integral of 10x^{3/7}+7x^{-6/7}

Lösung

\int 10 x^{\frac{3}{7}} + 7 x^{- \frac{6}{7}} d x

7 x^{\frac{10}{7}} + 49 x^{\frac{1}{7}} + C

Schritte zur Lösung

\int 10 x^{\frac{3}{7}} + 7 x^{- \frac{6}{7}} 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 10 x^{\frac{3}{7}} d x + \int 7 x^{- \frac{6}{7}} d x

\int 10 x^{\frac{3}{7}} d x = 7 x^{\frac{10}{7}}

\int 7 x^{- \frac{6}{7}} d x = 49 x^{\frac{1}{7}}

= 7 x^{\frac{10}{7}} + 49 x^{\frac{1}{7}}

Füge eine Konstante zur Lösung hinzu

= 7 x^{\frac{10}{7}} + 49 x^{\frac{1}{7}} + C

x \to 10 lim (x^{2})

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