integral of ln(x+16)

Lösung

\int ln (x + 16) d x

x ln (x + 16) + 16 ln (x + 16) - x - 16 + C

Schritte zur Lösung

\int ln (x + 16) 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 + 16

ein

= (x + 16) ln (x + 16) - (x + 16)

Vereinfache

(x + 16) ln (x + 16) - (x + 16) : x ln (x + 16) + 16 ln (x + 16) - x - 16

= x ln (x + 16) + 16 ln (x + 16) - x - 16

Füge eine Konstante zur Lösung hinzu

= x ln (x + 16) + 16 ln (x + 16) - x - 16 + C

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(tan^{2} (x))^{^{'}}

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