# Fourier Intergrals and transforms

How do I do a Fourier integral (and whats the point of them??)

$$F(\omega) = \frac{1}{\sqrt{2\pi}}\int dte^{-\alpha t}cos\omega t$$

and I've not the foggiest idea what to do. I thought I could just go about doing in the integral by parts (limits are 0 and infinity by the way), but on further research I don't think I can do that can I?

Try integration by parts.

mathman