integral from 0 to 1 of (1+e^x)/(e^x+x)

Lösung

\int_{0}^{1} \frac{1 + e ^{x}}{e ^{x} + x} d x

ln (e + 1)

Dezimale

1.31326 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1 + e ^{x}}{e ^{x} + x} d x

Wende U-Substitution an

= \int_{1}^{e + 1} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{e + 1}

Berechne die Grenzen:

ln (e + 1)

= ln (e + 1)

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