An integral symbol with a short horizontal bar in the middle (for instance, the "\strokedint" or "\intbar" commands)
https://de.wikipedia.org/wiki/Integralzeichen for the unicode symbols.
Technically this will be easy to implement. However, I'm not sure if there is really a demand. I created https://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Mathematics#Missing_macros_in_.3Cmath_.2F.3E_environment to start a discussion.
ok. I'm going to add
⨍ U+2A0D finite part integral Integral mit endlichem Teil ⨍ ⨍ \dashint
⨎ U+2A0E integral with double stroke Integral mit Doppelstrich ⨎ ⨎ \ddashint
unless there are any objections?