integral of (-9x^2+9x+2)

解

\int (- 9 x^{2} + 9 x + 2) d x

- 3 x^{3} + \frac{9 x ^{2}}{2} + 2 x + C

解答ステップ

\int - 9 x^{2} + 9 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 9 x^{2} d x + \int 9 x d x + \int 2 d x

\int 9 x^{2} d x = 3 x^{3}

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 2 d x = 2 x

= - 3 x^{3} + \frac{9 x ^{2}}{2} + 2 x

定数を解答に追加する

= - 3 x^{3} + \frac{9 x ^{2}}{2} + 2 x + C