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\int x^{2}+e^{2}\mathrm{d}x
Evaluate the indefinite integral first.
\int x^{2}\mathrm{d}x+\int e^{2}\mathrm{d}x
Integrate the sum term by term.
\frac{x^{3}}{3}+\int e^{2}\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.
Find the integral of e^{2}\approx 7.389056099 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{1^{3}}{3}+e^{2}\times 1-\left(\frac{0^{3}}{3}+e^{2}\times 0\right)\approx 7.722389432
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{1}{3}+e^{2}\approx 7.722389432