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Beliebt Rechnen >

integral of x^3(x^4-1)^2

Lösung

\int x^{3} (x^{4} - 1)^{2} d x

Lösung

\frac{x ^{12}}{12} - \frac{x ^{8}}{4} + \frac{x ^{4}}{4} + C

Schritte zur Lösung

\int x^{3} (x^{4} - 1)^{2} d x

Multipliziere aus

x^{3} (x^{4} - 1)^{2} : x^{11} - 2 x^{7} + x^{3}

= \int x^{11} - 2 x^{7} + 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 x^{11} d x - \int 2 x^{7} d x + \int x^{3} d x

\int x^{11} d x = \frac{x ^{12}}{12}

\int 2 x^{7} d x = \frac{x ^{8}}{4}

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

= \frac{x ^{12}}{12} - \frac{x ^{8}}{4} + \frac{x ^{4}}{4}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{12}}{12} - \frac{x ^{8}}{4} + \frac{x ^{4}}{4} + C

Graph

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