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Beliebt Rechnen >

integral of x^4(x-2)(x+3)

Lösung

\int x^{4} (x - 2) (x + 3) d x

Lösung

\frac{x ^{7}}{7} + \frac{x ^{6}}{6} - \frac{6 x ^{5}}{5} + C

Schritte zur Lösung

\int x^{4} (x - 2) (x + 3) d x

Multipliziere aus

x^{4} (x - 2) (x + 3) : x^{6} + x^{5} - 6 x^{4}

= \int x^{6} + x^{5} - 6 x^{4} 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^{6} d x + \int x^{5} d x - \int 6 x^{4} d x

\int x^{6} d x = \frac{x ^{7}}{7}

\int x^{5} d x = \frac{x ^{6}}{6}

\int 6 x^{4} d x = \frac{6 x ^{5}}{5}

= \frac{x ^{7}}{7} + \frac{x ^{6}}{6} - \frac{6 x ^{5}}{5}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{7}}{7} + \frac{x ^{6}}{6} - \frac{6 x ^{5}}{5} + C

Graph

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