Abstract: By introducing independent parameters and intermediate variables of exponential function, and using the method of the weight functions, we established a Hilberttype integral inequality in the whole plane related to the Gamma function of the best constant factor, and considered  the  equivalent forms,  homogeneous and nonhomogeneous forms under particular parameters.

Key words: Hilberttype integral inequality in , best constant factor, equivalent form, whole plane, Gamma function, weight function