How to compute infinite integrals involving products of trigonometric and Bessel functions?

Question

I am trying to evaluate analytically the following infinite integral $$ \int_0^\infty q J_1 (qr) \sin \rho q \, \mathrm{d} q \quad (0<\rho < r) \, . $$

I was wondering if such an integral is tabulated somewhere or whether there exists a commonly used technique for its evaluation. Any help will be welcome.

Thanks.

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