Abstract: By introducing some parameters and by using the way of weight function and the techniques of real analysis and Laplace's integral transform, a parametric Hilbert-type integral inequality and its equivalent form are given, and their constant factors are proved to be the best values. As applications, some meaningful results are obtained by selecting the special values for the parameters.

Key words: Hilbert-type integral inequality, weight function, Laplace's integral transform, the best constant factor