integral of 4+6x+24x^2

解

\int 4 + 6 x + 24 x^{2} d x

4 x + 3 x^{2} + 8 x^{3} + C

解答ステップ

\int 4 + 6 x + 24 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 4 d x + \int 6 x d x + \int 24 x^{2} d x

\int 4 d x = 4 x

\int 6 x d x = 3 x^{2}

\int 24 x^{2} d x = 8 x^{3}

= 4 x + 3 x^{2} + 8 x^{3}

定数を解答に追加する

= 4 x + 3 x^{2} + 8 x^{3} + C