One major error: the integral of is NOT as you can see by differentiating. Instead write it as . Integrating gives .
Personally, from , I would have left the "2" where it is: . Integrating both sides, so that (I have dropped the absolute values because "c" can be positive or negative itself).
We cannot solve your homework problems for you. I realize you have been showing your work and all (that's a good thing!), but we cannot allow this in general. Please do not do this again.
For anyone helping please only give broad help, not specifics.