1. S = $\int\limits_{}^{}\frac{x dx}{(x+1)^2} = \int\limits_{}^{}\frac{(x+1-1)dx}{(x+1)^2} = \int\limits_{}^{}[\frac{1}{x+1}-\frac{1}{(x+1)^2}]dx$ 2.$\int\limits_{}^{} \frac{1}{x^2.(x+1)}dx$.
ta có: $\frac{1}{x^2.(x+1)} = \frac{A}{x^2}+ \frac{B}{x}+\frac{C}{x+1}=\frac{A(x+1)+B(x^2+x) + Cx^2}{x^2(x+1)}$
vậy B + C =0
A+B=1
A=1 $\Rightarrow B =-1 \Rightarrow C =1$