Make a change rA=t and use indefinite integrals from A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, "Integrals and Series," V. 2, Gordon and Breach Science Publishers, Scripta Technica Inc., New York, 1987.
Sorry, this isn't an answer but a comment. In my PhD research, some results took the form of a Bessel function. My maths wasn't good enough to explain why until a couple of other researchers published the reason - only then could I submit my work for publication. It weighed on my mind so much that six years later, when I had to invent my 'signature' for letters from my law (patent) firm, I chose that same Bessel function. Anyhow, you have my best wishes for success in your own research.