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 = 0.08, antiderivative size = 79, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.36, size = 68, normalized size = 0.86 \[ \frac {1}{11} x^{11} - \frac {4}{5} x^{10} + \frac {32}{9} x^{9} - 10 x^{8} - \frac {2}{7} x^{7} a + \frac {128}{7} x^{7} + \frac {4}{3} x^{6} a - \frac {64}{3} x^{6} - \frac {16}{5} x^{5} a + \frac {64}{5} x^{5} + 4 x^{4} a + \frac {1}{3} x^{3} a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 68, normalized size = 0.86 \[ \frac {1}{11} \, x^{11} - \frac {4}{5} \, x^{10} + \frac {32}{9} \, x^{9} - \frac {2}{7} \, a x^{7} - 10 \, x^{8} + \frac {4}{3} \, a x^{6} + \frac {128}{7} \, x^{7} - \frac {16}{5} \, a x^{5} - \frac {64}{3} \, x^{6} + \frac {1}{3} \, a^{2} x^{3} + 4 \, a x^{4} + \frac {64}{5} \, x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 66, normalized size = 0.84 \[ \frac {x^{11}}{11}-\frac {4 x^{10}}{5}+\frac {32 x^{9}}{9}-10 x^{8}+\frac {\left (-2 a +128\right ) x^{7}}{7}+\frac {\left (8 a -128\right ) x^{6}}{6}+\frac {a^{2} x^{3}}{3}+4 a \,x^{4}+\frac {\left (-16 a +64\right ) x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 59, normalized size = 0.75 \[ \frac {1}{11} \, x^{11} - \frac {4}{5} \, x^{10} + \frac {32}{9} \, x^{9} - \frac {2}{7} \, {\left (a - 64\right )} x^{7} - 10 \, x^{8} + \frac {4}{3} \, {\left (a - 16\right )} x^{6} - \frac {16}{5} \, {\left (a - 4\right )} x^{5} + \frac {1}{3} \, a^{2} x^{3} + 4 \, a x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 64, normalized size = 0.81 \[ x^6\,\left (\frac {4\,a}{3}-\frac {64}{3}\right )-x^5\,\left (\frac {16\,a}{5}-\frac {64}{5}\right )-x^7\,\left (\frac {2\,a}{7}-\frac {128}{7}\right )+4\,a\,x^4-10\,x^8+\frac {32\,x^9}{9}-\frac {4\,x^{10}}{5}+\frac {x^{11}}{11}+\frac {a^2\,x^3}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 73, normalized size = 0.92 \[ \frac {a^{2} x^{3}}{3} + 4 a x^{4} + \frac {x^{11}}{11} - \frac {4 x^{10}}{5} + \frac {32 x^{9}}{9} - 10 x^{8} + x^{7} \left (\frac {128}{7} - \frac {2 a}{7}\right ) + x^{6} \left (\frac {4 a}{3} - \frac {64}{3}\right ) + x^{5} \left (\frac {64}{5} - \frac {16 a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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