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Beliebt Rechnen >

integral of 9(x^2+3x+5)(2x+3)

Lösung

\int 9 (x^{2} + 3 x + 5) (2 x + 3) d x

Lösung

9 (\frac{x ^{4}}{2} + 3 x^{3} + \frac{19 x ^{2}}{2} + 15 x) + C

Schritte zur Lösung

\int 9 (x^{2} + 3 x + 5) (2 x + 3) d x

Entferne die Konstante:

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

= 9 \cdot \int (x^{2} + 3 x + 5) (2 x + 3) d x

Multipliziere aus

(x^{2} + 3 x + 5) (2 x + 3) : 2 x^{3} + 9 x^{2} + 19 x + 15

= 9 \cdot \int 2 x^{3} + 9 x^{2} + 19 x + 15 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

= 9 (\int 2 x^{3} d x + \int 9 x^{2} d x + \int 19 x d x + \int 15 d x)

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

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

\int 19 x d x = \frac{19 x ^{2}}{2}

\int 15 d x = 15 x

= 9 (\frac{x ^{4}}{2} + 3 x^{3} + \frac{19 x ^{2}}{2} + 15 x)

Füge eine Konstante zur Lösung hinzu

= 9 (\frac{x ^{4}}{2} + 3 x^{3} + \frac{19 x ^{2}}{2} + 15 x) + C

Graph

Beliebte Beispiele

integral of (ln^2(x))/(sqrt(x^5))

\int \frac{ln ^{2} ( x )}{x ^{5}} d x

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\int (x^{5} - x^{3}) d x

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\int x (x + 1)^{10} d x

integral of ((sin(x))/(cos(x)))^2

\int (\frac{sin ( x )}{cos ( x )})^{2} d x

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\int \frac{1}{1 + x - 1} d x