`int_(2)^(e)((1)/(ln x)-(1)/(ln^(2)x))dx`

int_(2)^(e) ((1)/(ln x) - (1)/((ln x)^(2)))dx=

int e^(x)(ln x+(1)/(x^(2)))dx

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

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

int (1)/(log x)-(1)/((log x)^(2))dx=

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

int[(1)/(log x)-(1)/((log x)^(2))]dx=

The value of int_(1)^(e)(1+x^(2)ln x)/(x+x^(2)ln x)*dx is :

int_(1)^(e)(x^(4)ln x+2)/(x^(3)ln x+x)dx=(e^(2)+a)/(b)-ln(e^(2)+1) where a and b are positive integers then (a)/(b)=