Evaluate using long division first to write $f(x)$ as the sum of a polynomial and a proper rational function.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{(x^{3}2)dx}{x^{2}1}$

$($Express numbers in exact form. Use symbolic notation and fractions where needed. Use $C$ for the arbitrary constant: Absorb into $C$ as much as possible.$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{(x^{3}2)dx}{x^{2}1}=$

$$