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Beliebt Rechnen >

integral of (4+x^2)/(sqrt(x))

Lösung

\int \frac{4 + x ^{2}}{x} d x

Lösung

8 x + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int \frac{4 + x ^{2}}{x} d x

Multipliziere aus

\frac{4 + x ^{2}}{x} : \frac{4}{x} + x^{\frac{3}{2}}

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

\int \frac{4}{x} d x = 8 x

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

= 8 x + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= 8 x + \frac{2}{5} x^{\frac{5}{2}} + C

Graph

Beliebte Beispiele

limit as x approaches-3 of x^2-9

x \to - 3 lim (x^{2} - 9)

limit as x approaches 7-of 2/(x+7)

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

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\frac{d}{d x} (e^{(\frac{1}{x})})

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