Calculus (3rd Edition)

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: 38


$$\int \sinh^2 x \cosh x dx= \frac{1}{3}\sinh^3 x+c.$$

Work Step by Step

Let $ u=\sinh x $, then $ du=\cosh x dx $ and hence $$\int \sinh^2 x \cosh x dx=\int u^2du = \frac{1}{3}u^3+c \\=\frac{1}{3}\sinh^3 x+c.$$
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