Z = 1. 
f1 = 4*x^2*Exp[-Z*x]
u1 = Integrate[f1, {x, 0, 2/Z}]
f2 = -4*Z*x^3*Exp[-Z*x]
u2 = Integrate[f2, {x, 0, 2/Z}]
f3 = Z^2*x^4*Exp[-Z*x]
u3 = Integrate[f3, {x, 0, 2/Z}]
p = Z^3/8*(u1 + u2 + u3)
Plot[p, {Z, 1, 10}]

Z = 1
f1s = (Z^3)*4*x^2*Exp[-2*Z*x]
p1s = Integrate[f1s, {x, 0, 2/Z}]
Plot[p1s, {Z, 1, 10}]