3.71 \(\int \left (3-19 x^2+32 x^4-16 x^6\right )^3 \, dx\)

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]

27*x - 171*x^3 + (4113*x^5)/5 - 2605*x^7 + (16448*x^9)/3 - (84912*x^11)/11 + (93
440*x^13)/13 - (21248*x^15)/5 + (24576*x^17)/17 - (4096*x^19)/19

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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]

27*x - 171*x^3 + (4113*x^5)/5 - 2605*x^7 + (16448*x^9)/3 - (84912*x^11)/11 + (93
440*x^13)/13 - (21248*x^15)/5 + (24576*x^17)/17 - (4096*x^19)/19

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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((-16*x**6+32*x**4-19*x**2+3)**3,x)

[Out]

Timed out

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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]

27*x - 171*x^3 + (4113*x^5)/5 - 2605*x^7 + (16448*x^9)/3 - (84912*x^11)/11 + (93
440*x^13)/13 - (21248*x^15)/5 + (24576*x^17)/17 - (4096*x^19)/19

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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]

27*x-171*x^3+4113/5*x^5-2605*x^7+16448/3*x^9-84912/11*x^11+93440/13*x^13-21248/5
*x^15+24576/17*x^17-4096/19*x^19

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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]

-4096/19*x^19 + 24576/17*x^17 - 21248/5*x^15 + 93440/13*x^13 - 84912/11*x^11 + 1
6448/3*x^9 - 2605*x^7 + 4113/5*x^5 - 171*x^3 + 27*x

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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]

-4096/19*x^19 + 24576/17*x^17 - 21248/5*x^15 + 93440/13*x^13 - 84912/11*x^11 + 1
6448/3*x^9 - 2605*x^7 + 4113/5*x^5 - 171*x^3 + 27*x

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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]

-4096*x**19/19 + 24576*x**17/17 - 21248*x**15/5 + 93440*x**13/13 - 84912*x**11/1
1 + 16448*x**9/3 - 2605*x**7 + 4113*x**5/5 - 171*x**3 + 27*x

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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]

-4096/19*x^19 + 24576/17*x^17 - 21248/5*x^15 + 93440/13*x^13 - 84912/11*x^11 + 1
6448/3*x^9 - 2605*x^7 + 4113/5*x^5 - 171*x^3 + 27*x