Question

The value of the integral \( \int_{\frac{\pi}{24}}^{\frac{5\pi}{24}} \frac{dx}{1 + \sqrt[3]{\tan 2x}} \) is :

• A. \( \frac{\pi}{6} \)
• B. \( \frac{\pi}{18} \)
• C. \( \frac{\pi}{12} \)
• D. \( \frac{\pi}{3} \)

Hint:

For integrals of the form \( \frac{1}{1+\tan^n x} \) with limits \( a, b \), the answer is \( \frac{b-a}{2} \) if \( a+b = \pi/2 \).

Answer 1

The Correct Option is C