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