Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 387: 70


$$\sin (\ln x)+c.$$

Work Step by Step

Let $ u=\ln x $, then $ du=\frac{1}{x}dx $. Now, we have $$\int \frac{\cos(\ln x)}{x}dx = \int \cos udu = \sin u+c=\sin (\ln x)+c.$$
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