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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative of 2/(sqrt(x^2+1))

\frac{d}{d x} (\frac{2}{x ^{2} + 1})

integral from 0 to 2 of 2pi(5-x)(8-x^3)

\int_{0}^{2} 2 π (5 - x) (8 - x^{3}) d x

integral of (4/(x^2))

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

(xdy)/(dx)+5y=7x^2,f(2)=5

\frac{x d y}{d x} + 5 y = 7 x^{2}, f (2) = 5

derivative of Cxe^{-x}

\frac{d}{d x} (C x e^{- x})