Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.5 - The Substitution Rule - 5.5 Exercises - Page 418: 8


$$\int x^2e^{x^3}dx=\frac{e^{x^3}}{3}+C$$

Work Step by Step

$$A=\int x^2e^{x^3}dx$$ Let $u=x^3$ Then $du=(x^3)'dx=3x^2dx$. So $x^2dx=\frac{1}{3}du$ Substitute into $A$, we have $$A=\int e^u(\frac{1}{3})du$$ $$A=\frac{1}{3}\int e^udu$$ $$A=\frac{1}{3}e^u+C$$ $$A=\frac{e^{x^3}}{3}+C$$
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