Integration in LaTeX: \int Syntax, Limits and Set Notation

Short answer: in LaTeX, integration is written with the \int command inside math mode, with the limits attached as a subscript and a superscript: \int_{a}^{b} x^2 \,dx typesets the definite integral of x² from a to b. Load the amsmath package in the preamble to get the multiple-integral commands (\iint, \iiint). This page covers single, multiple and cyclic integrals, how to put an integral in running text, why the limits move between inline and display math, and how to write set notation such as { x ∈ ℝ | x > 0 }.

Who this is for: researchers and analysts writing equations in a manuscript, thesis or report who need correct, copy-ready syntax and an explanation of why a given line misbehaves.

What it is used for in research

Integrals appear wherever a manuscript defines a continuous quantity: expected values and probability densities in statistics, work and flux in physics, area under a curve in a methods section, and normalising constants in a model description. LaTeX typesets them in math mode, a separate mode with its own spacing rules, so the same characters typed in ordinary text will not produce an integral sign. Set notation (membership, union, intersection, subset) is written in the same mode and is covered below, because the searches for the two topics overlap.

Install or access (official source only)

Integrals need a working LaTeX distribution or an online LaTeX editor; nothing has to be installed for the basic \int command itself. For the multiple-integral commands, add the AMS maths package to the preamble:

\usepackage{amsmath}

The package is distributed through CTAN; its CTAN page lists amsmath version 2.17z, dated 2025-07-09, released under the LaTeX Project Public Licence 1.3c and maintained by the LaTeX Project Team, with the manual in amsldoc.pdf (page read 2026-11-07). Cyclic integrals additionally need the esint package according to Overleaf’s documentation. Overleaf and the standard TeX distributions bundle these packages, so in most setups a \usepackage line is all that is required. If you are new to the online editor, see what Overleaf is.

Step-by-step: how to write integration in LaTeX

How do you add integrals?

1. Put the document in math mode. For an integral inside a sentence use \( ... \) or $ ... $. For a displayed, unnumbered equation use \[ ... \]. For a numbered equation use the equation environment, or equation* (from amsmath) for an unnumbered one.
2. Type \int followed by the lower limit as a subscript and the upper limit as a superscript, each in braces: \int_{a}^{b}.
3. Type the integrand, then a thin space \, and the differential: \int_{a}^{b} x^2 \,dx. Overleaf’s own example uses exactly this form; the \, keeps the dx from touching the integrand.
4. Compile. The same source renders differently inline and in display mode (see below), which is expected behaviour, not an error.

A minimal complete document, following the pattern in Overleaf’s Integrals, sums and limits article:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Inline: \( \int_{a}^{b} x^2 \,dx \).

Display:
\[ \int_{a}^{b} x^2 \,dx \]
\end{document}

How do you write an integral in text?

Wrap it in inline math delimiters, $\int_{0}^{1} f(x)\,dx$ or \(\int_{0}^{1} f(x)\,dx\), inside the sentence. Overleaf’s Mathematical expressions article lists three inline forms: \( ... \), $ ... $ and \begin{math} ... \end{math}. Inline integrals are set compactly so they do not push the lines apart; if you need the larger display look in the middle of a sentence, see the \displaystyle note below.

Multiple and cyclic integrals

The variants below are the commands Overleaf documents for double, triple and higher integrals. Each takes limits the same way as \int.

Command	What it typesets	Package noted by Overleaf
\int	Single integral	Available in base LaTeX math mode
\iint	Double integral	amsmath
\iiint	Triple integral	amsmath
\iiiint	Quadruple integral	amsmath
\idotsint	Integral signs with dots between (n-fold integral)	amsmath
\oint	Cyclic (contour) integral	Overleaf: amsmath and esint for cyclic integrals

Sums, products and limits follow the same subscript/superscript pattern: \sum_{i=1}^{n}, \prod_{i=1}^{n} and \lim_{x \to \infty} f(x). For the limit command in depth, see LaTeX lim syntax and limits under or beside the operator. To put several integrals on separate lines, Overleaf’s article uses the gather* environment from amsmath; for line breaks inside one equation see a new line in a LaTeX equation.

