Question

The value of the integral $\int \frac{dx}{(x+3)(x+2)}$ is equal to

Answer 1

Now,

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

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

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

$=\log |(x+2)|-\log |(x+3)|+c$ [ Where $c$ being integrating constant]

$=\log \left|\frac{(x+2)}{(x+3)}\right|+c$