Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.1 Integration by Parts - Exercises - Page 395: 3


$$\int (2x+9)e^{x}dx=(2x+7)e^{x}+C$$

Work Step by Step

${\left ((2x+9)e^{x} \right )}'=2e^{x}+(2x+9)e^{x}$ $$(2x+9)e^{x}={\left ((2x+9)e^{x} \right )}'-2e^{x}$$ $$\int (2x+9)e^{x}dx=(2x+9)e^{x}-2\int e^{x}dx$$ $$=(2x+9)e^{x}-2e^{x}+C$$ $$=(2x+7)e^{x}+C$$
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