the bound are from 0 to infinity but i mostly would like to know how to go about this integral.
Thank you
To make things simpler, I will assume .
Integration by parts gives:
So I think, that with some effort you can express it using Phi-function or some of the related functions, but you cannot expect a closed form using only elementary functions.
(I hope I haven't made some embarrassing error in the calculation - but plenty of attentive eyes are here, ready to spot any mistake.)