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: 22

Answer

$$\int\sin x\sin(\cos x)dx=\cos(\cos x)+C$$

Work Step by Step

$$A=\int\sin x\sin(\cos x)dx$$ Let $u=\cos x$. Then $du=-\sin xdx$. So $\sin xdx=-du$ Substitute into $A$, we have $$A=-\int\sin udu$$ $$A=-(-\cos u)+C$$ $$A=\cos u+C$$ $$A=\cos(\cos x)+C$$
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