The comparison method is used here, because X-square is convergent, and the existence of this limit proves that fx and X-square converge and diverge the same, so fx, definite integral converges.

In fact, these discrimination methods are not written in the textbook. The discrimination method of convergence and divergence of generalized definite integral can be Baidu. I saw a PPT on Baidu before, which was quite good. You can refer to it In fact, the method is the same as the method of judging the convergence and divergence of series.