Answer
$$\int x^{2}e^{x}dx=x^{2}e^{x}-2x\,e^{x}+2e^{x}+C$$
Work Step by Step
$$\int x^{2}e^{x}dx= x^{2}e^{x}-\int 2x\,e^{x}dx$$
$$=x^{2}e^{x}-(2x\,e^{x}-\int 2e^{x}dx)$$
$$=x^{2}e^{x}-2x\,e^{x}+2e^{x}+C$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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