integration of ((1/ln(x) - (1/(lnx)^2)) is ? The answer is x/log(x)

I got the answer. Thanks anyways :)


First integrate 1/lnx by parts and then 1/(lnx)^2 gets cancelled and we get the answer as x/lnx 

For this problem what you do is first consider lnx to be u and convert the integral in to a form where everything is in terms of u.

Then take the integral of (e^u)/u seperately (which u get once u follow the above method )and try to integrate it using by parts and you see something amazing. theanswer is just in front of u. I hope you understoood it.