Where can I possibly find a source to demonstrate the following integral, or how should I even begin to demonstrate it (I am stuck)?
$$\oint \frac{\cos(\theta) \, d\theta}{\sqrt{a-b\cos(\theta)}}=\frac{4\sqrt{a+b}}{b} \left[\left(1-\frac{\beta^2}{2}\right)K(\beta)-E(\beta)\right]$$
where: $$\beta=\sqrt{\frac{2b}{a+b}}$$