$SPAD/src/input richder17.input

Albert Rich and Timothy Daly

December 3, 2016

Abstract

x^m (d+e x^n)^q (a+b x^n+c x^(2n))^p

Contents

2

— * —

)set break resume
)sys rm -f richder17.output
)spool richder17.output
)set message test on
)set message auto off
)clear all
--S 1 of 381
t0:=x^4*(d+e*x^3)/(a+b*x^3+c*x^6)
--E 1
--S 2 of 381
r0:=1/2*e*x^2/c-1/3*log(2^(1/3)*c^(1/3)*x+(b-sqrt(b^2-4*a*c))^(1/3))*_
   (c*d-b*e+(-b*c*d+b^2*e-2*a*c*e)/sqrt(b^2-4*a*c))/(2^(2/3)*c^(5/3)*_
   (b-sqrt(b^2-4*a*c))^(1/3))+1/6*log(2^(2/3)*c^(2/3)*x^2-2^(1/3)*_
   c^(1/3)*x*(b-sqrt(b^2-4*a*c))^(1/3)+(b-sqrt(b^2-4*a*c))^(2/3))*_
   (c*d-b*e+(-b*c*d+b^2*e-2*a*c*e)/sqrt(b^2-4*a*c))/(2^(2/3)*c^(5/3)*_
   (b-sqrt(b^2-4*a*c))^(1/3))-atan((-4*c^(1/3)*x+2^(2/3)*(b-_
   sqrt(b^2-4*a*c))^(1/3))/(2^(2/3)*sqrt(3)*(b-sqrt(b^2-4*a*c))^(1/3)))*_
   (c*d-b*e+(-b*c*d+b^2*e-2*a*c*e)/sqrt(b^2-4*a*c))/(2^(2/3)*c^(5/3)*_
   sqrt(3)*(b-sqrt(b^2-4*a*c))^(1/3))-1/3*log(2^(1/3)*c^(1/3)*x+_
   (b+sqrt(b^2-4*a*c))^(1/3))*(c*d-b*e+(b*c*d-b^2*e+2*a*c*e)/_
   sqrt(b^2-4*a*c))/(2^(2/3)*c^(5/3)*(b+sqrt(b^2-4*a*c))^(1/3))+_
   1/6*log(2^(2/3)*c^(2/3)*x^2-2^(1/3)*c^(1/3)*x*(b+sqrt(b^2-_
   4*a*c))^(1/3)+(b+sqrt(b^2-4*a*c))^(2/3))*(c*d-b*e+(b*c*d-b^2*e+_
   2*a*c*e)/sqrt(b^2-4*a*c))/(2^(2/3)*c^(5/3)*(b+sqrt(b^2-_
   4*a*c))^(1/3))-atan((-4*c^(1/3)*x+2^(2/3)*(b+sqrt(b^2-_
   4*a*c))^(1/3))/(2^(2/3)*sqrt(3)*(b+sqrt(b^2-4*a*c))^(1/3)))*_
   (c*d-b*e+(b*c*d-b^2*e+2*a*c*e)/sqrt(b^2-4*a*c))/(2^(2/3)*c^(5/3)*_
   sqrt(3)*(b+sqrt(b^2-4*a*c))^(1/3))
--E 2
--S 3 of 381
d0:=t0-normalize(D(r0,x))
--E 3
)clear all
--S 4 of 381
t0:=x^3*(d+e*x^3)/(a+b*x^3+c*x^6)
--E 4
--S 5 of 381
r0:=e*x/c+1/3*log(2^(1/3)*c^(1/3)*x+(b-sqrt(b^2-4*a*c))^(1/3))*(c*d-b*e+_
   (-b*c*d+b^2*e-2*a*c*e)/sqrt(b^2-4*a*c))/(2^(1/3)*c^(4/3)*(b-_
   sqrt(b^2-4*a*c))^(2/3))-1/6*log(2^(2/3)*c^(2/3)*x^2-2^(1/3)*c^(1/3)*_
   x*(b-sqrt(b^2-4*a*c))^(1/3)+(b-sqrt(b^2-4*a*c))^(2/3))*(c*d-b*e+_

(-b*c*d+b^2*e-2*a*c*e)/sqrt(b^2-4*a*c))/(2^(1/3)*c^(4/3)*_
(b-sqrt(b^2-4*a*c))^(2/3))-atan((-4*c^(1/3)*x+2^(2/3)*_
(b-sqrt(b^2-4*a*c))^(1/3))/(2^(2/3)*sqrt(3)*(b-sqrt(b^2-_
4*a*c))^(1/3)))*(c*d-b*e+(-b*c*d+b^2*e-2*a*c*e)/sqrt(b^2-4*a*c))/_
(2^(1/3)*c^(4/3)*sqrt(3)*(b-sqrt(b^2-4*a*c))^(2/3))+1/3*log(2^(1/3)*_
c^(1/3)*x+(b+sqrt(b^2-4*a*c))^(1/3))*(c*d-b*e+(b*c*d-b^2*e+2*a*c*e)/_
sqrt(b^2-4*a*c))/(2^(1/3)*c^(4/3)*(b+sqrt(b^2-4*a*c))^(2/3))-_
1/6*log(2^(2/3)*c^(2/3)*x^2-2^(1/3)*c^(1/3)*x*(b+sqrt(b^2-_
4*a*c))^(1/3)+(b+sqrt(b^2-4*a*c))^(2/3))*(c*d-b*e+(b*c*d-b^2*e+_
2*a*c*e)/sqrt(b^2-4*a*c))/(2^(1/3)*c^(4/3)*(b+sqrt(b^2-_
4*a*c))^(2/3))-atan((-4*c^(1/3)*x+2^(2/3)*(b+sqrt(b^2-_
4*a*c))^(1/3))/(2^(2/3)*sqrt(3)*(b+sqrt(b^2-4*a*c))^(1/3)))*_
(c*d-b*e+(b*c*d-b^2*e+2*a*c*e)/sqrt(b^2-4*a*c))/(2^(1/3)*c^(4/3)*_
sqrt(3)*(b+sqrt(b^2-4*a*c))^(2/3))
--E 5
--S 6 of 381
d0:=t0-normalize(D(r0,x))
--E 6
)clear all
--S 7 of 381
t0:=x^2*(d+e*x^3)/(a+b*x^3+c*x^6)
--E 7
--S 8 of 381
r0:=1/6*e*log(a+b*x^3+c*x^6)/c-1/3*(2*c*d-b*e)*atanh((b+2*c*x^3)/_
sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c))
--E 8
--S 9 of 381
d0:=t0-normalize(D(r0,x))
--E 9
)clear all
--S 10 of 381
t0:=x*(d+e*x^3)/(a+b*x^3+c*x^6)
--E 10
--S 11 of 381
r0:=-1/3*log(2^(1/3)*c^(1/3)*x+(b-sqrt(b^2-4*a*c))^(1/3))*(e+(2*c*d-b*e)/_
sqrt(b^2-4*a*c))/(2^(2/3)*c^(2/3)*(b-sqrt(b^2-4*a*c))^(1/3))+_
1/6*log(2^(2/3)*c^(2/3)*x^2-2^(1/3)*c^(1/3)*x*(b-sqrt(b^2-_
4*a*c))^(1/3)+(b-sqrt(b^2-4*a*c))^(2/3))*(e+(2*c*d-b*e)/sqrt(b^2-_
4*a*c))/(2^(2/3)*c^(2/3)*(b-sqrt(b^2-4*a*c))^(1/3))-atan((-4*_
c^(1/3)*x+2^(2/3)*(b-sqrt(b^2-4*a*c))^(1/3))/(2^(2/3)*sqrt(3)*_
(b-sqrt(b^2-4*a*c))^(1/3)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(2^(2/3)*_
c^(2/3)*sqrt(3)*(b-sqrt(b^2-4*a*c))^(1/3))-1/3*log(2^(1/3)*c^(1/3)*_

x+(b+sqrt(b^2-4*a*c))^(1/3))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(2^(2/3)*_
c^(2/3)*(b+sqrt(b^2-4*a*c))^(1/3))+1/6*log(2^(2/3)*c^(2/3)*x^2-2^(1/3)*_
c^(1/3)*x*(b+sqrt(b^2-4*a*c))^(1/3)+(b+sqrt(b^2-4*a*c))^(2/3))*_
(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(2^(2/3)*c^(2/3)*(b+sqrt(b^2-_
4*a*c))^(1/3))-atan((-4*c^(1/3)*x+2^(2/3)*(b+sqrt(b^2-4*a*c))^(1/3))/_
(2^(2/3)*sqrt(3)*(b+sqrt(b^2-4*a*c))^(1/3)))*(e+(-2*c*d+b*e)/_
sqrt(b^2-4*a*c))/(2^(2/3)*c^(2/3)*sqrt(3)*(b+sqrt(b^2-4*a*c))^(1/3))
--E 11
--S 12 of 381
d0:=t0-normalize(D(r0,x))
--E 12
)clear all
--S 13 of 381
t0:=(d+e*x^3)/(a+b*x^3+c*x^6)
--E 13
--S 14 of 381
r0:=1/3*log(2^(1/3)*c^(1/3)*x+(b-sqrt(b^2-4*a*c))^(1/3))*(e+(2*c*d-b*e)/_
sqrt(b^2-4*a*c))/(2^(1/3)*c^(1/3)*(b-sqrt(b^2-4*a*c))^(2/3))-_
1/6*log(2^(2/3)*c^(2/3)*x^2-2^(1/3)*c^(1/3)*x*(b-sqrt(b^2-_
4*a*c))^(1/3)+(b-sqrt(b^2-4*a*c))^(2/3))*(e+(2*c*d-b*e)/sqrt(b^2-_
4*a*c))/(2^(1/3)*c^(1/3)*(b-sqrt(b^2-4*a*c))^(2/3))-_
atan((-4*c^(1/3)*x+2^(2/3)*(b-sqrt(b^2-4*a*c))^(1/3))/(2^(2/3)*_
sqrt(3)*(b-sqrt(b^2-4*a*c))^(1/3)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/_
(2^(1/3)*c^(1/3)*sqrt(3)*(b-sqrt(b^2-4*a*c))^(2/3))+1/3*log(2^(1/3)*_
c^(1/3)*x+(b+sqrt(b^2-4*a*c))^(1/3))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/_
(2^(1/3)*c^(1/3)*(b+sqrt(b^2-4*a*c))^(2/3))-1/6*log(2^(2/3)*c^(2/3)*_
x^2-2^(1/3)*c^(1/3)*x*(b+sqrt(b^2-4*a*c))^(1/3)+(b+sqrt(b^2-_
4*a*c))^(2/3))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(2^(1/3)*c^(1/3)*_
(b+sqrt(b^2-4*a*c))^(2/3))-atan((-4*c^(1/3)*x+2^(2/3)*(b+sqrt(b^2-_
4*a*c))^(1/3))/(2^(2/3)*sqrt(3)*(b+sqrt(b^2-4*a*c))^(1/3)))*_
(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(2^(1/3)*c^(1/3)*sqrt(3)*_
(b+sqrt(b^2-4*a*c))^(2/3))
--E 14
--S 15 of 381
d0:=t0-normalize(D(r0,x))
--E 15
)clear all
--S 16 of 381
t0:=(d+e*x^3)/(x*(a+b*x^3+c*x^6))
--E 16
--S 17 of 381
r0:=d*log(x)/a-1/6*d*log(a+b*x^3+c*x^6)/a+1/3*(b*d-2*a*e)*_

   atanh((b+2*c*x^3)/sqrt(b^2-4*a*c))/(a*sqrt(b^2-4*a*c))
--E 17
--S 18 of 381
d0:=t0-normalize(D(r0,x))
--E 18
--S 19 of 381
m0b:=a0.2-r0
--E 19
--S 20 of 381
d0b:=D(m0b,x)
--E 20
)clear all
--S 21 of 381
t0:=(d+e*x^3)/(x^2*(a+b*x^3+c*x^6))
--E 21
--S 22 of 381
r0:=-d/(a*x)+1/3*c^(1/3)*log(2^(1/3)*c^(1/3)*x+(b-sqrt(b^2-4*a*c))^(1/3))*_
   (d+(b*d-2*a*e)/sqrt(b^2-4*a*c))/(2^(2/3)*a*(b-sqrt(b^2-4*a*c))^(1/3))-_
   1/6*c^(1/3)*log(2^(2/3)*c^(2/3)*x^2-2^(1/3)*c^(1/3)*x*(b-_
   sqrt(b^2-4*a*c))^(1/3)+(b-sqrt(b^2-4*a*c))^(2/3))*(d+(b*d-2*a*e)/_
   sqrt(b^2-4*a*c))/(2^(2/3)*a*(b-sqrt(b^2-4*a*c))^(1/3))+c^(1/3)*_
   atan((-4*c^(1/3)*x+2^(2/3)*(b-sqrt(b^2-4*a*c))^(1/3))/(2^(2/3)*_
   sqrt(3)*(b-sqrt(b^2-4*a*c))^(1/3)))*(d+(b*d-2*a*e)/sqrt(b^2-4*a*c))/_
   (2^(2/3)*a*sqrt(3)*(b-sqrt(b^2-4*a*c))^(1/3))+1/3*c^(1/3)*log(2^(1/3)*_
   c^(1/3)*x+(b+sqrt(b^2-4*a*c))^(1/3))*(d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/_
   (2^(2/3)*a*(b+sqrt(b^2-4*a*c))^(1/3))-1/6*c^(1/3)*log(2^(2/3)*c^(2/3)*_
   x^2-2^(1/3)*c^(1/3)*x*(b+sqrt(b^2-4*a*c))^(1/3)+(b+sqrt(b^2-_
   4*a*c))^(2/3))*(d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/(2^(2/3)*a*(b+_
   sqrt(b^2-4*a*c))^(1/3))+c^(1/3)*atan((-4*c^(1/3)*x+2^(2/3)*_
   (b+sqrt(b^2-4*a*c))^(1/3))/(2^(2/3)*sqrt(3)*(b+sqrt(b^2-_
   4*a*c))^(1/3)))*(d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/(2^(2/3)*a*_
   sqrt(3)*(b+sqrt(b^2-4*a*c))^(1/3))
--E 22
--S 23 of 381
d0:=t0-normalize(D(r0,x))
--E 23
)clear all
--S 24 of 381
t0:=(d+e*x^3)/(x^3*(a+b*x^3+c*x^6))
--E 24

