Special forms and miscellaneous limitsHard

Limit of Integral Power Expression

If $\mathop {\lim }\limits_{t \to 0} {\left( {\int\limits_0^1 {{{\left( {3x + 5} \right)}^t}dx} } \right)^{\frac{1}{t}}} = \frac{\alpha }{{5e}}{\left( {\frac{8}{5}} \right)^{\frac{2}{3}}}$ , then α is equal to _______ .

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