Question: Stuck again with improper integration

Sorry to bother you again,fellow primers.A few days ago I asked a similar kind of q.,but here is some change, & I'm stuck again.


int(p^(D-2)/(exp(beta*p)-1), p = 0 .. infinity) assuming beta::positive, D::posint #D>0 & is an integer,this two are the only restriction on D,nothing else.

 I'm not getting any result (correct/incorrect).

The  result is  GAMMA(D-2)*Zeta(D-2)/beta^(D-2).  #Zeta is the Riemann zeta function.

Also,there is another related problem , I did the integration by hand,and at the final step I need to find the value

of  series(1/n^(D-2),n=1..infinity) assuming D:: posint. Maple should give   Zeta(D-2), but it didn't.

I know that assigning value to D will solve the problem immediately,but I don't want to do that,I need to get the generalized result for arbitrary D.

Thanks in advance.

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