integral from 0 to 8 of x^3e^x

Lösung

\int_{0}^{8} x^{3} e^{x} d x

362 e^{8} + 6

Dezimale

1079112.79130 \dots

Schritte zur Lösung

\int_{0}^{8} x^{3} e^{x} d x

Wende die partielle Integration an

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{8}

\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}^{8}

Berechne die Grenzen:

362 e^{8} + 6

= 362 e^{8} + 6

d er i v a t i v e f (x) = 3 x^{\frac{1}{2}} + x^{- \frac{3}{2}}

t an g e n t y = x^{2} - 6 x + 9, (3, 0)

x \to \infty lim (x^{2} - 2 x)

\int \frac{1}{( x + 1 ) ( x + 2 )} d x

\int \frac{1}{x 3 ln ( x ) - 1} d x