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Differentiate w.r.t. k
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\frac{v}{kV^{2}+g}
Find the integral of \frac{1}{kV^{2}+g} using the table of common integrals rule \int a\mathrm{d}v=av.
\begin{matrix}\frac{v}{kV^{2}+g}+С_{3},&\end{matrix}
If F\left(v\right) is an antiderivative of f\left(v\right), then the set of all antiderivatives of f\left(v\right) is given by F\left(v\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.