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I need solve this integral, and I tried various methods of solving and did not get it. The integral is:

$$\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta,$$

where $t$ is a positive integer.

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    An integral of a rational function of sine and cosine can always be transformed to an integral of a rational function by the substitution $u=\tan(\theta/2)$.2012-10-11
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    $2t\pi/(t^2-1)^{3/2}$2012-10-11

4 Answers 4