I would like to solve the following integral. I have looked in Gradshteyn and Ryzhik but could not find a similar form. Maxima and Mathematica did not succeed in finding solutions. Is there a closed form solution for the following integral?
$$ \int_{0}^{\infty} \frac{ I_1(a \, r ) \, \, e^{-r^2}} { \sqrt{r^2 + b^2} } dr $$
$I_1$ is the modified Bessel function of the first kind.