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I was reading a derivation of equations of the two-body problem and I found the following statement:

[tex]\mu \frac{d}{dt}\left (\frac{\vec{r}}{r}\right ) = \frac{\mu}{r} \vec{v} - \frac{\mu \dot{r} }{r^2} \vec{r}[/tex]

Where μ is a constant. (If you're interested on where this came from, see page 19 http://books.google.com.br/books?id...resnum=3&ved=0CCUQ6AEwAg#v=onepage&q&f=false").

Calculating this derivative is easy, using the quotient rule. Anyway, I am trying to verify the inverse, that is, calculating the integral of the right member of the equation.

But my integration knowledge is very limited. I've tried using integration by parts, but I got stuck.

Could anyone give an idea on how I should proceed, or what technique I should use?

Thank you in advance.

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# Doubt about an integration

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