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\[ \displaystyle \int_{2005}^{2017} \frac{\big(\ln \left| x-2017 \right|\big)^{2017}}{\big(\ln \left| x-2005 \right|\big)^{2017} +\big(\ln \left| x-2017 \right|\big)^{2017}} \, dx = \, ? \]

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