I am working with a function where I need to solve an integral of the following form:
where $K$ is a modified Bessel function of the second kind. The image is from "Integrals and Series: Volume 1: Elementary Functions" by Prudnikov, Brychkov, and Marichev pg. 344.
I was working with the identity provided by the book, but I decided to see what I got via mathematica out of curiosity. However, when I solve the integral in mathematica I get the following solution
I am new to mathematica so I am unsure whether this is a true discrepancy (I don't think it is( and I am unable to find a derivation of the integral 2.3.16.1. I'm not a mathematician but every article I've found so far that uses 2.3.16.1 cites the lemma but does not rederive it.
Sources for the derivation would be appreciated. Thanks for taking a look.