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Beliebt Rechnen >

integral of 6x^2e^{4x}

Lösung

\int 6 x^{2} e^{4 x} d x

Lösung

6 (\frac{1}{4} e^{4 x} x^{2} - \frac{1}{32} (4 e^{4 x} x - e^{4 x})) + C

Schritte zur Lösung

\int 6 x^{2} e^{4 x} d x

Entferne die Konstante:

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

= 6 \cdot \int x^{2} e^{4 x} d x

Wende die partielle Integration an

= 6 (\frac{1}{4} e^{4 x} x^{2} - \int \frac{1}{2} e^{4 x} x d x)

\int \frac{1}{2} e^{4 x} x d x = \frac{1}{32} (4 e^{4 x} x - e^{4 x})

= 6 (\frac{1}{4} e^{4 x} x^{2} - \frac{1}{32} (4 e^{4 x} x - e^{4 x}))

Füge eine Konstante zur Lösung hinzu

= 6 (\frac{1}{4} e^{4 x} x^{2} - \frac{1}{32} (4 e^{4 x} x - e^{4 x})) + C

Graph

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