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TeX (original user input):

\begin{align}
  & {{T}^{\alpha }}{{_{\mathrm{;}}}_{\alpha }}=\frac{1}{\sqrt{-g}}{{\left( \sqrt{-g}{{T}^{\alpha }} \right)}_{\mathrm{,}}}_{\alpha } \\ 
 & \Rightarrow \int\limits_{{{V}_{4}}}{{{\left( \sqrt{-g}{{T}^{\alpha }} \right)}_{\mathrm{,}}}_{\alpha }{{d}^{4}}x}=\int\limits_{\partial {{V}_{4}}}{\left( \sqrt{-g}{{T}^{\alpha }} \right)d{{f}_{\alpha }}} \\ 
 & \left( {{T}^{\alpha }}:={{\xi }_{\beta }}{{T}^{\alpha }}^{\beta } \right) \\ 
\end{align}

TeX (checked):

{\begin{aligned}&{{T}^{\alpha }}{{_{\mathrm {;} }}_{\alpha }}={\frac {1}{\sqrt {-g}}}{{\left({\sqrt {-g}}{{T}^{\alpha }}\right)}_{\mathrm {,} }}_{\alpha }\\&\Rightarrow \int \limits _{{V}_{4}}{{{\left({\sqrt {-g}}{{T}^{\alpha }}\right)}_{\mathrm {,} }}_{\alpha }{{d}^{4}}x}=\int \limits _{\partial {{V}_{4}}}{\left({\sqrt {-g}}{{T}^{\alpha }}\right)d{{f}_{\alpha }}}\\&\left({{T}^{\alpha }}:={{\xi }_{\beta }}{{T}^{\alpha }}^{\beta }\right)\\\end{aligned}}

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\begin{aligned} T^{α};_{α} = \frac{1}{\sqrt{- g}} {(\sqrt{- g} T^{α})}_{,}_{α} \\ \Rightarrow \int_{V_{4}} {(\sqrt{- g} T^{α})}_{,}_{α} d^{4} x = \int_{\partial V_{4}} (\sqrt{- g} T^{α}) d f_{α} \\ (T^{α} : = ξ_{β} {T^{α}}^{β}) \end{aligned}

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$T$

$α$

$α$

$g$

$g$

$T$

$α$

$α$

$V_{4}$

$g$

$T$

$α$

$α$

$x$

$V_{4}$

$g$

$T$

$α$

$f_{α}$

$T$

$α$

$ξ_{β}$

$T$

$α$

$β$

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