75a b x + 300a b x
+--R (3) ----------------------------------------------------------------------
+--R 30
+--R Type: Union(Expression(Integer),...)
+--E 656
+
+--S 657 of 1325
+m0:=a0-r0
+--R
+--R
+--R 5 +-+ 5
+--R (4) 2a log(\|x ) - a log(x)
+--R Type: Expression(Integer)
+--E 657
+
+--S 658 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 658
+
+)clear all
+
+--S 659 of 1325
+t0:=(a+b*sqrt(x))^5/x^2
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a
+--R (1) ----------------------------------------------------
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 659
+
+--S 660 of 1325
+r0:=-a^5/x+5*a*b^4*x+2/3*b^5*x^(3/2)+10*a^3*b^2*log(x)-_
+ 10*a^4*b/sqrt(x)+20*a^2*b^3*sqrt(x)
+--R
+--R
+--R 3 2 4 2 5 +-+ 5 3 2 3 2 4
+--R (30a b x log(x) + 15a b x - 3a )\|x + 2b x + 60a b x - 30a b x
+--R (2) ------------------------------------------------------------------
+--R +-+
+--R 3x\|x
+--R Type: Expression(Integer)
+--E 660
+
+--S 661 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 2 +-+ 5 2 2 3 4 +-+ 4 2 5
+--R 60a b x log(\|x ) + (2b x + 60a b x - 30a b)\|x + 15a b x - 3a
+--R (3) ------------------------------------------------------------------
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 661
+
+--S 662 of 1325
+m0:=a0-r0
+--R
+--R
+--R 3 2 +-+ 3 2
+--R (4) 20a b log(\|x ) - 10a b log(x)
+--R Type: Expression(Integer)
+--E 662
+
+--S 663 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 663
+
+)clear all
+
+--S 664 of 1325
+t0:=(a+b*sqrt(x))^5/x^3
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a
+--R (1) ----------------------------------------------------
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 664
+
+--S 665 of 1325
+r0:=-1/2*a^5/x^2-10/3*a^4*b/x^(3/2)-10*a^3*b^2/x+5*a*b^4*log(x)-_
+ 20*a^2*b^3/sqrt(x)+2*b^5*sqrt(x)
+--R
+--R
+--R 4 2 3 2 5 +-+ 5 3 2 3 2 4
+--R (30a b x log(x) - 60a b x - 3a )\|x + 12b x - 120a b x - 20a b x
+--R (2) -------------------------------------------------------------------
+--R 2 +-+
+--R 6x \|x
+--R Type: Expression(Integer)
+--E 665
+
+--S 666 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2 +-+ 5 2 2 3 4 +-+ 3 2 5
+--R 60a b x log(\|x ) + (12b x - 120a b x - 20a b)\|x - 60a b x - 3a
+--R (3) -------------------------------------------------------------------
+--R 2
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 666
+
+--S 667 of 1325
+m0:=a0-r0
+--R
+--R
+--R 4 +-+ 4
+--R (4) 10a b log(\|x ) - 5a b log(x)
+--R Type: Expression(Integer)
+--E 667
+
+--S 668 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 668
+
+)clear all
+
+--S 669 of 1325
+t0:=(a+b*sqrt(x))^5/x^4
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a
+--R (1) ----------------------------------------------------
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 669
+
+--S 670 of 1325
+r0:=-1/3*(a+b*sqrt(x))^6/(a*x^3)
+--R
+--R
+--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 6
+--R (- 6a b x - 20a b x - 6a b)\|x - b x - 15a b x - 15a b x - a
+--R (2) -----------------------------------------------------------------
+--R 3
+--R 3a x
+--R Type: Expression(Integer)
+--E 670
+
+--S 671 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (- 6b x - 20a b x - 6a b)\|x - 15a b x - 15a b x - a
+--R (3) --------------------------------------------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 671
+
+--S 672 of 1325
+m0:=a0-r0
+--R
+--R
+--R 6
+--R b
+--R (4) --
+--R 3a
+--R Type: Expression(Integer)
+--E 672
+
+--S 673 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 673
+
+)clear all
+
+--S 674 of 1325
+t0:=(a+b*sqrt(x))^5/x^5
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a
+--R (1) ----------------------------------------------------
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 674
+
+--S 675 of 1325
+r0:=-1/4*a^5/x^4-10/7*a^4*b/x^(7/2)-10/3*a^3*b^2/x^3-_
+ 4*a^2*b^3/x^(5/2)-5/2*a*b^4/x^2-2/3*b^5/x^(3/2)
+--R
+--R
+--R 4 2 3 2 5 +-+ 5 3 2 3 2 4
+--R (- 210a b x - 280a b x - 21a )\|x - 56b x - 336a b x - 120a b x
+--R (2) -------------------------------------------------------------------
+--R 4 +-+
+--R 84x \|x
+--R Type: Expression(Integer)
+--E 675
+
+--S 676 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (- 56b x - 336a b x - 120a b)\|x - 210a b x - 280a b x - 21a
+--R (3) ----------------------------------------------------------------
+--R 4
+--R 84x
+--R Type: Union(Expression(Integer),...)
+--E 676
+
+--S 677 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 677
+
+--S 678 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 678
+
+)clear all
+
+--S 679 of 1325
+t0:=(a+b*sqrt(x))^5/x^6
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a
+--R (1) ----------------------------------------------------
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 679
+
+--S 680 of 1325
+r0:=-1/5*a^5/x^5-10/9*a^4*b/x^(9/2)-5/2*a^3*b^2/x^4-_
+ 20/7*a^2*b^3/x^(7/2)-5/3*a*b^4/x^3-2/5*b^5/x^(5/2)
+--R
+--R
+--R (2)
+--R 4 2 3 2 5 +-+ 5 3 2 3 2 4
+--R (- 1050a b x - 1575a b x - 126a )\|x - 252b x - 1800a b x - 700a b x
+--R ------------------------------------------------------------------------
+--R 5 +-+
+--R 630x \|x
+--R Type: Expression(Integer)
+--E 680
+
+--S 681 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (- 252b x - 1800a b x - 700a b)\|x - 1050a b x - 1575a b x - 126a
+--R (3) ---------------------------------------------------------------------
+--R 5
+--R 630x
+--R Type: Union(Expression(Integer),...)
+--E 681
+
+--S 682 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 682
+
+--S 683 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 683
+
+)clear all
+
+--S 684 of 1325
+t0:=(a+b*sqrt(x))^5/x^7
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a
+--R (1) ----------------------------------------------------
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 684
+
+--S 685 of 1325
+r0:=-1/6*a^5/x^6-10/11*a^4*b/x^(11/2)-2*a^3*b^2/x^5-_
+ 20/9*a^2*b^3/x^(9/2)-5/4*a*b^4/x^4-2/7*b^5/x^(7/2)
+--R
+--R
+--R (2)
+--R 4 2 3 2 5 +-+ 5 3 2 3 2 4
+--R (- 3465a b x - 5544a b x - 462a )\|x - 792b x - 6160a b x - 2520a b x
+--R -------------------------------------------------------------------------
+--R 6 +-+
+--R 2772x \|x
+--R Type: Expression(Integer)
+--E 685
+
+--S 686 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 2 2 3 4 +-+ 4 2 3 2 5
+--R (- 792b x - 6160a b x - 2520a b)\|x - 3465a b x - 5544a b x - 462a
+--R (3) ----------------------------------------------------------------------
+--R 6
+--R 2772x
+--R Type: Union(Expression(Integer),...)
+--E 686
+
+--S 687 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 687
+
+--S 688 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 688
+
+)clear all
+
+--S 689 of 1325
+t0:=x^m*(a+b*sqrt(x))^10
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 m +-+
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)x \|x
+--R +
+--R 10 5 2 8 4 4 6 3 6 4 2 8 2 10 m
+--R (b x + 45a b x + 210a b x + 210a b x + 45a b x + a )x
+--R Type: Expression(Integer)
+--E 689
+
+--S 690 of 1325
+r0:=a^10*x^(1+m)/(1+m)+20*a^9*b*x^(3/2+m)/(3+2*m)+45*a^8*b^2*x^(2+m)/(2+m)_
+ +240*a^7*b^3*x^(5/2+m)/(5+2*m)+210*a^6*b^4*x^(3+m)/(3+m)+_
+ 504*a^5*b^5*x^(7/2+m)/(7+2*m)+210*a^4*b^6*x^(4+m)/(4+m)+_
+ 240*a^3*b^7*x^(9/2+m)/(9+2*m)+45*a^2*b^8*x^(5+m)/(5+m)+_
+ 20*a*b^9*x^(11/2+m)/(11+2*m)+b^10*x^(6+m)/(6+m)
+--R
+--R
+--R (2)
+--R 10 10 10 9 10 8 10 7 10 6
+--R 32b m + 1040b m + 14880b m + 123240b m + 653226b m
+--R +
+--R 10 5 10 4 10 3 10 2
+--R 2310945b m + 5514295b m + 8741785b m + 8786367b m
+--R +
+--R 10 10
+--R 5039190b m + 1247400b
+--R *
+--R m + 6
+--R x
+--R +
+--R 9 10 9 9 9 8 9 7
+--R 320a b m + 10560a b m + 153120a b m + 1283040a b m
+--R +
+--R 9 6 9 5 9 4 9 3
+--R 6869940a b m + 24518340a b m + 58948780a b m + 94057260a b m
+--R +
+--R 9 2 9 9
+--R 95055840a b m + 54766800a b m + 13608000a b
+--R *
+--R 2m + 11
+--R -------
+--R 2
+--R x
+--R +
+--R 2 8 10 2 8 9 2 8 8 2 8 7
+--R 1440a b m + 48240a b m + 709200a b m + 6017400a b m
+--R +
+--R 2 8 6 2 8 5 2 8 4 2 8 3
+--R 32582970a b m + 117448695a b m + 284854950a b m + 457965225a b m
+--R +
+--R 2 8 2 2 8 2 8
+--R 465842340a b m + 269870940a b m + 67359600a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 3 7 10 3 7 9 3 7 8 3 7 7
+--R 3840a b m + 130560a b m + 1946880a b m + 16741440a b m
+--R +
+--R 3 7 6 3 7 5 3 7 4 3 7 3
+--R 91783440a b m + 334610640a b m + 819847920a b m + 1329990960a b m
+--R +
+--R 3 7 2 3 7 3 7
+--R 1363489920a b m + 795182400a b m + 199584000a b
+--R *
+--R 2m + 9
+--R ------
+--R 2
+--R x
+--R +
+--R 4 6 10 4 6 9 4 6 8 4 6 7
+--R 6720a b m + 231840a b m + 3507840a b m + 30597840a b m
+--R +
+--R 4 6 6 4 6 5 4 6 4
+--R 170068500a b m + 628089210a b m + 1557435810a b m
+--R +
+--R 4 6 3 4 6 2 4 6 4 6
+--R 2554043310a b m + 2643612930a b m + 1554600600a b m + 392931000a b
+--R *
+--R m + 4
+--R x
+--R +
+--R 5 5 10 5 5 9 5 5 8 5 5 7
+--R 8064a b m + 282240a b m + 4334400a b m + 38384640a b m
+--R +
+--R 5 5 6 5 5 5 5 5 4
+--R 216605592a b m + 811916280a b m + 2042044200a b m
+--R +
+--R 5 5 3 5 5 2 5 5 5 5
+--R 3393389160a b m + 3554881344a b m + 2112778080a b m + 538876800a b
+--R *
+--R 2m + 7
+--R ------
+--R 2
+--R x
+--R +
+--R 6 4 10 6 4 9 6 4 8 6 4 7
+--R 6720a b m + 238560a b m + 3719520a b m + 33470640a b m
+--R +
+--R 6 4 6 6 4 5 6 4 4
+--R 192047940a b m + 732219390a b m + 1873134480a b m
+--R +
+--R 6 4 3 6 4 2 6 4 6 4
+--R 3164383110a b m + 3366636840a b m + 2029141800a b m + 523908000a b
+--R *
+--R m + 3
+--R x
+--R +
+--R 7 3 10 7 3 9 7 3 8 7 3 7
+--R 3840a b m + 138240a b m + 2188800a b m + 20030400a b m
+--R +
+--R 7 3 6 7 3 5 7 3 4
+--R 117043920a b m + 455026320a b m + 1188030000a b m
+--R +
+--R 7 3 3 7 3 2 7 3 7 3
+--R 2049231600a b m + 2225370240a b m + 1367461440a b m + 359251200a b
+--R *
+--R 2m + 5
+--R ------
+--R 2
+--R x
+--R +
+--R 8 2 10 8 2 9 8 2 8 8 2 7
+--R 1440a b m + 52560a b m + 845280a b m + 7872840a b m
+--R +
+--R 8 2 6 8 2 5 8 2 4 8 2 3
+--R 46924290a b m + 186514965a b m + 499068495a b m + 884102985a b m
+--R +
+--R 8 2 2 8 2 8 2
+--R 987462495a b m + 624157650a b m + 168399000a b
+--R *
+--R m + 2
+--R x
+--R +
+--R 9 10 9 9 9 8 9 7
+--R 320a b m + 11840a b m + 193440a b m + 1835040a b m
+--R +
+--R 9 6 9 5 9 4 9 3
+--R 11174100a b m + 45541860a b m + 125486860a b m + 230045260a b m
+--R +
+--R 9 2 9 9
+--R 267302880a b m + 176619600a b m + 49896000a b
+--R *
+--R 2m + 3
+--R ------
+--R 2
+--R x
+--R +
+--R 10 10 10 9 10 8 10 7 10 6
+--R 32a m + 1200a m + 19920a m + 192600a m + 1200066a m
+--R +
+--R 10 5 10 4 10 3 10 2
+--R 5030235a m + 14349730a m + 27477825a m + 33759252a m
+--R +
+--R 10 10
+--R 23998140a m + 7484400a
+--R *
+--R m + 1
+--R x
+--R /
+--R 11 10 9 8 7 6 5
+--R 32m + 1232m + 21120m + 212520m + 1392666m + 6230301m + 19379965m
+--R +
+--R 4 3 2
+--R 41827555m + 61237077m + 57757392m + 31482540m + 7484400
+--R Type: Expression(Integer)
+--E 690
+
+--S 691 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 10 9 9 9 8 9 7
+--R 320a b m + 10560a b m + 153120a b m + 1283040a b m
+--R +
+--R 9 6 9 5 9 4
+--R 6869940a b m + 24518340a b m + 58948780a b m
+--R +
+--R 9 3 9 2 9 9
+--R 94057260a b m + 95055840a b m + 54766800a b m + 13608000a b
+--R *
+--R 5
+--R x
+--R +
+--R 3 7 10 3 7 9 3 7 8 3 7 7
+--R 3840a b m + 130560a b m + 1946880a b m + 16741440a b m
+--R +
+--R 3 7 6 3 7 5 3 7 4
+--R 91783440a b m + 334610640a b m + 819847920a b m
+--R +
+--R 3 7 3 3 7 2 3 7
+--R 1329990960a b m + 1363489920a b m + 795182400a b m
+--R +
+--R 3 7
+--R 199584000a b
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 10 5 5 9 5 5 8 5 5 7
+--R 8064a b m + 282240a b m + 4334400a b m + 38384640a b m
+--R +
+--R 5 5 6 5 5 5 5 5 4
+--R 216605592a b m + 811916280a b m + 2042044200a b m
+--R +
+--R 5 5 3 5 5 2 5 5
+--R 3393389160a b m + 3554881344a b m + 2112778080a b m
+--R +
+--R 5 5
+--R 538876800a b
+--R *
+--R 3
+--R x
+--R +
+--R 7 3 10 7 3 9 7 3 8 7 3 7
+--R 3840a b m + 138240a b m + 2188800a b m + 20030400a b m
+--R +
+--R 7 3 6 7 3 5 7 3 4
+--R 117043920a b m + 455026320a b m + 1188030000a b m
+--R +
+--R 7 3 3 7 3 2 7 3
+--R 2049231600a b m + 2225370240a b m + 1367461440a b m
+--R +
+--R 7 3
+--R 359251200a b
+--R *
+--R 2
+--R x
+--R +
+--R 9 10 9 9 9 8 9 7
+--R 320a b m + 11840a b m + 193440a b m + 1835040a b m
+--R +
+--R 9 6 9 5 9 4
+--R 11174100a b m + 45541860a b m + 125486860a b m
+--R +
+--R 9 3 9 2 9 9
+--R 230045260a b m + 267302880a b m + 176619600a b m + 49896000a b
+--R *
+--R x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 10 10 9 10 8 10 7 10 6
+--R 32b m + 1040b m + 14880b m + 123240b m + 653226b m
+--R +
+--R 10 5 10 4 10 3 10 2
+--R 2310945b m + 5514295b m + 8741785b m + 8786367b m
+--R +
+--R 10 10
+--R 5039190b m + 1247400b
+--R *
+--R 6
+--R x
+--R +
+--R 2 8 10 2 8 9 2 8 8 2 8 7
+--R 1440a b m + 48240a b m + 709200a b m + 6017400a b m
+--R +
+--R 2 8 6 2 8 5 2 8 4
+--R 32582970a b m + 117448695a b m + 284854950a b m
+--R +
+--R 2 8 3 2 8 2 2 8 2 8
+--R 457965225a b m + 465842340a b m + 269870940a b m + 67359600a b
+--R *
+--R 5
+--R x
+--R +
+--R 4 6 10 4 6 9 4 6 8 4 6 7
+--R 6720a b m + 231840a b m + 3507840a b m + 30597840a b m
+--R +
+--R 4 6 6 4 6 5 4 6 4
+--R 170068500a b m + 628089210a b m + 1557435810a b m
+--R +
+--R 4 6 3 4 6 2 4 6 4 6
+--R 2554043310a b m + 2643612930a b m + 1554600600a b m + 392931000a b
+--R *
+--R 4
+--R x
+--R +
+--R 6 4 10 6 4 9 6 4 8 6 4 7
+--R 6720a b m + 238560a b m + 3719520a b m + 33470640a b m
+--R +
+--R 6 4 6 6 4 5 6 4 4
+--R 192047940a b m + 732219390a b m + 1873134480a b m
+--R +
+--R 6 4 3 6 4 2 6 4 6 4
+--R 3164383110a b m + 3366636840a b m + 2029141800a b m + 523908000a b
+--R *
+--R 3
+--R x
+--R +
+--R 8 2 10 8 2 9 8 2 8 8 2 7
+--R 1440a b m + 52560a b m + 845280a b m + 7872840a b m
+--R +
+--R 8 2 6 8 2 5 8 2 4
+--R 46924290a b m + 186514965a b m + 499068495a b m
+--R +
+--R 8 2 3 8 2 2 8 2 8 2
+--R 884102985a b m + 987462495a b m + 624157650a b m + 168399000a b
+--R *
+--R 2
+--R x
+--R +
+--R 10 10 10 9 10 8 10 7 10 6
+--R 32a m + 1200a m + 19920a m + 192600a m + 1200066a m
+--R +
+--R 10 5 10 4 10 3 10 2
+--R 5030235a m + 14349730a m + 27477825a m + 33759252a m
+--R +
+--R 10 10
+--R 23998140a m + 7484400a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 11 10 9 8 7 6 5
+--R 32m + 1232m + 21120m + 212520m + 1392666m + 6230301m + 19379965m
+--R +
+--R 4 3 2
+--R 41827555m + 61237077m + 57757392m + 31482540m + 7484400
+--R Type: Union(Expression(Integer),...)
