Evaluate ∫ log(logx)/x dx\(\int\frac{ log\,(log\,x)}{x}\)dx

1.	Evaluate ∫ log(logx)/x dx\(\int\frac{ log\,(log\,x)}{x}\)dx
Answer» ∫ 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

Answer»

∫ 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

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