Re: Integrate[e/(1+Exp[e]),{e,ei,Infinity}]

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: Integrate[e/(1+Exp[e]),{e,ei,Infinity}]
• From: withoff
• Date: Fri, 11 Dec 92 15:08:33 CST

```> Integrate[e/(1+Exp[e]),{e,ei,Infinity}]
> this fermintegral of order 1 results in RecursionLimit errors.
> The indefinite integral can be found without any problems.
> Any ideas how to change the situation??
>
> Michael Trott
>
> trott at physik.tu-ilmenau.de

If the indefinite integral works, it can probably be used to compute
the definite integral.  The built-in Limit function can't handle the
limit at Infinity, but the package Calculus`Limit` can.

In[1]:= f = Integrate[e/(1+Exp[e]),e]

2
e               e                 e
Out[1]= -- - e Log[1 + E ] - PolyLog[2, -E ]
2

In[2]:= << Calculus`Limit`

In[3]:= Limit[f, e -> Infinity]

2
Pi
Out[3]= ---
6

In[4]:= Limit[f, e -> ei]

2
ei                ei                 ei
Out[4]= --- - ei Log[1 + E  ] - PolyLog[2, -E  ]
2

In[5]:= %% - %

2     2
-ei    Pi                ei                 ei
Out[5]= ---- + --- + ei Log[1 + E  ] + PolyLog[2, -E  ]
2      6

Dave Withoff
withoff at wri.com

```

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