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Beliebt Rechnen >

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

Lösung

\int_{1}^{2} \frac{e ^{x}}{e ^{x} - 1} d x

Lösung

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

+1

Dezimale

1.31326 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{e ^{x}}{e ^{x} - 1} d x

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{e - 1}^{e^{2} - 1}

Berechne die Grenzen:

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

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

Graph

Beliebte Beispiele

integral from 0 to 2 of x^3+3

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

integral from 1 to 3 of x^3+1

\int_{1}^{3} x^{3} + 1 d x

integral from 0 to 2 of f(3x)

\int_{0}^{2} f (3 x) d x

integral from 0 to 1 of (2-3x)^4

\int_{0}^{1} (2 - 3 x)^{4} d x

integral from-infinity to infinity of e^{-jwt}

\int_{- \infty}^{\infty} e^{- j wt} d t