The conversation between human and AI assistant.
How do I evaluate [math]\int \frac{\sec x}{1+\csc x} dx[/math]?
Yes, please.
Okay, we can start by using the identity [math]\cos^2 x = \frac{1}{1 + \tan^2 x}[/math] to rewrite the denominator as [math]\frac{\sin x + \cos x}{\cos x \sqrt{1 + \tan^2 x}}[/math]. Then, substitute [math]v = \tan \frac{x}{2}[/math] to obtain [math]\int \frac{4dv}{3v^2 + 1}[/math].