Let K(x_{1},ldots,x_{n}) satisfy \t\t\tK(x1,…,txi,…,xn)=tλλiK(t−λiλ1x1,…,xi,…,t−λiλnxn)\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$K(x_{1},\\ldots,tx_{i},\\ldots,x_{n})=t^{\\lambda\\lambda _{i}}K \\bigl(t^{-\\frac{\\lambda_{i}}{\\lambda_{1}}}x_{1},\\ldots,x_{i}, \\ldots,t^{-\\frac {\\lambda _{i}}{\\lambda_{n}}}x_{n} \\bigr) $$\\end{document} for t>0. With this integral kernel, by using the method and technique of weight coefficients, the equivalent conditions and the best constant factors for the validity of Hilbert-type integral inequalities involving multiple functions are discussed. Finally, the applications of the integral inequalities are considered.