--S 25 of 381
r0:=-1/2*d/(a*x^2)-1/3*c^(2/3)*log(2^(1/3)*c^(1/3)*x+(b-sqrt(b^2-_
   4*a*c))^(1/3))*(d+(b*d-2*a*e)/sqrt(b^2-4*a*c))/(2^(1/3)*a*_
   (b-sqrt(b^2-4*a*c))^(2/3))+1/6*c^(2/3)*log(2^(2/3)*c^(2/3)*x^2-_
   2^(1/3)*c^(1/3)*x*(b-sqrt(b^2-4*a*c))^(1/3)+(b-sqrt(b^2-_
   4*a*c))^(2/3))*(d+(b*d-2*a*e)/sqrt(b^2-4*a*c))/(2^(1/3)*a*(b-_
   sqrt(b^2-4*a*c))^(2/3))+c^(2/3)*atan((-4*c^(1/3)*x+2^(2/3)*_
   (b-sqrt(b^2-4*a*c))^(1/3))/(2^(2/3)*sqrt(3)*(b-sqrt(b^2-_
   4*a*c))^(1/3)))*(d+(b*d-2*a*e)/sqrt(b^2-4*a*c))/(2^(1/3)*a*sqrt(3)*_
   (b-sqrt(b^2-4*a*c))^(2/3))-1/3*c^(2/3)*log(2^(1/3)*c^(1/3)*x+_
   (b+sqrt(b^2-4*a*c))^(1/3))*(d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/(2^(1/3)*_
   a*(b+sqrt(b^2-4*a*c))^(2/3))+1/6*c^(2/3)*log(2^(2/3)*c^(2/3)*x^2-_
   2^(1/3)*c^(1/3)*x*(b+sqrt(b^2-4*a*c))^(1/3)+(b+sqrt(b^2-4*a*c))^(2/3))*_
   (d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/(2^(1/3)*a*(b+sqrt(b^2-4*a*c))^(2/3))+_
   c^(2/3)*atan((-4*c^(1/3)*x+2^(2/3)*(b+sqrt(b^2-4*a*c))^(1/3))/(2^(2/3)*_
   sqrt(3)*(b+sqrt(b^2-4*a*c))^(1/3)))*(d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/_
   (2^(1/3)*a*sqrt(3)*(b+sqrt(b^2-4*a*c))^(2/3))
--E 25
--S 26 of 381
d0:=t0-normalize(D(r0,x))
--E 26
)clear all
--S 27 of 381
t0:=(d+e*x^3)/(x^4*(a+b*x^3+c*x^6))
--E 27
--S 28 of 381
r0:=-1/3*d/(a*x^3)-(b*d-a*e)*log(x)/a^2+1/6*(b*d-a*e)*log(a+b*x^3+c*x^6)/a^2-_
   1/3*(b^2*d-2*a*c*d-a*b*e)*atanh((b+2*c*x^3)/sqrt(b^2-4*a*c))/(a^2*_
   sqrt(b^2-4*a*c))
--E 28
--S 29 of 381
d0:=t0-normalize(D(r0,x))
--E 29
)clear all
--S 30 of 381
t0:=x^6*(1-x^3)/(1-x^3+x^6)
--E 30
--S 31 of 381
r0:=-1/4*x^4+1/3*atan((4*x+2^(2/3)*(1+%i*sqrt(3))^(1/3))/(2^(2/3)*_
   (1+%i*sqrt(3))^(1/3)*sqrt(3)))*(%i-sqrt(3))/(2^(1/3)*(1+%i*_
   sqrt(3))^(2/3))+1/9*log(-2^(1/3)*x+(1+%i*sqrt(3))^(1/3))*(3-%i*_
   sqrt(3))/(2^(1/3)*(1+%i*sqrt(3))^(2/3))-1/18*log(2^(2/3)*x^2+2^(1/3)*_

   x*(1+%i*sqrt(3))^(1/3)+(1+%i*sqrt(3))^(2/3))*(3-%i*sqrt(3))/(2^(1/3)*_
   (1+%i*sqrt(3))^(2/3))+1/9*log(-2^(1/3)*x+(1-%i*sqrt(3))^(1/3))*_
   (3+%i*sqrt(3))/(2^(1/3)*(1-%i*sqrt(3))^(2/3))-1/18*log(2^(2/3)*x^2+_
   2^(1/3)*x*(1-%i*sqrt(3))^(1/3)+(1-%i*sqrt(3))^(2/3))*(3+%i*sqrt(3))/_
   (2^(1/3)*(1-%i*sqrt(3))^(2/3))-1/3*atan((4*x+2^(2/3)*(1-%i*_
   sqrt(3))^(1/3))/(2^(2/3)*(1-%i*sqrt(3))^(1/3)*sqrt(3)))*(%i+_
   sqrt(3))/(2^(1/3)*(1-%i*sqrt(3))^(2/3))
--E 31
--S 32 of 381
d0:=t0-normalize(D(r0,x))
--E 32
)clear all
--S 33 of 381
t0:=x^5*(1-x^3)/(1-x^3+x^6)
--E 33
--S 34 of 381
r0:=-1/3*x^3-2/3*atan((1-2*x^3)/sqrt(3))/sqrt(3)
--E 34
--S 35 of 381
d0:=t0-normalize(D(r0,x))
--E 35
)clear all
--S 36 of 381
t0:=x^4*(1-x^3)/(1-x^3+x^6)
--E 36
--S 37 of 381
r0:=-1/2*x^2+1/3*%i*2^(1/3)*atan((4*x+2^(2/3)*(1-%i*sqrt(3))^(1/3))/_
   (2^(2/3)*(1-%i*sqrt(3))^(1/3)*sqrt(3)))/(1-%i*sqrt(3))^(1/3)-_
   1/3*%i*2^(1/3)*atan((4*x+2^(2/3)*(1+%i*sqrt(3))^(1/3))/(2^(2/3)*_
   (1+%i*sqrt(3))^(1/3)*sqrt(3)))/(1+%i*sqrt(3))^(1/3)+1/3*%i*2^(1/3)*_
   log(-2^(1/3)*x+(1-%i*sqrt(3))^(1/3))/((1-%i*sqrt(3))^(1/3)*sqrt(3))-_
   1/3*%i*log(2^(2/3)*x^2+2^(1/3)*x*(1-%i*sqrt(3))^(1/3)+(1-%i*_
   sqrt(3))^(2/3))/(2^(2/3)*(1-%i*sqrt(3))^(1/3)*sqrt(3))-1/3*%i*2^(1/3)*_
   log(-2^(1/3)*x+(1+%i*sqrt(3))^(1/3))/((1+%i*sqrt(3))^(1/3)*sqrt(3))+_
   1/3*%i*log(2^(2/3)*x^2+2^(1/3)*x*(1+%i*sqrt(3))^(1/3)+(1+%i*_
   sqrt(3))^(2/3))/(2^(2/3)*(1+%i*sqrt(3))^(1/3)*sqrt(3))
--E 37
--S 38 of 381
d0:=t0-normalize(D(r0,x))
--E 38

)clear all
--S 39 of 381
t0:=x^3*(1-x^3)/(1-x^3+x^6)
--E 39
--S 40 of 381
r0:=-x-1/3*%i*2^(2/3)*atan((4*x+2^(2/3)*(1-%i*sqrt(3))^(1/3))/(2^(2/3)*_
   (1-%i*sqrt(3))^(1/3)*sqrt(3)))/(1-%i*sqrt(3))^(2/3)+1/3*%i*2^(2/3)*_
   atan((4*x+2^(2/3)*(1+%i*sqrt(3))^(1/3))/(2^(2/3)*(1+%i*sqrt(3))^(1/3)*_
   sqrt(3)))/(1+%i*sqrt(3))^(2/3)+1/3*%i*2^(2/3)*log(-2^(1/3)*x+(1-%i*_
   sqrt(3))^(1/3))/((1-%i*sqrt(3))^(2/3)*sqrt(3))-1/3*%i*log(2^(2/3)*_
   x^2+2^(1/3)*x*(1-%i*sqrt(3))^(1/3)+(1-%i*sqrt(3))^(2/3))/(2^(1/3)*_
   (1-%i*sqrt(3))^(2/3)*sqrt(3))-1/3*%i*2^(2/3)*log(-2^(1/3)*x+(1+%i*_
   sqrt(3))^(1/3))/((1+%i*sqrt(3))^(2/3)*sqrt(3))+1/3*%i*log(2^(2/3)*_
   x^2+2^(1/3)*x*(1+%i*sqrt(3))^(1/3)+(1+%i*sqrt(3))^(2/3))/(2^(1/3)*_
   (1+%i*sqrt(3))^(2/3)*sqrt(3))
--E 40
--S 41 of 381
d0:=t0-normalize(D(r0,x))
--E 41
)clear all
--S 42 of 381
t0:=x^2*(1-x^3)/(1-x^3+x^6)
--E 42
--S 43 of 381
r0:=-1/6*log(1-x^3+x^6)-1/3*atan((1-2*x^3)/sqrt(3))/sqrt(3)
--E 43
--S 44 of 381
d0:=t0-normalize(D(r0,x))
--E 44
)clear all
--S 45 of 381
t0:=x*(1-x^3)/(1-x^3+x^6)
--E 45
--S 46 of 381
r0:=1/3*atan((4*x+2^(2/3)*(1-%i*sqrt(3))^(1/3))/(2^(2/3)*(1-%i*_
   sqrt(3))^(1/3)*sqrt(3)))*(%i-sqrt(3))/(2^(2/3)*(1-%i*sqrt(3))^(1/3))-_
   1/9*log(-2^(1/3)*x+(1-%i*sqrt(3))^(1/3))*(3-%i*sqrt(3))/(2^(2/3)*_
   (1-%i*sqrt(3))^(1/3))+1/18*log(2^(2/3)*x^2+2^(1/3)*x*(1-%i*_
   sqrt(3))^(1/3)+(1-%i*sqrt(3))^(2/3))*(3-%i*sqrt(3))/(2^(2/3)*(1-_
   %i*sqrt(3))^(1/3))-1/9*log(-2^(1/3)*x+(1+%i*sqrt(3))^(1/3))*(3+%i*_

   sqrt(3))/(2^(2/3)*(1+%i*sqrt(3))^(1/3))+1/18*log(2^(2/3)*x^2+2^(1/3)*_
   x*(1+%i*sqrt(3))^(1/3)+(1+%i*sqrt(3))^(2/3))*(3+%i*sqrt(3))/(2^(2/3)*_
   (1+%i*sqrt(3))^(1/3))-1/3*atan((4*x+2^(2/3)*(1+%i*sqrt(3))^(1/3))/_
   (2^(2/3)*(1+%i*sqrt(3))^(1/3)*sqrt(3)))*(%i+sqrt(3))/(2^(2/3)*_
   (1+%i*sqrt(3))^(1/3))
--E 46
--S 47 of 381
d0:=t0-normalize(D(r0,x))
--E 47
)clear all
--S 48 of 381
t0:=(1-x^3)/(1-x^3+x^6)
--E 48
--S 49 of 381
r0:=-1/3*atan((4*x+2^(2/3)*(1-%i*sqrt(3))^(1/3))/(2^(2/3)*(1-_
   %i*sqrt(3))^(1/3)*sqrt(3)))*(%i-sqrt(3))/(2^(1/3)*(1-%i*_
   sqrt(3))^(2/3))-1/9*log(-2^(1/3)*x+(1-%i*sqrt(3))^(1/3))*(3-%i*_
   sqrt(3))/(2^(1/3)*(1-%i*sqrt(3))^(2/3))+1/18*log(2^(2/3)*x^2+_
   2^(1/3)*x*(1-%i*sqrt(3))^(1/3)+(1-%i*sqrt(3))^(2/3))*(3-%i*sqrt(3))/_
   (2^(1/3)*(1-%i*sqrt(3))^(2/3))-1/9*log(-2^(1/3)*x+(1+%i*_
   sqrt(3))^(1/3))*(3+%i*sqrt(3))/(2^(1/3)*(1+%i*sqrt(3))^(2/3))+_
   1/18*log(2^(2/3)*x^2+2^(1/3)*x*(1+%i*sqrt(3))^(1/3)+(1+%i*_
   sqrt(3))^(2/3))*(3+%i*sqrt(3))/(2^(1/3)*(1+%i*sqrt(3))^(2/3))+_
   1/3*atan((4*x+2^(2/3)*(1+%i*sqrt(3))^(1/3))/(2^(2/3)*(1+%i*_
   sqrt(3))^(1/3)*sqrt(3)))*(%i+sqrt(3))/(2^(1/3)*(1+%i*sqrt(3))^(2/3))
--E 49
--S 50 of 381
d0:=t0-normalize(D(r0,x))
--E 50
)clear all
--S 51 of 381
t0:=(1-x^3)/(x*(1-x^3+x^6))
--E 51
--S 52 of 381
r0:=log(x)-1/6*log(1-x^3+x^6)+1/3*atan((1-2*x^3)/sqrt(3))/sqrt(3)
--E 52
--S 53 of 381
d0:=t0-normalize(D(r0,x))
--E 53
)clear all

