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Beliebt Rechnen >

integral from 1 to 2 of (-8ln(x))/(x^2)

Lösung

\int_{1}^{2} \frac{- 8 ln ( x )}{x ^{2}} d x

Lösung

4 ln (2) - 4

+1

Dezimale

- 1.22741 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{- 8 ln ( x )}{x ^{2}} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 8 \cdot \int_{1}^{2} \frac{ln ( x )}{x ^{2}} d x

Wende die partielle Integration an

= - 8 [- \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x]_{1}^{2}

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

= - 8 [- \frac{ln ( x )}{x} - \frac{1}{x}]_{1}^{2}

Da die Nenner gleich sind, fasse die Brüche zusammen.:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= - 8 [\frac{- ln ( x ) - 1}{x}]_{1}^{2}

Berechne die Grenzen:

\frac{- ln ( 2 ) - 1}{2} + 1

= - 8 (\frac{- ln ( 2 ) - 1}{2} + 1)

Vereinfache

= 4 ln (2) - 4

Graph

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