Giải thích các bước giải:
Ta có:
$I=\displaystyle\int x(1-x)^{2019}dx$
$\to I=\displaystyle\int (x-1+1)(1-x)^{2019}dx$
$\to I=\displaystyle\int (x-1)\cdot (1-x)^{2019}+(1-x)^{2019}dx$
$\to I=\displaystyle\int -(1-x)\cdot (1-x)^{2019}+(1-x)^{2019}dx$
$\to I=\displaystyle\int - (1-x)^{2020}+(1-x)^{2019}dx$
$\to I=\displaystyle\int - (x-1)^{2020}-(x-1)^{2019}dx$
$\to I=-\dfrac{1}{2021}\cdot (x-1)^{2021}-\dfrac{1}{2020}\cdot (x-1)^{2020}$
