Tricky integral?

[Grand]

Homework Statement

Could anyone show me how integral (5) in this document is calculated. I've been trying and trying but nothing good came out.

$$\theta=\frac{\rho}{R}\int\sqrt{\frac{R^2-r^2}{r^2-\rho^2}}\frac{dr}{r}=$$
$$=\arctan\left(\frac{R}{\rho}\sqrt{\frac{r^2-\rho^2}{R^2-r^2}\right)-\frac{\rho}{R}\arctan\sqrt{\frac{r^2-\rho^2}{R^2-r^2}$$

Thank you in advance.

Homework Equations

The Attempt at a Solution

 

[dextercioby]

Hi, the article is not free to view. Please, write the integral yourself, or post a screenshot from the article containing it.

 

[Grand]

Thank you, fixd it.