Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 36



Work Step by Step

Given $$\int \frac{5 x^{4}+2 x}{\left(x^{5}+x^{2}\right)^{3}} d x$$ Let $$u=x^{5}+x^{2} \ \ \ \Rightarrow \ \ du=(5x^4+2x^2)dx $$ then \begin{align*} \int \frac{5 x^{4}+2 x}{\left(x^{5}+x^{2}\right)^{3}} d x&= \int \frac{du}{u^3} \\ &=\frac{-1}{2u^2}+c\\ &=\frac{-1}{2\left(x^{5}+x^{2}\right)^2}+c \end{align*}
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.