For `x >0,l e tf(x)=int_1^x((log)_e t)/(1+t)dtdot` Find the function `f(x)+f(1/x)` and show that `f(e)+f(1/e)=1/2dot`

Explanation

`f(x)=int_1^x((log)_e t)/(1+t)dt`

`f(1/x)=int_1^x frac{log t}{1+t}`

`t=1/y=> dt=(-1/y^2)dy`

`f(1/x)=int_1^x frac{log (1/y))}{1+ 1/y} xx -(1/y^2)dy`

`t=1/y=>1/x =1/y=> x=y`

`int_1^x frac{log y}{1+y} xx(1/y)dy`

`f(x)+f(1/x)=int_1^x frac{log t}{1+t} xx(1+ 1/t)dt`

`=int_1^x frac{log t}{t}dt`
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