Question

\( \int e^x \sec x (1+\tan x) dx = \)

• A. \( e^x \sec^2 x + C \)
• B. \( e^x \tan x + C \)
• C. \( e^x \sec x + C \)
• D. \( e^x \tan^2 x + C \)
• E. \( e^x \sec x \tan x + C \)

Hint:

Always check if integrand matches derivative of a product.

Answer 1

The Correct Option is C

Concept: Recognize derivative form.

Step 1: Differentiate \( e^x \sec x \).
\[ \frac{d}{dx}(e^x \sec x) = e^x \sec x + e^x \sec x \tan x \] \[ = e^x \sec x (1+\tan x) \]

Step 2: Match integrand.
\[ \int e^x \sec x (1+\tan x)dx = e^x \sec x + C \]