This Many Logs Inside An Integral Makes Me Sick!

Calculus Level 4

ee512dxxlnx+xlnx(ln(lnx))2 \large \int_e^{e^{512}} \dfrac{dx}{x \ln x + x \ln x ( \ln (\ln x))^2 }

If the integral above is equal to arctan(lnABC) \arctan\left(\ln A^{B^C} \right) , where A,BA,B and CC are prime numbers, find A+B+CA+B+C.

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