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Beliebt Rechnen >

integral of (x^2-5x+5)

Lösung

\int (x^{2} - 5 x + 5) d x

Lösung

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

Schritte zur Lösung

\int x^{2} - 5 x + 5 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 5 x d x + \int 5 d x

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

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

\int 5 d x = 5 x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 2(sin(x)-cos(x)+1)

\int 2 (sin (x) - cos (x) + 1) d x

(dy)/(dt)+y=cos(2t),y(0)=5

\frac{d y}{d t} + y = cos (2 t), y (0) = 5

(dy)/(dx)= 1/(xy)

\frac{d y}{d x} = \frac{1}{x y}

derivative f(x)=xsqrt(x^3-6)

d er i v a t i v e f (x) = x x^{3} - 6

derivative y=2x^2sqrt(2-x)

d er i v a t i v e y = 2 x^{2} 2 - x