University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Section 5.5 - Indefinite Integrals and the Substitution Method - Exercises: 4

Answer

$-\frac{1}{x^4+1}+c$

Work Step by Step

$u=x^4+1$, therefore $du=4x^3dx$. We do the substitution! $\int\frac{4x^3}{(x^4+1)^2} dx=\int \frac{du}{u^2}=-\frac{1}{u}+c$ We re-do the substitution! $-\frac{1}{u}+c=-\frac{1}{x^4+1}+c$
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