Question

Evaluate $\int \frac{dx}{\sqrt{x^4-9x^2}};x>3$
(where $C$ is constant of integration)

• A. ${\sec }^{-1}\frac{x}{3}+C$
• B. $\frac{1}{2}{\sec }^{-1}\frac{x}{2}+C$
• C. $\frac{1}{3}{\sec }^{-1}\frac{x}{3}+C$
• D. ${\sec }^{-1}\frac{x}{2}+C$

Answer 1

The correct option is C $\frac{1}{3}{\sec }^{-1}\frac{x}{3}+C$

Let $I=\int \frac{dx}{\sqrt{x^4-9x^2}}$
$\Rightarrow I=\int \frac{dx}{x\sqrt{x^2-9}}=\frac{1}{3}{\sec }^{-1}\frac{x}{3}+C$