$I=\displaystyle\int \dfrac{x^2}{(1-x)^{100}} \, dx\\ u=1-x \Rightarrow du=-dx\\ I=\displaystyle\int \dfrac{(u-1)^2}{u^{100}} \, dx\\ =\displaystyle\int (u-1)^2u^{-100} \, dx\\ =\displaystyle\int (u^2-2u+1)u^{-100} \, dx\\ =\displaystyle\int \left(u^{-98}-2^{-99}+u^{-100}\right) \, dx\\ =-\dfrac{1}{97u^{97}}+\dfrac{2}{98u^{98}}-\dfrac{1}{99u^{99}}+C\\ =-\dfrac{1}{97(1-x)^{97}}+\dfrac{1}{49(1-x)^{98}}-\dfrac{1}{99(1-x)^{99}}+C$
