Solve ∫ dv/kV^2+g

$$\int \frac { d v } { k V ^ { 2 } + g }$$

Evaluate

$$\frac{v}{kV^{2}+g}+С$$

$$g\neq -kV^{2}$$

Solution Steps

Find the integral of \frac{1}{kV^{2}+g} using the table of common integrals rule \int a\mathrm{d}v=av.

$$\frac{v}{kV^{2}+g}$$

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.

$$\begin{matrix}\frac{v}{kV^{2}+g}+С_{3},&\end{matrix}$$

Differentiate w.r.t. k

$$-\left(\frac{V}{kV^{2}+g}\right)^{2}v$$