함수식으로 정한 삼차함수의 정적분

$xf ( x ) - f ( x ) = 3 x ^{4} - 3 x$에서 $\left( x - 1 \right) f ( x ) = 3 x \left( x - 1 \right) \left( x ^{2} + x + 1 \right)$ $\therefore$ $f ( x ) = 3 x \left( x ^{2} + x + 1 \right)$ $\therefore$ $\displaystyle \int _{- 2} ^{2} {f ( x )} dx$$\displaystyle = \int _{- 2} ^{2} {\left( 3 x ^{3} + 3 x ^{2} + 3 x \right)} dx$ $\displaystyle = 2 \int _{0} ^{2} {3 x ^{2}} dx$ $\displaystyle = 2 \left[ \begin{array}{l} \begin{matrix} \\ \end{matrix} x ^{3} \end{array} \right] _{0} ^{2}$ $= 16$