I need to integrate:
$$\int_p^{\infty} x\sqrt{x^2+a}K_0(bx)dx$$
but I can't do it. Following Gradshteyn and Ryzhik 7th Edition, formula 6.565.7 I can resolve it from 0 to infinity but not from p to infinity. I have tried to take off to 6.565.7 the same but between 0 and p but neither I know how to solve it. Any ideas for an exact result or an approximation?