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Beliebt Rechnen >

integral from 1 to e^2 of (ln^8(x^2))/x

Lösung

\int_{1}^{e^{2}} \frac{ln ^{8} ( x ^{2} )}{x} d x

Lösung

\frac{131072}{9}

+1

Dezimale

14563.55555 \dots

Schritte zur Lösung

\int_{1}^{e^{2}} \frac{ln ^{8} ( x ^{2} )}{x} d x

Vereinfache

\frac{ln ^{8} ( x ^{2} )}{x} : \frac{256 ln ^{8} ( x )}{x}

= \int_{1}^{e^{2}} \frac{256 ln ^{8} ( x )}{x} d x

Entferne die Konstante:

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

= 256 \cdot \int_{1}^{e^{2}} \frac{ln ^{8} ( x )}{x} d x

Wende U-Substitution an

= 256 \cdot \int_{0}^{2} u^{8} d u

Wende die Potenzregel an

= 256 [\frac{u ^{9}}{9}]_{0}^{2}

Berechne die Grenzen:

\frac{512}{9}

= 256 \cdot \frac{512}{9}

Vereinfache

= \frac{131072}{9}

Graph

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