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人気のある微分積分 >

integral of x(12x+4)

解

\int x (12 x + 4) d x

解

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

解答ステップ

\int x (12 x + 4) d x

拡張

x (12 x + 4) : 12 x^{2} + 4 x

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

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

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

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

定数を解答に追加する

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

グラフ

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