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∫ [x^2/(x-1)^100] dx
= -(1/99)∫ x^2 d[ 1/(x-1)^99]
=-(1/99) [x^2/(x-1)^99] + (2/99) ∫ [x/(x-1)^99] dx
=-(1/99) [x^2/(x-1)^99] - (1/4851) ∫ x d(1/(x-1)^98)
=-(1/99) [x^2/(x-1)^99] - (1/4851) [x/(x-1)^98] + (1/4851)∫ [1/(x-1)^98] dx
=-(1/99) [x^2/(x-1)^99] - (1/4851) [x/(x-1)^98] - (1/470547)(1/(x-1)^97) + C
= -(1/99)∫ x^2 d[ 1/(x-1)^99]
=-(1/99) [x^2/(x-1)^99] + (2/99) ∫ [x/(x-1)^99] dx
=-(1/99) [x^2/(x-1)^99] - (1/4851) ∫ x d(1/(x-1)^98)
=-(1/99) [x^2/(x-1)^99] - (1/4851) [x/(x-1)^98] + (1/4851)∫ [1/(x-1)^98] dx
=-(1/99) [x^2/(x-1)^99] - (1/4851) [x/(x-1)^98] - (1/470547)(1/(x-1)^97) + C
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