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 $cx = \sinh^2\!u$.


Tags 
1 or sqrt1 or x, integration 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Integration (x^3)/sqrt(1x^2)  boneraw  Calculus  2  September 26th, 2012 12:33 PM 
integration of dx/sqrt(1k*sin[x])  yaakovf  Calculus  5  April 3rd, 2010 03:13 PM 
is this integration of sqrt(f(x)) correct?  questioner1  Calculus  3  March 27th, 2010 11:08 PM 
integration of sqrt.(x^2+a^2)  3hlang  Calculus  5  July 27th, 2009 09:11 AM 
integration: (sqrt tan x)  ~{FSM}~  Calculus  1  May 22nd, 2008 10:29 AM 