+--E 691
+
+--S 692 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 9 10 9 9 9 8 9 7
+--R 320a b m + 10560a b m + 153120a b m + 1283040a b m
+--R +
+--R 9 6 9 5 9 4
+--R 6869940a b m + 24518340a b m + 58948780a b m
+--R +
+--R 9 3 9 2 9 9
+--R 94057260a b m + 95055840a b m + 54766800a b m + 13608000a b
+--R *
+--R 5
+--R x
+--R +
+--R 3 7 10 3 7 9 3 7 8 3 7 7
+--R 3840a b m + 130560a b m + 1946880a b m + 16741440a b m
+--R +
+--R 3 7 6 3 7 5 3 7 4
+--R 91783440a b m + 334610640a b m + 819847920a b m
+--R +
+--R 3 7 3 3 7 2 3 7
+--R 1329990960a b m + 1363489920a b m + 795182400a b m
+--R +
+--R 3 7
+--R 199584000a b
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 10 5 5 9 5 5 8 5 5 7
+--R 8064a b m + 282240a b m + 4334400a b m + 38384640a b m
+--R +
+--R 5 5 6 5 5 5 5 5 4
+--R 216605592a b m + 811916280a b m + 2042044200a b m
+--R +
+--R 5 5 3 5 5 2 5 5
+--R 3393389160a b m + 3554881344a b m + 2112778080a b m
+--R +
+--R 5 5
+--R 538876800a b
+--R *
+--R 3
+--R x
+--R +
+--R 7 3 10 7 3 9 7 3 8 7 3 7
+--R 3840a b m + 138240a b m + 2188800a b m + 20030400a b m
+--R +
+--R 7 3 6 7 3 5 7 3 4
+--R 117043920a b m + 455026320a b m + 1188030000a b m
+--R +
+--R 7 3 3 7 3 2 7 3
+--R 2049231600a b m + 2225370240a b m + 1367461440a b m
+--R +
+--R 7 3
+--R 359251200a b
+--R *
+--R 2
+--R x
+--R +
+--R 9 10 9 9 9 8 9 7
+--R 320a b m + 11840a b m + 193440a b m + 1835040a b m
+--R +
+--R 9 6 9 5 9 4
+--R 11174100a b m + 45541860a b m + 125486860a b m
+--R +
+--R 9 3 9 2 9
+--R 230045260a b m + 267302880a b m + 176619600a b m
+--R +
+--R 9
+--R 49896000a b
+--R *
+--R x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 10 10 9 10 8 10 7 10 6
+--R 32b m + 1040b m + 14880b m + 123240b m + 653226b m
+--R +
+--R 10 5 10 4 10 3 10 2
+--R 2310945b m + 5514295b m + 8741785b m + 8786367b m
+--R +
+--R 10 10
+--R 5039190b m + 1247400b
+--R *
+--R 6
+--R x
+--R +
+--R 2 8 10 2 8 9 2 8 8 2 8 7
+--R 1440a b m + 48240a b m + 709200a b m + 6017400a b m
+--R +
+--R 2 8 6 2 8 5 2 8 4
+--R 32582970a b m + 117448695a b m + 284854950a b m
+--R +
+--R 2 8 3 2 8 2 2 8 2 8
+--R 457965225a b m + 465842340a b m + 269870940a b m + 67359600a b
+--R *
+--R 5
+--R x
+--R +
+--R 4 6 10 4 6 9 4 6 8 4 6 7
+--R 6720a b m + 231840a b m + 3507840a b m + 30597840a b m
+--R +
+--R 4 6 6 4 6 5 4 6 4
+--R 170068500a b m + 628089210a b m + 1557435810a b m
+--R +
+--R 4 6 3 4 6 2 4 6
+--R 2554043310a b m + 2643612930a b m + 1554600600a b m
+--R +
+--R 4 6
+--R 392931000a b
+--R *
+--R 4
+--R x
+--R +
+--R 6 4 10 6 4 9 6 4 8 6 4 7
+--R 6720a b m + 238560a b m + 3719520a b m + 33470640a b m
+--R +
+--R 6 4 6 6 4 5 6 4 4
+--R 192047940a b m + 732219390a b m + 1873134480a b m
+--R +
+--R 6 4 3 6 4 2 6 4
+--R 3164383110a b m + 3366636840a b m + 2029141800a b m
+--R +
+--R 6 4
+--R 523908000a b
+--R *
+--R 3
+--R x
+--R +
+--R 8 2 10 8 2 9 8 2 8 8 2 7
+--R 1440a b m + 52560a b m + 845280a b m + 7872840a b m
+--R +
+--R 8 2 6 8 2 5 8 2 4
+--R 46924290a b m + 186514965a b m + 499068495a b m
+--R +
+--R 8 2 3 8 2 2 8 2 8 2
+--R 884102985a b m + 987462495a b m + 624157650a b m + 168399000a b
+--R *
+--R 2
+--R x
+--R +
+--R 10 10 10 9 10 8 10 7 10 6
+--R 32a m + 1200a m + 19920a m + 192600a m + 1200066a m
+--R +
+--R 10 5 10 4 10 3 10 2
+--R 5030235a m + 14349730a m + 27477825a m + 33759252a m
+--R +
+--R 10 10
+--R 23998140a m + 7484400a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 10 10 10 9 10 8 10 7 10 6
+--R - 32b m - 1040b m - 14880b m - 123240b m - 653226b m
+--R +
+--R 10 5 10 4 10 3 10 2
+--R - 2310945b m - 5514295b m - 8741785b m - 8786367b m
+--R +
+--R 10 10
+--R - 5039190b m - 1247400b
+--R *
+--R m + 6
+--R x
+--R +
+--R 9 10 9 9 9 8 9 7
+--R - 320a b m - 10560a b m - 153120a b m - 1283040a b m
+--R +
+--R 9 6 9 5 9 4 9 3
+--R - 6869940a b m - 24518340a b m - 58948780a b m - 94057260a b m
+--R +
+--R 9 2 9 9
+--R - 95055840a b m - 54766800a b m - 13608000a b
+--R *
+--R 2m + 11
+--R -------
+--R 2
+--R x
+--R +
+--R 2 8 10 2 8 9 2 8 8 2 8 7
+--R - 1440a b m - 48240a b m - 709200a b m - 6017400a b m
+--R +
+--R 2 8 6 2 8 5 2 8 4
+--R - 32582970a b m - 117448695a b m - 284854950a b m
+--R +
+--R 2 8 3 2 8 2 2 8 2 8
+--R - 457965225a b m - 465842340a b m - 269870940a b m - 67359600a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 3 7 10 3 7 9 3 7 8 3 7 7
+--R - 3840a b m - 130560a b m - 1946880a b m - 16741440a b m
+--R +
+--R 3 7 6 3 7 5 3 7 4
+--R - 91783440a b m - 334610640a b m - 819847920a b m
+--R +
+--R 3 7 3 3 7 2 3 7 3 7
+--R - 1329990960a b m - 1363489920a b m - 795182400a b m - 199584000a b
+--R *
+--R 2m + 9
+--R ------
+--R 2
+--R x
+--R +
+--R 4 6 10 4 6 9 4 6 8 4 6 7
+--R - 6720a b m - 231840a b m - 3507840a b m - 30597840a b m
+--R +
+--R 4 6 6 4 6 5 4 6 4
+--R - 170068500a b m - 628089210a b m - 1557435810a b m
+--R +
+--R 4 6 3 4 6 2 4 6 4 6
+--R - 2554043310a b m - 2643612930a b m - 1554600600a b m - 392931000a b
+--R *
+--R m + 4
+--R x
+--R +
+--R 5 5 10 5 5 9 5 5 8 5 5 7
+--R - 8064a b m - 282240a b m - 4334400a b m - 38384640a b m
+--R +
+--R 5 5 6 5 5 5 5 5 4
+--R - 216605592a b m - 811916280a b m - 2042044200a b m
+--R +
+--R 5 5 3 5 5 2 5 5 5 5
+--R - 3393389160a b m - 3554881344a b m - 2112778080a b m - 538876800a b
+--R *
+--R 2m + 7
+--R ------
+--R 2
+--R x
+--R +
+--R 6 4 10 6 4 9 6 4 8 6 4 7
+--R - 6720a b m - 238560a b m - 3719520a b m - 33470640a b m
+--R +
+--R 6 4 6 6 4 5 6 4 4
+--R - 192047940a b m - 732219390a b m - 1873134480a b m
+--R +
+--R 6 4 3 6 4 2 6 4 6 4
+--R - 3164383110a b m - 3366636840a b m - 2029141800a b m - 523908000a b
+--R *
+--R m + 3
+--R x
+--R +
+--R 7 3 10 7 3 9 7 3 8 7 3 7
+--R - 3840a b m - 138240a b m - 2188800a b m - 20030400a b m
+--R +
+--R 7 3 6 7 3 5 7 3 4
+--R - 117043920a b m - 455026320a b m - 1188030000a b m
+--R +
+--R 7 3 3 7 3 2 7 3 7 3
+--R - 2049231600a b m - 2225370240a b m - 1367461440a b m - 359251200a b
+--R *
+--R 2m + 5
+--R ------
+--R 2
+--R x
+--R +
+--R 8 2 10 8 2 9 8 2 8 8 2 7
+--R - 1440a b m - 52560a b m - 845280a b m - 7872840a b m
+--R +
+--R 8 2 6 8 2 5 8 2 4
+--R - 46924290a b m - 186514965a b m - 499068495a b m
+--R +
+--R 8 2 3 8 2 2 8 2 8 2
+--R - 884102985a b m - 987462495a b m - 624157650a b m - 168399000a b
+--R *
+--R m + 2
+--R x
+--R +
+--R 9 10 9 9 9 8 9 7
+--R - 320a b m - 11840a b m - 193440a b m - 1835040a b m
+--R +
+--R 9 6 9 5 9 4 9 3
+--R - 11174100a b m - 45541860a b m - 125486860a b m - 230045260a b m
+--R +
+--R 9 2 9 9
+--R - 267302880a b m - 176619600a b m - 49896000a b
+--R *
+--R 2m + 3
+--R ------
+--R 2
+--R x
+--R +
+--R 10 10 10 9 10 8 10 7 10 6
+--R - 32a m - 1200a m - 19920a m - 192600a m - 1200066a m
+--R +
+--R 10 5 10 4 10 3 10 2
+--R - 5030235a m - 14349730a m - 27477825a m - 33759252a m
+--R +
+--R 10 10
+--R - 23998140a m - 7484400a
+--R *
+--R m + 1
+--R x
+--R /
+--R 11 10 9 8 7 6 5
+--R 32m + 1232m + 21120m + 212520m + 1392666m + 6230301m + 19379965m
+--R +
+--R 4 3 2
+--R 41827555m + 61237077m + 57757392m + 31482540m + 7484400
+--R Type: Expression(Integer)
+--E 692
+
+--S 693 of 1325
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 693
+
+)clear all
+
+--S 694 of 1325
+t0:=x^4*(a+b*sqrt(x))^10
+--R
+--R
+--R (1)
+--R 9 8 3 7 7 5 5 6 7 3 5 9 4 +-+ 10 9
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b x )\|x + b x
+--R +
+--R 2 8 8 4 6 7 6 4 6 8 2 5 10 4
+--R 45a b x + 210a b x + 210a b x + 45a b x + a x
+--R Type: Expression(Integer)
+--E 694
+
+--S 695 of 1325
+r0:=1/5*a^10*x^5+20/11*a^9*b*x^(11/2)+15/2*a^8*b^2*x^6+240/13*a^7*_
+ b^3*x^(13/2)+30*a^6*b^4*x^7+168/5*a^5*b^5*x^(15/2)+105/4*a^4*_
+ b^6*x^8+240/17*a^3*b^7*x^(17/2)+5*a^2*b^8*x^9+20/19*a*_
+ b^9*x^(19/2)+1/10*b^10*x^10
+--R
+--R
+--R (2)
+--R 9 9 3 7 8 5 5 7 7 3 6
+--R 972400a b x + 13041600a b x + 31039008a b x + 17054400a b x
+--R +
+--R 9 5
+--R 1679600a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 10 2 8 9 4 6 8 6 4 7
+--R 92378b x + 4618900a b x + 24249225a b x + 27713400a b x
+--R +
+--R 8 2 6 10 5
+--R 6928350a b x + 184756a x
+--R /
+--R 923780
+--R Type: Expression(Integer)
+--E 695
+
+--S 696 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 9 3 7 8 5 5 7 7 3 6
+--R 972400a b x + 13041600a b x + 31039008a b x + 17054400a b x
+--R +
+--R 9 5
+--R 1679600a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 10 2 8 9 4 6 8 6 4 7
+--R 92378b x + 4618900a b x + 24249225a b x + 27713400a b x
+--R +
+--R 8 2 6 10 5
+--R 6928350a b x + 184756a x
+--R /
+--R 923780
+--R Type: Union(Expression(Integer),...)
+--E 696
+
+--S 697 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 697
+
+--S 698 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 698
+
+)clear all
+
+--S 699 of 1325
+t0:=x^3*(a+b*sqrt(x))^10
+--R
+--R
+--R (1)
+--R 9 7 3 7 6 5 5 5 7 3 4 9 3 +-+ 10 8
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b x )\|x + b x
+--R +
+--R 2 8 7 4 6 6 6 4 5 8 2 4 10 3
+--R 45a b x + 210a b x + 210a b x + 45a b x + a x
+--R Type: Expression(Integer)
+--E 699
+
+--S 700 of 1325
+r0:=1/4*a^10*x^4+20/9*a^9*b*x^(9/2)+9*a^8*b^2*x^5+240/11*a^7*b^3*_
+ x^(11/2)+35*a^6*b^4*x^6+504/13*a^5*b^5*x^(13/2)+30*a^4*b^6*_
+ x^7+16*a^3*b^7*x^(15/2)+45/8*a^2*b^8*x^8+20/17*a*b^9*x^(17/2)+_
+ 1/9*b^10*x^9
+--R
+--R
+--R (2)
+--R 9 8 3 7 7 5 5 6 7 3 5
+--R 205920a b x + 2800512a b x + 6785856a b x + 3818880a b x
+--R +
+--R 9 4
+--R 388960a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 9 2 8 8 4 6 7 6 4 6 8 2 5
+--R 19448b x + 984555a b x + 5250960a b x + 6126120a b x + 1575288a b x
+--R +
+--R 10 4
+--R 43758a x
+--R /
+--R 175032
+--R Type: Expression(Integer)
+--E 700
+
+--S 701 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 8 3 7 7 5 5 6 7 3 5
+--R 205920a b x + 2800512a b x + 6785856a b x + 3818880a b x
+--R +
+--R 9 4
+--R 388960a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 9 2 8 8 4 6 7 6 4 6 8 2 5
+--R 19448b x + 984555a b x + 5250960a b x + 6126120a b x + 1575288a b x
+--R +
+--R 10 4
+--R 43758a x
+--R /
+--R 175032
+--R Type: Union(Expression(Integer),...)
+--E 701
+
+--S 702 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 702
+
+--S 703 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 703
+
+)clear all
+
+--S 704 of 1325
+t0:=x^2*(a+b*sqrt(x))^10
+--R
+--R
+--R (1)
+--R 9 6 3 7 5 5 5 4 7 3 3 9 2 +-+ 10 7
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b x )\|x + b x
+--R +
+--R 2 8 6 4 6 5 6 4 4 8 2 3 10 2
+--R 45a b x + 210a b x + 210a b x + 45a b x + a x
+--R Type: Expression(Integer)
+--E 704
+
+--S 705 of 1325
+r0:=-2/11*a^5*(a+b*sqrt(x))^11/b^6+5/6*a^4*(a+b*sqrt(x))^12/b^6-_
+ 20/13*a^3*(a+b*sqrt(x))^13/b^6+10/7*a^2*(a+b*sqrt(x))^14/b^6-_
+ 2/3*a*(a+b*sqrt(x))^15/b^6+1/8*(a+b*sqrt(x))^16/b^6
+--R
+--R
+--R (2)
+--R 15 7 3 13 6 5 11 5 7 9 4
+--R 32032a b x + 443520a b x + 1100736a b x + 640640a b x
+--R +
+--R 9 7 3
+--R 68640a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 16 8 2 14 7 4 12 6 6 10 5 8 8 4
+--R 3003b x + 154440a b x + 840840a b x + 1009008a b x + 270270a b x
+--R +
+--R 10 6 3 16
+--R 8008a b x - a
+--R /
+--R 6
+--R 24024b
+--R Type: Expression(Integer)
+--E 705
+
+--S 706 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 7 3 7 6 5 5 5 7 3 4
+--R 32032a b x + 443520a b x + 1100736a b x + 640640a b x
+--R +
+--R 9 3
+--R 68640a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 8 2 8 7 4 6 6 6 4 5 8 2 4
+--R 3003b x + 154440a b x + 840840a b x + 1009008a b x + 270270a b x
+--R +
+--R 10 3
+--R 8008a x
+--R /
+--R 24024
+--R Type: Union(Expression(Integer),...)
+--E 706
+
+--S 707 of 1325
+m0:=a0-r0
+--R
+--R
+--R 16
+--R a
+--R (4) -------
+--R 6
+--R 24024b
+--R Type: Expression(Integer)
+--E 707
+
+--S 708 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 708
+
+)clear all
+
+--S 709 of 1325
+t0:=x*(a+b*sqrt(x))^10
+--R
+--R
+--R (1)
+--R 9 5 3 7 4 5 5 3 7 3 2 9 +-+ 10 6
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b x)\|x + b x
+--R +
+--R 2 8 5 4 6 4 6 4 3 8 2 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a x
+--R Type: Expression(Integer)
+--E 709
+
+--S 710 of 1325
+r0:=-2/11*a^3*(a+b*sqrt(x))^11/b^4+1/2*a^2*(a+b*sqrt(x))^12/b^4-_
+ 6/13*a*(a+b*sqrt(x))^13/b^4+1/7*(a+b*sqrt(x))^14/b^4
+--R
+--R
+--R (2)
+--R 13 6 3 11 5 5 9 4 7 7 3 9 5 2
+--R (3080a b x + 43680a b x + 112112a b x + 68640a b x + 8008a b x )
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 2 12 6 4 10 5 6 8 4 8 6 3
+--R 286b x + 15015a b x + 84084a b x + 105105a b x + 30030a b x
+--R +
+--R 10 4 2 14
+--R 1001a b x - a
+--R /
+--R 4
+--R 2002b
+--R Type: Expression(Integer)
+--E 710
+
+--S 711 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 6 3 7 5 5 5 4 7 3 3 9 2 +-+
+--R (3080a b x + 43680a b x + 112112a b x + 68640a b x + 8008a b x )\|x
+--R +
+--R 10 7 2 8 6 4 6 5 6 4 4 8 2 3
+--R 286b x + 15015a b x + 84084a b x + 105105a b x + 30030a b x
+--R +
+--R 10 2
+--R 1001a x
+--R /
+--R 2002
+--R Type: Union(Expression(Integer),...)
+--E 711
+
+--S 712 of 1325
+m0:=a0-r0
+--R
+--R
+--R 14
+--R a
+--R (4) ------
+--R 4
+--R 2002b
+--R Type: Expression(Integer)
+--E 712
+
+--S 713 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 713
+
+)clear all
+
+--S 714 of 1325
+t0:=(a+b*sqrt(x))^10
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R Type: Expression(Integer)
+--E 714
+
+--S 715 of 1325
+r0:=-2/11*a*(a+b*sqrt(x))^11/b^2+1/6*(a+b*sqrt(x))^12/b^2
+--R
+--R
+--R (2)
+--R 11 5 3 9 4 5 7 3 7 5 2 9 3 +-+
+--R (120a b x + 1760a b x + 4752a b x + 3168a b x + 440a b x)\|x
+--R +
+--R 12 6 2 10 5 4 8 4 6 6 3 8 4 2 10 2
+--R 11b x + 594a b x + 3465a b x + 4620a b x + 1485a b x + 66a b x
+--R +
+--R 12
+--R - a
+--R /
+--R 2
+--R 66b
+--R Type: Expression(Integer)
+--E 715
+
+--S 716 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 5 3 7 4 5 5 3 7 3 2 9 +-+
+--R (120a b x + 1760a b x + 4752a b x + 3168a b x + 440a b x)\|x
+--R +
+--R 10 6 2 8 5 4 6 4 6 4 3 8 2 2 10
+--R 11b x + 594a b x + 3465a b x + 4620a b x + 1485a b x + 66a x
+--R /
+--R 66
+--R Type: Union(Expression(Integer),...)
+--E 716
+
+--S 717 of 1325
+m0:=a0-r0
+--R
+--R
+--R 12
+--R a
+--R (4) ----
+--R 2
+--R 66b
+--R Type: Expression(Integer)
+--E 717
+
+--S 718 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 718
+
+)clear all
+
+--S 719 of 1325
+t0:=(a+b*sqrt(x))^10/x
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R x
+--R Type: Expression(Integer)
+--E 719
+
+--S 720 of 1325
+r0:=45*a^8*b^2*x+80*a^7*b^3*x^(3/2)+105*a^6*b^4*x^2+504/5*a^5*b^5*_
+ x^(5/2)+70*a^4*b^6*x^3+240/7*a^3*b^7*x^(7/2)+45/4*a^2*b^8*x^4+_
+ 20/9*a*b^9*x^(9/2)+1/5*b^10*x^5+a^10*log(x)+20*a^9*b*sqrt(x)
+--R
+--R
+--R (2)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+
+--R (2800a b x + 43200a b x + 127008a b x + 100800a b x + 25200a b)\|x
+--R +
+--R 10 10 5 2 8 4 4 6 3 6 4 2
+--R 1260a log(x) + 252b x + 14175a b x + 88200a b x + 132300a b x
+--R +
+--R 8 2
+--R 56700a b x
+--R /
+--R 1260
+--R Type: Expression(Integer)
+--E 720
+
+--S 721 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 +-+
+--R 2520a log(\|x )
+--R +
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+
+--R (2800a b x + 43200a b x + 127008a b x + 100800a b x + 25200a b)\|x
+--R +
+--R 10 5 2 8 4 4 6 3 6 4 2 8 2
+--R 252b x + 14175a b x + 88200a b x + 132300a b x + 56700a b x
+--R /
+--R 1260
+--R Type: Union(Expression(Integer),...)
