integral of x^{1/8}ln(x)

Lösung

\int x^{\frac{1}{8}} ln (x) d x

\frac{8}{9} x^{\frac{9}{8}} ln (x) - \frac{64}{81} x^{\frac{9}{8}} + C

Schritte zur Lösung

\int x^{\frac{1}{8}} ln (x) d x

Wende die partielle Integration an

= \frac{8}{9} x^{\frac{9}{8}} ln (x) - \int \frac{8}{9} x^{\frac{1}{8}} d x

\int \frac{8}{9} x^{\frac{1}{8}} d x = \frac{64}{81} x^{\frac{9}{8}}

= \frac{8}{9} x^{\frac{9}{8}} ln (x) - \frac{64}{81} x^{\frac{9}{8}}

Füge eine Konstante zur Lösung hinzu

= \frac{8}{9} x^{\frac{9}{8}} ln (x) - \frac{64}{81} x^{\frac{9}{8}} + C

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