Line integral with square arrowed path

Question

I know esint package can type line integral with square paths: $\sqint$, but today I need a square arrowed line integral. Does anyone know how to do it ?

Answer 1

A proposotoin with the \stackinset command from stackengine, \squint from esint and \Lsh from mathabx (without loading mathabx):

\documentclass{article}
\usepackage{amsmath, amssymb,}
\usepackage{nccmath}
\usepackage{esint}


\DeclareFontFamily{U}{mathb}{\hyphenchar\font45}
\DeclareFontShape{U}{mathb}{m}{n}{ <-6> mathb5 <6-7> mathb6 <7-8>
mathb7 <8-9> mathb8 <9-10> mathb9 <10-12> mathb10 <12-> mathb12 }{}
\DeclareSymbolFont{mathb}{U}{mathb}{m}{n}
%
\DeclareMathSymbol{\Lsh}{\mathrel}{mathb}{"E8}
\usepackage{xcolor} 
 \usepackage{stackengine} %
\newcommand{\mysqint}{\mathop{{\stackMath\stackinset{c}{0.03ex}{c}{0.235ex}{\scriptstyle\Lsh}{\sqint}}}}

\begin{document}

\[ I = \mysqint g(z)\,\mathrm d z \]

\end{document} 

Answer 2

Today I also found myself wanting a similar symbol, the difference being that I wanted the arrow to be on the vertical edge to the right of the square. I found two helpful post: this one, and this one. Making some tweaks to these, I arrived at the following solution, which was sufficient for my purposes:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage[margin=1.2in]{geometry}
\usepackage{amsfonts,amssymb,amsmath,amsthm}
\usepackage{mathabx}
\usepackage{enumerate}
\usepackage{lmodern}
\usepackage{physics} % Differentials
\usepackage{xcolor}  % Colors 
\usepackage{placeins} % FloatBarrier
\usepackage{array}
\usepackage{tikz-cd} % Commutative diagrams
\usetikzlibrary{matrix,arrows,backgrounds}
\usepackage{centernot}
\usepackage{graphicx}
\usepackage{caption}
\usepackage{hyperref}
\usepackage{nccmath}
\usepackage{esint}
% Approach 1:
% Contour integral with box and upward-pointing arrow. 
% Needs the package esint and nccmath
\newcommand{\boxintanticlockwise}{\mathop{\mathpalette\docircint\relax}! \sqint}
% Determine what to do based on where the symbol is beign used:
\newcommand{\docircint}[2]{%
  \ifx#1\displaystyle
    \displaycircint
  \else
    \normalcircint{#1}%
  \fi
}
% (Display style = Math on separate line) 
\newcommand{\displaycircint}{\scriptsize \boldsymbol{\wedge} \mkern-30.5mu}
% (Textstyle = Inline math)
\newcommand{\normalcircint}[1]{%
  \smallerc{#1}\ifx#1\textstyle\mkern-9mu\else\mkern-14.3mu\fi
}
\newcommand{\smallerc}[1]{%
  \vcenter{\hbox{$\ifx#1\textstyle\scriptstyle\else\scriptscriptstyle\fi\wedge$}}%
}
% Approach 2: 
% Source: https://tex.stackexchange.com/questions/237784/how-to-increase-the-arrow-size-on-oint
% Clockwise BIG (Display Style):
\newcommand{\scalefactor}{0.7}
\newcommand{\rotatefactor}{0}
\newcommand{\raiseamt}{0.07em}
\newcommand{\leftamt}{-1.287em}
\newcommand{\clockboxintegral}{%
\phantom{\int} \hspace{-1mm}
  \raisebox{\raiseamt}{%
    \rotatebox{\rotatefactor}{%
      \scalebox{\scalefactor}{(\lor)}%
    }%
  }%
\hspace{\leftamt}\sqint}
% Counterclockwise BIG (Display Style):
\newcommand{\scalefactorr}{0.7}
\newcommand{\rotatefactorr}{0}
\newcommand{\raiseamtt}{0.15em}
\newcommand{\leftamtt}{-1.287em}
\newcommand{\counterclockboxintegral}{%
\phantom{\int} \hspace{-1mm}
  \raisebox{\raiseamtt}{%
    \rotatebox{\rotatefactorr}{%
      \scalebox{\scalefactorr}{(\land)}%
    }%
  }%
\hspace{\leftamtt}\sqint}
% Clockwise SMALL (Inline Mode):
\newcommand{\scalefactorrr}{0.6}
\newcommand{\rotatefactorrr}{0}
\newcommand{\raiseamttt}{0.07em}
\newcommand{\leftamttt}{-0.965em}
\newcommand{\clockboxintegralinline}{%
  \raisebox{\raiseamttt}{%
    \rotatebox{\rotatefactorrr}{%
      \scalebox{\scalefactorrr}{(\lor)}%
    }%
  }%
\hspace{\leftamttt}\sqint}
\begin{document}
[\boxintanticlockwise]
[
  A+\ointctrclockwise\frac{\dd t}{\log t} \text{ vs. } A+\clockboxintegral\frac{\dd t}{\log t} \text{ vs. } A+\counterclockboxintegral\frac{\dd t}{\log t}
]
[
  \ointctrclockwise_{a}^{b} \text{ vs. } \clockboxintegral_{a}^{b} \text{ vs. } \counterclockboxintegral_{a}^{b}
]
[
  \frac{1}{2\pi}\ointctrclockwise_{\gamma} \text{ vs. } \frac{1}{2\pi}\clockboxintegral_{\gamma} \text{ vs. } \frac{1}{2\pi}\counterclockboxintegral_{\gamma}
]
[
  \frac{1}{2\pi}\ointctrclockwise_{X} \text{ vs. } \frac{1}{2\pi}\clockboxintegral_{X} \text{ vs. } \frac{1}{2\pi}\counterclockboxintegral_{X}
]
\noindent 
\textbf{Inline examples} \[1mm]
There is a size difference between the inline integrals (\int \hspace{1mm} \sqint ). \[2mm]
But this can more or less fixed : (\int) \scalebox{1.1}{(\sqint)}. \
Example: The integral \(\int f(x)\dd x\) is harder to compute than \scalebox{1.1}{\(\sqint\)}\hspace{0.5mm}\(f(x)\dd x\).' \\[2mm]The integrals (\int f(z)\dd z) and (\int_{\Gamma} f(z)\dd z)...'\[2mm]
The integrals \(\sqint f(z)\dd z\) and \(\sqint_{\Gamma} f(z)\dd z\)...' (\textbackslash sqint' is incapable of handlign the subscript (\Gamma) by default)\[2mm]
`The integral (\hspace{2mm}\clockboxintegralinline f(z)\dd z) describes a ...'
\end{document}

Output:

My apologies for not providing a minimal working example; I was not quite able to determine exactly which packages were needed to produce the given output.

I am also not sure how to make the inline version of this symbol play well with subscripts and the surrounding text.