Hermite, Ostrogradsky

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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