I was trying to solve this integral x/(x-6)dx and I used substitution. u = x-6 and x = u+6.
In the end, I ended up with the answer x+6ln|x-6|-6+C, however, the answer is x+6ln|x-6|+C without the -6. Can someone help me understand why this is the case?
You shouldn’t be asking this here, but I’ll answer you anyway. A constant term “eats” any other constants. Because think about it. +C just denotes “plus any constant” and -6 + C means “Any constant - 6” which is still…”any constant”. So the +C effectively “eats” anything that is added or subtracted to it
