Question: What about this integral

What Should I do to get the correct result-which is obviously not something like my answer. 

> assume(a::(AndProp(NonZero, constant, real)));
> about(a);
Originally a, renamed a~:
  is assumed to be: AndProp(real,constant,Non(0))

> is(a, constant);
                                    true
> is(a = 0);
                                    false
> is(a^2 > 0);
                                    true
> assume(p::real, 0 < p and p < infinity);
> Int(p/(exp(a*p)-1), p = 0 .. infinity);
                           /infinity                
                          |               p         
                          |          ------------ dp
                          |          exp(a p) - 1   
                         /0                         
> value(%);
      /     2  2                                                        2  
      |  3 p  a  - 6 p ln(-exp(a p) + 1) a - 6 polylog(2, exp(a p)) + Pi   
 limit|- ----------------------------------------------------------------, 
      |                                   2                                
      \                                6 a                                 

               \
               |
   p = infinity|
               |
               /