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Calculus Level 4

\[I=\int _{ 0 }^{ 1 }{ \int _{ 0 }^{ x }{ \frac { 1 }{ \ln(s) } } } { x }^{ 4 }\frac { 1 }{ \sqrt { \ln\left(\frac { 1 }{ x } \right) } } dsdx\] If \(I\) can be expressed as \[-2\sqrt { \frac { \pi }{ A } } \ln(\sqrt { A } +\sqrt { M } )\] where \(A\) and \(M\) are square-free.

Give your answer as the 3-digit integer \(\overline{MAA}\).

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