Trigonometric identities for integral problem

[student85]

Homework Statement

I have this integral to solve:
\int \frac{ab}{a^2 cos^2 t + b^2 sin^2 t} dt

The limits are 0 to 2*pi.

Homework Equations

The Attempt at a Solution

I've tried using trigonometric identities, trigonometric substitution... and many kinds of algebraic manipulations but I can't do it! I'm beginning to think it can't be done analytically but I doubt it because my professor wants us to prove it is equal to something else which I found is 2*pi. I used my calculator to do the integration and I did get 2*pi, so at least I know what it is equal to. However I don't seem to get anywhere trying to solve it. Please help!

Thanks.

 

[jhicks]

It looks like latex is acting up (maybe just for me?). You might want to just write out the code. Most of us will be able to read it anyhow.

 

[student85]

I think if you click over the red text you see the latex code. Anyway here it is...
So it's an integral of: {ab} / {a^2 cos^2 t + b^2 sin^2 t} with respect to t.
From t=0 to 2*pi

 

[student85]

Nevermind, I solved the problem.