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Beliebt Rechnen >

integral of (x^{1/2}+5)/(\sqrt[3]{x)}

Lösung

\int \frac{x ^{\frac{1}{2}} + 5}{3 x} d x

Lösung

\frac{6}{7} x^{\frac{7}{6}} + \frac{15}{2} x^{\frac{2}{3}} + C

Schritte zur Lösung

\int \frac{x ^{\frac{1}{2}} + 5}{3 x} d x

Multipliziere aus

\frac{x ^{\frac{1}{2}} + 5}{3 x} : x^{\frac{1}{6}} + \frac{5}{3 x}

= \int x^{\frac{1}{6}} + \frac{5}{3 x} 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}{6}} d x + \int \frac{5}{3 x} d x

\int x^{\frac{1}{6}} d x = \frac{6}{7} x^{\frac{7}{6}}

\int \frac{5}{3 x} d x = \frac{15}{2} x^{\frac{2}{3}}

= \frac{6}{7} x^{\frac{7}{6}} + \frac{15}{2} x^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{6}{7} x^{\frac{7}{6}} + \frac{15}{2} x^{\frac{2}{3}} + C

Graph

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