Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises: 73


The required formula is $$\int z^3 dz=\frac{z^4}{4}+c.$$

Work Step by Step

The integral $$\int x(x^2+1)^3dx$$ with the substitution $z=x^2+1$ where $dz=2xdx$ can be transformed into integral $$\frac{1}{2}\int z^3dz,$$ so we need to use formula $$\int z^3 dz=\frac{z^4}{4}+c.$$
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