Optimal. Leaf size=63 \[ -\frac{4096 x^{19}}{19}+\frac{24576 x^{17}}{17}-\frac{21248 x^{15}}{5}+\frac{93440 x^{13}}{13}-\frac{84912 x^{11}}{11}+\frac{16448 x^9}{3}-2605 x^7+\frac{4113 x^5}{5}-171 x^3+27 x \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.292921, antiderivative size = 63, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{4096 x^{19}}{19}+\frac{24576 x^{17}}{17}-\frac{21248 x^{15}}{5}+\frac{93440 x^{13}}{13}-\frac{84912 x^{11}}{11}+\frac{16448 x^9}{3}-2605 x^7+\frac{4113 x^5}{5}-171 x^3+27 x \]
Antiderivative was successfully verified.
[In] Int[(3 - 19*x^2 + 32*x^4 - 16*x^6)^3,x]
[Out]
_______________________________________________________________________________________
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((-16*x**6+32*x**4-19*x**2+3)**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00329678, size = 63, normalized size = 1. \[ -\frac{4096 x^{19}}{19}+\frac{24576 x^{17}}{17}-\frac{21248 x^{15}}{5}+\frac{93440 x^{13}}{13}-\frac{84912 x^{11}}{11}+\frac{16448 x^9}{3}-2605 x^7+\frac{4113 x^5}{5}-171 x^3+27 x \]
Antiderivative was successfully verified.
[In] Integrate[(3 - 19*x^2 + 32*x^4 - 16*x^6)^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 50, normalized size = 0.8 \[ 27\,x-171\,{x}^{3}+{\frac{4113\,{x}^{5}}{5}}-2605\,{x}^{7}+{\frac{16448\,{x}^{9}}{3}}-{\frac{84912\,{x}^{11}}{11}}+{\frac{93440\,{x}^{13}}{13}}-{\frac{21248\,{x}^{15}}{5}}+{\frac{24576\,{x}^{17}}{17}}-{\frac{4096\,{x}^{19}}{19}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-16*x^6+32*x^4-19*x^2+3)^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.811283, size = 66, normalized size = 1.05 \[ -\frac{4096}{19} \, x^{19} + \frac{24576}{17} \, x^{17} - \frac{21248}{5} \, x^{15} + \frac{93440}{13} \, x^{13} - \frac{84912}{11} \, x^{11} + \frac{16448}{3} \, x^{9} - 2605 \, x^{7} + \frac{4113}{5} \, x^{5} - 171 \, x^{3} + 27 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(16*x^6 - 32*x^4 + 19*x^2 - 3)^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.25633, size = 1, normalized size = 0.02 \[ -\frac{4096}{19} x^{19} + \frac{24576}{17} x^{17} - \frac{21248}{5} x^{15} + \frac{93440}{13} x^{13} - \frac{84912}{11} x^{11} + \frac{16448}{3} x^{9} - 2605 x^{7} + \frac{4113}{5} x^{5} - 171 x^{3} + 27 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(16*x^6 - 32*x^4 + 19*x^2 - 3)^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.10067, size = 60, normalized size = 0.95 \[ - \frac{4096 x^{19}}{19} + \frac{24576 x^{17}}{17} - \frac{21248 x^{15}}{5} + \frac{93440 x^{13}}{13} - \frac{84912 x^{11}}{11} + \frac{16448 x^{9}}{3} - 2605 x^{7} + \frac{4113 x^{5}}{5} - 171 x^{3} + 27 x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-16*x**6+32*x**4-19*x**2+3)**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.261095, size = 66, normalized size = 1.05 \[ -\frac{4096}{19} \, x^{19} + \frac{24576}{17} \, x^{17} - \frac{21248}{5} \, x^{15} + \frac{93440}{13} \, x^{13} - \frac{84912}{11} \, x^{11} + \frac{16448}{3} \, x^{9} - 2605 \, x^{7} + \frac{4113}{5} \, x^{5} - 171 \, x^{3} + 27 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(16*x^6 - 32*x^4 + 19*x^2 - 3)^3,x, algorithm="giac")
[Out]