integral of e^x(4-e^x)^{2/3}

Lösung

\int e^{x} (4 - e^{x})^{\frac{2}{3}} d x

- \frac{3}{5} (4 - e^{x})^{\frac{5}{3}} + C

Schritte zur Lösung

\int e^{x} (4 - e^{x})^{\frac{2}{3}} d x

Wende U-Substitution an

= \int (4 - u)^{\frac{2}{3}} d u

Wende U-Substitution an

= \int - v^{\frac{2}{3}} d v

Entferne die Konstante:

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

= - \int v^{\frac{2}{3}} d v

Wende die Potenzregel an

= - \frac{3}{5} v^{\frac{5}{3}}

Ersetze zurück

= - \frac{3}{5} (4 - e^{x})^{\frac{5}{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{3}{5} (4 - e^{x})^{\frac{5}{3}} + C

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