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How do you evaluate the definite integral #int (e^x)/(1+e^x)# from #[0,1]#?

1 Answer

Sep 13, 2016

#=ln( (1+e)/2)#

Explanation:

note that #d/dx(ln (1+e^x)) = (e^x)/(1+e^x)#

So

#int_0^1 (e^x)/(1+e^x) \ dx#

#=int_0^1 d/dx(ln (1+e^x)) \ dx#

#=[ ln (1+e^x)]_0^1#

#=ln( (1+e)/2)#

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