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