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: 1



Work Step by Step

$\int$$xe^{2x}$; u=x, dv=$e^{2x}$dx; du=1, v=$\frac{1}{2}$$e^{2x}$ Now we use the formula: $\int$udv=uv-$\int$vdu $\int$$xe^{2x}$=x($\frac{1}{2}$$e^{2x}$)-$\int$$\frac{1}{2}$$e^{2x}$ =x$\frac{1}{2}$$e^{2x}$-$\frac{1}{2}$$\int$$e^{2x}$ =x$\frac{1}{2}$$e^{2x}$-$\frac{1}{2}$($\frac{1}{2}$$e^{2x}$) =x$\frac{1}{2}$$e^{2x}$-$\frac{1}{4}$$e^{2x}$ or $\frac{xe^{2x}}{2}$-$\frac{e^{2x}}{4}$
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