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

Lösung

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

\frac{x ^{10}}{10} - \frac{3 x ^{8}}{4} + 2 x^{6} - 2 x^{4} + C

Schritte zur Lösung

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

Multipliziere aus

(x^{2} - 2)^{3} x^{3} : x^{9} - 6 x^{7} + 12 x^{5} - 8 x^{3}

= \int x^{9} - 6 x^{7} + 12 x^{5} - 8 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^{9} d x - \int 6 x^{7} d x + \int 12 x^{5} d x - \int 8 x^{3} d x

\int x^{9} d x = \frac{x ^{10}}{10}

\int 6 x^{7} d x = \frac{3 x ^{8}}{4}

\int 12 x^{5} d x = 2 x^{6}

\int 8 x^{3} d x = 2 x^{4}

= \frac{x ^{10}}{10} - \frac{3 x ^{8}}{4} + 2 x^{6} - 2 x^{4}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{10}}{10} - \frac{3 x ^{8}}{4} + 2 x^{6} - 2 x^{4} + C

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