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: 64

Answer

\[ = \frac{{{{\sin }^6}x}}{6} + \frac{{3{{\sin }^4}x}}{4} - \frac{{{{\sin }^2}x}}{2} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\left( {{{\sin }^5}x + 3{{\sin }^3}x - \sin x} \right)\cos x\,dx} \hfill \\ \hfill \\ distribute \hfill \\ \hfill \\ = \int_{}^{} {{{\sin }^5}x\cos xdx + 3} \int_{}^{} {{{\sin }^3}x\cos xdx} - \int_{}^{} {\sin x\cos xdx} \hfill \\ \hfill \\ integrate\,, \hfill \\ \hfill \\ = \frac{{{{\sin }^6}x}}{6} + 3\,\left( {\frac{{{{\sin }^4}x}}{4}} \right) - \frac{{{{\sin }^2}x}}{2} + C \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ = \frac{{{{\sin }^6}x}}{6} + \frac{{3{{\sin }^4}x}}{4} - \frac{{{{\sin }^2}x}}{2} + C \hfill \\ \end{gathered} \]
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