Optimal. Leaf size=12 \[ \frac{3}{4} \log \left (x^{4/3}+1\right ) \]
[Out]
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Rubi [A] time = 0.00931854, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{3}{4} \log \left (x^{4/3}+1\right ) \]
Antiderivative was successfully verified.
[In] Int[(x^(-1/3) + x)^(-1),x]
[Out]
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Rubi in Sympy [A] time = 0.895945, size = 10, normalized size = 0.83 \[ \frac{3 \log{\left (x^{\frac{4}{3}} + 1 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1/x**(1/3)+x),x)
[Out]
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Mathematica [A] time = 0.00507557, size = 12, normalized size = 1. \[ \frac{3}{4} \log \left (x^{4/3}+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(x^(-1/3) + x)^(-1),x]
[Out]
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Maple [A] time = 0.003, size = 9, normalized size = 0.8 \[{\frac{3}{4}\ln \left ( 1+{x}^{{\frac{4}{3}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1/x^(1/3)+x),x)
[Out]
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Maxima [A] time = 1.49971, size = 11, normalized size = 0.92 \[ \frac{3}{4} \, \log \left (x^{\frac{4}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x + 1/x^(1/3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.208122, size = 11, normalized size = 0.92 \[ \frac{3}{4} \, \log \left (x^{\frac{4}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x + 1/x^(1/3)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.606153, size = 10, normalized size = 0.83 \[ \frac{3 \log{\left (x^{\frac{4}{3}} + 1 \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1/x**(1/3)+x),x)
[Out]
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GIAC/XCAS [A] time = 0.227831, size = 43, normalized size = 3.58 \[ \frac{3}{4} \,{\rm ln}\left (\sqrt{2} x^{\frac{1}{3}} + x^{\frac{2}{3}} + 1\right ) + \frac{3}{4} \,{\rm ln}\left (-\sqrt{2} x^{\frac{1}{3}} + x^{\frac{2}{3}} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x + 1/x^(1/3)),x, algorithm="giac")
[Out]