Nguyên hàm [U = int { frac{{{{ left( {x - 2} right)}^{2020}}}}{{{{ left( {x + 1} right)}^{2022}}}}dx} ] là: A. [U = frac{1}{3}{ left( { frac{{x - 2}}{{x + 1}}} right)^{2021}} + C ] B. [U = frac{1}{{60...

Hướng dẫn giải Xét [U = int { frac{{{{ left( {x - 2} right)}^{2020}}}}{{{{ left( {x + 1} right)}^{2022}}}}dx} = int {{{ left( { frac{{x - 2}}{{x + 1}}} right)}^{2020}} frac{1}{{{{ left( {x + 1} right)}^2}}}dx} ] Đặt [u = frac{{x - 2}}{{x + 1}} Rightarrow du = frac{3}{{{{ left( {x + 1} right)}^2}}}dx Rightarrow frac{1}{3}du = frac{1}{{{{ left( {x + 1} right)}^2}}}dx ]. Suy ra. [U = frac{1}{3} int {{u^{2020}}du} = frac{1}{{6063}}{u^{2021}} + C ]. Vậy [U = frac{1}{{6063}}{ left( { frac{{x - 2}}{{x + 1}}} right)^{2021}} + C ] Chọn C.