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