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Beliebt Rechnen >

integral from 1 to 3 of (e^x)/(e^x-1)

Lösung

\int_{1}^{3} \frac{e ^{x}}{e ^{x} - 1} d x

Lösung

ln (e^{3} - 1) - ln (e - 1)

+1

Dezimale

2.40760 \dots

Schritte zur Lösung

\int_{1}^{3} \frac{e ^{x}}{e ^{x} - 1} d x

Wende U-Substitution an

= \int_{e - 1}^{e^{3} - 1} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{e - 1}^{e^{3} - 1}

Berechne die Grenzen:

ln (e^{3} - 1) - ln (e - 1)

= ln (e^{3} - 1) - ln (e - 1)

Graph

Beliebte Beispiele

integral of 3-te^{-t}

\int 3 - t e^{- t} d t

integral of (1-3x)/(2sqrt(1-x))

\int \frac{1 - 3 x}{2 1 - x} d x

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\int 7 x e^{3 x} d x

integral of sqrt(484-x^2)

\int 484 - x^{2} d x

(\partial)/(\partial x)(xe^{x^2+2y^2})

\frac{\partial}{\partial x} (x e^{x^{2} + 2 y^{2}})