A study on complex integrals involving absolute values

摘要

In this paper, we present a useful mathematical framework for the solution of complex integrals involving absolute values. The analysis is effectively extended to real definite integrals where the integrands are rational functions of cos nθ or sin nθ, for n ≥ 1. The formulas we established are tested, and the results demonstrate the efficacy and validity of using these formulas.