For n∈N, I'm trying to find a closed form for the following integrals :
In=∫∞0e−xsin(nln(x))dx
My real objective is to evaluate ∞∑n=1Inn, and since interchanging the sum and the integral didn't lead anywhere, I suppose that finding a closed form expression for In is the way to go, but I'm lost as of how to proceed...
Maybe the residue theorem/contour integration could help, but I'm not familiar with complex analysis so I haven't tried it - feel free to use it though.
Any suggestion ?
No comments:
Post a Comment