Abstract
Integrating functions in the real domain tends to be challenging and can become complex as more functions and terms are inserted into the integrand. Shifting our lens to the complex domain can greatly simplify integration and the ability to deter mine trends among the primitives of families of functions. The trend relevant to this research paper is integral to finding the primitive function of higher-order elementary reciprocal functions by converting them into a summation of simpler terms. This result agrees with the results obtained from the residue theorem. Relating to fundamental complex analysis techniques such as the De Moivre theorem, Euler’s identity, and the analytical continuation of the logarithm. The goal of this paper is to expose the audience to the identities that arise from the primitives of these functions and other neat integration tools that many may want to add to their tool belt. We will be diving straight into the complex domain, so be ready to deal with all the residues!
Recommended Citation
George, Gavin
(2026)
"Unity Decomposition to Simplify Challenging Integrals: A Crossover between the Real and Complex Domains,"
Proceedings of GREAT Day: Vol. 17, Article 4.
Available at:
https://knightscholar.geneseo.edu/proceedings-of-great-day/vol17/iss1/4