The Principal Value Integral symbol

This symbol (an integral sign, “crossed”) does not appear in any of the fonts ordinarily available to $\LaTeX$ users, but it can be created by use of the following macros:

\def\Xint#1{\mathchoice
   {\XXint\displaystyle\textstyle{#1}}%
   {\XXint\textstyle\scriptstyle{#1}}%
   {\XXint\scriptstyle\scriptscriptstyle{#1}}%
   {\XXint\scriptscriptstyle\scriptscriptstyle{#1}}%
   \!\int}
\def\XXint#1#2#3{{\setbox0=\hbox{$#1{#2#3}{\int}$}
     \vcenter{\hbox{$#2#3$}}\kern-.5\wd0}}
\def\ddashint{\Xint=}
\def\dashint{\Xint-}

\dashint gives a single-dashed integral sign, \ddashint a double-dashed one.

Source: The Principal Value Integral symbol