integral of 5x^{-2/3}-2x^{5/3}

Lösung

\int 5 x^{- \frac{2}{3}} - 2 x^{\frac{5}{3}} d x

15 x^{\frac{1}{3}} - \frac{3}{4} x^{\frac{8}{3}} + C

Schritte zur Lösung

\int 5 x^{- \frac{2}{3}} - 2 x^{\frac{5}{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 5 x^{- \frac{2}{3}} d x - \int 2 x^{\frac{5}{3}} d x

\int 5 x^{- \frac{2}{3}} d x = 15 x^{\frac{1}{3}}

\int 2 x^{\frac{5}{3}} d x = \frac{3}{4} x^{\frac{8}{3}}

= 15 x^{\frac{1}{3}} - \frac{3}{4} x^{\frac{8}{3}}

Füge eine Konstante zur Lösung hinzu

= 15 x^{\frac{1}{3}} - \frac{3}{4} x^{\frac{8}{3}} + C

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