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<p/> <p>It is shown that an extension of the Hilbert's integral inequality can be established by introducing two parameters <inline-formula> <graphic file="1029-242X-2009-158690-i1.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-158690-i2.gif"/></inline-formula>. The constant factors expressed by the Euler number and <inline-formula> <graphic file="1029-242X-2009-158690-i3.gif"/></inline-formula> as well as by the Bernoulli number and <inline-formula> <graphic file="1029-242X-2009-158690-i4.gif"/></inline-formula>, respectively, are proved to be the best possible. Some important and especial results are enumerated. As applications, some equivalent forms are given.</p>