# 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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