3.2152 \(\int x^4 \left (3-4 x+x^2\right )^2 \, dx\)

Optimal. Leaf size=32 \[ \frac{x^9}{9}-x^8+\frac{22 x^7}{7}-4 x^6+\frac{9 x^5}{5} \]

[Out]

(9*x^5)/5 - 4*x^6 + (22*x^7)/7 - x^8 + x^9/9

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Rubi [A]  time = 0.0400116, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{x^9}{9}-x^8+\frac{22 x^7}{7}-4 x^6+\frac{9 x^5}{5} \]

Antiderivative was successfully verified.

[In]  Int[x^4*(3 - 4*x + x^2)^2,x]

[Out]

(9*x^5)/5 - 4*x^6 + (22*x^7)/7 - x^8 + x^9/9

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Rubi in Sympy [A]  time = 5.56044, size = 26, normalized size = 0.81 \[ \frac{x^{9}}{9} - x^{8} + \frac{22 x^{7}}{7} - 4 x^{6} + \frac{9 x^{5}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**4*(x**2-4*x+3)**2,x)

[Out]

x**9/9 - x**8 + 22*x**7/7 - 4*x**6 + 9*x**5/5

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Mathematica [A]  time = 0.00202773, size = 32, normalized size = 1. \[ \frac{x^9}{9}-x^8+\frac{22 x^7}{7}-4 x^6+\frac{9 x^5}{5} \]

Antiderivative was successfully verified.

[In]  Integrate[x^4*(3 - 4*x + x^2)^2,x]

[Out]

(9*x^5)/5 - 4*x^6 + (22*x^7)/7 - x^8 + x^9/9

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Maple [A]  time = 0.003, size = 27, normalized size = 0.8 \[{\frac{9\,{x}^{5}}{5}}-4\,{x}^{6}+{\frac{22\,{x}^{7}}{7}}-{x}^{8}+{\frac{{x}^{9}}{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^4*(x^2-4*x+3)^2,x)

[Out]

9/5*x^5-4*x^6+22/7*x^7-x^8+1/9*x^9

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Maxima [A]  time = 0.815203, size = 35, normalized size = 1.09 \[ \frac{1}{9} \, x^{9} - x^{8} + \frac{22}{7} \, x^{7} - 4 \, x^{6} + \frac{9}{5} \, x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*x^9 - x^8 + 22/7*x^7 - 4*x^6 + 9/5*x^5

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Fricas [A]  time = 0.176334, size = 1, normalized size = 0.03 \[ \frac{1}{9} x^{9} - x^{8} + \frac{22}{7} x^{7} - 4 x^{6} + \frac{9}{5} x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*x^9 - x^8 + 22/7*x^7 - 4*x^6 + 9/5*x^5

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Sympy [A]  time = 0.083709, size = 26, normalized size = 0.81 \[ \frac{x^{9}}{9} - x^{8} + \frac{22 x^{7}}{7} - 4 x^{6} + \frac{9 x^{5}}{5} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**4*(x**2-4*x+3)**2,x)

[Out]

x**9/9 - x**8 + 22*x**7/7 - 4*x**6 + 9*x**5/5

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GIAC/XCAS [A]  time = 0.202968, size = 35, normalized size = 1.09 \[ \frac{1}{9} \, x^{9} - x^{8} + \frac{22}{7} \, x^{7} - 4 \, x^{6} + \frac{9}{5} \, x^{5} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/9*x^9 - x^8 + 22/7*x^7 - 4*x^6 + 9/5*x^5