How the following integral can be computed:
$I = \int_0^1 (x-a_1)^{b_1}(x-a_2)^{b_2}...(x-a_n)^{b_n} dx$?
Here, $a_i,b_i$ are real numbers and $n$ is a natural number. Are there any techniques for computing this integral? I know that if $n=2$, a Special case will be the Beta function. Some hypergeometric functions can be obtained from this integral over a product. But what is for General $n$?