\documentclass{article}
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% calculus and other big operators

\[ \int_0^\infty x^2 dx \]

\[ \int_0^\infty x^2 d\mathord{x} \]

\[ \int_\infty^{(0+)} t\,dt \]

\[ \int_\infty^{(1+,0+,1-,0-)} t\,dt \]

\[ \sum_{i=0}^{50} x^i \]

% evaluated at 0
$\left. y \right|_0$

$\left. xyz \right|_0$

% courtesy of TeXbook, p.145
\[\sum_{\scriptstyle0\le i\le m\atop\scriptstyle0<j<n}P(i,j) \]

% courtesy of TeXbook, p.145
\[\sum_{i=1}^p\sum_{j=1}^q\sum_{k=1}^r a_{ij}b_{jk}c_{ki} \]

\[ x | ^{a}_{y=0} \] % maybe evaluate at for integral evaluation

% moreIntOpArgs
\[ \int F \times G dx \]

% moreOpArgFactors
$\sum f \times g $ 
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