Sử dụng TPTP
$I=\int\limits_{1}^{2}\dfrac{x+2\ln x}{\left(x+2\right)^2}dx=-\int\limits_{1}^{2}(x+2\ln x)d\left ( \frac{1}{x+2} \right )$
$=-\left[ {(x+2\ln x).\frac{1}{x+2}} \right]_{1}^{2} + \int\limits_{1}^{2} \frac{1}{x+2} \left ( 1+\frac2x \right )dx$
$=-\left[ {(x+2\ln x).\frac{1}{x+2}} \right]_{1}^{2} + \int\limits_{1}^{2} \frac{1}{x}dx$
$=\left[ {-(x+2\ln x).\frac{1}{x+2}+\ln x} \right]_{1}^{2} $