Optimal. Leaf size=22 \[ -4 x^3+\frac {1}{16} \left (7-4 x^2\right )^2+21 x \]
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Rubi [A] time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {641} \[ -4 x^3+\frac {1}{16} \left (7-4 x^2\right )^2+21 x \]
Antiderivative was successfully verified.
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Rule 641
Rubi steps
\begin {align*} \int (-3+x) \left (-7+4 x^2\right ) \, dx &=\frac {1}{16} \left (7-4 x^2\right )^2-3 \int \left (-7+4 x^2\right ) \, dx\\ &=21 x-4 x^3+\frac {1}{16} \left (7-4 x^2\right )^2\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 0.86 \[ x^4-4 x^3-\frac {7 x^2}{2}+21 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 17, normalized size = 0.77 \[ x^{4} - 4 x^{3} - \frac {7}{2} x^{2} + 21 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 17, normalized size = 0.77 \[ x^{4} - 4 \, x^{3} - \frac {7}{2} \, x^{2} + 21 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.82 \[ x^{4}-4 x^{3}-\frac {7}{2} x^{2}+21 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.88, size = 17, normalized size = 0.77 \[ x^{4} - 4 \, x^{3} - \frac {7}{2} \, x^{2} + 21 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 17, normalized size = 0.77 \[ x^4-4\,x^3-\frac {7\,x^2}{2}+21\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 17, normalized size = 0.77 \[ x^{4} - 4 x^{3} - \frac {7 x^{2}}{2} + 21 x \]
Verification of antiderivative is not currently implemented for this CAS.
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