integral of 300+20x-12x^2

解

\int 300 + 20 x - 12 x^{2} d x

300 x + 10 x^{2} - 4 x^{3} + C

解答ステップ

\int 300 + 20 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 300 d x + \int 20 x d x - \int 12 x^{2} d x

\int 300 d x = 300 x

\int 20 x d x = 10 x^{2}

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

= 300 x + 10 x^{2} - 4 x^{3}

定数を解答に追加する

= 300 x + 10 x^{2} - 4 x^{3} + C