Question

Solve $\int \frac{3x-1}{{\left(x+2\right)}^2}dx$

Answer 1

Solution -

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

$=\int \frac{3x-1+7-7}{(x+2{)}^2}dx$

$=\int \frac{3}{x+2}dx-7\int \frac{dx}{(x+2{)}^2}$

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