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: 15


$$\frac{1}{32} \sinh (4 x)-\frac{1}{8} x+C $$

Work Step by Step

\begin{aligned} \int \sinh ^{2} x \cosh^{2} x d x &=\frac{1}{4} \int \sinh ^{2}(2 x) d x \\ &=\frac{1}{8} \int \cosh (4 x)-1 d x \\ &=\frac{1}{32} \sinh (4 x)-\frac{1}{8} x+C \end{aligned}
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