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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{- 2 ln ( 2 ) - 1}{4} + 1

+1

Dezimale

0.40342 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [- \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x]_{1}^{4}

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

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

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

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

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

Berechne die Grenzen:

\frac{- 2 ln ( 2 ) - 1}{4} + 1

= \frac{- 2 ln ( 2 ) - 1}{4} + 1

Graph

Beliebte Beispiele

limit as x approaches 0 of cos(3/x)

x \to 0 lim (cos (\frac{3}{x}))

integral of (x^2-x+1)/(x^2+x)

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

limit as x approaches+(-35) of 34+x

x \to + (- 35) lim (34 + x)

derivative of ln(1+x^3)

\frac{d}{d x} (ln (1 + x^{3}))

tangent y=x^3-2x+1,(0,1)

t an g e n t y = x^{3} - 2 x + 1, (0, 1)