Evaluate
\frac{p^{2}x^{3}}{2}+С
Differentiate w.r.t. x
\frac{3\left(px\right)^{2}}{2}
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x^{3}\int p\mathrm{d}p
Factor out the constant using \int af\left(p\right)\mathrm{d}p=a\int f\left(p\right)\mathrm{d}p.
x^{3}\times \frac{p^{2}}{2}
Since \int p^{k}\mathrm{d}p=\frac{p^{k+1}}{k+1} for k\neq -1, replace \int p\mathrm{d}p with \frac{p^{2}}{2}.
\frac{x^{3}p^{2}}{2}
Simplify.
\frac{x^{3}p^{2}}{2}+С
If F\left(p\right) is an antiderivative of f\left(p\right), then the set of all antiderivatives of f\left(p\right) is given by F\left(p\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
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