Evaluate ∫(x^2-4)^(1/2) / x for x > 2
The Attempt at a Solution
I was able to solve this problem via substitution, and my answer is: (x^2-4)^(1/2) - 2arcsec(x/2) + C. However, when I put the question into Wolfram Alpha, it gets this answer: (x^2-4)^(1/2) + 2arctan(2/(x^2-4)^(1/2)) + C. When I ask Wolfam Alpha to show the steps to the solution, it's second to last step is exactly the same as my answer, and then it says "which is equivalent for restricted x values to:" and shows it's final answer as I just typed. I am confused about how those two answers are the same. It seems to be saying that 2arctan(2/(x^2-4)^(1/2)) and -2arcsec(x/2) are equivalent (+/- a constant as C could have changed). How is this so?
Link to Wolfram Alpha solution: http://www.wolframalpha.com/input/?i=integrate+(x^2-4)^(1/2)/xdx
Thank you very much for your help! :)