可以先把x+2提出来 1/[(x-1)^(1/3)*(x+2)^(2/3)] =1/(x+2) * [(x+2)/(x-1)]^(1/3) 做换元，令t=[(x+2)/(x-1)]^(1/3) 则x=1 + 3/(t^3-1) dx=9t^2dt/(t^3-1)^2 代入原式得 ∫3 / [t(t^3-1)] dt =∫ -3/t + 1/(t-1) + (2t+1)/(t^2+t+1) dt =-3ln|t| +...
