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Beliebt Rechnen >

integral of (x-1)(3x-1)

Lösung

\int (x - 1) (3 x - 1) d x

Lösung

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

Schritte zur Lösung

\int (x - 1) (3 x - 1) d x

Multipliziere aus

(x - 1) (3 x - 1) : 3 x^{2} - 4 x + 1

= \int 3 x^{2} - 4 x + 1 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 3 x^{2} d x - \int 4 x d x + \int 1 d x

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

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

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of e^{x^2+3x}

\int e^{x^{2} + 3 x} d x

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\int (3 x + 1)^{6} d x

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\int 6 x^{- \frac{6}{7}} d x