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Hard intergration

  1. May 6, 2010 #1
    I have derived the following equation for the velocity of a collapsing shell of a collapsing star.
    [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
     
  2. jcsd
  3. May 6, 2010 #2

    tiny-tim

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    Hi TheTourist! :smile:

    (have an integral: ∫ and a square-root: √ and a pi: π :wink:)

    hmm … that RHS can't possibly be correct :redface:

    shouldn't it be a function of r? :smile:
     
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