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Is there anything wrong?


I have a problem in calculating this integral shown below(I've posted
this question before, but I typed Exp[-x] as Exp[x] incorrectly so you
have figured out both of them were not converge):

Integrate[Log[1+Exp[-x]/Sqrt[x]],{x,0,Infinity}]
Pi^2/6

N[%]
1.64493

NIntegrate[Log[1+Exp[-x]/Sqrt[x]],{x,0,Infinity}]
1.01799

Where does this difference come from and which one is correct?



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