[SOLVED] Integral formulas

Hi MHF!

I need your help for some questions.

First, what is the method to find out that ? I find it stupid to learn it by heart. There are plenty of other formulas to know, so I would like to know how to recover them without learning all of them.

Second, I have to find in term of trigonometric or hyperbolic functions. Looking at my book, I found out that it is equal to . Which recalls me of an inverse of but cannot find exactly to what it's equal, so I'd appreciate help for this one.

And finally according to my book. But once again, how can I know it's worth an inverse of the sine function? I hope I don't have to learn this by heart.