Optimal. Leaf size=38 \[ \frac{x^6}{18}-\frac{x^2}{9}+\frac{1}{9} \sqrt{\frac{2}{3}} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x^2\right ) \]
[Out]
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Rubi [A] time = 0.0513045, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{x^6}{18}-\frac{x^2}{9}+\frac{1}{9} \sqrt{\frac{2}{3}} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x^2\right ) \]
Antiderivative was successfully verified.
[In] Int[x^9/(2 + 3*x^4),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{6}}{18} + \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x^{2}}{2} \right )}}{27} + \frac{\int ^{x^{2}} \left (- \frac{2}{9}\right )\, dx}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**9/(3*x**4+2),x)
[Out]
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Mathematica [A] time = 0.0285102, size = 34, normalized size = 0.89 \[ \frac{1}{54} \left (3 x^6-6 x^2+2 \sqrt{6} \tan ^{-1}\left (\sqrt{\frac{3}{2}} x^2\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^9/(2 + 3*x^4),x]
[Out]
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Maple [A] time = 0.005, size = 26, normalized size = 0.7 \[ -{\frac{{x}^{2}}{9}}+{\frac{{x}^{6}}{18}}+{\frac{\sqrt{6}}{27}\arctan \left ({\frac{{x}^{2}\sqrt{6}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^9/(3*x^4+2),x)
[Out]
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Maxima [A] time = 1.58673, size = 34, normalized size = 0.89 \[ \frac{1}{18} \, x^{6} - \frac{1}{9} \, x^{2} + \frac{1}{27} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(3*x^4 + 2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223301, size = 49, normalized size = 1.29 \[ \frac{1}{54} \, \sqrt{3}{\left (\sqrt{3}{\left (x^{6} - 2 \, x^{2}\right )} + 2 \, \sqrt{2} \arctan \left (\frac{1}{2} \, \sqrt{3} \sqrt{2} x^{2}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(3*x^4 + 2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.202807, size = 27, normalized size = 0.71 \[ \frac{x^{6}}{18} - \frac{x^{2}}{9} + \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x^{2}}{2} \right )}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**9/(3*x**4+2),x)
[Out]
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GIAC/XCAS [A] time = 0.219429, size = 34, normalized size = 0.89 \[ \frac{1}{18} \, x^{6} - \frac{1}{9} \, x^{2} + \frac{1}{27} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(3*x^4 + 2),x, algorithm="giac")
[Out]