integral of-2x^3+12x^2-20x+8.5

解

\int - 2 x^{3} + 12 x^{2} - 20 x + 8.5 d x

- 0.5 x^{4} + 4 x^{3} - 10 x^{2} + 8.5 x + C

解答ステップ

\int - 2 x^{3} + 12 x^{2} - 20 x + 8.5 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 x^{3} d x + \int 12 x^{2} d x - \int 20 x d x + \int 8.5 d x

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

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

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

\int 8.5 d x = 8.5 x

= - \frac{x ^{4}}{2} + 4 x^{3} - 10 x^{2} + 8.5 x

簡素化

= - 0.5 x^{4} + 4 x^{3} - 10 x^{2} + 8.5 x

定数を解答に追加する

= - 0.5 x^{4} + 4 x^{3} - 10 x^{2} + 8.5 x + C