Can't remember how to do this simple definite integral

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SUMMARY

The discussion focuses on integrating the equation of motion derived from Newton's second law, specifically for a system where Force F is defined as F = -gamma(dx/dt). The user seeks to integrate the left side of the equation (dv/v) over the interval kT to (k+1)T. The right side integrates to (-gamma/m)(T), while the left side results in ln(v) evaluated at the bounds, leading to the conclusion that the definite integral yields ln[v((k+1)T)/v(kT)].

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astonmartin
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If my Force = (-gamma)(dx/dt)
velocity v = dx/dt
Mass m

(m)(dv/dt) = F = (-gamma)(dx/dt)

Now I want to integrate it over kT<= t <= (k+1)T

Rearranging gives me (dv/v) = (-gamma/m)dt

The right side integrates to (-gamma/m)(T), but how do I integrate the left side over kT<= t <= (k+1)T??

Thanks
 
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\int \frac{1}{v} dv= ln(v)+ C
 
^but what does that give me for the definite integral?

ln [v(k+1)T / v(kT)] ?
 

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