Mathematica: Evaluating integral

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Niles
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Hi

I need some assistance with the attached integral. I have tried performing it in Mathematica, but it doesn't give me the result in closed form. It just shows the integral.

I have attached my notebook if someone wants to test it out. I would be very happy to receive some feedback as I have spent many hours trying to make this work.


Niles.
 
Attachments
  • Typeset equations from a physics paper: the transverse velocity condition v⊥/vz < (A′/πd²)^1/2, the flux integral Φc = A ∫ d³v vz f(v) = (1/4) nA (A′/(A′+πd²)) v̄ (A.4), and the approximation Φc ≈ nAA′v̄/(4πd²) (A.5).
    integral.JPG
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  • integral.nb
    integral.nb
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It has successfully done the two inner integrals and fails on the final integral.

If I have not made a mistake then a substantially simplified version of your third integral is

Integrate[(vZ*Erf[vZ]^2)/E^vZ^2, {vZ, 0, Infinity}]

and there does not appear to be a closed form solution to that so I do not expect your actual problem has one either.
 
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