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Beliebt Rechnen >

integral of (2x-sqrt(x))^2

Lösung

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

Lösung

\frac{4 x ^{3}}{3} - \frac{8}{5} x^{\frac{5}{2}} + \frac{x ^{2}}{2} + C

Schritte zur Lösung

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

Multipliziere aus

(2 x - x)^{2} : 4 x^{2} - 4 x^{\frac{3}{2}} + x

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

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 4 x^{\frac{3}{2}} d x = \frac{8}{5} x^{\frac{5}{2}}

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

= \frac{4 x ^{3}}{3} - \frac{8}{5} x^{\frac{5}{2}} + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{4 x ^{3}}{3} - \frac{8}{5} x^{\frac{5}{2}} + \frac{x ^{2}}{2} + C

Graph

Beliebte Beispiele

integral from 0 to 4 of sqrt(y)

\int_{0}^{4} y d y

integral from-1 to 3 of-x^2

\int_{- 1}^{3} - x^{2} d x

derivative of 6/(5x^3)

\frac{d}{d x} (\frac{6}{5 x ^{3}})

derivative f(x)=(6x+5)(x^3-2)

d er i v a t i v e f (x) = (6 x + 5) (x^{3} - 2)

limit as x approaches 0 of x^3sin(x)

x \to 0 lim (x^{3} sin (x))