integral of (9x+5)^2

解

\int (9 x + 5)^{2} d x

27 x^{3} + 45 x^{2} + 25 x + C

解答ステップ

\int (9 x + 5)^{2} d x

拡張

(9 x + 5)^{2} : 81 x^{2} + 90 x + 25

= \int 81 x^{2} + 90 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 81 x^{2} d x + \int 90 x d x + \int 25 d x

\int 81 x^{2} d x = 27 x^{3}

\int 90 x d x = 45 x^{2}

\int 25 d x = 25 x

= 27 x^{3} + 45 x^{2} + 25 x

定数を解答に追加する

= 27 x^{3} + 45 x^{2} + 25 x + C