Alternatively,

\(\displaystyle \int{\frac{2x+5}{x+4}}dx=\int{\frac{x+4+x+1}{x+4}}dx=\int{\left(1+\frac{x+1}{x+4}\right)}dx\)

\(\displaystyle u=x+4\)

\(\displaystyle x+1=u-3\)

\(\displaystyle \int{\left(1+\frac{u-3}{u}\right)}du=\int{\left(1+1-3u^{-1}\right)}du=\int{\left(2-3u^{-1}\right)}du\)

\(\displaystyle =2u-3ln|u|+C=2(x+4)-3ln|x+4|+C\)