+--E 721
+
+--S 722 of 1325
+m0:=a0-r0
+--R
+--R
+--R 10 +-+ 10
+--R (4) 2a log(\|x ) - a log(x)
+--R Type: Expression(Integer)
+--E 722
+
+--S 723 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 723
+
+)clear all
+
+--S 724 of 1325
+t0:=(a+b*sqrt(x))^10/x^2
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 724
+
+--S 725 of 1325
+r0:=-a^10/x+210*a^6*b^4*x+168*a^5*b^5*x^(3/2)+105*a^4*b^6*x^2+_
+ 48*a^3*b^7*x^(5/2)+15*a^2*b^8*x^3+20/7*a*b^9*x^(7/2)+_
+ 1/4*b^10*x^4+45*a^8*b^2*log(x)-20*a^9*b/sqrt(x)+240*a^7*b^3*sqrt(x)
+--R
+--R
+--R (2)
+--R 8 2 10 5 2 8 4 4 6 3 6 4 2
+--R 1260a b x log(x) + 7b x + 420a b x + 2940a b x + 5880a b x
+--R +
+--R 10
+--R - 28a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 9 5 3 7 4 5 5 3 7 3 2 9
+--R 80a b x + 1344a b x + 4704a b x + 6720a b x - 560a b x
+--R /
+--R +-+
+--R 28x\|x
+--R Type: Expression(Integer)
+--E 725
+
+--S 726 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 8 2 +-+
+--R 2520a b x log(\|x )
+--R +
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (80a b x + 1344a b x + 4704a b x + 6720a b x - 560a b)\|x + 7b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 10
+--R 420a b x + 2940a b x + 5880a b x - 28a
+--R /
+--R 28x
+--R Type: Union(Expression(Integer),...)
+--E 726
+
+--S 727 of 1325
+m0:=a0-r0
+--R
+--R
+--R 8 2 +-+ 8 2
+--R (4) 90a b log(\|x ) - 45a b log(x)
+--R Type: Expression(Integer)
+--E 727
+
+--S 728 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 728
+
+)clear all
+
+--S 729 of 1325
+t0:=(a+b*sqrt(x))^10/x^3
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 729
+
+--S 730 of 1325
+r0:=-1/2*a^10/x^2-20/3*a^9*b/x^(3/2)-45*a^8*b^2/x+210*a^4*b^6*x+_
+ 80*a^3*b^7*x^(3/2)+45/2*a^2*b^8*x^2+4*a*b^9*x^(5/2)+_
+ 1/3*b^10*x^3+210*a^6*b^4*log(x)-240*a^7*b^3/sqrt(x)+504*a^5*b^5*sqrt(x)
+--R
+--R
+--R (2)
+--R 6 4 2 10 5 2 8 4 4 6 3 8 2 10
+--R (1260a b x log(x) + 2b x + 135a b x + 1260a b x - 270a b x - 3a )
+--R *
+--R +-+
+--R \|x
+--R +
+--R 9 5 3 7 4 5 5 3 7 3 2 9
+--R 24a b x + 480a b x + 3024a b x - 1440a b x - 40a b x
+--R /
+--R 2 +-+
+--R 6x \|x
+--R Type: Expression(Integer)
+--E 730
+
+--S 731 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 4 2 +-+
+--R 2520a b x log(\|x )
+--R +
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (24a b x + 480a b x + 3024a b x - 1440a b x - 40a b)\|x + 2b x
+--R +
+--R 2 8 4 4 6 3 8 2 10
+--R 135a b x + 1260a b x - 270a b x - 3a
+--R /
+--R 2
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 731
+
+--S 732 of 1325
+m0:=a0-r0
+--R
+--R
+--R 6 4 +-+ 6 4
+--R (4) 420a b log(\|x ) - 210a b log(x)
+--R Type: Expression(Integer)
+--E 732
+
+--S 733 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 733
+
+)clear all
+
+--S 734 of 1325
+t0:=(a+b*sqrt(x))^10/x^4
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 734
+
+--S 735 of 1325
+r0:=-1/3*a^10/x^3-4*a^9*b/x^(5/2)-45/2*a^8*b^2/x^2-80*a^7*b^3/x^(3/2)-_
+ 210*a^6*b^4/x+45*a^2*b^8*x+20/3*a*b^9*x^(3/2)+1/2*b^10*x^2+_
+ 210*a^4*b^6*log(x)-504*a^5*b^5/sqrt(x)+240*a^3*b^7*sqrt(x)
+--R
+--R
+--R (2)
+--R 4 6 3 10 5 2 8 4 6 4 2 8 2 10
+--R (1260a b x log(x) + 3b x + 270a b x - 1260a b x - 135a b x - 2a )
+--R *
+--R +-+
+--R \|x
+--R +
+--R 9 5 3 7 4 5 5 3 7 3 2 9
+--R 40a b x + 1440a b x - 3024a b x - 480a b x - 24a b x
+--R /
+--R 3 +-+
+--R 6x \|x
+--R Type: Expression(Integer)
+--E 735
+
+--S 736 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 6 3 +-+
+--R 2520a b x log(\|x )
+--R +
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (40a b x + 1440a b x - 3024a b x - 480a b x - 24a b)\|x + 3b x
+--R +
+--R 2 8 4 6 4 2 8 2 10
+--R 270a b x - 1260a b x - 135a b x - 2a
+--R /
+--R 3
+--R 6x
+--R Type: Union(Expression(Integer),...)
+--E 736
+
+--S 737 of 1325
+m0:=a0-r0
+--R
+--R
+--R 4 6 +-+ 4 6
+--R (4) 420a b log(\|x ) - 210a b log(x)
+--R Type: Expression(Integer)
+--E 737
+
+--S 738 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 738
+
+)clear all
+
+--S 739 of 1325
+t0:=(a+b*sqrt(x))^10/x^5
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 5
+--R x
+--R Type: Expression(Integer)
+--E 739
+
+--S 740 of 1325
+r0:=-1/4*a^10/x^4-20/7*a^9*b/x^(7/2)-15*a^8*b^2/x^3-48*a^7*b^3/x^(5/2)-_
+ 105*a^6*b^4/x^2-168*a^5*b^5/x^(3/2)-210*a^4*b^6/x+b^10*x+45*_
+ a^2*b^8*log(x)-240*a^3*b^7/sqrt(x)+20*a*b^9*sqrt(x)
+--R
+--R
+--R (2)
+--R 2 8 4 10 5 4 6 3 6 4 2 8 2
+--R 1260a b x log(x) + 28b x - 5880a b x - 2940a b x - 420a b x
+--R +
+--R 10
+--R - 7a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 9 5 3 7 4 5 5 3 7 3 2 9
+--R 560a b x - 6720a b x - 4704a b x - 1344a b x - 80a b x
+--R /
+--R 4 +-+
+--R 28x \|x
+--R Type: Expression(Integer)
+--E 740
+
+--S 741 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 8 4 +-+
+--R 2520a b x log(\|x )
+--R +
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (560a b x - 6720a b x - 4704a b x - 1344a b x - 80a b)\|x + 28b x
+--R +
+--R 4 6 3 6 4 2 8 2 10
+--R - 5880a b x - 2940a b x - 420a b x - 7a
+--R /
+--R 4
+--R 28x
+--R Type: Union(Expression(Integer),...)
+--E 741
+
+--S 742 of 1325
+m0:=a0-r0
+--R
+--R
+--R 2 8 +-+ 2 8
+--R (4) 90a b log(\|x ) - 45a b log(x)
+--R Type: Expression(Integer)
+--E 742
+
+--S 743 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 743
+
+)clear all
+
+--S 744 of 1325
+t0:=(a+b*sqrt(x))^10/x^6
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 744
+
+--S 745 of 1325
+r0:=-1/5*a^10/x^5-20/9*a^9*b/x^(9/2)-45/4*a^8*b^2/x^4-240/7*a^7*_
+ b^3/x^(7/2)-70*a^6*b^4/x^3-504/5*a^5*b^5/x^(5/2)-105*a^4*_
+ b^6/x^2-80*a^3*b^7/x^(3/2)-45*a^2*b^8/x+b^10*log(x)-20*a*b^9/sqrt(x)
+--R
+--R
+--R (2)
+--R 10 5 2 8 4 4 6 3 6 4 2
+--R 1260b x log(x) - 56700a b x - 132300a b x - 88200a b x
+--R +
+--R 8 2 10
+--R - 14175a b x - 252a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 9 5 3 7 4 5 5 3 7 3 2 9
+--R - 25200a b x - 100800a b x - 127008a b x - 43200a b x - 2800a b x
+--R /
+--R 5 +-+
+--R 1260x \|x
+--R Type: Expression(Integer)
+--E 745
+
+--S 746 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 10 5 +-+
+--R 2520b x log(\|x )
+--R +
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+
+--R (- 25200a b x - 100800a b x - 127008a b x - 43200a b x - 2800a b)\|x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R - 56700a b x - 132300a b x - 88200a b x - 14175a b x - 252a
+--R /
+--R 5
+--R 1260x
+--R Type: Union(Expression(Integer),...)
+--E 746
+
+--S 747 of 1325
+m0:=a0-r0
+--R
+--R
+--R 10 +-+ 10
+--R (4) 2b log(\|x ) - b log(x)
+--R Type: Expression(Integer)
+--E 747
+
+--S 748 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 748
+
+)clear all
+
+--S 749 of 1325
+t0:=(a+b*sqrt(x))^10/x^7
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 749
+
+--S 750 of 1325
+r0:=-1/6*(a+b*sqrt(x))^11/(a*x^6)+1/66*b*(a+b*sqrt(x))^11/(a^2*x^(11/2))
+--R
+--R
+--R (2)
+--R 12 6 2 10 5 4 8 4 6 6 3 8 4 2 10 2
+--R b x - 66a b x - 1485a b x - 4620a b x - 3465a b x - 594a b x
+--R +
+--R 12
+--R - 11a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 3 9 5 5 7 4 7 5 3 9 3 2 11
+--R - 440a b x - 3168a b x - 4752a b x - 1760a b x - 120a b x
+--R /
+--R 2 6 +-+
+--R 66a x \|x
+--R Type: Expression(Integer)
+--E 750
+
+--S 751 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+
+--R (- 440a b x - 3168a b x - 4752a b x - 1760a b x - 120a b)\|x
+--R +
+--R 10 5 2 8 4 4 6 3 6 4 2 8 2 10
+--R - 66b x - 1485a b x - 4620a b x - 3465a b x - 594a b x - 11a
+--R /
+--R 6
+--R 66x
+--R Type: Union(Expression(Integer),...)
+--E 751
+
+--S 752 of 1325
+m0:=a0-r0
+--R
+--R
+--R 12
+--R b
+--R (4) - ----
+--R 2
+--R 66a
+--R Type: Expression(Integer)
+--E 752
+
+--S 753 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 753
+
+)clear all
+
+--S 754 of 1325
+t0:=(a+b*sqrt(x))^10/x^8
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 754
+
+--S 755 of 1325
+r0:=-1/7*(a+b*sqrt(x))^11/(a*x^7)+3/91*b*(a+b*sqrt(x))^11/(a^2*x^(13/2))-_
+ 1/182*b^2*(a+b*sqrt(x))^11/(a^3*x^6)+_
+ 1/2002*b^3*(a+b*sqrt(x))^11/(a^4*x^(11/2))
+--R
+--R
+--R (2)
+--R 14 7 4 10 5 6 8 4 8 6 3 10 4 2
+--R b x - 1001a b x - 30030a b x - 105105a b x - 84084a b x
+--R +
+--R 12 2 14
+--R - 15015a b x - 286a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 5 9 5 7 7 4 9 5 3 11 3 2 13
+--R - 8008a b x - 68640a b x - 112112a b x - 43680a b x - 3080a b x
+--R /
+--R 4 7 +-+
+--R 2002a x \|x
+--R Type: Expression(Integer)
+--E 755
+
+--S 756 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+
+--R (- 8008a b x - 68640a b x - 112112a b x - 43680a b x - 3080a b)\|x
+--R +
+--R 10 5 2 8 4 4 6 3 6 4 2 8 2
+--R - 1001b x - 30030a b x - 105105a b x - 84084a b x - 15015a b x
+--R +
+--R 10
+--R - 286a
+--R /
+--R 7
+--R 2002x
+--R Type: Union(Expression(Integer),...)
+--E 756
+
+--S 757 of 1325
+m0:=a0-r0
+--R
+--R
+--R 14
+--R b
+--R (4) - ------
+--R 4
+--R 2002a
+--R Type: Expression(Integer)
+--E 757
+
+--S 758 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 758
+
+)clear all
+
+--S 759 of 1325
+t0:=(a+b*sqrt(x))^10/x^9
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 759
+
+--S 760 of 1325
+r0:=-1/8*(a+b*sqrt(x))^11/(a*x^8)+1/24*b*(a+b*sqrt(x))^11/(a^2*x^(15/2))-_
+ 1/84*b^2*(a+b*sqrt(x))^11/(a^3*x^7)+1/364*b^3*(a+b*sqrt(x))^11/_
+ (a^4*x^(13/2))-1/2184*b^4*(a+b*sqrt(x))^11/(a^5*x^6)+1/24024*_
+ b^5*(a+b*sqrt(x))^11/(a^6*x^(11/2))
+--R
+--R
+--R (2)
+--R 16 8 6 10 5 8 8 4 10 6 3 12 4 2
+--R b x - 8008a b x - 270270a b x - 1009008a b x - 840840a b x
+--R +
+--R 14 2 16
+--R - 154440a b x - 3003a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 9 5 9 7 4 11 5 3 13 3 2 15
+--R - 68640a b x - 640640a b x - 1100736a b x - 443520a b x - 32032a b x
+--R /
+--R 6 8 +-+
+--R 24024a x \|x
+--R Type: Expression(Integer)
+--E 760
+
+--S 761 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 4 3 7 3 5 5 2 7 3 9
+--R (- 68640a b x - 640640a b x - 1100736a b x - 443520a b x - 32032a b)
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 5 2 8 4 4 6 3 6 4 2 8 2
+--R - 8008b x - 270270a b x - 1009008a b x - 840840a b x - 154440a b x
+--R +
+--R 10
+--R - 3003a
+--R /
+--R 8
+--R 24024x
+--R Type: Union(Expression(Integer),...)
+--E 761
+
+--S 762 of 1325
+m0:=a0-r0
+--R
+--R
+--R 16
+--R b
+--R (4) - -------
+--R 6
+--R 24024a
+--R Type: Expression(Integer)
+--E 762
+
+--S 763 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 763
+
+)clear all
+
+--S 764 of 1325
+t0:=(a+b*sqrt(x))^10/x^10
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 764
+
+--S 765 of 1325
+r0:=-1/9*a^10/x^9-20/17*a^9*b/x^(17/2)-45/8*a^8*b^2/x^8-16*a^7*_
+ b^3/x^(15/2)-30*a^6*b^4/x^7-504/13*a^5*b^5/x^(13/2)-35*a^4*_
+ b^6/x^6-240/11*a^3*b^7/x^(11/2)-9*a^2*b^8/x^5-20/9*a*_
+ b^9/x^(9/2)-1/4*b^10/x^4
+--R
+--R
+--R (2)
+--R 10 5 2 8 4 4 6 3 6 4 2
+--R - 43758b x - 1575288a b x - 6126120a b x - 5250960a b x
+--R +
+--R 8 2 10
+--R - 984555a b x - 19448a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 9 5 3 7 4 5 5 3 7 3 2
+--R - 388960a b x - 3818880a b x - 6785856a b x - 2800512a b x
+--R +
+--R 9
+--R - 205920a b x
+--R /
+--R 9 +-+
+--R 175032x \|x
+--R Type: Expression(Integer)
+--E 765
+
+--S 766 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 4 3 7 3 5 5 2 7 3
+--R - 388960a b x - 3818880a b x - 6785856a b x - 2800512a b x
+--R +
+--R 9
+--R - 205920a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 5 2 8 4 4 6 3 6 4 2
+--R - 43758b x - 1575288a b x - 6126120a b x - 5250960a b x
+--R +
+--R 8 2 10
+--R - 984555a b x - 19448a
+--R /
+--R 9
+--R 175032x
+--R Type: Union(Expression(Integer),...)
+--E 766
+
+--S 767 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 767
+
+--S 768 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 768
+
+)clear all
+
+--S 769 of 1325
+t0:=(a+b*sqrt(x))^10/x^11
+--R
+--R
+--R (1)
+--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5
+--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x
+--R +
+--R 2 8 4 4 6 3 6 4 2 8 2 10
+--R 45a b x + 210a b x + 210a b x + 45a b x + a
+--R /
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 769
+
+--S 770 of 1325
+r0:=-1/10*a^10/x^10-20/19*a^9*b/x^(19/2)-5*a^8*b^2/x^9-240/17*a^7*_
+ b^3/x^(17/2)-105/4*a^6*b^4/x^8-168/5*a^5*b^5/x^(15/2)-_
+ 30*a^4*b^6/x^7-240/13*a^3*b^7/x^(13/2)-15/2*a^2*b^8/x^6-_
+ 20/11*a*b^9/x^(11/2)-1/5*b^10/x^5
+--R
+--R
+--R (2)
+--R 10 5 2 8 4 4 6 3 6 4 2
+--R - 184756b x - 6928350a b x - 27713400a b x - 24249225a b x
+--R +
+--R 8 2 10
+--R - 4618900a b x - 92378a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 9 5 3 7 4 5 5 3 7 3 2
+--R - 1679600a b x - 17054400a b x - 31039008a b x - 13041600a b x
+--R +
+--R 9
+--R - 972400a b x
+--R /
+--R 10 +-+
+--R 923780x \|x
+--R Type: Expression(Integer)
+--E 770
+
+--S 771 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 4 3 7 3 5 5 2 7 3
+--R - 1679600a b x - 17054400a b x - 31039008a b x - 13041600a b x
+--R +
+--R 9
+--R - 972400a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 10 5 2 8 4 4 6 3 6 4 2
+--R - 184756b x - 6928350a b x - 27713400a b x - 24249225a b x
+--R +
+--R 8 2 10
+--R - 4618900a b x - 92378a
+--R /
+--R 10
+--R 923780x
+--R Type: Union(Expression(Integer),...)
