integral of x^2(4-x)

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

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

= \int 4 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 4 x^{2} d x - \int x^{3} d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

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

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

Füge eine Konstante zur Lösung hinzu

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

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