# Complex variables, integral

2. Homework 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?

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Tom Mattson
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