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: 24


$$\frac{1}{3}\sin (x^{3}+1) +c $$

Work Step by Step

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