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Calculus Level 5

\[\large I=\int _0^1 \int _0^x \frac {x^4}{\ln(s) \sqrt {\ln\left(\frac { 1 }{ x } \right)}} \ ds\ dx\] If \(I\) can be expressed as \(\displaystyle -2\sqrt { \frac \pi A} \ln(\sqrt A +\sqrt M)\), where \(A\) and \(M\) are square-free, find the 3-digit integer \(\overline{MAA}\).

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