e^2*x^2-5/2x>xlnx+lnx
x∈(0,e] 两边同除x e^2*x-5/2>lnx+lnx/x
即证e^2x-lnx>lnx/x+5/2
令f(x)=e^2x-lnx f'(x)=e^2-1/x f'(x)=0 x=1/e^2
x∈(0,1/e^2) f'(x)
e^2*x^2-5/2x>xlnx+lnx
x∈(0,e] 两边同除x e^2*x-5/2>lnx+lnx/x
即证e^2x-lnx>lnx/x+5/2
令f(x)=e^2x-lnx f'(x)=e^2-1/x f'(x)=0 x=1/e^2
x∈(0,1/e^2) f'(x)