(1/x)[sqrt((x+1)/(x-1))]

you must substitute sqrt((x+1)/(x-1))

thank you but you actually did a mistake that didn't affect the result in the 2nd line

dx=-4u/(u^2-1)^2

and 3rd line you switched between the numerator and the denominator

(u^2-1)/(u^2+1)

Yep, sorry, my bad, I didn't pay enough attention, I modified it.

@andrei.frit02 no problem thanks for the reply