What ∫ sec⁰ x d x is equal to ?

• A: log(sec⁰ x) + tan⁰ x + c
• B: π log(tan(π/4) + π/2) + c
• C: 180° log(tan(π/4) + x²) / π + c
• D: 180° log(tan(π/4) + x/360°) / π + c

The integral of secant squared, ∫ sec² x dx, is a well-known result in calculus. It equals the tangent function plus a constant of integration. Therefore, the correct answer is:

Correct Answer

The integral can be expressed as:

tan(x) + C

Understanding the Options

• A: log(sec⁰ x) + tan⁰ x + c - This is not correct.
• B: π log(tan(π/4) + π/2) + c - This does not relate to the integral.
• C: 180° log(tan(π/4) + x²) / π + c - This is also incorrect.
• D: 180° log(tan(π/4) + x/360°) / π + c - This option is not valid.

In summary, the integral of sec² x is simply tan(x) plus a constant, which is not represented in the provided options.