Answer
$$ \displaystyle\int \dfrac{7{x}^{2}+7x+18}{{x}^{3}+{x}^{2}+6x}\, \mathrm d x = {{2\,\sqrt{23}\,\ln \left(x^2+x+6\right)+4\,\arctan \left({{2\,x+1 }\over{\sqrt{23}}}\right)+3\,\sqrt{23}\,\ln x}\over{\sqrt{23}}} $$
Explanation
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