Optimal. Leaf size=120 \[ -\frac{3}{5} \left (a^2-128 a+512\right ) x^5+\left (3 a^2-96 a+128\right ) x^4+12 a^2 x^2+a^3 x-\frac{1}{3} (256-a) x^9+3 (64-a) x^8-\frac{32}{7} (70-3 a) x^7+8 (48-5 a) x^6+8 (8-a) a x^3-\frac{x^{13}}{13}+x^{12}-\frac{72 x^{11}}{11}+28 x^{10} \]
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Rubi [A] time = 0.0631218, antiderivative size = 120, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {2061} \[ -\frac{3}{5} \left (a^2-128 a+512\right ) x^5+\left (3 a^2-96 a+128\right ) x^4+12 a^2 x^2+a^3 x-\frac{1}{3} (256-a) x^9+3 (64-a) x^8-\frac{32}{7} (70-3 a) x^7+8 (48-5 a) x^6+8 (8-a) a x^3-\frac{x^{13}}{13}+x^{12}-\frac{72 x^{11}}{11}+28 x^{10} \]
Antiderivative was successfully verified.
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Rule 2061
Rubi steps
\begin{align*} \int \left (a+8 x-8 x^2+4 x^3-x^4\right )^3 \, dx &=\int \left (a^3+24 a^2 x+24 (8-a) a x^2+4 \left (128-96 a+3 a^2\right ) x^3-3 \left (512-128 a+a^2\right ) x^4+48 (48-5 a) x^5-32 (70-3 a) x^6+24 (64-a) x^7-3 (256-a) x^8+280 x^9-72 x^{10}+12 x^{11}-x^{12}\right ) \, dx\\ &=a^3 x+12 a^2 x^2+8 (8-a) a x^3+\left (128-96 a+3 a^2\right ) x^4-\frac{3}{5} \left (512-128 a+a^2\right ) x^5+8 (48-5 a) x^6-\frac{32}{7} (70-3 a) x^7+3 (64-a) x^8-\frac{1}{3} (256-a) x^9+28 x^{10}-\frac{72 x^{11}}{11}+x^{12}-\frac{x^{13}}{13}\\ \end{align*}
Mathematica [A] time = 0.0127656, size = 114, normalized size = 0.95 \[ -\frac{3}{5} \left (a^2-128 a+512\right ) x^5+\left (3 a^2-96 a+128\right ) x^4+12 a^2 x^2+a^3 x+\frac{1}{3} (a-256) x^9-3 (a-64) x^8+\frac{32}{7} (3 a-70) x^7-8 (5 a-48) x^6-8 (a-8) a x^3-\frac{x^{13}}{13}+x^{12}-\frac{72 x^{11}}{11}+28 x^{10} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 138, normalized size = 1.2 \begin{align*} -{\frac{{x}^{13}}{13}}+{x}^{12}-{\frac{72\,{x}^{11}}{11}}+28\,{x}^{10}+{\frac{ \left ( 3\,a-768 \right ){x}^{9}}{9}}+{\frac{ \left ( -24\,a+1536 \right ){x}^{8}}{8}}+{\frac{ \left ( 96\,a-2240 \right ){x}^{7}}{7}}+{\frac{ \left ( -240\,a+2304 \right ){x}^{6}}{6}}+{\frac{ \left ( a \left ( -2\,a+128 \right ) +256\,a-1536-{a}^{2} \right ){x}^{5}}{5}}+{\frac{ \left ( a \left ( 8\,a-128 \right ) -256\,a+512+4\,{a}^{2} \right ){x}^{4}}{4}}+{\frac{ \left ( a \left ( -16\,a+64 \right ) +128\,a-8\,{a}^{2} \right ){x}^{3}}{3}}+12\,{a}^{2}{x}^{2}+{a}^{3}x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.19175, size = 161, normalized size = 1.34 \begin{align*} -\frac{1}{13} \, x^{13} + x^{12} - \frac{72}{11} \, x^{11} + 28 \, x^{10} - \frac{256}{3} \, x^{9} + 192 \, x^{8} - 320 \, x^{7} + 384 \, x^{6} - \frac{1536}{5} \, x^{5} + a^{3} x + 128 \, x^{4} - \frac{1}{5} \,{\left (3 \, x^{5} - 15 \, x^{4} + 40 \, x^{3} - 60 \, x^{2}\right )} a^{2} + \frac{1}{105} \,{\left (35 \, x^{9} - 315 \, x^{8} + 1440 \, x^{7} - 4200 \, x^{6} + 8064 \, x^{5} - 10080 \, x^{4} + 6720 \, x^{3}\right )} a \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28333, size = 335, normalized size = 2.79 \begin{align*} -\frac{1}{13} x^{13} + x^{12} - \frac{72}{11} x^{11} + 28 x^{10} + \frac{1}{3} x^{9} a - \frac{256}{3} x^{9} - 3 x^{8} a + 192 x^{8} + \frac{96}{7} x^{7} a - 320 x^{7} - 40 x^{6} a - \frac{3}{5} x^{5} a^{2} + 384 x^{6} + \frac{384}{5} x^{5} a + 3 x^{4} a^{2} - \frac{1536}{5} x^{5} - 96 x^{4} a - 8 x^{3} a^{2} + 128 x^{4} + 64 x^{3} a + 12 x^{2} a^{2} + x a^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.086457, size = 114, normalized size = 0.95 \begin{align*} a^{3} x + 12 a^{2} x^{2} - \frac{x^{13}}{13} + x^{12} - \frac{72 x^{11}}{11} + 28 x^{10} + x^{9} \left (\frac{a}{3} - \frac{256}{3}\right ) + x^{8} \left (192 - 3 a\right ) + x^{7} \left (\frac{96 a}{7} - 320\right ) + x^{6} \left (384 - 40 a\right ) + x^{5} \left (- \frac{3 a^{2}}{5} + \frac{384 a}{5} - \frac{1536}{5}\right ) + x^{4} \left (3 a^{2} - 96 a + 128\right ) + x^{3} \left (- 8 a^{2} + 64 a\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11707, size = 173, normalized size = 1.44 \begin{align*} -\frac{1}{13} \, x^{13} + x^{12} - \frac{72}{11} \, x^{11} + \frac{1}{3} \, a x^{9} + 28 \, x^{10} - 3 \, a x^{8} - \frac{256}{3} \, x^{9} + \frac{96}{7} \, a x^{7} + 192 \, x^{8} - \frac{3}{5} \, a^{2} x^{5} - 40 \, a x^{6} - 320 \, x^{7} + 3 \, a^{2} x^{4} + \frac{384}{5} \, a x^{5} + 384 \, x^{6} - 8 \, a^{2} x^{3} - 96 \, a x^{4} - \frac{1536}{5} \, x^{5} + a^{3} x + 12 \, a^{2} x^{2} + 64 \, a x^{3} + 128 \, x^{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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