Hello I am having trouble with this question.
INtegrate:
f(2x+5)/(x+4) dx
My attempt:
1/2x+5f 1/x+4 dx
2x+5 Ln (x+4) + c
Alternatively,
$\displaystyle \int{\frac{2x+5}{x+4}}dx=\int{\frac{x+4+x+1}{x+4}} dx=\int{\left(1+\frac{x+1}{x+4}\right)}dx$
$\displaystyle u=x+4$
$\displaystyle x+1=u-3$
$\displaystyle \int{\left(1+\frac{u-3}{u}\right)}du=\int{\left(1+1-3u^{-1}\right)}du=\int{\left(2-3u^{-1}\right)}du$
$\displaystyle =2u-3ln|u|+C=2(x+4)-3ln|x+4|+C$