Originally Posted by

**AlvinCY** I'm currently stuck on a problem (it's a Fourier transform), I'm not sure it this is the right forum section to post it on, as it falls under several categories...

$\displaystyle \frac{1}{2\pi}\int\limits_{-\infty}^{\infty}e^{-|x|}e^{i\omega x}dx

$

I've broken the integral into two:

$\displaystyle \frac{1}{2\pi}[\int\limits_{-\infty}^{0}e^{x}e^{i\omega x}dx+\int\limits_{0}^{\infty}e^{-x}e^{i\omega x}dx]

$

Then combined the exponentials:

$\displaystyle \frac{1}{2\pi}[\int\limits_{-\infty}^{0}e^{x+i\omega x}dx+\int\limits_{0}^{\infty}e^{-x+i\omega x}dx]

$

But not sure where to go from here, I know the solution is meant to be:

$\displaystyle \frac{1}{\pi}\frac{1}{\omega^2+1}$

Any help you can offer me would be great!