My question concerns the notation that is used to describe Geometric Brownian motion. I don't know the theory of stochastic differential equations, currently reading Hull on Options, Futures and Derivatives (that's how I came across Geometric Brownian motion).
The process that I am interested in is the evolution of a stock price, given by
$$
\frac{dS}{S} = \mu dt + \sigma \epsilon \sqrt{dt}
$$
where $S$ denotes the stock price, $\mu$ and $\sigma$ are constants. Now if I want to integrate this equation then I get
$$
\ln S = \mu t + \sigma \int \sqrt{dt} + C
$$
where $C$ is the constant of integration. How do I perform the integral in the middle ? I am not sure how to deal with the square-root of a measure, so far I've learned about the Riemann integral and the basics of Lebesgue integration. Any hints or reference to (not too terse) textbooks in case the topic is too broad to cover here would be super helpful, thanks a lot !