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I'm reading up on Kepler's problem at the moment, and there's a step in the book that I don't understand.

Starting off with the equation of the path [tex]\phi=\int\frac{M dr/r^2}{\sqrt{2m[E-U(r)]-M^2/r^2}}+\mbox{constant}[/tex]

The step involves subbing in [tex]U=-\alpha/r[/tex], 'and effecting elementary integration' to get

[tex]\phi=\cos^{-1}\frac{(M/r)-(m\alpha/M)}{\sqrt{(2mE+\frac{m^2\alpha^2}{M^2}})}+\mbox{constant}[/tex]

But it doesn't look very elementary to me

Does anyone have any idea?

Thanks.

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# Awkward integration

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