Problem on Integration Techniques

Calculus Level 3

\[f(x) = \int \frac{\ln \sqrt{\ln\sqrt{x}}}{x \ln x} \, dx, \qquad f(e^2) =0, \qquad f(e) =a(\ln2)^2 \]

Given the above, find \(\dfrac{1}{|a|}\).

Clarification: \(e \approx 2.71828\) denotes the Euler's number.

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