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Homework Help: Complex analysis

  1. Feb 28, 2009 #1
    1. The problem statement, all variables and given/known data

    Hey guys.

    So, I need to calculate this integral. I uploaded what I tried to do.
    First of all, did the substitute, then I tried to use the residue theorem so I was looking for the residue of z=0 which is happen to be a removable singular point so it's just 0, then I went for the z=2*pi*k (when k can't be 0) residue and found out that it's 0.
    I guess I have a mistake there, any idea guys?

    Thanks.


    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Mar 1, 2009 #2

    gabbagabbahey

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    Gold Member

    Your substitutions a little fishy; does [tex]e^{z}=x^2+1[/tex] really mean that [tex]x=\sqrt{e^z-1}[/tex]? How are you excluding the negative root?
     
  4. Mar 1, 2009 #3

    HallsofIvy

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    If you are going to use residues, what close path are you going to integrate over?
     
  5. Mar 1, 2009 #4
    I thought about a closed contour consisting of the semi-circle with radius r and centre at z = 0 and the line segment going from z = -r to z = r and then doing the r --> oo thing. That way, I'll only have one pole, p=i.
    Then, I'll try to break it into -r to 0 and from 0 to r, and find the latter, does that seems right?

    Thanks.
     
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