To integrate sec² x, we can use the basic integral formula. The integral of sec² x is a standard result in calculus.
The integral of sec² x with respect to x is:
∫ sec² x dx = tan x + C
Here, C represents the constant of integration. This result comes directly from the fact that the derivative of tan x is sec² x. Therefore, the antiderivative of sec² x is tan x plus a constant.
Let’s break it down:
1. **Identify the function to integrate**: In this case, it’s sec² x.
2. **Recall the standard integral**: The integral of sec² x is tan x + C.
3. **Write the final answer**: ∫ sec² x dx = tan x + C.
This is a straightforward integration problem that relies on knowing the basic integral formulas. If you encounter more complex integrals involving sec² x, you might need to use substitution or other integration techniques.