Optimal. Leaf size=79 \[ \frac{a^2 x^3}{3}+\frac{2}{7} (64-a) x^7-\frac{4}{3} (16-a) x^6+\frac{16}{5} (4-a) x^5+4 a x^4+\frac{x^{11}}{11}-\frac{4 x^{10}}{5}+\frac{32 x^9}{9}-10 x^8 \]
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Rubi [A] time = 0.0767837, antiderivative size = 79, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038, Rules used = {6742} \[ \frac{a^2 x^3}{3}+\frac{2}{7} (64-a) x^7-\frac{4}{3} (16-a) x^6+\frac{16}{5} (4-a) x^5+4 a x^4+\frac{x^{11}}{11}-\frac{4 x^{10}}{5}+\frac{32 x^9}{9}-10 x^8 \]
Antiderivative was successfully verified.
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Rule 6742
Rubi steps
\begin{align*} \int x^2 \left (a+8 x-8 x^2+4 x^3-x^4\right )^2 \, dx &=\int \left (a^2 x^2+16 a x^3-16 (-4+a) x^4+8 (-16+a) x^5-2 (-64+a) x^6-80 x^7+32 x^8-8 x^9+x^{10}\right ) \, dx\\ &=\frac{a^2 x^3}{3}+4 a x^4+\frac{16}{5} (4-a) x^5-\frac{4}{3} (16-a) x^6+\frac{2}{7} (64-a) x^7-10 x^8+\frac{32 x^9}{9}-\frac{4 x^{10}}{5}+\frac{x^{11}}{11}\\ \end{align*}
Mathematica [A] time = 0.0083944, size = 73, normalized size = 0.92 \[ \frac{a^2 x^3}{3}-\frac{2}{7} (a-64) x^7+\frac{4}{3} (a-16) x^6-\frac{16}{5} (a-4) x^5+4 a x^4+\frac{x^{11}}{11}-\frac{4 x^{10}}{5}+\frac{32 x^9}{9}-10 x^8 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 66, normalized size = 0.8 \begin{align*}{\frac{{x}^{11}}{11}}-{\frac{4\,{x}^{10}}{5}}+{\frac{32\,{x}^{9}}{9}}-10\,{x}^{8}+{\frac{ \left ( -2\,a+128 \right ){x}^{7}}{7}}+{\frac{ \left ( 8\,a-128 \right ){x}^{6}}{6}}+{\frac{ \left ( -16\,a+64 \right ){x}^{5}}{5}}+4\,a{x}^{4}+{\frac{{a}^{2}{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08814, size = 80, normalized size = 1.01 \begin{align*} \frac{1}{11} \, x^{11} - \frac{4}{5} \, x^{10} + \frac{32}{9} \, x^{9} - \frac{2}{7} \,{\left (a - 64\right )} x^{7} - 10 \, x^{8} + \frac{4}{3} \,{\left (a - 16\right )} x^{6} - \frac{16}{5} \,{\left (a - 4\right )} x^{5} + \frac{1}{3} \, a^{2} x^{3} + 4 \, a x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.27528, size = 185, normalized size = 2.34 \begin{align*} \frac{1}{11} x^{11} - \frac{4}{5} x^{10} + \frac{32}{9} x^{9} - 10 x^{8} - \frac{2}{7} x^{7} a + \frac{128}{7} x^{7} + \frac{4}{3} x^{6} a - \frac{64}{3} x^{6} - \frac{16}{5} x^{5} a + \frac{64}{5} x^{5} + 4 x^{4} a + \frac{1}{3} x^{3} a^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.07261, size = 73, normalized size = 0.92 \begin{align*} \frac{a^{2} x^{3}}{3} + 4 a x^{4} + \frac{x^{11}}{11} - \frac{4 x^{10}}{5} + \frac{32 x^{9}}{9} - 10 x^{8} + x^{7} \left (\frac{128}{7} - \frac{2 a}{7}\right ) + x^{6} \left (\frac{4 a}{3} - \frac{64}{3}\right ) + x^{5} \left (\frac{64}{5} - \frac{16 a}{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14009, size = 92, normalized size = 1.16 \begin{align*} \frac{1}{11} \, x^{11} - \frac{4}{5} \, x^{10} + \frac{32}{9} \, x^{9} - \frac{2}{7} \, a x^{7} - 10 \, x^{8} + \frac{4}{3} \, a x^{6} + \frac{128}{7} \, x^{7} - \frac{16}{5} \, a x^{5} - \frac{64}{3} \, x^{6} + \frac{1}{3} \, a^{2} x^{3} + 4 \, a x^{4} + \frac{64}{5} \, x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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