Optimal. Leaf size=16 \[ \frac{\tan ^{-1}\left (\sqrt{\frac{3}{2}} x\right )}{\sqrt{6}} \]
[Out]
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Rubi [A] time = 0.00853843, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{\tan ^{-1}\left (\sqrt{\frac{3}{2}} x\right )}{\sqrt{6}} \]
Antiderivative was successfully verified.
[In] Int[(2 - 3*x^2)/(4 - 9*x^4),x]
[Out]
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Rubi in Sympy [A] time = 2.58155, size = 15, normalized size = 0.94 \[ \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x}{2} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-3*x**2+2)/(-9*x**4+4),x)
[Out]
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Mathematica [A] time = 0.00814293, size = 16, normalized size = 1. \[ \frac{\tan ^{-1}\left (\sqrt{\frac{3}{2}} x\right )}{\sqrt{6}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 - 3*x^2)/(4 - 9*x^4),x]
[Out]
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Maple [A] time = 0.004, size = 13, normalized size = 0.8 \[{\frac{\sqrt{6}}{6}\arctan \left ({\frac{x\sqrt{6}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-3*x^2+2)/(-9*x^4+4),x)
[Out]
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Maxima [A] time = 0.862497, size = 16, normalized size = 1. \[ \frac{1}{6} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 - 2)/(9*x^4 - 4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.279951, size = 16, normalized size = 1. \[ \frac{1}{6} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 - 2)/(9*x^4 - 4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.177656, size = 15, normalized size = 0.94 \[ \frac{\sqrt{6} \operatorname{atan}{\left (\frac{\sqrt{6} x}{2} \right )}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-3*x**2+2)/(-9*x**4+4),x)
[Out]
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GIAC/XCAS [A] time = 0.267811, size = 16, normalized size = 1. \[ \frac{1}{6} \, \sqrt{6} \arctan \left (\frac{1}{2} \, \sqrt{6} x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x^2 - 2)/(9*x^4 - 4),x, algorithm="giac")
[Out]