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Beliebt Rechnen >

integral of (e^y)/(1-e^y)

Lösung

\int \frac{e ^{y}}{1 - e ^{y}} d y

Lösung

- ln ∣ 1 - e^{y} ∣ + C

Schritte zur Lösung

\int \frac{e ^{y}}{1 - e ^{y}} d y

Wende U-Substitution an

= \int - \frac{1}{u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Setze in

u = 1 - e^{y}

ein

= - ln ∣ 1 - e^{y} ∣

Füge eine Konstante zur Lösung hinzu

= - ln ∣ 1 - e^{y} ∣ + C

Graph

Beliebte Beispiele

limit as x approaches 0 of (0x^4+e^{0x})/(x^4)

x \to 0 lim (\frac{0 x ^{4} + e ^{0 x}}{x ^{4}})

derivative of xln^2(x)

\frac{d}{d x} (x ln^{2} (x))

derivative (y+3/y)(y^2-5)

d er i v a t i v e (y + \frac{3}{y}) (y^{2} - 5)

derivative of sec^{n-2}(x)

\frac{d}{d x} (sec^{n - 2} (x))

limit as x approaches 0 of (10^x-1)/x

x \to 0 lim (\frac{1 0 ^{x} - 1}{x})