Equations making a new line and not lining up in multicol

Question

Each equation should sit directly next to its listing ie to the right of the a) not underneath it, just wondering how to fix it, and if my markup can be improved efficiency wise. What it looks like currently:

\documentclass[fleqn]{article}
\usepackage{amsmath}
\usepackage{multicol}
\usepackage{enumerate}
\begin{document}
\begin{enumerate}
\item \begin{equation*} \text{Factorise the following} \end{equation*}
\begin{multicols}{2}
\begin{enumerate}[(a)]
    \item  \begin{equation*} \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x). \end{equation*}
    \item  \begin{equation*} \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x). \end{equation*}
    \item  \begin{equation*} \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x). \end{equation*}
    \item  \begin{equation*} \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x). \end{equation*}
    \item  \begin{equation*} \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x). \end{equation*}
    \item  \begin{equation*} \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x). \end{equation*}
\end{enumerate}
\end{multicols}
\end{enumerate}

Answer 1

Instead of a displayed equation environment that goes underneath the enumerate numbering inline math can be used. \displaystyle chooses the settings for displayed equations.

\documentclass[fleqn]{article}
\usepackage{amsmath}
\usepackage{multicol}
\usepackage{enumerate}
\begin{document}
\begin{enumerate}
\item Factorise the following:
\begin{multicols}{2}
\begin{enumerate}[(a)]
    \item  $\displaystyle \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x)$.
    \item  $\displaystyle \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x)$.
    \item  $\displaystyle \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x)$.
    \item  $\displaystyle \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x)$.
    \item  $\displaystyle \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x)$.
    \item  $\displaystyle \frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x)$.
\end{enumerate}
\end{multicols}
\end{enumerate}
\end{document}

Result:

Edit: Werner's idea of centered equations added.

\documentclass[fleqn]{article}
\usepackage{amsmath}
\usepackage{multicol}
\usepackage{enumerate}
\newenvironment{cmath}{%
  \leavevmode
  \hfill
  $\displaystyle
}{%
  $\hfill\null
}
\begin{document}
\begin{enumerate}
\item Factorise the following:
\begin{multicols}{2}
\begin{enumerate}[(a)]
    \item  \begin{cmath}\frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x).\end{cmath}
    \item  \begin{cmath}\frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x).\end{cmath}
    \item  \begin{cmath}\frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x).\end{cmath}
    \item  \begin{cmath}\frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x).\end{cmath}
    \item  \begin{cmath}\frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x).\end{cmath}
    \item  \begin{cmath}\frac{d}{dx}\left( \int_{0}^{x},du\right)=f(x).\end{cmath}
\end{enumerate}
\end{multicols}
\end{enumerate}
\end{document}

Result: