This guide is a practical, step-by-step manual for reliably typesetting integrals in LaTeX. It covers everything from simple inline integrals to complex multiple and iterated integrals, how to place limits correctly, best practices for the differential dx, packages that improve appearance, and troubleshooting tips for common problems. Examples use standard LaTeX and the widely recommended amsmath package where appropriate, with short, copy-paste-ready code snippets so you can apply the patterns immediately.

Whether you’re preparing lecture notes, a journal article, or homework solutions, this guide gives concrete rules and visual examples so your integrals look professional and mathematically correct. We explain inline vs display math behavior, spacing conventions, multi-integral notation, and useful macros for consistent differentials. Follow along section by section and copy the code samples into your document.

Why typesetting integrals correctly matters

Mathematical typesetting is not only about aesthetics: correct spacing and font choices communicate meaning. For example, the differential operator in an integral should usually be set in an upright font to show it is an operator (not a product of variables or italicized variables). Likewise, the visual relationship between the integral sign, limits, integrand, and differential helps readers parse the expression quickly.

LaTeX provides the tools to produce mathematically precise output, but you must adopt consistent conventions (for example, \mathrm{d}x vs plain dx, and whether to use thin spaces before differentials). Following these conventions reduces ambiguity and ensures your output aligns with publishing and ISO typographic recommendations.

Small typographic details also matter in inline math vs display math: inline math compresses symbols to match the text baseline, while display math centers and enlarges symbols for clarity. Knowing how to force display style in inline contexts will keep limits and integral signs readable.

Basic integral syntax and display rules

Single integral — the basic command

Use the command \int to produce the integral sign. For definite integrals add sub- and superscripts using the usual underscore and caret syntax: \int_{a}^{b}. In display math the limits appear above and below the sign by default; in inline math they appear as subscripts and superscripts.

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Example (display):

\[ \int_{0}^{\pi} x^2 \, \mathrm{d}x \]

Example (inline forcing display style):

\( \displaystyle \int_{0}^{\pi} x^2 \, \mathrm{d}x \)

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Note that if you want limits to always appear above and below even in inline mode, use \limits: \int\limits_{a}^{b}. This is sometimes preferred for compact presentation in specialized layouts but is not the default semantic choice for inline math.

Spacing: making your integrals readable

Two spacing rules return over and over: insert a thin space before the differential, and set the differential in an upright font. Use \, for a thin space and \mathrm{d}x (or a macro that wraps that) to render the d upright. For example, write \int f(x)\, \mathrm{d}x.

Common spacing commands you will use:

\, — thin space, often used before the differential to separate the integrand from dx. This places a small but important visual gap so d reads as an operator rather than multiplying the integrand.
\: — medium space, for slightly larger separation when needed to emphasize grouping.
\! — negative thin space, useful to nudge symbols closer when automatic spacing leaves too much gap (use sparingly).

These commands let you fine-tune the look without changing the math semantics.

Best practice for the differential: dx vs \mathrm{d}x vs macros

Typographically, many publishers and standards bodies recommend typesetting the differential d upright because it is an operator. Two common patterns appear in professional documents:

Simple upright differential: \mathrm{d}x. This explicitly sets the d in roman (upright) font, distinguishing it from italic variables.
Macro-wrapped differential: Define a macro like \newcommand{\dif}{\mathop{}\!\mathrm{d}} and use \dif x. The macro handles spacing automatically and keeps source consistent across documents.

Example macro (copy into your preamble):

\usepackage{amsmath} \\ \newcommand{\dif}{\mathop{}\!\mathrm{d}}

Then use: \int f(x)\,\dif x. This macro approach is convenient because it centralizes spacing behavior and lets you change styling across the document by editing one definition.

Multiple integrals: \iint, \iiint, and \idotsint

For multiple integrals LaTeX (via amsmath) provides commands such as \iint, \iiint, and \iiiint which produce properly spaced double, triple, or quadruple integral signs. These commands automatically adjust spacing between adjacent integral symbols for consistent visual output.

If you need an integral with dotted intermediate signs use \idotsint. For iterated integrals where each integral has its own limits you can also chain single \int tokens; choose whichever gives better clarity for your expression.

Example of a double integral with combined limits:

\[ \iint_{D} f(x,y)\, \mathrm{d}A \]

Example of iterated integrals with separate bounds:

\[ \int_{a}^{b} \int_{c}^{d} f(x,y)\, \mathrm{d}y \,\mathrm{d}x \]

Limits, displaystyle, and forcing placement

By default, in display math limits on integrals (or sums/products) appear above and below the operator; in inline math they appear to the right as sub-/superscripts. To force display-style limits in inline math use \displaystyle or attach \limits to the operator.

Example showing forced display style in inline text:

The integral \( \displaystyle \int_{0}^{1} x^2 \, \mathrm{d}x \) converges to …

While forcing display style is useful for clarity, overuse in flowing paragraphs can break line spacing. Reserve forced display settings for short, critical inline expressions that must show full limits clearly.

Packages and tools that improve integral typography

Essential packages

amsmath is the standard package for extended math features; it offers improved alignment, additional math operators, and the multiple-integral commands. Always load it early in your preamble for robust math typesetting.

Other helpful packages:

mathtools — builds on amsmath adding fixes and convenience macros for spacing and tagged equations.
bigints — when you need visually larger integral symbols (for aesthetic reasons or poster-size math), this package lets you scale integral signs without manual fiddling.
diffcoeff — provides advanced macros for consistent differential notation and higher-order derivatives.

