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: 9


$$\ln |\cosh x|+C $$

Work Step by Step

Given $$ \int \tanh x d x $$ Let $$ u=\cosh x \ \ \ \to du = \sinh x dx$$ Then \begin{aligned} \int \tanh x d x &=\int \frac{\sinh x}{\cosh x} d x \\ &=\int \frac{1}{u} d u \\ &=\ln |u|+C \\ &=\ln |\cosh x|+C \end{aligned}
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