integral of x^2e^{x/7}

Lösung

\int x^{2} e^{\frac{x}{7}} d x

7 e^{\frac{x}{7}} x^{2} - 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}}) + C

Schritte zur Lösung

\int x^{2} e^{\frac{x}{7}} d x

Wende die partielle Integration an

= 7 e^{\frac{x}{7}} x^{2} - \int 14 e^{\frac{x}{7}} x d x

\int 14 e^{\frac{x}{7}} x d x = 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}})

= 7 e^{\frac{x}{7}} x^{2} - 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}})

Füge eine Konstante zur Lösung hinzu

= 7 e^{\frac{x}{7}} x^{2} - 14 (7 e^{\frac{x}{7}} x - 49 e^{\frac{x}{7}}) + C

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