I think you have two options. One is to rewrite the input as a valid Mathematica expression e.g. using Derivative, Integrate and the like rather than the palette formatting for FractionBox, PartialD etc., and then apply TeXForm. The alternative is to take the entire notebook and do File > Save As > LaTeX Document. I did this latter and show the result below. It would probably require a bit of tweaking but it might be useful as a start.
%% AMS-LaTeX Created with the Wolfram Language : www.wolfram.com
\documentclass{article}
\usepackage{amsmath, amssymb, graphics, setspace}
\newcommand{\mathsym}[1]{{}}
\newcommand{\unicode}[1]{{}}
\newcounter{mathematicapage}
\begin{document}
\begin{doublespace}
\noindent(\pmb{\frac{\partial u}{\partial t}-\hat{v}\circ \nabla u-v\left(\mu a+\mu s\right)u+\int \text{v$\mu $}sps\left(\Omega '\rightarrow
\Omega \right)u\left(r,\Omega ',t\right)d\Omega '+q(r,\Omega ,t)})
\end{doublespace}
\end{document}
