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

Lösung

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

1

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Wende U-Substitution an

= 2 \cdot \int_{0}^{1} u d u

Wende die Potenzregel an

= 2 [\frac{u ^{2}}{2}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2}

= 2 \cdot \frac{1}{2}

Vereinfache

= 1

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