It's a bit long

Calculus Level 5

\[\large\int_0^1\frac{3x+2}{\sqrt{(x^2+4x+1)^5}}\,dx = \dfrac A B - \dfrac C{D\sqrt E}\]

If the equation above holds true for positive integers \(A,B,C,D\) and \(E\) with least values and \(E\) being square-free, find \(A+B+C+D+E\).

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