University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.1 - Integration by Parts - Exercises - Page 427: 32


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

Work Step by Step

$$A=\int\frac{\cos\sqrt x}{\sqrt x}dx$$ Let $a=\sqrt x$. We then have $da=\frac{1}{2\sqrt x}dx$ Therefore, $\frac{1}{\sqrt x}dx=2da$ $$A=\int\cos a\times2da=2\int\cos ada$$ $$A=2\sin a+C$$ $$A=2\sin\sqrt x+C$$
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