integral from 0 to 2 of (e^x)/(10+e^x)

Lösung

\int_{0}^{2} \frac{e ^{x}}{10 + e ^{x}} d x

ln (10 + e^{2}) - ln (11)

Dezimale

0.45794 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{e ^{x}}{10 + e ^{x}} d x

Wende U-Substitution an

= \int_{11}^{10 + e^{2}} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{11}^{10 + e^{2}}

Berechne die Grenzen:

ln (10 + e^{2}) - ln (11)

= ln (10 + e^{2}) - ln (11)

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