Simple integration of bessel functions

[Mappe]

I seek a way to integrate J0, bessel function. I try to use some of the identities I can find, but it takes me no were. Please help!

 

[marcusl]

The simple integral of an integer order Bessel function is given by Struve functions. You can find them in ch. 11 , "Integrals of Bessel Functions" of Abramowitz and Stegun. If you are serious about math, buy a copy (the Dover edition is inexpensive). For now you can browse an old online copy here
http://www.convertit.com/Go/Convertit/Reference/AMS55.ASP" [Broken]

 

[Rosenheinrich]

Have a look at

http://www.fh-jena.de/~rsh/Forschung/Stoer/besint.pdf