Optimal. Leaf size=15 \[ \frac{1}{2} \log \left (x^4-x^2+1\right ) \]
[Out]
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Rubi [A] time = 0.00774903, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{1}{2} \log \left (x^4-x^2+1\right ) \]
Antiderivative was successfully verified.
[In] Int[(-x + 2*x^3)/(1 - x^2 + x^4),x]
[Out]
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Rubi in Sympy [A] time = 2.16588, size = 10, normalized size = 0.67 \[ \frac{\log{\left (x^{4} - x^{2} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*x**3-x)/(x**4-x**2+1),x)
[Out]
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Mathematica [A] time = 0.00636606, size = 15, normalized size = 1. \[ \frac{1}{2} \log \left (x^4-x^2+1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(-x + 2*x^3)/(1 - x^2 + x^4),x]
[Out]
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Maple [A] time = 0.003, size = 14, normalized size = 0.9 \[{\frac{\ln \left ({x}^{4}-{x}^{2}+1 \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*x^3-x)/(x^4-x^2+1),x)
[Out]
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Maxima [A] time = 1.33633, size = 18, normalized size = 1.2 \[ \frac{1}{2} \, \log \left (x^{4} - x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^3 - x)/(x^4 - x^2 + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.194308, size = 18, normalized size = 1.2 \[ \frac{1}{2} \, \log \left (x^{4} - x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^3 - x)/(x^4 - x^2 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.089786, size = 10, normalized size = 0.67 \[ \frac{\log{\left (x^{4} - x^{2} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x**3-x)/(x**4-x**2+1),x)
[Out]
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GIAC/XCAS [A] time = 0.207107, size = 18, normalized size = 1.2 \[ \frac{1}{2} \,{\rm ln}\left (x^{4} - x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*x^3 - x)/(x^4 - x^2 + 1),x, algorithm="giac")
[Out]