Methodology of Integrating Binomial Differential Expressions

This paper examines the problem of integrating binomial differential expressions, which are one of the important classes of indefinite integrals. In the study, the rational exponents appearing under the integral sign are identified, and the integration process is analyzed according to the cases where these exponents are integers, dividing the task into three main scenarios. For each case, methods for transforming the integral into an integral of rational functions using suitable substitutions are presented, and solutions are demonstrated through concrete examples related to the topic.