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Beliebt Rechnen >

integral ln(x-1)

Lösung

integral

ln (x - 1)

Lösung

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

Schritte zur Lösung

\int ln (x - 1) d x

Wende U-Substitution an

= \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 = x - 1

ein

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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