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

Lösung

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

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

Dezimale

0.72067 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{4} \frac{ln ( u )}{u} d u

Wende U-Substitution an

= \int_{l n (2)}^{2 l n (2)} v d v

Wende die Potenzregel an

= [\frac{v ^{2}}{2}]_{l n (2)}^{2 l n (2)}

Berechne die Grenzen:

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

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

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