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Beliebt Rechnen >

integral of (x+4)^2(x-4)

Lösung

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

Lösung

\frac{x ^{4}}{4} + \frac{4 x ^{3}}{3} - 8 x^{2} - 64 x + C

Schritte zur Lösung

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

Multipliziere aus

(x + 4)^{2} (x - 4) : x^{3} + 4 x^{2} - 16 x - 64

= \int x^{3} + 4 x^{2} - 16 x - 64 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 x^{3} d x + \int 4 x^{2} d x - \int 16 x d x - \int 64 d x

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

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

\int 16 x d x = 8 x^{2}

\int 64 d x = 64 x

= \frac{x ^{4}}{4} + \frac{4 x ^{3}}{3} - 8 x^{2} - 64 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} + \frac{4 x ^{3}}{3} - 8 x^{2} - 64 x + C

Graph

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