Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.5 - The Substitution Rule - 5.5 Exercises: 41

Answer

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

Work Step by Step

$$A=\int\cot xdx$$ $$A=\int\frac{\cos x}{\sin x}dx$$ Let $u=\sin x$ Then we have $du=\cos xdx$. Substitute into $A$: $$A=\int\frac{1}{u}du$$ $$A=\ln|u|+C$$ $$A=\ln|\sin x|+C$$
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