integral of (3x^2+5x-6)

解

\int (3 x^{2} + 5 x - 6) d x

x^{3} + \frac{5 x ^{2}}{2} - 6 x + C

解答ステップ

\int 3 x^{2} + 5 x - 6 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 3 x^{2} d x + \int 5 x d x - \int 6 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

= x^{3} + \frac{5 x ^{2}}{2} - 6 x

定数を解答に追加する

= x^{3} + \frac{5 x ^{2}}{2} - 6 x + C