How to Simplify the Integral 1/(1-x^2y^2) Using Substitution?

[Gekko]

Integral 1/(1-x^2y^2) dx?
From 0 to 1

Where x = sina/cosb and y=sinb/cosa


Using substitution and changing the limits yields

Integral from 0 to pi/4 of cos^3(a)cos(b) / (cos(a+b)cos(a-b)) du

But how to go from here?

 

[lanedance]

i don't understand yuor integral, you appear to have a lost any dependent variable in the integrand?

i would just try the substitution x = sin(u)/y