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I am starting with the Bessel functions and have some problems with it. I am getting stuck with this equation. I could not find this kind of integral in the handbooks.

1. [tex]\int_0^aJ_0^2(bx)dx[/tex]

Besides of this, I have other equations in similar form but I think this integral is the key to solve others:

2. [tex]\int_0^\infty J_0^2(bx)e^{-\frac{x}{c}}dx[/tex]

3. [tex]\int_0^\infty J_0^2(bx)e^{-\frac{x^2}{c}}dx[/tex]

3. [tex]\int_0^\infty J_0^2(bx)\frac{x}{c}dx[/tex]

Please help me. It is highly appriciated.