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Beliebt Rechnen >

integral of (x-1)(x+2)(x-3)

Lösung

\int (x - 1) (x + 2) (x - 3) d x

Lösung

\frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} - \frac{5 x ^{2}}{2} + 6 x + C

Schritte zur Lösung

\int (x - 1) (x + 2) (x - 3) d x

Multipliziere aus

(x - 1) (x + 2) (x - 3) : x^{3} - 2 x^{2} - 5 x + 6

= \int x^{3} - 2 x^{2} - 5 x + 6 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^{3} d x - \int 2 x^{2} d x - \int 5 x d x + \int 6 d x

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

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} - \frac{5 x ^{2}}{2} + 6 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} - \frac{2 x ^{3}}{3} - \frac{5 x ^{2}}{2} + 6 x + C

Graph

Beliebte Beispiele

derivative f(x)=(4x)/(x^3+5)

d er i v a t i v e f (x) = \frac{4 x}{x ^{3} + 5}

integral of (80)/(64-x^2)

\int \frac{80}{64 - x ^{2}} d x

(\partial)/(\partial x)({f}(x,b,y)(ax+by))

\frac{\partial}{\partial x} (f (x, b, y) (a x + b y))

fläche 5x, 1/7 x,50-x^2

a re a 5 x, \frac{1}{7} x, 50 - x^{2}

(x^2+1)y^'+7x(y-1)=0,y(0)=4

(x^{2} + 1) y^{^{'}} + 7 x (y - 1) = 0, y (0) = 4