## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 276: 50

#### Answer

$$-\frac{1}{3} \cos (x^{3}+1)+C$$

#### Work Step by Step

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

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