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Beliebt Rechnen >

integral of (2-3x)^2

Lösung

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

Lösung

4 x - 6 x^{2} + 3 x^{3} + C

Schritte zur Lösung

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

Multipliziere aus

(2 - 3 x)^{2} : 4 - 12 x + 9 x^{2}

= \int 4 - 12 x + 9 x^{2} 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 4 d x - \int 12 x d x + \int 9 x^{2} d x

\int 4 d x = 4 x

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

\int 9 x^{2} d x = 3 x^{3}

= 4 x - 6 x^{2} + 3 x^{3}

Füge eine Konstante zur Lösung hinzu

= 4 x - 6 x^{2} + 3 x^{3} + C

Graph

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