Cannot do the integral of the Hyper-geometric function?

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Chenkb
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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!

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Dr Transport said:
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!