\[ \large \int_0^3 \sqrt{9+x^2} \, dx \]

The integral above can be expressed as \( \dfrac{A\sqrt B}C + \dfrac{D \ln(\sqrt E + F)}G \), where \(A,B,C,D,E,F,G\) are all positive integers, with \((A,C)\) and \((D,G)\) coprime pairs, and both \(B,E\) square-free.

Calculate \(A+B+C+D+E+F+G\).

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