Question

The integral \( \int \frac{dx}{\cos x + \sqrt{5} \sin x} \) equals

• A. \( \frac{1}{2} \log \left( \frac{1 + \cos x}{\sin x} \right) + C \)
• B. \( \frac{1}{2} \log \left( \frac{1}{\cos x} \right) + C \)
• C. \( \int \frac{1}{\cos^2 x} dx \)
• D. \( \frac{1}{2} \log \left( \cos x + \frac{1}{5} \right) + C \)

Hint:

Use trigonometric substitution and simplifications to solve integrals involving sine and cosine functions.

Answer 1

The Correct Option is A

Use substitution methods to solve the integral and simplify it.