Topic: Engineering Mathematics
$\int\frac{dx}{x\sqrt{x^{2}-a^{2}}}$ is
- A. $\frac{1}{a}\text{cosec}^{-1}(\frac{x}{a})$
- B. $\frac{1}{a}\sin^{-1}(\frac{x}{a})$
- C. $\frac{1}{a}\cos^{-1}(\frac{x}{a})$
- D. $\frac{1}{a}\sec^{-1}(\frac{x}{a})$
Answer: D. $\frac{1}{a}\sec^{-1}(\frac{x}{a})$
Explanation: By standard integration formulas, the integral of $\frac{1}{x\sqrt{x^{2}-a^{2}}}$ with respect to $x$ is equal to $\frac{1}{a}\sec^{-1}(\frac{x}{a})$.