# Homework Help: Integral Mathematica

1. May 13, 2014

### ChrisVer

$\int \frac{dx}{(a(1+x^{-1})+b(1+x^{2})-1)^{1/2}}$

For better in your code the integral must be:
1/sqrt[a(1+(1/x))+b(1+x^(2))-1]

For $a≤1$ and for cases:

A)$0<b<1$
B)$b>1$

I am sorry,but I haven't been able to receive mathematica yet... *sad face*
Deep thanks in regard

*not to be misunderstood that I'm asking to find everything ready I even know the codes I'd use in such a case:
Expand[Assuming[0<a<1 && b>1, Integrate[1/sqrt[a(1+(1/x))+b(1+x^(2))-1]]]]
Expand[Assuming[0<a<1 && 0<b<1, Integrate[1/sqrt[a(1+(1/x))+b(1+x^(2))-1]]]]
(if there would be an error I'd try to remove the expand)...I just still don't have the software at hand

Last edited: May 13, 2014
2. May 13, 2014

### Ray Vickson

I don't understand your statement that you " haven't been able to receive mathematica yet...". Does that mean that you have placed an order to buy Mathematica but it has not arrived yet, or what?

Anyway, I don't have access to Mathematica, so I did it in Maple instead. The results are exceedingly complicated, involving Elliptic functions of complex arguments, etc. Here is the code and result for 0 < b < 1:
> lprint(f); <---I call your function 'f'
1/(a*(1+1/x)+b*(1+x^2)-1)^(1/2)
J1:=int(f,x) assuming a<1,b>0,b<1: <---output suppressed by ending in ':'
lprint(J1);-4*(EllipticF(6^(1/2)*((3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)/(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2),((-3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+3*12^(1/3)*b*a+3*12^(1/3)*b^2-3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(-((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+12^(1/3)*b*a+12^(1/3)*b^2-12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b))^(1/2))-EllipticPi(6^(1/2)*((3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)/(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2),(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b),((-3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+3*12^(1/3)*b*a+3*12^(1/3)*b^2-3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(-((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+12^(1/3)*b*a+12^(1/3)*b^2-12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b))^(1/2)))/((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)*(-(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b)*(12*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)+12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-b*12^(2/3)*a-12^(2/3)*b^2+12^(2/3)*b+I*3^(1/2)*12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(2/3)*b*a+I*3^(1/2)*12^(2/3)*b^2-I*3^(1/2)*12^(2/3)*b)/(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2)*((((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b)*(12*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)+12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-b*12^(2/3)*a-12^(2/3)*b^2+12^(2/3)*b-I*3^(1/2)*12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-I*3^(1/2)*12^(2/3)*b*a-I*3^(1/2)*12^(2/3)*b^2+I*3^(1/2)*12^(2/3)*b)/(-((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+12^(1/3)*b*a+12^(1/3)*b^2-12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2)*(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b)^2*((3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)/(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b))^(1/2)*(((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-12^(1/3)*b*a-12^(1/3)*b^2+12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)*x*((a*x+a+b*x+b*x^3-x)/x)^(1/2)/(x*(6*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)-12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+b*12^(2/3)*a+12^(2/3)*b^2-12^(2/3)*b)*(12*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)+12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-b*12^(2/3)*a-12^(2/3)*b^2+12^(2/3)*b-I*3^(1/2)*12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-I*3^(1/2)*12^(2/3)*b*a-I*3^(1/2)*12^(2/3)*b^2+I*3^(1/2)*12^(2/3)*b)*(12*x*b*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(1/3)+12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-b*12^(2/3)*a-12^(2/3)*b^2+12^(2/3)*b+I*3^(1/2)*12^(1/3)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(2/3)*b*a+I*3^(1/2)*12^(2/3)*b^2-I*3^(1/2)*12^(2/3)*b)/(-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2)))^(1/2)/(3*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)-3*12^(1/3)*b*a-3*12^(1/3)*b^2+3*12^(1/3)*b+I*3^(1/2)*((-9*a+3^(1/2)*((4*a^3+39*a^2*b-12*a^2+12*a*b^2-24*a*b+12*a+4*b^3-12*b^2+12*b-4)/b)^(1/2))*b^2)^(2/3)+I*3^(1/2)*12^(1/3)*b*a+I*3^(1/2)*12^(1/3)*b^2-I*3^(1/2)*12^(1/3)*b)/(x*(a*x+a+b*x+b*x^3-x))^(1/2)

Something similar is obtained for the case b > 1.

Note: the command 'lprint' gives AASCII output suitable for inclusion as text. The on-screen output looks much better, but still needs 9 pages to display.

3. May 13, 2014

### ChrisVer

$a(x+1)+b(x^3+x)-x=0$
a(x+1)+b(x^3+x)-x=0
for the same domains of a,b?

(Also for the mathematica, I'm having it offered by my univ, but unfortunately I learned today that I have to send a mail first to them in order to be able to download it.)

4. May 13, 2014

### Staff: Mentor

Questions about integrals should be posted in the Calculus & Beyond section.

5. May 13, 2014

### Ray Vickson

Yes, Maple can solve that equation---it just uses standard formulas for the solutions of a cubic equation, that you can find easily on-line. You can solve the equation yourself using Wolfram Alpha, which is like Mathematica lite and is freely available on the web. PF rules forbid me from writing the answer here.

6. May 13, 2014

### SammyS

Staff Emeritus
Hey Ray:

I think there's a mistake in line 57, the 31's chara...

Oh! Nevermind.

I had the wrong eyeglasses on.

7. May 13, 2014

### webdevelopment

Dear,
However $a=0.25=b$ have solution at $1$ and $0.618$...