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

Lösung

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

ln (2)

Dezimale

0.69314 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{2} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{2}

Berechne die Grenzen:

ln (2)

= ln (2)

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