∫x²/(1+e^x)dx 积分上下限为-1到1
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∫x²/(1+e^x)dx 积分上下限为-1到1
∫x²/(1+e^x)dx 积分上下限为-1到1
∫x²/(1+e^x)dx 积分上下限为-1到1
P=∫(-1,1)x²/(1+e^x)dx (1)
令x=-t,积分限变为(1,-1),dx=-dt
P=∫(1,-1)t²/(1+e^(-t))d(-t)
=∫(-1,1)t²e^t/(1+e^t)dt
=∫(-1,1)x²e^x/(1+e^x)dx (2)
(1)+(2)得
2P=∫(-1,1)x²(1+e^x)/(1+e^x)dx
=∫(-1,1)x²dx=2∫(0,1)x²dx=2/3
所以P=1/3