I would like to know if there is any method to make an estimation on how big it is a number, in terms of orders of magnitude of n! when n is a big number.

(x^2) (2-x)^2 = 1 + 2(2-x)^2 I asked this problem on this page a few months ago, but didn’t get any satisfactory answer. I think there is a trick solution to it

Just prove that the derivative of ln(x) is 1/x. This was already shown onthis YouTube channel.

I don't want it by the derivative.I want it using integration methods step by step

https://www.quora.com/How-do-you-prove-the-integral-of-1-x-is-the-natural-log-of-x