Chapter 5: Integrals - Section 5.5 - Indefinite Integrals and the Substitution Method - Exercises 5.5 - Page 294: 3

$-\frac{1}{3}(x^{2}+5)^{-3}+C$

Put $x^{2}+5$= u which gives $\frac{du}{dx}= 2x$ Or du= 2xdx Then, $\int 2x(x^{2}+5)^{-4}dx= \int u^{-4}du$ = $\frac{u^{-4+1}}{-4+1}+C$ (using power rule) = $\frac{u^{-3}}{-3} +C$= $-\frac{1}{3}(x^{2}+5)^{-3}+C$