Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.5 - The Substitution Rule - 5.5 Exercises - Page 419: 27



Work Step by Step

$$A=\int(x^2+1)(x^3+3x)^4dx$$ Let $u=x^3+3x$. We would have $du=3x^2+3dx=3(x^2+1)dx$. Therefore, $(x^2+1)dx=\frac{1}{3}du$ Substitute into $A$, we have $$A=\frac{1}{3}\int u^4du$$ $$A=\frac{1}{3}\frac{u^5}{5}+C$$ $$A=\frac{u^5}{15}+C$$ $$A=\frac{(x^3+3x)^5}{15}+C$$
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.