Optimal. Leaf size=22 \[ \frac{x \tanh ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \]
[Out]
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Rubi [A] time = 0.0113293, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{x \tanh ^{-1}\left (2 \sqrt [6]{x^6}\right )}{2 \sqrt [6]{x^6}} \]
Antiderivative was successfully verified.
[In] Int[(1 - 4*(x^6)^(1/3))^(-1),x]
[Out]
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Rubi in Sympy [A] time = 1.25759, size = 19, normalized size = 0.86 \[ \frac{x \operatorname{atanh}{\left (2 \sqrt [6]{x^{6}} \right )}}{2 \sqrt [6]{x^{6}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-4*(x**6)**(1/3)),x)
[Out]
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Mathematica [C] time = 0.17318, size = 123, normalized size = 5.59 \[ \frac{1}{24} \left (\frac{2 x B_{64 x^6}\left (\frac{1}{2},0\right )}{\sqrt [6]{x^6}}+\frac{2 x B_{64 x^6}\left (\frac{5}{6},0\right )}{\sqrt [6]{x^6}}-\log \left (4 x^2-2 x+1\right )+\log \left (4 x^2+2 x+1\right )-2 \log (1-2 x)+2 \log (2 x+1)+2 \sqrt{3} \tan ^{-1}\left (\frac{4 x-1}{\sqrt{3}}\right )+2 \sqrt{3} \tan ^{-1}\left (\frac{4 x+1}{\sqrt{3}}\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 4*(x^6)^(1/3))^(-1),x]
[Out]
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Maple [A] time = 0.079, size = 17, normalized size = 0.8 \[{\frac{x}{2}{\it Artanh} \left ( 2\,\sqrt [6]{{x}^{6}} \right ){\frac{1}{\sqrt [6]{{x}^{6}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-4*(x^6)^(1/3)),x)
[Out]
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Maxima [A] time = 1.33761, size = 23, normalized size = 1.05 \[ \frac{1}{4} \, \log \left (2 \, x + 1\right ) - \frac{1}{4} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(4*(x^6)^(1/3) - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.241611, size = 23, normalized size = 1.05 \[ \frac{1}{4} \, \log \left (2 \, x + 1\right ) - \frac{1}{4} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(4*(x^6)^(1/3) - 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.174726, size = 15, normalized size = 0.68 \[ - \frac{\log{\left (x - \frac{1}{2} \right )}}{4} + \frac{\log{\left (x + \frac{1}{2} \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-4*(x**6)**(1/3)),x)
[Out]
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GIAC/XCAS [A] time = 0.213384, size = 20, normalized size = 0.91 \[ \frac{1}{4} \,{\rm ln}\left ({\left | x + \frac{1}{2} \right |}\right ) - \frac{1}{4} \,{\rm ln}\left ({\left | x - \frac{1}{2} \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-1/(4*(x^6)^(1/3) - 1),x, algorithm="giac")
[Out]