Optimal. Leaf size=104 \[ \frac{4096 x^{17}}{17}-1920 x^{16}+\frac{102784 x^{15}}{15}-\frac{75504 x^{14}}{7}-\frac{12095 x^{13}}{13}+31128 x^{12}-\frac{331040 x^{11}}{11}-\frac{169584 x^{10}}{5}+\frac{641152 x^9}{9}+36384 x^8-\frac{566912 x^7}{7}-30720 x^6+\frac{538624 x^5}{5}+139776 x^4+\frac{237568 x^3}{3}+24576 x^2+4096 x \]
[Out]
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Rubi [A] time = 0.0668608, antiderivative size = 104, 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 \[ \frac{4096 x^{17}}{17}-1920 x^{16}+\frac{102784 x^{15}}{15}-\frac{75504 x^{14}}{7}-\frac{12095 x^{13}}{13}+31128 x^{12}-\frac{331040 x^{11}}{11}-\frac{169584 x^{10}}{5}+\frac{641152 x^9}{9}+36384 x^8-\frac{566912 x^7}{7}-30720 x^6+\frac{538624 x^5}{5}+139776 x^4+\frac{237568 x^3}{3}+24576 x^2+4096 x \]
Antiderivative was successfully verified.
[In] Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^4,x]
[Out]
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Rubi in Sympy [A] time = 74.7417, size = 100, normalized size = 0.96 \[ \frac{4096 x^{17}}{17} - 1920 x^{16} + \frac{102784 x^{15}}{15} - \frac{75504 x^{14}}{7} - \frac{12095 x^{13}}{13} + 31128 x^{12} - \frac{331040 x^{11}}{11} - \frac{169584 x^{10}}{5} + \frac{641152 x^{9}}{9} + 36384 x^{8} - \frac{566912 x^{7}}{7} - 30720 x^{6} + \frac{538624 x^{5}}{5} + 139776 x^{4} + \frac{237568 x^{3}}{3} + 24576 x^{2} + 4096 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((8*x**4-15*x**3+8*x**2+24*x+8)**4,x)
[Out]
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Mathematica [A] time = 0.00282705, size = 104, normalized size = 1. \[ \frac{4096 x^{17}}{17}-1920 x^{16}+\frac{102784 x^{15}}{15}-\frac{75504 x^{14}}{7}-\frac{12095 x^{13}}{13}+31128 x^{12}-\frac{331040 x^{11}}{11}-\frac{169584 x^{10}}{5}+\frac{641152 x^9}{9}+36384 x^8-\frac{566912 x^7}{7}-30720 x^6+\frac{538624 x^5}{5}+139776 x^4+\frac{237568 x^3}{3}+24576 x^2+4096 x \]
Antiderivative was successfully verified.
[In] Integrate[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^4,x]
[Out]
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Maple [A] time = 0.002, size = 85, normalized size = 0.8 \[ 4096\,x+24576\,{x}^{2}+{\frac{237568\,{x}^{3}}{3}}+139776\,{x}^{4}+{\frac{538624\,{x}^{5}}{5}}-30720\,{x}^{6}-{\frac{566912\,{x}^{7}}{7}}+36384\,{x}^{8}+{\frac{641152\,{x}^{9}}{9}}-{\frac{169584\,{x}^{10}}{5}}-{\frac{331040\,{x}^{11}}{11}}+31128\,{x}^{12}-{\frac{12095\,{x}^{13}}{13}}-{\frac{75504\,{x}^{14}}{7}}+{\frac{102784\,{x}^{15}}{15}}-1920\,{x}^{16}+{\frac{4096\,{x}^{17}}{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((8*x^4-15*x^3+8*x^2+24*x+8)^4,x)
[Out]
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Maxima [A] time = 0.807568, size = 113, normalized size = 1.09 \[ \frac{4096}{17} \, x^{17} - 1920 \, x^{16} + \frac{102784}{15} \, x^{15} - \frac{75504}{7} \, x^{14} - \frac{12095}{13} \, x^{13} + 31128 \, x^{12} - \frac{331040}{11} \, x^{11} - \frac{169584}{5} \, x^{10} + \frac{641152}{9} \, x^{9} + 36384 \, x^{8} - \frac{566912}{7} \, x^{7} - 30720 \, x^{6} + \frac{538624}{5} \, x^{5} + 139776 \, x^{4} + \frac{237568}{3} \, x^{3} + 24576 \, x^{2} + 4096 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)^4,x, algorithm="maxima")
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Fricas [A] time = 0.2239, size = 1, normalized size = 0.01 \[ \frac{4096}{17} x^{17} - 1920 x^{16} + \frac{102784}{15} x^{15} - \frac{75504}{7} x^{14} - \frac{12095}{13} x^{13} + 31128 x^{12} - \frac{331040}{11} x^{11} - \frac{169584}{5} x^{10} + \frac{641152}{9} x^{9} + 36384 x^{8} - \frac{566912}{7} x^{7} - 30720 x^{6} + \frac{538624}{5} x^{5} + 139776 x^{4} + \frac{237568}{3} x^{3} + 24576 x^{2} + 4096 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)^4,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.134125, size = 100, normalized size = 0.96 \[ \frac{4096 x^{17}}{17} - 1920 x^{16} + \frac{102784 x^{15}}{15} - \frac{75504 x^{14}}{7} - \frac{12095 x^{13}}{13} + 31128 x^{12} - \frac{331040 x^{11}}{11} - \frac{169584 x^{10}}{5} + \frac{641152 x^{9}}{9} + 36384 x^{8} - \frac{566912 x^{7}}{7} - 30720 x^{6} + \frac{538624 x^{5}}{5} + 139776 x^{4} + \frac{237568 x^{3}}{3} + 24576 x^{2} + 4096 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x**4-15*x**3+8*x**2+24*x+8)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.262244, size = 113, normalized size = 1.09 \[ \frac{4096}{17} \, x^{17} - 1920 \, x^{16} + \frac{102784}{15} \, x^{15} - \frac{75504}{7} \, x^{14} - \frac{12095}{13} \, x^{13} + 31128 \, x^{12} - \frac{331040}{11} \, x^{11} - \frac{169584}{5} \, x^{10} + \frac{641152}{9} \, x^{9} + 36384 \, x^{8} - \frac{566912}{7} \, x^{7} - 30720 \, x^{6} + \frac{538624}{5} \, x^{5} + 139776 \, x^{4} + \frac{237568}{3} \, x^{3} + 24576 \, x^{2} + 4096 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)^4,x, algorithm="giac")
[Out]