integral from 5 to 10 of (ln(x))/x

Lösung

\int_{5}^{10} \frac{ln ( x )}{x} d x

\frac{ln ^{2} ( 10 ) - ln ^{2} ( 5 )}{2}

Dezimale

1.35580 \dots

Schritte zur Lösung

\int_{5}^{10} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= \int_{l n (5)}^{l n (10)} u d u

Wende die Potenzregel an

= [\frac{u ^{2}}{2}]_{l n (5)}^{l n (10)}

Berechne die Grenzen:

\frac{ln ^{2} ( 10 ) - ln ^{2} ( 5 )}{2}

= \frac{ln ^{2} ( 10 ) - ln ^{2} ( 5 )}{2}

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