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Beliebt Rechnen >

integral from 0 to 1 of 1/(xln(x))

Lösung

\int_{0}^{1} \frac{1}{x ln ( x )} d x

Lösung

divergiert

Schritte zur Lösung

\int_{0}^{1} \frac{1}{x ln ( x )} d x

Wende die partielle Integration an

= [\frac{1}{ln ( x )} - \int - \frac{ln ( x ) + 1}{x ln ^{2} ( x )} d x]_{0}^{1}

\int - \frac{ln ( x ) + 1}{x ln ^{2} ( x )} d x = - ln ∣ ln (x) ∣ + \frac{1}{ln ( x )}

= [\frac{1}{ln ( x )} - (- ln ∣ ln (x) ∣ + \frac{1}{ln ( x )})]_{0}^{1}

Vereinfache

= [ln ∣ ln (x) ∣]_{0}^{1}

Berechne die Grenzen:

divergiert

= divergiert

Beliebte Beispiele

derivative y=e^{3e^x}

d er i v a t i v e y = e^{3 e^{x}}

f(x)=arctan(cos(x))

f (x) = arctan (cos (x))

derivative of 4x^6-3x^5-10x^2+5x+16

\frac{d}{d x} (4 x^{6} - 3 x^{5} - 10 x^{2} + 5 x + 16)

limit as x approaches 3 of 6

x \to 3 lim (6)

(1+e^x)yy^'=e^x

(1 + e^{x}) y y^{^{'}} = e^{x}