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\usepackage{amsmath}
\usepackage{amssymb}

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\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{align*}
\int_{U} \textit{u} \frac{d \varphi}{d x} dx &=
    \int_{(0,1)} \textit{x} \frac{d \varphi}{d x} \,\mathrm dx \\
    + \int_{(1,2)}\frac{d \varphi}{d x} \mathrm dx \\
  &= - \int_{(0,1)} \frac{d \varphi}{d x}dx + \varphi(1) - \varphi(1) \\
  &= - \int_{U} \textit{v} \varphi \,\mathrm dx
\end{align*}
\end{document}

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\usepackage{amsmath}