Answer
$$\sin (\ln x)+c.$$
Work Step by Step
Let $ u=\ln x $, then $ du=\frac{1}{x}dx $.
Now, we have
$$\int \frac{\cos(\ln x)}{x}dx = \int \cos udu
= \sin u+c=\sin (\ln x)+c.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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