integral from 0 to 1 of (ln(x^2))/(x^2)

Lösung

\int_{0}^{1} \frac{ln ( x ^{2} )}{x ^{2}} d x

divergiert

Schritte zur Lösung

\int_{0}^{1} \frac{ln ( x ^{2} )}{x ^{2}} d x

Wende die partielle Integration an

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

\int - \frac{2}{x ^{2}} d x = \frac{2}{x}

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

Vereinfache

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

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

Berechne die Grenzen:

divergiert

= divergiert

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