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∫(2x+3)/(x^2+3x+1)dx和∫1/(x^2+3x+1)dx结果一样吗?
题目详情
∫(2x+3)/(x^2+3x+1)dx和∫1/(x^2+3x+1)dx结果一样吗?
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答案和解析
∫(2x+3)/(x²+3x+1)dx和∫1/(x²+3x+1)dx结果一样吗?∫(2x+3)/(x²+3x+1)dx=∫d(x²+3x+1)/(x²+3x+1)=ln∣x²+3x+1∣+C.(1)∫1/(x²+3x+1)dx=∫dx/[(x+3/2)²-5/4]=(4/5)∫dx/{[2...
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