integral from-2 to 2 of x^3e^x

Lösung

\int_{- 2}^{2} x^{3} e^{x} d x

2 e^{2} + \frac{38}{e ^{2}}

Dezimale

19.92085 \dots

Schritte zur Lösung

\int_{- 2}^{2} x^{3} e^{x} d x

Wende die partielle Integration an

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{- 2}^{2}

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

= [x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))]_{- 2}^{2}

Berechne die Grenzen:

2 e^{2} + \frac{38}{e ^{2}}

= 2 e^{2} + \frac{38}{e ^{2}}

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