integral from 1 to 5 of (12(ln(x))^3)/x

Lösung

\int_{1}^{5} \frac{12 ( ln ( x ) ) ^{3}}{x} d x

3 ln^{4} (5)

Dezimale

20.12881 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{12 ( ln ( x ) ) ^{3}}{x} d x

Entferne die Konstante:

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

= 12 \cdot \int_{1}^{5} \frac{( ln ( x ) ) ^{3}}{x} d x

Wende U-Substitution an

= 12 \cdot \int_{0}^{l n (5)} u^{3} d u

Wende die Potenzregel an

= 12 [\frac{u ^{4}}{4}]_{0}^{l n (5)}

Berechne die Grenzen:

\frac{ln ^{4} ( 5 )}{4}

= 12 \cdot \frac{ln ^{4} ( 5 )}{4}

Vereinfache

= 3 ln^{4} (5)

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