integral of x^2e^{x/4}

Lösung

\int x^{2} e^{\frac{x}{4}} d x

4 e^{\frac{x}{4}} x^{2} - 8 (4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}}) + C

Schritte zur Lösung

\int x^{2} e^{\frac{x}{4}} d x

Wende die partielle Integration an

= 4 e^{\frac{x}{4}} x^{2} - \int 8 e^{\frac{x}{4}} x d x

\int 8 e^{\frac{x}{4}} x d x = 8 (4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}})

= 4 e^{\frac{x}{4}} x^{2} - 8 (4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}})

Füge eine Konstante zur Lösung hinzu

= 4 e^{\frac{x}{4}} x^{2} - 8 (4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}}) + C

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