I am trying to solve the following integral
beta^alpha*x^(alpha-1)*exp(-beta*x)/((1+x)*GAMMA(alpha))
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??
Bests
Manuele
