Some new results on integral divergence

This paper studies the divergence of certain simple and double integrals. In particular, a divergence result is established for simple integrals of submultiplicative functions. Several divergence integral results for double integrals involving functions of the sum and product of variables are also proved. One of these allows for the reconsideration of some existing theorems. Overall, the results provide novel techniques for evaluating divergent integrals that may be useful beyond the framework considered.