How to get this integral into standard form

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The discussion centers on transforming the definite integral of 1/sqrt(c² - dv²) into the standard form of an integral f(v) dv, where c is a real positive constant exceeding the upper limit of the integral. The user seeks to derive this integral from first principles, specifically in the context of special relativity and Lorentz transformations. The conversation highlights the complexities involved in this approach compared to more straightforward methods.

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nomadreid
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If I have the definite integral of 1/sqrt(c2-dv2) (without a dv after it), with c a real positive constant larger than the upper limit of the integral, how can I get it into the usual form of an integral f(v) dv ?
 
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What you have written makes no sense at all. Can you give the context? Where did you see
[tex]\int \frac{1}{\sqrt{c^2- dv^2}}[/tex]
 
I was attempting to work out from first principles an integration (which, I know, can be done much more easily with another point of view, but I wanted to see what this more difficult path would lead to) from special relativity, adding up infinitesimal increments dv of increases in velocity (I omitted the constants in my question). That is, this is from a Lorentz transformation.
 

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