Does every function has anti derivative? - Answers

I would think so, but I am sitting here thinking and I can not think of any function that can not be integrated. * * * * * Whether or not a function can be integrated depends, in part, on the measure that is used on the space. This is getting into seriously heavy mathematics. and the following is only a flavour of what I remember from 35 years ago! Functions with asymptotic values in their domain cannot be integrated over that domain. For example, 1/x is defined everywhere except at x = 0 and so it cannot be integrated over any interval that contains x = 0. Otherwise it is ln(|x|) + c. Another example is that of a function which has infinitely many discontinuities. For example: f(x) = 1 if x is rational and f(x) = 0 if x is irrational over any arbitrary interval, is a perfectly well defined, indicator function. But under some measures, it cannot be integrated.