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Complex variables, integral

  1. Mar 18, 2008 #1
    2. Relevant equations

    Using complex analysis, compute
    [tex]\int_{-\infty}^{\infty} \frac{e^{itx}}{1+x^2}dx [/tex]
    where t is real.

    3. The attempt at a solution

    I'm not good at complex analysis at all and am totally lost. I do know some Fourier analysis though and using it I got
    [tex]\pi e^{-|t|}[/tex].
    How should I solve it using complex analysis?
    Last edited: Mar 18, 2008
  2. jcsd
  3. Mar 19, 2008 #2

    Tom Mattson

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    Staff Emeritus
    Science Advisor
    Gold Member

    Try using the Residue Theorem.
  4. Mar 19, 2008 #3
    Great, I think I know how to do it now. I was trying the Cauchy integral formula too much. Thanks!
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