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Beliebt Rechnen >

integral of-2x^3+12x^2-20x+8.5

Lösung

\int - 2 x^{3} + 12 x^{2} - 20 x + 8.5 d x

Lösung

- 0.5 x^{4} + 4 x^{3} - 10 x^{2} + 8.5 x + C

Schritte zur Lösung

\int - 2 x^{3} + 12 x^{2} - 20 x + 8.5 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 2 x^{3} d x + \int 12 x^{2} d x - \int 20 x d x + \int 8.5 d x

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

\int 12 x^{2} d x = 4 x^{3}

\int 20 x d x = 10 x^{2}

\int 8.5 d x = 8.5 x

= - \frac{x ^{4}}{2} + 4 x^{3} - 10 x^{2} + 8.5 x

Vereinfache

= - 0.5 x^{4} + 4 x^{3} - 10 x^{2} + 8.5 x

Füge eine Konstante zur Lösung hinzu

= - 0.5 x^{4} + 4 x^{3} - 10 x^{2} + 8.5 x + C

Graph

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