I am working on some simulation, and the paper that I am basing some of the work off of involves several complex integrals.
In particular, the one I am trying to solve is
$\int_0^\infty \frac{1}{\omega}(\coth(\frac{\alpha\omega}{2})\cos(\omega t))d\omega$
(Part of Eq. 4 in the paper I linked)
I found a very similar question here, but the method given to solve it does not seem to work for me and I'm wondering if the $\frac{1}{\omega}$ drastically changes how I have to go about solving it?