Optimal. Leaf size=134 \[ -\frac{1}{2} \left (a^2-128 a+512\right ) x^6+\frac{4}{5} \left (3 a^2-96 a+128\right ) x^5+8 a^2 x^3+\frac{a^3 x^2}{2}-\frac{3}{10} (256-a) x^{10}+\frac{8}{3} (64-a) x^9-4 (70-3 a) x^8+\frac{48}{7} (48-5 a) x^7+6 (8-a) a x^4-\frac{x^{14}}{14}+\frac{12 x^{13}}{13}-6 x^{12}+\frac{280 x^{11}}{11} \]
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Rubi [A] time = 0.140292, antiderivative size = 134, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042, Rules used = {6742} \[ -\frac{1}{2} \left (a^2-128 a+512\right ) x^6+\frac{4}{5} \left (3 a^2-96 a+128\right ) x^5+8 a^2 x^3+\frac{a^3 x^2}{2}-\frac{3}{10} (256-a) x^{10}+\frac{8}{3} (64-a) x^9-4 (70-3 a) x^8+\frac{48}{7} (48-5 a) x^7+6 (8-a) a x^4-\frac{x^{14}}{14}+\frac{12 x^{13}}{13}-6 x^{12}+\frac{280 x^{11}}{11} \]
Antiderivative was successfully verified.
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Rule 6742
Rubi steps
\begin{align*} \int x \left (a+8 x-8 x^2+4 x^3-x^4\right )^3 \, dx &=\int \left (a^3 x+24 a^2 x^2-24 (-8+a) a x^3+4 \left (128-96 a+3 a^2\right ) x^4-3 \left (512-128 a+a^2\right ) x^5-48 (-48+5 a) x^6+32 (-70+3 a) x^7-24 (-64+a) x^8+3 (-256+a) x^9+280 x^{10}-72 x^{11}+12 x^{12}-x^{13}\right ) \, dx\\ &=\frac{a^3 x^2}{2}+8 a^2 x^3+6 (8-a) a x^4+\frac{4}{5} \left (128-96 a+3 a^2\right ) x^5-\frac{1}{2} \left (512-128 a+a^2\right ) x^6+\frac{48}{7} (48-5 a) x^7-4 (70-3 a) x^8+\frac{8}{3} (64-a) x^9-\frac{3}{10} (256-a) x^{10}+\frac{280 x^{11}}{11}-6 x^{12}+\frac{12 x^{13}}{13}-\frac{x^{14}}{14}\\ \end{align*}
Mathematica [A] time = 0.0152381, size = 130, normalized size = 0.97 \[ \frac{1}{2} \left (-a^2+128 a-512\right ) x^6+\frac{4}{5} \left (3 a^2-96 a+128\right ) x^5+8 a^2 x^3+\frac{a^3 x^2}{2}+\frac{3}{10} (a-256) x^{10}-\frac{8}{3} (a-64) x^9+4 (3 a-70) x^8-\frac{48}{7} (5 a-48) x^7-6 (a-8) a x^4-\frac{x^{14}}{14}+\frac{12 x^{13}}{13}-6 x^{12}+\frac{280 x^{11}}{11} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 143, normalized size = 1.1 \begin{align*} -{\frac{{x}^{14}}{14}}+{\frac{12\,{x}^{13}}{13}}-6\,{x}^{12}+{\frac{280\,{x}^{11}}{11}}+{\frac{ \left ( 3\,a-768 \right ){x}^{10}}{10}}+{\frac{ \left ( -24\,a+1536 \right ){x}^{9}}{9}}+{\frac{ \left ( 96\,a-2240 \right ){x}^{8}}{8}}+{\frac{ \left ( -240\,a+2304 \right ){x}^{7}}{7}}+{\frac{ \left ( a \left ( -2\,a+128 \right ) +256\,a-1536-{a}^{2} \right ){x}^{6}}{6}}+{\frac{ \left ( a \left ( 8\,a-128 \right ) -256\,a+512+4\,{a}^{2} \right ){x}^{5}}{5}}+{\frac{ \left ( a \left ( -16\,a+64 \right ) +128\,a-8\,{a}^{2} \right ){x}^{4}}{4}}+8\,{a}^{2}{x}^{3}+{\frac{{a}^{3}{x}^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11751, size = 153, normalized size = 1.14 \begin{align*} -\frac{1}{14} \, x^{14} + \frac{12}{13} \, x^{13} - 6 \, x^{12} + \frac{3}{10} \,{\left (a - 256\right )} x^{10} + \frac{280}{11} \, x^{11} - \frac{8}{3} \,{\left (a - 64\right )} x^{9} + 4 \,{\left (3 \, a - 70\right )} x^{8} - \frac{48}{7} \,{\left (5 \, a - 48\right )} x^{7} - \frac{1}{2} \,{\left (a^{2} - 128 \, a + 512\right )} x^{6} + \frac{4}{5} \,{\left (3 \, a^{2} - 96 \, a + 128\right )} x^{5} + \frac{1}{2} \, a^{3} x^{2} + 8 \, a^{2} x^{3} - 6 \,{\left (a^{2} - 8 \, a\right )} x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.30467, size = 367, normalized size = 2.74 \begin{align*} -\frac{1}{14} x^{14} + \frac{12}{13} x^{13} - 6 x^{12} + \frac{280}{11} x^{11} + \frac{3}{10} x^{10} a - \frac{384}{5} x^{10} - \frac{8}{3} x^{9} a + \frac{512}{3} x^{9} + 12 x^{8} a - 280 x^{8} - \frac{240}{7} x^{7} a - \frac{1}{2} x^{6} a^{2} + \frac{2304}{7} x^{7} + 64 x^{6} a + \frac{12}{5} x^{5} a^{2} - 256 x^{6} - \frac{384}{5} x^{5} a - 6 x^{4} a^{2} + \frac{512}{5} x^{5} + 48 x^{4} a + 8 x^{3} a^{2} + \frac{1}{2} x^{2} a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.124691, size = 128, normalized size = 0.96 \begin{align*} \frac{a^{3} x^{2}}{2} + 8 a^{2} x^{3} - \frac{x^{14}}{14} + \frac{12 x^{13}}{13} - 6 x^{12} + \frac{280 x^{11}}{11} + x^{10} \left (\frac{3 a}{10} - \frac{384}{5}\right ) + x^{9} \left (\frac{512}{3} - \frac{8 a}{3}\right ) + x^{8} \left (12 a - 280\right ) + x^{7} \left (\frac{2304}{7} - \frac{240 a}{7}\right ) + x^{6} \left (- \frac{a^{2}}{2} + 64 a - 256\right ) + x^{5} \left (\frac{12 a^{2}}{5} - \frac{384 a}{5} + \frac{512}{5}\right ) + x^{4} \left (- 6 a^{2} + 48 a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13084, size = 180, normalized size = 1.34 \begin{align*} -\frac{1}{14} \, x^{14} + \frac{12}{13} \, x^{13} - 6 \, x^{12} + \frac{3}{10} \, a x^{10} + \frac{280}{11} \, x^{11} - \frac{8}{3} \, a x^{9} - \frac{384}{5} \, x^{10} + 12 \, a x^{8} + \frac{512}{3} \, x^{9} - \frac{1}{2} \, a^{2} x^{6} - \frac{240}{7} \, a x^{7} - 280 \, x^{8} + \frac{12}{5} \, a^{2} x^{5} + 64 \, a x^{6} + \frac{2304}{7} \, x^{7} - 6 \, a^{2} x^{4} - \frac{384}{5} \, a x^{5} - 256 \, x^{6} + \frac{1}{2} \, a^{3} x^{2} + 8 \, a^{2} x^{3} + 48 \, a x^{4} + \frac{512}{5} \, x^{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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