for the integral \int 2x ~\text{dx} = x^2 + C, what exactly is that C symbol?

Hey pigbodine, thanks for the question. Have you taken calculus yet? When learning (indefinite) integration, the meaning of C is one of the first topics you learn. The basic idea is that x^2 + C is not one function, but a *family* of functions, i.e., the indefinite integral doesnâ€™t produce a single output but an *infinity* of outputs (since the number C can be any real number). Does that make some sense?

that makes sense to me. thanks! :)