Who's up to the challenge? 57

Calculus Level 5

\[ \large \int_0^\infty \left( \dfrac{ \ln x}{e^x } \right)^2 \, dx = \dfrac{\pi^A}B + \dfrac{\gamma^C}D + E \gamma \ln F + \dfrac GH (\ln I)^J \]

If the equation above holds true, where \(A,B,C,D,E,F,G,H\) and \(I \) are positive integers, find \(A+B+C+D+E+F+G+H+I+J \).

Notation: \( \gamma\) denotes the Euler-Mascheroni constant, \(\gamma \approx 0.5772 \).

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