Evaluate
С\left(vx+v\right)+\frac{vzx^{2}}{2}+С_{1}
Differentiate w.r.t. x
vxz+Сv
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\int \int z\mathrm{d}x\mathrm{d}xv
Find the integral of \int \int z\mathrm{d}x\mathrm{d}x using the table of common integrals rule \int a\mathrm{d}v=av.
\left(\frac{zx^{2}}{2}+Сx+С\right)v
Simplify.
\left(\frac{zx^{2}}{2}+Сx+С\right)v+С
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.
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