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Beliebt Rechnen >

integral of (1-sqrt(x))^2

Lösung

\int (1 - x)^{2} d x

Lösung

x - \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int (1 - x)^{2} d x

Multipliziere aus

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

= \int 1 - 2 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 1 d x - \int 2 x d x + \int x d x

\int 1 d x = x

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

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

= x - \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= x - \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

Graph

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