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Homework Help: Residues homework help

  1. May 9, 2010 #1
    1. The problem statement, all variables and given/known data

    show [tex]^{\infty}_{0}\int[/tex] x2 / (x6 + 1) = [tex]\pi[/tex]/6


    2. Relevant equations



    3. The attempt at a solution

    = 1/2 [tex]\int^{\infty}_{-\infty}[/tex] ...

    im not sure how to go about this any pointers pls?
     
  2. jcsd
  3. May 9, 2010 #2

    lanedance

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    Homework Helper

    Re: residues

    you're really supposed to attempt some working

    but note the function is symmetric on the real axis... and the magnitude will get small as the radius gets big, this should help you pick a contour to integrate

    it will help to find the poles as well...
     
  4. May 9, 2010 #3
    Re: residues

    Note that you don't need to integrate over the half circle and come back along the negative real axis. You would then have to sum over the three poles in the upper half plane. Instead, you can return along the line z = r exp(i pi/3).
     
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