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Residue of z/(1+z^n)

  1. Mar 17, 2014 #1
    Hello,
    I can't find the result to

    1. The problem statement, all variables and given/known data
    Have to prove that ∫x/(1+x^n) dx = π/n/sin(2π/n)
    so i'm trying to prove that by starting to find :
    2πi*res(z/(1+z^n), exp(iπ/n))

    but don't know what is res(z/(1+z^n), exp(iπ/n))

    Thanks
     
  2. jcsd
  3. Mar 17, 2014 #2

    vela

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    Try considering the cases where n=1, 2, and 3 and look for a pattern.
     
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