The topic of the research to conduct comparative study to determine the best numerical methods for finding the roots of Non-Linear Algebraic Equations where it with an internal stopping condition was taken three examples to know the best method to solve nonlinear equation for the previous examples We calculated the percent error for these examples in order to make a comparison between the results were rounded to six places after comma. The results written in tabular format to facilitate comparison, the results showed that using integration method to compute the numerical solution of the nonlinear equation with an internal stopping condition yields highly accurate results, with the degree of proximity to the actual values being the best. Additionally, it is an easy and quick method for calculations and plays a significant role in finding approximate solutions to higher-order nonlinear equations. When comparing the number of iterations required to find the solution using this method with other methods, the number of iterations is reduced compared to other numerical methods. However, the equality of the real roots with the approximate roots does not mean that this numerical method used to find the root is 100% accurate, as the calculated results in the previous examples were approximated to six decimal places after the decimal point............... Keywords: ...............Function, Actual Error, Relative Error, Linear Equation, Nonlinear Equation, Internal Stopping Condition.