Derivative function as a periodic function but primitive function not periodic one

Hi,

I have a problem to figure out an example of primitive (antiderivative) function (as much simple as possible) which is NOT periodic function that is f(x+T)!=f(x) (where T is a period)

but it's derivative IS a periodic one.

I can proof the opposite case (use definition of derivative) if f(x) is periodic then it's derivative is also periodic, but according to a book which I'm studing now,

the opposite direction need not be true.

Thanks for help,

jeel

Re: Derivative function as a periodic function but primitive function not periodic on

Re: Derivative function as a periodic function but primitive function not periodic on

Thanks, sometimes the simplest things are the hardest to grasp, of course definitely this is such kind of a function.

emakarov, thank you very much !!!