I=∫[-1,1] x?/(1+e^x)dx 令t=-x 则 I=∫[1,-1] t?/[1+e^(-t)] d(-t) =∫[-1,1] t?/[1+e^(-t)] dt =∫[-1,1] t? e^t/(1+e^t) dt =∫[-1,1] x? e^x/(1+e^x)dx 所以 I=1/2∫[-1,1] x?/(1+e^x)dx+1/2∫[-1,1] x?e^x/(1+e^x)dx =1/2∫[-1,1] x?dx=∫[0,1] x?dx=1/5
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