Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 6 - Applications of Integration - 6.8 Logarithmic and Exponential - 6.8 Exercises: 64

Answer

$$ - \frac{1}{4}\cos \left( {\ln x} \right) + C$$

Work Step by Step

$$\eqalign{ & \int {\frac{{\sin \left( {\ln x} \right)}}{{4x}}} dx \cr & = \frac{1}{4}\int {\frac{{\sin \left( {\ln x} \right)}}{x}} dx \cr & {\text{substitute }}u = \ln x,{\text{ }}du = \frac{1}{x}dx \cr & = \frac{1}{4}\int {\sin udu} \cr & {\text{find the antiderivative}} \cr & = - \frac{1}{4}\cos u + C \cr & {\text{with }}u = \ln x \cr & = - \frac{1}{4}\cos \left( {\ln x} \right) + C \cr} $$
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