Opened 10 years ago

# Ugly result for exponential integral

Reported by: Owned by: mjo burcin minor sage-6.4 calculus kcrisman N/A

### Description

As reported in this sage-support thread:

We expect,

```sage: integral( x / (exp(x) - 1) , (x,0,oo))
pi^2/6
```

but get,

```sage: integral( x / (exp(x) - 1) , (x,0,oo))
-1/6*pi^2 + limit(-1/2*x^2 + x*log(-e^x + 1) + polylog(2, e^x), x, +Infinity)
```

The above might not be incorrect, but it is not very useful either.

### comment:1 Changed 10 years ago by kcrisman

• Component changed from symbolics to calculus
• Priority changed from major to minor

### comment:2 Changed 9 years ago by mjo

Same result from Maxima 5.27:

```(%i1) display2d: false;

(%o1) false
(%i2) f: x/(%e^x - 1);

(%o2) x/(%e^x-1)
(%i3) integrate(f, x, 0, inf);

(%o3) 'limit(li[2](%e^x)+x*log(1-%e^x)-x^2/2,x,inf,minus)-%pi^2/6
```

### comment:3 Changed 8 years ago by jdemeyer

• Milestone changed from sage-5.11 to sage-5.12

### comment:4 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.1 to sage-6.2

### comment:5 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.2 to sage-6.3

### comment:6 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.3 to sage-6.4

### comment:7 Changed 4 years ago by mforets

more tests:

```sage: giac('integrate(x / (exp(x) - 1), x, 0, inf)')
pi^2/6
sage: integrate(x / (exp(x) - 1), x, 0, oo, algorithm='sympy')
integrate(x/(e^x - 1), x, 0, +Infinity)
```

i think this is another reason to make more user friendly the functionality that is offered through giac; stay tuned at the giac interface wiki.

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