Question

Evaluate the integral: \[ \int \sec x \, dx \] The correct answer is:

• A. \(\log \left| \sec x + \tan x \right| + c\)
• B. \(\log \left| \sec x - \tan x \right| + c\)
• C. \(\log \left| \sec x \right| + c\)
• D. \(\tan x + c\)

Hint:

For the integral of \(\sec x\), the result is \(\log \left| \sec x + \tan x \right| + c\).

Answer 1

The Correct Option is A

The integral of \(\sec x\) is a standard result: \[ \int \sec x \, dx = \log \left| \sec x + \tan x \right| + c. \] To verify, use the fact that: \[ \frac{d}{dx} \left( \log \left| \sec x + \tan x \right| \right) = \sec x. \] Thus, the correct answer is \( (A) \).