How to get this integration

∫((x)/(x+6))dx

Cannot seem to get it right using the partial fractions technique, as is the section I am doing.

∫(x)/(x+6) dx

Let u = x + 6
du = dx

∫(u - 6) / u du
∫du - 6∫du/u
u - 6ln|u| + C
x + 6 - 6ln|x +6| + C

The 6 can be absorbed by the constant:

x - 6ln|x + 6| + C

∫ x/(x+6) .dx

let u = x+6 => du = dx
I(u) = ∫ (u-6)/u .du = ∫ 1- (6/u) .du = u - 6log(u) +c
=>
I(x) = (x+6) - 6log(x+6) +C
= x - 6log(x+6) +C for some const C.