Optimal. Leaf size=31 \[ \frac{2 \tan ^{-1}\left (\frac{1-2 x^3}{\sqrt{3}}\right )}{3 \sqrt{3}}-\frac{1}{3 x^3} \]
[Out]
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Rubi [A] time = 0.102452, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.174 \[ \frac{2 \tan ^{-1}\left (\frac{1-2 x^3}{\sqrt{3}}\right )}{3 \sqrt{3}}-\frac{1}{3 x^3} \]
Antiderivative was successfully verified.
[In] Int[(1 - x^3)/(x^4*(1 - x^3 + x^6)),x]
[Out]
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Rubi in Sympy [A] time = 14.5165, size = 32, normalized size = 1.03 \[ - \frac{2 \sqrt{3} \operatorname{atan}{\left (\sqrt{3} \left (\frac{2 x^{3}}{3} - \frac{1}{3}\right ) \right )}}{9} - \frac{1}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**3+1)/x**4/(x**6-x**3+1),x)
[Out]
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Mathematica [C] time = 0.0202159, size = 45, normalized size = 1.45 \[ -\frac{1}{3} \text{RootSum}\left [\text{$\#$1}^6-\text{$\#$1}^3+1\&,\frac{\log (x-\text{$\#$1})}{2 \text{$\#$1}^3-1}\&\right ]-\frac{1}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(1 - x^3)/(x^4*(1 - x^3 + x^6)),x]
[Out]
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Maple [A] time = 0.006, size = 25, normalized size = 0.8 \[ -{\frac{1}{3\,{x}^{3}}}-{\frac{2\,\sqrt{3}}{9}\arctan \left ({\frac{ \left ( 2\,{x}^{3}-1 \right ) \sqrt{3}}{3}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^3+1)/x^4/(x^6-x^3+1),x)
[Out]
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Maxima [A] time = 0.816764, size = 32, normalized size = 1.03 \[ -\frac{2}{9} \, \sqrt{3} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x^{3} - 1\right )}\right ) - \frac{1}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^3 - 1)/((x^6 - x^3 + 1)*x^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253693, size = 41, normalized size = 1.32 \[ -\frac{\sqrt{3}{\left (2 \, x^{3} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x^{3} - 1\right )}\right ) + \sqrt{3}\right )}}{9 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^3 - 1)/((x^6 - x^3 + 1)*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.375926, size = 36, normalized size = 1.16 \[ - \frac{2 \sqrt{3} \operatorname{atan}{\left (\frac{2 \sqrt{3} x^{3}}{3} - \frac{\sqrt{3}}{3} \right )}}{9} - \frac{1}{3 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**3+1)/x**4/(x**6-x**3+1),x)
[Out]
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GIAC/XCAS [A] time = 0.27478, size = 32, normalized size = 1.03 \[ -\frac{2}{9} \, \sqrt{3} \arctan \left (\frac{1}{3} \, \sqrt{3}{\left (2 \, x^{3} - 1\right )}\right ) - \frac{1}{3 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x^3 - 1)/((x^6 - x^3 + 1)*x^4),x, algorithm="giac")
[Out]