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Beliebt Rechnen >

integral of ln(x+6)

Lösung

\int ln (x + 6) d x

Lösung

x ln (x + 6) + 6 ln (x + 6) - x - 6 + C

Schritte zur Lösung

\int ln (x + 6) 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 + 6

ein

= (x + 6) ln (x + 6) - (x + 6)

Vereinfache

(x + 6) ln (x + 6) - (x + 6) : x ln (x + 6) + 6 ln (x + 6) - x - 6

= x ln (x + 6) + 6 ln (x + 6) - x - 6

Füge eine Konstante zur Lösung hinzu

= x ln (x + 6) + 6 ln (x + 6) - x - 6 + C

Graph

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