+--E 771
+
+--S 772 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 772
+
+--S 773 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 773
+
+)clear all
+
+--S 774 of 1325
+t0:=x^m*(a+b*sqrt(x))^15
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R m +-+
+--R x \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R *
+--R m
+--R x
+--R Type: Expression(Integer)
+--E 774
+
+--S 775 of 1325
+r0:=a^15*x^(1+m)/(1+m)+30*a^14*b*x^(3/2+m)/(3+2*m)+105*a^13*b^2*_
+ x^(2+m)/(2+m)+910*a^12*b^3*x^(5/2+m)/(5+2*m)+1365*a^11*b^4*_
+ x^(3+m)/(3+m)+6006*a^10*b^5*x^(7/2+m)/(7+2*m)+5005*a^9*b^6*_
+ x^(4+m)/(4+m)+12870*a^8*b^7*x^(9/2+m)/(9+2*m)+6435*a^7*b^8*_
+ x^(5+m)/(5+m)+10010*a^6*b^9*x^(11/2+m)/(11+2*m)+3003*a^5*b^10*_
+ x^(6+m)/(6+m)+2730*a^4*b^11*x^(13/2+m)/(13+2*m)+455*a^3*b^12*_
+ x^(7+m)/(7+m)+210*a^2*b^13*x^(15/2+m)/(15+2*m)+15*a*b^14*_
+ x^(8+m)/(8+m)+2*b^15*x^(17/2+m)/(17+2*m)
+--R
+--R
+--R (2)
+--R 15 15 15 14 15 13 15 12
+--R 256b m + 17280b m + 535360b m + 10090080b m
+--R +
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+--R 129259312b m + 1190989800b m + 8144630780b m
+--R +
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+--R 42042004290b m + 164932175408b m + 490984554060b m
+--R +
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+--R +
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+--R 1661898510360b m + 778304570400b m + 163459296000b
+--R *
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+--R +
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+--R +
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+--R +
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+--R 211660437301950a b m + 249194988178920a b m
+--R +
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+--R 196353770737320a b m + 92313119858400a b m + 19451656224000a b
+--R *
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+--R -------
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+--R +
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+--R 4882375680a b m + 63659741600a b m + 596192556960a b m
+--R +
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+--R 4138612157680a b m + 21658186389840a b m + 86034286673335a b m
+--R +
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+--R 259033153774395a b m + 585303745975585a b m
+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R 1378711672884000a b m + 291774843360000a b
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+--R 768768a b m + 53813760a b m + 1725884160a b m
+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R 1281280a b m + 90330240a b m + 2917794880a b m
+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R *
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+--R -------
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R 17508616262563140a b m + 8367002368124400a b m + 1788162968592000a b
+--R *
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+--R 1647360a b m + 117786240a b m + 3860176320a b m
+--R +
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+--R 76841724960a b m + 1037898061200a b m + 10063639305720a b m
+--R +
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+--R 72268486779060a b m + 390823049189430a b m + 1602227357050320a b m
+--R +
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+--R +
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+--R 19713788347363110a b m + 23848253429406120a b m
+--R +
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+--R 19257237012241800a b m + 9252517125852000a b m + 1986847742880000a b
+--R *
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+--R ------
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+--R 9 6 15 9 6 14 9 6 13
+--R 1281280a b m + 92252160a b m + 3045602560a b m
+--R +
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+--R 61093992960a b m + 831824113120a b m + 8132621777280a b m
+--R +
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+--R 58901073511280a b m + 321308892384480a b m + 1328821935886445a b m
+--R +
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+--R 4158717021819360a b m + 9749025959082410a b m
+--R +
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+--R 16773633296980560a b m + 20452367584053405a b m
+--R +
+--R 9 6 2 9 6 9 6
+--R 16637267676229200a b m + 8047661046925500a b m + 1738491775020000a b
+--R *
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+--R x
+--R +
+--R 10 5 15 10 5 14 10 5 13
+--R 768768a b m + 55735680a b m + 1853691840a b m
+--R +
+--R 10 5 12 10 5 11 10 5 10
+--R 37477920480a b m + 514547329296a b m + 5075035285320a b m
+--R +
+--R 10 5 9 10 5 8
+--R 37096312873620a b m + 204310816800090a b m
+--R +
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+--R 853346644454304a b m + 2697689603629020a b m
+--R +
+--R 10 5 5 10 5 4
+--R 6388422815114340a b m + 11102362427085930a b m
+--R +
+--R 10 5 3 10 5 2
+--R 13669871968384632a b m + 11223490918119480a b m
+--R +
+--R 10 5 10 5
+--R 5475820837687200a b m + 1192108645728000a b
+--R *
+--R 2m + 7
+--R ------
+--R 2
+--R x
+--R +
+--R 11 4 15 11 4 14 11 4 13
+--R 349440a b m + 25509120a b m + 854730240a b m
+--R +
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+--R 17420282880a b m + 241248265440a b m + 2401687448160a b m
+--R +
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+--R 17730817824720a b m + 98692961006640a b m
+--R +
+--R 11 4 7 11 4 6
+--R 416845891186725a b m + 1333281807903045a b m
+--R +
+--R 11 4 5 11 4 4
+--R 3195762043479915a b m + 5622642178644855a b m
+--R +
+--R 11 4 3 11 4 2
+--R 7008500947331520a b m + 5823607525035300a b m
+--R +
+--R 11 4 11 4
+--R 2873740629942000a b m + 632178827280000a b
+--R *
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+--R +
+--R 12 3 15 12 3 14 12 3 13
+--R 116480a b m + 8561280a b m + 289016000a b m
+--R +
+--R 12 3 12 12 3 11 12 3 10
+--R 5938951200a b m + 82988993360a b m + 834338264760a b m
+--R +
+--R 12 3 9 12 3 8 12 3 7
+--R 6226114394500a b m + 35063185507350a b m + 149983627633840a b m
+--R +
+--R 12 3 6 12 3 5
+--R 486314091403140a b m + 1182750593888500a b m
+--R +
+--R 12 3 4 12 3 3
+--R 2113099618306950a b m + 2676060115321320a b m
+--R +
+--R 12 3 2 12 3 12 3
+--R 2259553167373320a b m + 1132638149916000a b m + 252871530912000a b
+--R *
+--R 2m + 5
+--R ------
+--R 2
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+--R +
+--R 13 2 15 13 2 14 13 2 13
+--R 26880a b m + 1989120a b m + 67656960a b m
+--R +
+--R 13 2 12 13 2 11 13 2 10
+--R 1401953280a b m + 19773717600a b m + 200870429760a b m
+--R +
+--R 13 2 9 13 2 8 13 2 7
+--R 1516403768880a b m + 8650685883840a b m + 37538995478985a b m
+--R +
+--R 13 2 6 13 2 5
+--R 123677353769970a b m + 306153559166910a b m
+--R +
+--R 13 2 4 13 2 3
+--R 557687366980380a b m + 721273533982785a b m
+--R +
+--R 13 2 2 13 2 13 2
+--R 622769114113650a b m + 319428172161000a b m + 72943710840000a b
+--R *
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+--R +
+--R 14 15 14 14 14 13 14 12
+--R 3840a b m + 286080a b m + 9804480a b m + 204902880a b m
+--R +
+--R 14 11 14 10 14 9
+--R 2918020560a b m + 29968378440a b m + 229068093540a b m
+--R +
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+--R 1325468348490a b m + 5846135655360a b m + 19624417192380a b m
+--R +
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+--R 49635983740980a b m + 92688093719130a b m
+--R +
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+--R 123346183413240a b m + 110025893748600a b m
+--R +
+--R 14 14
+--R 58527788004000a b m + 13894040160000a b
+--R *
+--R 2m + 3
+--R ------
+--R 2
+--R x
+--R +
+--R 15 15 15 14 15 13 15 12
+--R 256a m + 19200a m + 663040a m + 13977600a m
+--R +
+--R 15 11 15 10 15 9
+--R 201047392a m + 2088646560a m + 16179397520a m
+--R +
+--R 15 8 15 7 15 6
+--R 95091968400a m + 427197243473a m + 1465710801555a m
+--R +
+--R 15 5 15 4 15 3
+--R 3805796500415a m + 7337008121625a m + 10154880144504a m
+--R +
+--R 15 2 15 15
+--R 9514797780060a m + 5389644128400a m + 1389404016000a
+--R *
+--R m + 1
+--R x
+--R /
+--R 16 15 14 13 12
+--R 256m + 19456m + 682240m + 14640640m + 215024992m
+--R +
+--R 11 10 9 8
+--R 2289693952m + 18268044080m + 111271365920m + 522289211873m
+--R +
+--R 7 6 5 4
+--R 1892908045028m + 5271507301970m + 11142804622040m + 17491888266129m
+--R +
+--R 3 2
+--R 19669677924564m + 14904441908460m + 6779048144400m + 1389404016000
+--R Type: Expression(Integer)
+--E 775
+
+--S 776 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 15 15 14 15 13 15 12
+--R 256b m + 17280b m + 535360b m + 10090080b m
+--R +
+--R 15 11 15 10 15 9
+--R 129259312b m + 1190989800b m + 8144630780b m
+--R +
+--R 15 8 15 7 15 6
+--R 42042004290b m + 164932175408b m + 490984554060b m
+--R +
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+--R 1098138592460b m + 1808626586130b m + 2118562284024b m
+--R +
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+--R 26880a b m + 1841280a b m + 57825600a b m
+--R +
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+--R 1103575200a b m + 14300810160a b m + 133161788760a b m
+--R +
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+--R 919431212700a b m + 4787759326350a b m
+--R +
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+--R 18932172299040a b m + 56764052485140a b m
+--R +
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+--R 127777873068300a b m + 211660437301950a b m
+--R +
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+--R +
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+--R 349440a b m + 24286080a b m + 773398080a b m
+--R +
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+--R +
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+--R 1849572564840a b m + 12913658497740a b m
+--R +
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+--R +
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+--R +
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+--R 3106875540516930a b m + 3681736469906040a b m
+--R +
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+--R +
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+--R 1281280a b m + 90330240a b m + 2917794880a b m
+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R *
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R +
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+--R 5075035285320a b m + 37096312873620a b m
+--R +
+--R 10 5 8 10 5 7
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+--R 37538995478985a b m + 123677353769970a b m
+--R +
+--R 13 2 5 13 2 4
+--R 306153559166910a b m + 557687366980380a b m
+--R +
+--R 13 2 3 13 2 2
+--R 721273533982785a b m + 622769114113650a b m
+--R +
+--R 13 2 13 2
+--R 319428172161000a b m + 72943710840000a b
+--R *
+--R 2
+--R x
+--R +
+--R 15 15 15 14 15 13 15 12
+--R 256a m + 19200a m + 663040a m + 13977600a m
+--R +
+--R 15 11 15 10 15 9
+--R 201047392a m + 2088646560a m + 16179397520a m
+--R +
+--R 15 8 15 7 15 6
+--R 95091968400a m + 427197243473a m + 1465710801555a m
+--R +
+--R 15 5 15 4 15 3
+--R 3805796500415a m + 7337008121625a m + 10154880144504a m
+--R +
+--R 15 2 15 15
+--R 9514797780060a m + 5389644128400a m + 1389404016000a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 15 15 15 14 15 13 15 12
+--R - 256b m - 17280b m - 535360b m - 10090080b m
+--R +
+--R 15 11 15 10 15 9
+--R - 129259312b m - 1190989800b m - 8144630780b m
+--R +
+--R 15 8 15 7 15 6
+--R - 42042004290b m - 164932175408b m - 490984554060b m
+--R +
+--R 15 5 15 4 15 3
+--R - 1098138592460b m - 1808626586130b m - 2118562284024b m
+--R +
+--R 15 2 15 15
+--R - 1661898510360b m - 778304570400b m - 163459296000b
+--R *
+--R 2m + 17
+--R -------
+--R 2
+--R x
+--R +
+--R 14 15 14 14 14 13 14 12
+--R - 3840a b m - 261120a b m - 8144640a b m - 154452480a b m
+--R +
+--R 14 11 14 10 14 9
+--R - 1989755040a b m - 18427368960a b m - 126601709520a b m
+--R +
+--R 14 8 14 7 14 6
+--R - 656256812640a b m - 2584283676975a b m - 7719351259620a b m
+--R +
+--R 14 5 14 4
+--R - 17317799452590a b m - 28599673709880a b m
+--R +
+--R 14 3 14 2
+--R - 33580934312895a b m - 26397694365300a b m
+--R +
+--R 14 14
+--R - 12385073704500a b m - 2605132530000a b
+--R *
+--R m + 8
+--R x
+--R +
+--R 2 13 15 2 13 14 2 13 13
+--R - 26880a b m - 1841280a b m - 57825600a b m
+--R +
+--R 2 13 12 2 13 11 2 13 10
+--R - 1103575200a b m - 14300810160a b m - 133161788760a b m
+--R +
+--R 2 13 9 2 13 8 2 13 7
+--R - 919431212700a b m - 4787759326350a b m - 18932172299040a b m
+--R +
+--R 2 13 6 2 13 5
+--R - 56764052485140a b m - 127777873068300a b m
+--R +
+--R 2 13 4 2 13 3
+--R - 211660437301950a b m - 249194988178920a b m
+--R +
+--R 2 13 2 2 13 2 13
+--R - 196353770737320a b m - 92313119858400a b m - 19451656224000a b
+--R *
+--R 2m + 15
+--R -------
+--R 2
+--R x
+--R +
+--R 3 12 15 3 12 14 3 12 13
+--R - 116480a b m - 8037120a b m - 254159360a b m
+--R +
+--R 3 12 12 3 12 11 3 12 10
+--R - 4882375680a b m - 63659741600a b m - 596192556960a b m
+--R +
+--R 3 12 9 3 12 8
+--R - 4138612157680a b m - 21658186389840a b m
+--R +
+--R 3 12 7 3 12 6
+--R - 86034286673335a b m - 259033153774395a b m
+--R +
+--R 3 12 5 3 12 4
+--R - 585303745975585a b m - 972849881199105a b m
+--R +
+--R 3 12 3 3 12 2
+--R - 1148859992694960a b m - 907683506811900a b m
+--R +
+--R 3 12 3 12
+--R - 427736520666000a b m - 90311261040000a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 4 11 15 4 11 14 4 11 13
+--R - 349440a b m - 24286080a b m - 773398080a b m
+--R +
+--R 4 11 12 4 11 11 4 11 10
+--R - 14957386080a b m - 196286104560a b m - 1849572564840a b m
+--R +
+--R 4 11 9 4 11 8
+--R - 12913658497740a b m - 67946634245490a b m
+--R +
+--R 4 11 7 4 11 6
+--R - 271271651610960a b m - 820553745991980a b m
+--R +
+--R 4 11 5 4 11 4
+--R - 1862008118241180a b m - 3106875540516930a b m
+--R +
+--R 4 11 3 4 11 2
+--R - 3681736469906040a b m - 2917823312640600a b m
+--R +
+--R 4 11 4 11
+--R - 1378711672884000a b m - 291774843360000a b
+--R *
+--R 2m + 13
+--R -------
+--R 2
+--R x
+--R +
+--R 5 10 15 5 10 14 5 10 13
+--R - 768768a b m - 53813760a b m - 1725884160a b m
+--R +
+--R 5 10 12 5 10 11 5 10 10
+--R - 33610536960a b m - 444056829216a b m - 4211609962560a b m
+--R +
+--R 5 10 9 5 10 8
+--R - 29589276596880a b m - 156612252276480a b m
+--R +
+--R 5 10 7 5 10 6
+--R - 628760989595739a b m - 1911836921644650a b m
+--R +
+--R 5 10 5 5 10 4
+--R - 4359314897948010a b m - 7305952892298060a b m
+--R +
+--R 5 10 3 5 10 2
+--R - 8692423109397027a b m - 6913504151083530a b m
+--R +
+--R 5 10 5 10
+--R - 3277014144604200a b m - 695396710008000a b
+--R *
+--R m + 6
+--R x
+--R +
+--R 6 9 15 6 9 14 6 9 13
+--R - 1281280a b m - 90330240a b m - 2917794880a b m
+--R +
+--R 6 9 12 6 9 11 6 9 10
+--R - 57228531360a b m - 761443162480a b m - 7271980836120a b m
+--R +
+--R 6 9 9 6 9 8
+--R - 51435666021740a b m - 274017023310030a b m
+--R +
+--R 6 9 7 6 9 6
+--R - 1106963877219200a b m - 3385703440659540a b m
+--R +
+--R 6 9 5 6 9 4
+--R - 7762525122732380a b m - 13075848958282110a b m
+--R +
+--R 6 9 3 6 9 2
+--R - 15629731501424040a b m - 12483214754610600a b m
+--R +
+--R 6 9 6 9
+--R - 5939050601484000a b m - 1264357654560000a b
+--R *
+--R 2m + 11
+--R -------
+--R 2
+--R x
+--R +
+--R 7 8 15 7 8 14 7 8 13
+--R - 1647360a b m - 116962560a b m - 3805401600a b m
+--R +
+--R 7 8 12 7 8 11 7 8 10
+--R - 75185510400a b m - 1007758271520a b m - 9695389223520a b m
+--R +
+--R 7 8 9 7 8 8
+--R - 69077917537200a b m - 370641652009200a b m
+--R +
+--R 7 8 7 7 8 6
+--R - 1507722818356755a b m - 4642249177971405a b m
+--R +
+--R 7 8 5 7 8 4
+--R - 10710903598319925a b m - 18149429751227775a b m
+--R +
+--R 7 8 3 7 8 2
+--R - 21813152236401240a b m - 17508616262563140a b m
+--R +
+--R 7 8 7 8
+--R - 8367002368124400a b m - 1788162968592000a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 8 7 15 8 7 14 8 7 13
+--R - 1647360a b m - 117786240a b m - 3860176320a b m
+--R +
+--R 8 7 12 8 7 11 8 7 10
+--R - 76841724960a b m - 1037898061200a b m - 10063639305720a b m
+--R +
+--R 8 7 9 8 7 8
+--R - 72268486779060a b m - 390823049189430a b m
+--R +
+--R 8 7 7 8 7 6
+--R - 1602227357050320a b m - 4970840163028740a b m
+--R +
+--R 8 7 5 8 7 4
+--R - 11553368754547620a b m - 19713788347363110a b m
+--R +
+--R 8 7 3 8 7 2
+--R - 23848253429406120a b m - 19257237012241800a b m
+--R +
+--R 8 7 8 7
+--R - 9252517125852000a b m - 1986847742880000a b
+--R *
+--R 2m + 9
+--R ------
+--R 2
+--R x
+--R +
+--R 9 6 15 9 6 14 9 6 13
+--R - 1281280a b m - 92252160a b m - 3045602560a b m
+--R +
+--R 9 6 12 9 6 11 9 6 10
+--R - 61093992960a b m - 831824113120a b m - 8132621777280a b m
+--R +
+--R 9 6 9 9 6 8
+--R - 58901073511280a b m - 321308892384480a b m
+--R +
+--R 9 6 7 9 6 6
+--R - 1328821935886445a b m - 4158717021819360a b m
+--R +
+--R 9 6 5 9 6 4
+--R - 9749025959082410a b m - 16773633296980560a b m
+--R +
+--R 9 6 3 9 6 2
+--R - 20452367584053405a b m - 16637267676229200a b m
+--R +
+--R 9 6 9 6
+--R - 8047661046925500a b m - 1738491775020000a b
+--R *
+--R m + 4
+--R x
+--R +
+--R 10 5 15 10 5 14 10 5 13
+--R - 768768a b m - 55735680a b m - 1853691840a b m
+--R +
+--R 10 5 12 10 5 11 10 5 10
+--R - 37477920480a b m - 514547329296a b m - 5075035285320a b m
+--R +
+--R 10 5 9 10 5 8
+--R - 37096312873620a b m - 204310816800090a b m
+--R +
+--R 10 5 7 10 5 6
+--R - 853346644454304a b m - 2697689603629020a b m
+--R +
+--R 10 5 5 10 5 4
+--R - 6388422815114340a b m - 11102362427085930a b m
+--R +
+--R 10 5 3 10 5 2
+--R - 13669871968384632a b m - 11223490918119480a b m
+--R +
+--R 10 5 10 5
+--R - 5475820837687200a b m - 1192108645728000a b
+--R *
+--R 2m + 7
+--R ------
+--R 2
+--R x
+--R +
+--R 11 4 15 11 4 14 11 4 13
+--R - 349440a b m - 25509120a b m - 854730240a b m
+--R +
+--R 11 4 12 11 4 11 11 4 10
+--R - 17420282880a b m - 241248265440a b m - 2401687448160a b m
+--R +
+--R 11 4 9 11 4 8
+--R - 17730817824720a b m - 98692961006640a b m
+--R +
+--R 11 4 7 11 4 6
+--R - 416845891186725a b m - 1333281807903045a b m
+--R +
+--R 11 4 5 11 4 4
+--R - 3195762043479915a b m - 5622642178644855a b m
+--R +
+--R 11 4 3 11 4 2
+--R - 7008500947331520a b m - 5823607525035300a b m
+--R +
+--R 11 4 11 4
+--R - 2873740629942000a b m - 632178827280000a b
+--R *
+--R m + 3
+--R x
+--R +
+--R 12 3 15 12 3 14 12 3 13
+--R - 116480a b m - 8561280a b m - 289016000a b m
+--R +
+--R 12 3 12 12 3 11 12 3 10
+--R - 5938951200a b m - 82988993360a b m - 834338264760a b m
+--R +
+--R 12 3 9 12 3 8
+--R - 6226114394500a b m - 35063185507350a b m
+--R +
+--R 12 3 7 12 3 6
+--R - 149983627633840a b m - 486314091403140a b m
+--R +
+--R 12 3 5 12 3 4
+--R - 1182750593888500a b m - 2113099618306950a b m
+--R +
+--R 12 3 3 12 3 2
+--R - 2676060115321320a b m - 2259553167373320a b m
+--R +
+--R 12 3 12 3
+--R - 1132638149916000a b m - 252871530912000a b
+--R *
+--R 2m + 5
+--R ------
+--R 2
+--R x
+--R +
+--R 13 2 15 13 2 14 13 2 13
+--R - 26880a b m - 1989120a b m - 67656960a b m
+--R +
+--R 13 2 12 13 2 11 13 2 10
+--R - 1401953280a b m - 19773717600a b m - 200870429760a b m
+--R +
+--R 13 2 9 13 2 8 13 2 7
+--R - 1516403768880a b m - 8650685883840a b m - 37538995478985a b m
+--R +
+--R 13 2 6 13 2 5
+--R - 123677353769970a b m - 306153559166910a b m
+--R +
+--R 13 2 4 13 2 3
+--R - 557687366980380a b m - 721273533982785a b m
+--R +
+--R 13 2 2 13 2 13 2
+--R - 622769114113650a b m - 319428172161000a b m - 72943710840000a b
+--R *
+--R m + 2
+--R x
+--R +
+--R 14 15 14 14 14 13 14 12
+--R - 3840a b m - 286080a b m - 9804480a b m - 204902880a b m
+--R +
+--R 14 11 14 10 14 9
+--R - 2918020560a b m - 29968378440a b m - 229068093540a b m
+--R +
+--R 14 8 14 7 14 6
+--R - 1325468348490a b m - 5846135655360a b m - 19624417192380a b m
+--R +
+--R 14 5 14 4
+--R - 49635983740980a b m - 92688093719130a b m
+--R +
+--R 14 3 14 2
+--R - 123346183413240a b m - 110025893748600a b m
+--R +
+--R 14 14
+--R - 58527788004000a b m - 13894040160000a b
+--R *
+--R 2m + 3
+--R ------
+--R 2
+--R x
+--R +
+--R 15 15 15 14 15 13 15 12
+--R - 256a m - 19200a m - 663040a m - 13977600a m
+--R +
+--R 15 11 15 10 15 9
+--R - 201047392a m - 2088646560a m - 16179397520a m
+--R +
+--R 15 8 15 7 15 6
+--R - 95091968400a m - 427197243473a m - 1465710801555a m
+--R +
+--R 15 5 15 4 15 3
+--R - 3805796500415a m - 7337008121625a m - 10154880144504a m
+--R +
+--R 15 2 15 15
+--R - 9514797780060a m - 5389644128400a m - 1389404016000a
+--R *
+--R m + 1
+--R x
+--R /
+--R 16 15 14 13 12
+--R 256m + 19456m + 682240m + 14640640m + 215024992m
+--R +
+--R 11 10 9 8
+--R 2289693952m + 18268044080m + 111271365920m + 522289211873m
+--R +
+--R 7 6 5 4
+--R 1892908045028m + 5271507301970m + 11142804622040m + 17491888266129m
+--R +
+--R 3 2
+--R 19669677924564m + 14904441908460m + 6779048144400m + 1389404016000
+--R Type: Expression(Integer)
+--E 777
+
+--S 778 of 1325
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 778
+
+)clear all
+
+--S 779 of 1325
+t0:=x^5*(a+b*sqrt(x))^15
+--R
+--R
+--R (1)
+--R 15 12 2 13 11 4 11 10 6 9 9 8 7 8
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 7 12 3 6 14 5
+--R 3003a b x + 455a b x + 15a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 12 3 12 11 5 10 10 7 8 9 9 6 8
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 7 13 2 6 15 5
+--R 1365a b x + 105a b x + a x
+--R Type: Expression(Integer)
+--E 779
+
+--S 780 of 1325
+r0:=1/6*a^15*x^6+30/13*a^14*b*x^(13/2)+15*a^13*b^2*x^7+182/3*a^12*_
+ b^3*x^(15/2)+1365/8*a^11*b^4*x^8+6006/17*a^10*b^5*x^(17/2)+_
+ 5005/9*a^9*b^6*x^9+12870/19*a^8*b^7*x^(19/2)+1287/2*a^7*b^8*_
+ x^10+1430/3*a^6*b^9*x^(21/2)+273*a^5*b^10*x^11+2730/23*a^4*_
+ b^11*x^(23/2)+455/12*a^3*b^12*x^12+42/5*a^2*b^13*x^(25/2)+_
+ 15/13*a*b^14*x^13+2/27*b^15*x^(27/2)
+--R
+--R
+--R (2)
+--R 15 13 2 13 12 4 11 11
+--R 7726160b x + 876146544a b x + 12380331600a b x
+--R +
+--R 6 9 10 8 7 9 10 5 8
+--R 49717839600a b x + 70651666800a b x + 36849692880a b x
+--R +
+--R 12 3 7 14 6
+--R 6327725040a b x + 240699600a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 13 3 12 12 5 10 11
+--R 120349800a b x + 3954828150a b x + 28474762680a b x
+--R +
+--R 7 8 10 9 6 9 11 4 8
+--R 67119083460a b x + 58004146200a b x + 17796726675a b x
+--R +
+--R 13 2 7 15 6
+--R 1564547400a b x + 17383860a x
+--R /
+--R 104303160
+--R Type: Expression(Integer)
+--E 780
+
+--S 781 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 13 2 13 12 4 11 11
+--R 7726160b x + 876146544a b x + 12380331600a b x
+--R +
+--R 6 9 10 8 7 9 10 5 8
+--R 49717839600a b x + 70651666800a b x + 36849692880a b x
+--R +
+--R 12 3 7 14 6
+--R 6327725040a b x + 240699600a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 13 3 12 12 5 10 11
+--R 120349800a b x + 3954828150a b x + 28474762680a b x
+--R +
+--R 7 8 10 9 6 9 11 4 8
+--R 67119083460a b x + 58004146200a b x + 17796726675a b x
+--R +
+--R 13 2 7 15 6
+--R 1564547400a b x + 17383860a x
+--R /
+--R 104303160
+--R Type: Union(Expression(Integer),...)
