Antiderivative of $\frac {dy}{dx}$

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This is probably a very simple question, but I think its interesting.

What I would think, based on my intuition (which I think is correct in this case) is that $$\int \frac {dy}{dx}=y$$ However, to me it doesn't seem like there is something you are "integrating with respect to", meaning $$\int \frac {dy}{dx}(?)$$

doesn't have an extra d(something) tacked on to the end, like most other antiderivatives do.

If you tried to make the "dy" the thing you "tacked on", then it would become $$\int \frac 1{dx}dy$$ Which doesn't make any sense to me at all.

So, my question is, if you were trying to solve this without simply recognizing that the antiderivative of a derivative is just the function itself, then how would you solve it?

Apologies for this question being very vague.

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Yes, you have to find an antiderivative with respect to something.

Since it is unspecified, the antiderivative of $\;\frac{\mathrm d y}{\mathrm d x}\;$ will implicitly be made with respect to the same variable of derivation. $x$.

$$\int \dfrac{\mathrm d y}{\mathrm d x}\mathrm d x = y+c$$

What else can you do?