Answer
$$ \displaystyle\int \dfrac{1}{\left({x}^{4}+1\right){\cdot}{x}^{2}}\, \mathrm d x = {{\sqrt{2}\,x\,\ln \left(x^2+\sqrt{2}\,x+1\right)-\sqrt{2}\,x\, \ln \left(x^2-\sqrt{2}\,x+1\right)-2\sqrt{2}\,x\,\arctan \left({{2\,x+\sqrt{2}}\over{\sqrt{2}}}\right)-2\sqrt{2}\,x\, \arctan \left({{2\,x-\sqrt{2}}\over{\sqrt{2}}}\right)-8}\over{8\,x}} $$
Explanation
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