Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 7 - Section 7.5 - Strategy for Integration - 7.5 Exercises: 10

Answer

$$ C -(\frac{sin\frac{1}{x}}{x}+cos\frac{1}{x})$$

Work Step by Step

$$Let \,u=\frac{1}{x}\,,So\,du=-\frac{dx}{x^{2}}$$ $$\int \frac{cos\frac{1}{x}}{x^{3}}dx=-\int \frac{cosu}{\frac{1}{u}}du=-\int u \, cosu \,du$$ $$\int u \, cosu \,du=u\,sinu + C1 -\int sinu\,du$$ $$\int u \, cosu \,du=u\,sinu +cosu +C2$$ $$\int \frac{cos\frac{1}{x}}{x^{3}}dx=-\int u \, cosu \,du=C-u\,sinu -cosu$$ $$=C -(\frac{sin\frac{1}{x}}{x}+cos\frac{1}{x})$$
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