Tuesday, 25 December 2012

real analysis - Need help to evaluate In=intinfty0exsin(nln(x))dx

For nN, I'm trying to find a closed form for the following integrals :
In=0exsin(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 ?

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