integral of x^2e^{12x}

Lösung

\int x^{2} e^{12 x} d x

\frac{1}{12} e^{12 x} x^{2} - \frac{1}{864} (12 e^{12 x} x - e^{12 x}) + C

Schritte zur Lösung

\int x^{2} e^{12 x} d x

Wende die partielle Integration an

= \frac{1}{12} e^{12 x} x^{2} - \int \frac{1}{6} e^{12 x} x d x

\int \frac{1}{6} e^{12 x} x d x = \frac{1}{864} (12 e^{12 x} x - e^{12 x})

= \frac{1}{12} e^{12 x} x^{2} - \frac{1}{864} (12 e^{12 x} x - e^{12 x})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{12} e^{12 x} x^{2} - \frac{1}{864} (12 e^{12 x} x - e^{12 x}) + C

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