Journal of Generalized Lie Theory and Applications

This paper’s results came from a combination of complex and real analysis methods in solving improper integrals. This Result is easier method instead of the function convergent (Residue theorem) and applying Cauchy integration formula, in addition some of these results and examples are shown in the paper are very hard to be evaluated using the contour integration (Residue theorem). I’ll discuss 4 results (formulas) and the modified version of the result, all of the results came from the master Result for Mohammad Hussein Abughuwaleh. For some of these results I used conditions for a, b, β, γ to let the integral convergent on it's boundaries.