integral of (ln(ln(k)))/(2k)

Lösung

\int \frac{ln ( ln ( k ) )}{2 k} d k

\frac{1}{2} (ln (k) ln (ln (k)) - ln (k)) + C

Schritte zur Lösung

\int \frac{ln ( ln ( k ) )}{2 k} d k

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{ln ( ln ( k ) )}{k} d k

Wende U-Substitution an

= \frac{1}{2} \cdot \int ln (u) d u

Wende die partielle Integration an

= \frac{1}{2} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{2} (u ln (u) - u)

Setze in

u = ln (k)

ein

= \frac{1}{2} (ln (k) ln (ln (k)) - ln (k))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (ln (k) ln (ln (k)) - ln (k)) + C

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