Question

∫ x^3 e^(-x) dx

Answer 1

use integration by parts!

Answer 2

but how....

Answer 3

\[u = x^3\]\[\,du = 3x^2 \,dx\]\[v = -e^{-x}\]\[\,dv = e^{-x} \,dx\]\[\int x^3 e^{-x} \,dx = -e^{-x}x^3 + 3\int e^{-x}x^2 \,dx\]

See the pattern? Keep integrating until you hit 0.