My Math Forum Integration of 1/sqrt(1/x + c)

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 August 1st, 2017, 01:21 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, 02:27 AM #2 Global Moderator   Joined: Dec 2006 Posts: 18,037 Thanks: 1394 For c > 0, try substituting $cx = \sinh^2\!u$.

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