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: 7



Work Step by Step

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