Integration of chemical potential

I want to ask a question about chemical potential, $mu$.

I dislike the use of integrals to describe quantities in thermodynamics. If we observe the definition of chemical potential for constant pressure:

$$mu_i = left(frac{partial G}{partial N_i} right)_{T, P, N_i neq N_j}$$

which I can understand to mean the change in Gibbs free energy G for a small change caused by the number of molecules of species i.

However, using some high school mathematics, I wondered if the following interpretation was valid.

If we consider that if $N_i = 0$, $G = 0$ and logically if $N_i = N_i$, $G = G_i$, integration by separation of variables will yield:

$$partial G = mu_i times partial N_i$$
$$int_{0}^{G_i} partial G = mu_iint_{0}^{N_i}partial N_i$$

such that

$$G = mu_i times N_i$$

and hence

$$mu_i = frac{G}{N_i}$$
where the chemical potential of a species $mu_i$ can better be expressed as the Gibbs free energy of a species $G$ divided by the amount of substance $N_i$.

Is this a more reasonable yet valid understanding of the chemical potential?

EDIT a similar equation is derived in [1].

[1] Chen, L. (2019). Chemical potential and Gibbs free energy. MRS Bulletin, 44(7), 520-523. doi:10.1557/mrs.2019.162