+--E 781
+
+--S 782 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 782
+
+--S 783 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 783
+
+)clear all
+
+--S 784 of 1325
+t0:=x^4*(a+b*sqrt(x))^15
+--R
+--R
+--R (1)
+--R 15 11 2 13 10 4 11 9 6 9 8 8 7 7
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 6 12 3 5 14 4
+--R 3003a b x + 455a b x + 15a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 11 3 12 10 5 10 9 7 8 8 9 6 7
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 6 13 2 5 15 4
+--R 1365a b x + 105a b x + a x
+--R Type: Expression(Integer)
+--E 784
+
+--S 785 of 1325
+r0:=-1/8*a^9*(a+b*sqrt(x))^16/b^10+18/17*a^8*(a+b*sqrt(x))^17/b^10-_
+ 4*a^7*(a+b*sqrt(x))^18/b^10+168/19*a^6*(a+b*sqrt(x))^19/b^10-_
+ 63/5*a^5*(a+b*sqrt(x))^20/b^10+12*a^4*(a+b*sqrt(x))^21/b^10-_
+ 84/11*a^3*(a+b*sqrt(x))^22/b^10+72/23*a^2*(a+b*sqrt(x))^23/b^10-_
+ 3/4*a*(a+b*sqrt(x))^24/b^10+2/25*(a+b*sqrt(x))^25/b^10
+--R
+--R
+--R (2)
+--R 25 12 2 23 11 4 21 10
+--R 1307504b x + 149226000a b x + 2124694000a b x
+--R +
+--R 6 19 9 8 17 8 10 15 7
+--R 8610602000a b x + 12373218000a b x + 6544057520a b x
+--R +
+--R 12 13 6 14 11 5
+--R 1144066000a b x + 44574000a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 24 12 3 22 11 5 20 10
+--R 20429750a b x + 676039000a b x + 4908043140a b x
+--R +
+--R 7 18 9 9 16 8 11 14 7
+--R 11685817000a b x + 10225089875a b x + 3187041000a b x
+--R +
+--R 13 12 6 15 10 5 25
+--R 286016500a b x + 3268760a b x - a
+--R /
+--R 10
+--R 16343800b
+--R Type: Expression(Integer)
+--E 785
+
+--S 786 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 12 2 13 11 4 11 10
+--R 1307504b x + 149226000a b x + 2124694000a b x
+--R +
+--R 6 9 9 8 7 8 10 5 7
+--R 8610602000a b x + 12373218000a b x + 6544057520a b x
+--R +
+--R 12 3 6 14 5
+--R 1144066000a b x + 44574000a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 12 3 12 11 5 10 10
+--R 20429750a b x + 676039000a b x + 4908043140a b x
+--R +
+--R 7 8 9 9 6 8 11 4 7
+--R 11685817000a b x + 10225089875a b x + 3187041000a b x
+--R +
+--R 13 2 6 15 5
+--R 286016500a b x + 3268760a x
+--R /
+--R 16343800
+--R Type: Union(Expression(Integer),...)
+--E 786
+
+--S 787 of 1325
+m0:=a0-r0
+--R
+--R
+--R 25
+--R a
+--R (4) -----------
+--R 10
+--R 16343800b
+--R Type: Expression(Integer)
+--E 787
+
+--S 788 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 788
+
+)clear all
+
+--S 789 of 1325
+t0:=x^3*(a+b*sqrt(x))^15
+--R
+--R
+--R (1)
+--R 15 10 2 13 9 4 11 8 6 9 7 8 7 6
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 5 12 3 4 14 3
+--R 3003a b x + 455a b x + 15a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 10 3 12 9 5 10 8 7 8 7 9 6 6
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 5 13 2 4 15 3
+--R 1365a b x + 105a b x + a x
+--R Type: Expression(Integer)
+--E 789
+
+--S 790 of 1325
+r0:=-1/8*a^7*(a+b*sqrt(x))^16/b^8+14/17*a^6*(a+b*sqrt(x))^17/b^8-_
+ 7/3*a^5*(a+b*sqrt(x))^18/b^8+70/19*a^4*(a+b*sqrt(x))^19/b^8-_
+ 7/2*a^3*(a+b*sqrt(x))^20/b^8+2*a^2*(a+b*sqrt(x))^21/b^8-_
+ 7/11*a*(a+b*sqrt(x))^22/b^8+2/23*(a+b*sqrt(x))^23/b^8
+--R
+--R
+--R (2)
+--R 23 11 2 21 10 4 19 9
+--R 170544b x + 19612560a b x + 281801520a b x
+--R +
+--R 6 17 8 8 15 7 10 13 6
+--R 1154833680a b x + 1682757648a b x + 906100272a b x
+--R +
+--R 12 11 5 14 9 4
+--R 162249360a b x + 6537520a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 22 11 3 20 10 5 18 9 7 16 8
+--R 2674440a b x + 89237148a b x + 654405752a b x + 1577585295a b x
+--R +
+--R 9 14 7 11 12 6 13 10 5 15 8 4
+--R 1402298040a b x + 446185740a b x + 41186376a b x + 490314a b x
+--R +
+--R 23
+--R - a
+--R /
+--R 8
+--R 1961256b
+--R Type: Expression(Integer)
+--E 790
+
+--S 791 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 11 2 13 10 4 11 9 6 9 8
+--R 170544b x + 19612560a b x + 281801520a b x + 1154833680a b x
+--R +
+--R 8 7 7 10 5 6 12 3 5 14 4
+--R 1682757648a b x + 906100272a b x + 162249360a b x + 6537520a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 11 3 12 10 5 10 9 7 8 8
+--R 2674440a b x + 89237148a b x + 654405752a b x + 1577585295a b x
+--R +
+--R 9 6 7 11 4 6 13 2 5 15 4
+--R 1402298040a b x + 446185740a b x + 41186376a b x + 490314a x
+--R /
+--R 1961256
+--R Type: Union(Expression(Integer),...)
+--E 791
+
+--S 792 of 1325
+m0:=a0-r0
+--R
+--R
+--R 23
+--R a
+--R (4) ---------
+--R 8
+--R 1961256b
+--R Type: Expression(Integer)
+--E 792
+
+--S 793 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 793
+
+)clear all
+
+--S 794 of 1325
+t0:=x^2*(a+b*sqrt(x))^15
+--R
+--R
+--R (1)
+--R 15 9 2 13 8 4 11 7 6 9 6 8 7 5
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 4 12 3 3 14 2
+--R 3003a b x + 455a b x + 15a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 9 3 12 8 5 10 7 7 8 6 9 6 5
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 4 13 2 3 15 2
+--R 1365a b x + 105a b x + a x
+--R Type: Expression(Integer)
+--E 794
+
+--S 795 of 1325
+r0:=-1/8*a^5*(a+b*sqrt(x))^16/b^6+10/17*a^4*(a+b*sqrt(x))^17/b^6-_
+ 10/9*a^3*(a+b*sqrt(x))^18/b^6+20/19*a^2*(a+b*sqrt(x))^19/b^6-_
+ 1/2*a*(a+b*sqrt(x))^20/b^6+2/21*(a+b*sqrt(x))^21/b^6
+--R
+--R
+--R (2)
+--R 21 10 2 19 9 4 17 8 6 15 7
+--R 15504b x + 1799280a b x + 26142480a b x + 108636528a b x
+--R +
+--R 8 13 6 10 11 5 12 9 4 14 7 3
+--R 161164080a b x + 88884432a b x + 16460080a b x + 697680a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 20 10 3 18 9 5 16 8 7 14 7
+--R 244188a b x + 8230040a b x + 61108047a b x + 149652360a b x
+--R +
+--R 9 12 6 11 10 5 13 8 4 15 6 3 21
+--R 135795660a b x + 44442216a b x + 4273290a b x + 54264a b x - a
+--R /
+--R 6
+--R 162792b
+--R Type: Expression(Integer)
+--E 795
+
+--S 796 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 10 2 13 9 4 11 8 6 9 7
+--R 15504b x + 1799280a b x + 26142480a b x + 108636528a b x
+--R +
+--R 8 7 6 10 5 5 12 3 4 14 3
+--R 161164080a b x + 88884432a b x + 16460080a b x + 697680a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 10 3 12 9 5 10 8 7 8 7
+--R 244188a b x + 8230040a b x + 61108047a b x + 149652360a b x
+--R +
+--R 9 6 6 11 4 5 13 2 4 15 3
+--R 135795660a b x + 44442216a b x + 4273290a b x + 54264a x
+--R /
+--R 162792
+--R Type: Union(Expression(Integer),...)
+--E 796
+
+--S 797 of 1325
+m0:=a0-r0
+--R
+--R
+--R 21
+--R a
+--R (4) --------
+--R 6
+--R 162792b
+--R Type: Expression(Integer)
+--E 797
+
+--S 798 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 798
+
+)clear all
+
+--S 799 of 1325
+t0:=x*(a+b*sqrt(x))^15
+--R
+--R
+--R (1)
+--R 15 8 2 13 7 4 11 6 6 9 5 8 7 4
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 3 12 3 2 14
+--R 3003a b x + 455a b x + 15a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 8 3 12 7 5 10 6 7 8 5 9 6 4
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 3 13 2 2 15
+--R 1365a b x + 105a b x + a x
+--R Type: Expression(Integer)
+--E 799
+
+--S 800 of 1325
+r0:=-1/8*a^3*(a+b*sqrt(x))^16/b^4+6/17*a^2*(a+b*sqrt(x))^17/b^4-_
+ 1/3*a*(a+b*sqrt(x))^18/b^4+2/19*(a+b*sqrt(x))^19/b^4
+--R
+--R
+--R (2)
+--R 19 9 2 17 8 4 15 7 6 13 6
+--R 816b x + 95760a b x + 1410864a b x + 5969040a b x
+--R +
+--R 8 11 5 10 9 4 12 7 3 14 5 2
+--R 9069840a b x + 5173168a b x + 1007760a b x + 46512a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 18 9 3 16 8 5 14 7 7 12 6
+--R 12920a b x + 440895a b x + 3325608a b x + 8314020a b x
+--R +
+--R 9 10 5 11 8 4 13 6 3 15 4 2 19
+--R 7759752a b x + 2645370a b x + 271320a b x + 3876a b x - a
+--R /
+--R 4
+--R 7752b
+--R Type: Expression(Integer)
+--E 800
+
+--S 801 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 9 2 13 8 4 11 7 6 9 6
+--R 816b x + 95760a b x + 1410864a b x + 5969040a b x
+--R +
+--R 8 7 5 10 5 4 12 3 3 14 2
+--R 9069840a b x + 5173168a b x + 1007760a b x + 46512a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 9 3 12 8 5 10 7 7 8 6
+--R 12920a b x + 440895a b x + 3325608a b x + 8314020a b x
+--R +
+--R 9 6 5 11 4 4 13 2 3 15 2
+--R 7759752a b x + 2645370a b x + 271320a b x + 3876a x
+--R /
+--R 7752
+--R Type: Union(Expression(Integer),...)
+--E 801
+
+--S 802 of 1325
+m0:=a0-r0
+--R
+--R
+--R 19
+--R a
+--R (4) ------
+--R 4
+--R 7752b
+--R Type: Expression(Integer)
+--E 802
+
+--S 803 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 803
+
+)clear all
+
+--S 804 of 1325
+t0:=(a+b*sqrt(x))^15
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R Type: Expression(Integer)
+--E 804
+
+--S 805 of 1325
+r0:=-1/8*a*(a+b*sqrt(x))^16/b^2+2/17*(a+b*sqrt(x))^17/b^2
+--R
+--R
+--R (2)
+--R 17 8 2 15 7 4 13 6 6 11 5 8 9 4
+--R 16b x + 1904a b x + 28560a b x + 123760a b x + 194480a b x
+--R +
+--R 10 7 3 12 5 2 14 3
+--R 116688a b x + 24752a b x + 1360a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 16 8 3 14 7 5 12 6 7 10 5 9 8 4
+--R 255a b x + 8840a b x + 68068a b x + 175032a b x + 170170a b x
+--R +
+--R 11 6 3 13 4 2 15 2 17
+--R 61880a b x + 7140a b x + 136a b x - a
+--R /
+--R 2
+--R 136b
+--R Type: Expression(Integer)
+--E 805
+
+--S 806 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 8 2 13 7 4 11 6 6 9 5 8 7 4
+--R 16b x + 1904a b x + 28560a b x + 123760a b x + 194480a b x
+--R +
+--R 10 5 3 12 3 2 14
+--R 116688a b x + 24752a b x + 1360a b x
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 8 3 12 7 5 10 6 7 8 5 9 6 4
+--R 255a b x + 8840a b x + 68068a b x + 175032a b x + 170170a b x
+--R +
+--R 11 4 3 13 2 2 15
+--R 61880a b x + 7140a b x + 136a x
+--R /
+--R 136
+--R Type: Union(Expression(Integer),...)
+--E 806
+
+--S 807 of 1325
+m0:=a0-r0
+--R
+--R
+--R 17
+--R a
+--R (4) -----
+--R 2
+--R 136b
+--R Type: Expression(Integer)
+--E 807
+
+--S 808 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 808
+
+)clear all
+
+--S 809 of 1325
+t0:=(a+b*sqrt(x))^15/x
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R x
+--R Type: Expression(Integer)
+--E 809
+
+--S 810 of 1325
+r0:=105*a^13*b^2*x+910/3*a^12*b^3*x^(3/2)+1365/2*a^11*b^4*x^2+_
+ 6006/5*a^10*b^5*x^(5/2)+5005/3*a^9*b^6*x^3+12870/7*a^8*b^7*_
+ x^(7/2)+6435/4*a^7*b^8*x^4+10010/9*a^6*b^9*x^(9/2)+3003/5*a^5*_
+ b^10*x^5+2730/11*a^4*b^11*x^(11/2)+455/6*a^3*b^12*x^6+210/13*_
+ a^2*b^13*x^(13/2)+15/7*a*b^14*x^7+2/15*b^15*x^(15/2)+a^15*_
+ log(x)+30*a^14*b*sqrt(x)
+--R
+--R
+--R (2)
+--R 15 7 2 13 6 4 11 5 6 9 4
+--R 24024b x + 2910600a b x + 44717400a b x + 200400200a b x
+--R +
+--R 8 7 3 10 5 2 12 3 14
+--R 331273800a b x + 216432216a b x + 54654600a b x + 5405400a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 14 7 3 12 6 5 10 5
+--R 180180a log(x) + 386100a b x + 13663650a b x + 108216108a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2 13 2
+--R 289864575a b x + 300600300a b x + 122972850a b x + 18918900a b x
+--R /
+--R 180180
+--R Type: Expression(Integer)
+--E 810
+
+--S 811 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 +-+
+--R 360360a log(\|x )
+--R +
+--R 15 7 2 13 6 4 11 5 6 9 4
+--R 24024b x + 2910600a b x + 44717400a b x + 200400200a b x
+--R +
+--R 8 7 3 10 5 2 12 3 14
+--R 331273800a b x + 216432216a b x + 54654600a b x + 5405400a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4
+--R 386100a b x + 13663650a b x + 108216108a b x + 289864575a b x
+--R +
+--R 9 6 3 11 4 2 13 2
+--R 300600300a b x + 122972850a b x + 18918900a b x
+--R /
+--R 180180
+--R Type: Union(Expression(Integer),...)