--S 54 of 381
t0:=(1-x^3)/(x^2*(1-x^3+x^6))
--E 54
--S 55 of 381
r0:=(-1)/x+1/3*atan((4*x+2^(2/3)*(1+%i*sqrt(3))^(1/3))/(2^(2/3)*_
   (1+%i*sqrt(3))^(1/3)*sqrt(3)))*(%i-sqrt(3))/(2^(2/3)*(1+%i*_
   sqrt(3))^(1/3))-1/9*log(-2^(1/3)*x+(1+%i*sqrt(3))^(1/3))*(3-%i*_
   sqrt(3))/(2^(2/3)*(1+%i*sqrt(3))^(1/3))+1/18*log(2^(2/3)*x^2+_
   2^(1/3)*x*(1+%i*sqrt(3))^(1/3)+(1+%i*sqrt(3))^(2/3))*(3-%i*_
   sqrt(3))/(2^(2/3)*(1+%i*sqrt(3))^(1/3))-1/9*log(-2^(1/3)*x+(1-%i*_
   sqrt(3))^(1/3))*(3+%i*sqrt(3))/(2^(2/3)*(1-%i*sqrt(3))^(1/3))+_
   1/18*log(2^(2/3)*x^2+2^(1/3)*x*(1-%i*sqrt(3))^(1/3)+(1-%i*_
   sqrt(3))^(2/3))*(3+%i*sqrt(3))/(2^(2/3)*(1-%i*sqrt(3))^(1/3))-_
   1/3*atan((4*x+2^(2/3)*(1-%i*sqrt(3))^(1/3))/(2^(2/3)*(1-%i*_
   sqrt(3))^(1/3)*sqrt(3)))*(%i+sqrt(3))/(2^(2/3)*(1-%i*sqrt(3))^(1/3))
--E 55
--S 56 of 381
d0:=t0-normalize(D(r0,x))
--E 56
)clear all
--S 57 of 381
t0:=(1-x^3)/(x^3*(1-x^3+x^6))
--E 57
--S 58 of 381
r0:=(-1/2)/x^2-1/3*atan((4*x+2^(2/3)*(1+%i*sqrt(3))^(1/3))/(2^(2/3)*(1+%i*_
   sqrt(3))^(1/3)*sqrt(3)))*(%i-sqrt(3))/(2^(1/3)*(1+%i*sqrt(3))^(2/3))-_
   1/9*log(-2^(1/3)*x+(1+%i*sqrt(3))^(1/3))*(3-%i*sqrt(3))/(2^(1/3)*_
   (1+%i*sqrt(3))^(2/3))+1/18*log(2^(2/3)*x^2+2^(1/3)*x*(1+%i*_
   sqrt(3))^(1/3)+(1+%i*sqrt(3))^(2/3))*(3-%i*sqrt(3))/(2^(1/3)*_
   (1+%i*sqrt(3))^(2/3))-1/9*log(-2^(1/3)*x+(1-%i*sqrt(3))^(1/3))*_
   (3+%i*sqrt(3))/(2^(1/3)*(1-%i*sqrt(3))^(2/3))+1/18*log(2^(2/3)*_
   x^2+2^(1/3)*x*(1-%i*sqrt(3))^(1/3)+(1-%i*sqrt(3))^(2/3))*(3+%i*_
   sqrt(3))/(2^(1/3)*(1-%i*sqrt(3))^(2/3))+1/3*atan((4*x+2^(2/3)*_
   (1-%i*sqrt(3))^(1/3))/(2^(2/3)*(1-%i*sqrt(3))^(1/3)*sqrt(3)))*_
   (%i+sqrt(3))/(2^(1/3)*(1-%i*sqrt(3))^(2/3))
--E 58
--S 59 of 381
d0:=t0-normalize(D(r0,x))
--E 59
)clear all
--S 60 of 381

t0:=(1-x^3)/(x^4*(1-x^3+x^6))
--E 60
--S 61 of 381
r0:=(-1/3)/x^3+2/3*atan((1-2*x^3)/sqrt(3))/sqrt(3)
--E 61
--S 62 of 381
d0:=t0-normalize(D(r0,x))
--E 62
)clear all
--S 63 of 381
t0:=x^2*(-2+x^3)/(1-x^3+x^6)
--E 63
--S 64 of 381
r0:=1/6*log(1-x^3+x^6)+atan((1-2*x^3)/sqrt(3))/sqrt(3)
--E 64
--S 65 of 381
d0:=t0-normalize(D(r0,x))
--E 65
)clear all
--S 66 of 381
t0:=(1+x^3)/(x*(1-x^3+x^6))
--E 66
--S 67 of 381
r0:=log(x)-1/6*log(1-x^3+x^6)-atan((1-2*x^3)/sqrt(3))/sqrt(3)
--E 67
--S 68 of 381
d0:=t0-normalize(D(r0,x))
--E 68
)clear all
--S 69 of 381
t0:=(d+e*x^3)^5*(a+b*x^3+c*x^6)
--E 69
--S 70 of 381
r0:=a*d^5*x+1/4*d^4*(b*d+5*a*e)*x^4+1/7*d^3*(c*d^2+5*e*(b*d+2*a*e))*x^7+_
   1/2*d^2*e*(c*d^2+2*e*(b*d+a*e))*x^10+5/13*d*e^2*(2*c*d^2+e*_
   (2*b*d+a*e))*x^13+1/16*e^3*(10*c*d^2+e*(5*b*d+a*e))*x^16+_
   1/19*e^4*(5*c*d+b*e)*x^19+1/22*c*e^5*x^22

--E 70
--S 71 of 381
d0:=t0-normalize(D(r0,x))
--E 71
)clear all
--S 72 of 381
t0:=(d+e*x^3)^4*(a+b*x^3+c*x^6)
--E 72
--S 73 of 381
r0:=a*d^4*x+1/4*d^3*(b*d+4*a*e)*x^4+1/7*d^2*(c*d^2+4*b*d*e+6*a*e^2)*x^7+_
   1/5*d*e*(2*c*d^2+e*(3*b*d+2*a*e))*x^10+1/13*e^2*(6*c*d^2+_
   e*(4*b*d+a*e))*x^13+1/16*e^3*(4*c*d+b*e)*x^16+1/19*c*e^4*x^19
--E 73
--S 74 of 381
d0:=t0-normalize(D(r0,x))
--E 74
)clear all
--S 75 of 381
t0:=(d+e*x^3)^3*(a+b*x^3+c*x^6)
--E 75
--S 76 of 381
r0:=a*d^3*x+1/4*d^2*(b*d+3*a*e)*x^4+1/7*d*(c*d^2+3*e*(b*d+a*e))*x^7+_
   1/10*e*(3*c*d^2+e*(3*b*d+a*e))*x^10+1/13*e^2*(3*c*d+b*e)*x^13+_
   1/16*c*e^3*x^16
--E 76
--S 77 of 381
d0:=t0-normalize(D(r0,x))
--E 77
)clear all
--S 78 of 381
t0:=(d+e*x^3)^2*(a+b*x^3+c*x^6)
--E 78
--S 79 of 381
r0:=a*d^2*x+1/4*d*(b*d+2*a*e)*x^4+1/7*(c*d^2+e*(2*b*d+a*e))*x^7+_
   1/10*e*(2*c*d+b*e)*x^10+1/13*c*e^2*x^13
--E 79
--S 80 of 381

d0:=t0-normalize(D(r0,x))
--E 80
)clear all
--S 81 of 381
t0:=(d+e*x^3)*(a+b*x^3+c*x^6)
--E 81
--S 82 of 381
r0:=a*d*x+1/4*(b*d+a*e)*x^4+1/7*(c*d+b*e)*x^7+1/10*c*e*x^10
--E 82
--S 83 of 381
d0:=t0-normalize(D(r0,x))
--E 83
)clear all
--S 84 of 381
t0:=(a+b*x^3+c*x^6)/(d+e*x^3)
--E 84
--S 85 of 381
r0:=-(c*d-b*e)*x/e^2+1/4*c*x^4/e+1/3*(c*d^2-b*d*e+a*e^2)*log(d^(1/3)+_
   e^(1/3)*x)/(d^(2/3)*e^(7/3))-1/6*(c*d^2-b*d*e+a*e^2)*log(d^(2/3)-_
   d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/(d^(2/3)*e^(7/3))-(c*d^2-b*d*e+a*e^2)*_
   atan((d^(1/3)-2*e^(1/3)*x)/(d^(1/3)*sqrt(3)))/(d^(2/3)*e^(7/3)*sqrt(3))
--E 85
--S 86 of 381
d0:=t0-normalize(D(r0,x))
--E 86
)clear all
--S 87 of 381
t0:=(a+b*x^3+c*x^6)/(d+e*x^3)^2
--E 87
--S 88 of 381
r0:=c*x/e^2+1/3*(c*d^2-b*d*e+a*e^2)*x/(d*e^2*(d+e*x^3))-1/9*(4*c*d^2-_
   e*(b*d+2*a*e))*log(d^(1/3)+e^(1/3)*x)/(d^(5/3)*e^(7/3))+1/18*(4*c*d^2-_
   e*(b*d+2*a*e))*log(d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/(d^(5/3)*_
   e^(7/3))+1/3*(4*c*d^2-e*(b*d+2*a*e))*atan((d^(1/3)-2*e^(1/3)*x)/_
   (d^(1/3)*sqrt(3)))/(d^(5/3)*e^(7/3)*sqrt(3))
--E 88
--S 89 of 381
d0:=t0-normalize(D(r0,x))

--E 89
)clear all
--S 90 of 381
t0:=(a+b*x^3+c*x^6)/(d+e*x^3)^3
--E 90
--S 91 of 381
r0:=1/6*(c*d^2-b*d*e+a*e^2)*x/(d*e^2*(d+e*x^3)^2)-1/18*(7*c*d^2-_
   e*(b*d+5*a*e))*x/(d^2*e^2*(d+e*x^3))+1/27*(2*c*d^2+e*(b*d+5*a*e))*_
   log(d^(1/3)+e^(1/3)*x)/(d^(8/3)*e^(7/3))-1/54*(2*c*d^2+e*(b*d+5*a*e))*_
   log(d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/(d^(8/3)*e^(7/3))-_
   1/9*(2*c*d^2+e*(b*d+5*a*e))*atan((d^(1/3)-2*e^(1/3)*x)/(d^(1/3)*_
   sqrt(3)))/(d^(8/3)*e^(7/3)*sqrt(3))
--E 91
--S 92 of 381
d0:=t0-normalize(D(r0,x))
--E 92
)clear all
--S 93 of 381
t0:=(d+e*x^3)^(3/2)*(a+b*x^3+c*x^6)
--E 93
--S 94 of 381
--r0:=2/4301*(16*c*d^2-46*b*d*e+391*a*e^2)*x*(d+e*x^3)^(3/2)/e^2-_
--  2/15*(c*d^2-b*d*e+a*e^2)*x*(d+e*x^3)^(5/2)/(d*e^2)+2/5865*(16*c*d^2-_
--  46*b*d*e+391*a*e^2)*x*(d+e*x^3)^(5/2)/(d*e^2)+2/23*c*x*_
--  (d+e*x^3)^(7/2)/e^2+18/21505*d*(16*c*d^2-46*b*d*e+391*a*e^2)*x*_
--  sqrt(d+e*x^3)/e^2+27/21505*d^(13/6)*(16*c*d^2-23*e*(2*b*d-17*a*e))*_
--  elliptic_f(asin(e^(1/6)*sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)/(d^(1/6)*_
--  sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3))))),(3*e^(1/3)-sqrt(3)*_
--  sqrt(-e^(2/3)))/(3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))*sqrt(2)*_
--  sqrt(d^(1/3)+e^(1/3)*x)*sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))*_
--  sqrt((2*e^(2/3)*x+d^(1/3)*(-e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*_
--  (-3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3)))))*sqrt((-2*e^(2/3)*x+d^(1/3)*_
--  (e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*(3*e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3)))))/(e^(5/2)*sqrt(d+e*x^3))
--E 94
--S 95 of 381
--d0:=t0-normalize(D(r0,x))
--E 95
)clear all
--S 96 of 381

