Optimal. Leaf size=138 \[ \frac{a^3 x^3}{3}-\frac{3}{7} \left (a^2-128 a+512\right ) x^7+\frac{2}{3} \left (3 a^2-96 a+128\right ) x^6+6 a^2 x^4-\frac{3}{11} (256-a) x^{11}+\frac{12}{5} (64-a) x^{10}-\frac{32}{9} (70-3 a) x^9+6 (48-5 a) x^8+\frac{24}{5} (8-a) a x^5-\frac{x^{15}}{15}+\frac{6 x^{14}}{7}-\frac{72 x^{13}}{13}+\frac{70 x^{12}}{3} \]
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Rubi [A] time = 0.323994, 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 \[ \frac{a^3 x^3}{3}-\frac{3}{7} \left (a^2-128 a+512\right ) x^7+\frac{2}{3} \left (3 a^2-96 a+128\right ) x^6+6 a^2 x^4-\frac{3}{11} (256-a) x^{11}+\frac{12}{5} (64-a) x^{10}-\frac{32}{9} (70-3 a) x^9+6 (48-5 a) x^8+\frac{24}{5} (8-a) a x^5-\frac{x^{15}}{15}+\frac{6 x^{14}}{7}-\frac{72 x^{13}}{13}+\frac{70 x^{12}}{3} \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(-x**4+4*x**3-8*x**2+a+8*x)**3,x)
[Out]
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Mathematica [A] time = 0.0301622, size = 132, normalized size = 0.96 \[ \frac{a^3 x^3}{3}-\frac{3}{7} \left (a^2-128 a+512\right ) x^7+\frac{2}{3} \left (3 a^2-96 a+128\right ) x^6+6 a^2 x^4+\frac{3}{11} (a-256) x^{11}-\frac{12}{5} (a-64) x^{10}+\frac{32}{9} (3 a-70) x^9-6 (5 a-48) x^8-\frac{24}{5} (a-8) a x^5-\frac{x^{15}}{15}+\frac{6 x^{14}}{7}-\frac{72 x^{13}}{13}+\frac{70 x^{12}}{3} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^3,x]
[Out]
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Maple [A] time = 0.002, size = 143, normalized size = 1. \[ -{\frac{{x}^{15}}{15}}+{\frac{6\,{x}^{14}}{7}}-{\frac{72\,{x}^{13}}{13}}+{\frac{70\,{x}^{12}}{3}}+{\frac{ \left ( 3\,a-768 \right ){x}^{11}}{11}}+{\frac{ \left ( -24\,a+1536 \right ){x}^{10}}{10}}+{\frac{ \left ( 96\,a-2240 \right ){x}^{9}}{9}}+{\frac{ \left ( -240\,a+2304 \right ){x}^{8}}{8}}+{\frac{ \left ( a \left ( -2\,a+128 \right ) +256\,a-1536-{a}^{2} \right ){x}^{7}}{7}}+{\frac{ \left ( a \left ( 8\,a-128 \right ) -256\,a+512+4\,{a}^{2} \right ){x}^{6}}{6}}+{\frac{ \left ( a \left ( -16\,a+64 \right ) +128\,a-8\,{a}^{2} \right ){x}^{5}}{5}}+6\,{a}^{2}{x}^{4}+{\frac{{a}^{3}{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(-x^4+4*x^3-8*x^2+a+8*x)^3,x)
[Out]
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Maxima [A] time = 0.803474, size = 153, normalized size = 1.11 \[ -\frac{1}{15} \, x^{15} + \frac{6}{7} \, x^{14} - \frac{72}{13} \, x^{13} + \frac{3}{11} \,{\left (a - 256\right )} x^{11} + \frac{70}{3} \, x^{12} - \frac{12}{5} \,{\left (a - 64\right )} x^{10} + \frac{32}{9} \,{\left (3 \, a - 70\right )} x^{9} - 6 \,{\left (5 \, a - 48\right )} x^{8} - \frac{3}{7} \,{\left (a^{2} - 128 \, a + 512\right )} x^{7} + \frac{2}{3} \,{\left (3 \, a^{2} - 96 \, a + 128\right )} x^{6} + \frac{1}{3} \, a^{3} x^{3} + 6 \, a^{2} x^{4} - \frac{24}{5} \,{\left (a^{2} - 8 \, a\right )} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^4 - 4*x^3 + 8*x^2 - a - 8*x)^3*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237487, size = 1, normalized size = 0.01 \[ -\frac{1}{15} x^{15} + \frac{6}{7} x^{14} - \frac{72}{13} x^{13} + \frac{70}{3} x^{12} + \frac{3}{11} x^{11} a - \frac{768}{11} x^{11} - \frac{12}{5} x^{10} a + \frac{768}{5} x^{10} + \frac{32}{3} x^{9} a - \frac{2240}{9} x^{9} - 30 x^{8} a - \frac{3}{7} x^{7} a^{2} + 288 x^{8} + \frac{384}{7} x^{7} a + 2 x^{6} a^{2} - \frac{1536}{7} x^{7} - 64 x^{6} a - \frac{24}{5} x^{5} a^{2} + \frac{256}{3} x^{6} + \frac{192}{5} x^{5} a + 6 x^{4} a^{2} + \frac{1}{3} x^{3} a^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^4 - 4*x^3 + 8*x^2 - a - 8*x)^3*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.176813, size = 134, normalized size = 0.97 \[ \frac{a^{3} x^{3}}{3} + 6 a^{2} x^{4} - \frac{x^{15}}{15} + \frac{6 x^{14}}{7} - \frac{72 x^{13}}{13} + \frac{70 x^{12}}{3} + x^{11} \left (\frac{3 a}{11} - \frac{768}{11}\right ) + x^{10} \left (- \frac{12 a}{5} + \frac{768}{5}\right ) + x^{9} \left (\frac{32 a}{3} - \frac{2240}{9}\right ) + x^{8} \left (- 30 a + 288\right ) + x^{7} \left (- \frac{3 a^{2}}{7} + \frac{384 a}{7} - \frac{1536}{7}\right ) + x^{6} \left (2 a^{2} - 64 a + \frac{256}{3}\right ) + x^{5} \left (- \frac{24 a^{2}}{5} + \frac{192 a}{5}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(-x**4+4*x**3-8*x**2+a+8*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.261684, size = 180, normalized size = 1.3 \[ -\frac{1}{15} \, x^{15} + \frac{6}{7} \, x^{14} - \frac{72}{13} \, x^{13} + \frac{3}{11} \, a x^{11} + \frac{70}{3} \, x^{12} - \frac{12}{5} \, a x^{10} - \frac{768}{11} \, x^{11} + \frac{32}{3} \, a x^{9} + \frac{768}{5} \, x^{10} - \frac{3}{7} \, a^{2} x^{7} - 30 \, a x^{8} - \frac{2240}{9} \, x^{9} + 2 \, a^{2} x^{6} + \frac{384}{7} \, a x^{7} + 288 \, x^{8} - \frac{24}{5} \, a^{2} x^{5} - 64 \, a x^{6} - \frac{1536}{7} \, x^{7} + \frac{1}{3} \, a^{3} x^{3} + 6 \, a^{2} x^{4} + \frac{192}{5} \, a x^{5} + \frac{256}{3} \, x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^4 - 4*x^3 + 8*x^2 - a - 8*x)^3*x^2,x, algorithm="giac")
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