integral from 2 to 8 of (e^x)/(1+e^x)

Lösung

\int_{2}^{8} \frac{e ^{x}}{1 + e ^{x}} d x

ln (1 + e^{8}) - ln (1 + e^{2})

Dezimale

5.87340 \dots

Schritte zur Lösung

\int_{2}^{8} \frac{e ^{x}}{1 + e ^{x}} d x

Wende U-Substitution an

= \int_{1 + e^{2}}^{1 + e^{8}} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1 + e^{2}}^{1 + e^{8}}

Berechne die Grenzen:

ln (1 + e^{8}) - ln (1 + e^{2})

= ln (1 + e^{8}) - ln (1 + e^{2})

\int_{- 4}^{1} x d x

\int_{0}^{4} \frac{1}{x ^{2} + 2 x - 8} d x

\int_{- R}^{R} R^{2} - x^{2} d x

\int_{0}^{3} - x^{2} + 4 x d x

\int_{0}^{l n (6)} e^{x - e^{x}} d x