Integration of Rational Functions

Laxmi Rathour (Department of Mathematics, National Institute of Technology, Mizoram -796012 (India))
Dragan Obradovic (Elementary School "Jovan Cvijic", Pozarevac-12208 (Serbia))
Kejal Khatri (Department of Mathematics, Government College, Simalwara, Dungarpur -314403 (India))
Shiv Kant Tiwari (Department of Mathematics, Lukhdhirji Engineering College, Morbi-363642 (India))
Lakshmi Narayan Mishra (Department of Mathematics, Vellore Institute of Technology, Vellore-632014 (India))
Vishnu Narayan Mishra (Department of Mathematics, Indira Gandhi National Tribal University, Amarkantak-484887 (India))

Journal of Multidisciplinary Applied Natural Science
Vol. 4 No. 1 (2024): Journal of Multidisciplinary Applied Natural Science

A rational function can always be integrated, that is, the integral of such a function is always an elementary function. The integration procedure is complex and consists of four steps: elimination of the common zero-points of the numerator and denominator, reduction to a true rational function, decomposition into partial fractions and integration of the obtained expressions using direct integration, substitution method or partial integration method. Integrating rational functions is important because integrals of rational functions of trigonometric functions as well as integrals of some irrational functions are reduced to integrals of rational functions by appropriate transformations.