Question: Integral with GAMMA functions

I am trying to solve the following integral


with respect to x, between zero and infinity.

If i just integrate it the result that I obtain is

(alpha^2*beta^(alpha+1)*exp(beta)*GAMMA(-alpha-1, beta)+alpha*beta^(alpha+1)*exp(beta)*GAMMA(-alpha-1, beta)+beta-alpha)/beta

My problem is that the alpha is positive and consequently the GAMMA functions do not exist, since the argument in the result is now negative. Is there a way I can tell Maple that alpha is positive and obtain a sensible solution??


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