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Beliebt Rechnen >

integral of (ln(2x))/(ln(4x)x)

Lösung

\int \frac{ln ( 2 x )}{ln ( 4 x ) x} d x

Lösung

ln (4 x) - ln (2) ln ∣ ln (4 x) ∣ + C

Schritte zur Lösung

\int \frac{ln ( 2 x )}{ln ( 4 x ) x} d x

Wende U-Substitution an

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

Wende U-Substitution an

= \int \frac{v - ln ( 2 )}{v} d v

Multipliziere aus

\frac{v - ln ( 2 )}{v} : 1 - \frac{ln ( 2 )}{v}

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

Wende die Summenregel an:

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

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

\int 1 d v = v

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

= v - ln (2) ln ∣ v ∣

Ersetze zurück

= ln (4 x) - ln (2) ln ∣ ln (4 x) ∣

Füge eine Konstante zur Lösung hinzu

= ln (4 x) - ln (2) ln ∣ ln (4 x) ∣ + C

Graph

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