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We consider Hardy's integral inequality and we obtain some newgeneralizations of Bicheng-Debnath's recent results. We derive two distinguished classes of inequalities covering all admissible choices of parameter k from Hardy's original relation. Moreover, we prove the constant factors involved in the right-hand sides of some particular inequalities from both classes to be the best possible, that is, none of them can be replaced with a smaller constant

On Bicheng-Debnath's generalizations of Hardy's integral inequality