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How do I evaluate [math]\int \frac{\sec x}{1+\csc x} dx[/math]?
I see, and then you can use partial fractions to evaluate the integral, right?
Yes, that's correct. Using partial fractions and simplifying, we get [math]\int \frac{\sec x}{1+\csc x} dx = 2\ln | \sqrt{3} \tan \frac{x}{2} + 2| + C[/math], where C is the constant of integration.