\documentclass{report}

\usepackage{amsthm,amsmath,amssymb}

\newtheorem{defe}{تعریف}[section]
\newtheorem{theorem}{قضیه}[section]
\newtheorem{lemma}{لم}[section]
\newtheorem{proposition}{گزاره}[section]
\usepackage{xepersian}
\begin{document}
\begin{equation}
\begin{split}
f(y,w)= \int_{-\infty}^{+\infty}f(y,w|x)f(x)dx=\\
  & \quad \int_{-\infty}^{+\infty}(\frac{\varsigma}{\sigma_e(1+\varsigma^2)}exp{\frac{-\varsigma(y-\alpha-\beta x)}{\sigma_e}I(y)_{(\alpha+\beta x,+\infty)}+\frac{\varsigma}{\sigma_e(1+\varsigma^2)}exp{\frac{(y-\alpha-\beta x)}{\sigma_e \varsigma}I(y)_{(-\infty,\alpha+\beta x)})\\
    & \quad *(\frac{\iota}{\sigma_m(1+\iota^2)}exp{\frac{-\iota(w-x)}{\sigma_m}I(w)_{(x,+\infty)+\frac{\iota}{\sigma_m(1+\iota^2)}exp{\frac{(w-x)}{\sigma_m \iota}}I(w)_{(-\infty,x)}\\
      & \quad*(\frac{\varrho}{\sigma_x(1+\varrho^2)}exp{\frac{-\varrho(x-\mu_x)}{\sigma_x}I(x)_{(\mu_x,+\infty)+\frac{\varrho}{\sigma_x(1+\varrho^2)}exp{\frac{(x-\mu_x)}{\sigma_x \varrho}}I(x)_{(-\infty,\mu_x)}d(x),
      \end{split}
\end{equation} 
\end{document}