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: 35



Work Step by Step

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