t0:=(d+e*x^3)^(1/2)*(a+b*x^3+c*x^6)
--E 96
--S 97 of 381
--r0:=-2/9*(c*d^2-b*d*e+a*e^2)*x*(d+e*x^3)^(3/2)/(d*e^2)+2/1683*_
--  (16*c*d^2-34*b*d*e+187*a*e^2)*x*(d+e*x^3)^(3/2)/(d*e^2)+2/17*c*x*_
--  (d+e*x^3)^(5/2)/e^2+2/935*(16*c*d^2-34*b*d*e+187*a*e^2)*x*_
--  sqrt(d+e*x^3)/e^2+3/935*d^(7/6)*(16*c*d^2-17*e*(2*b*d-11*a*e))*_
--  elliptic_f(asin(e^(1/6)*sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)/(d^(1/6)*_
--  sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3))))),(3*e^(1/3)-sqrt(3)*_
--  sqrt(-e^(2/3)))/(3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))*sqrt(2)*_
--  sqrt(d^(1/3)+e^(1/3)*x)*sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))*_
--  sqrt((2*e^(2/3)*x+d^(1/3)*(-e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*_
--  (-3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3)))))*sqrt((-2*e^(2/3)*x+d^(1/3)*_
--  (e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*(3*e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3)))))/(e^(5/2)*sqrt(d+e*x^3))
--E 97
--S 98 of 381
--d0:=t0-normalize(D(r0,x))
--E 98
)clear all
--S 99 of 381
t0:=(a+b*x^3+c*x^6)/(d+e*x^3)^(1/2)
--E 99
--S 100 of 381
--r0:=2/11*c*x*(d+e*x^3)^(3/2)/e^2-2/3*(c*d^2-b*d*e+a*e^2)*x*_
--  sqrt(d+e*x^3)/(d*e^2)+2/165*(16*c*d^2-22*b*d*e+55*a*e^2)*x*_
--  sqrt(d+e*x^3)/(d*e^2)+1/55*d^(1/6)*(16*c*d^2-11*e*(2*b*d-5*a*e))*_
--  elliptic_f(asin(e^(1/6)*sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)/(d^(1/6)*_
--  sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3))))),(3*e^(1/3)-sqrt(3)*_
--  sqrt(-e^(2/3)))/(3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))*sqrt(2)*_
--  sqrt(d^(1/3)+e^(1/3)*x)*sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))*_
--  sqrt((2*e^(2/3)*x+d^(1/3)*(-e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*_
--  (-3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3)))))*sqrt((-2*e^(2/3)*x+d^(1/3)*_
--  (e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*(3*e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3)))))/(e^(5/2)*sqrt(d+e*x^3))
--E 100
--S 101 of 381
--d0:=t0-normalize(D(r0,x))
--E 101
)clear all
--S 102 of 381
t0:=(a+b*x^3+c*x^6)/(d+e*x^3)^(3/2)

--E 102
--S 103 of 381
--r0:=2/3*(c*d^2-b*d*e+a*e^2)*x/(d*e^2*sqrt(d+e*x^3))+2/5*c*x*_
--  sqrt(d+e*x^3)/e^2-1/15*(16*c*d^2-5*e*(2*b*d+a*e))*_
--  elliptic_f(asin(e^(1/6)*sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)/(d^(1/6)*_
--  sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3))))),(3*e^(1/3)-sqrt(3)*_
--  sqrt(-e^(2/3)))/(3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))*sqrt(2)*_
--  sqrt(d^(1/3)+e^(1/3)*x)*sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))*_
--  sqrt((2*e^(2/3)*x+d^(1/3)*(-e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*_
--  (-3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3)))))*sqrt((-2*e^(2/3)*x+d^(1/3)*_
--  (e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*(3*e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3)))))/(d^(5/6)*e^(5/2)*sqrt(d+e*x^3))
--E 103
--S 104 of 381
--d0:=t0-normalize(D(r0,x))
--E 104
)clear all
--S 105 of 381
t0:=(a+b*x^3+c*x^6)/(d+e*x^3)^(5/2)
--E 105
--S 106 of 381
--r0:=2/9*(c*d^2-b*d*e+a*e^2)*x/(d*e^2*(d+e*x^3)^(3/2))-_
--  2/27*(11*c*d^2-2*b*d*e-7*a*e^2)*x/(d^2*e^2*sqrt(d+e*x^3))+_
--  1/27*(16*c*d^2+e*(2*b*d+7*a*e))*elliptic_f(asin(e^(1/6)*sqrt(2)*_
--  sqrt(d^(1/3)+e^(1/3)*x)/(d^(1/6)*sqrt(3*e^(1/3)-sqrt(3)*_
--  sqrt(-e^(2/3))))),(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))/(3*e^(1/3)+_
--  sqrt(3)*sqrt(-e^(2/3))))*sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)*_
--  sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))*sqrt((2*e^(2/3)*x+d^(1/3)*_
--  (-e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*(-3*e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3)))))*sqrt((-2*e^(2/3)*x+d^(1/3)*(e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3))))/(d^(1/3)*(3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3)))))/_
--  (d^(11/6)*e^(5/2)*sqrt(d+e*x^3))
--E 106
--S 107 of 381
--d0:=t0-normalize(D(r0,x))
--E 107
)clear all
--S 108 of 381
t0:=(a+b*x^3+c*x^6)/(d+e*x^3)^(7/2)
--E 108
--S 109 of 381

--r0:=2/15*(c*d^2-b*d*e+a*e^2)*x/(d*e^2*(d+e*x^3)^(5/2))-_
--  2/135*(17*c*d^2-2*b*d*e-13*a*e^2)*x/(d^2*e^2*(d+e*x^3)^(3/2))+_
--  2/405*(16*c*d^2+14*b*d*e+91*a*e^2)*x/(d^3*e^2*sqrt(d+e*x^3))+_
--  1/405*(16*c*d^2+7*e*(2*b*d+13*a*e))*elliptic_f(asin(e^(1/6)*sqrt(2)*_
--  sqrt(d^(1/3)+e^(1/3)*x)/(d^(1/6)*sqrt(3*e^(1/3)-sqrt(3)*_
--  sqrt(-e^(2/3))))),(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))/(3*e^(1/3)+_
--  sqrt(3)*sqrt(-e^(2/3))))*sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)*_
--  sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))*sqrt((2*e^(2/3)*x+d^(1/3)*_
--  (-e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*(-3*e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3)))))*sqrt((-2*e^(2/3)*x+d^(1/3)*(e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3))))/(d^(1/3)*(3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3)))))/_
--  (d^(17/6)*e^(5/2)*sqrt(d+e*x^3))
--E 109
--S 110 of 381
--d0:=t0-normalize(D(r0,x))
--E 110
)clear all
--S 111 of 381
t0:=(a+b*x^3+c*x^6)/(d+e*x^3)^(9/2)
--E 111
--S 112 of 381
--r0:=2/21*(c*d^2-b*d*e+a*e^2)*x/(d*e^2*(d+e*x^3)^(7/2))-_
--  2/315*(23*c*d^2-2*b*d*e-19*a*e^2)*x/(d^2*e^2*(d+e*x^3)^(5/2))+_
--  2/2835*(16*c*d^2+26*b*d*e+247*a*e^2)*x/(d^3*e^2*(d+e*x^3)^(3/2))+_
--  2/1215*(16*c*d^2+26*b*d*e+247*a*e^2)*x/(d^4*e^2*sqrt(d+e*x^3))+_
--  1/1215*(16*c*d^2+13*e*(2*b*d+19*a*e))*elliptic_f(asin(e^(1/6)*_
--  sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)/(d^(1/6)*sqrt(3*e^(1/3)-sqrt(3)*_
--  sqrt(-e^(2/3))))),(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))/(3*e^(1/3)+_
--  sqrt(3)*sqrt(-e^(2/3))))*sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)*_
--  sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))*sqrt((2*e^(2/3)*x+d^(1/3)*_
--  (-e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*(-3*e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3)))))*sqrt((-2*e^(2/3)*x+d^(1/3)*(e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3))))/(d^(1/3)*(3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3)))))/_
--  (d^(23/6)*e^(5/2)*sqrt(d+e*x^3))
--E 112
--S 113 of 381
--d0:=t0-normalize(D(r0,x))
--E 113
)clear all
--S 114 of 381
t0:=(a+b*x^3+c*x^6)/(d+e*x^3)^(11/2)
--E 114

--S 115 of 381
--r0:=2/27*(c*d^2-b*d*e+a*e^2)*x/(d*e^2*(d+e*x^3)^(9/2))-_
--  2/567*(29*c*d^2-2*b*d*e-25*a*e^2)*x/(d^2*e^2*(d+e*x^3)^(7/2))+_
--  2/8505*(16*c*d^2+38*b*d*e+475*a*e^2)*x/(d^3*e^2*(d+e*x^3)^(5/2))+_
--  26/76545*(16*c*d^2+38*b*d*e+475*a*e^2)*x/(d^4*e^2*(d+e*x^3)^(3/2))+_
--  26/32805*(16*c*d^2+38*b*d*e+475*a*e^2)*x/(d^5*e^2*sqrt(d+e*x^3))+_
--  13/32805*(16*c*d^2+19*e*(2*b*d+25*a*e))*elliptic_f(asin(e^(1/6)*_
--  sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)/(d^(1/6)*sqrt(3*e^(1/3)-sqrt(3)*_
--  sqrt(-e^(2/3))))),(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))/(3*e^(1/3)+_
--  sqrt(3)*sqrt(-e^(2/3))))*sqrt(2)*sqrt(d^(1/3)+e^(1/3)*x)*_
--  sqrt(3*e^(1/3)-sqrt(3)*sqrt(-e^(2/3)))*sqrt((2*e^(2/3)*x+d^(1/3)*_
--  (-e^(1/3)+sqrt(3)*sqrt(-e^(2/3))))/(d^(1/3)*(-3*e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3)))))*sqrt((-2*e^(2/3)*x+d^(1/3)*(e^(1/3)+sqrt(3)*_
--  sqrt(-e^(2/3))))/(d^(1/3)*(3*e^(1/3)+sqrt(3)*sqrt(-e^(2/3)))))/_
--  (d^(29/6)*e^(5/2)*sqrt(d+e*x^3))
--E 115
--S 116 of 381
--d0:=t0-normalize(D(r0,x))
--E 116
)clear all
--S 117 of 381
t0:=x^4*(d+e*x^4)/(a+b*x^4+c*x^8)
--E 117
--S 118 of 381
r0:=e*x/c-1/2*atan(2^(1/4)*c^(1/4)*x/(-b-sqrt(b^2-4*a*c))^(1/4))*_
   (c*d-b*e+(b*c*d-b^2*e+2*a*c*e)/sqrt(b^2-4*a*c))/(2^(1/4)*c^(5/4)*_
   (-b-sqrt(b^2-4*a*c))^(3/4))-1/2*atanh(2^(1/4)*c^(1/4)*x/(-b-_
   sqrt(b^2-4*a*c))^(1/4))*(c*d-b*e+(b*c*d-b^2*e+2*a*c*e)/sqrt(b^2-_
   4*a*c))/(2^(1/4)*c^(5/4)*(-b-sqrt(b^2-4*a*c))^(3/4))-_
   1/2*atan(2^(1/4)*c^(1/4)*x/(-b+sqrt(b^2-4*a*c))^(1/4))*(c*d-b*e+_
   (-b*c*d+b^2*e-2*a*c*e)/sqrt(b^2-4*a*c))/(2^(1/4)*c^(5/4)*(-b+_
   sqrt(b^2-4*a*c))^(3/4))-1/2*atanh(2^(1/4)*c^(1/4)*x/(-b+sqrt(b^2-_
   4*a*c))^(1/4))*(c*d-b*e+(-b*c*d+b^2*e-2*a*c*e)/sqrt(b^2-4*a*c))/_
   (2^(1/4)*c^(5/4)*(-b+sqrt(b^2-4*a*c))^(3/4))
--E 118
--S 119 of 381
d0:=t0-normalize(D(r0,x))
--E 119
)clear all
--S 120 of 381
t0:=x^3*(d+e*x^4)/(a+b*x^4+c*x^8)
--E 120

