Answer
-ln|1-sin(x)| + C
Work Step by Step
$\int\frac{cos(x)}{1-sin(x)}dx$
$u = 1 - sin(x)$
$du = -cos(x)dx$
$dx = \frac{1}{-cos(x)}du$
Substitute u:
$\int\frac{cos(x)}{u}dx$
$-\int\frac{1}{u}du$
Solve:
$-ln|u| + C$
Substitute:
$-ln|1-sin(x)| + C$
