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

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

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*}