Maple integral will not evaluate the limit?

Question

Maple will not evaluate fully evaluate this integral, instead it gives the solution as a limit for r approaching infinity. How do I foce maple to actually evaluate this limit?

Here is the integral:

int(Z^3*Z^2*r^3*exp(-Z*r/a)/(pi*a^5), r = 0 .. infinity);

Answer 1

The result depends upon signum(Z/a) (ie. whether Z/a is greater or less than zero).

int(Z^3*Z^2*r^3*exp(-Z*r/a)/(Pi*a^5),
    r = 0 .. infinity) assuming Z/a>0;

      6 Z 
      ----
      Pi a

int(Z^3*Z^2*r^3*exp(-Z*r/a)/(Pi*a^5),
    r = 0 .. infinity) assuming Z/a<0;

    -infinity

ps. Also, I used Pi as the symbol for the well-known constant. The lowercase name pi doesn't mean anything special in Maple.