integral from 0 to 4 of (e^x)/(1+e^x)

Lösung

\int_{0}^{4} \frac{e ^{x}}{1 + e ^{x}} d x

ln (1 + e^{4}) - ln (2)

Dezimale

3.32500 \dots

Schritte zur Lösung

\int_{0}^{4} \frac{e ^{x}}{1 + e ^{x}} d x

Wende U-Substitution an

= \int_{2}^{1 + e^{4}} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{2}^{1 + e^{4}}

Berechne die Grenzen:

ln (1 + e^{4}) - ln (2)

= ln (1 + e^{4}) - ln (2)

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