integral of (x+2)/(x^{1/2)}

Lösung

\int \frac{x + 2}{x ^{\frac{1}{2}}} d x

\frac{2}{3} x^{\frac{3}{2}} + 4 x^{\frac{1}{2}} + C

Schritte zur Lösung

\int \frac{x + 2}{x ^{\frac{1}{2}}} d x

Multipliziere aus

\frac{x + 2}{x ^{\frac{1}{2}}} : x^{\frac{1}{2}} + \frac{2}{x ^{\frac{1}{2}}}

= \int x^{\frac{1}{2}} + \frac{2}{x ^{\frac{1}{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 x^{\frac{1}{2}} d x + \int \frac{2}{x ^{\frac{1}{2}}} d x

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

\int \frac{2}{x ^{\frac{1}{2}}} d x = 4 x^{\frac{1}{2}}

= \frac{2}{3} x^{\frac{3}{2}} + 4 x^{\frac{1}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} + 4 x^{\frac{1}{2}} + C

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