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: 33

Answer

$$\int\cos(1+5t)dt=\frac{\sin(1+5t)}{5}+C$$

Work Step by Step

$$A=\int\cos(1+5t)dt$$ Let $u=1+5t$ Then we have $du=5dt$. That means $dt=\frac{1}{5}du$ Substitute into $A$: $$A=\frac{1}{5}\int\cos udu$$ $$A=\frac{1}{5}\sin u+C$$ $$A=\frac{\sin(1+5t)}{5}+C$$
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