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Branch Cut

  1. Oct 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Define the branch cut prior to solving the following:
    integrate from 0 to infinity of [log x]^4/ [1+x^2]


    2. Relevant equations

    The only poles inside the upper half plane is i

    3. The attempt at a solution

    How do I separate the countour?---help.

    Thanks.
     
  2. jcsd
  3. Oct 14, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    Just put a branch cut along the negative real axis. Now integrate along the real axis avoiding the singularity at z=0 with a little arc and closing in a big arc. I think you need to work out the lower powers of log(x) before you go direct to log(x)^4, but there may be a trick.
     
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