integral from 1 to 4 of (sqrt(ln(x)))/x

Lösung

\int_{1}^{4} \frac{ln ( x )}{x} d x

\frac{4 2}{3} ln^{\frac{3}{2}} (2)

Dezimale

1.08815 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= \int_{0}^{2 l n (2)} u d u

Wende die Potenzregel an

= [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{2 l n (2)}

Berechne die Grenzen:

\frac{4 2}{3} ln^{\frac{3}{2}} (2)

= \frac{4 2}{3} ln^{\frac{3}{2}} (2)

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