3.2155 \(\int x \left (3-4 x+x^2\right )^2 \, dx\)

Optimal. Leaf size=34 \[ \frac{x^6}{6}-\frac{8 x^5}{5}+\frac{11 x^4}{2}-8 x^3+\frac{9 x^2}{2} \]

[Out]

(9*x^2)/2 - 8*x^3 + (11*x^4)/2 - (8*x^5)/5 + x^6/6

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Rubi [A]  time = 0.032676, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ \frac{x^6}{6}-\frac{8 x^5}{5}+\frac{11 x^4}{2}-8 x^3+\frac{9 x^2}{2} \]

Antiderivative was successfully verified.

[In]  Int[x*(3 - 4*x + x^2)^2,x]

[Out]

(9*x^2)/2 - 8*x^3 + (11*x^4)/2 - (8*x^5)/5 + x^6/6

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{x^{6}}{6} - \frac{8 x^{5}}{5} + \frac{11 x^{4}}{2} - 8 x^{3} + 9 \int x\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

x**6/6 - 8*x**5/5 + 11*x**4/2 - 8*x**3 + 9*Integral(x, x)

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Mathematica [A]  time = 0.0019135, size = 34, normalized size = 1. \[ \frac{x^6}{6}-\frac{8 x^5}{5}+\frac{11 x^4}{2}-8 x^3+\frac{9 x^2}{2} \]

Antiderivative was successfully verified.

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

[Out]

(9*x^2)/2 - 8*x^3 + (11*x^4)/2 - (8*x^5)/5 + x^6/6

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Maple [A]  time = 0.002, size = 27, normalized size = 0.8 \[{\frac{9\,{x}^{2}}{2}}-8\,{x}^{3}+{\frac{11\,{x}^{4}}{2}}-{\frac{8\,{x}^{5}}{5}}+{\frac{{x}^{6}}{6}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(x^2-4*x+3)^2,x)

[Out]

9/2*x^2-8*x^3+11/2*x^4-8/5*x^5+1/6*x^6

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Maxima [A]  time = 0.79722, size = 35, normalized size = 1.03 \[ \frac{1}{6} \, x^{6} - \frac{8}{5} \, x^{5} + \frac{11}{2} \, x^{4} - 8 \, x^{3} + \frac{9}{2} \, x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*x^6 - 8/5*x^5 + 11/2*x^4 - 8*x^3 + 9/2*x^2

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Fricas [A]  time = 0.174803, size = 1, normalized size = 0.03 \[ \frac{1}{6} x^{6} - \frac{8}{5} x^{5} + \frac{11}{2} x^{4} - 8 x^{3} + \frac{9}{2} x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*x^6 - 8/5*x^5 + 11/2*x^4 - 8*x^3 + 9/2*x^2

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Sympy [A]  time = 0.078639, size = 29, normalized size = 0.85 \[ \frac{x^{6}}{6} - \frac{8 x^{5}}{5} + \frac{11 x^{4}}{2} - 8 x^{3} + \frac{9 x^{2}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(x**2-4*x+3)**2,x)

[Out]

x**6/6 - 8*x**5/5 + 11*x**4/2 - 8*x**3 + 9*x**2/2

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GIAC/XCAS [A]  time = 0.202356, size = 35, normalized size = 1.03 \[ \frac{1}{6} \, x^{6} - \frac{8}{5} \, x^{5} + \frac{11}{2} \, x^{4} - 8 \, x^{3} + \frac{9}{2} \, x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*x^6 - 8/5*x^5 + 11/2*x^4 - 8*x^3 + 9/2*x^2