Question

Evaluate: $\int \frac{\cos 2x}{\sin x}dx$

Answer 1

$I=\int \frac{\cos 2x}{\sin x}dx$

$=\int \frac{1-2{\sin }^{2}x}{\sin x}dx$

$=\int cosecxdx-2\int \sin xdx$

$=log|cosecx+\cot x|+2\cos x+c$.