Optimal. Leaf size=280 \[ \frac{\log \left (\sqrt [3]{2}-\sqrt [3]{1-x^3}\right )}{2\ 2^{2/3}}+\frac{3 \log \left (\sqrt [3]{1-x^3}-\sqrt [3]{2} (x-1)\right )}{2\ 2^{2/3}}+\frac{1}{2} \log \left (\sqrt [3]{1-x^3}+x\right )-\frac{\log \left (\sqrt [3]{1-x^3}+\sqrt [3]{2} x\right )}{2\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left (\frac{\frac{2 \sqrt [3]{2} (x-1)}{\sqrt [3]{1-x^3}}+1}{\sqrt{3}}\right )}{2^{2/3}}+\frac{\tan ^{-1}\left (\frac{1-\frac{2 x}{\sqrt [3]{1-x^3}}}{\sqrt{3}}\right )}{\sqrt{3}}-\frac{\tan ^{-1}\left (\frac{1-\frac{2 \sqrt [3]{2} x}{\sqrt [3]{1-x^3}}}{\sqrt{3}}\right )}{2^{2/3} \sqrt{3}}-\frac{\tan ^{-1}\left (\frac{2^{2/3} \sqrt [3]{1-x^3}+1}{\sqrt{3}}\right )}{2^{2/3} \sqrt{3}}-\frac{\log \left (-3 (x-1) \left (x^2-x+1\right )\right )}{2\ 2^{2/3}} \]
[Out]
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Rubi [F] time = 0.385211, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{\sqrt [3]{1-x^3}}{1-x+x^2},x\right ) \]
Verification is Not applicable to the result.
[In] Int[(1 - x^3)^(1/3)/(1 - x + x^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{2 \sqrt{3} i \int \frac{\sqrt [3]{- x^{3} + 1}}{2 x - 1 - \sqrt{3} i}\, dx}{3} + \frac{2 \sqrt{3} i \int \frac{\sqrt [3]{- x^{3} + 1}}{2 x - 1 + \sqrt{3} i}\, dx}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**3+1)**(1/3)/(x**2-x+1),x)
[Out]
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Mathematica [A] time = 0.0416973, size = 0, normalized size = 0. \[ \int \frac{\sqrt [3]{1-x^3}}{1-x+x^2} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(1 - x^3)^(1/3)/(1 - x + x^2),x]
[Out]
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Maple [F] time = 0.112, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{2}-x+1}\sqrt [3]{-{x}^{3}+1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^3+1)^(1/3)/(x^2-x+1),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (-x^{3} + 1\right )}^{\frac{1}{3}}}{x^{2} - x + 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^3 + 1)^(1/3)/(x^2 - x + 1),x, algorithm="maxima")
[Out]
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Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^3 + 1)^(1/3)/(x^2 - x + 1),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt [3]{- \left (x - 1\right ) \left (x^{2} + x + 1\right )}}{x^{2} - x + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**3+1)**(1/3)/(x**2-x+1),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (-x^{3} + 1\right )}^{\frac{1}{3}}}{x^{2} - x + 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x^3 + 1)^(1/3)/(x^2 - x + 1),x, algorithm="giac")
[Out]