Question

Evaluate :
$\int \frac{dx}{(x+1)(x+2)}$

Answer 1

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

$=\int \frac{dx}{x+1}-\int \frac{dx}{x+2}$

$=\ln |x+1|-\ln |x+2|+C$

$=\ln \left|\frac{x+1}{x+2}\right|+C$