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If $$\lim_{t \to 0} \left(\int_{0}^{1} (3x+5)^t \, dx\right)^{\frac{1}{t}} = \frac{\alpha}{5e}\left(\frac{8}{5}\right)^{\frac{2}{3}}$$, then $$\alpha$$ is equal to ________
Correct Answer: 64
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