Optimal. Leaf size=25 \[ \frac{x^2}{2}+\frac{1}{2} \log \left (1-x^2\right )+x-\log (x) \]
[Out]
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Rubi [A] time = 0.0540746, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.115 \[ \frac{x^2}{2}+\frac{1}{2} \log \left (1-x^2\right )+x-\log (x) \]
Antiderivative was successfully verified.
[In] Int[(1 - x - x^2 + x^3 + x^4)/(-x + x^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ x - \log{\left (x \right )} + \frac{\log{\left (- x^{2} + 1 \right )}}{2} + \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**4+x**3-x**2-x+1)/(x**3-x),x)
[Out]
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Mathematica [A] time = 0.00918447, size = 25, normalized size = 1. \[ \frac{x^2}{2}+\frac{1}{2} \log \left (1-x^2\right )+x-\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - x - x^2 + x^3 + x^4)/(-x + x^3),x]
[Out]
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Maple [A] time = 0.01, size = 24, normalized size = 1. \[ x+{\frac{{x}^{2}}{2}}+{\frac{\ln \left ( -1+x \right ) }{2}}+{\frac{\ln \left ( 1+x \right ) }{2}}-\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^4+x^3-x^2-x+1)/(x^3-x),x)
[Out]
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Maxima [A] time = 0.800667, size = 31, normalized size = 1.24 \[ \frac{1}{2} \, x^{2} + x + \frac{1}{2} \, \log \left (x + 1\right ) + \frac{1}{2} \, \log \left (x - 1\right ) - \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + x^3 - x^2 - x + 1)/(x^3 - x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.252461, size = 26, normalized size = 1.04 \[ \frac{1}{2} \, x^{2} + x + \frac{1}{2} \, \log \left (x^{2} - 1\right ) - \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + x^3 - x^2 - x + 1)/(x^3 - x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.177694, size = 17, normalized size = 0.68 \[ \frac{x^{2}}{2} + x - \log{\left (x \right )} + \frac{\log{\left (x^{2} - 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**4+x**3-x**2-x+1)/(x**3-x),x)
[Out]
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GIAC/XCAS [A] time = 0.260299, size = 35, normalized size = 1.4 \[ \frac{1}{2} \, x^{2} + x + \frac{1}{2} \,{\rm ln}\left ({\left | x + 1 \right |}\right ) + \frac{1}{2} \,{\rm ln}\left ({\left | x - 1 \right |}\right ) -{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 + x^3 - x^2 - x + 1)/(x^3 - x),x, algorithm="giac")
[Out]