integral of (12x^2-7x+2)

解

\int (12 x^{2} - 7 x + 2) d x

4 x^{3} - \frac{7 x ^{2}}{2} + 2 x + C

解答ステップ

\int 12 x^{2} - 7 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 12 x^{2} d x - \int 7 x d x + \int 2 d x

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

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 2 d x = 2 x

= 4 x^{3} - \frac{7 x ^{2}}{2} + 2 x

定数を解答に追加する

= 4 x^{3} - \frac{7 x ^{2}}{2} + 2 x + C