I'm not sure what "integration" you're talking about. All you need is the distance from your test particle to each object in the galaxy and the approximate mass of each object. I think you could simplify it to a single central black hole 5% to 10% of the total mass, and the rest solar-sized masses. Let the computer add up the resultant accelerations....

This "infinite gravity" is obviously an error.

__________________
Everyone is entitled to his own opinion, but not his own facts.