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## Homework Statement

Need to integrate

dt=da (8*pi*rho0/3a-1)^-1/2

to get

t=(8*pi*rho0/3)*arctan(1/sqrt(8*pi*rho0/3a-1))-sqrt(a)*sqrt(8*pi*rho0/3-a)

## Homework Equations

## The Attempt at a Solution

I'm totally lost. I'm guessing there's substitution involved, but unsure on how to get the arctan in. Any thoughts. If someone can tell me how to get the arctan in I think I'll be able to give a better go at it.

Thanks in advance.

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