integral of 9x(1-x)

Lösung

\int 9 x (1 - x) d x

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

Schritte zur Lösung

\int 9 x (1 - x) d x

Entferne die Konstante:

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

= 9 \cdot \int x (1 - x) d x

Multipliziere aus

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

= 9 \cdot \int 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

= 9 (\int x d x - \int x^{2} d x)

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

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

= 9 (\frac{x ^{2}}{2} - \frac{x ^{3}}{3})

Füge eine Konstante zur Lösung hinzu

= 9 (\frac{x ^{2}}{2} - \frac{x ^{3}}{3}) + C

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