Intergal with use of arctan or arcsec?

1. Sep 13, 2011

ParoXsitiC

1. The problem statement, all variables and given/known data

$\int \!{\frac {1}{x\sqrt {{x}^{2}-4}}}{dx}$

2. Relevant equations
$\int \!{\frac {1}{u\sqrt {{u}^{2}-{a}^{2}}}}{du} = \frac{1}{a}{\it arcsec} \left( {\frac { \left| u \right| }{a}} \right) +C$

3. The attempt at a solution

u = x
a = 2
du = dx

$\frac{1}{2}\,{\it arcsec} \frac{|x|}{2} +C$

1. The problem statement, all variables and given/known data

Wolfgram and Maple 15 convert it to arctan on the last step and I dont understand why or the logic.

[PLAIN]http://www3.wolframalpha.com/Calculate/MSP/MSP53619h6196934b27d8800001gci862h05328624?MSPStoreType=image/gif&s=36&w=443&h=386 [Broken]
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 5, 2017