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: 14


$$\frac{\cosh ^{9} x}{9}-\frac{\cosh ^{7} x}{7}+C$$

Work Step by Step

\begin{aligned} \int \sinh ^{3} x \cosh ^{6} x d x &=\int \sinh ^{2} x \cosh ^{6} x \sinh x d x \\ &=\int\left(\cosh ^{2} x-1\right) \cosh ^{6} x \sinh x d x \\ &=\int \cosh ^{8} x \sinh x-\cosh ^{6} x \sinh x d x \\ &=\int \cosh ^{8} x \sinh x d x-\int \cosh ^{6} x \sinh x d x \\ &=\frac{\cosh ^{9} x}{9}-\frac{\cosh ^{7} x}{7}+C \end{aligned}
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