I have derived the following equation for the velocity of a collapsing shell of a collapsing star.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dr}{dt}[/tex]=-[GM([tex]\frac{1}{2}[/tex]-[tex]\frac{1}{R}[/tex])]^{1/2}

I now need to integrate this to find the free-fall time, and the hint is to manipulate the equation into a form where you can use a standard integral: substitute x=r/R and then use the standard integral [tex]\int[/tex][[tex]\frac{x}{1-x}][/tex]^{1/2}dx=[tex]\pi[/tex]/2

I am completely stuck on how to do this

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Hard intergration

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