integral of 2x(4-x)

Lösung

\int 2 x (4 - x) d x

2 (2 x^{2} - \frac{x ^{3}}{3}) + C

Schritte zur Lösung

\int 2 x (4 - x) d x

Entferne die Konstante:

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

= 2 \cdot \int x (4 - x) d x

Multipliziere aus

x (4 - x) : 4 x - x^{2}

= 2 \cdot \int 4 x - x^{2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int 4 x d x - \int x^{2} d x)

\int 4 x d x = 2 x^{2}

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

= 2 (2 x^{2} - \frac{x ^{3}}{3})

Füge eine Konstante zur Lösung hinzu

= 2 (2 x^{2} - \frac{x ^{3}}{3}) + C

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