e^(- 2·x)·(e^x/√(e^(4·x)) - e^(2·x))·(e^(2·x) - e^3) > 0
e^x = t
t^(-2)·(t/√(t^4) - t^2)·(t^2 - e^3) > 0
t^(-2)·(1/t - t^2)·(t^2 - e^3) > 0
(e^3 - t^2)·(t^3 - 1)/t^3 > 0
(e^3 - t^2)·(t^3 - 1) > 0
risolvo:
t < - e^(3/2) ∨ 1 < t < e^(3/2)
e^x < - e^(3/2) ∨ 1 < e^x < e^(3/2)
e^x < - e^(3/2) IMPOSSIBILE
1 < e^x < e^(3/2)----> 0 < x < 3/2