Evaluate
X\left(6-X\right)^{2}
Differentiate w.r.t. X
3\left(X-6\right)\left(X-2\right)
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\int \left(-X^{2}+6X\right)\left(3-\frac{X}{2}\right)\mathrm{d}x
Evaluate the indefinite integral first.
\left(-X^{2}+6X\right)\left(3-\frac{X}{2}\right)x
Find the integral of \left(-X^{2}+6X\right)\left(3-\frac{X}{2}\right) using the table of common integrals rule \int a\mathrm{d}x=ax.
\left(-X^{2}+6X\right)\left(3-\frac{1}{2}X\right)\times 5-\left(-X^{2}+6X\right)\left(3-\frac{1}{2}X\right)\times 3
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.
X\left(6-X\right)^{2}
Simplify.
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