integral of (12x^3-4x-2)

解

\int (12 x^{3} - 4 x - 2) d x

3 x^{4} - 2 x^{2} - 2 x + C

解答ステップ

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

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

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

\int 2 d x = 2 x

= 3 x^{4} - 2 x^{2} - 2 x

定数を解答に追加する

= 3 x^{4} - 2 x^{2} - 2 x + C