Cho (int {{{left( {dfrac{x}{{x + 1}}} right)}^2}dx = mx + nln left| {x + 1} right|} + dfrac{p}{{x + 1}} + C). Giá trị của biểu thức (m + n + p) bằng

(int {{{left( {dfrac{x}{{x + 1}}} right)}^2}dx}  = int {dfrac{{{x^2}}}{{{{left( {x + 1} right)}^2}}}dx}  = int {left( {1 – dfrac{{2x + 1}}{{{{left( {x + 1} right)}^2}}}} right)dx = } int {left( {1 – dfrac{{2x + 2}}{{{{left( {x + 1} right)}^2}}} + dfrac{1}{{{{left( {x + 1} right)}^2}}}} right)dx} )(begin{array}{l} = int {dx}  – int {dfrac{{2x + 2}}{{{{left( {x + 1} right)}^2}}}dx}  + int {dfrac{1}{{{{left( {x + 1} right)}^2}}}dx}  = x – int {dfrac{{dleft( {{{left( {x + 1} right)}^2}} right)}}{{{{left( {x + 1} right)}^2}}} – dfrac{1}{{x + 1}} + C} \ = x – ln left| {{{left( {x + 1} right)}^2}} right| – dfrac{1}{{x + 1}} + C = x – 2ln left| {x + 1} right| – dfrac{1}{{x + 1}} + Cend{array})

( Rightarrow m = 1,n =  – 2,p =  – 1 Rightarrow )(m + n + p =  – 2).

Chọn: D