As the title suggests, how may I start evaluating the following integral:
\begin{align}I=\displaystyle\int\dfrac{\left(-x_{0}+R\cos\left(\theta\right)\right)\,d\theta}{\left((-x_{0}+R\cos(\theta))^2+(-R\sin(\theta))^2\right)^{3/2}},\;\text{for }\color{red}{x_{0}>R}.\end{align}
It appeared while trying to find the resultant electric field in a plane containing a circular ring of charge. My Physics professor suggested that an elliptic integral would pop up, is this that elliptic integral? I don't know which substitution to make to make it look more obvious.