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Beliebt Rechnen >

integral of 2/(3\sqrt[3]{2x)}

Lösung

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

Lösung

\frac{2}{3} 3 \frac{x ^{2}}{2} + \frac{1}{3 3 2} x^{\frac{2}{3}} + C

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{2}{3} \cdot \int \frac{1}{3 2 x} d x

Wende die partielle Integration an

= \frac{2}{3} (3 \frac{x ^{2}}{2} - \int - \frac{1}{3 3 2 x ^{\frac{1}{3}}} d x)

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

= \frac{2}{3} (3 \frac{x ^{2}}{2} - (- \frac{1}{2 3 2} x^{\frac{2}{3}}))

Vereinfache

\frac{2}{3} (3 \frac{x ^{2}}{2} - (- \frac{1}{2 3 2} x^{\frac{2}{3}})) : \frac{2}{3} 3 \frac{x ^{2}}{2} + \frac{1}{3 3 2} x^{\frac{2}{3}}

= \frac{2}{3} 3 \frac{x ^{2}}{2} + \frac{1}{3 3 2} x^{\frac{2}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} 3 \frac{x ^{2}}{2} + \frac{1}{3 3 2} x^{\frac{2}{3}} + C

Graph

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