integral from 1 to 2 of x^3e^x

Lösung

\int_{1}^{2} x^{3} e^{x} d x

2 e^{2} + 2 e

Dezimale

20.21467 \dots

Schritte zur Lösung

\int_{1}^{2} x^{3} e^{x} d x

Wende die partielle Integration an

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{1}^{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}))]_{1}^{2}

Berechne die Grenzen:

2 e^{2} + 2 e

= 2 e^{2} + 2 e

\int_{0}^{1} sin (π) y d y

\int_{2}^{5} x^{2} - 4 x + 5 d x

\int_{0}^{\infty} \frac{1}{4 x + 3} d x

\int_{4}^{16} 2 x - 1 d x

\int_{0}^{x} x^{3} y^{2} d y