∫(5x-1)/(x2-x-2)dx=________.

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问题 ∫(5x-1)/(x2-x-2)dx=________.

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答案2ln|x+1|+3ln|x-2|+C

解析 令(5x-1)/(x2-x-2)=(5x-1)/[(x+1)(x-2)]=A/(x+1)+B/(x-2),解得A=2,B=3,则∫(5x-1)/(x2-x-2)dx=2∫dx/(x+1)+3∫dx/(x-2)=2ln|x+1|+3ln|x-2|+C.
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