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Beliebt Rechnen >

integral of x(4-x^2)

Lösung

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

Lösung

2 x^{2} - \frac{x ^{4}}{4} + C

Schritte zur Lösung

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

Multipliziere aus

x (4 - x^{2}) : 4 x - x^{3}

= \int 4 x - x^{3} 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

= \int 4 x d x - \int x^{3} d x

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

\int x^{3} d x = \frac{x ^{4}}{4}

= 2 x^{2} - \frac{x ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= 2 x^{2} - \frac{x ^{4}}{4} + C

Graph

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