I'm trying to find [itex]\frac{1}{2\pi}\int \limits_{-\infty}^{\infty}e^{-itx}\frac{1}{a^2+x^2}\mathrm{d}x[/itex] where 'a' is a constant.(adsbygoogle = window.adsbygoogle || []).push({});

First I noticed that there is [itex]\frac {\partial \arctan x}{\partial x}[/itex] in this and using a substitute got [itex]\int \limits_0^{\pi / 2}\cos( t \tan x )\mathrm{d}x[/itex] with some constants in the gaps.

I then remember that I'm working in complex numbers, factored [itex]a^2+x^2[/itex] and got something essentially along the lines of [itex]\int \frac{e^x}{x}\mathrm{d}x[/itex], or maybe rather [itex]\int \limits_0^{\infty} \frac {\cos tx} {a - ix}\mathrm{d}x[/itex].

I can't integrate either.

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# Homework Help: Fourier transform truoble

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