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Beliebt Rechnen >

integral of sqrt(x)sqrt(x^{3/2)}-1

Lösung

\int x x^{\frac{3}{2}} - 1 d x

Lösung

\frac{4}{9} x^{\frac{9}{4}} - x + C

Schritte zur Lösung

\int x x^{\frac{3}{2}} - 1 d x

x^{\frac{3}{2}} = x x^{0.5}

= \int x x x^{0.5} - 1 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 x x^{0.5} d x - \int 1 d x

\int x x x^{0.5} d x = \frac{4}{9} x^{\frac{9}{4}}

\int 1 d x = x

= \frac{4}{9} x^{\frac{9}{4}} - x

Füge eine Konstante zur Lösung hinzu

= \frac{4}{9} x^{\frac{9}{4}} - x + C

Graph

Beliebte Beispiele

fläche sin(x),cos(x),x=-pi/6

a re a sin (x), cos (x), x = - \frac{π}{6}

derivative of x^2e^{5x}

\frac{d}{d x} (x^{2} e^{5 x})

derivative sqrt(7+4x)

d er i v a t i v e 7 + 4 x

integral from 0 to 4 of-x^2

\int_{0}^{4} - x^{2} d x

limit as x approaches 2 of 4-2x

x \to 2 lim (4 - 2 x)