∫1+∞dx/(ex+e(2-x))=________.

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问题1+∞dx/(ex+e(2-x))=________.

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答案π/4e

解析1+∞dx/(ex+e(2-x))=1+∞exdx/(e2x+e2)=1/e1+∞ex-1dx/(e2(x-1)+1)=1/earctanex-11+∞=1/e(π/2-π/4)=π/4e.
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