# Help with an integral

1. Jan 21, 2014

### eoghan

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

Thank you

2. Jan 21, 2014

### eoghan

Ok... I applied the integration by part and now I have
$$\int dx\frac{1}{x\sqrt{x-1}}$$
I know that the result is proportional to $atan(\sqrt{x-1})$ 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....

3. Jan 21, 2014

### eoghan

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

4. Jan 21, 2014