Question

If \[ \int \frac{\sin x + \cos x}{\sqrt{1 + 2 \sin x \cos x}} \, dx = \varphi(x) + C, \text{ then } \varphi(x) = \]

• A. \( \log x \)
• B. \( x \)
• C. \( \log (\sin x + \cos x) \)
• D. \( \log \sin (\cos x) \)

Hint:

For integrals involving trigonometric functions, try using standard trigonometric identities and substitution to simplify the integral before solving.

Answer 1

The Correct Option is B