While I am solving an elasticity situation I came across the following integral: $$ \int_0^\infty \left( q^2 (A+B\cos (qR))+q C \sin(qR) \right) J_0 (qr) \, \mathrm{d} q = 0 \, , \quad\quad (0<r<R) \, , $$ wherein $A, B, C$ are real numbers. I am looking for an equation between $A$, $B$ and $C$ to have this integral identically null.
Any hint of help is highly appreciated. Thanks!
Federiko