University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Section 5.5 - Indefinite Integrals and the Substitution Method - Exercises - Page 330: 71


$$\int\cot xdx=\ln|\sin x|+C$$

Work Step by Step

$$A=\int\cot xdx=\int\frac{\cos x}{\sin x}dx$$ Set $u=\sin x$, then $$du=\cos xdx$$ Therefore, $$A=\int\frac{du}{u}=\ln|u|+C$$ $$A=\ln|\sin x|+C$$
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