不定积分3x/(x^3-1)求答案!
问题描述：
不定积分3x/(x^3-1)求答案!
答
∫3xdx/(x^3-1) = ∫[1/(x-1)+(1-x)/(x^2+x+1)]dx
=∫1/(x-1)dx -(1/2)∫[(1+2x)/(x^2+x+1)]dx +(3/2)∫dx/(x^2+x+1)
= ln|x-1| -(1/2)ln(x^2+x+1) +(3/2)∫d(x+1/2)/[(x+1/2)^2+3/4)
= (1/2)ln[(x-1)^2/(x^2+x+1)] +√3arctan[(2x+1)/√3]+C