Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 4 - Integration - 4.3 Integration By Substitution - Exercises Set 4.3 - Page 286: 25


$-\frac{\cos^5 3t}{15}+C$

Work Step by Step

Let $u=\cos 3t$, so $du=-3\sin 3tdt$. Then $\sin3tdt=-\frac{1}{3}du$. $\int\cos^4 3t\sin 3tdt$ $=\int u^4*(-\frac{1}{3})du$ $=-\frac{1}{3}*\frac{u^5}{5}+C$ $=-\frac{1}{3}*\frac{\cos^5 3t}{5}+C$ $=-\frac{\cos^5 3t}{15}+C$
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