\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}

\title{Bibliography management: BibTeX}
\author{Share\LaTeX}

\begin{document}

\maketitle
\begin{flalign*}
    g_{{\bf X}^{(1)}}(&x^{(1)}_{1},x^{(1)}_{2},\cdots, x^{(1)}_{m}) \nonumber\\
          =&\int_{X^{(2)}_{p-m}} \cdots \int_{X^{(2)}_{1}}   \prod_{i=1}^{m} (\frac{\partial}{\partial x^{(1)}_{i}} W^{(1)}_{i} (F^{(1)}_{i}(x^{(1)}_{i})))    \prod_{i=1}^{p-m} (\frac{\partial}{\partial x^{(2)}_{i}} W^{(2)}_{i} (F^{(2)}_{i}(x^{(2)}_{i}))) \times \\
                &r(W^{(1 \text{or} 2)}_{1}(F^{(1 \text{or} 2)}_1(x_1^{(1 \text{or} 2)})), \cdots, W^{(1 \text{or} 2)}_{m \text{or} p-m}(F^{(1 \text{or} 2)}_{m \text{or} p-m}(x^{(1 \text{or} 2)}_{
                m \text{or}  p-m})))  \times\\
        & dx_1^{(2)} dx_{2}^{(2)} \cdots dx_{p-m}^{(2)}\\
          =&\prod_{i=1}^{m} (\frac{\partial}{\partial x^{(1)}_{i}} W^{(1)}_{i} (F^{(1)}_{i}(x^{(1)}_{i})))  \times\\
\end{flalign*}
\medskip

\end{document}