If you have access to it, section 1.5.2 of 'Introduction to Electrodynamics: Fourth Edition' by Griffiths has a good explanation.
Initially, I solved in Cartesian coordinates, which is a bit of a process. First, you can say that ##\vec{v}= \frac{\vec{r}}{r^3}= \frac{x \hat{x}+y \hat{y} +z...