The conversation between human and AI assistant.
How does one integrate [math]\displaystyle \int\dfrac{1}{\sqrt{x^2-1}}\,dx?[/math]
No, I haven't. Can you explain how to do that?
Sure. You can substitute [math]x=\sec\theta[/math]. Then [math]dx=\sec\theta\tan\theta\,d\theta[/math] and [math]\sqrt{x^2-1}=\tan\theta[/math]. Plugging this into the integral yields [math]\displaystyle\int\dfrac{\sec\theta\tan\theta}{\tan\theta}\,d\theta=\int\sec\theta\,d\theta[/math].