2. 考研
  3. ∫(x+3)/(x2+2x+5)dx=________．

∫(x+3)/(x2+2x+5)dx=________．

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问题 ∫(x+3)/(x2+2x+5)dx=________．
选项
答案1/2ln(x2+2x+5)+arctan(x+1)/2+C
解析 ∫(x+3)/(x2+2x+5)dx=1/2∫[(2x+2)+4]/(x2+2x+5)dx=1/2∫(2x+2)/(x2+2x+5)dx+2∫1/(x2+2x+5)dx=1/2∫1/(x2+2x+5)d(x2+2x+5)+2∫1/[22+(x+1)2]d(x+1)=1/2ln(x2+2x+5)+arctan(x+1)/2+C．
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考研数学二

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