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Beliebt Rechnen >

integral from 0 to 1 of (ln(t))/t

Lösung

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

Lösung

divergiert

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{1 - ln ( t )}{t} d t = - \frac{( 1 - ln ( t ) ) ^{2}}{2}

= [ln (t) - (- \frac{( 1 - ln ( t ) ) ^{2}}{2})]_{0}^{1}

Vereinfache

[ln (t) - (- \frac{( 1 - ln ( t ) ) ^{2}}{2})]_{0}^{1} : [\frac{1}{2} (ln^{2} (t) + 1)]_{0}^{1}

= [\frac{1}{2} (ln^{2} (t) + 1)]_{0}^{1}

Berechne die Grenzen:

divergiert

= divergiert

Beliebte Beispiele

integral of+x^3e^{3x^2}

\int + x^{3} e^{3 x^{2}} d x

limit as x approaches 1+of (x^2-4)/(x-1)

x \to 1 + lim (\frac{x ^{2} - 4}{x - 1})

integral of (20000)/((x+100)^3)

\int \frac{20000}{( x + 100 ) ^{3}} d x

integral of 8xe^{x^2}

\int 8 x e^{x^{2}} d x

integral of (-1)

\int (- 1) d x