Answer
$$\frac{1}{3}e^{x^3}+c $$
Work Step by Step
Let $ u=x^3$, then $ du=3x^2dx $.
Now, we have
$$\int x^2e^{x^2}dx =\frac{1}{3}\int e^udu
=\frac{1}{3}e^u+c=\frac{1}{3}e^{x^3}+c.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 387: 68
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