Answer
$ \displaystyle \frac{x^{2}}{2}-2\ln|x|+C$
Work Step by Step
$\displaystyle \frac{x^{2}-2}{x}=\frac{x^{2}}{x}-\frac{2}{x}=x-2x^{-1}$
$\displaystyle \int\frac{x^{2}-2}{x}dx$ = $\displaystyle \int(x-2x^{-1})dx$
... Sum and Difference RuIes,
$= \displaystyle \int xdx-\int 2x^{-1}dx$
... Constant MultipIe Rule
$= \displaystyle \int xdx-2\int x^{-1}dx$
... 1st integral: Power Rule, $n\neq-1$
... 2nd integral, $n=-1$
$=\displaystyle \frac{x^{2}}{2}-2\ln|x|+C$
