Answer
$$\int \tanh x dx
=\ln |\cosh x| +c.$$
Work Step by Step
Let $ u=\cosh x $, then $ du=\sinh x dx $ and hence
$$\int \tanh x dx= \int \frac{\sinh x}{\cosh x} dx =\int \frac{du}{u} \\
= \ln |u|+c
=\ln |\cosh x| +c.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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