So, I'm doing an extensive homework of electromagnetism and we are searching for the total electromagnetic angular momentum of the Thomson dipole. In the end, there is one integral we cannot solve. By '"we" I mean the entire class: nobody is getting how to solve it. Professor swears there are no expansions or approximations, so...
The integral is, in spherical coordinates
$$\int_0^{2\pi} d\phi \int_0^\pi \frac{r^2(r-q\cos\theta)\cdot \sin\theta \cdot \cos\theta}{(r^2+q^2-2rq\cdot \cos\theta)^{3/2}}d\theta.$$
The solution is supposed to be $\frac{8\pi}{3}\frac{q}{r}$ for $r > q$ (q is the distance separating the monopoles). I could find only $\frac{4\pi}{3}\frac{q}{r}$, and with a negative sign. Can anybody illuminate me on a possible solution?