integral of (2-3x)^2

解

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

4 x - 6 x^{2} + 3 x^{3} + C

解答ステップ

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

拡張

(2 - 3 x)^{2} : 4 - 12 x + 9 x^{2}

= \int 4 - 12 x + 9 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 12 x d x + \int 9 x^{2} d x

\int 4 d x = 4 x

\int 12 x d x = 6 x^{2}

\int 9 x^{2} d x = 3 x^{3}

= 4 x - 6 x^{2} + 3 x^{3}

定数を解答に追加する

= 4 x - 6 x^{2} + 3 x^{3} + C