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Calculus Level 3

\[ \large \int_0^1 \frac{2x+3}{\sqrt{x^2+2x+3}} \, dx \]

If the integral above equals to \(\displaystyle \sqrt A - \sqrt B - \ln \left( \frac{\sqrt C+ 2}{\sqrt D + 1} \right) \) for integers \(A,B,C\) and \(D\), find the value of \(A+B+C+D \).

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