3.2153 \(\int x^3 \left (3-4 x+x^2\right )^2 \, dx\)

Optimal. Leaf size=36 \[ \frac{x^8}{8}-\frac{8 x^7}{7}+\frac{11 x^6}{3}-\frac{24 x^5}{5}+\frac{9 x^4}{4} \]

[Out]

(9*x^4)/4 - (24*x^5)/5 + (11*x^6)/3 - (8*x^7)/7 + x^8/8

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Rubi [A]  time = 0.0391173, antiderivative size = 36, 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 \[ \frac{x^8}{8}-\frac{8 x^7}{7}+\frac{11 x^6}{3}-\frac{24 x^5}{5}+\frac{9 x^4}{4} \]

Antiderivative was successfully verified.

[In]  Int[x^3*(3 - 4*x + x^2)^2,x]

[Out]

(9*x^4)/4 - (24*x^5)/5 + (11*x^6)/3 - (8*x^7)/7 + x^8/8

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Rubi in Sympy [A]  time = 5.57668, size = 31, normalized size = 0.86 \[ \frac{x^{8}}{8} - \frac{8 x^{7}}{7} + \frac{11 x^{6}}{3} - \frac{24 x^{5}}{5} + \frac{9 x^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**8/8 - 8*x**7/7 + 11*x**6/3 - 24*x**5/5 + 9*x**4/4

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Mathematica [A]  time = 0.0011497, size = 36, normalized size = 1. \[ \frac{x^8}{8}-\frac{8 x^7}{7}+\frac{11 x^6}{3}-\frac{24 x^5}{5}+\frac{9 x^4}{4} \]

Antiderivative was successfully verified.

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

[Out]

(9*x^4)/4 - (24*x^5)/5 + (11*x^6)/3 - (8*x^7)/7 + x^8/8

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Maple [A]  time = 0.002, size = 27, normalized size = 0.8 \[{\frac{9\,{x}^{4}}{4}}-{\frac{24\,{x}^{5}}{5}}+{\frac{11\,{x}^{6}}{3}}-{\frac{8\,{x}^{7}}{7}}+{\frac{{x}^{8}}{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^3*(x^2-4*x+3)^2,x)

[Out]

9/4*x^4-24/5*x^5+11/3*x^6-8/7*x^7+1/8*x^8

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Maxima [A]  time = 0.803599, size = 35, normalized size = 0.97 \[ \frac{1}{8} \, x^{8} - \frac{8}{7} \, x^{7} + \frac{11}{3} \, x^{6} - \frac{24}{5} \, x^{5} + \frac{9}{4} \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8*x^8 - 8/7*x^7 + 11/3*x^6 - 24/5*x^5 + 9/4*x^4

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Fricas [A]  time = 0.174942, size = 1, normalized size = 0.03 \[ \frac{1}{8} x^{8} - \frac{8}{7} x^{7} + \frac{11}{3} x^{6} - \frac{24}{5} x^{5} + \frac{9}{4} x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8*x^8 - 8/7*x^7 + 11/3*x^6 - 24/5*x^5 + 9/4*x^4

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Sympy [A]  time = 0.086922, size = 31, normalized size = 0.86 \[ \frac{x^{8}}{8} - \frac{8 x^{7}}{7} + \frac{11 x^{6}}{3} - \frac{24 x^{5}}{5} + \frac{9 x^{4}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**8/8 - 8*x**7/7 + 11*x**6/3 - 24*x**5/5 + 9*x**4/4

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GIAC/XCAS [A]  time = 0.202025, size = 35, normalized size = 0.97 \[ \frac{1}{8} \, x^{8} - \frac{8}{7} \, x^{7} + \frac{11}{3} \, x^{6} - \frac{24}{5} \, x^{5} + \frac{9}{4} \, x^{4} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/8*x^8 - 8/7*x^7 + 11/3*x^6 - 24/5*x^5 + 9/4*x^4