Optimal. Leaf size=21 \[ x F_1\left (\frac{1}{3};\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right ) \]
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Rubi [A] time = 0.0328469, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053 \[ x F_1\left (\frac{1}{3};\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right ) \]
Antiderivative was successfully verified.
[In] Int[1/((1 - x^3)^(2/3)*(1 + x^3)),x]
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Rubi in Sympy [A] time = 4.62193, size = 14, normalized size = 0.67 \[ x \operatorname{appellf_{1}}{\left (\frac{1}{3},\frac{2}{3},1,\frac{4}{3},x^{3},- x^{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-x**3+1)**(2/3)/(x**3+1),x)
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Mathematica [B] time = 0.185074, size = 111, normalized size = 5.29 \[ -\frac{4 x F_1\left (\frac{1}{3};\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right )}{\left (1-x^3\right )^{2/3} \left (x^3+1\right ) \left (x^3 \left (3 F_1\left (\frac{4}{3};\frac{2}{3},2;\frac{7}{3};x^3,-x^3\right )-2 F_1\left (\frac{4}{3};\frac{5}{3},1;\frac{7}{3};x^3,-x^3\right )\right )-4 F_1\left (\frac{1}{3};\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right )\right )} \]
Warning: Unable to verify antiderivative.
[In] Integrate[1/((1 - x^3)^(2/3)*(1 + x^3)),x]
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Maple [F] time = 0.054, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{3}+1} \left ( -{x}^{3}+1 \right ) ^{-{\frac{2}{3}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-x^3+1)^(2/3)/(x^3+1),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (x^{3} + 1\right )}{\left (-x^{3} + 1\right )}^{\frac{2}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^3 + 1)*(-x^3 + 1)^(2/3)),x, algorithm="maxima")
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{{\left (x^{3} + 1\right )}{\left (-x^{3} + 1\right )}^{\frac{2}{3}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^3 + 1)*(-x^3 + 1)^(2/3)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (- \left (x - 1\right ) \left (x^{2} + x + 1\right )\right )^{\frac{2}{3}} \left (x + 1\right ) \left (x^{2} - x + 1\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-x**3+1)**(2/3)/(x**3+1),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (x^{3} + 1\right )}{\left (-x^{3} + 1\right )}^{\frac{2}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x^3 + 1)*(-x^3 + 1)^(2/3)),x, algorithm="giac")
[Out]