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

Lösung

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

3

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{8} \frac{1}{2 u ^{\frac{2}{3}}} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{8} \frac{1}{u ^{\frac{2}{3}}} d u

Wende die Potenzregel an

= \frac{1}{2} [3 u^{\frac{1}{3}}]_{0}^{8}

Berechne die Grenzen:

6

= \frac{1}{2} \cdot 6

Vereinfache

= 3

\int_{- \infty}^{0} 2 e^{- 3 x} d x

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