`int_(e )^(e^(2))log x dx =`

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

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

Show that (a) int_(e)^(e^(2))(1)/(log x)dx = int_(1)^(2)(e^(x))/(x)dx (b) int_(t)^(1)(dx)/(1+x^(2)) = int_(1)^(1//t)(dx)/(1+x^(2))

int_(1)^(e) log (x) dx=

If I_(1)=int_(e )^(e^(2)) (dx)/(log x) and I_(2)= int_(1)^(2)(e^(x))/(x)dx , then which of the following is correct ?

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

int_((1)/(e))^(e)|log x|dx=

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