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

Answer

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 $$\int z^3 dz=\frac{z^4}{4}+c.$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.