integral of 7x^{2/5}+8x^{-4/5}

Lösung

\int 7 x^{\frac{2}{5}} + 8 x^{- \frac{4}{5}} d x

5 x^{\frac{7}{5}} + 40 x^{\frac{1}{5}} + C

Schritte zur Lösung

\int 7 x^{\frac{2}{5}} + 8 x^{- \frac{4}{5}} 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 7 x^{\frac{2}{5}} d x + \int 8 x^{- \frac{4}{5}} d x

\int 7 x^{\frac{2}{5}} d x = 5 x^{\frac{7}{5}}

\int 8 x^{- \frac{4}{5}} d x = 40 x^{\frac{1}{5}}

= 5 x^{\frac{7}{5}} + 40 x^{\frac{1}{5}}

Füge eine Konstante zur Lösung hinzu

= 5 x^{\frac{7}{5}} + 40 x^{\frac{1}{5}} + C

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