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Complex variables, integral

  • Thread starter babyrudin
  • Start date
8
0
2. Homework 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:

Answers and Replies

Tom Mattson
Staff Emeritus
Science Advisor
Gold Member
5,474
20
Try using the Residue Theorem.
 
8
0
Great, I think I know how to do it now. I was trying the Cauchy integral formula too much. Thanks!
 

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