This may be aimed at PH(or whomever), since he is up on CA and I am just learning it a little as I find time.
How could we go about using complex integration to solve this integral from a previous post?. Assuming it's worthwhile in this case. Are cases where there are infinite poles more difficult?.
I see it has poles at and a double at 0, I think.
Should we end up with something like
Or maybe even