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The Askey--Wilson integral is very important in the theory of orthogonalpolynomials. Liu's integral is a generalization of the Askey--Wilson integralwith many parameters. With the help of the series rearrangement method, we givethe elementary proof of them. Furthermore, we establish two new Askey--Wilsontype integrals in the similar way and find a generalization of a knowntransformation formula containing three $_{3}\phi_{2}$ series.

On the Askey--Wilson type integrals