Weird integration issue: $\ln(x+1)=\ln(2x+2)$ ?! Weird integration issue: Using $(\ln[f(x)])'=\frac {f'(x)}{f(x)}$ we get that $\int \frac{2\,dx}{2x+2}=\ln(2x+2)$. Yet, $\int \frac{2\,dx}{2x+2}= \int\frac{dx}{x+1}=\ln(x+1)$ using the same rule as earlier.
What is wrong here?

Just add a constant term and also notice that $\ln2$ is also a constant.
