Evaluate the integral. Round the answer to 6 decimal places.
∫569x2(3x3+6)2dx\displaystyle {\int_{{{5}}}^{{{6}}}}\frac{{{9}{x}^{{{2}}}}}{{\left({3}{x}^{{{3}}}+{6}\right)}^{{2}}}{\left.{d}{x}\right.}∫56(3x3+6)29x2dx
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