Optimal. Leaf size=16 \[ \frac{x^3}{6 \sqrt{x^6+2}} \]
[Out]
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Rubi [A] time = 0.0136617, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{x^3}{6 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In] Int[x^2/(2 + x^6)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 2.28054, size = 12, normalized size = 0.75 \[ \frac{x^{3}}{6 \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(x**6+2)**(3/2),x)
[Out]
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Mathematica [A] time = 0.00915727, size = 16, normalized size = 1. \[ \frac{x^3}{6 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(2 + x^6)^(3/2),x]
[Out]
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Maple [A] time = 0.005, size = 13, normalized size = 0.8 \[{\frac{{x}^{3}}{6}{\frac{1}{\sqrt{{x}^{6}+2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(x^6+2)^(3/2),x)
[Out]
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Maxima [A] time = 1.43471, size = 16, normalized size = 1. \[ \frac{x^{3}}{6 \, \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^6 + 2)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225076, size = 28, normalized size = 1.75 \[ \frac{1}{3 \,{\left (x^{6} - \sqrt{x^{6} + 2} x^{3} + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^6 + 2)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.62997, size = 12, normalized size = 0.75 \[ \frac{x^{3}}{6 \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(x**6+2)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.228558, size = 16, normalized size = 1. \[ \frac{x^{3}}{6 \, \sqrt{x^{6} + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(x^6 + 2)^(3/2),x, algorithm="giac")
[Out]