## Multiple integral of a product

sorry posted something similar to this before but

How do i integrate this function

$\int_u^v \prod_{i=1}^k X_i^{Y_i} dx$

I think this is clearly a multiple integral as each value of $X_i$ but i am not sure how to actually evaluate this integral. I will need to program this so should i use an approximation method or can i find an analytic solution