Optimal. Leaf size=20 \[ 3 \sqrt [3]{x}+3 \log \left (1-\sqrt [3]{x}\right ) \]
[Out]
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Rubi [A] time = 0.0202348, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ 3 \sqrt [3]{x}+3 \log \left (1-\sqrt [3]{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[(-x^(1/3) + x^(2/3))^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.90405, size = 15, normalized size = 0.75 \[ 3 \sqrt [3]{x} + 3 \log{\left (- \sqrt [3]{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-x**(1/3)+x**(2/3)),x)
[Out]
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Mathematica [A] time = 0.0093595, size = 20, normalized size = 1. \[ 3 \sqrt [3]{x}+3 \log \left (1-\sqrt [3]{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(-x^(1/3) + x^(2/3))^(-1),x]
[Out]
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Maple [A] time = 0.002, size = 15, normalized size = 0.8 \[ 3\,\sqrt [3]{x}+3\,\ln \left ( \sqrt [3]{x}-1 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-x^(1/3)+x^(2/3)),x)
[Out]
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Maxima [A] time = 0.716103, size = 19, normalized size = 0.95 \[ 3 \, x^{\frac{1}{3}} + 3 \, \log \left (x^{\frac{1}{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^(2/3) - x^(1/3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.274374, size = 19, normalized size = 0.95 \[ 3 \, x^{\frac{1}{3}} + 3 \, \log \left (x^{\frac{1}{3}} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^(2/3) - x^(1/3)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.340885, size = 15, normalized size = 0.75 \[ 3 \sqrt [3]{x} + 3 \log{\left (\sqrt [3]{x} - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-x**(1/3)+x**(2/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.277788, size = 20, normalized size = 1. \[ 3 \, x^{\frac{1}{3}} + 3 \,{\rm ln}\left ({\left | x^{\frac{1}{3}} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^(2/3) - x^(1/3)),x, algorithm="giac")
[Out]