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Complex integral without cauchy

  1. Oct 13, 2011 #1

    I've been trying to do this integral without cauchy's theorem (with the theorem i get 6ipi in like 2 steps). Im stuck at this point, I have found afew ways to do the integral im stuck on but they all involve multiple variable changes and I was wondering if there is a simple way to do this that i'm not seeing.

    [PLAIN]http://img832.imageshack.us/img832/7958/intup.jpg [Broken]

    sorry typo, its not supposed to be 1/2 ln(1+2e^(it)) just ln(1+2e^(it))

    Thanks in advanced
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 13, 2011 #2


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    It helps to note that the numerators are all of the form i(2eit)n. Try using the substitution u=2eit+1 on all of them.
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