How to get this integral into standard form

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 ?

 

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.