I'd like to compute the following integral in closed form:
I assume this is possible via complex analysis, but I can't figure out how to extend this to a complex integration problem. Any ideas?
By the way, I happened to find the exact value of this integral by playing around with WolframAlpha and doing some extra algebra. It reads as follows:
and is in agreement with the numerical computation.
But that doesn't tell me the steps to get to this resultů