Solving Difficult Integrals with WolframAlpha

[Ry122]

How did wolframalpha get this solution?

Is it necessary to use the quotient rule and the product rule together?
If so, in which order do i apply them?

http://www.wolframalpha.com/input/?i=integral+1%2F%28x*sqrt%281-x^2%29%29

 

[Hootenanny]

How did wolframalpha get this solution?

Is it necessary to use the quotient rule and the product rule together?
If so, in which order do i apply them?

http://www.wolframalpha.com/input/?i=integral+1%2F%28x*sqrt%281-x^2%29%29

If you notice, there is a show steps link on the right hand side, just below the entry text box.