+--E 811
+
+--S 812 of 1325
+m0:=a0-r0
+--R
+--R
+--R 15 +-+ 15
+--R (4) 2a log(\|x ) - a log(x)
+--R Type: Expression(Integer)
+--E 812
+
+--S 813 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 813
+
+)clear all
+
+--S 814 of 1325
+t0:=(a+b*sqrt(x))^15/x^2
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 2
+--R x
+--R Type: Expression(Integer)
+--E 814
+
+--S 815 of 1325
+r0:=-a^15/x+1365*a^11*b^4*x+2002*a^10*b^5*x^(3/2)+5005/2*a^9*b^6*x^2+_
+ 2574*a^8*b^7*x^(5/2)+2145*a^7*b^8*x^3+1430*a^6*b^9*x^(7/2)+_
+ 3003/4*a^5*b^10*x^4+910/3*a^4*b^11*x^(9/2)+91*a^3*b^12*x^5+_
+ 210/11*a^2*b^13*x^(11/2)+5/2*a*b^14*x^6+2/13*b^15*x^(13/2)+_
+ 105*a^13*b^2*log(x)-30*a^14*b/sqrt(x)+910*a^12*b^3*sqrt(x)
+--R
+--R
+--R (2)
+--R 13 2 14 7 3 12 6 5 10 5
+--R 180180a b x log(x) + 4290a b x + 156156a b x + 1288287a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2 15
+--R 3680820a b x + 4294290a b x + 2342340a b x - 1716a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6 6 9 5 8 7 4
+--R 264b x + 32760a b x + 520520a b x + 2453880a b x + 4416984a b x
+--R +
+--R 10 5 3 12 3 2 14
+--R 3435432a b x + 1561560a b x - 51480a b x
+--R /
+--R +-+
+--R 1716x\|x
+--R Type: Expression(Integer)
+--E 815
+
+--S 816 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 13 2 +-+
+--R 360360a b x log(\|x )
+--R +
+--R 15 7 2 13 6 4 11 5 6 9 4
+--R 264b x + 32760a b x + 520520a b x + 2453880a b x
+--R +
+--R 8 7 3 10 5 2 12 3 14
+--R 4416984a b x + 3435432a b x + 1561560a b x - 51480a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4
+--R 4290a b x + 156156a b x + 1288287a b x + 3680820a b x
+--R +
+--R 9 6 3 11 4 2 15
+--R 4294290a b x + 2342340a b x - 1716a
+--R /
+--R 1716x
+--R Type: Union(Expression(Integer),...)
+--E 816
+
+--S 817 of 1325
+m0:=a0-r0
+--R
+--R
+--R 13 2 +-+ 13 2
+--R (4) 210a b log(\|x ) - 105a b log(x)
+--R Type: Expression(Integer)
+--E 817
+
+--S 818 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 818
+
+)clear all
+
+--S 819 of 1325
+t0:=(a+b*sqrt(x))^15/x^3
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 3
+--R x
+--R Type: Expression(Integer)
+--E 819
+
+--S 820 of 1325
+r0:=-1/2*a^15/x^2-10*a^14*b/x^(3/2)-105*a^13*b^2/x+5005*a^9*b^6*x+_
+ 4290*a^8*b^7*x^(3/2)+6435/2*a^7*b^8*x^2+2002*a^6*b^9*x^(5/2)+_
+ 1001*a^5*b^10*x^3+390*a^4*b^11*x^(7/2)+455/4*a^3*b^12*x^4+_
+ 70/3*a^2*b^13*x^(9/2)+3*a*b^14*x^5+2/11*b^15*x^(11/2)+_
+ 1365*a^11*b^4*log(x)-910*a^12*b^3/sqrt(x)+6006*a^10*b^5*sqrt(x)
+--R
+--R
+--R (2)
+--R 11 4 2 14 7 3 12 6 5 10 5
+--R 180180a b x log(x) + 396a b x + 15015a b x + 132132a b x
+--R +
+--R 7 8 4 9 6 3 13 2 15
+--R 424710a b x + 660660a b x - 13860a b x - 66a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6 6 9 5 8 7 4
+--R 24b x + 3080a b x + 51480a b x + 264264a b x + 566280a b x
+--R +
+--R 10 5 3 12 3 2 14
+--R 792792a b x - 120120a b x - 1320a b x
+--R /
+--R 2 +-+
+--R 132x \|x
+--R Type: Expression(Integer)
+--E 820
+
+--S 821 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 11 4 2 +-+
+--R 360360a b x log(\|x )
+--R +
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R 24b x + 3080a b x + 51480a b x + 264264a b x + 566280a b x
+--R +
+--R 10 5 2 12 3 14
+--R 792792a b x - 120120a b x - 1320a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 396a b x + 15015a b x + 132132a b x + 424710a b x + 660660a b x
+--R +
+--R 13 2 15
+--R - 13860a b x - 66a
+--R /
+--R 2
+--R 132x
+--R Type: Union(Expression(Integer),...)
+--E 821
+
+--S 822 of 1325
+m0:=a0-r0
+--R
+--R
+--R 11 4 +-+ 11 4
+--R (4) 2730a b log(\|x ) - 1365a b log(x)
+--R Type: Expression(Integer)
+--E 822
+
+--S 823 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 823
+
+)clear all
+
+--S 824 of 1325
+t0:=(a+b*sqrt(x))^15/x^4
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 4
+--R x
+--R Type: Expression(Integer)
+--E 824
+
+--S 825 of 1325
+r0:=-1/3*a^15/x^3-6*a^14*b/x^(5/2)-105/2*a^13*b^2/x^2-910/3*a^12*_
+ b^3/x^(3/2)-1365*a^11*b^4/x+6435*a^7*b^8*x+10010/3*a^6*b^9*_
+ x^(3/2)+3003/2*a^5*b^10*x^2+546*a^4*b^11*x^(5/2)+455/3*a^3*_
+ b^12*x^3+30*a^2*b^13*x^(7/2)+15/4*a*b^14*x^4+2/9*b^15*x^(9/2)+_
+ 5005*a^9*b^6*log(x)-6006*a^10*b^5/sqrt(x)+12870*a^8*b^7*sqrt(x)
+--R
+--R
+--R (2)
+--R 9 6 3 14 7 3 12 6 5 10 5
+--R 180180a b x log(x) + 135a b x + 5460a b x + 54054a b x
+--R +
+--R 7 8 4 11 4 2 13 2 15
+--R 231660a b x - 49140a b x - 1890a b x - 12a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6 6 9 5 8 7 4
+--R 8b x + 1080a b x + 19656a b x + 120120a b x + 463320a b x
+--R +
+--R 10 5 3 12 3 2 14
+--R - 216216a b x - 10920a b x - 216a b x
+--R /
+--R 3 +-+
+--R 36x \|x
+--R Type: Expression(Integer)
+--E 825
+
+--S 826 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 9 6 3 +-+
+--R 360360a b x log(\|x )
+--R +
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R 8b x + 1080a b x + 19656a b x + 120120a b x + 463320a b x
+--R +
+--R 10 5 2 12 3 14
+--R - 216216a b x - 10920a b x - 216a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 11 4 2
+--R 135a b x + 5460a b x + 54054a b x + 231660a b x - 49140a b x
+--R +
+--R 13 2 15
+--R - 1890a b x - 12a
+--R /
+--R 3
+--R 36x
+--R Type: Union(Expression(Integer),...)
+--E 826
+
+--S 827 of 1325
+m0:=a0-r0
+--R
+--R
+--R 9 6 +-+ 9 6
+--R (4) 10010a b log(\|x ) - 5005a b log(x)
+--R Type: Expression(Integer)
+--E 827
+
+--S 828 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 828
+
+)clear all
+
+--S 829 of 1325
+t0:=(a+b*sqrt(x))^15/x^6
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 6
+--R x
+--R Type: Expression(Integer)
+--E 829
+
+--S 830 of 1325
+r0:=-1/5*a^15/x^5-10/3*a^14*b/x^(9/2)-105/4*a^13*b^2/x^4-130*a^12*_
+ b^3/x^(7/2)-455*a^11*b^4/x^3-6006/5*a^10*b^5/x^(5/2)-5005/2*_
+ a^9*b^6/x^2-4290*a^8*b^7/x^(3/2)-6435*a^7*b^8/x+455*a^3*b^12*_
+ x+70*a^2*b^13*x^(3/2)+15/2*a*b^14*x^2+2/5*b^15*x^(5/2)+3003*_
+ a^5*b^10*log(x)-10010*a^6*b^9/sqrt(x)+2730*a^4*b^11*sqrt(x)
+--R
+--R
+--R (2)
+--R 5 10 5 14 7 3 12 6 7 8 4
+--R 180180a b x log(x) + 450a b x + 27300a b x - 386100a b x
+--R +
+--R 9 6 3 11 4 2 13 2 15
+--R - 150150a b x - 27300a b x - 1575a b x - 12a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6 6 9 5 8 7 4
+--R 24b x + 4200a b x + 163800a b x - 600600a b x - 257400a b x
+--R +
+--R 10 5 3 12 3 2 14
+--R - 72072a b x - 7800a b x - 200a b x
+--R /
+--R 5 +-+
+--R 60x \|x
+--R Type: Expression(Integer)
+--E 830
+
+--S 831 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 10 5 +-+
+--R 360360a b x log(\|x )
+--R +
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R 24b x + 4200a b x + 163800a b x - 600600a b x - 257400a b x
+--R +
+--R 10 5 2 12 3 14
+--R - 72072a b x - 7800a b x - 200a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 7 8 4 9 6 3 11 4 2
+--R 450a b x + 27300a b x - 386100a b x - 150150a b x - 27300a b x
+--R +
+--R 13 2 15
+--R - 1575a b x - 12a
+--R /
+--R 5
+--R 60x
+--R Type: Union(Expression(Integer),...)
+--E 831
+
+--S 832 of 1325
+m0:=a0-r0
+--R
+--R
+--R 5 10 +-+ 5 10
+--R (4) 6006a b log(\|x ) - 3003a b log(x)
+--R Type: Expression(Integer)
+--E 832
+
+--S 833 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 833
+
+)clear all
+
+--S 834 of 1325
+t0:=(a+b*sqrt(x))^15/x^7
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 7
+--R x
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 1325
+r0:=-1/6*a^15/x^6-30/11*a^14*b/x^(11/2)-21*a^13*b^2/x^5-910/9*a^12*_
+ b^3/x^(9/2)-1365/4*a^11*b^4/x^4-858*a^10*b^5/x^(7/2)-5005/3*_
+ a^9*b^6/x^3-2574*a^8*b^7/x^(5/2)-6435/2*a^7*b^8/x^2-10010/3*_
+ a^6*b^9/x^(3/2)-3003*a^5*b^10/x+15*a*b^14*x+2/3*b^15*x^(3/2)+_
+ 455*a^3*b^12*log(x)-2730*a^4*b^11/sqrt(x)+210*a^2*b^13*sqrt(x)
+--R
+--R
+--R (2)
+--R 3 12 6 14 7 5 10 5 7 8 4
+--R 180180a b x log(x) + 5940a b x - 1189188a b x - 1274130a b x
+--R +
+--R 9 6 3 11 4 2 13 2 15
+--R - 660660a b x - 135135a b x - 8316a b x - 66a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6 6 9 5 8 7 4
+--R 264b x + 83160a b x - 1081080a b x - 1321320a b x - 1019304a b x
+--R +
+--R 10 5 3 12 3 2 14
+--R - 339768a b x - 40040a b x - 1080a b x
+--R /
+--R 6 +-+
+--R 396x \|x
+--R Type: Expression(Integer)
+--E 835
+
+--S 836 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 12 6 +-+
+--R 360360a b x log(\|x )
+--R +
+--R 15 7 2 13 6 4 11 5 6 9 4
+--R 264b x + 83160a b x - 1081080a b x - 1321320a b x
+--R +
+--R 8 7 3 10 5 2 12 3 14
+--R - 1019304a b x - 339768a b x - 40040a b x - 1080a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 5 10 5 7 8 4 9 6 3
+--R 5940a b x - 1189188a b x - 1274130a b x - 660660a b x
+--R +
+--R 11 4 2 13 2 15
+--R - 135135a b x - 8316a b x - 66a
+--R /
+--R 6
+--R 396x
+--R Type: Union(Expression(Integer),...)
+--E 836
+
+--S 837 of 1325
+m0:=a0-r0
+--R
+--R
+--R 3 12 +-+ 3 12
+--R (4) 910a b log(\|x ) - 455a b log(x)
+--R Type: Expression(Integer)
+--E 837
+
+--S 838 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 838
+
+)clear all
+
+--S 839 of 1325
+t0:=(a+b*sqrt(x))^15/x^8
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 8
+--R x
+--R Type: Expression(Integer)
+--E 839
+
+--S 840 of 1325
+r0:=-1/7*a^15/x^7-30/13*a^14*b/x^(13/2)-35/2*a^13*b^2/x^6-910/11*_
+ a^12*b^3/x^(11/2)-273*a^11*b^4/x^5-2002/3*a^10*b^5/x^(9/2)-_
+ 5005/4*a^9*b^6/x^4-12870/7*a^8*b^7/x^(7/2)-2145*a^7*b^8/x^3-_
+ 2002*a^6*b^9/x^(5/2)-3003/2*a^5*b^10/x^2-910*a^4*b^11/x^(3/2)-_
+ 455*a^3*b^12/x+15*a*b^14*log(x)-210*a^2*b^13/sqrt(x)+2*b^15*sqrt(x)
+--R
+--R
+--R (2)
+--R 14 7 3 12 6 5 10 5
+--R 180180a b x log(x) - 5465460a b x - 18036018a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2 13 2
+--R - 25765740a b x - 15030015a b x - 3279276a b x - 210210a b x
+--R +
+--R 15
+--R - 1716a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6 6 9 5
+--R 24024b x - 2522520a b x - 10930920a b x - 24048024a b x
+--R +
+--R 8 7 4 10 5 3 12 3 2 14
+--R - 22084920a b x - 8016008a b x - 993720a b x - 27720a b x
+--R /
+--R 7 +-+
+--R 12012x \|x
+--R Type: Expression(Integer)
+--E 840
+
+--S 841 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 14 7 +-+
+--R 360360a b x log(\|x )
+--R +
+--R 15 7 2 13 6 4 11 5 6 9 4
+--R 24024b x - 2522520a b x - 10930920a b x - 24048024a b x
+--R +
+--R 8 7 3 10 5 2 12 3 14
+--R - 22084920a b x - 8016008a b x - 993720a b x - 27720a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 3 12 6 5 10 5 7 8 4 9 6 3
+--R - 5465460a b x - 18036018a b x - 25765740a b x - 15030015a b x
+--R +
+--R 11 4 2 13 2 15
+--R - 3279276a b x - 210210a b x - 1716a
+--R /
+--R 7
+--R 12012x
+--R Type: Union(Expression(Integer),...)
+--E 841
+
+--S 842 of 1325
+m0:=a0-r0
+--R
+--R
+--R 14 +-+ 14
+--R (4) 30a b log(\|x ) - 15a b log(x)
+--R Type: Expression(Integer)
+--E 842
+
+--S 843 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 843
+
+)clear all
+
+--S 844 of 1325
+t0:=(a+b*sqrt(x))^15/x^9
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 9
+--R x
+--R Type: Expression(Integer)
+--E 844
+
+--S 845 of 1325
+r0:=-1/8*(a+b*sqrt(x))^16/(a*x^8)
+--R
+--R
+--R (2)
+--R 15 7 3 13 6 5 11 5 7 9 4 9 7 3
+--R - 16a b x - 560a b x - 4368a b x - 11440a b x - 11440a b x
+--R +
+--R 11 5 2 13 3 15
+--R - 4368a b x - 560a b x - 16a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 16 8 2 14 7 4 12 6 6 10 5 8 8 4
+--R - b x - 120a b x - 1820a b x - 8008a b x - 12870a b x
+--R +
+--R 10 6 3 12 4 2 14 2 16
+--R - 8008a b x - 1820a b x - 120a b x - a
+--R /
+--R 8
+--R 8a x
+--R Type: Expression(Integer)
+--E 845
+
+--S 846 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R - 16b x - 560a b x - 4368a b x - 11440a b x - 11440a b x
+--R +
+--R 10 5 2 12 3 14
+--R - 4368a b x - 560a b x - 16a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R - 120a b x - 1820a b x - 8008a b x - 12870a b x - 8008a b x
+--R +
+--R 11 4 2 13 2 15
+--R - 1820a b x - 120a b x - a
+--R /
+--R 8
+--R 8x
+--R Type: Union(Expression(Integer),...)
+--E 846
+
+--S 847 of 1325
+m0:=a0-r0
+--R
+--R
+--R 16
+--R b
+--R (4) ---
+--R 8a
+--R Type: Expression(Integer)
+--E 847
+
+--S 848 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 848
+
+)clear all
+
+--S 849 of 1325
+t0:=(a+b*sqrt(x))^15/x^10
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 10
+--R x
+--R Type: Expression(Integer)
+--E 849
+
+--S 850 of 1325
+r0:=-1/9*(a+b*sqrt(x))^16/(a*x^9)+2/153*b*(a+b*sqrt(x))^16/_
+ (a^2*x^(17/2))-1/1224*b^2*(a+b*sqrt(x))^16/(a^3*x^8)
+--R
+--R
+--R (2)
+--R 18 9 4 14 7 6 12 6 8 10 5
+--R - b x - 9180a b x - 185640a b x - 918918a b x
+--R +
+--R 10 8 4 12 6 3 14 4 2 16 2
+--R - 1575288a b x - 1021020a b x - 238680a b x - 16065a b x
+--R +
+--R 18
+--R - 136a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 3 15 8 5 13 7 7 11 6 9 9 5
+--R - 816a b x - 51408a b x - 477360a b x - 1361360a b x
+--R +
+--R 11 7 4 13 5 3 15 3 2 17
+--R - 1432080a b x - 565488a b x - 74256a b x - 2160a b x
+--R /
+--R 3 9 +-+
+--R 1224a x \|x
+--R Type: Expression(Integer)
+--E 850
+
+--S 851 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 7 2 13 6 4 11 5 6 9 4
+--R - 816b x - 51408a b x - 477360a b x - 1361360a b x
+--R +
+--R 8 7 3 10 5 2 12 3 14
+--R - 1432080a b x - 565488a b x - 74256a b x - 2160a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4
+--R - 9180a b x - 185640a b x - 918918a b x - 1575288a b x
+--R +
+--R 9 6 3 11 4 2 13 2 15
+--R - 1021020a b x - 238680a b x - 16065a b x - 136a
+--R /
+--R 9
+--R 1224x
+--R Type: Union(Expression(Integer),...)
+--E 851
+
+--S 852 of 1325
+m0:=a0-r0
+--R
+--R
+--R 18
+--R b
+--R (4) ------
+--R 3
+--R 1224a
+--R Type: Expression(Integer)
+--E 852
+
+--S 853 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 853
+
+)clear all
+
+--S 854 of 1325
+t0:=(a+b*sqrt(x))^15/x^11
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 11
+--R x
+--R Type: Expression(Integer)
+--E 854
+
+--S 855 of 1325
+r0:=-1/10*(a+b*sqrt(x))^16/(a*x^10)+2/95*b*(a+b*sqrt(x))^16/_
+ (a^2*x^(19/2))-1/285*b^2*(a+b*sqrt(x))^16/(a^3*x^9)+2/4845*_
+ b^3*(a+b*sqrt(x))^16/(a^4*x^(17/2))-1/38760*b^4*_
+ (a+b*sqrt(x))^16/(a^5*x^8)
+--R
+--R
+--R (2)
+--R 20 10 6 14 7 8 12 6 10 10 5
+--R - b x - 193800a b x - 4408950a b x - 23279256a b x
+--R +
+--R 12 8 4 14 6 3 16 4 2 18 2
+--R - 41570100a b x - 27713400a b x - 6613425a b x - 452200a b x
+--R +
+--R 20
+--R - 3876a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 5 15 8 7 13 7 9 11 6 11 9 5
+--R - 15504a b x - 1162800a b x - 11757200a b x - 35271600a b x
+--R +
+--R 13 7 4 15 5 3 17 3 2 19
+--R - 38372400a b x - 15519504a b x - 2074800a b x - 61200a b x
+--R /
+--R 5 10 +-+
+--R 38760a x \|x
+--R Type: Expression(Integer)
+--E 855
+
+--S 856 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 7 2 13 6 4 11 5 6 9 4
+--R - 15504b x - 1162800a b x - 11757200a b x - 35271600a b x
+--R +
+--R 8 7 3 10 5 2 12 3 14
+--R - 38372400a b x - 15519504a b x - 2074800a b x - 61200a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4
+--R - 193800a b x - 4408950a b x - 23279256a b x - 41570100a b x
+--R +
+--R 9 6 3 11 4 2 13 2 15
+--R - 27713400a b x - 6613425a b x - 452200a b x - 3876a
+--R /
+--R 10
+--R 38760x
+--R Type: Union(Expression(Integer),...)
