Answer
$$ \displaystyle\int \dfrac{4x}{\left(x-1\right){\cdot}\left({x}^{2}+x+2\right)}\, \mathrm d x = -{{\sqrt{7}\,\ln \left(x^2+x+2\right)-10\,\arctan \left({{2\,x+1 }\over{\sqrt{7}}}\right)-2\,\sqrt{7}\,\ln \left(x-1\right)}\over{2 \,\sqrt{7}}} $$
Explanation
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