To integrate the function $\sec^2(x)$, we can use the established formula:

where $C$ represents the constant of integration.

To understand this formula, we start with the derivative of $\tan(x)$:

By integrating both sides with respect to $x$, we arrive at:

Thus, to find the integral of $\sec^2(x)$, simply apply the formula and include the constant of integration:

For instance, if we want to compute the integral of $\sec^2(3x)$, we can use the formula as follows:

It’s important to note that this formula specifically applies to $\sec^2(x)$ and does not extend to other powers of $\sec(x)$. For integrating different powers of $\sec(x)$, alternative techniques must be employed.