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Beliebt Rechnen >

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

Lösung

\int (x - 1) (2 - x) d x

Lösung

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

Schritte zur Lösung

\int (x - 1) (2 - x) d x

Multipliziere aus

(x - 1) (2 - x) : 3 x - x^{2} - 2

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

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

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

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

\int 2 d x = 2 x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (x-4)/(x^2-3x+2)

\int \frac{x - 4}{x ^{2} - 3 x + 2} d x

integral of (x^2+4x)/(x^3-x^2+x-1)

\int \frac{x ^{2} + 4 x}{x ^{3} - x ^{2} + x - 1} d x

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

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

integral of ((x+2)/(x^2-4x))

\int (\frac{x + 2}{x ^{2} - 4 x}) d x

integral of sin(18x)cos(15x)

\int sin (18 x) cos (15 x) d x