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Beliebt Rechnen >

integral of (6x^6-2)^2(36x)

Lösung

\int (6 x^{6} - 2)^{2} (36 x) d x

Lösung

36 (\frac{18 x ^{14}}{7} - 3 x^{8} + 2 x^{2}) + C

Schritte zur Lösung

\int (6 x^{6} - 2)^{2} \cdot 36 x d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 36 \cdot \int (6 x^{6} - 2)^{2} x d x

Multipliziere aus

(6 x^{6} - 2)^{2} x : 36 x^{13} - 24 x^{7} + 4 x

= 36 \cdot \int 36 x^{13} - 24 x^{7} + 4 x 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

= 36 (\int 36 x^{13} d x - \int 24 x^{7} d x + \int 4 x d x)

\int 36 x^{13} d x = \frac{18 x ^{14}}{7}

\int 24 x^{7} d x = 3 x^{8}

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

= 36 (\frac{18 x ^{14}}{7} - 3 x^{8} + 2 x^{2})

Füge eine Konstante zur Lösung hinzu

= 36 (\frac{18 x ^{14}}{7} - 3 x^{8} + 2 x^{2}) + C

Graph

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