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Beliebt Rechnen >

integral of ln(x+17)

Lösung

\int ln (x + 17) d x

Lösung

x ln (x + 17) + 17 ln (x + 17) - x - 17 + C

Schritte zur Lösung

\int ln (x + 17) 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 + 17

ein

= (x + 17) ln (x + 17) - (x + 17)

Vereinfache

(x + 17) ln (x + 17) - (x + 17) : x ln (x + 17) + 17 ln (x + 17) - x - 17

= x ln (x + 17) + 17 ln (x + 17) - x - 17

Füge eine Konstante zur Lösung hinzu

= x ln (x + 17) + 17 ln (x + 17) - x - 17 + C

Graph

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