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Beliebt Rechnen >

integral of 10(3x+4)^2

Lösung

\int 10 (3 x + 4)^{2} d x

Lösung

10 (3 x^{3} + 12 x^{2} + 16 x) + C

Schritte zur Lösung

\int 10 (3 x + 4)^{2} d x

Entferne die Konstante:

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

= 10 \cdot \int (3 x + 4)^{2} d x

Multipliziere aus

(3 x + 4)^{2} : 9 x^{2} + 24 x + 16

= 10 \cdot \int 9 x^{2} + 24 x + 16 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

= 10 (\int 9 x^{2} d x + \int 24 x d x + \int 16 d x)

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

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

\int 16 d x = 16 x

= 10 (3 x^{3} + 12 x^{2} + 16 x)

Füge eine Konstante zur Lösung hinzu

= 10 (3 x^{3} + 12 x^{2} + 16 x) + C

Graph

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