I understand that integrating 1/x is lnx and 1/2x is 1/2ln2x.
I also know that differentiating lnx is 1/x and ln3x+1 is also 1/x but as differentiating and integrating are reverse functions, why is the differential of ln2x+1 not 1/2x+1, as surly if you integrate 1/x you won't get ln2x+1. Is it covered by the +c?