# Hard intergration

1. May 6, 2010

### TheTourist

I have derived the following equation for the velocity of a collapsing shell of a collapsing star.
$$\frac{dr}{dt}$$=-[GM($$\frac{1}{2}$$-$$\frac{1}{R}$$)]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 $$\int$$[$$\frac{x}{1-x}]$$1/2 dx=$$\pi$$/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. May 6, 2010

### tiny-tim

Hi TheTourist!

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

hmm … that RHS can't possibly be correct

shouldn't it be a function of r?

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