These packages let you maintain consistent styling across documents and solve many small typesetting headaches in one place.

Step-by-step examples and patterns

1) Simple definite integral (clean, semantic)

Code:

\documentclass{article} \\ \usepackage{amsmath} \\ \newcommand{\dif}{\mathop{}\!\mathrm{d}} \\ \begin{document} \\ \[ \int_{0}^{\pi} x^2 \, \dif x = \frac{\pi^3}{3} \] \\ \end{document}

This pattern uses a macro for the differential and a thin space before it to produce correct spacing. The result is consistent and semantically correct across both inline and display modes.

2) Multiple integrals with region-specific limits

Code:

\[ \iint_{D} f(x,y)\, \dif A = \int_{x=a}^{b} \int_{y=g_1(x)}^{g_2(x)} f(x,y)\, \dif y \,\dif x \]

This example demonstrates combining the \iint form with iterated integrals; choose the one that best communicates the region of integration to the reader.

3) Line integrals and path differentials

For line integrals you can use upright differentials for path parameters as well: \int_{C} \mathbf{F}\cdot \mathrm{d}\mathbf{r} or define \dif \mathbf{r} macros for consistency. When vectors are present, use bold or arrow notation as your style requires.

Common mistakes and how to avoid them

Neglecting spacing before dx: Writing \int f(x) dx without spacing often looks cramped. Use \, or a differential macro to separate integrand and differential correctly.
Italicizing the differential: Using plain dx leaves the d italicized which may confuse readers. Prefer \mathrm{d}x or a macro that enforces upright d.
Misusing \limits in text: Forcing limits in inline math can disrupt line spacing; prefer \displaystyle or move the integral into display math if large limits are needed.
Over-scaling integral signs: Using oversized integrals can look disproportionate; choose packages like bigints cautiously and test printing at actual size.
Inconsistent macro definitions: Defining multiple differential macros with different behavior will produce inconsistent documents; define once and reuse.

Addressing these mistakes upfront prevents tedious late-stage edits when preparing submissions or printed materials.

Pro Tips

Define a universal differential macro: Create a single macro such as \newcommand{\dif}{\mathop{}\!\mathrm{d}} in your preamble and use it everywhere to keep spacing and styling consistent. Changing this macro adjusts all differentials across the document instantly.
Keep inline math short: If an integral includes large limits or long expressions, use display math to preserve readability rather than forcing display style in inline text.
Use mathtools and amsmath together: Load mathtools after amsmath for small improvements and bug fixes. Mathtools also offers handy extensible symbols and spacing utilities.
Test on target output: Always compile and inspect the PDF at final page size. What looks fine on a screen can shift at print resolution or when converted to publisher templates.
Use semantic markup for variables: When authorship or coauthoring is involved, use named macros for frequently used integrands (e.g., \newcommand{\kernel}{K(x,y)}) to make collaborative edits safer and consistent.

These pro tips are practical habits that save time and maintain document quality across versions and collaborators.

Frequently Asked Questions

Should I always use \mathrm{d}x instead of dx?

Prefer \mathrm{d}x or a macro that uses it because it clarifies the d is an operator rather than a variable. Many publishers and style guides suggest upright differentials for this reason. If your target journal has a style guide, follow that, but use upright d by default for clarity.

When are \iint and chained \int\int different?

Functionally both approaches can show the same mathematical object. The dedicated multiple-integral commands provided by amsmath handle spacing between symbols automatically and are preferable for compact notation, while chained \int forms are useful when each integral has separate explicit limits.

How do I make integrals look good in inline text?

Keep inline integrals short, use \, before \mathrm{d}x, and avoid forcing large display-style operators in flowing paragraphs. If the expression is complex, place it in display mode for improved legibility rather than squeezing it inline.

Which packages are essential?

Start with amsmath for robust math features, add mathtools for improvements, and consider diffcoeff or bigints for specific needs related to differentials or symbol sizing. Avoid gratuitous packages that change global math behavior unless you need their features.

Troubleshooting and advanced tips

If you discover inconsistent spacing or unexpected symbol shapes, compile a minimal working example that isolates the issue. Often conflicts arise from package load order or from class-specific redefinitions. Use the minimal example to test alternative package orders or to remove packages until the issue disappears; this helps pinpoint the cause.

For typesetting complex integrals in presentations, choose larger fonts or scale only the integral sign with packages like bigints, but always preview slides at presentation size: what works in a PDF may be illegible on a projector if you do not check scale.

Summary checklist before submission

Ensure \usepackage{amsmath} (and mathtools if needed) is in the preamble.
Define and use a consistent differential macro such as \dif to guarantee spacing and upright d.
Use \iint, \iiint, etc., for multiple integrals when appropriate; use chained integrals when each has distinct limits.
Place complex integrals in display math and avoid forcing display mode in many inline expressions.
Compile and proof the final PDF at publication size and test any special packages for compatibility.

Conclusion

Typesetting integrals in LaTeX is straightforward once you adopt a few consistent habits: load amsmath, use upright differentials (preferably via a macro), insert a thin space before the differential, and choose the appropriate integral command (\int, \iint, etc.) for clarity. Leverage mathtools and other small utility packages when you need enhanced control, and always proof at the actual output size. These practices will produce mathematically clear, publication-ready integrals that improve readability and communicate your mathematics precisely.