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Beliebt Rechnen >

integral of ((u-2)/(sqrt(u)))

Lösung

\int (\frac{u - 2}{u}) d u

Lösung

\frac{2}{3} u^{\frac{3}{2}} - 4 u + C

Schritte zur Lösung

\int \frac{u - 2}{u} d u

Multipliziere aus

\frac{u - 2}{u} : u - \frac{2}{u}

= \int u - \frac{2}{u} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u d u - \int \frac{2}{u} d u

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

\int \frac{2}{u} d u = 4 u

= \frac{2}{3} u^{\frac{3}{2}} - 4 u

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (X^2)/2

\int \frac{X ^{2}}{2} d X

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integral of (x^2+2)/(x-1)

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\int (x^{\frac{3}{2}} + 4 x + 4) d x