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Beliebt Rechnen >

integral of (1-x^3)^2x^2

Lösung

\int (1 - x^{3})^{2} x^{2} d x

Lösung

\frac{x ^{3}}{3} - \frac{x ^{6}}{3} + \frac{x ^{9}}{9} + C

Schritte zur Lösung

\int (1 - x^{3})^{2} x^{2} d x

Multipliziere aus

(1 - x^{3})^{2} x^{2} : x^{2} - 2 x^{5} + x^{8}

= \int x^{2} - 2 x^{5} + x^{8} 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^{2} d x - \int 2 x^{5} d x + \int x^{8} d x

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

\int 2 x^{5} d x = \frac{x ^{6}}{3}

\int x^{8} d x = \frac{x ^{9}}{9}

= \frac{x ^{3}}{3} - \frac{x ^{6}}{3} + \frac{x ^{9}}{9}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - \frac{x ^{6}}{3} + \frac{x ^{9}}{9} + C

Graph

Beliebte Beispiele

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\int_{- 1}^{1} (y^{2} - 2) - e^{y} d y

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n \to \infty lim (- n^{2})

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