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Beliebt Rechnen >

integral of (ln(2x))/(xsqrt(1+ln(x)))

Lösung

\int \frac{ln ( 2 x )}{x 1 + ln ( x )} d x

Lösung

2 ln (2 x) 1 + ln (x) - \frac{4}{3} (1 + ln (x))^{\frac{3}{2}} + C

Schritte zur Lösung

\int \frac{ln ( 2 x )}{x 1 + ln ( x )} d x

Wende die partielle Integration an

= 2 ln (2 x) 1 + ln (x) - \int \frac{2 1 + ln ( x )}{x} d x

\int \frac{2 1 + ln ( x )}{x} d x = \frac{4}{3} (1 + ln (x))^{\frac{3}{2}}

= 2 ln (2 x) 1 + ln (x) - \frac{4}{3} (1 + ln (x))^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= 2 ln (2 x) 1 + ln (x) - \frac{4}{3} (1 + ln (x))^{\frac{3}{2}} + C

Graph

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