integral of (6x+5)^2

解

\int (6 x + 5)^{2} d x

12 x^{3} + 30 x^{2} + 25 x + C

解答ステップ

\int (6 x + 5)^{2} d x

拡張

(6 x + 5)^{2} : 36 x^{2} + 60 x + 25

= \int 36 x^{2} + 60 x + 25 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 36 x^{2} d x + \int 60 x d x + \int 25 d x

\int 36 x^{2} d x = 12 x^{3}

\int 60 x d x = 30 x^{2}

\int 25 d x = 25 x

= 12 x^{3} + 30 x^{2} + 25 x

定数を解答に追加する

= 12 x^{3} + 30 x^{2} + 25 x + C