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## Homework Statement

I am trying to solve one definite integral

## Homework Equations

[tex] \int_0^{2 \pi} \frac{\sin^2{t}}{\sqrt{a\cos{t} + b}} dt[/tex]

where [tex]a, b[/tex] are some positive numbers.

## The Attempt at a Solution

I tried integrate by parts, also differentiate by parameter [tex]a[/tex]. Does not help because of the square root. In this case I got some diff.equation for the integral I want, but I need to solve even more nasty integrals:

either

[tex] \int_0^{2 \pi} \sqrt{a\cos{t} + b} \cos{t} dt[/tex]

or

[tex] \int_0^{2 \pi} \frac{1}{\sqrt{a\cos{t} + b}} dt[/tex]