Optimal. Leaf size=31 \[ -\frac{x^3}{3}-\frac{2 \tan ^{-1}\left (\frac{1-2 x^3}{\sqrt{3}}\right )}{3 \sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0831293, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.174 \[ -\frac{x^3}{3}-\frac{2 \tan ^{-1}\left (\frac{1-2 x^3}{\sqrt{3}}\right )}{3 \sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[(x^5*(1 - x^3))/(1 - x^3 + x^6),x]
[Out]
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Rubi in Sympy [A] time = 14.2477, size = 29, normalized size = 0.94 \[ - \frac{x^{3}}{3} + \frac{2 \sqrt{3} \operatorname{atan}{\left (\sqrt{3} \left (\frac{2 x^{3}}{3} - \frac{1}{3}\right ) \right )}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**5*(-x**3+1)/(x**6-x**3+1),x)
[Out]
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Mathematica [A] time = 0.0123437, size = 31, normalized size = 1. \[ \frac{2 \tan ^{-1}\left (\frac{2 x^3-1}{\sqrt{3}}\right )}{3 \sqrt{3}}-\frac{x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[(x^5*(1 - x^3))/(1 - x^3 + x^6),x]
[Out]
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Maple [A] time = 0.004, size = 25, normalized size = 0.8 \[ -{\frac{{x}^{3}}{3}}+{\frac{2\,\sqrt{3}}{9}\arctan \left ({\frac{ \left ( 2\,{x}^{3}-1 \right ) \sqrt{3}}{3}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^5*(-x^3+1)/(x^6-x^3+1),x)
[Out]
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Maxima [A] time = 0.816813, size = 32, normalized size = 1.03 \[ -\frac{1}{3} \, x^{3} + \frac{2}{9} \, \sqrt{3} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x^{3} - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^3 - 1)*x^5/(x^6 - x^3 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.272018, size = 38, normalized size = 1.23 \[ -\frac{1}{9} \, \sqrt{3}{\left (\sqrt{3} x^{3} - 2 \, \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x^{3} - 1\right )}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^3 - 1)*x^5/(x^6 - x^3 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.269313, size = 32, normalized size = 1.03 \[ - \frac{x^{3}}{3} + \frac{2 \sqrt{3} \operatorname{atan}{\left (\frac{2 \sqrt{3} x^{3}}{3} - \frac{\sqrt{3}}{3} \right )}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**5*(-x**3+1)/(x**6-x**3+1),x)
[Out]
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GIAC/XCAS [A] time = 0.271258, size = 32, normalized size = 1.03 \[ -\frac{1}{3} \, x^{3} + \frac{2}{9} \, \sqrt{3} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x^{3} - 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^3 - 1)*x^5/(x^6 - x^3 + 1),x, algorithm="giac")
[Out]