Question

The integral \( \int e^{\sec x} \tan x \sec x \, dx \) is equal to

• A. \( e^{\tan x} + C \)
• B. \( e^{\sec x} + C \)
• C. \( e^{\sec x} \sec x + C \)
• D. \( e^{\sec x} \tan x + C \)

Hint:

When integrating expressions involving \( \sec x \) and \( \tan x \), substitution is often the key to simplifying the integral.

Answer 1

The Correct Option is B

The integral given is \( \int e^{\sec x} \tan x \sec x \, dx \). We can use the substitution \( u = \sec x \), which gives \( du = \sec x \tan x \, dx \). The integral then simplifies to: \[ \int e^{u} \, du = e^{u} + C \] Substituting back \( u = \sec x \), we get: \[ e^{\sec x} + C \]