Sir, I have a doubt ,

Let, we want to find area of this function between any limit, then how can we find it ?

f(x) =∫ 1/ln(x) dx

Dear student 

lnx = t 
x = e^t 
1/x dx = dt 
dx = xdt
∫e^t/t dt 
=> Now apply ILATE RULE 
Let u = e^t 
v = 1/t 
I = -1/t^2 * e^t - ∫1/t *e^tdt 
2I = -e^t/t^2
I = -e^t/2t^2
and put the limit in which you want to find the area.
Hope this helps