August 1st, 2017, 02:21 AM  #1 
Newbie Joined: Aug 2017 From: Birmingham Posts: 1 Thanks: 0  Integration of 1/sqrt(1/x + c)
$\displaystyle \int \frac{1}{\sqrt{\frac{1}{x} + c}} \text{ d}x$ Where c is a constant. I've tried integration by substitution but I'm basically failing  I can see it's probably going to end up being trigonometric in some way but can't figure it out. Any advice greatly appreciated! 
August 1st, 2017, 03:27 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,243 Thanks: 1439 
For c > 0, try substituting $cx = \sinh^2\!u$.


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1 or sqrt1 or x, integration 
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