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Beliebt Rechnen >

integral of (x^{1/2}-2)^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

(x^{\frac{1}{2}} - 2)^{2} : x - 4 x^{\frac{1}{2}} + 4

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

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

\int 4 x^{\frac{1}{2}} d x = \frac{8}{3} x^{\frac{3}{2}}

\int 4 d x = 4 x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of-5x+3

\frac{d}{d x} (- 5 x + 3)

y^{''}-24y^'+144y=0

y^{^{''}} - 24 y^{^{'}} + 144 y = 0

limit as x approaches-2-of x

x \to - 2 - lim (x)

limit as x approaches 7+of sqrt(x^2-49)

x \to 7 + lim (x^{2} - 49)

integral of 20-2x

\int 20 - 2 x d x