Integral (∫) in LaTeX
\int produces the integral sign. Limits of integration attach as a subscript (lower) and superscript (upper), and a thin space \, separates the integrand from dx.
LaTeX command
\intNot the symbol you meant? Draw it to find the command →
Write a definite integral as \int_a^b f(x)\,dx and an indefinite one as \int f(x)\,dx. Attach the bounds with _ and ^, bracing any multi-character limit: \int_{-\infty}^{\infty}. Always insert \, (or an upright \mathrm{d}) before the differential so the integrand and dx do not run together.
By default the limits sit to the side of the sign, even in a displayed equation; this is standard for integrals. If you truly want them stacked above and below, force it with \int\limits_a^b. In inline math the sign is drawn small; \displaystyle\int enlarges it to full display size within a line.
For higher dimensions use \iint and \iiint (double and triple), which keep the correct spacing between signs, and \oint for a contour integral, commonly \oint_C. Surface and volume circle integrals \oiint and \oiiint need the esint package in a full LaTeX document.
Other forms
\iintdouble (∬)\iiinttriple (∭)\ointcontour (∮)Examples
$\int_a^b f(x)\,dx$a definite integral with limits
$\int_0^\infty e^{-x}\,dx = 1$an improper integral
$\int f(x)\,dx = F(x) + C$an indefinite integral
$\iint_D f(x,y)\,dA$a double integral over a region
$\oint_C \mathbf{F} \cdot d\mathbf{r}$a contour integral
Tips and common mistakes
- Attach limits with _ and ^:
\int_0^1. Brace multi-character limits, e.g.\int_{-\infty}^{\infty}. - Put a thin space
\,(or\mathrm{d}) before the differential:\intf(x)\,dx. - Integral limits sit beside the sign by default; force stacking with
\int\limits_a^b. - Inline, the sign is small; use
\displaystyle\intfor the full-size sign within a line. - Use
\iint,\iiintand\ointfor multiple and contour integrals;\oiint/\oiiintneed esint in LaTeX. - For an evaluation bar use
\left. F(x)\right|_a^b so the bar sizes correctly.
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Convert your maths to LaTeX →FAQ
How do I add limits to an integral in LaTeX?
Use subscript and superscript on \int: . Brace multi-character limits, e.g. \int_{0}^{\infty}.
Why is my integral sign small and the limits beside it?
That is inline math. In a displayed equation () the sign is larger; you can also force display size inline with \displaystyle\int.
How do I write a double or contour integral?
Use \iint and \iiint for double and triple integrals, and \oint for a contour integral. They take limits the same way as \int.
How do I space dx from the integrand?
Put \, before it: \int f(x)\,dx. Some styles also set the differential upright with \mathrm{d}x.