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

Lösung

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

- \frac{4}{e} + 2

Dezimale

0.52848 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

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

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

Berechne die Grenzen:

- \frac{4}{e} + 2

= - \frac{4}{e} + 2

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