Cannot do the integral of the Hyper-geometric function?

[Chenkb]

Dear friends:
It's strange that Mathematica can do the integral of $\int_0^\infty dx~x~_2F_1(a,b,c,1-x^2)$, however, fails when it's changed to $\int_0^\infty dx~x~_2F_1(a,b,c,1-x-x^2)$.
Are there any major differences between this two types? Is it possible to do the second kind of integral?
Best regards!

 

[Dr Transport]

I don't believe that that particular integral can be solved analytically. Best place to look is in Rydzik and Gradstien (sp)...

 

[Chenkb]

I don't believe that that particular integral can be solved analytically. Best place to look is in Rydzik and Gradstien (sp)...

Many thanks! That reference is excellent!