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Beliebt Rechnen >

integral of (4x+3)(2x^2+3x)3

Lösung

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

Lösung

3 (2 x^{4} + 6 x^{3} + \frac{9 x ^{2}}{2}) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Multipliziere aus

(4 x + 3) (2 x^{2} + 3 x) : 8 x^{3} + 18 x^{2} + 9 x

= 3 \cdot \int 8 x^{3} + 18 x^{2} + 9 x 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

= 3 (\int 8 x^{3} d x + \int 18 x^{2} d x + \int 9 x d x)

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

\int 18 x^{2} d x = 6 x^{3}

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

= 3 (2 x^{4} + 6 x^{3} + \frac{9 x ^{2}}{2})

Füge eine Konstante zur Lösung hinzu

= 3 (2 x^{4} + 6 x^{3} + \frac{9 x ^{2}}{2}) + C

Graph

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