Question

Evaluate the integral:
\[ \int \frac{dx}{x \sqrt{4x^2 - 9}} \]

• A. \( \frac{2}{3} \log \left( \left| x + 3 \right| \right) + c \)
• B. \( \frac{4}{3} \tan^{-1} \left( \frac{\sqrt{4x^2 - 9}}{3} \right) + c \)
• C. \( \frac{2}{3} \log \left( \left| x + 3 \right| \right) + c \)
• D. \( \frac{1}{3} \tan^{-1} \left( \frac{\sqrt{4x^2 - 9}}{3} \right) + c \)

Hint:

When dealing with square roots in integrals, recognize forms that suggest trigonometric substitution or use identities that can simplify the expression.

Answer 1

The Correct Option is D