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\begin{equation}
\int_a^b f(x)g'(x) dx = \left[ f(x) g(x) \right]_a^b - \int_a^b f(x)g(x) dx
\end{equation}
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$$
y = 
\left\{
\begin{array}{l@{\quad :\quad }l}
0 & x < 0 \\
1 & x = 0 \\
2 & x > 0 \\
\end{array} \right.
$$

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