Answer
$\displaystyle \ln|x|-2x^{-1}+\frac{x^{-2}}{2}+C$
Work Step by Step
Written in exponent form,
applying Sum and Difference RuIes,
...$=\displaystyle \int x^{-1}dx+\displaystyle \int(2x^{-2})dx-\int x^{-3}dx$
... second integral: Constant MultipIe Rule
$=\displaystyle \int x^{-1}dx+2\displaystyle \int x^{-2}dx-\int x^{-3}dx$
... Power Rule, first: $n=-1$
... second and third: $n\neq-1$
$=\displaystyle \ln|x|+2\cdot\frac{x^{-2+1}}{-2+1}-\frac{x^{-3+1}}{-3+1}+C$
$=\displaystyle \ln|x|-2x^{-1}+\frac{x^{-2}}{2}+C$
