Optimal. Leaf size=18 \[ -\frac{\sqrt{1-x^4}}{2 x^2} \]
[Out]
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Rubi [A] time = 0.0151032, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{\sqrt{1-x^4}}{2 x^2} \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*Sqrt[1 - x^4]),x]
[Out]
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Rubi in Sympy [A] time = 2.53008, size = 14, normalized size = 0.78 \[ - \frac{\sqrt{- x^{4} + 1}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/(-x**4+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0104622, size = 18, normalized size = 1. \[ -\frac{\sqrt{1-x^4}}{2 x^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*Sqrt[1 - x^4]),x]
[Out]
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Maple [A] time = 0.007, size = 26, normalized size = 1.4 \[{\frac{ \left ( -1+x \right ) \left ( 1+x \right ) \left ({x}^{2}+1 \right ) }{2\,{x}^{2}}{\frac{1}{\sqrt{-{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/(-x^4+1)^(1/2),x)
[Out]
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Maxima [A] time = 1.42646, size = 19, normalized size = 1.06 \[ -\frac{\sqrt{-x^{4} + 1}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 1)*x^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.237728, size = 50, normalized size = 2.78 \[ \frac{x^{4} + \sqrt{-x^{4} + 1} - 1}{2 \,{\left (\sqrt{-x^{4} + 1} x^{2} - x^{2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 1)*x^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.87038, size = 34, normalized size = 1.89 \[ \begin{cases} - \frac{i \sqrt{x^{4} - 1}}{2 x^{2}} & \text{for}\: \left |{x^{4}}\right | > 1 \\- \frac{\sqrt{- x^{4} + 1}}{2 x^{2}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/(-x**4+1)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.213929, size = 12, normalized size = 0.67 \[ -\frac{1}{2} \, \sqrt{\frac{1}{x^{4}} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 1)*x^3),x, algorithm="giac")
[Out]