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This integral can be solved using u-substitution.Let u = sec x. Then, the differential du = d/dx(sec x) dx = sec x tan x dx.However, the integrand is sec²x tan x. We can write it as sec x (sec x tan x) dx.So, if u = sec x, then du = sec x tan x dx, and the integral becomes ∫u du = u²/2 + C.Substituting back u = sec x, we get (sec²x)/2 + C.Alternatively, let u = tan x. Then, du = d/dx(tan x) dx = sec²x dx.In this case, the integral becomes ∫u du = u²/2 + C.Substituting back u = tan x, we get (tan²x)/2 + C.Since tan²x + 1 = sec²x, (tan²x)/2 = (sec²x - 1)/2 = (sec²x)/2 - 1/2. The constant of integration absorbs the -1/2.Option C, 1/2 sec²x, is equivalent to one of the valid forms (ignoring the constant of integration).