Integrating $dS/S = \mu dt$ between time $0$ and time $T$ we get $S_T = S_0e^{\mu T}$, for $S_0$ and $S_T$ stock prices at time $0$ and $T$.
I'm trying to figure out how they came to this conclusion.
So if I do $\int_o^{T} dS/S$ I get $\ln (T) + C$ and integrating $\int_0^{T}\mu dt$ I get $\mu T + C$. Setting them equal to each other and raising $e$ to both sides I get $T = e^{\mu T}$. Finance notation notwithstanding, did I do something wrong in my calculations?