Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.5 - The Substitution Rule - 5.5 Exercises - Page 419: 37


$$\int\sinh^2 x\cosh xdx=\frac{\sinh^3 x}{3}+C$$

Work Step by Step

$$A=\int\sinh^2 x\cosh xdx$$ Let $u=\sinh x$ Then we have $du=\cosh xdx$. Substitute into $A$: $$A=\int u^2du$$ $$A=\frac{u^3}{3}+C$$ $$A=\frac{\sinh^3 x}{3}+C$$
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