sin(x)exp(-a/sin(x))dx integral

by Ashkhen Nalbandian   Last Updated April 16, 2018 12:20 PM - source

I'm looking for a way to integrate sin(x)exp(-a/sin(x))dx to get a second order Bickley function (K_2(a)), which is basically the same expression as I have under the integral, but cos(x) in stead of sin(x) and the limits change from 0 to pi/2, which is understandable. I'm a bit lost what kind of variable substitution could I do. Any suggestions? I have tried -a/sin(x)=u, but that doesnt seem to give reasonable results. Thanks in advance

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