Integration Problem

Calculus Level 2

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

The value of the integral above is equal to \( \dfrac1A (B\sqrt B + C \sqrt C ) \), where \(A,B\) and \(C\) are positive integers with \(B,C\) square-free. Find \(A+B+C\).

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