Question Detail
Question
Obtain ∫sec x dx
Correct Answer
Option C is the correct answer.
Detailed Explanation
The integral of sec x is a standard result in calculus.∫sec x dx = ln|sec x + tan x| + CTo verify this, one can differentiate ln|sec x + tan x|:d/dx [ln|sec x + tan x|] = (1 / (sec x + tan x)) * d/dx (sec x + tan x)= (1 / (sec x + tan x)) * (sec x tan x + sec² x)= (1 / (sec x + tan x)) * (sec x (tan x + sec x))= sec xThus, the integral of sec x is ln|sec x + tan x| + C.
Hint
This is a fundamental integral that should be memorized or derived. Recall how multiplying by (sec x + tan x) / (sec x + tan x) can simplify the integral for substitution, leading to a logarithmic form.