integration of a multiple Laurent series

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let be an multiple integral given by

$$ \int_{0}^{\infty}dx_{1}\dots\int_{0}^{\infty}dx_{n}F(x_{1} ,x_{2},...x_{n}) $$

i have a question can i solve this integral equation by exapnding the integrand into a multiple Laurent/Taylor series?

$$ F(x_{1},x_{2},\dots ,x_{n})= \sum_{n1}\sum_{n2}\dots\sum_{mn}C_{n1,n2,\dots ,n_m}\prod_{i} (x_{i}-a_{i}) $$

or if the integral (1) is divergent i sbustract from it a Laurent series/POlynomial to make it convergent is this valid to substract something to a multiple integral to make this convergent?

I need to know because in physics there are lots of multidimensional divergent integrals.