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!