Evaluate
\frac{x^{2}}{2}
Differentiate w.r.t. x
x
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\int u\mathrm{d}u
Evaluate the indefinite integral first.
\frac{u^{2}}{2}
Since \int u^{k}\mathrm{d}u=\frac{u^{k+1}}{k+1} for k\neq -1, replace \int u\mathrm{d}u with \frac{u^{2}}{2}.
\frac{x^{2}}{2}-\frac{0^{2}}{2}
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
\frac{x^{2}}{2}
Simplify.
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