∫1/(x^3-1)dx满意加二十分
问题描述：
∫1/(x^3-1)dx
满意加二十分
答
x³-1=(x-1)(x²+x+1)1/(x³-1)=A/(x-1)+(Bx+C)/(x²+x+1)=1/3(x-1)-(x+2)/3(x²+x+1)=1/3(x-1)-(2x+1)/6(x²+x+1)-1/2(x²+x+1)∫1/(x³-1)dx=∫dx/(x-1)[(x+½)²+&fra...