这直接凑微分不就行咯
∫ x^10/[x(x^10 + 1)] dx
= ∫ x^9/(x^10 + 1) dx
= (1/10)∫ 1/(x^10 + 1) d(x^10)
= (1/10)∫ 1/(x^10 + 1) d(x^10 + 1)
= (1/10)ln(x^10 + 1) + C