I would propose that all physicists should learn non-standard analysis, just for the sake of replying to pretentious mathematicians who mock physicists for using infinitesimals.
- You cannot take away a loved infinitesimal from physicists.
Physicists don't do any substitutions anyway. They solve integrals either by looking into a comprehensive math handbook such as Bronstein et al (especially if they are old enough), or put it into Mathematica.
- Half of them would immediately lose the ability to perform a correct substitution.