Question Detail

This integral can be solved using a u-substitution. There are two common approaches:

1. Let u = tan x. Then du = sec² x dx. The integral becomes ∫u du = u²/2 + C = (tan² x)/2 + C.
2. Let u = sec x. Then du = sec x tan x dx. Rewrite the integral as ∫sec x (sec x tan x dx). This becomes ∫u du = u²/2 + C = (sec² x)/2 + C.

Both (tan² x)/2 and (sec² x)/2 are valid antiderivatives because they differ only by a constant (since sec²x = tan²x + 1, then (sec²x)/2 = (tan²x+1)/2 = (tan²x)/2 + 1/2). Option B, (1/2)sec² x, is available and correct.