# Integration Mania Continued v2

Calculus Level 5

$\large \int_2^3 \dfrac{2x^5 + x^4 - 2x^3 + 2x^2 + 1}{x^6 + x^4-x^2 - 1} \, dx$

If the integral above can be expressed in the form of

$\dfrac AB \ln 6 - \dfrac DE \; ,$

where $$A,B,D$$ and $$E$$ are positive integers with $$\gcd(A,B) = \gcd(D,E) = 1$$, find $$6\times A \times B \times D \times E$$.

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