integral from 0 to 2 of (ln(x))/x

Lösung

\int_{0}^{2} \frac{ln ( x )}{x} d x

divergiert

Schritte zur Lösung

\int_{0}^{2} \frac{ln ( x )}{x} d x

Wende die partielle Integration an

= [ln (x) - \int \frac{1 - ln ( x )}{x} d x]_{0}^{2}

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

= [ln (x) - (- \frac{( 1 - ln ( x ) ) ^{2}}{2})]_{0}^{2}

Vereinfache

[ln (x) - (- \frac{( 1 - ln ( x ) ) ^{2}}{2})]_{0}^{2} : [\frac{1}{2} (ln^{2} (x) + 1)]_{0}^{2}

= [\frac{1}{2} (ln^{2} (x) + 1)]_{0}^{2}

Berechne die Grenzen:

divergiert

= divergiert

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