integral from 1 to e^2 of 1/(x(1+ln(x)))

Lösung

\int_{1}^{e^{2}} \frac{1}{x ( 1 + ln ( x ) )} d x

ln (3)

Dezimale

1.09861 \dots

Schritte zur Lösung

\int_{1}^{e^{2}} \frac{1}{x ( 1 + ln ( x ) )} d x

Wende U-Substitution an

= \int_{1}^{3} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{3}

Berechne die Grenzen:

ln (3)

= ln (3)

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