Question

Evaluate ∫ log(logx)/x dx

\(\int\frac{ log\,(log\,x)}{x}\)dx

Answer 1

∫ log(logx)/x dx

Let, 

log x = t 

Differentiating both side with respect to t,

\(\frac{1}{x}\frac{dx}{dt}\) = 1

⇒ \(\frac{dx}{x}\) = dt

Note :-  Always use direct formula for ∫log x dx 

y = ∫log t dt 

y = t log t – t + c 

Again, 

Put t = log x 

y = (log x)log(log x) – log x + c