Optimal. Leaf size=33 \[ \frac{\sqrt{x^6+2}}{18 x^3}-\frac{\sqrt{x^6+2}}{18 x^9} \]
[Out]
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Rubi [A] time = 0.0251987, antiderivative size = 33, 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 \[ \frac{\sqrt{x^6+2}}{18 x^3}-\frac{\sqrt{x^6+2}}{18 x^9} \]
Antiderivative was successfully verified.
[In] Int[1/(x^10*Sqrt[2 + x^6]),x]
[Out]
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Rubi in Sympy [A] time = 3.22543, size = 26, normalized size = 0.79 \[ \frac{\sqrt{x^{6} + 2}}{18 x^{3}} - \frac{\sqrt{x^{6} + 2}}{18 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**10/(x**6+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0118733, size = 21, normalized size = 0.64 \[ \frac{\left (x^6-1\right ) \sqrt{x^6+2}}{18 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^10*Sqrt[2 + x^6]),x]
[Out]
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Maple [A] time = 0.006, size = 18, normalized size = 0.6 \[{\frac{{x}^{6}-1}{18\,{x}^{9}}\sqrt{{x}^{6}+2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^10/(x^6+2)^(1/2),x)
[Out]
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Maxima [A] time = 1.48146, size = 34, normalized size = 1.03 \[ \frac{\sqrt{x^{6} + 2}}{12 \, x^{3}} - \frac{{\left (x^{6} + 2\right )}^{\frac{3}{2}}}{36 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^6 + 2)*x^10),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218311, size = 70, normalized size = 2.12 \[ \frac{3 \, x^{6} - 3 \, \sqrt{x^{6} + 2} x^{3} + 2}{18 \,{\left (2 \, x^{18} + 3 \, x^{12} -{\left (2 \, x^{15} + x^{9}\right )} \sqrt{x^{6} + 2}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^6 + 2)*x^10),x, algorithm="fricas")
[Out]
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Sympy [A] time = 5.2497, size = 26, normalized size = 0.79 \[ \frac{\sqrt{1 + \frac{2}{x^{6}}}}{18} - \frac{\sqrt{1 + \frac{2}{x^{6}}}}{18 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**10/(x**6+2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.229089, size = 43, normalized size = 1.3 \[ -\frac{{\left (\frac{2}{x^{6}} + 1\right )}^{\frac{3}{2}} - 3 \, \sqrt{\frac{2}{x^{6}} + 1}}{36 \,{\rm sign}\left (x\right )} - \frac{1}{18} \,{\rm sign}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x^6 + 2)*x^10),x, algorithm="giac")
[Out]