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Beliebt Rechnen >

integral of 10x-3x^2-x^3

Lösung

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

Lösung

5 x^{2} - x^{3} - \frac{x ^{4}}{4} + C

Schritte zur Lösung

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

\int 10 x d x = 5 x^{2}

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

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

= 5 x^{2} - x^{3} - \frac{x ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= 5 x^{2} - x^{3} - \frac{x ^{4}}{4} + C

Graph

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