Calculus Level 5

$\displaystyle \int_{0}^2 \frac{x^5 + 2x^4 + 4x^3 - 2x^2 - x}{(x + 1)^2(x^2 + 1)^2} \space dx$

The above integral can be written $$- \dfrac{A}{B} + \ln(C) + \arctan(D)$$, where $$A$$ and $$B$$ are coprime positive integers and $$C$$ and $$D$$ are positive integers. Submit $$A + B + C + D$$.

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