Answer
$-\frac{1}{5} \cos^5 x$
Work Step by Step
Let $u=\cos x$. Then $-du=\sin x \ dx$. Replace the integral to make it
$$-\int u^4 \ du = -\frac{1}{5} u^5=-\frac{1}{5} \cos^5 x$$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
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: 52
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