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

Lösung

\int \frac{x + 2}{3 x} d x

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

Schritte zur Lösung

\int \frac{x + 2}{3 x} d x

Multipliziere aus

\frac{x + 2}{3 x} : 6 x + \frac{2}{3 x}

= \int 6 x + \frac{2}{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 6 x d x + \int \frac{2}{3 x} d x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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