Integration similaring to Fourier transform of Gaussian function I would like to calculate the integral: 
$$\int^{\infty}_{0}x\cdot \exp(-x^2)\cdot \exp(-ikx)dx$$
Are there some tricks to solve it?
Many thanks.

\begin{align}
  \int_{0}^{\infty}xe^{-x^2}e^{-ikx}dx
   & = -\frac{1}{2}\int_{0}^{\infty}e^{-ikx}\frac{d}{dx}e^{-x^2}dx \\
   & = -\left.\frac{1}{2}e^{-ikx}e^{-x^2}\right|_{0}^{\infty}-\frac{ik}{2}\int_{0}^{\infty}e^{-x^2}e^{-ikx}dx \\
   & = \frac{1}{2}-\frac{ik}{4}\sqrt{2\pi}\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}e^{-x^2}e^{-ikx}dx
\end{align}
So the problem reduces to the Fourier transform of a Gaussian.
