∫dx/(2-3x)(2x+1)

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/10/06 14:46:14

∫dx/(2-3x)(2x+1)

令1/[(2-3x)(2x+1)] = M/(2-3x) + N/(2x+1)
1 = M(2x+1) + N(2-3x)
代x = -1/2,1 = N(7/2) => N = 2/7
代x = 2/3,1 = M(7/3) => M = 3/7
∴∫ dx/[(2-3x)(2x+1)]
= (2/7)∫ dx/(2x+1) + (3/7)∫ dx/(2-3x)
= (2/7)(1/2)∫ d(2x+1)/(2x+1) + (3/7)(-1/3)∫ d(2-3x)/(2-3x)
= (1/7)ln|2x+1| - (1/7)ln|2-3x| + C
= (1/7)ln|(2x+1)/(2-3x)| + C

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