How can I solve the improper integral $\int_{1}^\infty {dx \over {(x+1)(x+2)}}$ $$\int_{1}^\infty {dx \over {(x+1)(x+2)}}$$

I have the indefinite integral solved for:

$$\ln(x+1)-\ln(x+2) + C$$

But I don't know how to finish with $[1, \infty]$.
Use

$$\ln(x+1)-\ln(x+2)=\ln\left(\frac{x+1}{x+2}\right)$$
$\ln(x+1)-\ln(x+2) + C = \ln(\frac{x+1}{x+2}) + C$ evaluated at 1 and $\infty$ gives $\ln(\frac{\infty}{\infty}) - \ln\frac{2}{3}=\ln\frac{3}{2}$