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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{2}{e} + 1

+1

Dezimale

0.26424 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int - \frac{1}{z ^{2}} d z = \frac{1}{z}

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

z \frac{1}{z} = 1

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

Berechne die Grenzen:

- \frac{2}{e} + 1

= - \frac{2}{e} + 1

Graph

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