Answer
$$ \displaystyle\int \dfrac{3x-1}{2{x}^{2}+2x+3}\, \mathrm d x = {{3\,\ln \left(2\,x^2+2\,x+3\right)-2\,\sqrt{5}\,\arctan \left({{2 \,x+1}\over{\sqrt{5}}}\right)}\over{4}} $$
Explanation
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