How do I solve the integral of √(1/x - 1)?

eoghan · Jan 21, 2014

Hi all!
I'm trying to solve the Schrödinger equation for a fusion process. I came up with this integral
[tex] \int dx\sqrt{\frac{1}{x}-1}[/tex]
I can't see how to solve it... can you please give me an hint?

Thank you

eoghan · Jan 21, 2014

Ok... I applied the integration by part and now I have
[tex] \int dx\frac{1}{x\sqrt{x-1}}[/tex]
I know that the result is proportional to [itex]atan(\sqrt{x-1})[/itex] and this is also correct by a physical point of view. The problem is how to prove that the integral is proportional to the arctangent...

eoghan · Jan 21, 2014

Ok... I got it! I made the substitution [itex]y=\sqrt{x-1}[/itex] and I finally solved the integral

phyzguy · Jan 21, 2014

Glad we could help!

How do I solve the integral of √(1/x - 1)?

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