Answer
$$\sin (\ln t)+c.$$
Work Step by Step
Let $u=\ln t$, then $du=\frac{dt}{t}$, then
$$\int \frac{\cos(\ln t)}{t}dt=\int \cos u du=\sin u+c=\sin (\ln t)+c.$$
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 - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 80
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