Optimal. Leaf size=30 \[ -3 x^{2/3}-x-6 \sqrt [3]{x}-6 \log \left (1-\sqrt [3]{x}\right ) \]
[Out]
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Rubi [A] time = 0.0549251, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.176 \[ -3 x^{2/3}-x-6 \sqrt [3]{x}-6 \log \left (1-\sqrt [3]{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 + x^(-1/3))/(-1 + x^(-1/3)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - 6 \sqrt [3]{x} - x - 6 \log{\left (- \sqrt [3]{x} + 1 \right )} - 6 \int ^{\sqrt [3]{x}} x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1+1/x**(1/3))/(-1+1/x**(1/3)),x)
[Out]
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Mathematica [A] time = 0.0105902, size = 30, normalized size = 1. \[ -3 x^{2/3}-x-6 \sqrt [3]{x}-6 \log \left (1-\sqrt [3]{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + x^(-1/3))/(-1 + x^(-1/3)),x]
[Out]
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Maple [A] time = 0.004, size = 23, normalized size = 0.8 \[ -x-3\,{x}^{2/3}-6\,\sqrt [3]{x}-6\,\ln \left ( -1+\sqrt [3]{x} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1+1/x^(1/3))/(-1+1/x^(1/3)),x)
[Out]
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Maxima [A] time = 1.37639, size = 30, normalized size = 1. \[ -x - 3 \, x^{\frac{2}{3}} - 6 \, x^{\frac{1}{3}} - 6 \, \log \left (x^{\frac{1}{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1/x^(1/3) + 1)/(1/x^(1/3) - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2368, size = 30, normalized size = 1. \[ -x - 3 \, x^{\frac{2}{3}} - 6 \, x^{\frac{1}{3}} - 6 \, \log \left (x^{\frac{1}{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1/x^(1/3) + 1)/(1/x^(1/3) - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.405284, size = 26, normalized size = 0.87 \[ - 3 x^{\frac{2}{3}} - 6 \sqrt [3]{x} - x - 6 \log{\left (\sqrt [3]{x} - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1+1/x**(1/3))/(-1+1/x**(1/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.215655, size = 31, normalized size = 1.03 \[ -x - 3 \, x^{\frac{2}{3}} - 6 \, x^{\frac{1}{3}} - 6 \,{\rm ln}\left ({\left | x^{\frac{1}{3}} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1/x^(1/3) + 1)/(1/x^(1/3) - 1),x, algorithm="giac")
[Out]