∫(x^3)/((x-1)^100)dy=?

∫(x^3)/((x-1)^100)dx
=-1/100∫(x^3)d((x-1)^(-99)
=-x^3*(x-1)^(-99)/100+1/100∫(x-1)^(-99)dx^3
=-x^(-96)/100+3/100∫(x-1)^(-99)*x^2dx
=-x^(-96)/100-3/(100*99)*(x-1)^(-99)*x^2+6/(100*99)∫(x-1)^(-98)*xdx
=-x^(-96)/100-3/(100*99)*(x-1)^(-99)*x^2-6/(100*99*98)*(x-1)^(-97)*x+6/(100*99*98)∫(x-1)^(-98)dx
=-x^(-96)/100-3/(100*99)*(x-1)^(-99)*x^2-6/(100*99*98)*(x-1)^(-97)*x+6/(100*99*98*97)*(x-1)^(-97)+C

∫(x^3)/((x-1)^100)dx
let
y=(x-1)
dy = dx
∫[(y+1)^3/(y^100) ]dy
= ∫ [ y^(-197)+3y^(-198)+3y^(-199) + y^(-100) ] dy
= (-1/196)y^(-196) - (3/197)y^(-197) -(1/66)y^(-198) -(1/99)y^(-99) + C
= (-1/196)(x-1)^(-196) - (3/197)(x-1)^(-197) -(1/66)(x-1)^(-198) -(1/99)(x-1)^(-99) + C