Integrate 2secx

To integrate 2secx, also written as ∫2secx dx, we focus on the constant 2 and how it impacts the integration.

A constant can be brought outside of the integral sign to simplify the integration, and therefore the two expressions mean the same thing.

We use a standard proof from formula booklet, as shown above, and therefore ∫secx dx = ln|secx+tanx| + C.

Hence we substitute that into the equation and reintroduce the constant.

After simplifying, the answer is ∫2secx dx = 2ln|secx+tanx| + C.