If I have a function:
f(x) = 1 / (x+1), and I want to find it's indefinite integral, I can apply the log rule and get:
F(x) = ln |x+1| + C
If, however, I multiply both the numerator and the denominator by 2, before integrating, I get:
f(x) = 1 / (x+1) = 2 / 2x + 2
F(x) = ln |2x+2| + C
Clearly, f(x) are equal in both cases, but I can't see how ln |2x+2| equals ln |x+1|
Any explanation? Thanks