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Beliebt Rechnen >

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

Lösung

\int \frac{3}{2} (1 - x)^{2} d x

Lösung

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

Schritte zur Lösung

\int \frac{3}{2} (1 - x)^{2} d x

Entferne die Konstante:

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

= \frac{3}{2} \cdot \int (1 - x)^{2} d x

Multipliziere aus

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

= \frac{3}{2} \cdot \int 1 - 2 x + x^{2} 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

= \frac{3}{2} (\int 1 d x - \int 2 x d x + \int x^{2} d x)

\int 1 d x = x

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of-9x^2

\int - 9 x^{2} d x

integral of x-1/3

\int x - \frac{1}{3} d x

integral of e^{4x}cos(-1x)

\int e^{4 x} cos (- 1 x) d x

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

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

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

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