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 - Page 419: 41


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

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 $A$: $$A=\int\frac{1}{u}du$$ $$A=\ln|u|+C$$ $$A=\ln|\sin x|+C$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.