\[ \large \int_0^\infty \frac{x^{21}+x^{20} +x^{19}+ \ldots+x^2 +x+1}{x^{23} + x^{22}+x^{21} +\ldots+x^2+x+1} \, dx \]

Given that the integral above equals to \[ \dfrac{\pi}{\sqrt A} \left( \dfrac1{\sqrt B}+\dfrac1{\sqrt C}+\dfrac1{\sqrt D}+\dfrac1{\sqrt E} \right) \] for positive integers \(A,B,C,D\) and \(E\).

Find the minimum value of \(B\times C\times D \times E \div A\).

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