1. The problem is to find the integral of the function $\sec^2(x)$. 2. Recall that the derivative of $\tan(x)$ is $\sec^2(x)$, so the antiderivative (integral) of $\sec^2(x)$ is $\tan(x)$. 3. Therefore, the integral is given by: $$\int \sec^2(x) \, dx = \tan(x) + C$$ where $C$ is the constant of integration.