integral from 1 to 2 of 1/((x-2)^{1/3)}

Lösung

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

- \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{- 1}^{0} \frac{1}{u ^{\frac{1}{3}}} d u

Wende die Potenzregel an

= [\frac{3}{2} u^{\frac{2}{3}}]_{- 1}^{0}

Berechne die Grenzen:

- (- 1)^{\frac{2}{3}} \frac{3}{2}

= - (- 1)^{\frac{2}{3}} \frac{3}{2}

Vereinfache

= - \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2}

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