--S 121 of 381
r0:=1/8*e*log(a+b*x^4+c*x^8)/c-1/4*(2*c*d-b*e)*atanh((b+2*c*x^4)/_
   sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c))
--E 121
--S 122 of 381
d0:=t0-normalize(D(r0,x))
--E 122
)clear all
--S 123 of 381
t0:=x^2*(d+e*x^4)/(a+b*x^4+c*x^8)
--E 123
--S 124 of 381
r0:=1/2*atan(2^(1/4)*c^(1/4)*x/(-b-sqrt(b^2-4*a*c))^(1/4))*_
   (e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(2^(3/4)*c^(3/4)*(-b-_
   sqrt(b^2-4*a*c))^(1/4))-1/2*atanh(2^(1/4)*c^(1/4)*x/(-b-_
   sqrt(b^2-4*a*c))^(1/4))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(2^(3/4)*_
   c^(3/4)*(-b-sqrt(b^2-4*a*c))^(1/4))+1/2*atan(2^(1/4)*c^(1/4)*x/_
   (-b+sqrt(b^2-4*a*c))^(1/4))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/_
   (2^(3/4)*c^(3/4)*(-b+sqrt(b^2-4*a*c))^(1/4))-1/2*atanh(2^(1/4)*_
   c^(1/4)*x/(-b+sqrt(b^2-4*a*c))^(1/4))*(e+(2*c*d-b*e)/sqrt(b^2-_
   4*a*c))/(2^(3/4)*c^(3/4)*(-b+sqrt(b^2-4*a*c))^(1/4))
--E 124
--S 125 of 381
d0:=t0-normalize(D(r0,x))
--E 125
)clear all
--S 126 of 381
t0:=x*(d+e*x^4)/(a+b*x^4+c*x^8)
--E 126
--S 127 of 381
r0:=1/2*atan(x^2*sqrt(2)*sqrt(c)/sqrt(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/_
   sqrt(b^2-4*a*c))/(sqrt(2)*sqrt(c)*sqrt(b-sqrt(b^2-4*a*c)))+_
   1/2*atan(x^2*sqrt(2)*sqrt(c)/sqrt(b+sqrt(b^2-4*a*c)))*_
   (e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(sqrt(2)*sqrt(c)*sqrt(b+sqrt(b^2-4*a*c)))
--E 127
--S 128 of 381
d0:=t0-normalize(D(r0,x))
--E 128
)clear all

--S 129 of 381
t0:=(d+e*x^4)/(a+b*x^4+c*x^8)
--E 129
--S 130 of 381
r0:=-1/2*atan(2^(1/4)*c^(1/4)*x/(-b-sqrt(b^2-4*a*c))^(1/4))*_
   (e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(2^(1/4)*c^(1/4)*(-b-_
   sqrt(b^2-4*a*c))^(3/4))-1/2*atanh(2^(1/4)*c^(1/4)*x/(-b-_
   sqrt(b^2-4*a*c))^(1/4))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(2^(1/4)*_
   c^(1/4)*(-b-sqrt(b^2-4*a*c))^(3/4))-1/2*atan(2^(1/4)*c^(1/4)*_
   x/(-b+sqrt(b^2-4*a*c))^(1/4))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/_
   (2^(1/4)*c^(1/4)*(-b+sqrt(b^2-4*a*c))^(3/4))-1/2*atanh(2^(1/4)*_
   c^(1/4)*x/(-b+sqrt(b^2-4*a*c))^(1/4))*(e+(2*c*d-b*e)/sqrt(b^2-_
   4*a*c))/(2^(1/4)*c^(1/4)*(-b+sqrt(b^2-4*a*c))^(3/4))
--E 130
--S 131 of 381
d0:=t0-normalize(D(r0,x))
--E 131
)clear all
--S 132 of 381
t0:=(d+e*x^4)/(x*(a+b*x^4+c*x^8))
--E 132
--S 133 of 381
r0:=d*log(x)/a-1/8*d*log(a+b*x^4+c*x^8)/a+1/4*(b*d-2*a*e)*_
   atanh((b+2*c*x^4)/sqrt(b^2-4*a*c))/(a*sqrt(b^2-4*a*c))
--E 133
--S 134 of 381
d0:=t0-normalize(D(r0,x))
--E 134
)clear all
--S 135 of 381
t0:=(d+e*x^4)/(x^2*(a+b*x^4+c*x^8))
--E 135
--S 136 of 381
r0:=-d/(a*x)-1/2*c^(1/4)*atan(2^(1/4)*c^(1/4)*x/(-b-sqrt(b^2-4*a*c))^(1/4))*_
   (d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/(2^(3/4)*a*(-b-sqrt(b^2-_
   4*a*c))^(1/4))+1/2*c^(1/4)*atanh(2^(1/4)*c^(1/4)*x/(-b-sqrt(b^2-_
   4*a*c))^(1/4))*(d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/(2^(3/4)*a*_
   (-b-sqrt(b^2-4*a*c))^(1/4))-1/2*c^(1/4)*atan(2^(1/4)*c^(1/4)*_
   x/(-b+sqrt(b^2-4*a*c))^(1/4))*(d+(b*d-2*a*e)/sqrt(b^2-4*a*c))/_
   (2^(3/4)*a*(-b+sqrt(b^2-4*a*c))^(1/4))+1/2*c^(1/4)*atanh(2^(1/4)*_
   c^(1/4)*x/(-b+sqrt(b^2-4*a*c))^(1/4))*(d+(b*d-2*a*e)/_

   sqrt(b^2-4*a*c))/(2^(3/4)*a*(-b+sqrt(b^2-4*a*c))^(1/4))
--E 136
--S 137 of 381
d0:=t0-normalize(D(r0,x))
--E 137
)clear all
--S 138 of 381
t0:=(d+e*x^4)/(x^3*(a+b*x^4+c*x^8))
--E 138
--S 139 of 381
r0:=-1/2*d/(a*x^2)-1/2*atan(x^2*sqrt(2)*sqrt(c)/sqrt(b-sqrt(b^2-4*a*c)))*_
   sqrt(c)*(d+(b*d-2*a*e)/sqrt(b^2-4*a*c))/(a*sqrt(2)*sqrt(b-_
   sqrt(b^2-4*a*c)))-1/2*atan(x^2*sqrt(2)*sqrt(c)/sqrt(b+sqrt(b^2-_
   4*a*c)))*sqrt(c)*(d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/(a*sqrt(2)*_
   sqrt(b+sqrt(b^2-4*a*c)))
--E 139
--S 140 of 381
d0:=t0-normalize(D(r0,x))
--E 140
)clear all
--S 141 of 381
t0:=(d+e*x^4)/(x^4*(a+b*x^4+c*x^8))
--E 141
--S 142 of 381
r0:=-1/3*d/(a*x^3)+1/2*c^(3/4)*atan(2^(1/4)*c^(1/4)*x/(-b-sqrt(b^2-_
   4*a*c))^(1/4))*(d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/(2^(1/4)*a*(-b-_
   sqrt(b^2-4*a*c))^(3/4))+1/2*c^(3/4)*atanh(2^(1/4)*c^(1/4)*x/(-b-_
   sqrt(b^2-4*a*c))^(1/4))*(d+(-b*d+2*a*e)/sqrt(b^2-4*a*c))/(2^(1/4)*_
   a*(-b-sqrt(b^2-4*a*c))^(3/4))+1/2*c^(3/4)*atan(2^(1/4)*c^(1/4)*x/_
   (-b+sqrt(b^2-4*a*c))^(1/4))*(d+(b*d-2*a*e)/sqrt(b^2-4*a*c))/(2^(1/4)*_
   a*(-b+sqrt(b^2-4*a*c))^(3/4))+1/2*c^(3/4)*atanh(2^(1/4)*c^(1/4)*x/_
   (-b+sqrt(b^2-4*a*c))^(1/4))*(d+(b*d-2*a*e)/sqrt(b^2-4*a*c))/(2^(1/4)*_
   a*(-b+sqrt(b^2-4*a*c))^(3/4))
--E 142
--S 143 of 381
d0:=t0-normalize(D(r0,x))
--E 143
)clear all
--S 144 of 381

t0:=x^4*(1-x^4)/(1-x^4+x^8)
--E 144
--S 145 of 381
r0:=-x-1/2*atan((-2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))/sqrt(6)+_
   1/2*atan((2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))/sqrt(6)-_
   1/2*atan((-2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))/sqrt(6)+_
   1/2*atan((2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))/sqrt(6)-_
   1/4*log(1+x^2-x*sqrt(2-sqrt(3)))/sqrt(6)+1/4*log(1+x^2+_
   x*sqrt(2-sqrt(3)))/sqrt(6)-1/4*log(1+x^2-x*sqrt(2+sqrt(3)))/_
   sqrt(6)+1/4*log(1+x^2+x*sqrt(2+sqrt(3)))/sqrt(6)
--E 145
--S 146 of 381
d0:=t0-normalize(D(r0,x))
--E 146
)clear all
--S 147 of 381
t0:=x^3*(1-x^4)/(1-x^4+x^8)
--E 147
--S 148 of 381
r0:=-1/8*log(1-x^4+x^8)-1/4*atan((1-2*x^4)/sqrt(3))/sqrt(3)
--E 148
--S 149 of 381
d0:=t0-normalize(D(r0,x))
--E 149
)clear all
--S 150 of 381
t0:=x^2*(1-x^4)/(1-x^4+x^8)
--E 150
--S 151 of 381
r0:=-1/4*atan((-2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))*sqrt(1/3*(2-sqrt(3)))+_
   1/4*atan((2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))*sqrt(1/3*(2-sqrt(3)))+_
   1/8*log(1+x^2-x*sqrt(2-sqrt(3)))*sqrt(1/3*(2-sqrt(3)))-_
   1/8*log(1+x^2+x*sqrt(2-sqrt(3)))*sqrt(1/3*(2-sqrt(3)))+_
   1/4*atan((-2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))*sqrt(1/3*(2+sqrt(3)))-_
   1/4*atan((2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))*sqrt(1/3*(2+sqrt(3)))-_
   1/8*log(1+x^2-x*sqrt(2+sqrt(3)))*sqrt(1/3*(2+sqrt(3)))+_
   1/8*log(1+x^2+x*sqrt(2+sqrt(3)))*sqrt(1/3*(2+sqrt(3)))
--E 151
--S 152 of 381
d0:=t0-normalize(D(r0,x))

--E 152
)clear all
--S 153 of 381
t0:=x*(1-x^4)/(1-x^4+x^8)
--E 153
--S 154 of 381
r0:=-1/4*log(1+x^4-x^2*sqrt(3))/sqrt(3)+1/4*log(1+x^4+x^2*sqrt(3))/sqrt(3)
--E 154
--S 155 of 381
d0:=t0-normalize(D(r0,x))
--E 155
)clear all
--S 156 of 381
t0:=(1-x^4)/(1-x^4+x^8)
--E 156
--S 157 of 381
r0:=1/4*atan((-2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))*sqrt(1/3*(2-sqrt(3)))-_
   1/4*atan((2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))*sqrt(1/3*(2-sqrt(3)))+_
   1/8*log(1+x^2-x*sqrt(2-sqrt(3)))*sqrt(1/3*(2-sqrt(3)))-_
   1/8*log(1+x^2+x*sqrt(2-sqrt(3)))*sqrt(1/3*(2-sqrt(3)))-_
   1/4*atan((-2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))*sqrt(1/3*(2+sqrt(3)))+_
   1/4*atan((2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))*sqrt(1/3*(2+sqrt(3)))-_
   1/8*log(1+x^2-x*sqrt(2+sqrt(3)))*sqrt(1/3*(2+sqrt(3)))+_
   1/8*log(1+x^2+x*sqrt(2+sqrt(3)))*sqrt(1/3*(2+sqrt(3)))
--E 157
--S 158 of 381
d0:=t0-normalize(D(r0,x))
--E 158
)clear all
--S 159 of 381
t0:=(1-x^4)/(x*(1-x^4+x^8))
--E 159
--S 160 of 381
r0:=log(x)-1/8*log(1-x^4+x^8)+1/4*atan((1-2*x^4)/sqrt(3))/sqrt(3)
--E 160
--S 161 of 381
d0:=t0-normalize(D(r0,x))
--E 161

