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Residue theorem problem involving real value Intergral

  1. May 15, 2012 #1
    1. The problem statement, all variables and given/known data

    ∫ from infinity to 0 of x^2/(x^2+1)(x^2+16)

    2. Relevant equations

    The Integral will be the sum of the residues times 2πi

    3. The attempt at a solution

    The only singularities that matter are at i and 4i and they are simple poles. So x^2/(x^2+1)/(2x) and I plug in 4i and get -2i/(15) then I plug in i into x^2/(x^2+16)/(2x) and get i/30 and when I add them I get -3i/30. Because it's only from 0 and to negative infinity I mult that by ∏i and I get ∏/10.
     
  2. jcsd
  3. May 15, 2012 #2

    vela

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    Looks good.

    You glossed over several steps, which I'm assuming you understand. Just make sure you know why you can do what you did.
     
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