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Beliebt Rechnen >

integral of (5-x)sqrt(x)

Lösung

\int (5 - x) x d x

Lösung

\frac{10}{3} x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int (5 - x) x d x

Multipliziere aus

(5 - x) x : 5 x - x^{\frac{3}{2}}

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

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

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

= \frac{10}{3} x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{10}{3} x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + C

Graph

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