When doing differentiation, I know that if $f$ is a function on $x$, then
$ { d \over dx } f^2 = 2 f {df \over dx} $
so the opposite in integration is also clear:
$ \int 2 f { df \over dx } dx = f^2 $
I also know that
$ \int x^2 dx = { x^3 \over 3} $
But I'm not sure as to how I can evaluate:
$ \int f^2 dx $
I mean is there any identity for this? That the above is equal to another function of $f$ (such as $f^3 \over 3$ times something)? Is there any method to find this? I googled some but perhaps I wasn't using proper search terms so I didn't get any clear results so I'm asking here. [I hope my question is clear enough :-(]