integral of-2+24x-12x^2

解

\int - 2 + 24 x - 12 x^{2} d x

- 2 x + 12 x^{2} - 4 x^{3} + C

解答ステップ

\int - 2 + 24 x - 12 x^{2} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 2 d x + \int 24 x d x - \int 12 x^{2} d x

\int 2 d x = 2 x

\int 24 x d x = 12 x^{2}

\int 12 x^{2} d x = 4 x^{3}

= - 2 x + 12 x^{2} - 4 x^{3}

定数を解答に追加する

= - 2 x + 12 x^{2} - 4 x^{3} + C