What are the LaTeX codes for clockwise and counter-clockwise integrals (∱ and ⨑)?

Question

If you do know, which package do I need to use? Thanks.

Answer 1

With the MnSymbol package, you could use the following symbols:

\documentclass{article}

\usepackage{MnSymbol}

\begin{document}

\[
\rcirclerightint
\lcirclerightint
\rcircleleftint
\lcircleleftint
\]

\end{document}

(other package might know these symbols as \ointclockwise and \ointctrclockwise)

---

If you only want half a circle, you can use the mathdesign package:

\documentclass{article}

\usepackage[charter]{mathdesign}

\begin{document}

\[
\intclockwise
\]

\end{document}

Answer 2

\documentclass{standalone}
\usepackage{array,esint}
\def\CMD#1{%
   $ \csname#1\endcsname \displaystyle\csname#1\endcsname $ & \texttt{\textbackslash#1} &}

\begin{document}
\def\arraystretch{2}
\begin{tabular}{@{}*{2}{r@{\kern3pt}l}r@{\kern3pt}l@{}l@{}}
\CMD{int}   \CMD{iint}     \CMD{iiintop} \\
\CMD{iiiintop}\CMD{dotsintop}\CMD{ointop}  \\
\CMD{oiint}   \CMD{sqint}    \CMD{sqiint} \\
\CMD{ointctrclockwise} \CMD{ointclockwise} \CMD{varointclockwise} \\
\CMD{varointctrclockwise} \CMD{fint} \CMD{varoiint}\\
\CMD{landupint} \CMD{landdownint}
\end{tabular}
\end{document}

Answer 3

Although some of the symbols in esint come very close, I don't believe there is any package (for pdfLaTeX) that provides a version of this symbol compatible with the computer modern maths font.

The following is a (very simple) adaption of this answer by Heiko Oberdiek. It can be used to superimpose any symbol on top of an integral sign.

\documentclass{article}

\usepackage{graphicx} %% <- for \resizebox and \rotatebox
\usepackage{amsmath}
\usepackage{amssymb} %% <- for \curverightarrow, \curveleftarrow

\makeatletter %% <- make @ usable in macro names

\let\DOTSI\relax % amsmath support for \dots
\newcommand*{\letteronint}[1]{%
  \DOTSI
  \mathop{%
    \mathpalette\@LetterOnInt{#1}%
  }%
  \mkern-\thinmuskip % thin space is inserted between two \mathop
  \int
}
\newcommand*{\@LetterOnInt}[2]{%
  \sbox0{$#1\int\m@th$}%
  \sbox2{$%
    \ifx#1\displaystyle
      \textstyle
    \else
      \scriptscriptstyle
    \fi
    #2%
  \m@th$}%
  \dimen@=.4\dimexpr\ht0+\dp0\relax
  \ifdim\dimexpr\ht2+\dp2\relax>\dimen@
    \sbox2{\resizebox*{!}{\dimen@}{\unhcopy2}}%
  \fi
  \dimen@=\wd0 %
  \ifdim\wd2>\dimen@
    \dimen@=\wd2 %
  \fi
  \rlap{\hbox to \dimen@{\hfil
    $#1\vcenter{\copy2}\m@th$%
  \hfil}}%
  \ifdim\dimen@>\wd0 %
    \kern.5\dimexpr\dimen@-\wd0\relax
  \fi
}

%% Define arrow curving downwards:
\newcommand*{\curvearrowbotright}{\mathpalette\rotmath@internal\curvearrowleft}
\newcommand*\rotmath@internal[2]{\rotatebox{180}{$\m@th#1#2$}}

\makeatother %% <- revert @

\newcommand*{\intcw}{\letteronint{\mspace{3mu}\curvearrowright}}
\newcommand*{\intccw}{\letteronint{\mspace{3mu}\curvearrowbotright}}


\begin{document}

\[
  \displaystyle      \intcw_a^b f \dots \intccw_a^b f \qquad
  \textstyle         \intcw_a^b f \dots \intccw_a^b f \qquad
  \scriptstyle       \intcw_a^b f \dots \intccw_a^b f \qquad
  \scriptscriptstyle \intcw_a^b f \dots \intccw_a^b f
\]

\end{document}

The \scriptscriptstyle version does not look good, but you probably won't want to use this symbol at that scale.

Answer 4

\documentclass[varwidth, preview]{standalone}
\usepackage{unicode-math}

\begin{document}
\( \intclockwise \awint \)
\end{document}

The symbols are also in a number of legacy NFSS packages, including: fdsymbol, newpxmath, newtxmath, pxfonts, txfonts, stix and stix2. Some also support other aliases, but all have been updated to understand \intclockwise and \awint.

Some of these also include variants, such as \intclockwiseup and \smallintclockwise in stix. These are available in unicode-math as stylistic variants in some math fonts.

See “The Comptehensive LaTeX Symbol List” and “Every symbol (most symbols) defined by unicode-math.”