Notice that  4x^2 + 8x + 4 = 4*(x^2 + 2x + 1) = 4*(x+1)^2


Therefore,  


     =  = use properties of logarithms =  +  = 2 + .    ANSWER



Notice that in the last term, my expression includes  absolute value  |x+1|  under the logarithm sign.


It is because, although  (x+1)^2  is always positive,  (x+1)  CAN BE NEGATIVE.


Therefore, to avoid a catastrophe under the logarithm sign, I introduced  |x+1|  in my last term.



It is NECESSARY (!),  and  if you do not make it, your answer will be WRONG (!)


Actually, it is the most important moment in the solution of this problem, and the entire problem 
is designed and intended for you would learn it from my post (!)