$\int\limits_{}^{}\frac{dx}{(sinx + 2cosx)^2}= \int\limits_{}^{}\frac{\frac{dx}{cos^2x}}{(\frac{sinx}{cosx}-2\frac{cosx}{cosx})^2}$$\int\limits_{}^{} \frac{\frac{dx}{cos^2x}}{(tanx -2)^2}$
đặt u = tanx $\Rightarrow du = \frac{dx}{cos^2x}$
$\int\limits_{}^{}\frac{du}{(u-2)^2} = -\frac{1}{u-2} + C$