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Beliebt Rechnen >

integral of (ln(1-x))

Lösung

\int (ln (1 - x)) d x

Lösung

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

Schritte zur Lösung

\int ln (1 - x) d x

Wende U-Substitution an

= \int - ln (u) d u

Entferne die Konstante:

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

= - \int ln (u) d u

Wende die partielle Integration an

= - (u ln (u) - \int 1 d u)

\int 1 d u = u

= - (u ln (u) - u)

Setze in

u = 1 - x

ein

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

Vereinfache

- ((1 - x) ln (1 - x) - (1 - x)) : - ln (1 - x) + x ln (1 - x) + 1 - x

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (cos^4(x))/(csc^3(x))

\int \frac{cos ^{4} ( x )}{csc ^{3} ( x )} d x

integral of (x+5)/(x-5)

\int \frac{x + 5}{x - 5} d x

integral of-sin(3x)(5+cos(3x))^4

\int - sin (3 x) (5 + cos (3 x))^{4} d x

integral of 1/(sqrt(x^{10))}

\int \frac{1}{x ^{10}} d x

integral of-x^6

\int - x^{6} d x