1/3*x^3+1/3*ln|x^3-1|+C，C为任意常数
详细过程点下图查看
凑微分即可:=§(x^3-1+1)/3(x^3-1)dx^3=c+1/3 x^3+1/3 ln(x^3-1).
∫[x⁵/(x³-1)]dx=∫[x²+x²/(x³-1)]dx=∫x²dx+∫[x²/(x³-1)]dx=x³/3+(1/3)∫d(x³-1)/(x³-1)=x³/3+(1/3)ln(x³-1)+C.
