Calculus: Early Transcendentals 8th Edition

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

Chapter 7 - Review - Exercises - Page 538: 24


$\frac{e^x}{2}(\sin x+ \cos x)+C$

Work Step by Step

Integrating by parts, we have $I= \int e^{x}\cos xdx= $$e^{x}\sin x-\int e^{x}\sin xdx$$=e^{x}\sin x-I_{1}$ $I_{1}=\int e^{x}\sin xdx$ $= e^{x}(-\cos x)+\int e^{x}\cos xdx$ Substituting the value of $I_{1}$, we get $I= e^{x}\sin x+ e^{x}\cos x- I$ or $2I= e^{x}(\sin x+ \cos x)$ or $I= \frac{e^x}{2}(\sin x+ \cos x)$
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