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I am able to solve this problem by Cauchy Residue theorem, but not by contour integration. (i.e Taking integration in semicircle of radius R and x-axis from -R to +R). $$ I = \int_0^{2\pi} \frac{1}{1-2a\cos(t)+a^2}dt\,. $$

$$ Given : a^2 < 1 $$

PS: Not a homework question, but practice question

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  • $\begingroup$ What is the question? $\endgroup$
    – zokomoko
    Aug 13, 2017 at 20:15
  • $\begingroup$ The contour is a circle here. $\endgroup$
    – FDP
    Aug 13, 2017 at 20:24
  • $\begingroup$ Choosing $z$ correctly $\cos(t) = \frac{z+z^{-1}}{2}$ $\endgroup$
    – reuns
    Aug 13, 2017 at 20:36
  • $\begingroup$ @zokomoko Finding the given integral using contour integration. $\endgroup$
    – user1611542
    Aug 13, 2017 at 20:40
  • $\begingroup$ @FDP I got your point. Thanks! $\endgroup$
    – user1611542
    Aug 13, 2017 at 20:41

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