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: 4


$$\frac{1}{3} \sinh ^{3} x+C $$

Work Step by Step

Given $$\int \sinh ^{2} x \cosh x d x$$ Let $$ u=\sinh x \ \ \ \to du =\cosh xdx$$ Then \begin{aligned} \int \sinh ^{2} x \cosh x d x &=\int u^{2} d u \\ &=\frac{u^{3}}{3}+C \\ &=\frac{1}{3} \sinh ^{3} x+C \end{aligned}
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