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Beliebt Rechnen >

integral of x(x-1)

Lösung

\int x (x - 1) d x

Lösung

\frac{x ^{3}}{3} - \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int x (x - 1) d x

Multipliziere aus

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

= \int x^{2} - 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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - \frac{x ^{2}}{2} + C

Graph

Beliebte Beispiele

fläche g(x)=sin(x),0, pi/4

a re a g (x) = sin (x), 0, \frac{π}{4}

derivative of (x^2+1(x^2-1))

\frac{d}{d x} ((x^{2} + 1) (x^{2} - 1))

derivative of 100xe^{-0.5x}

\frac{d}{d x} (100 x e^{- 0.5 x})

d/(dt)(e^{t/2})

\frac{d}{d t} (e^{\frac{t}{2}})

integral of 1/(x^2+3x)

\int \frac{1}{x ^{2} + 3 x} d x