Answer
$$\frac{1}{5}\ln (\cosh 5x)+c.$$
Work Step by Step
We have
$$\int \tanh(5x)dx=\int \frac{\sinh 5x}{\cosh 5x}dx=\frac{1}{5}\int \frac{\sinh 5x}{\cosh 5x}dx\\
=\frac{1}{5}\int \frac{(\cosh5x)'}{\cosh 5x}=\frac{1}{5}\ln (\cosh 5x)+c.$$
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 - Chapter Review Exercises - Page 387: 88
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