Optimal. Leaf size=138 \[ -\frac{3}{7} \left (a^2-128 a+512\right ) x^7+\frac{2}{3} \left (3 a^2-96 a+128\right ) x^6+6 a^2 x^4+\frac{a^3 x^3}{3}-\frac{3}{11} (256-a) x^{11}+\frac{12}{5} (64-a) x^{10}-\frac{32}{9} (70-3 a) x^9+6 (48-5 a) x^8+\frac{24}{5} (8-a) a x^5-\frac{x^{15}}{15}+\frac{6 x^{14}}{7}-\frac{72 x^{13}}{13}+\frac{70 x^{12}}{3} \]
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Rubi [A] time = 0.120811, antiderivative size = 138, 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} \[ -\frac{3}{7} \left (a^2-128 a+512\right ) x^7+\frac{2}{3} \left (3 a^2-96 a+128\right ) x^6+6 a^2 x^4+\frac{a^3 x^3}{3}-\frac{3}{11} (256-a) x^{11}+\frac{12}{5} (64-a) x^{10}-\frac{32}{9} (70-3 a) x^9+6 (48-5 a) x^8+\frac{24}{5} (8-a) a x^5-\frac{x^{15}}{15}+\frac{6 x^{14}}{7}-\frac{72 x^{13}}{13}+\frac{70 x^{12}}{3} \]
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 )^3 \, dx &=\int \left (a^3 x^2+24 a^2 x^3-24 (-8+a) a x^4+4 \left (128-96 a+3 a^2\right ) x^5-3 \left (512-128 a+a^2\right ) x^6-48 (-48+5 a) x^7+32 (-70+3 a) x^8-24 (-64+a) x^9+3 (-256+a) x^{10}+280 x^{11}-72 x^{12}+12 x^{13}-x^{14}\right ) \, dx\\ &=\frac{a^3 x^3}{3}+6 a^2 x^4+\frac{24}{5} (8-a) a x^5+\frac{2}{3} \left (128-96 a+3 a^2\right ) x^6-\frac{3}{7} \left (512-128 a+a^2\right ) x^7+6 (48-5 a) x^8-\frac{32}{9} (70-3 a) x^9+\frac{12}{5} (64-a) x^{10}-\frac{3}{11} (256-a) x^{11}+\frac{70 x^{12}}{3}-\frac{72 x^{13}}{13}+\frac{6 x^{14}}{7}-\frac{x^{15}}{15}\\ \end{align*}
Mathematica [A] time = 0.014738, size = 132, normalized size = 0.96 \[ -\frac{3}{7} \left (a^2-128 a+512\right ) x^7+\frac{2}{3} \left (3 a^2-96 a+128\right ) x^6+6 a^2 x^4+\frac{a^3 x^3}{3}+\frac{3}{11} (a-256) x^{11}-\frac{12}{5} (a-64) x^{10}+\frac{32}{9} (3 a-70) x^9-6 (5 a-48) x^8-\frac{24}{5} (a-8) a x^5-\frac{x^{15}}{15}+\frac{6 x^{14}}{7}-\frac{72 x^{13}}{13}+\frac{70 x^{12}}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 143, normalized size = 1. \begin{align*} -{\frac{{x}^{15}}{15}}+{\frac{6\,{x}^{14}}{7}}-{\frac{72\,{x}^{13}}{13}}+{\frac{70\,{x}^{12}}{3}}+{\frac{ \left ( 3\,a-768 \right ){x}^{11}}{11}}+{\frac{ \left ( -24\,a+1536 \right ){x}^{10}}{10}}+{\frac{ \left ( 96\,a-2240 \right ){x}^{9}}{9}}+{\frac{ \left ( -240\,a+2304 \right ){x}^{8}}{8}}+{\frac{ \left ( a \left ( -2\,a+128 \right ) +256\,a-1536-{a}^{2} \right ){x}^{7}}{7}}+{\frac{ \left ( a \left ( 8\,a-128 \right ) -256\,a+512+4\,{a}^{2} \right ){x}^{6}}{6}}+{\frac{ \left ( a \left ( -16\,a+64 \right ) +128\,a-8\,{a}^{2} \right ){x}^{5}}{5}}+6\,{a}^{2}{x}^{4}+{\frac{{a}^{3}{x}^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00186, size = 153, normalized size = 1.11 \begin{align*} -\frac{1}{15} \, x^{15} + \frac{6}{7} \, x^{14} - \frac{72}{13} \, x^{13} + \frac{3}{11} \,{\left (a - 256\right )} x^{11} + \frac{70}{3} \, x^{12} - \frac{12}{5} \,{\left (a - 64\right )} x^{10} + \frac{32}{9} \,{\left (3 \, a - 70\right )} x^{9} - 6 \,{\left (5 \, a - 48\right )} x^{8} - \frac{3}{7} \,{\left (a^{2} - 128 \, a + 512\right )} x^{7} + \frac{2}{3} \,{\left (3 \, a^{2} - 96 \, a + 128\right )} x^{6} + \frac{1}{3} \, a^{3} x^{3} + 6 \, a^{2} x^{4} - \frac{24}{5} \,{\left (a^{2} - 8 \, a\right )} x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.25447, size = 379, normalized size = 2.75 \begin{align*} -\frac{1}{15} x^{15} + \frac{6}{7} x^{14} - \frac{72}{13} x^{13} + \frac{70}{3} x^{12} + \frac{3}{11} x^{11} a - \frac{768}{11} x^{11} - \frac{12}{5} x^{10} a + \frac{768}{5} x^{10} + \frac{32}{3} x^{9} a - \frac{2240}{9} x^{9} - 30 x^{8} a - \frac{3}{7} x^{7} a^{2} + 288 x^{8} + \frac{384}{7} x^{7} a + 2 x^{6} a^{2} - \frac{1536}{7} x^{7} - 64 x^{6} a - \frac{24}{5} x^{5} a^{2} + \frac{256}{3} x^{6} + \frac{192}{5} x^{5} a + 6 x^{4} a^{2} + \frac{1}{3} x^{3} a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.091309, size = 134, normalized size = 0.97 \begin{align*} \frac{a^{3} x^{3}}{3} + 6 a^{2} x^{4} - \frac{x^{15}}{15} + \frac{6 x^{14}}{7} - \frac{72 x^{13}}{13} + \frac{70 x^{12}}{3} + x^{11} \left (\frac{3 a}{11} - \frac{768}{11}\right ) + x^{10} \left (\frac{768}{5} - \frac{12 a}{5}\right ) + x^{9} \left (\frac{32 a}{3} - \frac{2240}{9}\right ) + x^{8} \left (288 - 30 a\right ) + x^{7} \left (- \frac{3 a^{2}}{7} + \frac{384 a}{7} - \frac{1536}{7}\right ) + x^{6} \left (2 a^{2} - 64 a + \frac{256}{3}\right ) + x^{5} \left (- \frac{24 a^{2}}{5} + \frac{192 a}{5}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13438, size = 180, normalized size = 1.3 \begin{align*} -\frac{1}{15} \, x^{15} + \frac{6}{7} \, x^{14} - \frac{72}{13} \, x^{13} + \frac{3}{11} \, a x^{11} + \frac{70}{3} \, x^{12} - \frac{12}{5} \, a x^{10} - \frac{768}{11} \, x^{11} + \frac{32}{3} \, a x^{9} + \frac{768}{5} \, x^{10} - \frac{3}{7} \, a^{2} x^{7} - 30 \, a x^{8} - \frac{2240}{9} \, x^{9} + 2 \, a^{2} x^{6} + \frac{384}{7} \, a x^{7} + 288 \, x^{8} - \frac{24}{5} \, a^{2} x^{5} - 64 \, a x^{6} - \frac{1536}{7} \, x^{7} + \frac{1}{3} \, a^{3} x^{3} + 6 \, a^{2} x^{4} + \frac{192}{5} \, a x^{5} + \frac{256}{3} \, x^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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