I'm a physicist trying to do physics things and I have gotten a bit stumped on a maths thing - an integral to be exact. I searched Table of Integrals by Gradshteyn and Ryzhik (2007, 7th ed.), and was able to find similar (single powered Bessel functions) but was unable to find what I'm looking for, which has the form
$$\int_0^{\infty}x^m e^{-Ax^2} [j_L(b x)]^2 dx$$
I see the potential of needing to use a more general equation
$$\int_0^{\infty}x^m e^{-Ax^2} [j_L(b x)]^n dx$$
in the future as well, but understand that may have no simple solution. Could anyone please point me in the right direction? Thank you so much.