Answer
$$\int x^3e^{x^4}dx=\frac{e^{x^4}}{4}+C$$
Work Step by Step
$$A=\int x^3e^{x^4}dx$$
We set $u=x^4$. We then have $$du=4x^3dx$$ $$x^3dx=\frac{1}{4}du$$
Therefore, $$A=\frac{1}{4}\int e^udu$$ $$A=\frac{e^u}{4}+C$$ $$A=\frac{e^{x^4}}{4}+C$$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 8 - Section 8.1 - Integration by Parts - Exercises - Page 427: 37
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