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.

You can complete the square in the exponent, and get an answer in terms of the Dawson function:
$$\frac{1}{4} \left(2-\sqrt{\pi } i k e^{\frac{i^2 k^2}{4}} \text{erfc}\left(\frac{i
   k}{2}\right)\right).$$
