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I Integral of a special trigonometic functions

  1. Sep 21, 2016 #1

    KFC

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    Hi all,
    I am working on the following integral

    ##
    \int_0^{2\pi}\frac{1+\cos[\alpha x]}{1+\sin x}dx
    ##

    where ##\alpha## is odd integer. Unless I set the ##\alpha## to a number then I can find the integral with mathematica easily. For general case with symbolic ##\alpha##, I cannot find the integral like this kind from any table and mathematica won't give the result as well. I am trying to apply the following relation to simplify the integrand

    ##
    \cos[\alpha x] = 2\cos x \cos[(\alpha-1)x] - \cos[(\alpha-2)x]
    ##

    it doesn't help to compute the integral. Any idea is welcomed. Thanks.
     
  2. jcsd
  3. Sep 22, 2016 #2

    Orodruin

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    Your integral does not converge.
     
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