integral from e to 4 of (ln(ln(x)))/x

Lösung

\int_{e}^{4} \frac{ln ( ln ( x ) )}{x} d x

2 ln (2) ln (2 ln (2)) - 2 ln (2) + 1

Dezimale

0.06651 \dots

Schritte zur Lösung

\int_{e}^{4} \frac{ln ( ln ( x ) )}{x} d x

Wende U-Substitution an

= \int_{1}^{2 l n (2)} ln (u) d u

Wende die partielle Integration an

= [u ln (u) - \int 1 d u]_{1}^{2 l n (2)}

\int 1 d u = u

= [u ln (u) - u]_{1}^{2 l n (2)}

Berechne die Grenzen:

2 ln (2) ln (2 ln (2)) - 2 ln (2) + 1

= 2 ln (2) ln (2 ln (2)) - 2 ln (2) + 1