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I need some help to calculate this integral:

[tex]\int _0^{2\pi}\frac{x^n}{\sqrt{1-m\cos x}}dx[/tex], where 0<m<1.

What I've already tried:

took the binomial series of (1-m cos(x))^(-1/2), this results in integrals like

[tex]\int_0^{2\pi} x^n(\cos x)^k dx[/tex]

After this I've replaced cos(x)^k as a polynomial of cos(r*x) (r=1,2,...,k). With this I've managed to get a formula (involving two summas), but it is so ugly that I cannot use them in any furhter calculations.

(sorry, I don't know how to make formulas in PF, so I've inserted the LaTex code of it)

Thank You!

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# Integral help

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