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Beliebt Rechnen >

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

Lösung

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

Lösung

x^{3} - 3 x^{2} - 9 x + C

Schritte zur Lösung

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

Entferne die Konstante:

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

= 3 \cdot \int (x - 3) (x + 1) d x

Multipliziere aus

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

= 3 \cdot \int x^{2} - 2 x - 3 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 x^{2} d x - \int 2 x d x - \int 3 d x)

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

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

\int 3 d x = 3 x

= 3 (\frac{x ^{3}}{3} - x^{2} - 3 x)

Vereinfache

3 (\frac{x ^{3}}{3} - x^{2} - 3 x) : x^{3} - 3 x^{2} - 9 x

= x^{3} - 3 x^{2} - 9 x

Füge eine Konstante zur Lösung hinzu

= x^{3} - 3 x^{2} - 9 x + C

Graph

Beliebte Beispiele

inverselaplace-3

in v erse l a pl a ce - 3

fläche x=y^2-8y,x=3y-y^2

a re a x = y^{2} - 8 y, x = 3 y - y^{2}

integral of 10x+6

\int 10 x + 6 d x

y^{''}-(3/x)y^'-(4/(x^2))y=0

y^{^{''}} - (\frac{3}{x}) y^{^{'}} - (\frac{4}{x ^{2}}) y = 0

integral of (((x+1)(x-1))/x)

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