Evaluating $\int \frac{\sin^2(x)}{\sqrt{\cos(x)}} \mathrm dx$ I would like to get some advice how to evaluate the integral,
$$\int \frac{\sin^2{x}}{\sqrt{\cos{x}}} \mathrm dx$$

Integration by parts, with $g(x)=\sin x$, and $$f'(x)=\frac{\sin x}{\sqrt{\cos x}}=-2\cdot\frac{\cos'x}{2\cdot\sqrt{\cos x}}=-2\cdot(\sqrt{\cos x})'\iff f(x)=-2\cdot\sqrt{\cos x}$$ then recognizing the expression of the incomplete elliptic integral of the first kind in $\int f(x)g'(x)dx$
