How to adjust this expression
\documentclass[a4paper,twoside,12pt]{ article}
\usepackage[latin1,utf8,utf8x]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[french]{babel}
\frenchbsetup{StandardLists=true}
\usepackage{lmodern}
\usepackage{amsmath}
%%%%%%%
\usepackage{tabstackengine}
\TABstackMath
\TABstackMathstyle{\displaystyle}
\renewcommand\stacktype{L}
\renewcommand\stackalignment{r}
\setstackgap{L}{24pt}
%%%%%%%%%
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{mathrsfs}
\usepackage{mathtools}
\usepackage{hyperref}
\usepackage{amsthm}
\usepackage[mathscr]{euscript}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepackage{wrapfig}
\usepackage{latexsym}
\usepackage{mathtools}
\begin{document}
\begin{equation*}
\partial_tu(t,x)=\left\{
\begin{array}{l l}
\tabbedstackanchor{\Bigl(\partial_t\xi^t(x)R'(\xi^t(x))-\partial_xG(t,x)R(\xi^t(x))-R(\xi^t(x))\int_{\xi^t(x)}^t\partial_x^2G(s,\Phi(s,t,x))\partial_t\Phi(s,t,x)\,\mbox{d}s}{+\partial_t\xi^t(x)R(\xi^t(x))\partial_xG(\xi^t(x),1)\Bigr)\times\exp\left(-\int_{\xi^t(x)}^t\partial_x
G(s,\Phi_{(t,x)}(s))\,\mbox{d}s\right) },&(t,x)\in \Omega_1\\[20pt]
\tabbedstackanchor{\Bigl(\partial_xG(t,x)u_0(\chi^t(x))+G(t,x)\partial_x\chi^t(x)u'_0(\chi^t(x))-u_0(\chi^t(x))\int_{t_)}^t\partial_x^2G(s,\Phi(s,t,x))\partial_t\Phi(s,t,x)\,\,\mbox{d}s\Bigr)}
{\times\exp\left(-\int_{t_0}^t\partial_xG(s,\Phi_{(t,x)}(s))\,\mbox{d}s\right) },&(t,x)\in \Omega_2\\[24pt]
0,&(t,x)\in\Omega_3
\end{array}
\right.
\end{equation*}
\end{document}

\documentclass, all the\usepackages(and libraries if you usetikzor something like that), as well as the\begin{document}and\end{document}. Please refer to this and to this – Vinccool96 Apr 02 '19 at 01:37