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Answer
$$ \displaystyle\int {\left(\ln\left(x-2\right)\right)}^{3}\, \mathrm d x = \left(\left(\ln \left(x-2\right)\right)^3-3\,\left(\ln \left(x-2 \right)\right)^2+6\,\ln \left(x-2\right)-6\right)\,\left(x-2\right) $$
Explanation
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