Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.3 Derivatives Of Inverse Functions; Derivatives And Integrals Involving Exponential Functions - Exercises Set 6.3: 68

Answer

$\frac{1}{4}e^{x^4}+C$

Work Step by Step

Let $u=x^4$. Then $du=4x^3dx$, so $x^3dx=\frac{1}{4}du$. $\int x^3e^{x^4}dx$ $=\int e^u*\frac{1}{4}du$ $=\frac{1}{4}e^u+C$ $=\frac{1}{4}e^{x^4}+C$
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