Consider following integral: $$13\int{\frac{1}{8x-4}dx}\tag{1}$$ By factorizing the denominator and then taking the factor outside the integral sign, it can be rewritten as $$\frac{13}{4}\int{\frac{1}{2x-1}dx}\tag{2}$$
Now $(1)$ and $(2)$ should be equivalent, yet they evaluate into different integrals namely $$13\,\int{\frac{1}{8x-4}dx}=\frac{13}{8}\ln{|8x-4|}+C\tag{1a}$$ $$\frac{13}{4}\int{\frac{1}{2x-1}dx}=\frac{13}{8}\ln{|2x-1|}+C \tag{2a}$$
Since $(1)\equiv(2)$, then $(1a)\text{ and }(2a)$ should be equivalent as well, which reduces to $$\ln{|8x-4|}=\ln{|2x-1|}$$ which clearly isn't true. What am I missing here?