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We can solve this integral using a u-substitution.Let u = sec x.Then, the derivative of u with respect to x is du/dx = sec x tan x, so du = sec x tan x dx.The integral ∫sec² x tan x dx can be rewritten as ∫(sec x)(sec x tan x) dx.Substitute u and du into the integral:∫u du = u²/2 + CNow, substitute back u = sec x:= sec² x/2 + C = 1/2 sec² x + C. This matches option C.(Alternatively, if you let u = tan x, then du = sec² x dx. The integral becomes ∫u du = u²/2 + C = tan² x/2 + C. Since tan² x = sec² x - 1, this is (sec² x - 1)/2 + C = 1/2 sec² x - 1/2 + C. The constant -1/2 is absorbed into C, making both forms equivalent.)