integral of ln(ln(x)) 1/x

Lösung

\int ln (ln (x)) \frac{1}{x} d x

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

Schritte zur Lösung

\int ln (ln (x)) \frac{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 = ln (x)

ein

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

Füge eine Konstante zur Lösung hinzu

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

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