Optimal. Leaf size=14 \[ \frac{2}{3} \tan ^{-1}\left (\sqrt{x^3-1}\right ) \]
[Out]
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Rubi [A] time = 0.0239718, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{2}{3} \tan ^{-1}\left (\sqrt{x^3-1}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(x*Sqrt[-1 + x^3]),x]
[Out]
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Rubi in Sympy [A] time = 3.26201, size = 12, normalized size = 0.86 \[ \frac{2 \operatorname{atan}{\left (\sqrt{x^{3} - 1} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(x**3-1)**(1/2),x)
[Out]
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Mathematica [B] time = 0.0230429, size = 36, normalized size = 2.57 \[ \frac{2 \sqrt{x^3-1} \tanh ^{-1}\left (\sqrt{1-x^3}\right )}{3 \sqrt{1-x^3}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*Sqrt[-1 + x^3]),x]
[Out]
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Maple [A] time = 0.029, size = 11, normalized size = 0.8 \[{\frac{2}{3}\arctan \left ( \sqrt{{x}^{3}-1} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(x^3-1)^(1/2),x)
[Out]
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Maxima [A] time = 1.59016, size = 14, normalized size = 1. \[ \frac{2}{3} \, \arctan \left (\sqrt{x^{3} - 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^3 - 1)*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230918, size = 14, normalized size = 1. \[ \frac{2}{3} \, \arctan \left (\sqrt{x^{3} - 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^3 - 1)*x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.45547, size = 31, normalized size = 2.21 \[ \begin{cases} \frac{2 i \operatorname{acosh}{\left (\frac{1}{x^{\frac{3}{2}}} \right )}}{3} & \text{for}\: \left |{\frac{1}{x^{3}}}\right | > 1 \\- \frac{2 \operatorname{asin}{\left (\frac{1}{x^{\frac{3}{2}}} \right )}}{3} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(x**3-1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214851, size = 14, normalized size = 1. \[ \frac{2}{3} \, \arctan \left (\sqrt{x^{3} - 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^3 - 1)*x),x, algorithm="giac")
[Out]