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If $$\int_0^{\sqrt{3}} \frac{15x^3}{\sqrt{(1+x^2)} + \sqrt{(1+x^2)^3}} dx = \alpha\sqrt{2} + \beta\sqrt{3}$$, where $$\alpha, \beta$$ are integers, then $$\alpha + \beta$$ is equal to
Correct Answer: 10
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