+--E 856
+
+--S 857 of 1325
+m0:=a0-r0
+--R
+--R
+--R 20
+--R b
+--R (4) -------
+--R 5
+--R 38760a
+--R Type: Expression(Integer)
+--E 857
+
+--S 858 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 858
+
+)clear all
+
+--S 859 of 1325
+t0:=(a+b*sqrt(x))^15/x^12
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 12
+--R x
+--R Type: Expression(Integer)
+--E 859
+
+--S 860 of 1325
+r0:=-1/11*(a+b*sqrt(x))^16/(a*x^11)+2/77*b*(a+b*sqrt(x))^16/_
+ (a^2*x^(21/2))-1/154*b^2*(a+b*sqrt(x))^16/(a^3*x^10)+_
+ 2/1463*b^3*(a+b*sqrt(x))^16/(a^4*x^(19/2))-1/4389*b^4*_
+ (a+b*sqrt(x))^16/(a^5*x^9)+2/74613*b^5*(a+b*sqrt(x))^16/_
+ (a^6*x^(17/2))-1/596904*b^6*(a+b*sqrt(x))^16/(a^7*x^8)
+--R
+--R
+--R (2)
+--R 22 11 8 14 7 10 12 6 12 10 5
+--R - b x - 2238390a b x - 54318264a b x - 298750452a b x
+--R +
+--R 14 8 4 16 6 3 18 4 2
+--R - 548725320a b x - 373438065a b x - 90530440a b x
+--R +
+--R 20 2 22
+--R - 6267492a b x - 54264a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 7 15 8 9 13 7 11 11 6 13 9 5
+--R - 170544a b x - 13927760a b x - 148140720a b x - 459616080a b x
+--R +
+--R 15 7 4 17 5 3 19 3 2 21
+--R - 512143632a b x - 210882672a b x - 28588560a b x - 852720a b x
+--R /
+--R 7 11 +-+
+--R 596904a x \|x
+--R Type: Expression(Integer)
+--E 860
+
+--S 861 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 7 2 13 6 4 11 5 6 9 4
+--R - 170544b x - 13927760a b x - 148140720a b x - 459616080a b x
+--R +
+--R 8 7 3 10 5 2 12 3 14
+--R - 512143632a b x - 210882672a b x - 28588560a b x - 852720a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4
+--R - 2238390a b x - 54318264a b x - 298750452a b x - 548725320a b x
+--R +
+--R 9 6 3 11 4 2 13 2 15
+--R - 373438065a b x - 90530440a b x - 6267492a b x - 54264a
+--R /
+--R 11
+--R 596904x
+--R Type: Union(Expression(Integer),...)
+--E 861
+
+--S 862 of 1325
+m0:=a0-r0
+--R
+--R
+--R 22
+--R b
+--R (4) --------
+--R 7
+--R 596904a
+--R Type: Expression(Integer)
+--E 862
+
+--S 863 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 863
+
+)clear all
+
+--S 864 of 1325
+t0:=(a+b*sqrt(x))^15/x^13
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 13
+--R x
+--R Type: Expression(Integer)
+--E 864
+
+--S 865 of 1325
+r0:=-1/12*(a+b*sqrt(x))^16/(a*x^12)+2/69*b*(a+b*sqrt(x))^16/_
+ (a^2*x^(23/2))-7/759*b^2*(a+b*sqrt(x))^16/(a^3*x^11)+2/759*_
+ b^3*(a+b*sqrt(x))^16/(a^4*x^(21/2))-1/1518*b^4*(a+_
+ b*sqrt(x))^16/(a^5*x^10)+2/14421*b^5*(a+b*sqrt(x))^16/_
+ (a^6*x^(19/2))-1/43263*b^6*(a+b*sqrt(x))^16/(a^7*x^9)+_
+ 2/735471*b^7*(a+b*sqrt(x))^16/(a^8*x^(17/2))-1/5883768*_
+ b^8*(a+b*sqrt(x))^16/(a^9*x^8)
+--R
+--R
+--R (2)
+--R 24 12 10 14 7 12 12 6 14 10 5
+--R - b x - 17651304a b x - 446185740a b x - 2524136472a b x
+--R +
+--R 16 8 4 18 6 3 20 4 2
+--R - 4732755885a b x - 3272028760a b x - 803134332a b x
+--R +
+--R 22 2 24
+--R - 56163240a b x - 490314a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 9 15 8 11 13 7 13 11 6
+--R - 1307504a b x - 112326480a b x - 1235591280a b x
+--R +
+--R 15 9 5 17 7 4 19 5 3
+--R - 3926434512a b x - 4454358480a b x - 1859890032a b x
+--R +
+--R 21 3 2 23
+--R - 254963280a b x - 7674480a b x
+--R /
+--R 9 12 +-+
+--R 5883768a x \|x
+--R Type: Expression(Integer)
+--E 865
+
+--S 866 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 7 2 13 6 4 11 5
+--R - 1307504b x - 112326480a b x - 1235591280a b x
+--R +
+--R 6 9 4 8 7 3 10 5 2
+--R - 3926434512a b x - 4454358480a b x - 1859890032a b x
+--R +
+--R 12 3 14
+--R - 254963280a b x - 7674480a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5
+--R - 17651304a b x - 446185740a b x - 2524136472a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2 13 2
+--R - 4732755885a b x - 3272028760a b x - 803134332a b x - 56163240a b x
+--R +
+--R 15
+--R - 490314a
+--R /
+--R 12
+--R 5883768x
+--R Type: Union(Expression(Integer),...)
+--E 866
+
+--S 867 of 1325
+m0:=a0-r0
+--R
+--R
+--R 24
+--R b
+--R (4) ---------
+--R 9
+--R 5883768a
+--R Type: Expression(Integer)
+--E 867
+
+--S 868 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 868
+
+)clear all
+
+--S 869 of 1325
+t0:=(a+b*sqrt(x))^15/x^14
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 14
+--R x
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 1325
+r0:=-1/13*a^15/x^13-6/5*a^14*b/x^(25/2)-35/4*a^13*b^2/x^12-910/23*_
+ a^12*b^3/x^(23/2)-1365/11*a^11*b^4/x^11-286*a^10*b^5/x^(21/2)-_
+ 1001/2*a^9*b^6/x^10-12870/19*a^8*b^7/x^(19/2)-715*a^7*b^8/x^9-_
+ 10010/17*a^6*b^9/x^(17/2)-3003/8*a^5*b^10/x^8-182*a^4*b^11/_
+ x^(15/2)-65*a^3*b^12/x^7-210/13*a^2*b^13/x^(13/2)-5/2*a*b^14/_
+ x^6-2/11*b^15/x^(11/2)
+--R
+--R
+--R (2)
+--R 14 7 3 12 6 5 10 5
+--R - 106234700a b x - 2762102200a b x - 15951140205a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2
+--R - 30383124200a b x - 21268186940a b x - 5273104200a b x
+--R +
+--R 13 2 15
+--R - 371821450a b x - 3268760a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6 6 9 5
+--R - 7726160b x - 686439600a b x - 7733886160a b x - 25021396400a b x
+--R +
+--R 8 7 4 10 5 3 12 3 2
+--R - 28784012400a b x - 12153249680a b x - 1681279600a b x
+--R +
+--R 14
+--R - 50992656a b x
+--R /
+--R 13 +-+
+--R 42493880x \|x
+--R Type: Expression(Integer)
+--E 870
+
+--S 871 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 7 2 13 6 4 11 5
+--R - 7726160b x - 686439600a b x - 7733886160a b x
+--R +
+--R 6 9 4 8 7 3 10 5 2
+--R - 25021396400a b x - 28784012400a b x - 12153249680a b x
+--R +
+--R 12 3 14
+--R - 1681279600a b x - 50992656a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5
+--R - 106234700a b x - 2762102200a b x - 15951140205a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2
+--R - 30383124200a b x - 21268186940a b x - 5273104200a b x
+--R +
+--R 13 2 15
+--R - 371821450a b x - 3268760a
+--R /
+--R 13
+--R 42493880x
+--R Type: Union(Expression(Integer),...)
+--E 871
+
+--S 872 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 872
+
+--S 873 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 873
+
+)clear all
+
+--S 874 of 1325
+t0:=(a+b*sqrt(x))^15/x^15
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 15
+--R x
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 1325
+r0:=-1/14*a^15/x^14-10/9*a^14*b/x^(27/2)-105/13*a^13*b^2/x^13-182/5*_
+ a^12*b^3/x^(25/2)-455/4*a^11*b^4/x^12-6006/23*a^10*b^5/x^(23/2)-_
+ 455*a^9*b^6/x^11-4290/7*a^8*b^7/x^(21/2)-1287/2*a^7*b^8/x^10-_
+ 10010/19*a^6*b^9/x^(19/2)-1001/3*a^5*b^10/x^9-2730/17*a^4*_
+ b^11/x^(17/2)-455/8*a^3*b^12/x^8-14*a^2*b^13/x^(15/2)-15/7*_
+ a*b^14/x^7-2/13*b^15/x^(13/2)
+--R
+--R
+--R (2)
+--R 14 7 3 12 6 5 10 5
+--R - 521515800a b x - 13841898525a b x - 81205804680a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2
+--R - 156611194740a b x - 110735188200a b x - 27683797050a b x
+--R +
+--R 13 2 15
+--R - 1965713400a b x - 17383860a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6
+--R - 37442160b x - 3407236560a b x - 39083007600a b x
+--R +
+--R 6 9 5 8 7 4 10 5 3
+--R - 128219691600a b x - 149153518800a b x - 63552368880a b x
+--R +
+--R 12 3 2 14
+--R - 8858815056a b x - 270415600a b x
+--R /
+--R 14 +-+
+--R 243374040x \|x
+--R Type: Expression(Integer)
+--E 875
+
+--S 876 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 7 2 13 6 4 11 5
+--R - 37442160b x - 3407236560a b x - 39083007600a b x
+--R +
+--R 6 9 4 8 7 3 10 5 2
+--R - 128219691600a b x - 149153518800a b x - 63552368880a b x
+--R +
+--R 12 3 14
+--R - 8858815056a b x - 270415600a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5
+--R - 521515800a b x - 13841898525a b x - 81205804680a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2
+--R - 156611194740a b x - 110735188200a b x - 27683797050a b x
+--R +
+--R 13 2 15
+--R - 1965713400a b x - 17383860a
+--R /
+--R 14
+--R 243374040x
+--R Type: Union(Expression(Integer),...)
+--E 876
+
+--S 877 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 877
+
+--S 878 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 878
+
+)clear all
+
+--S 879 of 1325
+t0:=(a+b*sqrt(x))^15/x^16
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 16
+--R x
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 1325
+r0:=-1/15*a^15/x^15-30/29*a^14*b/x^(29/2)-15/2*a^13*b^2/x^14-910/27*_
+ a^12*b^3/x^(27/2)-105*a^11*b^4/x^13-6006/25*a^10*b^5/x^(25/2)-_
+ 5005/12*a^9*b^6/x^12-12870/23*a^8*b^7/x^(23/2)-585*a^7*b^8/x^11-_
+ 1430/3*a^6*b^9/x^(21/2)-3003/10*a^5*b^10/x^10-2730/19*a^4*b^11/_
+ x^(19/2)-455/9*a^3*b^12/x^9-210/17*a^2*b^13/x^(17/2)-15/8*a*_
+ b^14/x^8-2/15*b^15/x^(15/2)
+--R
+--R
+--R (2)
+--R 14 7 3 12 6 5 10 5
+--R - 2181340125a b x - 58815393000a b x - 349363434420a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2
+--R - 680578119000a b x - 485226992250a b x - 122155047000a b x
+--R +
+--R 13 2 15
+--R - 8725360500a b x - 77558760a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6
+--R - 155117520b x - 14371182000a b x - 167159538000a b x
+--R +
+--R 6 9 5 8 7 4 10 5 3
+--R - 554545134000a b x - 650987766000a b x - 279490747536a b x
+--R +
+--R 12 3 2 14
+--R - 39210262000a b x - 1203498000a b x
+--R /
+--R 15 +-+
+--R 1163381400x \|x
+--R Type: Expression(Integer)
+--E 880
+
+--S 881 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 7 2 13 6 4 11 5
+--R - 155117520b x - 14371182000a b x - 167159538000a b x
+--R +
+--R 6 9 4 8 7 3 10 5 2
+--R - 554545134000a b x - 650987766000a b x - 279490747536a b x
+--R +
+--R 12 3 14
+--R - 39210262000a b x - 1203498000a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5
+--R - 2181340125a b x - 58815393000a b x - 349363434420a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2
+--R - 680578119000a b x - 485226992250a b x - 122155047000a b x
+--R +
+--R 13 2 15
+--R - 8725360500a b x - 77558760a
+--R /
+--R 15
+--R 1163381400x
+--R Type: Union(Expression(Integer),...)
+--E 881
+
+--S 882 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 882
+
+--S 883 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 883
+
+)clear all
+
+--S 884 of 1325
+t0:=(a+b*sqrt(x))^15/x^17
+--R
+--R
+--R (1)
+--R 15 7 2 13 6 4 11 5 6 9 4 8 7 3
+--R b x + 105a b x + 1365a b x + 5005a b x + 6435a b x
+--R +
+--R 10 5 2 12 3 14
+--R 3003a b x + 455a b x + 15a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5 7 8 4 9 6 3
+--R 15a b x + 455a b x + 3003a b x + 6435a b x + 5005a b x
+--R +
+--R 11 4 2 13 2 15
+--R 1365a b x + 105a b x + a
+--R /
+--R 17
+--R x
+--R Type: Expression(Integer)
+--E 884
+
+--S 885 of 1325
+r0:=-1/16*a^15/x^16-30/31*a^14*b/x^(31/2)-7*a^13*b^2/x^15-910/29*a^12*_
+ b^3/x^(29/2)-195/2*a^11*b^4/x^14-2002/9*a^10*b^5/x^(27/2)-385*a^9*_
+ b^6/x^13-2574/5*a^8*b^7/x^(25/2)-2145/4*a^7*b^8/x^12-10010/23*_
+ a^6*b^9/x^(23/2)-273*a^5*b^10/x^11-130*a^4*b^11/x^(21/2)-91/2*_
+ a^3*b^12/x^10-210/19*a^2*b^13/x^(19/2)-5/3*a*b^14/x^9-2/17*b^15/x^(17/2)
+--R
+--R
+--R (2)
+--R 14 7 3 12 6 5 10 5
+--R - 8014405200a b x - 218793261960a b x - 1312759571760a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2
+--R - 2578634873100a b x - 1851327601200a b x - 468842704200a b x
+--R +
+--R 13 2 15
+--R - 33660501840a b x - 300540195a
+--R *
+--R +-+
+--R \|x
+--R +
+--R 15 8 2 13 7 4 11 6
+--R - 565722720b x - 53148160800a b x - 625123605600a b x
+--R +
+--R 6 9 5 8 7 4 10 5 3
+--R - 2092805114400a b x - 2475489478176a b x - 1069655947360a b x
+--R +
+--R 12 3 2 14
+--R - 150891904800a b x - 4653525600a b x
+--R /
+--R 16 +-+
+--R 4808643120x \|x
+--R Type: Expression(Integer)
+--E 885
+
+--S 886 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 15 7 2 13 6 4 11 5
+--R - 565722720b x - 53148160800a b x - 625123605600a b x
+--R +
+--R 6 9 4 8 7 3 10 5 2
+--R - 2092805114400a b x - 2475489478176a b x - 1069655947360a b x
+--R +
+--R 12 3 14
+--R - 150891904800a b x - 4653525600a b
+--R *
+--R +-+
+--R \|x
+--R +
+--R 14 7 3 12 6 5 10 5
+--R - 8014405200a b x - 218793261960a b x - 1312759571760a b x
+--R +
+--R 7 8 4 9 6 3 11 4 2
+--R - 2578634873100a b x - 1851327601200a b x - 468842704200a b x
+--R +
+--R 13 2 15
+--R - 33660501840a b x - 300540195a
+--R /
+--R 16
+--R 4808643120x
+--R Type: Union(Expression(Integer),...)
+--E 886
+
+--S 887 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 887
+
+--S 888 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 888
+
+)clear all
+
+--S 889 of 1325
+t0:=x^3/(a+b*sqrt(x))
+--R
+--R
+--R 3
+--R x
+--R (1) ---------
+--R +-+
+--R b\|x + a
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 1325
+r0:=-a^5*x/b^6+2/3*a^4*x^(3/2)/b^5-1/2*a^3*x^2/b^4+2/5*a^2*x^(5/2)/b^3-_
+ 1/3*a*x^3/b^2+2/7*x^(7/2)/b-2*a^7*log(a+b*sqrt(x))/b^8+2*a^6*sqrt(x)/b^7
+--R
+--R
+--R (2)
+--R 7 +-+ 7 3 2 5 2 4 3 6 +-+
+--R - 420a log(b\|x + a) + (60b x + 84a b x + 140a b x + 420a b)\|x
+--R +
+--R 6 3 3 4 2 5 2
+--R - 70a b x - 105a b x - 210a b x
+--R /
+--R 8
+--R 210b
+--R Type: Expression(Integer)
+--E 890
+
+--S 891 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 +-+ 7 3 2 5 2 4 3 6 +-+
+--R - 420a log(b\|x + a) + (60b x + 84a b x + 140a b x + 420a b)\|x
+--R +
+--R 6 3 3 4 2 5 2
+--R - 70a b x - 105a b x - 210a b x
+--R /
+--R 8
+--R 210b
+--R Type: Union(Expression(Integer),...)
+--E 891
+
+--S 892 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 892
+
+--S 893 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 893
+
+)clear all
+
+--S 894 of 1325
+t0:=x^2/(a+b*sqrt(x))
+--R
+--R
+--R 2
+--R x
+--R (1) ---------
+--R +-+
+--R b\|x + a
+--R Type: Expression(Integer)
+--E 894
+
+--S 895 of 1325
+r0:=-a^3*x/b^4+2/3*a^2*x^(3/2)/b^3-1/2*a*x^2/b^2+2/5*x^(5/2)/b-_
+ 2*a^5*log(a+b*sqrt(x))/b^6+2*a^4*sqrt(x)/b^5
+--R
+--R
+--R (2)
+--R 5 +-+ 5 2 2 3 4 +-+ 4 2 3 2
+--R - 60a log(b\|x + a) + (12b x + 20a b x + 60a b)\|x - 15a b x - 30a b x
+--R --------------------------------------------------------------------------
+--R 6
+--R 30b
+--R Type: Expression(Integer)
+--E 895
+
+--S 896 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 +-+ 5 2 2 3 4 +-+ 4 2 3 2
+--R - 60a log(b\|x + a) + (12b x + 20a b x + 60a b)\|x - 15a b x - 30a b x
+--R --------------------------------------------------------------------------
+--R 6
+--R 30b
+--R Type: Union(Expression(Integer),...)
+--E 896
+
+--S 897 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 897
+
+--S 898 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 898
+
+)clear all
+
+--S 899 of 1325
+t0:=x/(a+b*sqrt(x))
+--R
+--R
+--R x
+--R (1) ---------
+--R +-+
+--R b\|x + a
+--R Type: Expression(Integer)
+--E 899
+
+--S 900 of 1325
+r0:=-a*x/b^2+2/3*x^(3/2)/b-2*a^3*log(a+b*sqrt(x))/b^4+2*a^2*sqrt(x)/b^3
+--R
+--R
+--R 3 +-+ 3 2 +-+ 2
+--R - 6a log(b\|x + a) + (2b x + 6a b)\|x - 3a b x
+--R (2) ------------------------------------------------
+--R 4
+--R 3b
+--R Type: Expression(Integer)
+--E 900
+
+--S 901 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 3 +-+ 3 2 +-+ 2
+--R - 6a log(b\|x + a) + (2b x + 6a b)\|x - 3a b x
+--R (3) ------------------------------------------------
+--R 4
+--R 3b
+--R Type: Union(Expression(Integer),...)
+--E 901
+
+--S 902 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 902
+
+--S 903 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 903
+
+)clear all
+
+--S 904 of 1325
+t0:=1/(a+b*sqrt(x))
+--R
+--R
+--R 1
+--R (1) ---------
+--R +-+
+--R b\|x + a
+--R Type: Expression(Integer)
+--E 904
+
+--S 905 of 1325
+r0:=-2*a*log(a+b*sqrt(x))/b^2+2*sqrt(x)/b
+--R
+--R
+--R +-+ +-+
+--R - 2a log(b\|x + a) + 2b\|x
+--R (2) ----------------------------
+--R 2
+--R b
+--R Type: Expression(Integer)
+--E 905
+
+--S 906 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +-+
+--R - 2a log(b\|x + a) + 2b\|x
+--R (3) ----------------------------
+--R 2
+--R b
+--R Type: Union(Expression(Integer),...)
+--E 906
+
+--S 907 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 907
+
+--S 908 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 908
+
+)clear all
+
+--S 909 of 1325
+t0:=1/(x*(a+b*sqrt(x)))
+--R
+--R
+--R 1
+--R (1) -------------
+--R +-+
+--R b x\|x + a x
+--R Type: Expression(Integer)
+--E 909
+
+--S 910 of 1325
+r0:=log(x)/a-2*log(a+b*sqrt(x))/a
+--R
+--R
+--R +-+
+--R - 2log(b\|x + a) + log(x)
+--R (2) --------------------------
+--R a
+--R Type: Expression(Integer)
+--E 910
+
+--S 911 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +-+
+--R - 2log(b\|x + a) + 2log(\|x )
+--R (3) ------------------------------
+--R a
+--R Type: Union(Expression(Integer),...)
