How can we compute the following triple integral (electromagnetic diffusion in a sphericall shell)?
$ E(\mathbf{r}) = \int_0^{2 \pi} d\phi' \int_0^{\pi} \sin \theta' d\theta' \int_R^{R+h} d r' r'^2 \frac{ e^{i k | \mathbf{r} - \mathbf{r'} |} }{|\mathbf{r} - \mathbf{r'} |} $
Using $\mathbf{r} . \mathbf{r'} = r r' \left( \sin \theta \sin \theta' \cos(\phi - \phi') + \cos \theta \cos \theta' \right) $, I tried to integrate first by $r'$ or $\theta'$ but I did not found primitives with online integrator. I think the answer is simple but I can't find it (I have the result for an integration over a cylinder only but not for the spherical shell).
Thanks for reading.