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Evaluate $$\int_{0}^{2\pi}\frac{1}{\rho^2+r^2-2r\rho \cos(t-\theta)}dt.$$


I found this under some exercises about Poisson's integral formula, to my surprise the problem looks simple but I do not have a single idea of how to go with it. Can somebody help?

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    You can assume, wlog $\theta = 0$ and $p^2 + r^2 = 1$.2012-03-24
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    @late_learner: Of course there is a loss generality, what of if my $\theta \ne 0$?2012-03-24
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    $\cos$ is $2 \pi$ periodic, no loss!2012-03-24
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    @late_learner: Can the answer be the same with that of sashu after assumption?2012-03-24
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    The result is independant of $\theta$!2012-03-25
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    And the extra assumption $p^2+r^2=1$ only applies scaling, but I have to admit that Sasha's computation is excellent, and the extra assumptions will not improve upon his short argument.2012-03-25

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