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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]
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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]