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: 42

Answer

$$\int\frac{\cos(\ln t)}{t}dt=\sin(\ln t)+C$$

Work Step by Step

$$A=\int\frac{\cos(\ln t)}{t}dt$$ Let $u=\ln t$ Then we have $du=\frac{1}{t}dt$. Substitute into $A$: $$A=\int\cos udu$$ $$A=\sin u+C$$ $$A=\sin(\ln t)+C$$
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