How to integrate $\int \frac {\cos^4 x}{\sqrt {1- \sin x}} $ I frankly don't know where to start. Looked for some identities to get rid of the square root below.
$$\int \frac {\cos^4 x}{\sqrt {1- \sin x}} \, dx  $$

hint
if we multiply both the numerator and denominator by $\sqrt{1 + \sin x}$, it becomes
$$\int (\cos^3 x) \, \sqrt {1+\sin x} \, dx $$
Perform the change of variables $ u = \sin x $.
