∫1/(1+e的x次方)dx 等于多少
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∫1/(1+e的x次方)dx 等于多少
∫1/(1+e的x次方)dx 等于多少
∫1/(1+e的x次方)dx 等于多少
原式=∫1/(1+e^x)dx
=∫e^x/(e^x+e^2x)dx
=∫de^x/(e^x+e^2x)
令t=e^x
则原式=∫dt/t(t+1)
=∫[1/t-1/(1+t)]dt
=lnt-ln(t+1)
即原式=x-ln(1+e^x)
∫1/(1+e^x)dx
let
y=e^x
dy =e^xdx
∫1/(1+e^x)dx
=∫{1/[y(y+1)]}dy
=∫ [1/y-1/(y+1)] dy
=ln| y/(y+1)| + C
=ln |e^x/(e^x+1)| + C