This question is similar to this one, but not the same.
Code
\documentclass{article}
\usepackage{libertinus-otf}
\usepackage{showframe}
\usepackage{amsmath}
\usepackage{enumitem}
\usepackage{enumext}
\usepackage{fixdif}
\setenumext[enumext*]{widest=10,columns=2,label=(\arabic{enumi}-\arabic*),before=\everymath{\displaystyle}}
\newcommand{\myitem}[1]{\item #1 ;}
\begin{document}
\begin{enumerate}[start=3]
\item \begin{enumext*}
\item $\int x^2 \d x = \frac{x^3}{3} + C$ ;
\item $\int x^2 \d x = \frac{x^3}{3} + C$ ;
\item $\int x^2 \d x = \frac{x^3}{3} + C$ ;
\item $\int x^2 \d x = \frac{x^3}{3} + C$ ;
\end{enumext*}
\item \begin{enumext*}
\myitem{$\int x^2 \d x = \frac{x^3}{3} + C$}
\myitem{$\int x^2 \d x = \frac{x^3}{3} + C$}
\myitem{$\int x^2 \d x = \frac{x^3}{3} + C$}
\myitem{$\int x^2 \d x = \frac{x^3}{3} + C$}
\myitem{$\int x^2 \d x = \frac{x^3}{3} + C$}
\myitem{$\int x^2 \d x = \frac{x^3}{3} + C$}
\myitem{$\int x^2 \d x = \frac{x^3}{3} + C$}
\end{enumext*}
\end{enumerate}
\end{document}
I want to put ; after each \item inside enumext* and it doesn't affect the outer enumerate.
Exploration
(1)I have tried samcarter's lualatex solution autopunc, but it doesn't work with enumext*;
(2) For Werner's solution with \renewcommand the enumerate, I don't know how to make it only affect only specific enumext*
(3) I have try the Iacobus1983's \myitem case, it worked(shown above), but is that possible to patch the \item but not with\myitem{<content>}, I prefer syntax of the original \item <something> but not \myitem{something}
Question
Is that better or elegant solution to automatically add something after each \item? I have looked through the enumitem and enumext, but only found hook like before,after and first, without which insert something after each \item's content.



\item's content"..at the end of the last one. It is all one sentence.enumext-like package is good for something like this.