I am trying to compute the following Fourier transform
$$\int_{-\infty}^\infty\text{d}x\,e^{i k x}e^{-x^2/a^2}\frac{1}{[x-(d-i\epsilon)]^3}$$
where $d\in\mathbb{R}$, and $\epsilon$ is a small, real, positive number. I feel like it should be easily doable with the residue theorem, but I can't come up with a suitable contour. Anyone knows a solution or at least has some indications on how to perform the integral?
There are many integrals that mathematica can't do and yet there exists a closed form for them... It just takes someone more clever than us! ;)