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Differentiate w.r.t. x
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\int x^{1}\mathrm{d}x
To multiply powers of the same base, add their exponents. Add \frac{1}{3} and \frac{2}{3} to get 1.
\int x\mathrm{d}x
Calculate x to the power of 1 and get x.
\frac{x^{2}}{2}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}.
\frac{x^{2}}{2}+С
If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.