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: 10


$$\int x^{2}e^{x}dx=x^{2}e^{x}-2x\,e^{x}+2e^{x}+C$$

Work Step by Step

$$\int x^{2}e^{x}dx= x^{2}e^{x}-\int 2x\,e^{x}dx$$ $$=x^{2}e^{x}-(2x\,e^{x}-\int 2e^{x}dx)$$ $$=x^{2}e^{x}-2x\,e^{x}+2e^{x}+C$$
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