--S 162 of 381
t0:=(1-x^4)/(x^2*(1-x^4+x^8))
--E 162
--S 163 of 381
r0:=(-1)/x+1/2*atan((-2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))/sqrt(6)-_
   1/2*atan((2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))/sqrt(6)+_
   1/2*atan((-2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))/sqrt(6)-_
   1/2*atan((2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))/sqrt(6)-_
   1/4*log(1+x^2-x*sqrt(2-sqrt(3)))/sqrt(6)+1/4*log(1+x^2+_
   x*sqrt(2-sqrt(3)))/sqrt(6)-1/4*log(1+x^2-x*sqrt(2+sqrt(3)))/_
   sqrt(6)+1/4*log(1+x^2+x*sqrt(2+sqrt(3)))/sqrt(6)
--E 163
--S 164 of 381
d0:=t0-normalize(D(r0,x))
--E 164
)clear all
--S 165 of 381
t0:=(1-x^4)/(x^3*(1-x^4+x^8))
--E 165
--S 166 of 381
r0:=(-1/2)/x^2+1/4*atan(-2*x^2+sqrt(3))-1/4*atan(2*x^2+sqrt(3))-_
   1/8*log(1+x^4-x^2*sqrt(3))/sqrt(3)+1/8*log(1+x^4+x^2*sqrt(3))/sqrt(3)
--E 166
--S 167 of 381
d0:=t0-normalize(D(r0,x))
--E 167
)clear all
--S 168 of 381
t0:=(1-x^4)/(x^4*(1-x^4+x^8))
--E 168
--S 169 of 381
r0:=(-1/3)/x^3+1/4*atan((-2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))/_
   sqrt(3*(2-sqrt(3)))-1/4*atan((2*x+sqrt(2+sqrt(3)))/sqrt(2-sqrt(3)))/_
   sqrt(3*(2-sqrt(3)))+1/8*log(1+x^2-x*sqrt(2-sqrt(3)))/sqrt(3*(2-_
   sqrt(3)))-1/8*log(1+x^2+x*sqrt(2-sqrt(3)))/sqrt(3*(2-sqrt(3)))-_
   1/4*atan((-2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))/sqrt(3*(2+sqrt(3)))+_
   1/4*atan((2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))/sqrt(3*(2+sqrt(3)))-_
   1/8*log(1+x^2-x*sqrt(2+sqrt(3)))/sqrt(3*(2+sqrt(3)))+1/8*log(1+x^2+_

   x*sqrt(2+sqrt(3)))/sqrt(3*(2+sqrt(3)))
--E 169
--S 170 of 381
d0:=t0-normalize(D(r0,x))
--E 170
)clear all
--S 171 of 381
t0:=(1+x^4)/(1+x^4+x^8)
--E 171
--S 172 of 381
r0:=-1/4*atan(-2*x+sqrt(3))+1/4*atan(2*x+sqrt(3))-1/8*log(1-x+x^2)+_
   1/8*log(1+x+x^2)-1/4*atan((1-2*x)/sqrt(3))/sqrt(3)+1/4*atan((1+2*x)/_
   sqrt(3))/sqrt(3)-1/8*log(1+x^2-x*sqrt(3))/sqrt(3)+1/8*log(1+x^2+_
   x*sqrt(3))/sqrt(3)
--E 172
--S 173 of 381
d0:=t0-normalize(D(r0,x))
--E 173
)clear all
--S 174 of 381
t0:=(1-x^4)/(1+x^4+x^8)
--E 174
--S 175 of 381
r0:=1/4*atan(-2*x+sqrt(3))-1/4*atan(2*x+sqrt(3))+1/8*log(1-x+x^2)-_
   1/8*log(1+x+x^2)-1/4*atan((1-2*x)/sqrt(3))*sqrt(3)+1/4*atan((1+2*x)/_
   sqrt(3))*sqrt(3)-1/8*log(1+x^2-x*sqrt(3))*sqrt(3)+1/8*log(1+x^2+_
   x*sqrt(3))*sqrt(3)
--E 175
--S 176 of 381
d0:=t0-normalize(D(r0,x))
--E 176
)clear all
--S 177 of 381
t0:=(1+x^4)/(1-x^4+x^8)
--E 177
--S 178 of 381
r0:=-1/4*atan((-2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))*sqrt(2-sqrt(3))+_
   1/4*atan((2*x+sqrt(2-sqrt(3)))/sqrt(2+sqrt(3)))*sqrt(2-sqrt(3))-_

   1/8*log(1+x^2-x*sqrt(2+sqrt(3)))*sqrt(2-sqrt(3))+1/8*log(1+x^2+_
   x*sqrt(2+sqrt(3)))*sqrt(2-sqrt(3))-1/4*atan((-2*x+sqrt(2+sqrt(3)))/_
   sqrt(2-sqrt(3)))*sqrt(2+sqrt(3))+1/4*atan((2*x+sqrt(2+sqrt(3)))/_
   sqrt(2-sqrt(3)))*sqrt(2+sqrt(3))-1/8*log(1+x^2-x*sqrt(2-sqrt(3)))*_
   sqrt(2+sqrt(3))+1/8*log(1+x^2+x*sqrt(2-sqrt(3)))*sqrt(2+sqrt(3))
--E 178
--S 179 of 381
d0:=t0-normalize(D(r0,x))
--E 179
)clear all
--S 180 of 381
t0:=(1-x^4)/(1-3*x^4+x^8)
--E 180
--S 181 of 381
r0:=1/2*atan(2^(1/4)*x*(1/(3+sqrt(5)))^(1/4))*(3-sqrt(5))^(1/4)/(2^(1/4)*_
   sqrt(5))+1/2*atanh(2^(1/4)*x*(1/(3+sqrt(5)))^(1/4))*(3-sqrt(5))^(1/4)/_
   (2^(1/4)*sqrt(5))+1/2*atan(x*(3+sqrt(5))^(1/4)/2^(1/4))*_
   (3+sqrt(5))^(1/4)/(2^(1/4)*sqrt(5))+1/2*atanh(x*(3+sqrt(5))^(1/4)/_
   2^(1/4))*(3+sqrt(5))^(1/4)/(2^(1/4)*sqrt(5))
--E 181
--S 182 of 381
d0:=t0-normalize(D(r0,x))
--E 182
)clear all
--S 183 of 381
t0:=(-1+2*x^4+sqrt(3))/(1-x^4+x^8)
--E 183
--S 184 of 381
r0:=-atan((-2*x*(3-sqrt(3))+sqrt(6))/sqrt(6*(7-4*sqrt(3))))/sqrt(2)+_
   atan((2*x*(3-sqrt(3))+sqrt(6))/sqrt(6*(7-4*sqrt(3))))/sqrt(2)+_
   1/2*log(3+x^2*(3-sqrt(3))-sqrt(3)-x*sqrt(6*(7-4*sqrt(3))))/sqrt(2)-_
   1/2*log(3+x^2*(3-sqrt(3))-sqrt(3)+x*sqrt(6*(7-4*sqrt(3))))/sqrt(2)
--E 184
--S 185 of 381
d0:=t0-normalize(D(r0,x))
--E 185
)clear all
--S 186 of 381
t0:=(1+x^4*(1+sqrt(3)))/(1-x^4+x^8)

--E 186
--S 187 of 381
r0:=-1/2*atan((-2*x*sqrt(3)+sqrt(3*(2+sqrt(3))))/sqrt(3*(2-sqrt(3))))*_
   sqrt(2+sqrt(3))+1/2*atan((2*x*sqrt(3)+sqrt(3*(2+sqrt(3))))/sqrt(3*_
   (2-sqrt(3))))*sqrt(2+sqrt(3))-1/4*log(sqrt(3)+x^2*sqrt(3)-x*sqrt(3*_
   (2-sqrt(3))))*sqrt(2+sqrt(3))+1/4*log(sqrt(3)+x^2*sqrt(3)+_
   x*sqrt(3*(2-sqrt(3))))*sqrt(2+sqrt(3))
--E 187
--gcd not gcd in QF cancelGcd (numerator)
--S 188 of 381
d0:=t0-normalize(D(r0,x))
--E 188
)clear all
--S 189 of 381
t0:=(3+x^4*(-3+sqrt(3))-2*sqrt(3))/(1-x^4+x^8)
--E 189
--S 190 of 381
r0:=1/2*atan((-2*x*(2-sqrt(3))+sqrt(2-sqrt(3)))/sqrt(26-15*sqrt(3)))*_
   sqrt(3*(2-sqrt(3)))-1/2*atan((2*x*(2-sqrt(3))+sqrt(2-sqrt(3)))/_
   sqrt(26-15*sqrt(3)))*sqrt(3*(2-sqrt(3)))+1/4*log(-3-x^2*(3-_
   2*sqrt(3))+2*sqrt(3)-x*sqrt(3*(26-15*sqrt(3))))*sqrt(3*(2-sqrt(3)))-_
   1/4*log(-3-x^2*(3-2*sqrt(3))+2*sqrt(3)+x*sqrt(3*(26-15*sqrt(3))))*_
   sqrt(3*(2-sqrt(3)))
--E 190
--S 191 of 381
d0:=t0-normalize(D(r0,x))
--E 191
)clear all
--S 192 of 381
t0:=(d+e*x^n)/(a+c*x^(2*n))
--E 192
--S 193 of 381
--r0:=1/2*x*hypergeometric(1,1/n,1+1/n,-x^n*sqrt(c)/sqrt(-a))*_
--  (d-e*sqrt(-a)/sqrt(c))/a+1/2*x*hypergeometric(1,1/n,1+1/n,x^n*_
--  sqrt(c)/sqrt(-a))*(d+e*sqrt(-a)/sqrt(c))/a
--E 193
--S 194 of 381
--d0:=t0-normalize(D(r0,x))
--E 194

--S 195 of 381
t0:=(d+e*x)/(a+c*x^2)
--E 195
--S 196 of 381
r0:=1/2*e*log(a+c*x^2)/c+d*atan(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c))
--E 196
--S 197 of 381
d0:=t0-normalize(D(r0,x))
--E 197
)clear all
--S 198 of 381
t0:=(d+e*x^2)/(a+c*x^4)
--E 198
--S 199 of 381
r0:=-1/4*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))*(-e*sqrt(a)+_
   d*sqrt(c))/(a^(3/4)*c^(3/4)*sqrt(2))+1/4*log(a^(1/4)*c^(1/4)*x*sqrt(2)+_
   sqrt(a)+x^2*sqrt(c))*(-e*sqrt(a)+d*sqrt(c))/(a^(3/4)*c^(3/4)*sqrt(2))-_
   1/2*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))*(e*sqrt(a)+d*sqrt(c))/(a^(3/4)*_
   c^(3/4)*sqrt(2))+1/2*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))*(e*sqrt(a)+_
   d*sqrt(c))/(a^(3/4)*c^(3/4)*sqrt(2))
--E 199
--S 200 of 381
d0:=t0-normalize(D(r0,x))
--E 200
)clear all
--S 201 of 381
t0:=(d+e*x^3)/(a+c*x^6)
--E 201
--S 202 of 381
r0:=-1/6*log((-a)^(1/6)+c^(1/6)*x)*(-e*sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*_
   c^(2/3))+1/12*log((-a)^(1/3)-(-a)^(1/6)*c^(1/6)*x+c^(1/3)*x^2)*_
   (-e*sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*c^(2/3))+1/2*atan(((-a)^(1/6)-_
   2*c^(1/6)*x)/((-a)^(1/6)*sqrt(3)))*(-e*sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*_
   c^(2/3)*sqrt(3))+1/6*log((-a)^(1/6)-c^(1/6)*x)*(e*sqrt(-a)+d*sqrt(c))/_
   ((-a)^(5/6)*c^(2/3))-1/12*log((-a)^(1/3)+(-a)^(1/6)*c^(1/6)*x+_
   c^(1/3)*x^2)*(e*sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*c^(2/3))-_
   1/2*atan(((-a)^(1/6)+2*c^(1/6)*x)/((-a)^(1/6)*sqrt(3)))*(e*_
   sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*c^(2/3)*sqrt(3)),-1/6*log((-a)^(1/6)+_
   c^(1/6)*x)*(-e*sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*c^(2/3))-1/6*(-1)^(2/3)*_

