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Answer
$$ \displaystyle\int \dfrac{1}{\left(1+{x}^{3}\right){\cdot}\left(1+{x}^{2}\right)}\, \mathrm d x = -{{4\,\ln \left(x^2-x+1\right)-3\,\ln \left(x^2+1\right)-2\,\ln \left(x+1\right)-6\,\arctan x}\over{12}} $$
Explanation
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