integral of 3/7 x^{-1/7}

Lösung

\int \frac{3}{7} x^{- \frac{1}{7}} d x

\frac{1}{2} x^{\frac{6}{7}} + C

Schritte zur Lösung

\int \frac{3}{7} x^{- \frac{1}{7}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{3}{7} \cdot \int x^{- \frac{1}{7}} d x

Wende die Potenzregel an

= \frac{3}{7} \cdot \frac{7}{6} x^{\frac{6}{7}}

Vereinfache

\frac{3}{7} \cdot \frac{7}{6} x^{\frac{6}{7}} : \frac{1}{2} x^{\frac{6}{7}}

= \frac{1}{2} x^{\frac{6}{7}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{\frac{6}{7}} + C

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