integral from 0 to 4 of x^3e^x

Lösung

\int_{0}^{4} x^{3} e^{x} d x

34 e^{4} + 6

Dezimale

1862.33710 \dots

Schritte zur Lösung

\int_{0}^{4} x^{3} e^{x} d x

Wende die partielle Integration an

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{4}

\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}))]_{0}^{4}

Berechne die Grenzen:

34 e^{4} + 6

= 34 e^{4} + 6

a re a x, 2 x - 12, 0, 8

\frac{d}{d x} (\frac{1}{8} x)

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

x \to \infty lim (\frac{x}{- 1})

d er i v a t i v e 6 e^{3 x} (3 cos (4 x) - 4 sin (4 x))