integral of 8x^{1/3}-8x^{-1/3}

Lösung

\int 8 x^{\frac{1}{3}} - 8 x^{- \frac{1}{3}} d x

6 x^{\frac{4}{3}} - 12 x^{\frac{2}{3}} + C

Schritte zur Lösung

\int 8 x^{\frac{1}{3}} - 8 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 8 x^{\frac{1}{3}} d x - \int 8 x^{- \frac{1}{3}} d x

\int 8 x^{\frac{1}{3}} d x = 6 x^{\frac{4}{3}}

\int 8 x^{- \frac{1}{3}} d x = 12 x^{\frac{2}{3}}

= 6 x^{\frac{4}{3}} - 12 x^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= 6 x^{\frac{4}{3}} - 12 x^{\frac{2}{3}} + C

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