How do we get Mathematica to express generally what substitution has been employed in obtaining DSolve outputs?
e.g.for solving particular:
$ \int \sqrt {\sin^{-1} {\sqrt x }}dx $
EDIT1:
Context is when sometimes I am unable to readily find a substitution and Mathematica turns up a full solution based on a substitution( when it exists).. naturally I like to know my error or what I missed out by consulting the best text-book answer for the correct substitution from Mathematica. When DSolve does not give anything at least the failing learning student has a consolation... Look! even Mathematica has nothing in closed form!
EDIT2:
It is an essential part of mathematical communication.Suppose I succeed integrating with a correct substitution (or an integrating factor etc.) and my friend tried it but could not, and on being informed he would like "Hey, how did you get it?" Then I cannot show him only the answer. It appears to me that the how part is also important. But I guess there could be difficulties in its implementation.
DSolve,Integrate, etc.---ones that do not conform to basic "textbook" methods. I don't think you can easily display Mathematica's derivations, nor do I think most would be valuable to you, even if you could. Why do you want to know the "substitution" (assuming there was one)? – David G. Stork Mar 17 '15 at 11:33