integral of (2x-2)^3

Lösung

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

2 x^{4} - 8 x^{3} + 12 x^{2} - 8 x + C

Schritte zur Lösung

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

Multipliziere aus

(2 x - 2)^{3} : 8 x^{3} - 24 x^{2} + 24 x - 8

= \int 8 x^{3} - 24 x^{2} + 24 x - 8 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 8 x^{3} d x - \int 24 x^{2} d x + \int 24 x d x - \int 8 d x

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

\int 24 x^{2} d x = 8 x^{3}

\int 24 x d x = 12 x^{2}

\int 8 d x = 8 x

= 2 x^{4} - 8 x^{3} + 12 x^{2} - 8 x

Füge eine Konstante zur Lösung hinzu

= 2 x^{4} - 8 x^{3} + 12 x^{2} - 8 x + C

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