Published 2025-08-08
DOI:
https://doi.org/10.71712/kkgf-rv90Keywords
- Integration techniques

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
Benim, R. W. (2025). Integrals of Functions of Roots of \(x\). Scientia Series A: Mathematical Sciences, 34, 23-26. https://doi.org/10.71712/kkgf-rv90
Abstract
This note will show that the only integrals of the form \(\int f(x^\alpha) \, dx\) that can be evaluated via the substitution \(t = x^\alpha\) followed by repeated integration by parts are those where \(\alpha\) is the reciprocal of a positive integer, \(\alpha = \frac{1}{n}\), and \(f\) is an arbitrary function which can be antidifferentiated at least \(n\) times.
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