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Beliebt Rechnen >

integral of ln(1/(1-x))

Lösung

\int ln (\frac{1}{1 - x}) d x

Lösung

- x ln (1 - x) - 1 + x + ln ∣ 1 - x ∣ + C

Schritte zur Lösung

\int ln (\frac{1}{1 - x}) d x

Wende die partielle Integration an

= - x ln (1 - x) - \int \frac{x}{1 - x} d x

\int \frac{x}{1 - x} d x = 1 - x - ln ∣ 1 - x ∣

= - x ln (1 - x) - (1 - x - ln ∣ 1 - x ∣)

Vereinfache

= - x ln (1 - x) - 1 + x + ln ∣ 1 - x ∣

Füge eine Konstante zur Lösung hinzu

= - x ln (1 - x) - 1 + x + ln ∣ 1 - x ∣ + C

Graph

Beliebte Beispiele

integral of x/((x-1)(x-2)^2)

\int \frac{x}{( x - 1 ) ( x - 2 ) ^{2}} d x

integral of xsqrt(10x-x^2)

\int x 10 x - x^{2} d x

integral of x^2sqrt(81-4x^2)

\int x^{2} 81 - 4 x^{2} d x

integral of 1/(t^2)sqrt(1/t-1)

\int \frac{1}{t ^{2}} \frac{1}{t} - 1 d t

integral of (6t-7)/(3t^2-7t+15)

\int \frac{6 t - 7}{3 t ^{2} - 7 t + 15} d t