∫(5x-1)/(x2-x-2)dx=________．

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问题 ∫(5x-1)/(x²-x-2)dx=________．

选项

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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考研数学二

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