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**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?

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