integral of (2x+3x^{1/2})x^{1/3}

Lösung

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

\frac{6}{7} x^{\frac{7}{3}} + \frac{18}{11} x^{\frac{11}{6}} + C

Schritte zur Lösung

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

Multipliziere aus

(2 x + 3 x^{\frac{1}{2}}) x^{\frac{1}{3}} : 2 x^{\frac{4}{3}} + 3 x^{\frac{5}{6}}

= \int 2 x^{\frac{4}{3}} + 3 x^{\frac{5}{6}} 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 2 x^{\frac{4}{3}} d x + \int 3 x^{\frac{5}{6}} d x

\int 2 x^{\frac{4}{3}} d x = \frac{6}{7} x^{\frac{7}{3}}

\int 3 x^{\frac{5}{6}} d x = \frac{18}{11} x^{\frac{11}{6}}

= \frac{6}{7} x^{\frac{7}{3}} + \frac{18}{11} x^{\frac{11}{6}}

Füge eine Konstante zur Lösung hinzu

= \frac{6}{7} x^{\frac{7}{3}} + \frac{18}{11} x^{\frac{11}{6}} + C

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