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Beliebt Rechnen >

integral of (1-x^{-1/3})

Lösung

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

Lösung

x - \frac{3}{2} x^{\frac{2}{3}} + C

Schritte zur Lösung

\int 1 - x^{- \frac{1}{3}} 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 1 d x - \int x^{- \frac{1}{3}} d x

\int 1 d x = x

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

= x - \frac{3}{2} x^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= x - \frac{3}{2} x^{\frac{2}{3}} + C

Graph

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