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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

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

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