Question

∫3/(x³+1)dx

∫3/(x³+1)dx求学霸解答，最好带步骤。谢谢

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Answer 1

∫dx/(1+x3) =∫dx/[(x+1)(x²-x+1)] =∫[(1/3)/(x+1)+(-x/3+2/3)/(x²-x+1)]dx =(1/3)ln│x+1│+(1/6)∫(3+1-2x)/(x²-x+1)dx =(1/3)ln│x+1│+(1/2)∫dx/(x²-x+1)-(1/6)∫(2x-1)/(x²-x+1)dx =(1/3)ln│x+1│+(1/2)∫dx/[3/4+(x-1/2)&...