sorry, but i dont integrate with substituting. I learnt another method that is... let me give an example
i add the power by 1 and divide the whole function by the new power, and divide it once again by the derivative.
however, this function has x in both the denominator and the numerator, which is what makes it tough for me
NO! You cannot!
You have been shown how to do this question: The integrand can be written as (see below) and you claim in an earlier post to be able to integrate expressions like these. So there shouldn't be any problem.
This is misleading at best and wrong at worst.