Evaluate the following integrals: ∫ (log(log x))/x dx

Question

Evaluate the following integrals:

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

∫ (log(log x))/x dx

Answer 1

Let log x = t

1/x dx = dt

Using BY PART METHOD. Using the superiority list as ILATE (Inverse Logarithm Algebra Trigonometric Exponential). Taking the first function to the one which comes first in the list.

Here log t is first function and 1 as the second function.