Answer
$ -\displaystyle \frac{1}{x}-\frac{1}{x^{2}}+C$
Work Step by Step
$\displaystyle \frac{x+2}{x^{3}}=\frac{x}{x^{3}}+\frac{2}{x^{3}}=x^{-2}+2x^{-3}$
$\displaystyle \int\frac{x+2}{x^{3}}dx$ = $\displaystyle \int(x^{-2}+2x^{-3})dx$
... Sum and Difference RuIes,
$= \displaystyle \int x^{-2}dx+\int 2x^{-3}dx$
... Constant MultipIe Rule
$= \displaystyle \int x^{-2}dx+2\int x^{-3}dx$
... both integrals: Power Rule, $n\neq-1$
$=\displaystyle \frac{x^{-1}}{-1}+2\cdot\frac{x^{-2}}{-2}+C$
$=-\displaystyle \frac{1}{x}-\frac{1}{x^{2}}+C$
