integral of (4x+7)^2

解

\int (4 x + 7)^{2} d x

\frac{16 x ^{3}}{3} + 28 x^{2} + 49 x + C

解答ステップ

\int (4 x + 7)^{2} d x

拡張

(4 x + 7)^{2} : 16 x^{2} + 56 x + 49

= \int 16 x^{2} + 56 x + 49 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 16 x^{2} d x + \int 56 x d x + \int 49 d x

\int 16 x^{2} d x = \frac{16 x ^{3}}{3}

\int 56 x d x = 28 x^{2}

\int 49 d x = 49 x

= \frac{16 x ^{3}}{3} + 28 x^{2} + 49 x

定数を解答に追加する

= \frac{16 x ^{3}}{3} + 28 x^{2} + 49 x + C