Answer
$$\int \sinh^2 x \cosh x dx= \frac{1}{3}\sinh^3 x+c.$$
Work Step by Step
Let $ u=\sinh x $, then $ du=\cosh x dx $ and hence
$$\int \sinh^2 x \cosh x dx=\int u^2du = \frac{1}{3}u^3+c
\\=\frac{1}{3}\sinh^3 x+c.$$
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: 38
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