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: 1


$$\int\cos 2xdx=\frac{\sin 2x}{2}+C$$

Work Step by Step

$$A=\int\cos 2xdx$$ Let $u=2x$ Then $du=(2x)'dx=2dx$. So $dx=\frac{1}{2}du$. Substitute into $A$, we have $$A=\int\cos u\frac{1}{2}du$$ $$A=\frac{1}{2}\int\cos udu$$ $$A=\frac{1}{2}\sin u+C$$ $$A=\frac{\sin 2x}{2}+C$$
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