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August 1st, 2017, 01:21 AM   #1
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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!
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August 1st, 2017, 02:27 AM   #2
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For c > 0, try substituting $cx = \sinh^2\!u$.
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