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How do I evaluate [math]\int \frac{\sec x}{1+\csc x} dx[/math]?
Okay, I see. After making that substitution, how do I rewrite the secant term?
You can use the identity [math]\sec x = \frac{1}{\cos x}[/math] and the fact that [math](\sin x + 1)^2 = \sin^2 x + 2\sin x + 1 = \cos^2 x + 2\sin x + 2[/math] to rewrite the secant term as [math]\frac{2}{\cos x (\sin x + 1)}[/math].