Calculus: Early Transcendentals (2nd Edition)

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

Chapter 5 - Integration - 5.5 Substitution Rule - 5.5 Exercises: 15

Answer

\[\frac{{{{\sin }^4}x}}{4} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {{{\sin }^3}x\cos xdx} \hfill \\ \hfill \\ set \hfill \\ u = \sin \,x\,\,\,\,\,\,then\,\,\,\,\,du = \cos xdx\, \hfill \\ \hfill \\ {\text{Therefore}}{\text{,}} \hfill \\ \hfill \\ \int_{}^{} {{u^3}\,du} \hfill \\ \hfill \\ {\text{integrating}} \hfill \\ \hfill \\ = \frac{{{u^4}}}{4} + C \hfill \\ \hfill \\ replace\,\,u\,\,with\,\,\,u = \sin x \hfill \\ \hfill \\ \frac{{{{\sin }^4}x}}{4} + C \hfill \\ \end{gathered} \]
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