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

Lösung

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

\frac{ln ^{2} ( t )}{2}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{l n (t)} u d u

Wende die Potenzregel an

= [\frac{u ^{2}}{2}]_{0}^{l n (t)}

Berechne die Grenzen:

\frac{ln ^{2} ( t )}{2}

= \frac{ln ^{2} ( t )}{2}

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