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Beliebt Rechnen >

integral of 2x(8x^2-20)^2

Lösung

\int 2 x (8 x^{2} - 20)^{2} d x

Lösung

2 (\frac{32 x ^{6}}{3} - 80 x^{4} + 200 x^{2}) + C

Schritte zur Lösung

\int 2 x (8 x^{2} - 20)^{2} d x

Entferne die Konstante:

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

= 2 \cdot \int x (8 x^{2} - 20)^{2} d x

Multipliziere aus

x (8 x^{2} - 20)^{2} : 64 x^{5} - 320 x^{3} + 400 x

= 2 \cdot \int 64 x^{5} - 320 x^{3} + 400 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

= 2 (\int 64 x^{5} d x - \int 320 x^{3} d x + \int 400 x d x)

\int 64 x^{5} d x = \frac{32 x ^{6}}{3}

\int 320 x^{3} d x = 80 x^{4}

\int 400 x d x = 200 x^{2}

= 2 (\frac{32 x ^{6}}{3} - 80 x^{4} + 200 x^{2})

Füge eine Konstante zur Lösung hinzu

= 2 (\frac{32 x ^{6}}{3} - 80 x^{4} + 200 x^{2}) + C

Graph

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