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Given two positive constants α and β,we prove that the integral inequality ∫1 0fα+β(x)dx≥∫1 0fα(x)xβdx holds for all non-negative valued continuous functions f satisfying ∫1 xf(t)dt≥∫1 x tdt for x∈[0,1]if and only if α+β≥1.This solves an open problem proposed recently by Ngo,Thang,Dat,and Tuan.