Let Jn = 0 x n e x dx, where n 1 is an integer and >0. Prove that and J 0

Let Jn = ∫^∞₀ xⁿ e^−αx dx, where n ≥ 1 is an integer and α>0. Prove that

and J₀ = 1/α. Use this to compute J₄. Show that J_n = n!/αⁿ⁺¹.

Jn n -J-1 a