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Beliebt Rechnen >

integral of x^4e^{12x}

Lösung

\int x^{4} e^{12 x} d x

Lösung

\frac{1}{12} e^{12 x} x^{4} - \frac{1}{10368} e^{12 x} (288 x^{3} - 72 x^{2} + 12 x - 1) + C

Schritte zur Lösung

\int x^{4} e^{12 x} d x

Wende die partielle Integration an

= \frac{1}{12} e^{12 x} x^{4} - \int \frac{1}{3} e^{12 x} x^{3} d x

\int \frac{1}{3} e^{12 x} x^{3} d x = \frac{1}{10368} e^{12 x} (288 x^{3} - 72 x^{2} + 12 x - 1)

= \frac{1}{12} e^{12 x} x^{4} - \frac{1}{10368} e^{12 x} (288 x^{3} - 72 x^{2} + 12 x - 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{12} e^{12 x} x^{4} - \frac{1}{10368} e^{12 x} (288 x^{3} - 72 x^{2} + 12 x - 1) + C

Graph

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