∫(2x+2)/[(x-1)*(x^2+1)^2]dx_数学解答

∫(2x+2)/[(x-1)*(x^2+1)^2]dx

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解答

令(2x+2)/[(x-1)(x²+1)²]=A/(x-1) + (Bx+C)/(x²+1) + (Dx+E)/(x²+1)²右边通分合并后,与左边比较系数得：A=1,B=-1,C=-1,D=-2,E=0,因此：(2x+2)/[(x-1)(x²+1)²]=1/(x-1) - (x+1)/(...