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

Lösung

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

\frac{9}{2}

Dezimale

4.5

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{e^{3}}^{e^{6}} \frac{ln ( u )}{3 u} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{e^{3}}^{e^{6}} \frac{ln ( u )}{u} d u

Wende U-Substitution an

= \frac{1}{3} \cdot \int_{3}^{6} v d v

Wende die Potenzregel an

= \frac{1}{3} [\frac{v ^{2}}{2}]_{3}^{6}

Berechne die Grenzen:

\frac{27}{2}

= \frac{1}{3} \cdot \frac{27}{2}

Vereinfache

= \frac{9}{2}

\int_{- 2}^{2} \frac{1}{x ^{3}} d x

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