How can software such as Wolfram Mathematica to be able to calculate integrals like \int_0^1\frac{\arctan x}{x \sqrt{1-x^2}} \text{d}x = \frac{\pi}{2} \log\left(1+\sqrt{2}\right)?
I know many ways to calculate it manually, but none of them even remotely algoritmizzabile. Some idea? Thank you!