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Beliebt Rechnen >

integral of 6(3x+1)^2

Lösung

\int 6 (3 x + 1)^{2} d x

Lösung

6 (3 x^{3} + 3 x^{2} + x) + C

Schritte zur Lösung

\int 6 (3 x + 1)^{2} d x

Entferne die Konstante:

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

= 6 \cdot \int (3 x + 1)^{2} d x

Multipliziere aus

(3 x + 1)^{2} : 9 x^{2} + 6 x + 1

= 6 \cdot \int 9 x^{2} + 6 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

= 6 (\int 9 x^{2} d x + \int 6 x d x + \int 1 d x)

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

\int 6 x d x = 3 x^{2}

\int 1 d x = x

= 6 (3 x^{3} + 3 x^{2} + x)

Füge eine Konstante zur Lösung hinzu

= 6 (3 x^{3} + 3 x^{2} + x) + C

Graph

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