3.11 \(\int \left (-4 x+3 x^3\right )^6 \, dx\)

Optimal. Leaf size=46 \[ \frac{729 x^{19}}{19}-\frac{5832 x^{17}}{17}+1296 x^{15}-\frac{34560 x^{13}}{13}+\frac{34560 x^{11}}{11}-2048 x^9+\frac{4096 x^7}{7} \]

[Out]

(4096*x^7)/7 - 2048*x^9 + (34560*x^11)/11 - (34560*x^13)/13 + 1296*x^15 - (5832*
x^17)/17 + (729*x^19)/19

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Rubi [A]  time = 0.0410244, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{729 x^{19}}{19}-\frac{5832 x^{17}}{17}+1296 x^{15}-\frac{34560 x^{13}}{13}+\frac{34560 x^{11}}{11}-2048 x^9+\frac{4096 x^7}{7} \]

Antiderivative was successfully verified.

[In]  Int[(-4*x + 3*x^3)^6,x]

[Out]

(4096*x^7)/7 - 2048*x^9 + (34560*x^11)/11 - (34560*x^13)/13 + 1296*x^15 - (5832*
x^17)/17 + (729*x^19)/19

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Rubi in Sympy [A]  time = 3.03478, size = 42, normalized size = 0.91 \[ \frac{729 x^{19}}{19} - \frac{5832 x^{17}}{17} + 1296 x^{15} - \frac{34560 x^{13}}{13} + \frac{34560 x^{11}}{11} - 2048 x^{9} + \frac{4096 x^{7}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((3*x**3-4*x)**6,x)

[Out]

729*x**19/19 - 5832*x**17/17 + 1296*x**15 - 34560*x**13/13 + 34560*x**11/11 - 20
48*x**9 + 4096*x**7/7

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Mathematica [A]  time = 0.00302032, size = 46, normalized size = 1. \[ \frac{729 x^{19}}{19}-\frac{5832 x^{17}}{17}+1296 x^{15}-\frac{34560 x^{13}}{13}+\frac{34560 x^{11}}{11}-2048 x^9+\frac{4096 x^7}{7} \]

Antiderivative was successfully verified.

[In]  Integrate[(-4*x + 3*x^3)^6,x]

[Out]

(4096*x^7)/7 - 2048*x^9 + (34560*x^11)/11 - (34560*x^13)/13 + 1296*x^15 - (5832*
x^17)/17 + (729*x^19)/19

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Maple [A]  time = 0.003, size = 37, normalized size = 0.8 \[{\frac{4096\,{x}^{7}}{7}}-2048\,{x}^{9}+{\frac{34560\,{x}^{11}}{11}}-{\frac{34560\,{x}^{13}}{13}}+1296\,{x}^{15}-{\frac{5832\,{x}^{17}}{17}}+{\frac{729\,{x}^{19}}{19}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3*x^3-4*x)^6,x)

[Out]

4096/7*x^7-2048*x^9+34560/11*x^11-34560/13*x^13+1296*x^15-5832/17*x^17+729/19*x^
19

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Maxima [A]  time = 1.37253, size = 49, normalized size = 1.07 \[ \frac{729}{19} \, x^{19} - \frac{5832}{17} \, x^{17} + 1296 \, x^{15} - \frac{34560}{13} \, x^{13} + \frac{34560}{11} \, x^{11} - 2048 \, x^{9} + \frac{4096}{7} \, x^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^3 - 4*x)^6,x, algorithm="maxima")

[Out]

729/19*x^19 - 5832/17*x^17 + 1296*x^15 - 34560/13*x^13 + 34560/11*x^11 - 2048*x^
9 + 4096/7*x^7

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Fricas [A]  time = 0.178534, size = 1, normalized size = 0.02 \[ \frac{729}{19} x^{19} - \frac{5832}{17} x^{17} + 1296 x^{15} - \frac{34560}{13} x^{13} + \frac{34560}{11} x^{11} - 2048 x^{9} + \frac{4096}{7} x^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^3 - 4*x)^6,x, algorithm="fricas")

[Out]

729/19*x^19 - 5832/17*x^17 + 1296*x^15 - 34560/13*x^13 + 34560/11*x^11 - 2048*x^
9 + 4096/7*x^7

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Sympy [A]  time = 0.101324, size = 42, normalized size = 0.91 \[ \frac{729 x^{19}}{19} - \frac{5832 x^{17}}{17} + 1296 x^{15} - \frac{34560 x^{13}}{13} + \frac{34560 x^{11}}{11} - 2048 x^{9} + \frac{4096 x^{7}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x**3-4*x)**6,x)

[Out]

729*x**19/19 - 5832*x**17/17 + 1296*x**15 - 34560*x**13/13 + 34560*x**11/11 - 20
48*x**9 + 4096*x**7/7

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GIAC/XCAS [A]  time = 0.216305, size = 49, normalized size = 1.07 \[ \frac{729}{19} \, x^{19} - \frac{5832}{17} \, x^{17} + 1296 \, x^{15} - \frac{34560}{13} \, x^{13} + \frac{34560}{11} \, x^{11} - 2048 \, x^{9} + \frac{4096}{7} \, x^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((3*x^3 - 4*x)^6,x, algorithm="giac")

[Out]

729/19*x^19 - 5832/17*x^17 + 1296*x^15 - 34560/13*x^13 + 34560/11*x^11 - 2048*x^
9 + 4096/7*x^7