Now, the concepts of differenencials, splitting the dy and the dx as if they are fractions.
Like for example,
Is not really acceptable among mathemations because they are not fractions. Thus, I use a more formal approach which does not involve splitting the denominator of the differencial.
I wrote a Calculus thread over here.
(The math program that is used to generate math code is math working properly now, thus you might not see everything).
In that thread I explain how I do integration via the substitution rule my way.
And yes, that is my own techinque.