## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 45

#### Answer

$$\frac{4}{9} (x+1)^{9 / 4}+\frac{4}{5} (x+1)^{5 / 4}+C$$

#### Work Step by Step

Given $$\int(x+2)(x+1)^{1 / 4} d x$$ Let $$u=x+1\ \ \ \Rightarrow \ \ \ du=dx$$ Then \begin{aligned} \int(x+2)(x+1)^{1 / 4} d x &=\int(u+1) u^{1 / 4} d u \\ &=\int\left(u^{5 / 4}+u^{1 / 4}\right) d u \\ &=\frac{4}{9} u^{9 / 4}+\frac{4}{5} u^{5 / 4}+C\\ &= \frac{4}{9} (x+1)^{9 / 4}+\frac{4}{5} (x+1)^{5 / 4}+C \end{aligned}

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