+--E 911
+
+--S 912 of 1325
+m0:=a0-r0
+--R
+--R
+--R +-+
+--R 2log(\|x ) - log(x)
+--R (4) -------------------
+--R a
+--R Type: Expression(Integer)
+--E 912
+
+--S 913 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 913
+
+)clear all
+
+--S 914 of 1325
+t0:=1/(x*(2+b*sqrt(x)))
+--R
+--R
+--R 1
+--R (1) ------------
+--R +-+
+--R b x\|x + 2x
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 1325
+r0:=-2*atanh(1+b*sqrt(x))
+--R
+--R
+--R +-+
+--R (2) - 2atanh(b\|x + 1)
+--R Type: Expression(Integer)
+--E 915
+
+--S 916 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +-+
+--R (3) - log(b\|x + 2) + log(\|x )
+--R Type: Union(Expression(Integer),...)
+--E 916
+
+--S 917 of 1325
+m0:=a0-r0
+--R
+--R
+--R +-+ +-+ +-+
+--R (4) - log(b\|x + 2) + log(\|x ) + 2atanh(b\|x + 1)
+--R Type: Expression(Integer)
+--E 917
+
+--S 918 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 918
+
+)clear all
+
+--S 919 of 1325
+t0:=1/(x^2*(a+b*sqrt(x)))
+--R
+--R
+--R 1
+--R (1) ---------------
+--R 2 +-+ 2
+--R b x \|x + a x
+--R Type: Expression(Integer)
+--E 919
+
+--S 920 of 1325
+r0:=(-1)/(a*x)+b^2*log(x)/a^3-2*b^2*log(a+b*sqrt(x))/a^3+2*b/(a^2*sqrt(x))
+--R
+--R
+--R 2 +-+ +-+ 2 2 +-+
+--R - 2b x\|x log(b\|x + a) + (b x log(x) - a )\|x + 2a b x
+--R (2) ---------------------------------------------------------
+--R 3 +-+
+--R a x\|x
+--R Type: Expression(Integer)
+--E 920
+
+--S 921 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+ 2 +-+ +-+ 2
+--R - 2b x log(b\|x + a) + 2b x log(\|x ) + 2a b\|x - a
+--R (3) ------------------------------------------------------
+--R 3
+--R a x
+--R Type: Union(Expression(Integer),...)
+--E 921
+
+--S 922 of 1325
+m0:=a0-r0
+--R
+--R
+--R 2 +-+ 2
+--R 2b log(\|x ) - b log(x)
+--R (4) -----------------------
+--R 3
+--R a
+--R Type: Expression(Integer)
+--E 922
+
+--S 923 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 923
+
+)clear all
+
+--S 924 of 1325
+t0:=1/(x^3*(a+b*sqrt(x)))
+--R
+--R
+--R 1
+--R (1) ---------------
+--R 3 +-+ 3
+--R b x \|x + a x
+--R Type: Expression(Integer)
+--E 924
+
+--S 925 of 1325
+r0:=(-1/2)/(a*x^2)+2/3*b/(a^2*x^(3/2))-b^2/(a^3*x)+b^4*log(x)/a^5-_
+ 2*b^4*log(a+b*sqrt(x))/a^5+2*b^3/(a^4*sqrt(x))
+--R
+--R
+--R (2)
+--R 4 2 +-+ +-+ 4 2 2 2 4 +-+ 3 2
+--R - 12b x \|x log(b\|x + a) + (6b x log(x) - 6a b x - 3a )\|x + 12a b x
+--R +
+--R 3
+--R 4a b x
+--R /
+--R 5 2 +-+
+--R 6a x \|x
+--R Type: Expression(Integer)
+--E 925
+
+--S 926 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 +-+ 4 2 +-+ 3 3 +-+ 2 2
+--R - 12b x log(b\|x + a) + 12b x log(\|x ) + (12a b x + 4a b)\|x - 6a b x
+--R +
+--R 4
+--R - 3a
+--R /
+--R 5 2
+--R 6a x
+--R Type: Union(Expression(Integer),...)
+--E 926
+
+--S 927 of 1325
+m0:=a0-r0
+--R
+--R
+--R 4 +-+ 4
+--R 2b log(\|x ) - b log(x)
+--R (4) -----------------------
+--R 5
+--R a
+--R Type: Expression(Integer)
+--E 927
+
+--S 928 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 928
+
+)clear all
+
+--S 929 of 1325
+t0:=1/(x^4*(a+b*sqrt(x)))
+--R
+--R
+--R 1
+--R (1) ---------------
+--R 4 +-+ 4
+--R b x \|x + a x
+--R Type: Expression(Integer)
+--E 929
+
+--S 930 of 1325
+r0:=(-1/3)/(a*x^3)+2/5*b/(a^2*x^(5/2))-1/2*b^2/(a^3*x^2)+2/3*_
+ b^3/(a^4*x^(3/2))-b^4/(a^5*x)+b^6*log(x)/a^7-2*b^6*log(a+b*_
+ sqrt(x))/a^7+2*b^5/(a^6*sqrt(x))
+--R
+--R
+--R (2)
+--R 6 3 +-+ +-+
+--R - 60b x \|x log(b\|x + a)
+--R +
+--R 6 3 2 4 2 4 2 6 +-+ 5 3 3 3 2
+--R (30b x log(x) - 30a b x - 15a b x - 10a )\|x + 60a b x + 20a b x
+--R +
+--R 5
+--R 12a b x
+--R /
+--R 7 3 +-+
+--R 30a x \|x
+--R Type: Expression(Integer)
+--E 930
+
+--S 931 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 3 +-+ 6 3 +-+
+--R - 60b x log(b\|x + a) + 60b x log(\|x )
+--R +
+--R 5 2 3 3 5 +-+ 2 4 2 4 2 6
+--R (60a b x + 20a b x + 12a b)\|x - 30a b x - 15a b x - 10a
+--R /
+--R 7 3
+--R 30a x
+--R Type: Union(Expression(Integer),...)
+--E 931
+
+--S 932 of 1325
+m0:=a0-r0
+--R
+--R
+--R 6 +-+ 6
+--R 2b log(\|x ) - b log(x)
+--R (4) -----------------------
+--R 7
+--R a
+--R Type: Expression(Integer)
+--E 932
+
+--S 933 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 933
+
+)clear all
+
+--S 934 of 1325
+t0:=x^3/(a+b*sqrt(x))^2
+--R
+--R
+--R 3
+--R x
+--R (1) -------------------
+--R +-+ 2 2
+--R 2a b\|x + b x + a
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 1325
+r0:=5*a^4*x/b^6-8/3*a^3*x^(3/2)/b^5+3/2*a^2*x^2/b^4-4/5*a*x^(5/2)/b^3+_
+ 1/3*x^3/b^2+14*a^6*log(a+b*sqrt(x))/b^8-12*a^5*sqrt(x)/b^7+_
+ 2*a^7/(b^8*(a+b*sqrt(x)))
+--R
+--R
+--R (2)
+--R 6 +-+ 7 +-+
+--R (420a b\|x + 420a )log(b\|x + a)
+--R +
+--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2
+--R (10b x + 21a b x + 70a b x - 360a b)\|x - 14a b x - 35a b x
+--R +
+--R 5 2 7
+--R - 210a b x + 60a
+--R /
+--R 9 +-+ 8
+--R 30b \|x + 30a b
+--R Type: Expression(Integer)
+--E 935
+
+--S 936 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 +-+ 7 +-+
+--R (420a b\|x + 420a )log(b\|x + a)
+--R +
+--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2
+--R (10b x + 21a b x + 70a b x - 360a b)\|x - 14a b x - 35a b x
+--R +
+--R 5 2 7
+--R - 210a b x + 60a
+--R /
+--R 9 +-+ 8
+--R 30b \|x + 30a b
+--R Type: Union(Expression(Integer),...)
+--E 936
+
+--S 937 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 937
+
+--S 938 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 938
+
+)clear all
+
+--S 939 of 1325
+t0:=x^2/(a+b*sqrt(x))^2
+--R
+--R
+--R 2
+--R x
+--R (1) -------------------
+--R +-+ 2 2
+--R 2a b\|x + b x + a
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 1325
+r0:=3*a^2*x/b^4-4/3*a*x^(3/2)/b^3+1/2*x^2/b^2+10*a^4*log(a+b*sqrt(x))/b^6-_
+ 8*a^3*sqrt(x)/b^5+2*a^5/(b^6*(a+b*sqrt(x)))
+--R
+--R
+--R (2)
+--R 4 +-+ 5 +-+ 5 2 2 3 4 +-+
+--R (60a b\|x + 60a )log(b\|x + a) + (3b x + 10a b x - 48a b)\|x
+--R +
+--R 4 2 3 2 5
+--R - 5a b x - 30a b x + 12a
+--R /
+--R 7 +-+ 6
+--R 6b \|x + 6a b
+--R Type: Expression(Integer)
+--E 940
+
+--S 941 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 +-+ 5 +-+ 5 2 2 3 4 +-+
+--R (60a b\|x + 60a )log(b\|x + a) + (3b x + 10a b x - 48a b)\|x
+--R +
+--R 4 2 3 2 5
+--R - 5a b x - 30a b x + 12a
+--R /
+--R 7 +-+ 6
+--R 6b \|x + 6a b
+--R Type: Union(Expression(Integer),...)
+--E 941
+
+--S 942 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 942
+
+--S 943 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 943
+
+)clear all
+
+--S 944 of 1325
+t0:=x/(a+b*sqrt(x))^2
+--R
+--R
+--R x
+--R (1) -------------------
+--R +-+ 2 2
+--R 2a b\|x + b x + a
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 1325
+r0:=x/b^2+6*a^2*log(a+b*sqrt(x))/b^4-4*a*sqrt(x)/b^3+2*a^3/(b^4*(a+b*sqrt(x)))
+--R
+--R
+--R 2 +-+ 3 +-+ 3 2 +-+ 2 3
+--R (6a b\|x + 6a )log(b\|x + a) + (b x - 4a b)\|x - 3a b x + 2a
+--R (2) ----------------------------------------------------------------
+--R 5 +-+ 4
+--R b \|x + a b
+--R Type: Expression(Integer)
+--E 945
+
+--S 946 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+ 3 +-+ 3 2 +-+ 2 3
+--R (6a b\|x + 6a )log(b\|x + a) + (b x - 4a b)\|x - 3a b x + 2a
+--R (3) ----------------------------------------------------------------
+--R 5 +-+ 4
+--R b \|x + a b
+--R Type: Union(Expression(Integer),...)
+--E 946
+
+--S 947 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 947
+
+--S 948 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 948
+
+)clear all
+
+--S 949 of 1325
+t0:=1/(a+b*sqrt(x))^2
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +-+ 2 2
+--R 2a b\|x + b x + a
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 1325
+r0:=2*log(a+b*sqrt(x))/b^2+2*a/(b^2*(a+b*sqrt(x)))
+--R
+--R
+--R +-+ +-+
+--R (2b\|x + 2a)log(b\|x + a) + 2a
+--R (2) --------------------------------
+--R 3 +-+ 2
+--R b \|x + a b
+--R Type: Expression(Integer)
+--E 950
+
+--S 951 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +-+
+--R (2b\|x + 2a)log(b\|x + a) + 2a
+--R (3) --------------------------------
+--R 3 +-+ 2
+--R b \|x + a b
+--R Type: Union(Expression(Integer),...)
+--E 951
+
+--S 952 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 952
+
+--S 953 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 953
+
+)clear all
+
+--S 954 of 1325
+t0:=1/(x*(a+b*sqrt(x))^2)
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +-+ 2 2 2
+--R 2a b x\|x + b x + a x
+--R Type: Expression(Integer)
+--E 954
+
+--S 955 of 1325
+r0:=log(x)/a^2-2*log(a+b*sqrt(x))/a^2+2/(a*(a+b*sqrt(x)))
+--R
+--R
+--R +-+ +-+ +-+
+--R (- 2b\|x - 2a)log(b\|x + a) + b log(x)\|x + a log(x) + 2a
+--R (2) ------------------------------------------------------------
+--R 2 +-+ 3
+--R a b\|x + a
+--R Type: Expression(Integer)
+--E 955
+
+--S 956 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R +-+ +-+ +-+ +-+
+--R (- 2b\|x - 2a)log(b\|x + a) + (2b\|x + 2a)log(\|x ) + 2a
+--R (3) -----------------------------------------------------------
+--R 2 +-+ 3
+--R a b\|x + a
+--R Type: Union(Expression(Integer),...)
+--E 956
+
+--S 957 of 1325
+m0:=a0-r0
+--R
+--R
+--R +-+
+--R 2log(\|x ) - log(x)
+--R (4) -------------------
+--R 2
+--R a
+--R Type: Expression(Integer)
+--E 957
+
+--S 958 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 958
+
+)clear all
+
+--S 959 of 1325
+t0:=1/(x^2*(a+b*sqrt(x))^2)
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R 2 +-+ 2 3 2 2
+--R 2a b x \|x + b x + a x
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 1325
+r0:=(-3)/(a^2*x)+3*b^2*log(x)/a^4-6*b^2*log(a+b*sqrt(x))/a^4+_
+ 6*b/(a^3*sqrt(x))+2/(a*x*(a+b*sqrt(x)))
+--R
+--R
+--R (2)
+--R 2 +-+ 3 2 +-+ 2 2 3 +-+
+--R (- 6a b x\|x - 6b x )log(b\|x + a) + (3a b x log(x) + 6a b x - a )\|x
+--R +
+--R 3 2 2
+--R 3b x log(x) + 3a b x
+--R /
+--R 5 +-+ 4 2
+--R a x\|x + a b x
+--R Type: Expression(Integer)
+--E 960
+
+--S 961 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 +-+ 2 +-+ 3 +-+ 2 +-+
+--R (- 6b x\|x - 6a b x)log(b\|x + a) + (6b x\|x + 6a b x)log(\|x )
+--R +
+--R 2 +-+ 2 3
+--R 3a b\|x + 6a b x - a
+--R /
+--R 4 +-+ 5
+--R a b x\|x + a x
+--R Type: Union(Expression(Integer),...)
+--E 961
+
+--S 962 of 1325
+m0:=a0-r0
+--R
+--R
+--R 2 +-+ 2
+--R 6b log(\|x ) - 3b log(x)
+--R (4) ------------------------
+--R 4
+--R a
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 963
+
+)clear all
+
+--S 964 of 1325
+t0:=1/(x^3*(a+b*sqrt(x))^2)
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R 3 +-+ 2 4 2 3
+--R 2a b x \|x + b x + a x
+--R Type: Expression(Integer)
+--E 964
+
+--S 965 of 1325
+r0:=(-5/2)/(a^2*x^2)+10/3*b/(a^3*x^(3/2))-5*b^2/(a^4*x)+_
+ 5*b^4*log(x)/a^6-10*b^4*log(a+b*sqrt(x))/a^6+10*b^3/(a^5*_
+ sqrt(x))+2/(a*x^2*(a+b*sqrt(x)))
+--R
+--R
+--R (2)
+--R 4 2 +-+ 5 3 +-+
+--R (- 60a b x \|x - 60b x )log(b\|x + a)
+--R +
+--R 4 2 4 2 3 2 5 +-+ 5 3 2 3 2
+--R (30a b x log(x) + 60a b x - 10a b x - 3a )\|x + 30b x log(x) + 30a b x
+--R +
+--R 4
+--R 5a b x
+--R /
+--R 7 2 +-+ 6 3
+--R 6a x \|x + 6a b x
+--R Type: Expression(Integer)
+--E 965
+
+--S 966 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 2 +-+ 4 2 +-+
+--R (- 60b x \|x - 60a b x )log(b\|x + a)
+--R +
+--R 5 2 +-+ 4 2 +-+ 2 3 4 +-+ 4 2
+--R (60b x \|x + 60a b x )log(\|x ) + (30a b x + 5a b)\|x + 60a b x
+--R +
+--R 3 2 5
+--R - 10a b x - 3a
+--R /
+--R 6 2 +-+ 7 2
+--R 6a b x \|x + 6a x
+--R Type: Union(Expression(Integer),...)
+--E 966
+
+--S 967 of 1325
+m0:=a0-r0
+--R
+--R
+--R 4 +-+ 4
+--R 10b log(\|x ) - 5b log(x)
+--R (4) -------------------------
+--R 6
+--R a
+--R Type: Expression(Integer)
+--E 967
+
+--S 968 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 968
+
+)clear all
+
+--S 969 of 1325
+t0:=1/(x^4*(a+b*sqrt(x))^2)
+--R
+--R
+--R 1
+--R (1) -------------------------
+--R 4 +-+ 2 5 2 4
+--R 2a b x \|x + b x + a x
+--R Type: Expression(Integer)
+--E 969
+
+--S 970 of 1325
+r0:=(-7/3)/(a^2*x^3)+14/5*b/(a^3*x^(5/2))-7/2*b^2/(a^4*x^2)+_
+ 14/3*b^3/(a^5*x^(3/2))-7*b^4/(a^6*x)+7*b^6*log(x)/a^8-_
+ 14*b^6*log(a+b*sqrt(x))/a^8+14*b^5/(a^7*sqrt(x))+2/(a*x^3*(a+b*sqrt(x)))
+--R
+--R
+--R (2)
+--R 6 3 +-+ 7 4 +-+
+--R (- 420a b x \|x - 420b x )log(b\|x + a)
+--R +
+--R 6 3 6 3 3 4 2 5 2 7 +-+
+--R (210a b x log(x) + 420a b x - 70a b x - 21a b x - 10a )\|x
+--R +
+--R 7 4 2 5 3 4 3 2 6
+--R 210b x log(x) + 210a b x + 35a b x + 14a b x
+--R /
+--R 9 3 +-+ 8 4
+--R 30a x \|x + 30a b x
+--R Type: Expression(Integer)
+--E 970
+
+--S 971 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 7 3 +-+ 6 3 +-+
+--R (- 420b x \|x - 420a b x )log(b\|x + a)
+--R +
+--R 7 3 +-+ 6 3 +-+ 2 5 2 4 3 6 +-+
+--R (420b x \|x + 420a b x )log(\|x ) + (210a b x + 35a b x + 14a b)\|x
+--R +
+--R 6 3 3 4 2 5 2 7
+--R 420a b x - 70a b x - 21a b x - 10a
+--R /
+--R 8 3 +-+ 9 3
+--R 30a b x \|x + 30a x
+--R Type: Union(Expression(Integer),...)
+--E 971
+
+--S 972 of 1325
+m0:=a0-r0
+--R
+--R
+--R 6 +-+ 6
+--R 14b log(\|x ) - 7b log(x)
+--R (4) -------------------------
+--R 8
+--R a
+--R Type: Expression(Integer)
+--E 972
+
+--S 973 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 973
+
+)clear all
+
+--S 974 of 1325
+t0:=x^3/(a+b*sqrt(x))^3
+--R
+--R
+--R 3
+--R x
+--R (1) ------------------------------
+--R 3 2 +-+ 2 3
+--R (b x + 3a b)\|x + 3a b x + a
+--R Type: Expression(Integer)
+--E 974
+
+--S 975 of 1325
+r0:=-10*a^3*x/b^6+4*a^2*x^(3/2)/b^5-3/2*a*x^2/b^4+2/5*x^(5/2)/b^3-_
+ 42*a^5*log(a+b*sqrt(x))/b^8+30*a^4*sqrt(x)/b^7+_
+ a^7/(b^8*(a+b*sqrt(x))^2)-14*a^6/(b^8*(a+b*sqrt(x)))
+--R
+--R
+--R (2)
+--R 5 3 7 +-+ 6 2 8 +-+
+--R ((- 420a b x - 1260a b)\|x - 1260a b x - 420a )log(b\|x + a)
+--R +
+--R 7 3 3 5 2 5 3 7 +-+ 8 4 2 6 3
+--R (- 3a b x - 21a b x + 640a b x + 30a b)\|x + 4b x + 7a b x
+--R +
+--R 4 4 2 6 2 8
+--R 105a b x + 660a b x - 130a
+--R /
+--R 11 2 9 +-+ 10 3 8
+--R (10b x + 30a b )\|x + 30a b x + 10a b
+--R Type: Expression(Integer)
+--E 975
+
+--S 976 of 1325
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 6 +-+ 5 2 7 +-+
+--R (- 840a b\|x - 420a b x - 420a )log(b\|x + a)
+--R +
+--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2
+--R (4b x + 14a b x + 140a b x + 160a b)\|x - 7a b x - 35a b x
+--R +
+--R 5 2 7
+--R 500a b x - 130a
+--R /
+--R 9 +-+ 10 2 8
+--R 20a b \|x + 10b x + 10a b
+--R Type: Union(Expression(Integer),...)
+--E 976
+
+--S 977 of 1325
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 977
+
+--S 978 of 1325
+d0:=D(m0,x)
+--R
+--R
+--R