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Beliebt Rechnen >

integral of (ln(2x))/(xln(x))

Lösung

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

Lösung

ln (2) ln ∣ ln (x) ∣ + ln (x) + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int \frac{ln ( 2 ) + u}{u} d u

Multipliziere aus

\frac{ln ( 2 ) + u}{u} : \frac{ln ( 2 )}{u} + 1

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{ln ( 2 )}{u} d u = ln (2) ln ∣ u ∣

\int 1 d u = u

= ln (2) ln ∣ u ∣ + u

Setze in

u = ln (x)

ein

= ln (2) ln ∣ ln (x) ∣ + ln (x)

Füge eine Konstante zur Lösung hinzu

= ln (2) ln ∣ ln (x) ∣ + ln (x) + C

Graph

Beliebte Beispiele

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