Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 7 - Techniques of Integration - Review - Exercises - Page 578: 9


$$-\cos (\ln t)+c$$

Work Step by Step

Given $$\int \frac{\sin (\ln t)}{t} d t$$ Let $ u= \ln t\ \ \ \Rightarrow \ \ du=\frac{1}{t}dt $, then \begin{align*} \int \frac{\sin (\ln t)}{t} d t&=\int \sin (u) du\\ &=-\cos u+c\\ &= -\cos (\ln t)+c \end{align*}
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