Simple maths question that is annoying me

what is the intergral of (0.5) / (x + 1) ??
i understand it would be .5 ln (x + 1).

alternatively.... isnt (.5) / (x+ 1) the same as 1 / (2x + 2)???? correct me if i am wrong, but isnt the intergral of this now 0.5 ln (2x + 2)
what am i doing wrong?? thanks alot

You are right but the integral includes a constant.
y = 0.5ln(x+1) + k
dy/dx = 0.5/(x+1)
z = 0.5ln(2x+2) + c
dz/dx = 0.5*2/2(x+1) = 0.5/(x+1)
So the k and c would be different.

If u = 2x+2 then du = 2dx, not 1dx