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

Lösung

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

\frac{2}{5} x^{\frac{5}{3}} + C

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{2}{3} \cdot \int x^{\frac{2}{3}} d x

Wende die Potenzregel an

= \frac{2}{3} \cdot \frac{3}{5} x^{\frac{5}{3}}

Vereinfache

\frac{2}{3} \cdot \frac{3}{5} x^{\frac{5}{3}} : \frac{2}{5} x^{\frac{5}{3}}

= \frac{2}{5} x^{\frac{5}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} x^{\frac{5}{3}} + C

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