integral of (5s+3)^2

解

\int (5 s + 3)^{2} d s

\frac{25 s ^{3}}{3} + 15 s^{2} + 9 s + C

解答ステップ

\int (5 s + 3)^{2} d s

拡張

(5 s + 3)^{2} : 25 s^{2} + 30 s + 9

= \int 25 s^{2} + 30 s + 9 d s

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 25 s^{2} d s + \int 30 s d s + \int 9 d s

\int 25 s^{2} d s = \frac{25 s ^{3}}{3}

\int 30 s d s = 15 s^{2}

\int 9 d s = 9 s

= \frac{25 s ^{3}}{3} + 15 s^{2} + 9 s

定数を解答に追加する

= \frac{25 s ^{3}}{3} + 15 s^{2} + 9 s + C