integral of 3x^2e^{x-1}

Lösung

\int 3 x^{2} e^{x - 1} d x

3 (x^{2} e^{x - 1} - 2 (e^{x - 1} x - e^{x - 1})) + C

Schritte zur Lösung

\int 3 x^{2} e^{x - 1} d x

Entferne die Konstante:

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

= 3 \cdot \int x^{2} e^{x - 1} d x

Wende die partielle Integration an

= 3 (x^{2} e^{x - 1} - \int 2 x e^{x - 1} d x)

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

= 3 (x^{2} e^{x - 1} - 2 (e^{x - 1} x - e^{x - 1}))

Füge eine Konstante zur Lösung hinzu

= 3 (x^{2} e^{x - 1} - 2 (e^{x - 1} x - e^{x - 1})) + C

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