integral from 1 to 3 of (2ln(x))/x

Lösung

\int_{1}^{3} \frac{2 ln ( x )}{x} d x

ln^{2} (3)

Dezimale

1.20694 \dots

Schritte zur Lösung

\int_{1}^{3} \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}^{3} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= 2 \cdot \int_{0}^{l n (3)} u d u

Wende die Potenzregel an

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

Berechne die Grenzen:

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

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

Vereinfache

= ln^{2} (3)

\int_{0}^{1} sin (x) cos (x) d x

\int_{1}^{1} 1 + x^{4} d x

\int_{1}^{3} 2 (1 + ln (x)) x^{2 x} d x

\int_{- 3}^{0} 1 d x

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