Optimal. Leaf size=30 \[ \frac{x^2}{2}+x+\frac{2}{1-x}+\log (1-x)-\log (x+1) \]
[Out]
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Rubi [A] time = 0.0609606, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.034 \[ \frac{x^2}{2}+x+\frac{2}{1-x}+\log (1-x)-\log (x+1) \]
Antiderivative was successfully verified.
[In] Int[(1 + 4*x - 2*x^2 + x^4)/(1 - x - x^2 + x^3),x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**4-2*x**2+4*x+1)/(x**3-x**2-x+1),x)
[Out]
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Mathematica [A] time = 0.0261004, size = 29, normalized size = 0.97 \[ \frac{1}{2} (x+1)^2-\frac{2}{x-1}+\log (1-x)-\log (x+1) \]
Antiderivative was successfully verified.
[In] Integrate[(1 + 4*x - 2*x^2 + x^4)/(1 - x - x^2 + x^3),x]
[Out]
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Maple [A] time = 0.01, size = 25, normalized size = 0.8 \[ x+{\frac{{x}^{2}}{2}}+\ln \left ( -1+x \right ) -2\, \left ( -1+x \right ) ^{-1}-\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^4-2*x^2+4*x+1)/(x^3-x^2-x+1),x)
[Out]
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Maxima [A] time = 0.797626, size = 32, normalized size = 1.07 \[ \frac{1}{2} \, x^{2} + x - \frac{2}{x - 1} - \log \left (x + 1\right ) + \log \left (x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 - 2*x^2 + 4*x + 1)/(x^3 - x^2 - x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.253166, size = 49, normalized size = 1.63 \[ \frac{x^{3} + x^{2} - 2 \,{\left (x - 1\right )} \log \left (x + 1\right ) + 2 \,{\left (x - 1\right )} \log \left (x - 1\right ) - 2 \, x - 4}{2 \,{\left (x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 - 2*x^2 + 4*x + 1)/(x^3 - x^2 - x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.194386, size = 20, normalized size = 0.67 \[ \frac{x^{2}}{2} + x + \log{\left (x - 1 \right )} - \log{\left (x + 1 \right )} - \frac{2}{x - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**4-2*x**2+4*x+1)/(x**3-x**2-x+1),x)
[Out]
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GIAC/XCAS [A] time = 0.260329, size = 35, normalized size = 1.17 \[ \frac{1}{2} \, x^{2} + x - \frac{2}{x - 1} -{\rm ln}\left ({\left | x + 1 \right |}\right ) +{\rm ln}\left ({\left | x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 - 2*x^2 + 4*x + 1)/(x^3 - x^2 - x + 1),x, algorithm="giac")
[Out]