Answer
$-\ln (1-\sin x)+C$
Work Step by Step
$\int\frac{\cos x}{1-\sin x}dx$
Let $u=1-\sin x$. Then $du=-\cos x dx$, and $\cos xdx=-du$.
$=\int\frac{-du}{u}$
$=-\ln |u|+C$
$=-\ln |1-\sin x|+C$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 7 - Techniques of Integration - 7.5 Strategy for Integration - 7.5 Exercises - Page 547: 1
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