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

Optimal. Leaf size=44 \[ \frac{256 x^{13}}{13}-\frac{1024 x^{11}}{11}+\frac{544 x^9}{3}-\frac{1312 x^7}{7}+\frac{553 x^5}{5}-38 x^3+9 x \]

[Out]

9*x - 38*x^3 + (553*x^5)/5 - (1312*x^7)/7 + (544*x^9)/3 - (1024*x^11)/11 + (256*
x^13)/13

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Rubi [A]  time = 0.233078, antiderivative size = 44, 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 \[ \frac{256 x^{13}}{13}-\frac{1024 x^{11}}{11}+\frac{544 x^9}{3}-\frac{1312 x^7}{7}+\frac{553 x^5}{5}-38 x^3+9 x \]

Antiderivative was successfully verified.

[In]  Int[(3 - 19*x^2 + 32*x^4 - 16*x^6)^2,x]

[Out]

9*x - 38*x^3 + (553*x^5)/5 - (1312*x^7)/7 + (544*x^9)/3 - (1024*x^11)/11 + (256*
x^13)/13

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \left (- 16 x^{6} + 32 x^{4} - 19 x^{2} + 3\right )^{2}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((-16*x**6+32*x**4-19*x**2+3)**2,x)

[Out]

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

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Mathematica [A]  time = 0.0011097, size = 44, normalized size = 1. \[ \frac{256 x^{13}}{13}-\frac{1024 x^{11}}{11}+\frac{544 x^9}{3}-\frac{1312 x^7}{7}+\frac{553 x^5}{5}-38 x^3+9 x \]

Antiderivative was successfully verified.

[In]  Integrate[(3 - 19*x^2 + 32*x^4 - 16*x^6)^2,x]

[Out]

9*x - 38*x^3 + (553*x^5)/5 - (1312*x^7)/7 + (544*x^9)/3 - (1024*x^11)/11 + (256*
x^13)/13

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Maple [A]  time = 0.002, size = 35, normalized size = 0.8 \[ 9\,x-38\,{x}^{3}+{\frac{553\,{x}^{5}}{5}}-{\frac{1312\,{x}^{7}}{7}}+{\frac{544\,{x}^{9}}{3}}-{\frac{1024\,{x}^{11}}{11}}+{\frac{256\,{x}^{13}}{13}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((-16*x^6+32*x^4-19*x^2+3)^2,x)

[Out]

9*x-38*x^3+553/5*x^5-1312/7*x^7+544/3*x^9-1024/11*x^11+256/13*x^13

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Maxima [A]  time = 0.818507, size = 46, normalized size = 1.05 \[ \frac{256}{13} \, x^{13} - \frac{1024}{11} \, x^{11} + \frac{544}{3} \, x^{9} - \frac{1312}{7} \, x^{7} + \frac{553}{5} \, x^{5} - 38 \, x^{3} + 9 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((16*x^6 - 32*x^4 + 19*x^2 - 3)^2,x, algorithm="maxima")

[Out]

256/13*x^13 - 1024/11*x^11 + 544/3*x^9 - 1312/7*x^7 + 553/5*x^5 - 38*x^3 + 9*x

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Fricas [A]  time = 0.230174, size = 1, normalized size = 0.02 \[ \frac{256}{13} x^{13} - \frac{1024}{11} x^{11} + \frac{544}{3} x^{9} - \frac{1312}{7} x^{7} + \frac{553}{5} x^{5} - 38 x^{3} + 9 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((16*x^6 - 32*x^4 + 19*x^2 - 3)^2,x, algorithm="fricas")

[Out]

256/13*x^13 - 1024/11*x^11 + 544/3*x^9 - 1312/7*x^7 + 553/5*x^5 - 38*x^3 + 9*x

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Sympy [A]  time = 0.085475, size = 41, normalized size = 0.93 \[ \frac{256 x^{13}}{13} - \frac{1024 x^{11}}{11} + \frac{544 x^{9}}{3} - \frac{1312 x^{7}}{7} + \frac{553 x^{5}}{5} - 38 x^{3} + 9 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((-16*x**6+32*x**4-19*x**2+3)**2,x)

[Out]

256*x**13/13 - 1024*x**11/11 + 544*x**9/3 - 1312*x**7/7 + 553*x**5/5 - 38*x**3 +
9*x

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GIAC/XCAS [A]  time = 0.260387, size = 46, normalized size = 1.05 \[ \frac{256}{13} \, x^{13} - \frac{1024}{11} \, x^{11} + \frac{544}{3} \, x^{9} - \frac{1312}{7} \, x^{7} + \frac{553}{5} \, x^{5} - 38 \, x^{3} + 9 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((16*x^6 - 32*x^4 + 19*x^2 - 3)^2,x, algorithm="giac")

[Out]

256/13*x^13 - 1024/11*x^11 + 544/3*x^9 - 1312/7*x^7 + 553/5*x^5 - 38*x^3 + 9*x