यदि $\lim\limits _{t \rightarrow 0}\left(\int\limits_0^1(3 x+5)^t d x\right)^{\frac{1}{t}}=\frac{\alpha}{5 e}\left(\frac{8}{5}\right)^{\frac{2}{3}}$, तो $\alpha$ के बराबर है ________________.