Output and how to read it

Why the limits move between inline and display

In display math the limits of \int are placed above and below the integral sign’s ends; inline they are set as small side scripts to save vertical space. That is the style change Overleaf describes under its display-style article: math mode has four styles (\textstyle, \displaystyle, \scriptstyle, \scriptscriptstyle), and the placement of limits changes with the style. Forcing \displaystyle inside running text enlarges the formula, but Overleaf warns that it “does impact heavily on the line spacing”, so reserve it for the cases where legibility of a limit matters more than even leading.

If you want to control limit position yourself, standard TeX provides \limits and \nolimits after the operator: \int\limits_{a}^{b} forces the limits above and below, \int\nolimits_{a}^{b} forces them to the side. These two commands are not documented on the Overleaf pages cited here; they come from standard TeX math typesetting, so test the result in your own document class.

How do you write set notation in LaTeX?

Set notation uses ordinary math-mode symbols. Curly braces must be escaped, because bare { } only group characters:

$A = \{ x \in \mathbb{R} \mid x > 0 \}$

This produces A = { x ∈ ℝ | x > 0 }. The pieces: \{ and \} print literal braces; \in is the membership relation; \mid is the “such that” bar; \mathbb{R} is the blackboard-bold letter, which requires the amssymb (or amsfonts) package. Overleaf’s Mathematical expressions article lists the set operators and relations below. For other uses of the vertical bar, see the vertical line in LaTeX.

Command	Meaning	Type
\cup	Union	Binary operator
\cap	Intersection	Binary operator
\subset	Subset	Relation
\supset	Superset	Relation
\subseteq	Subset or equal	Relation
\supseteq	Superset or equal	Relation

Greek letters used for integration variables and parameters are covered in Greek symbols in LaTeX, and arrays of values in matrices in LaTeX.

Troubleshooting

Symptom	Likely cause	Fix
“Undefined control sequence” on \iint, \iiint or \idotsint	The amsmath package is not loaded	Add \usepackage{amsmath} to the preamble
“Undefined control sequence” on a cyclic-integral variant	The esint package is not loaded (Overleaf lists amsmath and esint for cyclic integrals)	Add \usepackage{esint} after amsmath
“Missing $ inserted” or the integral sign prints nothing useful	The command was typed outside math mode	Wrap it in $ ... $, \( ... \) or \[ ... \]
The dx collides with the integrand	No space before the differential	Write \,dx, as in Overleaf’s example
Limits appear beside the sign when you wanted them above and below	Inline (text) style is active	Use a display environment, \displaystyle, or \limits
Braces in set notation do not print	Unescaped { } only group	Use \{ and \}
\mathbb is undefined	The AMS symbol fonts are not loaded	Add \usepackage{amssymb}

Free alternatives (where to write and render LaTeX math)

The syntax above is the same in every LaTeX environment. These are options for producing or displaying it; none is endorsed over another here, and plan terms and prices are deliberately not stated.

Tool	What it is
Overleaf	Browser-based LaTeX editor with its own documentation library (the source for most commands on this page)
TeX Live	A TeX distribution for installing LaTeX locally
MiKTeX	A TeX distribution, mainly used on Windows
TeXstudio	A desktop editor that works with a local TeX distribution
MathJax and KaTeX	JavaScript libraries that render LaTeX-style math on web pages; they cover common math commands but are not full LaTeX, so check unusual commands against their own documentation

FAQ

How to write integration in LaTeX?

Use \int_{lower}^{upper} integrand \,dx in math mode, for example \int_{a}^{b} x^2 \,dx. Load amsmath for multiple integrals.

How do I write set notation in LaTeX?

Use \{ x \in A \mid condition \} in math mode, with \cup, \cap, \subset and \subseteq for operations and relations. Escape the braces.

How do you add integrals?

Type \int with a subscript for the lower limit and a superscript for the upper limit, then the integrand and \,dx. Use \iint or \iiint for double and triple integrals.

How do you write an integral in text?

Place it between $ ... $ or \( ... \) within the sentence. For a standalone equation use \[ ... \].

Sources (official documentation)

• Overleaf, Integrals, sums and limits (read 2026-11-07).
• Overleaf, Mathematical expressions (read 2026-11-07).
• Overleaf, Display style in math mode (read 2026-11-07).
• CTAN, amsmath package page (read 2026-11-07).