Optimal. Leaf size=76 \[ \frac{512 x^{13}}{13}-240 x^{12}+\frac{6936 x^{11}}{11}-\frac{4527 x^{10}}{10}-\frac{2936 x^9}{3}+2097 x^8+\frac{5528 x^7}{7}-2976 x^6-\frac{384 x^5}{5}+5040 x^4+5120 x^3+2304 x^2+512 x \]
[Out]
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Rubi [A] time = 0.0500937, antiderivative size = 76, 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 \[ \frac{512 x^{13}}{13}-240 x^{12}+\frac{6936 x^{11}}{11}-\frac{4527 x^{10}}{10}-\frac{2936 x^9}{3}+2097 x^8+\frac{5528 x^7}{7}-2976 x^6-\frac{384 x^5}{5}+5040 x^4+5120 x^3+2304 x^2+512 x \]
Antiderivative was successfully verified.
[In] Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^3,x]
[Out]
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Rubi in Sympy [A] time = 61.2572, size = 73, normalized size = 0.96 \[ \frac{512 x^{13}}{13} - 240 x^{12} + \frac{6936 x^{11}}{11} - \frac{4527 x^{10}}{10} - \frac{2936 x^{9}}{3} + 2097 x^{8} + \frac{5528 x^{7}}{7} - 2976 x^{6} - \frac{384 x^{5}}{5} + 5040 x^{4} + 5120 x^{3} + 2304 x^{2} + 512 x \]
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)**3,x)
[Out]
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Mathematica [A] time = 0.00154104, size = 76, normalized size = 1. \[ \frac{512 x^{13}}{13}-240 x^{12}+\frac{6936 x^{11}}{11}-\frac{4527 x^{10}}{10}-\frac{2936 x^9}{3}+2097 x^8+\frac{5528 x^7}{7}-2976 x^6-\frac{384 x^5}{5}+5040 x^4+5120 x^3+2304 x^2+512 x \]
Antiderivative was successfully verified.
[In] Integrate[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^3,x]
[Out]
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Maple [A] time = 0.002, size = 65, normalized size = 0.9 \[ 512\,x+2304\,{x}^{2}+5120\,{x}^{3}+5040\,{x}^{4}-{\frac{384\,{x}^{5}}{5}}-2976\,{x}^{6}+{\frac{5528\,{x}^{7}}{7}}+2097\,{x}^{8}-{\frac{2936\,{x}^{9}}{3}}-{\frac{4527\,{x}^{10}}{10}}+{\frac{6936\,{x}^{11}}{11}}-240\,{x}^{12}+{\frac{512\,{x}^{13}}{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((8*x^4-15*x^3+8*x^2+24*x+8)^3,x)
[Out]
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Maxima [A] time = 0.806273, size = 86, normalized size = 1.13 \[ \frac{512}{13} \, x^{13} - 240 \, x^{12} + \frac{6936}{11} \, x^{11} - \frac{4527}{10} \, x^{10} - \frac{2936}{3} \, x^{9} + 2097 \, x^{8} + \frac{5528}{7} \, x^{7} - 2976 \, x^{6} - \frac{384}{5} \, x^{5} + 5040 \, x^{4} + 5120 \, x^{3} + 2304 \, x^{2} + 512 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236993, size = 1, normalized size = 0.01 \[ \frac{512}{13} x^{13} - 240 x^{12} + \frac{6936}{11} x^{11} - \frac{4527}{10} x^{10} - \frac{2936}{3} x^{9} + 2097 x^{8} + \frac{5528}{7} x^{7} - 2976 x^{6} - \frac{384}{5} x^{5} + 5040 x^{4} + 5120 x^{3} + 2304 x^{2} + 512 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.110758, size = 73, normalized size = 0.96 \[ \frac{512 x^{13}}{13} - 240 x^{12} + \frac{6936 x^{11}}{11} - \frac{4527 x^{10}}{10} - \frac{2936 x^{9}}{3} + 2097 x^{8} + \frac{5528 x^{7}}{7} - 2976 x^{6} - \frac{384 x^{5}}{5} + 5040 x^{4} + 5120 x^{3} + 2304 x^{2} + 512 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x**4-15*x**3+8*x**2+24*x+8)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.262088, size = 86, normalized size = 1.13 \[ \frac{512}{13} \, x^{13} - 240 \, x^{12} + \frac{6936}{11} \, x^{11} - \frac{4527}{10} \, x^{10} - \frac{2936}{3} \, x^{9} + 2097 \, x^{8} + \frac{5528}{7} \, x^{7} - 2976 \, x^{6} - \frac{384}{5} \, x^{5} + 5040 \, x^{4} + 5120 \, x^{3} + 2304 \, x^{2} + 512 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((8*x^4 - 15*x^3 + 8*x^2 + 24*x + 8)^3,x, algorithm="giac")
[Out]