Evaluate
-3
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\int x^{2}-4\mathrm{d}x
Evaluate the indefinite integral first.
\int x^{2}\mathrm{d}x+\int -4\mathrm{d}x
Integrate the sum term by term.
\frac{x^{3}}{3}+\int -4\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}.
\frac{x^{3}}{3}-4x
Find the integral of -4 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{3^{3}}{3}-4\times 3-\left(\frac{0^{3}}{3}-4\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.
-3
Simplify.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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