∫1/1+x^3dx怎么算

题目

∫1/1+x^3dx怎么算

答案

原式=(1/3)∫[1/(x+1)+(2-x)/(x²-x+1)]dx
=(1/3)∫[1/(x+1)+(1/2)(3-(2x-1))/(x²-x+1)]dx
=(1/3)∫dx/(x+1)+(1/2)∫dx/(x²-x+1)-(1/6)∫(2x-1)dx/(x²-x+1)
=(1/3)∫dx/(x+1)+(1/√3)∫d((2x-1)/√3)/(1+((2x-1)/√3)²)-(1/6)∫d(x²-x+1)/(x²-x+1)
=(1/3)ln│x+1│+(1/√3)arctan((2x-1)/√3)-(1/6)ln(x²-x+1)+C (C是积分常数).