Complex variables, integral

1. Mar 18, 2008

babyrudin

2. Relevant equations

Using complex analysis, compute
$$\int_{-\infty}^{\infty} \frac{e^{itx}}{1+x^2}dx$$
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
$$\pi e^{-|t|}$$.
How should I solve it using complex analysis?

Last edited: Mar 18, 2008
2. Mar 19, 2008

Tom Mattson

Staff Emeritus
Try using the Residue Theorem.

3. Mar 19, 2008

babyrudin

Great, I think I know how to do it now. I was trying the Cauchy integral formula too much. Thanks!