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

Lösung

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

- \frac{2}{e} + 1

Dezimale

0.26424 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

x \frac{1}{x} = 1

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

Berechne die Grenzen:

- \frac{2}{e} + 1

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

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