How do constant c gone inside the log in integrals?

Question

∫dx/(x+1) - ∫dx/(x+2) = log| (x+1)c/(x+2) |

Answer 1

 log| (x+1)c/(x+2) |= log[x+1|+log|c|-log|x+2|.

When integrating it was written log|c| instead C, which is also constant and C=log|c|.

 

Answer 2

∫dx/(x+1) - ∫dx/(x+2) = ln lx+1l - ln lx+2l + c₁

 

             For a given real number, c₁, there is a positive real number, c, so that lnc = c₁

 

So, lnlx+1l + c₁ - lnlx+2l = lnlx+1l + lnc - lnlx+2l

 

                                     = ln[lx+1lc]  - lnlx+2l

 

                                     = lnl (x+1)c/(x-2) l