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Calculus Level 4

033/2x3(4x2+9)3dx\large\int_0^{{3\sqrt{3}} / {2}} \dfrac{x^3}{\sqrt{(4x^2+9)^3}} \, dx

If the above integral equals ab\dfrac{a}{b}, where aa and bb are coprime positive integers, find a+ba+b.

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