1. The problem statement, all variables and given/known data How do I integrate [itex]\int_0^1 xJ_0(ax)J_0(bx)dx[/itex] where [itex]J_0[/itex] is the zeroth order Bessel function? 2. Relevant equations See above. Also, the zeroth order Bessel equation is [itex](xy')'+xy=0[/itex] 3. The attempt at a solution Surely we must use the fact that [itex]J_0[/itex] is a Bessel function, since we can't integrate any old function in the given integral. But I don't know how. Thanks for any help.