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Beliebt Rechnen >

integral from 1 to e^3 of (ln^5(x^2))/x

Lösung

\int_{1}^{e^{3}} \frac{ln ^{5} ( x ^{2} )}{x} d x

Lösung

3888

Schritte zur Lösung

\int_{1}^{e^{3}} \frac{ln ^{5} ( x ^{2} )}{x} d x

Wende U-Substitution an

= \int_{1}^{e^{6}} \frac{ln ^{5} ( u )}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{e^{6}} \frac{ln ^{5} ( u )}{u} d u

Wende U-Substitution an

= \frac{1}{2} \cdot \int_{0}^{6} v^{5} d v

Wende die Potenzregel an

= \frac{1}{2} [\frac{v ^{6}}{6}]_{0}^{6}

Berechne die Grenzen:

7776

= \frac{1}{2} \cdot 7776

Vereinfache

= 3888

Graph

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