integral from 0 to 2 of (e^x)/(3+e^x)

Lösung

\int_{0}^{2} \frac{e ^{x}}{3 + e ^{x}} d x

ln (3 + e^{2}) - 2 ln (2)

Dezimale

0.95445 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{e ^{x}}{3 + e ^{x}} d x

Wende U-Substitution an

= \int_{4}^{3 + e^{2}} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{4}^{3 + e^{2}}

Berechne die Grenzen:

ln (3 + e^{2}) - 2 ln (2)

= ln (3 + e^{2}) - 2 ln (2)

\int_{1}^{2} 5 - 2 x d x

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