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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e \frac{1}{3 ^{x}}

d er i v a t i v e f (x) = \frac{x ^{2} - 1}{2 x + 2}

d er i v a t i v e f (x) = 4 x^{4} - 5 x^{3} + 2 x - 3

\frac{d}{d x} (\frac{x}{a ^{2} a ^{2} + x ^{2}})

\frac{d}{d x} (25 ln (x^{2}) - x^{2})