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Beliebt Rechnen >

integral of sqrt(x)(1-sqrt(x))

Lösung

\int x (1 - x) d x

Lösung

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

Schritte zur Lösung

\int x (1 - x) d x

Multipliziere aus

x (1 - x) : x - x

= \int x - 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 d x - \int x d x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(sqrt(|xy|))

\frac{\partial}{\partial x} (∣ x y ∣)

(dy)/(dx)+y/x =x^2

\frac{d y}{d x} + \frac{y}{x} = x^{2}

derivative sqrt(t^2+9)

d er i v a t i v e t^{2} + 9

limit as x approaches 2 of e^x

x \to 2 lim (e^{x})

integral of 1/(6-36x^2)

\int \frac{1}{6 - 36 x ^{2}} d x