Spherical Co-Ordinate Integral

[Ayame17]

Homework Statement

I'm trying to integrate the following:

\int_0^{2\pi} \int_0^\pi \int_0^r \frac{m^2r}{4\pi} e^{-r(m+iqcos\theta)} sin\theta dr d\theta d\phi

The Attempt at a Solution

Well, the question wasn't just that, my attempt was to get this far!

I know that \int_0^{2\pi} d\phi can just sit off to one side to be put in later, since there is no \phi in the equation. Trying to do the next integral in, however, has proved difficult. I'd have to use integration by parts, since \theta appears twice, but since I have an exponential and sin\theta will just go around to cos\theta and back again, I don't see how it will work. Any help will be appreciated!

 

[CompuChip]

Try substituting x = cos theta (this is a common trick in theoretical physics, so remember it!)

 

[Ayame17]

I've had a play around with that and, although it gives quite a nice number, I know the answer I need but can't seem to reach it...I've been told that I should get:

F(q^{2})=\frac{m^2}{m^2+q^2}

The problem being, my integral still has an exponential factor - I'm not sure how to make it disappear!