From a preceding question I have worked on, an integral to evaluate:
$$\frac{2i\sqrt{a}}{(a^2+1)}\cdot\int_{-\infty}^\infty k\cdot\exp\bigg[i\bigg(k-\frac{k^{2}ht}{2m}\bigg)\bigg]~dk$$
I need to determine the limiting cases for large a and small a.
However, the integrand looks rather messy. Would I be required to resort to generalized functions, or is this a case of brute force integration by parts ?