Optimal. Leaf size=19 \[ \frac {1}{6} \left (x^3+6 x^2-12 x+5\right )^2 \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {1588} \[ \frac {1}{6} \left (x^3+6 x^2-12 x+5\right )^2 \]
Antiderivative was successfully verified.
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Rule 1588
Rubi steps
\begin {align*} \int \left (-4+4 x+x^2\right ) \left (5-12 x+6 x^2+x^3\right ) \, dx &=\frac {1}{6} \left (5-12 x+6 x^2+x^3\right )^2\\ \end {align*}
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Mathematica [A] time = 0.00, size = 33, normalized size = 1.74 \[ \frac {x^6}{6}+2 x^5+2 x^4-\frac {67 x^3}{3}+34 x^2-20 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 29, normalized size = 1.53 \[ \frac {1}{6} x^{6} + 2 x^{5} + 2 x^{4} - \frac {67}{3} x^{3} + 34 x^{2} - 20 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 30, normalized size = 1.58 \[ \frac {5}{3} \, x^{3} + \frac {1}{6} \, {\left (x^{3} + 6 \, x^{2} - 12 \, x\right )}^{2} + 10 \, x^{2} - 20 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 30, normalized size = 1.58 \[ \frac {1}{6} x^{6}+2 x^{5}+2 x^{4}-\frac {67}{3} x^{3}+34 x^{2}-20 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 17, normalized size = 0.89 \[ \frac {1}{6} \, {\left (x^{3} + 6 \, x^{2} - 12 \, x + 5\right )}^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 29, normalized size = 1.53 \[ \frac {x^6}{6}+2\,x^5+2\,x^4-\frac {67\,x^3}{3}+34\,x^2-20\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 29, normalized size = 1.53 \[ \frac {x^{6}}{6} + 2 x^{5} + 2 x^{4} - \frac {67 x^{3}}{3} + 34 x^{2} - 20 x \]
Verification of antiderivative is not currently implemented for this CAS.
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