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I need to evaluate this integral

[tex]\int_0^{\infty}(1+\alpha_2)^{-2}\left(\alpha_2+b\right)^{-1}\,d\alpha_2[/tex]

I found the following integral in the table of integrals (eq 3.197.1, 7th edition)

[tex]\int_0^{\infty}x^{v-1}(\beta+x)^{-\mu}(x+\gamma)^{-\rho}\,dx=\beta^{-\mu}\gamma^{\mu-\rho}B(v,\mu-v+\rho)_2F_1(\mu,\,v;\,\mu+\rho;1-\frac{\gamma}{\beta})[/tex]

The integral and the conditions are in the image attached. Comparing the two integrals I set ##v=1,\,\beta=1,\,\gamma=b##, which implies that ##\mu=2## and ##\rho=1##. I satisfy the last two conditions, but I'm not sure about the first two. What does it mean arg x if x is a constant?

##b## varies in a loop, and when I evaluate the integral I get results. However, the final result, in which the above integral is a part, isn't right. I'm not sure where the error is, and I wanted to make sure it isn't in using the integral.

I appreciate any help. Thanks

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# I How to evaluate this integral?

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