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We use the method of brackets to evaluate quadratic and quartic typeintegrals. We recall the operational rules of the method and give examples toillustrate its working. The method is then used to evaluate the quadratic typeintegrals which occur in entries 3.251.1,3,4 in the table of integrals byGradshteyn and Ryzhik and obtain closed form expressions in terms ofhypergeometric functions. The method is further used to evaluate the quarticintegrals, entry 2.161.5 and 6 in the table. We also present generalization ofboth types of integrals with closed form expression in terms of hypergeometricfunctions.

Quadratic and quartic integrals using the method of brackets