Question

Integrate: $\frac{3x-1}{(x+2{)}^2}$

Answer 1

$I=\int \frac{3x-1}{(x+2{)}^2}dx$

$u=x+2\Rightarrow x=u-2\Rightarrow dx=du$

$I=\int \frac{3(u-2)-1}{u^2}du$

$I=\int \frac{3u-7}{u^2}du=\int (\frac{3}{u}-\frac{7}{u^2})du$

$I=3\ln u+\frac{7}{u}+c$

$I=3\ln |x+2|+\frac{7}{x+2}+c$