Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions - Exercises - Page 415: 10


$$-\frac{1}{2} \operatorname{csch}\left(x^{2}\right)+C$$

Work Step by Step

Given $$\int x \operatorname{csch}\left(x^{2}\right) \operatorname{coth}\left(x^{2}\right) d x $$ Let $$ u= x^2 \ \ \ \to du = 2x dx$$ Then \begin{aligned} \int x \operatorname{csch}\left(x^{2}\right) \operatorname{coth}\left(x^{2}\right) d x &=-\frac{1}{2} \int d u \\ &=-\frac{1}{2} u+C \\ &=-\frac{1}{2} \operatorname{csch}\left(x^{2}\right)+C\end{aligned}
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.