What is the fourier transform of $xe^{-x}$ for $x \in (-\infty, \infty)$?

Question

Calculating $\mathcal{F}[xe^{-x}] = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty xe^{-x}e^{i \omega x} dx$ gives me an infinite value whereas i need it to converge! Is there another way to calculate this? I can't find it on tables!