Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 387: 88


$$\frac{1}{5}\ln (\cosh 5x)+c.$$

Work Step by Step

We have $$\int \tanh(5x)dx=\int \frac{\sinh 5x}{\cosh 5x}dx=\frac{1}{5}\int \frac{\sinh 5x}{\cosh 5x}dx\\ =\frac{1}{5}\int \frac{(\cosh5x)'}{\cosh 5x}=\frac{1}{5}\ln (\cosh 5x)+c.$$
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