\[ {\bf \int_{Z = e^e}^{Z = e^{e^2}} \int_{Y= e}^{Y = e^2} \int_{X = 2N + M + 1}^{\infty} (\frac{1}{Z * ln(Z) * ln(ln(Z)) * Y * ln(Y)}) \sum_{J = 1}^{N} \frac{1}{(X - J - M){(X - J - M - 1})} \, dx dy dz} \]

Evaluate the integral above.

Express the result to four decimal places.

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