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Beliebt Rechnen >

integral of-(x-1)^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Multipliziere aus

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

= - \int x^{2} - 2 x + 1 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 2 x d x + \int 1 d x)

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

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

\int 1 d x = x

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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derivative of cos(x-4tan(x))

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derivative of xarctan(x)

\frac{d}{d x} (x arctan (x))

2y^{''}-y^'+3y=0

2 y^{^{''}} - y^{^{'}} + 3 y = 0

x^2y^{''}-14xy^'+56y=0

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