integral of a rational function (1+a_i s)/prod((1+a_j s)^k)

Is there any closed-form expression for the following integral:

$\int_0^\infty \frac{1+a_i s}{\prod_{j=1}^n (1+a_j s)^k} ds$

where the $a_i$ are >0 and k is an integer. And, if k is not an integer?

Thank you.

-
 It's a rational function of course so such integrals always have closed-form expressions by the partial fraction technique. Did you mean for $k$ to be positive by the way? – magnetohydrodynamic Jan 26 2012 at 21:55