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 = 0.0088695, antiderivative size = 19, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0015824, 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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Maple [A] time = 0.001, size = 30, normalized size = 1.6 \begin{align*}{\frac{{x}^{6}}{6}}+2\,{x}^{5}+2\,{x}^{4}-{\frac{67\,{x}^{3}}{3}}+34\,{x}^{2}-20\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05212, size = 23, normalized size = 1.21 \begin{align*} \frac{1}{6} \,{\left (x^{3} + 6 \, x^{2} - 12 \, x + 5\right )}^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.11781, size = 70, normalized size = 3.68 \begin{align*} \frac{1}{6} x^{6} + 2 x^{5} + 2 x^{4} - \frac{67}{3} x^{3} + 34 x^{2} - 20 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058059, size = 29, normalized size = 1.53 \begin{align*} \frac{x^{6}}{6} + 2 x^{5} + 2 x^{4} - \frac{67 x^{3}}{3} + 34 x^{2} - 20 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19765, size = 39, normalized size = 2.05 \begin{align*} \frac{1}{6} \, x^{6} + 2 \, x^{5} + 2 \, x^{4} - \frac{67}{3} \, x^{3} + 34 \, x^{2} - 20 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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