Optimal. Leaf size=22 \[ \frac{x^8}{8}-\frac{2 x^5}{5}+\frac{x^2}{2} \]
[Out]
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Rubi [A] time = 0.0204988, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{x^8}{8}-\frac{2 x^5}{5}+\frac{x^2}{2} \]
Antiderivative was successfully verified.
[In] Int[x*(1 - x^3)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{8}}{8} - \frac{2 x^{5}}{5} + \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(-x**3+1)**2,x)
[Out]
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Mathematica [A] time = 0.00106874, size = 22, normalized size = 1. \[ \frac{x^8}{8}-\frac{2 x^5}{5}+\frac{x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[x*(1 - x^3)^2,x]
[Out]
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Maple [A] time = 0.001, size = 17, normalized size = 0.8 \[{\frac{{x}^{2}}{2}}-{\frac{2\,{x}^{5}}{5}}+{\frac{{x}^{8}}{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(-x^3+1)^2,x)
[Out]
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Maxima [A] time = 0.810013, size = 22, normalized size = 1. \[ \frac{1}{8} \, x^{8} - \frac{2}{5} \, x^{5} + \frac{1}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 1)^2*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229898, size = 1, normalized size = 0.05 \[ \frac{1}{8} x^{8} - \frac{2}{5} x^{5} + \frac{1}{2} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 1)^2*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.064682, size = 15, normalized size = 0.68 \[ \frac{x^{8}}{8} - \frac{2 x^{5}}{5} + \frac{x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(-x**3+1)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.258153, size = 22, normalized size = 1. \[ \frac{1}{8} \, x^{8} - \frac{2}{5} \, x^{5} + \frac{1}{2} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^3 - 1)^2*x,x, algorithm="giac")
[Out]