integral of-75x^2+600x+C

解

\int - 75 x^{2} + 600 x + C d x

- 25 x^{3} + 300 x^{2} + C x + C

解答ステップ

\int - 75 x^{2} + 600 x + C 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 75 x^{2} d x + \int 600 x d x + \int C d x

\int 75 x^{2} d x = 25 x^{3}

\int 600 x d x = 300 x^{2}

\int C d x = C x

= - 25 x^{3} + 300 x^{2} + C x

定数を解答に追加する

= - 25 x^{3} + 300 x^{2} + C x + C