Integrate (x^2)(sqrt(x^2-a^2))^(-1)

[coverband]

Anyone know how to integrate this?

Thanks

 

[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" 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 >>

 

[Fredrik]

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