Why do I get a different answer by using substitution and integral by parts for this integral?
$$\int \dfrac{2x}{(x-5)^2} dx$$
Substitution:
let $u=x-5$. $du = dx, x = u+5$
$$=\int\dfrac{2(u+5)}{u^2} du = 2u^{-1}+10u^{-2} du = 2 \ln{|u|}-\dfrac{10}{u} + C = 2 \ln{|x-5|}-\dfrac{10}{x-5}+C$$
Integral by parts:
$u = 2x, dv = \dfrac{1}{(x-5)^2}$
$du = 2 dx, v = -\dfrac{1}{x-5}$
$$=-2x\dfrac{1}{x-5} +\int{\dfrac{2}{x-5} dx} = 2 \ln{|x-5|}-\dfrac{2x}{x-5}+C$$