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Beliebt Rechnen >

integral from 1 to e^4 of (ln(x))/(x^2)

Lösung

\int_{1}^{e^{4}} \frac{ln ( x )}{x ^{2}} d x

Lösung

- \frac{5}{e ^{4}} + 1

+1

Dezimale

0.90842 \dots

Schritte zur Lösung

\int_{1}^{e^{4}} \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^{4}}

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

= [\frac{- ln ( x ) - x \frac{1}{x}}{x}]_{1}^{e^{4}}

x \frac{1}{x} = 1

= [\frac{- ln ( x ) - 1}{x}]_{1}^{e^{4}}

Berechne die Grenzen:

- \frac{5}{e ^{4}} + 1

= - \frac{5}{e ^{4}} + 1

Graph

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