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55800
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\int 5x-3\mathrm{d}x
Evaluate the indefinite integral first.
\int 5x\mathrm{d}x+\int -3\mathrm{d}x
Integrate the sum term by term.
5\int x\mathrm{d}x+\int -3\mathrm{d}x
Factor out the constant in each of the terms.
\frac{5x^{2}}{2}+\int -3\mathrm{d}x
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}. Multiply 5 times \frac{x^{2}}{2}.
\frac{5x^{2}}{2}-3x
Find the integral of -3 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{5}{2}\times 150^{2}-3\times 150-\left(\frac{5}{2}\times 0^{2}-3\times 0\right)
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.
55800
Simplify.
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