Question

Evaluate $\int \frac{2x}{x^2+3x+2}dx$

Answer 1

$\frac{2x}{(x+2)(x+1)}=\frac{A}{x+2}+\frac{B}{x+1}$
$A=4;B=-2$
$\int \frac{2x}{x^2+3x+2}=\int \frac{2x}{(x+2)(x+1)}$
$=\int \frac{4}{x+2}dx-\int \frac{2}{x+1}$

$=4\log |x+2|-2\log |x+1|+c$