log((-a)^(1/6)-(-1)^(1/3)*c^(1/6)*x)*(-e*sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*_
c^(2/3))+1/6*(-1)^(1/3)*log((-a)^(1/6)+(-1)^(2/3)*c^(1/6)*x)*_
(-e*sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*c^(2/3))+1/6*log((-a)^(1/6)-_
c^(1/6)*x)*(e*sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*c^(2/3))+1/6*(-1)^(2/3)*_
log((-a)^(1/6)+(-1)^(1/3)*c^(1/6)*x)*(e*sqrt(-a)+d*sqrt(c))/_
((-a)^(5/6)*c^(2/3))-1/6*(-1)^(1/3)*log((-a)^(1/6)-(-1)^(2/3)*_
c^(1/6)*x)*(e*sqrt(-a)+d*sqrt(c))/((-a)^(5/6)*c^(2/3))
--E 202
--S 203 of 381
d0:=t0-normalize(D(r0,x))
--E 203
)clear all
--S 204 of 381
t0:=(d+e*x^4)/(a+c*x^8)
--E 204
--S 205 of 381
r0a:=-1/4*atan(2^(1/4)*c^(1/8)*x/sqrt(-a^(1/4)+sqrt(-sqrt(a))))*_
(-e*sqrt(a)+d*sqrt(c)+a^(1/4)*(e*sqrt(a)+d*sqrt(c))/sqrt(-sqrt(a)))/_
(2^(1/4)*a^(3/4)*c^(5/8)*sqrt(-a^(1/4)+sqrt(-sqrt(a))))-_
1/4*atanh(2^(1/4)*c^(1/8)*x/sqrt(-a^(1/4)+sqrt(-sqrt(a))))*_
(-e*sqrt(a)+d*sqrt(c)+a^(1/4)*(e*sqrt(a)+d*sqrt(c))/sqrt(-sqrt(a)))/_
(2^(1/4)*a^(3/4)*c^(5/8)*sqrt(-a^(1/4)+sqrt(-sqrt(a))))+_
1/4*atan(2^(1/4)*c^(1/8)*x/sqrt(a^(1/4)+sqrt(-sqrt(a))))*_
(-e*sqrt(a)+d*sqrt(c)-a^(1/4)*(e*sqrt(a)+d*sqrt(c))/sqrt(-sqrt(a)))/_
(2^(1/4)*a^(3/4)*c^(5/8)*sqrt(a^(1/4)+sqrt(-sqrt(a))))+_
1/4*atanh(2^(1/4)*c^(1/8)*x/sqrt(a^(1/4)+sqrt(-sqrt(a))))*_
(-e*sqrt(a)+d*sqrt(c)-a^(1/4)*(e*sqrt(a)+d*sqrt(c))/sqrt(-sqrt(a)))/_
(2^(1/4)*a^(3/4)*c^(5/8)*sqrt(a^(1/4)+sqrt(-sqrt(a))))
--E 205
--S 206 of 381
r0b:=-1/8*(-1)^(3/4)*log((-a)^(1/8)-(-1)^(1/4)*c^(1/8)*x)*(-e*sqrt(-a)+_
d*sqrt(c))/((-a)^(7/8)*c^(5/8))+1/8*(-1)^(3/4)*log((-a)^(1/8)+_
(-1)^(1/4)*c^(1/8)*x)*(-e*sqrt(-a)+d*sqrt(c))/((-a)^(7/8)*c^(5/8))-_
1/8*(-1)^(1/4)*log((-a)^(1/8)-(-1)^(3/4)*c^(1/8)*x)*(-e*sqrt(-a)+_
d*sqrt(c))/((-a)^(7/8)*c^(5/8))+1/8*(-1)^(1/4)*log((-a)^(1/8)+_
(-1)^(3/4)*c^(1/8)*x)*(-e*sqrt(-a)+d*sqrt(c))/((-a)^(7/8)*c^(5/8))+_
1/8*log((-a)^(1/8)-c^(1/8)*x)*(e*sqrt(-a)+d*sqrt(c))/((-a)^(7/8)*_
c^(5/8))-1/8*%i*log((-a)^(1/8)-%i*c^(1/8)*x)*(e*sqrt(-a)+d*sqrt(c))/_
((-a)^(7/8)*c^(5/8))+1/8*%i*log((-a)^(1/8)+%i*c^(1/8)*x)*(e*sqrt(-a)+_
d*sqrt(c))/((-a)^(7/8)*c^(5/8))-1/8*log((-a)^(1/8)+c^(1/8)*x)*_
(e*sqrt(-a)+d*sqrt(c))/((-a)^(7/8)*c^(5/8))
--E 206
--S 207 of 381
d0:=t0-normalize(D(r0,x))

--E 207
)clear all
--S 208 of 381
t0:=(d+e*x^n)/(a-c*x^(2*n))
--E 208
--S 209 of 381
--r0:=1/2*x*hypergeometric(1,1/n,1+1/n,-x^n*sqrt(c)/sqrt(a))*_
--  (d-e*sqrt(a)/sqrt(c))/a+1/2*x*hypergeometric(1,1/n,1+1/n,x^n*_
--  sqrt(c)/sqrt(a))*(d+e*sqrt(a)/sqrt(c))/a
--E 209
--S 210 of 381
--d0:=t0-normalize(D(r0,x))
--E 210
)clear all
--S 211 of 381
t0:=(d+e*x)/(a-c*x^2)
--E 211
--S 212 of 381
r0:=-1/2*e*log(a-c*x^2)/c+d*atanh(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c))
--E 212
--S 213 of 381
d0:=t0-normalize(D(r0,x))
--E 213
)clear all
--S 214 of 381
t0:=(d+e*x^2)/(a-c*x^4)
--E 214
--S 215 of 381
r0:=1/2*atan(c^(1/4)*x/a^(1/4))*(-e*sqrt(a)+d*sqrt(c))/(a^(3/4)*c^(3/4))+_
   1/2*atanh(c^(1/4)*x/a^(1/4))*(e*sqrt(a)+d*sqrt(c))/(a^(3/4)*c^(3/4))
--E 215
--S 216 of 381
d0:=t0-normalize(D(r0,x))
--E 216
)clear all
--S 217 of 381

t0:=(d+e*x^3)/(a-c*x^6)
--E 217
--S 218 of 381
r0:=1/6*log(a^(1/6)+c^(1/6)*x)*(d-e*sqrt(a)/sqrt(c))/(a^(5/6)*c^(1/6))+_
   1/6*(-1)^(2/3)*log(a^(1/6)-(-1)^(1/3)*c^(1/6)*x)*(d-e*sqrt(a)/sqrt(c))/_
   (a^(5/6)*c^(1/6))-1/6*(-1)^(1/3)*log(a^(1/6)+(-1)^(2/3)*c^(1/6)*x)*_
   (d-e*sqrt(a)/sqrt(c))/(a^(5/6)*c^(1/6))-1/6*log(a^(1/6)-c^(1/6)*x)*_
   (e*sqrt(a)+d*sqrt(c))/(a^(5/6)*c^(2/3))-1/6*(-1)^(2/3)*log(a^(1/6)+_
   (-1)^(1/3)*c^(1/6)*x)*(e*sqrt(a)+d*sqrt(c))/(a^(5/6)*c^(2/3))+_
   1/6*(-1)^(1/3)*log(a^(1/6)-(-1)^(2/3)*c^(1/6)*x)*(e*sqrt(a)+d*_
   sqrt(c))/(a^(5/6)*c^(2/3))
--E 218
--S 219 of 381
d0:=t0-normalize(D(r0,x))
--E 219
)clear all
--S 220 of 381
t0:=(d+e*x^4)/(a-c*x^8)
--E 220
--S 221 of 381
r0:=1/8*(-1)^(3/4)*log(a^(1/8)-(-1)^(1/4)*c^(1/8)*x)*(d-e*sqrt(a)/sqrt(c))/_
   (a^(7/8)*c^(1/8))-1/8*(-1)^(3/4)*log(a^(1/8)+(-1)^(1/4)*c^(1/8)*x)*_
   (d-e*sqrt(a)/sqrt(c))/(a^(7/8)*c^(1/8))+1/8*(-1)^(1/4)*log(a^(1/8)-_
   (-1)^(3/4)*c^(1/8)*x)*(d-e*sqrt(a)/sqrt(c))/(a^(7/8)*c^(1/8))-_
   1/8*(-1)^(1/4)*log(a^(1/8)+(-1)^(3/4)*c^(1/8)*x)*(d-e*sqrt(a)/_
   sqrt(c))/(a^(7/8)*c^(1/8))-1/8*log(a^(1/8)-c^(1/8)*x)*(e*sqrt(a)+_
   d*sqrt(c))/(a^(7/8)*c^(5/8))+1/8*%i*log(a^(1/8)-%i*c^(1/8)*x)*(e*_
   sqrt(a)+d*sqrt(c))/(a^(7/8)*c^(5/8))-1/8*%i*log(a^(1/8)+%i*c^(1/8)*x)*_
   (e*sqrt(a)+d*sqrt(c))/(a^(7/8)*c^(5/8))+1/8*log(a^(1/8)+c^(1/8)*x)*_
   (e*sqrt(a)+d*sqrt(c))/(a^(7/8)*c^(5/8))
--E 221
--S 222 of 381
d0:=t0-normalize(D(r0,x))
--E 222
)clear all
--S 223 of 381
t0:=(b+2*c*x)*(a+b*x+c*x^2)^13
--E 223
--S 224 of 381
r0:=1/14*(a+b*x+c*x^2)^14
--E 224

--S 225 of 381
d0:=t0-normalize(D(r0,x))
--E 225
)clear all
--S 226 of 381
t0:=x*(b+2*c*x^2)*(a+b*x^2+c*x^4)^13
--E 226
--S 227 of 381
r0:=1/28*(a+b*x^2+c*x^4)^14
--E 227
--S 228 of 381
d0:=t0-normalize(D(r0,x))
--E 228
)clear all
--S 229 of 381
t0:=x^2*(b+2*c*x^3)*(a+b*x^3+c*x^6)^13
--E 229
--S 230 of 381
r0:=1/42*(a+b*x^3+c*x^6)^14
--E 230
--S 231 of 381
d0:=t0-normalize(D(r0,x))
--E 231
)clear all
--S 232 of 381
t0:=x^(-1+n)*(b+2*c*x^n)*(a+b*x^n+c*x^(2*n))^13
--E 232
--S 233 of 381
r0:=1/14*(a+b*x^n+c*x^(2*n))^14/n
--E 233
--S 234 of 381
d0:=t0-normalize(D(r0,x))
--E 234
)clear all
--S 235 of 381

t0:=(b+2*c*x)*(-a+b*x+c*x^2)^13
--E 235
--S 236 of 381
r0:=1/14*(a-b*x-c*x^2)^14
--E 236
--S 237 of 381
d0:=t0-normalize(D(r0,x))
--E 237
)clear all
--S 238 of 381
t0:=x*(b+2*c*x^2)*(-a+b*x^2+c*x^4)^13
--E 238
--S 239 of 381
r0:=1/28*(a-b*x^2-c*x^4)^14
--E 239
--S 240 of 381
d0:=t0-normalize(D(r0,x))
--E 240
)clear all
--S 241 of 381
t0:=x^2*(b+2*c*x^3)*(-a+b*x^3+c*x^6)^13
--E 241
--S 242 of 381
r0:=1/42*(a-b*x^3-c*x^6)^14
--E 242
--S 243 of 381
d0:=t0-normalize(D(r0,x))
--E 243
)clear all
--S 244 of 381
t0:=x^(-1+n)*(b+2*c*x^n)*(-a+b*x^n+c*x^(2*n))^13
--E 244
--S 245 of 381
r0:=1/14*(a-b*x^n-c*x^(2*n))^14/n
--E 245
--S 246 of 381

)clear all
--S 247 of 381
t0:=(b+2*c*x)*(b*x+c*x^2)^13
--E 247
--S 248 of 381
r0:=1/14*x^14*(b+c*x)^14
--E 248
--S 249 of 381
d0:=t0-normalize(D(r0,x))
--E 249
)clear all
--S 250 of 381
t0:=x*(b+2*c*x^2)*(b*x^2+c*x^4)^13
--E 250
--S 251 of 381
r0:=1/28*x^28*(b+c*x^2)^14
--E 251
--S 252 of 381
d0:=t0-normalize(D(r0,x))
--E 252
)clear all
--S 253 of 381
t0:=x^2*(b+2*c*x^3)*(b*x^3+c*x^6)^13
--E 253
--S 254 of 381
r0:=1/42*x^42*(b+c*x^3)^14
--E 254
--S 255 of 381
d0:=t0-normalize(D(r0,x))
--E 255
)clear all
--S 256 of 381
t0:=x^(-1+n)*(b+2*c*x^n)*(b*x^n+c*x^(2*n))^13
--E 256

--S 257 of 381
r0:=1/14*x^(14*n)*(b+c*x^n)^14/n
--E 257
--S 258 of 381
d0:=t0-normalize(D(r0,x))
--E 258
)clear all
--S 259 of 381
t0:=(b+2*c*x)/(a+b*x+c*x^2)
--E 259
--S 260 of 381
r0:=log(a+b*x+c*x^2)
--E 260
--S 261 of 381
d0:=t0-normalize(D(r0,x))
--E 261
)clear all
--S 262 of 381
t0:=x*(b+2*c*x^2)/(a+b*x^2+c*x^4)
--E 262
--S 263 of 381
r0:=1/2*log(a+b*x^2+c*x^4)
--E 263
--S 264 of 381
d0:=t0-normalize(D(r0,x))
--E 264
)clear all
--S 265 of 381
t0:=x^2*(b+2*c*x^3)/(a+b*x^3+c*x^6)
--E 265
--S 266 of 381
r0:=1/3*log(a+b*x^3+c*x^6)
--E 266
--S 267 of 381
d0:=t0-normalize(D(r0,x))
--E 267

