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Math Help - integral of ratio of cosine and polynomial

  1. #1
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    integral of ratio of cosine and polynomial

    hi there,

    i have problems solving the following integral:

    \int_{-\infty}^{\infty} \dfrac{\cos(x\k)}{x^2+k^4}\,dx

    i could not come up with an appropriate substitution (even for k = 1). i also tried integration via Euler's formula - could not work that out either.

    anybody an idea on how to attack this problem? many thanks in advance!!!

    best,
    Stefan
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  2. #2
    Super Member girdav's Avatar
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    (Hi, you can put t=kx then use residues).
    Sorry, t=x/k is better.
    Last edited by girdav; April 21st 2011 at 01:53 PM.
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  3. #3
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    Quote Originally Posted by girdav View Post
    Hi, you can put t=kx then use residues.
    ok, i see. thanks a lot for your support, it's really much appreciated!

    best,
    Stefan
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