## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 41

#### Answer

$$\frac{-1}{2(x+5)^{2}}+c$$

#### Work Step by Step

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

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