Can someone explain to me the substiution which is made for these integrals, I never find out why, it is they just just do it, and have no reasoning, perhaps a little insight could help
Yes, I know you use that to arrive by substituting the denominator to get the natural log, however, I am one of those that want to know why rather than this is how you do it and the hows its goes with no reason. sorry to be a pain thanks for the input though. I just wanted to know how do you manage or who decided this will work, as in the reasoning.
math is like that sometimes. sometimes someone recognizes a pattern and applies it backwards to get somewhere. being very familiar with trig derivatives no doubt was a motivating factor here. seeing how that would work backwards might have led to such a method.
sometimes, you don't know where it came from or why someone would even think of that. yet you can't deny that it works, and that it is stunningly elegant.