--S 268 of 381
t0:=x^(-1+n)*(b+2*c*x^n)/(a+b*x^n+c*x^(2*n))
--E 268
--S 269 of 381
r0:=log(a+b*x^n+c*x^(2*n))/n
--E 269
--S 270 of 381
d0:=t0-normalize(D(r0,x))
--E 270
)clear all
--S 271 of 381
t0:=(b+2*c*x)/(a+b*x+c*x^2)^8
--E 271
--S 272 of 381
r0:=(-1/7)/(a+b*x+c*x^2)^7
--E 272
--S 273 of 381
d0:=t0-normalize(D(r0,x))
--E 273
)clear all
--S 274 of 381
t0:=x*(b+2*c*x^2)/(a+b*x^2+c*x^4)^8
--E 274
--S 275 of 381
r0:=(-1/14)/(a+b*x^2+c*x^4)^7
--E 275
--S 276 of 381
d0:=t0-normalize(D(r0,x))
--E 276
)clear all
--S 277 of 381
t0:=x^2*(b+2*c*x^3)/(a+b*x^3+c*x^6)^8
--E 277
--S 278 of 381

r0:=(-1/21)/(a+b*x^3+c*x^6)^7
--E 278
--S 279 of 381
d0:=t0-normalize(D(r0,x))
--E 279
)clear all
--S 280 of 381
t0:=x^(-1+n)*(b+2*c*x^n)/(a+b*x^n+c*x^(2*n))^8
--E 280
--S 281 of 381
r0:=(-1/7)/(n*(a+b*x^n+c*x^(2*n))^7)
--E 281
--S 282 of 381
d0:=t0-normalize(D(r0,x))
--E 282
)clear all
--S 283 of 381
t0:=(b+2*c*x)/(-a+b*x+c*x^2)
--E 283
--S 284 of 381
r0:=log(a-b*x-c*x^2)
--E 284
--S 285 of 381
d0:=t0-normalize(D(r0,x))
--E 285
)clear all
--S 286 of 381
t0:=x*(b+2*c*x^2)/(-a+b*x^2+c*x^4)
--E 286
--S 287 of 381
r0:=1/2*log(a-b*x^2-c*x^4)
--E 287
--S 288 of 381
d0:=t0-normalize(D(r0,x))
--E 288
)clear all

--S 289 of 381
t0:=x^2*(b+2*c*x^3)/(-a+b*x^3+c*x^6)
--E 289
--S 290 of 381
r0:=1/3*log(a-b*x^3-c*x^6)
--E 290
--S 291 of 381
d0:=t0-normalize(D(r0,x))
--E 291
)clear all
--S 292 of 381
t0:=x^(-1+n)*(b+2*c*x^n)/(-a+b*x^n+c*x^(2*n))
--E 292
--S 293 of 381
r0:=log(a-b*x^n-c*x^(2*n))/n
--E 293
--S 294 of 381
d0:=t0-normalize(D(r0,x))
--E 294
)clear all
--S 295 of 381
t0:=(b+2*c*x)/(-a+b*x+c*x^2)^8
--E 295
--S 296 of 381
r0:=1/7/(a-b*x-c*x^2)^7
--E 296
--S 297 of 381
d0:=t0-normalize(D(r0,x))
--E 297
)clear all
--S 298 of 381
t0:=x*(b+2*c*x^2)/(-a+b*x^2+c*x^4)^8
--E 298
--S 299 of 381
r0:=1/14/(a-b*x^2-c*x^4)^7
--E 299

)clear all
--S 301 of 381
t0:=x^2*(b+2*c*x^3)/(-a+b*x^3+c*x^6)^8
--E 301
--S 302 of 381
r0:=1/21/(a-b*x^3-c*x^6)^7
--E 302
--S 303 of 381
d0:=t0-normalize(D(r0,x))
--E 303
)clear all
--S 304 of 381
t0:=x^(-1+n)*(b+2*c*x^n)/(-a+b*x^n+c*x^(2*n))^8
--E 304
--S 305 of 381
r0:=1/7/(n*(a-b*x^n-c*x^(2*n))^7)
--E 305
--S 306 of 381
d0:=t0-normalize(D(r0,x))
--E 306
)clear all
--S 307 of 381
t0:=(b+2*c*x)/(b*x+c*x^2)
--E 307
--S 308 of 381
r0:=log(x*(b+c*x)),log(x)+log(b+c*x)
--E 308
--S 309 of 381
d0:=t0-normalize(D(r0,x))
--E 309
)clear all
--S 310 of 381

t0:=x*(b+2*c*x^2)/(b*x^2+c*x^4)
--E 310
--S 311 of 381
r0:=log(x)+1/2*log(b+c*x^2)
--E 311
--S 312 of 381
d0:=t0-normalize(D(r0,x))
--E 312
)clear all
--S 313 of 381
t0:=x^2*(b+2*c*x^3)/(b*x^3+c*x^6)
--E 313
--S 314 of 381
r0:=log(x)+1/3*log(b+c*x^3)
--E 314
--S 315 of 381
d0:=t0-normalize(D(r0,x))
--E 315
)clear all
--S 316 of 381
t0:=x^(-1+n)*(b+2*c*x^n)/(b*x^n+c*x^(2*n))
--E 316
--S 317 of 381
r0:=log(x)+log(b+c*x^n)/n
--E 317
--S 318 of 381
d0:=t0-normalize(D(r0,x))
--E 318
)clear all
--S 319 of 381
t0:=(b+2*c*x)/(b*x+c*x^2)^8
--E 319
--S 320 of 381
r0:=(-1/7)/(x^7*(b+c*x)^7)
--E 320
--S 321 of 381

)clear all
--S 322 of 381
t0:=x*(b+2*c*x^2)/(b*x^2+c*x^4)^8
--E 322
--S 323 of 381
r0:=(-1/14)/(x^14*(b+c*x^2)^7)
--E 323
--S 324 of 381
d0:=t0-normalize(D(r0,x))
--E 324
)clear all
--S 325 of 381
t0:=x^2*(b+2*c*x^3)/(b*x^3+c*x^6)^8
--E 325
--S 326 of 381
r0:=(-1/21)/(x^21*(b+c*x^3)^7)
--E 326
--S 327 of 381
d0:=t0-normalize(D(r0,x))
--E 327
)clear all
--S 328 of 381
t0:=x^(-1+n)*(b+2*c*x^n)/(b*x^n+c*x^(2*n))^8
--E 328
--S 329 of 381
r0:=(-1/7)/(n*x^(7*n)*(b+c*x^n)^7)
--E 329
--S 330 of 381
d0:=t0-normalize(D(r0,x))
--E 330
)clear all
--S 331 of 381
t0:=(b+2*c*x)*(a+b*x+c*x^2)^p
--E 331

--S 332 of 381
r0:=(a+b*x+c*x^2)^(1+p)/(1+p)
--E 332
--S 333 of 381
d0:=t0-normalize(D(r0,x))
--E 333
)clear all
--S 334 of 381
t0:=x*(b+2*c*x^2)*(a+b*x^2+c*x^4)^p
--E 334
--S 335 of 381
r0:=1/2*(a+b*x^2+c*x^4)^(1+p)/(1+p)
--E 335
--S 336 of 381
d0:=t0-normalize(D(r0,x))
--E 336
)clear all
--S 337 of 381
t0:=x^2*(b+2*c*x^3)*(a+b*x^3+c*x^6)^p
--E 337
--S 338 of 381
r0:=1/3*(a+b*x^3+c*x^6)^(1+p)/(1+p)
--E 338
--S 339 of 381
d0:=t0-normalize(D(r0,x))
--E 339
)clear all
--S 340 of 381
t0:=x^(-1+n)*(b+2*c*x^n)*(a+b*x^n+c*x^(2*n))^p
--E 340
--S 341 of 381
r0:=(a+b*x^n+c*x^(2*n))^(1+p)/(n*(1+p))
--E 341
--S 342 of 381
d0:=t0-normalize(D(r0,x))
--E 342

--S 343 of 381
t0:=(b+2*c*x)*(-a+b*x+c*x^2)^p
--E 343
--S 344 of 381
r0:=(-a+b*x+c*x^2)^(1+p)/(1+p)
--E 344
--S 345 of 381
d0:=t0-normalize(D(r0,x))
--E 345
)clear all
--S 346 of 381
t0:=x*(b+2*c*x^2)*(-a+b*x^2+c*x^4)^p
--E 346
--S 347 of 381
r0:=1/2*(-a+b*x^2+c*x^4)^(1+p)/(1+p)
--E 347
--S 348 of 381
d0:=t0-normalize(D(r0,x))
--E 348
)clear all
--S 349 of 381
t0:=x^2*(b+2*c*x^3)*(-a+b*x^3+c*x^6)^p
--E 349
--S 350 of 381
r0:=1/3*(-a+b*x^3+c*x^6)^(1+p)/(1+p)
--E 350
--S 351 of 381
d0:=t0-normalize(D(r0,x))
--E 351
)clear all
--S 352 of 381
t0:=x^(-1+n)*(b+2*c*x^n)*(-a+b*x^n+c*x^(2*n))^p
--E 352
--S 353 of 381

r0:=(-a+b*x^n+c*x^(2*n))^(1+p)/(n*(1+p))
--E 353
--S 354 of 381
d0:=t0-normalize(D(r0,x))
--E 354
)clear all
--S 355 of 381
t0:=(b+2*c*x)*(b*x+c*x^2)^p
--E 355
--S 356 of 381
r0:=(b*x+c*x^2)^(1+p)/(1+p)
--E 356
--S 357 of 381
d0:=t0-normalize(D(r0,x))
--E 357
)clear all
--S 358 of 381
t0:=x*(b+2*c*x^2)*(b*x^2+c*x^4)^p
--E 358
--S 359 of 381
r0:=1/2*(b*x^2+c*x^4)^(1+p)/(1+p)
--E 359
--S 360 of 381
d0:=t0-normalize(D(r0,x))
--E 360
)clear all
--S 361 of 381
t0:=x^2*(b+2*c*x^3)*(b*x^3+c*x^6)^p
--E 361
--S 362 of 381
r0:=1/3*(b*x^3+c*x^6)^(1+p)/(1+p)
--E 362
--S 363 of 381
d0:=t0-normalize(D(r0,x))
--E 363
)clear all

--S 364 of 381
t0:=x^(-1+n)*(b+2*c*x^n)*(b*x^n+c*x^(2*n))^p
--E 364
--S 365 of 381
r0:=(b*x^n+c*x^(2*n))^(1+p)/(n*(1+p))
--E 365
--S 366 of 381
d0:=t0-normalize(D(r0,x))
--E 366
)clear all
--S 367 of 381
t0:=(d+e*x^n)/(a+b*x^n+c*x^(2*n))
--E 367
--S 368 of 381
--r0:=x*hypergeometric(1,1/n,1+1/n,-2*c*x^n/(b-sqrt(b^2-4*a*c)))*_
--  (e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(b-sqrt(b^2-4*a*c))+x*_
--  hypergeometric(1,1/n,1+1/n,-2*c*x^n/(b+sqrt(b^2-4*a*c)))*_
--  (e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(b+sqrt(b^2-4*a*c))
--E 368
--S 369 of 381
d0:=t0-normalize(D(r0,x))
--E 369
)clear all
--S 370 of 381
t0:=(d+e*x)/(a+b*x+c*x^2)
--E 370
--S 371 of 381
r0:=1/2*e*log(a+b*x+c*x^2)/c-(2*c*d-b*e)*atanh((b+2*c*x)/_
   sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c))
--E 371
--S 372 of 381
d0:=t0-normalize(D(r0,x))
--E 372
)clear all
--S 373 of 381
t0:=(d+e*x^2)/(a+b*x^2+c*x^4)
--E 373

--S 374 of 381
r0:=atan(x*sqrt(2)*sqrt(c)/sqrt(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/_
   sqrt(b^2-4*a*c))/(sqrt(2)*sqrt(c)*sqrt(b-sqrt(b^2-4*a*c)))+_
   atan(x*sqrt(2)*sqrt(c)/sqrt(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/_
   sqrt(b^2-4*a*c))/(sqrt(2)*sqrt(c)*sqrt(b+sqrt(b^2-4*a*c)))
--E 374
--S 375 of 381
d0:=t0-normalize(D(r0,x))
--E 375
)clear all
--S 376 of 381
t0:=(d+e*x^4)/(a+b*x^4+c*x^8)
--E 376
--S 377 of 381
r0:=-1/2*atan(2^(1/4)*c^(1/4)*x/(-b-sqrt(b^2-4*a*c))^(1/4))*_
   (e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(2^(1/4)*c^(1/4)*_
   (-b-sqrt(b^2-4*a*c))^(3/4))-1/2*atanh(2^(1/4)*c^(1/4)*_
   x/(-b-sqrt(b^2-4*a*c))^(1/4))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/_
   (2^(1/4)*c^(1/4)*(-b-sqrt(b^2-4*a*c))^(3/4))-1/2*atan(2^(1/4)*_
   c^(1/4)*x/(-b+sqrt(b^2-4*a*c))^(1/4))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/_
   (2^(1/4)*c^(1/4)*(-b+sqrt(b^2-4*a*c))^(3/4))-1/2*atanh(2^(1/4)*_
   c^(1/4)*x/(-b+sqrt(b^2-4*a*c))^(1/4))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/_
   (2^(1/4)*c^(1/4)*(-b+sqrt(b^2-4*a*c))^(3/4))
--E 377
--S 378 of 381
d0:=t0-normalize(D(r0,x))
--E 378
)clear all
--S 379 of 381
t0:=(1+x^3)/(x-x^4+x^7)
--E 379
--S 380 of 381
r0:=log(x)-1/6*log(1-x^3+x^6)-atan((1-2*x^3)/sqrt(3))/sqrt(3)
--E 380
--S 381 of 381
d0:=t0-normalize(D(r0,x))
--E 381
)spool
)lisp (bye)

———- 48

References^{[1] nothing}

49