integral of (x^4-\sqrt[3]{x})/(6sqrt(x))

Lösung

\frac{1}{135} (5 x^{\frac{9}{2}} - 27 x^{\frac{5}{6}}) + C

Schritte zur Lösung

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Multipliziere aus

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{7}{2}} d x = \frac{2}{9} x^{\frac{9}{2}}

= \frac{1}{6} (\frac{2}{9} x^{\frac{9}{2}} - \frac{6}{5} x^{\frac{5}{6}})

Vereinfache

\frac{1}{6} (\frac{2}{9} x^{\frac{9}{2}} - \frac{6}{5} x^{\frac{5}{6}}) : \frac{1}{135} (5 x^{\frac{9}{2}} - 27 x^{\frac{5}{6}})

= \frac{1}{135} (5 x^{\frac{9}{2}} - 27 x^{\frac{5}{6}})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{135} (5 x^{\frac{9}{2}} - 27 x^{\frac{5}{6}}) + C