Optimal. Leaf size=26 \[ -3 x^{2/3}+x+6 \sqrt [3]{x}-6 \log \left (\sqrt [3]{x}+1\right ) \]
[Out]
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Rubi [A] time = 0.0462667, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ -3 x^{2/3}+x+6 \sqrt [3]{x}-6 \log \left (\sqrt [3]{x}+1\right ) \]
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+x**(1/3))/(1+x**(1/3)),x)
[Out]
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Mathematica [A] time = 0.0100471, size = 26, normalized size = 1. \[ -3 x^{2/3}+x+6 \sqrt [3]{x}-6 \log \left (\sqrt [3]{x}+1\right ) \]
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 = 21, normalized size = 0.8 \[ 6\,\sqrt [3]{x}-3\,{x}^{2/3}+x-6\,\ln \left ( 1+\sqrt [3]{x} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-1+x^(1/3))/(1+x^(1/3)),x)
[Out]
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Maxima [A] time = 1.40036, size = 27, normalized size = 1.04 \[ x - 3 \, x^{\frac{2}{3}} + 6 \, x^{\frac{1}{3}} - 6 \, \log \left (x^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^(1/3) - 1)/(x^(1/3) + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229914, size = 27, normalized size = 1.04 \[ x - 3 \, x^{\frac{2}{3}} + 6 \, x^{\frac{1}{3}} - 6 \, \log \left (x^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^(1/3) - 1)/(x^(1/3) + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.471564, size = 24, normalized size = 0.92 \[ - 3 x^{\frac{2}{3}} + 6 \sqrt [3]{x} + x - 6 \log{\left (\sqrt [3]{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-1+x**(1/3))/(1+x**(1/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.215143, size = 27, normalized size = 1.04 \[ x - 3 \, x^{\frac{2}{3}} + 6 \, x^{\frac{1}{3}} - 6 \,{\rm ln}\left (x^{\frac{1}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^(1/3) - 1)/(x^(1/3) + 1),x, algorithm="giac")
[Out]