Question

The antiderivative of $\dfrac{1}{x\sqrt{x^2-1}},\; x>1$ with respect to $x$ is

• A. $\sin^{-1}x + C$
• B. $\cos^{-1}x + C$
• C. $\sec^{-1}x + C$
• D. $\cot^{-1}x + C$

Hint:

Remember the important identity: $\dfrac{d}{dx}(\sec^{-1}x) = \dfrac{1}{x\sqrt{x^2-1}}$ for $x>1$.

Answer 1

The Correct Option is C