integral from 0 to 6 of 1/((x-9)^{2/3)}

Lösung

\int_{0}^{6} \frac{1}{( x - 9 ) ^{\frac{2}{3}}} d x

3 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}} - 3 (- 1)^{\frac{1}{3}} \cdot 9^{\frac{1}{3}}

Schritte zur Lösung

\int_{0}^{6} \frac{1}{( x - 9 ) ^{\frac{2}{3}}} d x

Wende U-Substitution an

= \int_{- 9}^{- 3} \frac{1}{u ^{\frac{2}{3}}} d u

Wende die Potenzregel an

= [3 u^{\frac{1}{3}}]_{- 9}^{- 3}

Berechne die Grenzen:

3 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}} - 3 (- 1)^{\frac{1}{3}} \cdot 9^{\frac{1}{3}}

= 3 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}} - 3 (- 1)^{\frac{1}{3}} \cdot 9^{\frac{1}{3}}

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