# Homework Help: Integrate (x^2)(sqrt(x^2-a^2))^(-1)

1. Dec 15, 2008

### coverband

Anyone know how to integrate this?

Thanks

2. Dec 15, 2008

### Citan Uzuki

Yes. Start by factoring out 1/a, then make the trig substitution $$x = a \sec \theta$$. After simplification, you will obtain an integral in terms of secant cubed, for which there is an entire http://en.wikipedia.org/wiki/Integral_of_secant_cubed" [Broken] devoted to explaining how to integrate that. Do so, back-substitute, and simplify. Or alternatively, simply look this up in your handy table of integrals, and find that the solution is:

<< complete solution deleted by berkeman >>

Last edited by a moderator: May 3, 2017
3. Dec 15, 2008

### Fredrik

Staff Emeritus
$y=\sqrt{x^2-a^2}$ simplifies it a bit.