How to find the solution to this integral:
$$\int_0^a J_0\left(b\sqrt{a^2-x^2}\right)\ \sin{c x}\ \mathrm{d}x$$
I found a similar integral, but instead of the sine is a cosine function in Gradshteyn and Ryzhik's book, section 6.677, equation number 6.
$\int_0^a J_0\left(b\sqrt{a^2-x^2}\right)\ \cos{c x}\ \mathrm{d}x=\frac{\sin\left(a\sqrt{b^2+c^2}\right)}{\sqrt{b^2+c^2}}$ for $b > 0$
Any help and hints will be appreciated