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int(e)^(e^(2))(dx)/(x log x)...

int_(e)^(e^(2))(dx)/(x log x)

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Show that int_(e)^(e^(2))(1)/(log x) dx = int_(1)^(2)(e^(x))/(x) dx

If I_(1)=int_(e)^(e^(2))(dx)/(ln x) and I_(2)=int_(1)^(2)(e^(x))/(x)dx

If I_(1) = int_e^(e^(2)) (dx)/(log x) and I_(2) = int_1^(2) (e^(x)dx)/(x) then

Evaluate :int_(e)^(e^(2)){(1)/(log x)-(1)/((log x)^(2))}dx

int_(1)^(e^(2))(dx)/(x(1+log x)^(2))=

int_(1//e)^(e) (dx)/(x(log x)^(1//3))

int_(1//e)^(e) (dx)/(x(log x)^(1//3))

If I _(1) = int _(e) ^(e ^(2)) (dx )/( ln x ) and I _(2) = int _(1) ^(2) (e ^(x))/(x) dx, then