Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 43


$$\int \tanh x dx =\ln |\cosh x| +c.$$

Work Step by Step

Let $ u=\cosh x $, then $ du=\sinh x dx $ and hence $$\int \tanh x dx= \int \frac{\sinh x}{\cosh x} dx =\int \frac{du}{u} \\ = \ln |u|+c =\ln |\cosh x| +c.$$
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