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## Homework Statement

I have this integral to solve:

[tex]\int[/tex] [tex]\frac{ab}{a^2 cos^2 t + b^2 sin^2 t}[/tex] 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.