Question

\[ \int_{\log \sqrt{n}}^{\log \sqrt{r}} 2x \sec^2\left( \frac{1}{3} \cdot 2x \right) \, dx \] is equal to:

• A. \( \sqrt{3} \)
• B. \( \frac{1}{\sqrt{3}} \)
• C. \( \frac{3\sqrt{3}}{2} \)
• D. None of these

Hint:

Use substitution to simplify integrals involving trigonometric functions like \( \sec^2(x) \).

Answer 1

The Correct Option is A

By solving the integral using the substitution method and simplifying the expression, we obtain the result \( \sqrt{3} \).