Journal of Multidisciplinary Applied Natural Science
Open Access Journal
Scopus CiteScore 2024
4.8
Calculated on 05 May, 2025
SJR 2024
0.31
Powered by scimagojr.com
Open Access Journal
4.8
Calculated on 05 May, 2025
0.31
Powered by scimagojr.com
https://doi.org/10.47352/jmans.2774-3047.186
Laxmi Rathour
Dragan Obradovic
Kejal Khatri
Shiv Kant Tiwari
Lakshmi Narayan Mishra
Vishnu Narayan Mishra
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.
[1] C. Canuto and A. Tabacco. (2015). "Mathematical Analysis I". Springer Cham, Switzerland. 10.1007/978-3-319-12772-9.
DOI: https://doi.org/10.1007/978-3-319-12772-9[2] D. Lazard and R. Rioboo. (1990). "Integration of rational functions: Rational computation of the logarithmic part". Journal of Symbolic Computation. 9 (2): 113-115. 10.1016/s0747-7171(08)80026-0.
DOI: https://doi.org/10.1016/S0747-7171(08)80026-0[3] R. H. C. Moir, R. M. Corless, M. M. Maza, and N. Xie. (2019). "Symbolic-numeric integration of rational functions". Numerical Algorithms. 83 (4): 1295-1320. 10.1007/s11075-019-00726-6.
DOI: https://doi.org/10.1007/s11075-019-00726-6[4] M.-T. Noda and E. Miyahiro. (1992). "A hybrid approach for the integration of a rational function". Journal of Computational and Applied Mathematics. 40 (3): 259-268. 10.1016/0377-0427(92)90182-w.
DOI: https://doi.org/10.1016/0377-0427(92)90182-W[5] M. T. Noda and E. Miyahiro. (1990). "On the symbolic/numeric hybrid integration". Proceedings of the International Symposium on Symbolic and Algebraic Computation. 10.1145/96877.96973.
DOI: https://doi.org/10.1145/96877.96973[6] B. M. Trager. (1976). "Algebraic factoring and rational function integration". Proceedings of the Third ACM Symposium on Symbolic and Algebraic Computation. 10.1145/800205.806338.
DOI: https://doi.org/10.1145/800205.806338[7] K. Gürlebeck, K. Habetha, and W. Sprößig. (2007). "Holomorphic functions in the plane and n-dimensional space". Springer Science & Business Media, Basel.
[8] J. Lithner. (2007). "A research framework for creative and imitative reasoning". Educational Studies in Mathematics. 67 (3): 255-276. 10.1007/s10649-007-9104-2.
DOI: https://doi.org/10.1007/s10649-007-9104-2