Question

Evaluate \( \int \frac{dx}{\cos 2x + \sin^2 x} \)

• A. \( \sin x + c \)
• B. \( \tan x + c \)
• C. \( \sec^2 x + c \)
• D. \( \cos x + c \)

Hint:

For integrals involving trigonometric functions, use trigonometric identities and substitution to simplify the integrand.

Answer 1

The Correct Option is B

Step 1: Simplify the integrand.
The integrand can be simplified by recognizing that \( \cos 2x + \sin^2 x \) can be rewritten using trigonometric identities.
Step 2: Use substitution.
Substitute and simplify the integral, then apply the standard integral formula to get the result \( \tan x + c \).
Step 3: Conclusion.
The correct answer is (B) \( \tan x + c \).