Integrating Hard Integrals: No Closed Form Solution

[semigroups]

Please see the attachment. Under the given range of parameters the integral converges, but I can't find a closed form solution. It seems one has to integrate very special functions other than simple Beta, Gamma, Error functions etc..

 

[chiro]

Please see the attachment. Under the given range of parameters the integral converges, but I can't find a closed form solution. It seems one has to integrate very special functions other than simple Beta, Gamma, Error functions etc..

Hey semigroups and welcome to the forums.

Have you considered changing the region of integration to get things in terms of one variable?

My guess is if this is a problem from a problem set, that a change of variables and some extra stuff will give you something that ends up being in the form of a Beta (complete or incomplete) or a Gamma (complete or incomplete) and then you can just leave it at that.

If you have tried changing the region (I think it should look something like a triangle in the [0,1]x[0,1] region) then what did you try exactly and what did you find out?

 

[semigroups]

Thanks for reply!
Please find the attachements for deatailed working (due to the size of screen capture I have to divide it into three pictures).