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人気のある微分積分 >

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

解

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

解

15 (\frac{x ^{3}}{3} - x) + C

解答ステップ

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

(5 x + 5) (3 x - 3) = 5 \cdot 3 (x + 1) (x - 1)

= \int 5 \cdot 3 (x + 1) (x - 1) d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot 3 \cdot \int (x + 1) (x - 1) d x

簡素化

= 15 \cdot \int (x + 1) (x - 1) d x

拡張

(x + 1) (x - 1) : x^{2} - 1

= 15 \cdot \int x^{2} - 1 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

= 15 (\int x^{2} d x - \int 1 d x)

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

\int 1 d x = x

= 15 (\frac{x ^{3}}{3} - x)

定数を解答に追加する

= 15 (\frac{x ^{3}}{3} - x) + C

グラフ

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