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

Lösung

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

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

Dezimale

0.36033 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= \frac{1}{2} \cdot \int_{2}^{4} \frac{ln ( u )}{u} d u

Wende U-Substitution an

= \frac{1}{2} \cdot \int_{l n (2)}^{2 l n (2)} v d v

Wende die Potenzregel an

= \frac{1}{2} [\frac{v ^{2}}{2}]_{l n (2)}^{2 l n (2)}

Berechne die Grenzen:

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

= \frac{1}{2} (2 ln^{2} (2) - \frac{ln ^{2} ( 2 )}{2})

Vereinfache

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