integral of (2x-3)(5x+1)

解

\int (2 x - 3) (5 x + 1) d x

\frac{10 x ^{3}}{3} - \frac{13 x ^{2}}{2} - 3 x + C

解答ステップ

\int (2 x - 3) (5 x + 1) d x

拡張

(2 x - 3) (5 x + 1) : 10 x^{2} - 13 x - 3

= \int 10 x^{2} - 13 x - 3 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 10 x^{2} d x - \int 13 x d x - \int 3 d x

\int 10 x^{2} d x = \frac{10 x ^{3}}{3}

\int 13 x d x = \frac{13 x ^{2}}{2}

\int 3 d x = 3 x

= \frac{10 x ^{3}}{3} - \frac{13 x ^{2}}{2} - 3 x

定数を解答に追加する

= \frac{10 x ^{3}}{3} - \frac{13 x ^{2}}{2} - 3 x + C