Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 7 - Techniques of Integration - 7.1 Integration by Parts - 7.1 Exercises - Page 516: 3


\begin{equation*} =x\frac{\sin{5x}}{5}+\frac{\cos{5x}}{25}+C \end{equation*}

Work Step by Step

$\int x\cos{5x}dx$ Let $u=x$ and $dv=\cos{5x}dx$ then $du=dx$ and $v=\frac{\sin{5x}}{5}$ and therefore \begin{equation*} \int x\cos{5x}dx=x\frac{\sin{5x}}{5}-\int\frac{\sin{5x}}{5}dx \end{equation*} \begin{equation*} =x\frac{\sin{5x}}{5}+\frac{\cos{5x}}{25}+C \end{equation*}
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