integral from 1 to 11 of (4(ln(x))^3)/x

Lösung

\int_{1}^{11} \frac{4 ( ln ( x ) ) ^{3}}{x} d x

ln^{4} (11)

Dezimale

33.06137 \dots

Schritte zur Lösung

\int_{1}^{11} \frac{4 ( ln ( x ) ) ^{3}}{x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{11} \frac{( ln ( x ) ) ^{3}}{x} d x

Wende U-Substitution an

= 4 \cdot \int_{0}^{l n (11)} u^{3} d u

Wende die Potenzregel an

= 4 [\frac{u ^{4}}{4}]_{0}^{l n (11)}

Berechne die Grenzen:

\frac{ln ^{4} ( 11 )}{4}

= 4 \cdot \frac{ln ^{4} ( 11 )}{4}

Vereinfache

= ln^{4} (11)

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