integral of x^{2/3}ln(x)

Lösung

\int x^{\frac{2}{3}} ln (x) d x

\frac{3}{5} x^{\frac{5}{3}} ln (x) - \frac{9}{25} x^{\frac{5}{3}} + C

Schritte zur Lösung

\int x^{\frac{2}{3}} ln (x) d x

Wende die partielle Integration an

= \frac{3}{5} x^{\frac{5}{3}} ln (x) - \int \frac{3}{5} x^{\frac{2}{3}} d x

\int \frac{3}{5} x^{\frac{2}{3}} d x = \frac{9}{25} x^{\frac{5}{3}}

= \frac{3}{5} x^{\frac{5}{3}} ln (x) - \frac{9}{25} x^{\frac{5}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{5} x^{\frac{5}{3}} ln (x) - \frac{9}{25} x^{\frac{5}{3}} + C

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