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If all parameters are positive, there are no problems:

a, z, q, r, R, s = var("a, z, q, r, R, s")

assume(a>0)

assume(R>0)

assume(r>0)

assume(s>0)

assume(z>0)

assume(q>0)

Ex = (4/(a^3)((zq^2)/r-(zq^2)/rexp(-s(r-R)))r^2exp(-2r/a))

%display latex

Im = integrate(Ex,(r,R,oo))

factor(Im)

If all parameters are positive, there are no problems:problems with integrate

If all parameters are positive, there are no problems with integrate

a, z, q, r, R, s = var("a, z, q, r, R, s")
assume(a>0);assume(R>0);assume(r>0) 
assume(s>0);assume(z>0);assume(q>0)
Ex = (4/(a^3)*((z*q^2)/r-(z*q^2)/r*exp(-s*(r-R)))*r^2*exp(-2*r/a))
Im = integrate(Ex,(r,R,oo))
factor(Im)