Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Section 8.2 - Integration by Parts - Exercises 8.2 - Page 455: 8



Work Step by Step

We use the formula $\int udv=uv-\int vdu$ with $u=x$, $dv=e^{3x}dx$ $du=dx$, $v=\frac{e^{3x}}{3}$ Then $\int xe^{3x}dx=x\times \frac{e^{3x}}{3}-\int \frac{e^{3x}}{3}dx$ $=\frac{xe^{3x}}{3}-\frac{e^{3x}}{9}+C$
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