Evaluate the indefinite integral dx/(xlnxln(lnx))

Question

anonymous · Answer

$$\int\limits_{}^{}\frac{ dx }{ xlnxln(lnx) }$$

anonymous · Answer

A clever u substitution will do the trick, what have you tried so far?

anonymous · Answer

banging my head against the wall

anonymous · Answer

I really don't know where to start with this one

dumbcow · Answer

haha this is a fun one ... you need to do repeated substitutions

u = ln x  

then 

w = ln u

anonymous · Answer

so, I will have $$\int\limits_{}^{}\frac{ dx }{ xuw }$$

anonymous · Answer

$$lnx \int\limits_{}^{}\frac{ 1 }{ uw }$$

dumbcow · Answer

you need to substitute for dx as well

you can only integrate with respect to 1 variable
so at the end it will be in terms of w and dw

dumbcow · Answer

u = lnx
du = dx/x

anonymous · Answer

I'm sorry, I'm not getting it (I know I should be), I think I need to study some more before this will make sense. I'm not very good w/ the substitutions

dumbcow · Answer

maybe this will help http://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinite.aspx

dumbcow · Answer

the answer is ln(ln(ln x))

anonymous · Answer

thanks

dumbcow · Answer

yw