integral from 1 to e^6 of (6ln(x))/x

Lösung

\int_{1}^{e^{6}} \frac{6 ln ( x )}{x} d x

108

Schritte zur Lösung

\int_{1}^{e^{6}} \frac{6 ln ( x )}{x} d x

Entferne die Konstante:

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

= 6 \cdot \int_{1}^{e^{6}} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= 6 \cdot \int_{0}^{6} u d u

Wende die Potenzregel an

= 6 [\frac{u ^{2}}{2}]_{0}^{6}

Berechne die Grenzen:

18

= 6 \cdot 18

Vereinfache

= 108

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