By trying to find a marginal distribution I came accross integration of the product seriesof products. For the sake of generality, lets assume the integral is of following form: $$\int \prod_{k=1}^{n}\left ( x+a_{k} \right )^{b_{k}}dx.$$ $a_{k}$ is a real coefficient and $b_{k}$ is positive integers. Is there any method, that could be used to integrate this analyticaly? It is of no problem to calculate it by some numerical method. But the first thing I would like to try is to find its analytical expression.
By trying to find a marginal distribution I came accross integration of the series of products. For the sake of generality, lets assume the integral is of following form: $$\int \prod_{k=1}^{n}\left ( x+a_{k} \right )^{b_{k}}dx.$$ $a_{k}$ is a real coefficient and $b_{k}$ Is there any method, that could be used to integrate this analyticaly? It is of no problem to calculate it by some numerical method. But the first thing I would like to try is to find its analytical expression.