Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.2 Integration by Parts - 7.2 Exercises: 7

Answer

\[ = x\sin x + \cos \,x + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {x\cos x\,dx} \hfill \\ \hfill \\ set{\text{ }}u = x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,then\,\,\,du = dx \hfill \\ du = \cos x\,dx\,\,\,\,\,\,\,\,then\,\,\,\,\,\,\,\,\,v = \sin x \hfill \\ \hfill \\ use\,\,\,uv - \int_{}^{} {vdu} \hfill \\ \hfill \\ {\text{replacing the values }}{\text{in the equation}} \hfill \\ \hfill \\ x\sin x - \int_{}^{} {\sin x\,dx} \hfill \\ \hfill \\ \operatorname{int} egrate\,\, \hfill \\ \hfill \\ = x\sin x + \cos \,x + C \hfill \\ \hfill \\ \end{gathered} \]
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